Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 504183 12 pageshttpdxdoiorg1011552013504183

Research ArticleMolecular Dynamics Simulation of Barnase Contribution ofNoncovalent Intramolecular Interaction to Thermostability

Zhiguo Chen1 Yi Fu1 Wenbo Xu1 and Ming Li2

1 Key Laboratory of Advanced Process Control for Light Industry-Ministry of Education School of IoT Engineering JiangnanUniversityWuxi 214122 China

2 School of Information Science amp Technology East China Normal University No 500 Dong-Chuan Road Shanghai 200241 China

Correspondence should be addressed to Zhiguo Chen chenzg777yahoocom

Received 10 October 2013 Accepted 7 November 2013

Academic Editor Shuping He

Copyright copy 2013 Zhiguo Chen et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Bacillus amyloliquefaciens ribonuclease Barnase (RNase Ba) is a 12 kD (kilodalton) small extracellular ribonuclease It has broadapplication prospects in agriculture clinical medicine pharmaceutical and so forth In this work the thermal stability of Barnasehas been studied using molecular dynamics simulation at different temperatures The present study focuses on the contribution ofnoncovalent intramolecular interaction to protein stability and how they affect the thermal stability of the enzyme Profiles of rootmean square deviation and root mean square fluctuation identify thermostable and thermosensitive regions of Barnase Analysesof trajectories in terms of secondary structure content intramolecular hydrogen bonds and salt bridge interactions indicate distinctdifferences in different temperature simulations In the simulations Four three-member salt bridge networks (Asp8-Arg110-Asp12Arg83-Asp75-Arg87 Lys66-Asp93-Arg69 and Asp54-Lys27-Glu73) have been identified as critical salt bridges for thermostabilitywhich aremaintained stably at higher temperature enhancing stability of three hydrophobic coresThe studymay help enlighten ourknowledge of protein structural properties noncovalent interactions which can stabilize secondary peptide structures or promotefolding and also help understand their actions better Such an understanding is required for designing efficient enzymes withcharacteristics for particular applications at desired working temperatures

1 Introduction

The stability of thermophilic proteins has been viewed fromdifferent perspectives and there is yet no unified principle tounderstand this stability Detailed knowledge of the thermalstability of proteins and the phenomenon of protein foldingare essential not only to understand protein structure andfunction but also to design thermostable proteins for indus-trial applications [1ndash5] Comparisons of homologous proteinsfrom thermophiles and mesophiles have shown that relatedproteins can perform similar functions yet have very differentstabilities [6ndash8] Recent comparisons between the structuresofmesophilic and hyperthermophilic proteins have identifieda number of structural features that are believed to give riseto increased thermal stability such as optimized electrostaticinteractions [9ndash11] integrating disulfide bridges [12] com-pacting of the hydrophobic core [13] the greater number ofsalt bridges [14ndash17] and stabilization of the 120572-helices [18] It

is clear that many different factors and methodologies [19ndash21] can contribute to enzymatic temperature adaptation andthat no single factor can be invoked to explain adaptation ingeneral Although considerable progress has been made intheoretical and experimental studies of the protein foldingand thermal stability our knowledge is still limited for fullyunderstanding this subject especially on mathematical mod-eling [22 23] Therefore further investigations of the proteinfolding and thermal stability mechanisms are crucial since itmay provide relevant information on the evolutionary aspectsinvolved and on the general mechanisms underlying proteinstability Moreover it may help in the design of thermostablebiomolecules that are functional at high temperature

Barnase (EC3127) is an extracellular 110 residue ribo-nuclease from Bacillus amyloliquefaciens It has broad appli-cation prospects in agriculture clinical medicine pharma-ceutical and so forth especially that its special biologicalfunction of resistance to virus and tumor attracts more

2 Mathematical Problems in Engineering

researchersrsquo attention recently [24ndash27] Barnase is a mul-tidomain protein with three helices in the first half of thesequence followed by a five-stranded antiparallel 120573-sheetThere are three hydrophobic cores in protein It is well suitedfor studying protein folding and stability because it is oneof the smallest globular proteins that does not contain anyprosthetic groups metal cofactors or disulfide bonds whichall contribute to protein stability It has beenwell studied [28ndash31] whereas the role of electrostatic interactions in Barnasethermal stability has not yet been investigated in detail Thequestion of whether salt bridges stabilize the native state ofproteins has yet not definite answerThis is most likely relatedto the fact that the location geometry and optimization of theelectrostatics vary greatly in proteins We aim to address thisissue byMD (molecular dynamics) simulation and themajorfocus of this study was to investigate the contributions ofnoncovalent intramolecular interactions to protein stabilityand how changes in these interactions are correlated with theinitial events associated with tertiary structure unfolding inresponse to thermal stress

The small size of the protein the absence of metalcofactors and the absence of disulfide bonds make Barnasean ideal test case for studying the contribution of salt bridgeto thermostability by computer simulation In this paper wehave performed molecular dynamics simulation of Barnaseat five different temperatures namely 300K 400K 500K550K and 600K By calculating the root mean squaredeviation (RMSD) and root mean square fluctuation (RMSF)values for backbone and C120572 atoms the thermal sensitiveregions have been identified The dynamic properties ofBarnase at different temperatures have been compared interms of secondary structure content molecular flexibilityintramolecular hydrogen bonds and salt bridge interactionsOur analysis specifically focuses on the contribution of saltbridge to the stability of the protein along the unfoldingtransition The study provides insight into the structure-stability relationship of Barnase which may help enlightenour knowledge of protein structural properties and noncova-lent interactions that stabilize secondary peptide structuresor promote folding A better understanding of specific inter-actions change during the unfolding simulation also allowsus to predict more precisely a specific site or region critical toincrease Barnasersquos thermostability

2 Methodology

21 Molecular Dynamics Simulation Molecular dynamicssimulations [32] are based on classical mechanics such asNewtonrsquos second equation of motion If the force acting oneach atom is known the acceleration in a system can beacquired The equations of motion can be determined viathe acceleration resulting in a trajectory of the positionsvelocities and accelerations of each particle in given systemThe force 119865

119894on an atom with mass 119898

119894and position 119903

119894is

determined from the potential of the system 119881 as shown in(1)The potential energy can be used to derive the position ofa particle as a function of time in (2)The equations ofmotionare got for each atom in the systemThe forces acting on atoms

in new positions can be calculated and the simulation willcontinue as many time steps as necessary

119865 = minusnabla119881 (1)

119889119881

119889119903119894

= 119898119894

1198892119903119894

1198891199052 (2)

22 The Potential Function Empirical energy functions canonly be used to approach the force fields for large biologicalsystems composed of many atoms Here the CHARMM(Chemistry at HARvard Macromolecular Mechanics) forcefield is selected which has been developed and continuouslyrevised to better match new experimental data for over 25years

The potential function is a sum of some interaction ener-gies The value of the potential is determined by summingthe bonded terms119881bonded with the nonbonded potential terms119881nonbonded

119881 = 119881bonded + 119881nonbonded (3)

The nonbonded energy terms specify interactions betweennonbonded atoms and atoms that are more than threecovalent bonds away from each other in a molecule Theseenergy terms are modeled by the van der Waals energy andelectrostatic energy namely the first and second summationitems in (4) separately

119881nonbonded = sum

nonbonded-pairs4120576119894119895[(

120590119894119895

119903119894119895

)

12

minus (

120590119894119895

119903119894119895

)

6

]

+ sum

nonbonded-pairs

119902119894119902119895

119863119903119894119895

(4)

where 120590119894119895= (120590119894+120590119895)2 120590119894and 120590119895represent the Lennard-Jones

diameters of the 119894 and 119895 atoms respectively 120576119894119895

= (120576119894120576119895)12

with 120576119894and 120576119895being the Lennard-Joneswell-depth of the 119894 and

119895 atoms and 119902119894is the effective charge on atom 119894

The nonbonded terms calculation in the potential func-tion is the most time-consuming part of the MD simulationGenerally the interactions between every pair of atomsshould be calculated definitely meaning that for an N-atomsystem 1198732 number of operations would be required Toreduce the computation complexity methods were developedto ignore the interactions between two atoms separated bya distance greater than given cutoff distance For the vander Waals interactions the potential is ldquoshiftedrdquo off over adistance from 119903on to 119903off Atoms farther from each otherthan the distance 119903off are supposed not to interact For theelectrostatic interactions the Ewald summation [33] is usedto separate the potential into a slowly decaying long-rangecomponent and a quickly varying short-range component

23 Temperature and Pressure Control TheLangevin dynam-ics [34] is used for constant temperature control Langevindynamics is an effective method for controlling the kineticenergy of the system thus controlling the temperature andor

Mathematical Problems in Engineering 3

pressure This methodology uses the Langevin equation[35] for a single particle The friction kernel in Langevinequation is taken to be space and time independent foreach particle and the influence of the environment on theinternal force is denoted as an average sense Thus explicithydrodynamic interactions can be ignored and the internalforce is introduced by a frictional term proportional to thevelocity and a random force 119877 which approximately simulatemolecular collisions and viscosity in the realistic cellularcircumstance

119872

1198892119909

1198891199052= minusnabla119864 (119909) minus119872120574

119889119909

119889119905

+ 119877 (119905) (5)

Here 119872 is the mass matrix 119864 is the potential energygoverning the solute 120574 is the damping coefficient and 119877(119905)

is a Gaussian white noise force vector that has mean zeroFrom classic theories on Brownian motion it can be

seen that although molecular collisions are random theensemble of these collisions produces a systematic effectThatis to say the molecular random motions exist at thermalequilibrium as a fluctuation Hence one can see that thefrictional force is a correlate of the random force by thefluctuationdissipation theorem [35] This relation can beexpressed by the 120574-dependence of the covariance of 119877

⟨119877 (119905) 119877(1199051015840)

119879

⟩ = 2120574119896119861119879119872120575 (119905 minus 119905

1015840) (6)

where 119896119861is the Boltzmann constant 119879 is the target tempera-

ture and 120575 is the usual Dirac symbolThe Dirac-120575 function is in the form

120575 (119905) =

infin 119905 = 0

0 119905 = 0

int

infin

minusinfin

119891 (119905) 120575 (119905) 119889119905 = 1

(7)

The random force is chosen independently for each stepAnd the covariance matrix is diagonal as hydrodynamicinteractions between particles have been discounted

A physical value of 120574 for each particle can be selectedaccording to Stokesrsquo law for a hydrodynamic particle withradius 119886

119903 Stokesrsquo lawdescribes how the frictional resistance of

a spherical particle in solution varies linearly with its radiusThe practical force magnitude is 6120587120578119886

119903times the particlersquos

velocity where 120578 is the solvent viscosity Stokesrsquo law is oftenapplied to particles of molecular size Therefore the 120574 inLangevin equation can be expressed as

120574 =

6120587120578119886119903

119898

(8)

where119898 is the particlersquos massThe damping coefficient 120574 controls not only the magni-

tude of the frictional force but also the variance of the randomforces It can ensure that the system converges to a Boltzmanndistribution characterized by the temperature 119879 The largerthe value of 120574 the greater the influence of the surroundingfluctuating force Small value of 120574 implies inertial motion In

this study themain objective is to control the temperature sowe need to use small value of 120574The temperature of the systemis maintained via the relationship between 119877(119905) and 120574

For constant pressure and temperature simulations inwhich Langevin dynamics are used to control temperaturethe pressure can be controlled in NAMD with a modifiedNose-Hoover method This method entitled Nose-Hoover[36ndash38] adds a fictive degree of freedom to the physicalsystem with ldquocoordinaterdquo parameter 119909

119905(effectively a scal-

ing parameter [39]) mass 119898119905 and thermodynamic friction

coefficient 120589119905 (This friction coefficient is relative to 119909

119905and

the corresponding momentum 119905) Besides the effective

coordinate mass and friction set (119909119905 119898119905 120589119905) associated with

the fictive thermostat variable a set (119909119901 119898119901 120589119901) associated

with virtual pressure piston (barostat) is also adopted Theeffective equations of motion for a 3-dimensional system canbe expressed as

(119905) = 119881 (119905) + 120589119901119883

119872 (119905) = 119865 (119883 (119905)) minus 119872 (119905) [(1 +

3

119892

) 120589119901+ 120589119905]

V119897 = 3V119897120589119901

119898119901120589119901 (119905) = 3V119897 (119875in minus 119875

0) +

3

119892

(2119881119879119872119881) minus 119898

119901120589119905120589119901

119898119905120589119905 (119905) = 2119881

119879119872119881 +

1205892

119901

119898119901

minus (119892 + 1) 1198961198611198790

(9)

where V119897 is an external volume variable 119892 is the number ofdegrees of freedom in the system 119875

0is the external applied

pressure and 119875in is the internal pressure defined as

119875in =2

3V119897[119864119896minus vir minus (

3V1198972

)

120597119864 (119883 V119897)120597V119897

] (10)

The internal virial vir is proportional to the inner productof the each atomrsquos position vector 119903

119894with the corresponding

force component acting on atom 119894 due to all particles 119865119894

vir = minussum

119894

(119903119879

119894119865119894) (11)

The conserved quantity under these augmented equationsof motion is

119873119875119879

=

1

2

(119881119879119872119881) + 119864 (119883 V119897) +

1

2

(1198981199051205892

119905+ 1198981199011205892

119901)

+ (119892 + 1) 1198961198611198790119909119905+ 1198750V119897

(12)

By this means the magnitude of the system fluctuatesunder specified thermostat and barostats and the system isdriven to steady state at which the average internal pressure119875 is equal to the external applied force 119875

0

3 Results and Discussion

All simulations were performed on a PC with a Pentium4 28GHz dual core processor running Windows operating

4 Mathematical Problems in Engineering

system and using the molecular dynamics program NAMD[40] with CHARMM27 [41] force fields In order to run MDsimulation we need to do the following things

(1) A Protein Data Bank (pdb) file which stores atomiccoordinates andor velocities for the system is neededThe coordinates for starting configurations Barnasewas obtained from the Protein Data Bank (PDB entrycodes 1RNB [42]) which consisted of 110 residues

(2) A Protein Structure File (psf) which contains all ofthe molecule-specific information needed to apply aparticular force field to a molecular system is neededCoordinates of the atoms that were missing in thecrystallographic structure were reconstructed usingthe PSFGEN structure building utility a module ofNAMD

(3) The protein needs to be solvated and put insidewater to more closely resemble the cellular envi-ronment The protein was solvated in a cubic boxconsisting of TIP3 water molecules [43] with periodicboundary conditions The system was neutralizedby adding ions (Clminus) at physiological concentrationusing VMDrsquos solvate and autoionize plugins [44]

(4) We need a force field parameter file A force field is amathematical expression of the potential which atomsexperience in the system A CHARMM forcefieldparameter file contains all of the numerical constantsneeded to evaluate forces and energies given a PSFstructure file and atomic coordinatesThe CHARMMparameters are available for download from the web-site httpwwwcharmmorg

(5) Create the simulation script in which we specified allthe options that NAMD should adopt in running asimulation NAMD parses its configuration file usingthe Tcl scripting language

(i) First we specify the files that contain the molec-ular structure and initial conditions Setting theTcl variable temperaturemakes it easy to changethe target temperature for many options TheoutputName prefix will be used to create all ofthe trajectory output and restart files generatedby NAMD run

(ii) Next is the parameter file itself and the optionsthat control the nonbonded potential functionsThese are mostly specified by the CHARMMforce field In force-field parameters the cut-off distance was specified to 12 A Electrostaticinteractions were calculated using the ParticleMesh Ewald (PME) summation scheme Turnon switching for the van der Waals interactionswhich were calculated with a switching functionfrom 10 A to 12 A SHAKE method [45] wasused for constraining the bonds with hydrogenThe number of time steps between each outputwas 2 fs Set up the temperature and pressurecontrollersThe Langevinwas turned on and thevalue of the Langevin damping coefficient was

set to 5ps The value of the Langevin temper-ature was set equal to the target temperaturefor the simulation of temperature control Thepressure control of the system was set to 1 atm

(6) The system was subjected to energy minimizationfor 1000 steps by steepest descents and subsequentlyequilibrated for 500 ps and then the equilibratedsystem was subjected to molecular dynamics simu-lations for 2 ns each at five different temperaturesnamely 300K 400K 500K 550K and 600K Thecoordinates were saved at every 500 time steps

31 Global Structural Stability MD simulations generatean ensemble of conformations and thus include valuableinformation of the protein dynamics In the following wepresent a detailed analysis of the four molecular dynamicstrajectories in water generated for the protein of BarnaseThe RMSD of the backbone atoms of the protein from thestarting structure over the course of simulation may be usedas a measure of the conformational stability of a proteinduring the simulation The plots of RMSD of the proteinversus time at different temperatures are shown in Figure 1(a)The plots show that the MD simulation of enzyme at 300K isvery stable throughout the simulation time In the trajectoryrun at 400K the backbone RMSD increases slightly from thestarting conformation which fluctuates between 11 A and17 A during the simulation The average value of RMSD isabout 120 A in 400K simulation slightly above the valueof 096 A for the 300K structure simulation The curvecorresponding to the 500K simulation fluctuates more anddisplays a sharp rise (173 A) about 662 ps after that RMSDincreases further and oscillates between 236 A and 371 A forthe remainder of the simulation At 600K the RMSD rises toabout 3 A over the first 200 ps of the simulation and reachesa value of 378 A at around 900 ps Therefore it records adescent to about 256 A at 1184 ps and another sharp rise to416 A after 1295 psThe rise in RMSD indicates large changesto the protein structure and some disruption of the tertiarystructure of the protein

32 Structural Flexibility Following molecular dynamicssimulations at multiple temperatures it was of interest todetermine which general regions of the Barnase polypeptidechain exhibit hypersensitivity to thermal stress The resultsare shown in Figure 1(b) There is a relatively small bump-like peak for the structure at 300K At 400K the loopsbetween 120573-sheet1 and 120573-sheet2 120573-sheet2 and 120573-sheet3 showsignificant increase together with the N- and C-terminalsThe interesting finding is a dramatic increase in RMSF valuesbetween residues 5 and 7 at 500K which implies the begin-ning of the unfolding process for the N-terminal loop regionand the N-terminal of 120572-helix1 region As the temperatureincreases these above-mentioned peaks generally becomemore pronounced This pattern is especially noted in the600K simulation As can be seen most of the changesoccurred in the loop region N-terminal and C-terminalTheregular secondary structure regions such as 120572-helix and 120573-sheet showed much less mobility during the simulationsThe

Mathematical Problems in Engineering 5

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

RMSD

(Aring)

300K400K

500K600K

(a)

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100 110Residue number

RMSF

(Aring)

300K400K

500K600K

(b)

Figure 1 Time evolution (a) Backbone RMSD of Barnase at different temperatures (b) RMSFs as a function of residue number of Barnaseat different temperatures The color-coding scheme is as follows 300K (red) 400K (blue) 500K (magenta) and 600K (cyan)

curves observed for four temperature simulations exhibitedmore or less similarly distributed fluctuations Only at hightemperature simulations most of the residues become highlymobile therefore the curve shows a lot more fluctuationThis is due to the loss of secondary structure at these hightemperatures These observations clearly reveal the differentbehavior of the residues of Barnase molecule in response toincreasing thermal stress and give an indication of the regionsof the Barnase polypeptide chain which are most sensitive orresponsive to heating

33 Secondary Structure Analysis At high temperature sim-ulations dramatically increased RMSD values were observedfor the loop regions and both terminal regions in Barnasewhich indicate these regions extensive local conformationalchanges upon thermal unfolding A close analysis of the timeevolution of the secondary structure (Figure 2) can presentfurther information about its structural flexibilities

Figure 2(a) reveals that 120572-helices 120573-sheets and loopsobserved within Barnase structure are maintained stablythroughout the whole simulation period at 300K Theoverall conformation hydrophobic core compactness andsecondary structural elements are all stable and there is nowater penetration into the protein The simulation at 300Kalso appears to agree well with the stability of the RMSDand RMSF curves (Figure 1) In case of 400K simulationthe structure exhibits slight deviation from starting structureThere is a high degree of similarity between the graphscorresponding to the simulations at 300K and 400K Onlymarginal structural fluctuations were observed and no sig-nificant structural changes

At 500K protein structure fluctuation is significantlymore pronounced In this time period the dominant struc-tural change was the expansion of the protein in responseto the temperature increase and the packing density in thethree hydrophobic cores decreased During the simulationthe edge residues particularly those at or near theN-terminalpart of 120572-helix1 are less stable and unfold first At 2 nssimulation 120572-helix1 maintains a regular shape 120572-helix2 was

perturbed but mostly at the termini 120572-helix 3 was graduallyunfolded after 1687 ps 1205723 was lost completely Among thefive 120573-sheets the first obvious observation is that 120573-sheet1of the structure is partially unfolded after 959 ps and ashortening of 120573-sheet1 is observed for residues 50 51 and56 A similar shortening also occurs at 1205732 1205733 and 1205734 forresidues 71 75 91 and 96 As shown in Figure 2(c) it is foundthat the 120573-sheet began to unfold at the edges and associatedturns and the center of the sheet is mostly stronger thanthe edges In addition the loops and turns unfold to variousdegrees However in spite of these important fluctuationsin the protein it appears that the main chain still showsessentially the same overall fold as in the native structureandmost native secondary structure elements remain presentuntil the end of simulation (Figure 3)

When the temperature is increased to 550K the structureof the protein shows a continuous and progressive unfoldingThe N terminus begins to unfold during the first 250 psThis is followed by partial denaturation of 120572-helix1 the 120572-helix1 lost one turn at the N-terminal about 1000 ps andmoved away from the rest of the protein during most ofthe simulation 120572-helix3 was unfolded in the beginning ofthe simulation In the 120573-sheet its disruption starts at theedges of the 120573-sheet and near the irregular element of the120573-sheet1 (120573-bulge at residues 53 and 54) it is promoted byan increase in the twist and an influx of water moleculesand the 120573-sheet1 lost mostly about 850 ps Actually fromthe time dependence of secondary structure as well as theoverlap view of tertiary structure (Figure 3) we can find thatcentral 120573-sheet3 seems to be the most stable in five 120573-sheetsMeanwhile rearrangements of secondary structural elementswere observed along with the simulation and additional 120572-helix and 120573-sheet developed in the structure However thesenonnative interactions were not stable enough as they wouldbe disrupted over time When the temperature was raisedto 600K unfolding began almost immediately Destructionof the native protein structure occurred very fast as alsoindicated by the RMSF and RMSD values (Figure 1) Theprotein was highly coiled in the early stage simulation and

6 Mathematical Problems in Engineering

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

(a)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

(b)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(c)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(d)

Figure 2 Time evolution of secondary structure in unfolding trajectory at different temperatures for Barnase (a) 300K (b) 400K (c) 500K(d) 550K The different secondary elements are presented in a color code format indicated at the bottom of the figure

only a few rearrangement secondary structures remained inthe protein The MD trajectories can provide a detailed viewof the conformational transitions in the early stage of thermalunfolding Figure 3 shows snapshots of protein Barnase fromthe different temperature trajectories The correspondingsnapshots at 300K are also shown as references

34 Intramolecular Contacts

341 Hydrogen Bonding Pattern Hydrogen bond is oneof the factors influencing the thermal stability of proteinIn the hydrogen bond calculations a distance cutoff of

30 A and an angle cutoff of 20∘ were applied The averagenumbers of hydrogen bonds are 29 24 17 and 18 for the300K 400K 500K and 600K simulations respectivelyThus as the simulation temperature is increased there is aconcomitant decrease in number of intact hydrogen bondsThis is reasonable as the structures become more distorted asthe simulation temperature is raised It is also evident fromthe plot (Figure 4) that although the number of hydrogenbonds varies in different temperature it is steadily maintainedthroughout the simulations except for 600K simulationThe interesting finding is the rapid increase of hydrogenbonding number along with the simulation at 600K after

Mathematical Problems in Engineering 7

300K 05ns 10ns 15ns

400K 05ns 10ns 15ns

500K 05ns 10ns 15ns

600K 50ps 05ns 10ns

Figure 3 Snapshots from the thermal unfolding simulations of BarnaseThe structures are made with the VMD program 120572-helices and 3ndash10helices are shown as ribbons 120573-sheets as arrows and the rest are shown as loops

94 psDue to a large distortion of regular secondary structuralelements and unpacking of the hydrophobic cores someof water molecules are inserted in hydrophobic cores andparticipate in hydrogen bonds as both donors and acceptorswith the main-chain polar groups This observation suggeststhe gradual destabilization of the protein in concert withincreasing thermal stress

342 Salt Bridge Analysis To further probe the stabil-ity behavior of Barnase under thermal stress we ana-lyzed another important intramolecular contact namely saltbridge Charged residues in globular proteins frequently formsalt bridges The electrostatic contribution of salt bridge hasbeen suggested to be important for protein stability Further-more the statistical analysis of salt bridges from mesophilic

and thermophilic organisms has shown a higher frequencyof complex salt bridges in thermophilic proteins suggestingthat they have a special role in thermostabilization

In the structure of Barnase nine salt bridges Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27 Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 and Glu60-Lys62 can be identified with the help of VMD Interestinglyamong these salt bridges there are four salt bridge networksNetworks of ionic interactions occur when more than twoionic residues interact and an increased occurrence has beensuggested to be essential in explaining the enhanced thermalstability of protein [46] In order to estimate the behaviorof unfolding under thermal stress the lifetimeoccupancy ofthese pairs were analyzed in detail In dynamic simulation at300K these bridges were found to be stable during the periodof 20 ns Figure 5 shows the distance as a function of time in

8 Mathematical Problems in Engineering

05

101520253035404550

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(a)

05

1015202530354045

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(b)

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(c)

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time(ps)

Num

ber o

f hyd

roge

n bo

nds

(d)

Figure 4 Time evolution of hydrogen bonds of the protein at four different temperatures (a) 300K (b) 400K (c) 500K (d) 600K

protein unfolding trajectory among these salt bridges Fromthe profiles it was found how changes in these salt bridgenetwork interactions are correlated with the initial eventsassociated with tertiary structure unfolding in response tothermal stress

The salt bridge network of Asp8-Arg110-Asp12 is locatedin the main hydrophobic core1 which is formed by thepacking of 120572-helix1 against the 120573-sheet and it is thought tobe the major stabilizing element of Barnase In hydrophobiccore1 the two residues Asp8 and Asp12 located in 120572-helix1could form salt bridge with Arg110 located in C-terminalThe C-terminal is docked to 120572-helix1 in the simulationand this stable docking is dominated by strong electrostaticinteractions between Arg110 and two acidic residues on thehelix Asp8 andAsp12 An interesting finding is that theAsp8-Arg110-Asp12 double salt bridge is not stable very much inthe native structure of Barnase As shown in Figure 5(a) thesalt bridge network of Asp8-Arg110-Asp12may be kept withina short distance in solution after 600 ps at 400K When thetemperature is increased to 500K the salt bridgeAsp8-Arg110was maintained within a relatively short distance duringthe 1750 ps simulation while the salt bridge Asp12-Arg110was maintained within a relatively short distance only about400 ps during the whole simulation and the two residues fellapart eventually after 600 ps

The rupture of the double salt bridge initiates the separa-tion of the 120572-helix1 and 120573-sheet The side chain of lle109 has

moved away from the aromatic ring of Phe7 and the Asp8Asp12 Then some water moves into the center of the corethe inward motion of Lys98 is coupled to the Arg110 outwardmotion of the side chain The exterior strands of the 120573-sheetwere solvated by water molecules that replace some of thehydrogen bonds between 120573-sheets 4 and 5 The break of twosalt bridges lead to the increase in accessible surface areaand partial penetration of the water molecules and thus core1undergoes a partial opening

In the 550K simulation ruptures and restorations ofthe salt bridge Asp8-Arg110 were observed along the firsthalf of unfolding simulations and the Asp8 and Arg110 sidechains begin to recover during the 1110 to 1890 ps periodTheseparation of theAsp12 andArg110 side chains begins at initialstage of simulation and the side chains of two residues camewithin a relatively short distance during the 381 to 1005 psand 1099 to 1500 ps period of the simulation but they fellapart eventually The denaturation of the N-terminal part of120572-helix1 (Phe7) the unfolding of the edges of the 120573-sheet thedenaturation of the C-terminal (Ile109) and the separatingmotion of loop1 (which contributes the Leu20 and Tyr24sidechains to core1) contribute significantly to the unfoldingof the main hydrophobic core1 Meanwhile accompanyingthe solvation of hydrophobic core upon thermal unfolding120572-helix1 and strands of the 120573-sheet also undergo dramaticstructural distortion changes again

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

researchersrsquo attention recently [24ndash27] Barnase is a mul-tidomain protein with three helices in the first half of thesequence followed by a five-stranded antiparallel 120573-sheetThere are three hydrophobic cores in protein It is well suitedfor studying protein folding and stability because it is oneof the smallest globular proteins that does not contain anyprosthetic groups metal cofactors or disulfide bonds whichall contribute to protein stability It has beenwell studied [28ndash31] whereas the role of electrostatic interactions in Barnasethermal stability has not yet been investigated in detail Thequestion of whether salt bridges stabilize the native state ofproteins has yet not definite answerThis is most likely relatedto the fact that the location geometry and optimization of theelectrostatics vary greatly in proteins We aim to address thisissue byMD (molecular dynamics) simulation and themajorfocus of this study was to investigate the contributions ofnoncovalent intramolecular interactions to protein stabilityand how changes in these interactions are correlated with theinitial events associated with tertiary structure unfolding inresponse to thermal stress

The small size of the protein the absence of metalcofactors and the absence of disulfide bonds make Barnasean ideal test case for studying the contribution of salt bridgeto thermostability by computer simulation In this paper wehave performed molecular dynamics simulation of Barnaseat five different temperatures namely 300K 400K 500K550K and 600K By calculating the root mean squaredeviation (RMSD) and root mean square fluctuation (RMSF)values for backbone and C120572 atoms the thermal sensitiveregions have been identified The dynamic properties ofBarnase at different temperatures have been compared interms of secondary structure content molecular flexibilityintramolecular hydrogen bonds and salt bridge interactionsOur analysis specifically focuses on the contribution of saltbridge to the stability of the protein along the unfoldingtransition The study provides insight into the structure-stability relationship of Barnase which may help enlightenour knowledge of protein structural properties and noncova-lent interactions that stabilize secondary peptide structuresor promote folding A better understanding of specific inter-actions change during the unfolding simulation also allowsus to predict more precisely a specific site or region critical toincrease Barnasersquos thermostability

2 Methodology

21 Molecular Dynamics Simulation Molecular dynamicssimulations [32] are based on classical mechanics such asNewtonrsquos second equation of motion If the force acting oneach atom is known the acceleration in a system can beacquired The equations of motion can be determined viathe acceleration resulting in a trajectory of the positionsvelocities and accelerations of each particle in given systemThe force 119865

119894on an atom with mass 119898

119894and position 119903

119894is

determined from the potential of the system 119881 as shown in(1)The potential energy can be used to derive the position ofa particle as a function of time in (2)The equations ofmotionare got for each atom in the systemThe forces acting on atoms

in new positions can be calculated and the simulation willcontinue as many time steps as necessary

119865 = minusnabla119881 (1)

119889119881

119889119903119894

= 119898119894

1198892119903119894

1198891199052 (2)

22 The Potential Function Empirical energy functions canonly be used to approach the force fields for large biologicalsystems composed of many atoms Here the CHARMM(Chemistry at HARvard Macromolecular Mechanics) forcefield is selected which has been developed and continuouslyrevised to better match new experimental data for over 25years

The potential function is a sum of some interaction ener-gies The value of the potential is determined by summingthe bonded terms119881bonded with the nonbonded potential terms119881nonbonded

119881 = 119881bonded + 119881nonbonded (3)

The nonbonded energy terms specify interactions betweennonbonded atoms and atoms that are more than threecovalent bonds away from each other in a molecule Theseenergy terms are modeled by the van der Waals energy andelectrostatic energy namely the first and second summationitems in (4) separately

119881nonbonded = sum

nonbonded-pairs4120576119894119895[(

120590119894119895

119903119894119895

)

12

minus (

120590119894119895

119903119894119895

)

6

]

+ sum

nonbonded-pairs

119902119894119902119895

119863119903119894119895

(4)

where 120590119894119895= (120590119894+120590119895)2 120590119894and 120590119895represent the Lennard-Jones

diameters of the 119894 and 119895 atoms respectively 120576119894119895

= (120576119894120576119895)12

with 120576119894and 120576119895being the Lennard-Joneswell-depth of the 119894 and

119895 atoms and 119902119894is the effective charge on atom 119894

The nonbonded terms calculation in the potential func-tion is the most time-consuming part of the MD simulationGenerally the interactions between every pair of atomsshould be calculated definitely meaning that for an N-atomsystem 1198732 number of operations would be required Toreduce the computation complexity methods were developedto ignore the interactions between two atoms separated bya distance greater than given cutoff distance For the vander Waals interactions the potential is ldquoshiftedrdquo off over adistance from 119903on to 119903off Atoms farther from each otherthan the distance 119903off are supposed not to interact For theelectrostatic interactions the Ewald summation [33] is usedto separate the potential into a slowly decaying long-rangecomponent and a quickly varying short-range component

23 Temperature and Pressure Control TheLangevin dynam-ics [34] is used for constant temperature control Langevindynamics is an effective method for controlling the kineticenergy of the system thus controlling the temperature andor

Mathematical Problems in Engineering 3

pressure This methodology uses the Langevin equation[35] for a single particle The friction kernel in Langevinequation is taken to be space and time independent foreach particle and the influence of the environment on theinternal force is denoted as an average sense Thus explicithydrodynamic interactions can be ignored and the internalforce is introduced by a frictional term proportional to thevelocity and a random force 119877 which approximately simulatemolecular collisions and viscosity in the realistic cellularcircumstance

119872

1198892119909

1198891199052= minusnabla119864 (119909) minus119872120574

119889119909

119889119905

+ 119877 (119905) (5)

Here 119872 is the mass matrix 119864 is the potential energygoverning the solute 120574 is the damping coefficient and 119877(119905)

is a Gaussian white noise force vector that has mean zeroFrom classic theories on Brownian motion it can be

seen that although molecular collisions are random theensemble of these collisions produces a systematic effectThatis to say the molecular random motions exist at thermalequilibrium as a fluctuation Hence one can see that thefrictional force is a correlate of the random force by thefluctuationdissipation theorem [35] This relation can beexpressed by the 120574-dependence of the covariance of 119877

⟨119877 (119905) 119877(1199051015840)

119879

⟩ = 2120574119896119861119879119872120575 (119905 minus 119905

1015840) (6)

where 119896119861is the Boltzmann constant 119879 is the target tempera-

ture and 120575 is the usual Dirac symbolThe Dirac-120575 function is in the form

120575 (119905) =

infin 119905 = 0

0 119905 = 0

int

infin

minusinfin

119891 (119905) 120575 (119905) 119889119905 = 1

(7)

The random force is chosen independently for each stepAnd the covariance matrix is diagonal as hydrodynamicinteractions between particles have been discounted

A physical value of 120574 for each particle can be selectedaccording to Stokesrsquo law for a hydrodynamic particle withradius 119886

119903 Stokesrsquo lawdescribes how the frictional resistance of

a spherical particle in solution varies linearly with its radiusThe practical force magnitude is 6120587120578119886

119903times the particlersquos

velocity where 120578 is the solvent viscosity Stokesrsquo law is oftenapplied to particles of molecular size Therefore the 120574 inLangevin equation can be expressed as

120574 =

6120587120578119886119903

119898

(8)

where119898 is the particlersquos massThe damping coefficient 120574 controls not only the magni-

tude of the frictional force but also the variance of the randomforces It can ensure that the system converges to a Boltzmanndistribution characterized by the temperature 119879 The largerthe value of 120574 the greater the influence of the surroundingfluctuating force Small value of 120574 implies inertial motion In

this study themain objective is to control the temperature sowe need to use small value of 120574The temperature of the systemis maintained via the relationship between 119877(119905) and 120574

For constant pressure and temperature simulations inwhich Langevin dynamics are used to control temperaturethe pressure can be controlled in NAMD with a modifiedNose-Hoover method This method entitled Nose-Hoover[36ndash38] adds a fictive degree of freedom to the physicalsystem with ldquocoordinaterdquo parameter 119909

119905(effectively a scal-

ing parameter [39]) mass 119898119905 and thermodynamic friction

coefficient 120589119905 (This friction coefficient is relative to 119909

119905and

the corresponding momentum 119905) Besides the effective

coordinate mass and friction set (119909119905 119898119905 120589119905) associated with

the fictive thermostat variable a set (119909119901 119898119901 120589119901) associated

with virtual pressure piston (barostat) is also adopted Theeffective equations of motion for a 3-dimensional system canbe expressed as

(119905) = 119881 (119905) + 120589119901119883

119872 (119905) = 119865 (119883 (119905)) minus 119872 (119905) [(1 +

3

119892

) 120589119901+ 120589119905]

V119897 = 3V119897120589119901

119898119901120589119901 (119905) = 3V119897 (119875in minus 119875

0) +

3

119892

(2119881119879119872119881) minus 119898

119901120589119905120589119901

119898119905120589119905 (119905) = 2119881

119879119872119881 +

1205892

119901

119898119901

minus (119892 + 1) 1198961198611198790

(9)

where V119897 is an external volume variable 119892 is the number ofdegrees of freedom in the system 119875

0is the external applied

pressure and 119875in is the internal pressure defined as

119875in =2

3V119897[119864119896minus vir minus (

3V1198972

)

120597119864 (119883 V119897)120597V119897

] (10)

The internal virial vir is proportional to the inner productof the each atomrsquos position vector 119903

119894with the corresponding

force component acting on atom 119894 due to all particles 119865119894

vir = minussum

119894

(119903119879

119894119865119894) (11)

The conserved quantity under these augmented equationsof motion is

119873119875119879

=

1

2

(119881119879119872119881) + 119864 (119883 V119897) +

1

2

(1198981199051205892

119905+ 1198981199011205892

119901)

+ (119892 + 1) 1198961198611198790119909119905+ 1198750V119897

(12)

By this means the magnitude of the system fluctuatesunder specified thermostat and barostats and the system isdriven to steady state at which the average internal pressure119875 is equal to the external applied force 119875

0

3 Results and Discussion

All simulations were performed on a PC with a Pentium4 28GHz dual core processor running Windows operating

4 Mathematical Problems in Engineering

system and using the molecular dynamics program NAMD[40] with CHARMM27 [41] force fields In order to run MDsimulation we need to do the following things

(1) A Protein Data Bank (pdb) file which stores atomiccoordinates andor velocities for the system is neededThe coordinates for starting configurations Barnasewas obtained from the Protein Data Bank (PDB entrycodes 1RNB [42]) which consisted of 110 residues

(2) A Protein Structure File (psf) which contains all ofthe molecule-specific information needed to apply aparticular force field to a molecular system is neededCoordinates of the atoms that were missing in thecrystallographic structure were reconstructed usingthe PSFGEN structure building utility a module ofNAMD

(3) The protein needs to be solvated and put insidewater to more closely resemble the cellular envi-ronment The protein was solvated in a cubic boxconsisting of TIP3 water molecules [43] with periodicboundary conditions The system was neutralizedby adding ions (Clminus) at physiological concentrationusing VMDrsquos solvate and autoionize plugins [44]

(4) We need a force field parameter file A force field is amathematical expression of the potential which atomsexperience in the system A CHARMM forcefieldparameter file contains all of the numerical constantsneeded to evaluate forces and energies given a PSFstructure file and atomic coordinatesThe CHARMMparameters are available for download from the web-site httpwwwcharmmorg

(5) Create the simulation script in which we specified allthe options that NAMD should adopt in running asimulation NAMD parses its configuration file usingthe Tcl scripting language

(i) First we specify the files that contain the molec-ular structure and initial conditions Setting theTcl variable temperaturemakes it easy to changethe target temperature for many options TheoutputName prefix will be used to create all ofthe trajectory output and restart files generatedby NAMD run

(ii) Next is the parameter file itself and the optionsthat control the nonbonded potential functionsThese are mostly specified by the CHARMMforce field In force-field parameters the cut-off distance was specified to 12 A Electrostaticinteractions were calculated using the ParticleMesh Ewald (PME) summation scheme Turnon switching for the van der Waals interactionswhich were calculated with a switching functionfrom 10 A to 12 A SHAKE method [45] wasused for constraining the bonds with hydrogenThe number of time steps between each outputwas 2 fs Set up the temperature and pressurecontrollersThe Langevinwas turned on and thevalue of the Langevin damping coefficient was

set to 5ps The value of the Langevin temper-ature was set equal to the target temperaturefor the simulation of temperature control Thepressure control of the system was set to 1 atm

(6) The system was subjected to energy minimizationfor 1000 steps by steepest descents and subsequentlyequilibrated for 500 ps and then the equilibratedsystem was subjected to molecular dynamics simu-lations for 2 ns each at five different temperaturesnamely 300K 400K 500K 550K and 600K Thecoordinates were saved at every 500 time steps

31 Global Structural Stability MD simulations generatean ensemble of conformations and thus include valuableinformation of the protein dynamics In the following wepresent a detailed analysis of the four molecular dynamicstrajectories in water generated for the protein of BarnaseThe RMSD of the backbone atoms of the protein from thestarting structure over the course of simulation may be usedas a measure of the conformational stability of a proteinduring the simulation The plots of RMSD of the proteinversus time at different temperatures are shown in Figure 1(a)The plots show that the MD simulation of enzyme at 300K isvery stable throughout the simulation time In the trajectoryrun at 400K the backbone RMSD increases slightly from thestarting conformation which fluctuates between 11 A and17 A during the simulation The average value of RMSD isabout 120 A in 400K simulation slightly above the valueof 096 A for the 300K structure simulation The curvecorresponding to the 500K simulation fluctuates more anddisplays a sharp rise (173 A) about 662 ps after that RMSDincreases further and oscillates between 236 A and 371 A forthe remainder of the simulation At 600K the RMSD rises toabout 3 A over the first 200 ps of the simulation and reachesa value of 378 A at around 900 ps Therefore it records adescent to about 256 A at 1184 ps and another sharp rise to416 A after 1295 psThe rise in RMSD indicates large changesto the protein structure and some disruption of the tertiarystructure of the protein

32 Structural Flexibility Following molecular dynamicssimulations at multiple temperatures it was of interest todetermine which general regions of the Barnase polypeptidechain exhibit hypersensitivity to thermal stress The resultsare shown in Figure 1(b) There is a relatively small bump-like peak for the structure at 300K At 400K the loopsbetween 120573-sheet1 and 120573-sheet2 120573-sheet2 and 120573-sheet3 showsignificant increase together with the N- and C-terminalsThe interesting finding is a dramatic increase in RMSF valuesbetween residues 5 and 7 at 500K which implies the begin-ning of the unfolding process for the N-terminal loop regionand the N-terminal of 120572-helix1 region As the temperatureincreases these above-mentioned peaks generally becomemore pronounced This pattern is especially noted in the600K simulation As can be seen most of the changesoccurred in the loop region N-terminal and C-terminalTheregular secondary structure regions such as 120572-helix and 120573-sheet showed much less mobility during the simulationsThe

Mathematical Problems in Engineering 5

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

RMSD

(Aring)

300K400K

500K600K

(a)

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100 110Residue number

RMSF

(Aring)

300K400K

500K600K

(b)

Figure 1 Time evolution (a) Backbone RMSD of Barnase at different temperatures (b) RMSFs as a function of residue number of Barnaseat different temperatures The color-coding scheme is as follows 300K (red) 400K (blue) 500K (magenta) and 600K (cyan)

curves observed for four temperature simulations exhibitedmore or less similarly distributed fluctuations Only at hightemperature simulations most of the residues become highlymobile therefore the curve shows a lot more fluctuationThis is due to the loss of secondary structure at these hightemperatures These observations clearly reveal the differentbehavior of the residues of Barnase molecule in response toincreasing thermal stress and give an indication of the regionsof the Barnase polypeptide chain which are most sensitive orresponsive to heating

33 Secondary Structure Analysis At high temperature sim-ulations dramatically increased RMSD values were observedfor the loop regions and both terminal regions in Barnasewhich indicate these regions extensive local conformationalchanges upon thermal unfolding A close analysis of the timeevolution of the secondary structure (Figure 2) can presentfurther information about its structural flexibilities

Figure 2(a) reveals that 120572-helices 120573-sheets and loopsobserved within Barnase structure are maintained stablythroughout the whole simulation period at 300K Theoverall conformation hydrophobic core compactness andsecondary structural elements are all stable and there is nowater penetration into the protein The simulation at 300Kalso appears to agree well with the stability of the RMSDand RMSF curves (Figure 1) In case of 400K simulationthe structure exhibits slight deviation from starting structureThere is a high degree of similarity between the graphscorresponding to the simulations at 300K and 400K Onlymarginal structural fluctuations were observed and no sig-nificant structural changes

At 500K protein structure fluctuation is significantlymore pronounced In this time period the dominant struc-tural change was the expansion of the protein in responseto the temperature increase and the packing density in thethree hydrophobic cores decreased During the simulationthe edge residues particularly those at or near theN-terminalpart of 120572-helix1 are less stable and unfold first At 2 nssimulation 120572-helix1 maintains a regular shape 120572-helix2 was

perturbed but mostly at the termini 120572-helix 3 was graduallyunfolded after 1687 ps 1205723 was lost completely Among thefive 120573-sheets the first obvious observation is that 120573-sheet1of the structure is partially unfolded after 959 ps and ashortening of 120573-sheet1 is observed for residues 50 51 and56 A similar shortening also occurs at 1205732 1205733 and 1205734 forresidues 71 75 91 and 96 As shown in Figure 2(c) it is foundthat the 120573-sheet began to unfold at the edges and associatedturns and the center of the sheet is mostly stronger thanthe edges In addition the loops and turns unfold to variousdegrees However in spite of these important fluctuationsin the protein it appears that the main chain still showsessentially the same overall fold as in the native structureandmost native secondary structure elements remain presentuntil the end of simulation (Figure 3)

When the temperature is increased to 550K the structureof the protein shows a continuous and progressive unfoldingThe N terminus begins to unfold during the first 250 psThis is followed by partial denaturation of 120572-helix1 the 120572-helix1 lost one turn at the N-terminal about 1000 ps andmoved away from the rest of the protein during most ofthe simulation 120572-helix3 was unfolded in the beginning ofthe simulation In the 120573-sheet its disruption starts at theedges of the 120573-sheet and near the irregular element of the120573-sheet1 (120573-bulge at residues 53 and 54) it is promoted byan increase in the twist and an influx of water moleculesand the 120573-sheet1 lost mostly about 850 ps Actually fromthe time dependence of secondary structure as well as theoverlap view of tertiary structure (Figure 3) we can find thatcentral 120573-sheet3 seems to be the most stable in five 120573-sheetsMeanwhile rearrangements of secondary structural elementswere observed along with the simulation and additional 120572-helix and 120573-sheet developed in the structure However thesenonnative interactions were not stable enough as they wouldbe disrupted over time When the temperature was raisedto 600K unfolding began almost immediately Destructionof the native protein structure occurred very fast as alsoindicated by the RMSF and RMSD values (Figure 1) Theprotein was highly coiled in the early stage simulation and

6 Mathematical Problems in Engineering

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

(a)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

(b)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(c)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(d)

Figure 2 Time evolution of secondary structure in unfolding trajectory at different temperatures for Barnase (a) 300K (b) 400K (c) 500K(d) 550K The different secondary elements are presented in a color code format indicated at the bottom of the figure

only a few rearrangement secondary structures remained inthe protein The MD trajectories can provide a detailed viewof the conformational transitions in the early stage of thermalunfolding Figure 3 shows snapshots of protein Barnase fromthe different temperature trajectories The correspondingsnapshots at 300K are also shown as references

34 Intramolecular Contacts

341 Hydrogen Bonding Pattern Hydrogen bond is oneof the factors influencing the thermal stability of proteinIn the hydrogen bond calculations a distance cutoff of

30 A and an angle cutoff of 20∘ were applied The averagenumbers of hydrogen bonds are 29 24 17 and 18 for the300K 400K 500K and 600K simulations respectivelyThus as the simulation temperature is increased there is aconcomitant decrease in number of intact hydrogen bondsThis is reasonable as the structures become more distorted asthe simulation temperature is raised It is also evident fromthe plot (Figure 4) that although the number of hydrogenbonds varies in different temperature it is steadily maintainedthroughout the simulations except for 600K simulationThe interesting finding is the rapid increase of hydrogenbonding number along with the simulation at 600K after

Mathematical Problems in Engineering 7

300K 05ns 10ns 15ns

400K 05ns 10ns 15ns

500K 05ns 10ns 15ns

600K 50ps 05ns 10ns

Figure 3 Snapshots from the thermal unfolding simulations of BarnaseThe structures are made with the VMD program 120572-helices and 3ndash10helices are shown as ribbons 120573-sheets as arrows and the rest are shown as loops

94 psDue to a large distortion of regular secondary structuralelements and unpacking of the hydrophobic cores someof water molecules are inserted in hydrophobic cores andparticipate in hydrogen bonds as both donors and acceptorswith the main-chain polar groups This observation suggeststhe gradual destabilization of the protein in concert withincreasing thermal stress

342 Salt Bridge Analysis To further probe the stabil-ity behavior of Barnase under thermal stress we ana-lyzed another important intramolecular contact namely saltbridge Charged residues in globular proteins frequently formsalt bridges The electrostatic contribution of salt bridge hasbeen suggested to be important for protein stability Further-more the statistical analysis of salt bridges from mesophilic

and thermophilic organisms has shown a higher frequencyof complex salt bridges in thermophilic proteins suggestingthat they have a special role in thermostabilization

In the structure of Barnase nine salt bridges Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27 Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 and Glu60-Lys62 can be identified with the help of VMD Interestinglyamong these salt bridges there are four salt bridge networksNetworks of ionic interactions occur when more than twoionic residues interact and an increased occurrence has beensuggested to be essential in explaining the enhanced thermalstability of protein [46] In order to estimate the behaviorof unfolding under thermal stress the lifetimeoccupancy ofthese pairs were analyzed in detail In dynamic simulation at300K these bridges were found to be stable during the periodof 20 ns Figure 5 shows the distance as a function of time in

8 Mathematical Problems in Engineering

05

101520253035404550

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(a)

05

1015202530354045

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(b)

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(c)

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time(ps)

Num

ber o

f hyd

roge

n bo

nds

(d)

Figure 4 Time evolution of hydrogen bonds of the protein at four different temperatures (a) 300K (b) 400K (c) 500K (d) 600K

protein unfolding trajectory among these salt bridges Fromthe profiles it was found how changes in these salt bridgenetwork interactions are correlated with the initial eventsassociated with tertiary structure unfolding in response tothermal stress

The salt bridge network of Asp8-Arg110-Asp12 is locatedin the main hydrophobic core1 which is formed by thepacking of 120572-helix1 against the 120573-sheet and it is thought tobe the major stabilizing element of Barnase In hydrophobiccore1 the two residues Asp8 and Asp12 located in 120572-helix1could form salt bridge with Arg110 located in C-terminalThe C-terminal is docked to 120572-helix1 in the simulationand this stable docking is dominated by strong electrostaticinteractions between Arg110 and two acidic residues on thehelix Asp8 andAsp12 An interesting finding is that theAsp8-Arg110-Asp12 double salt bridge is not stable very much inthe native structure of Barnase As shown in Figure 5(a) thesalt bridge network of Asp8-Arg110-Asp12may be kept withina short distance in solution after 600 ps at 400K When thetemperature is increased to 500K the salt bridgeAsp8-Arg110was maintained within a relatively short distance duringthe 1750 ps simulation while the salt bridge Asp12-Arg110was maintained within a relatively short distance only about400 ps during the whole simulation and the two residues fellapart eventually after 600 ps

The rupture of the double salt bridge initiates the separa-tion of the 120572-helix1 and 120573-sheet The side chain of lle109 has

moved away from the aromatic ring of Phe7 and the Asp8Asp12 Then some water moves into the center of the corethe inward motion of Lys98 is coupled to the Arg110 outwardmotion of the side chain The exterior strands of the 120573-sheetwere solvated by water molecules that replace some of thehydrogen bonds between 120573-sheets 4 and 5 The break of twosalt bridges lead to the increase in accessible surface areaand partial penetration of the water molecules and thus core1undergoes a partial opening

In the 550K simulation ruptures and restorations ofthe salt bridge Asp8-Arg110 were observed along the firsthalf of unfolding simulations and the Asp8 and Arg110 sidechains begin to recover during the 1110 to 1890 ps periodTheseparation of theAsp12 andArg110 side chains begins at initialstage of simulation and the side chains of two residues camewithin a relatively short distance during the 381 to 1005 psand 1099 to 1500 ps period of the simulation but they fellapart eventually The denaturation of the N-terminal part of120572-helix1 (Phe7) the unfolding of the edges of the 120573-sheet thedenaturation of the C-terminal (Ile109) and the separatingmotion of loop1 (which contributes the Leu20 and Tyr24sidechains to core1) contribute significantly to the unfoldingof the main hydrophobic core1 Meanwhile accompanyingthe solvation of hydrophobic core upon thermal unfolding120572-helix1 and strands of the 120573-sheet also undergo dramaticstructural distortion changes again

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

pressure This methodology uses the Langevin equation[35] for a single particle The friction kernel in Langevinequation is taken to be space and time independent foreach particle and the influence of the environment on theinternal force is denoted as an average sense Thus explicithydrodynamic interactions can be ignored and the internalforce is introduced by a frictional term proportional to thevelocity and a random force 119877 which approximately simulatemolecular collisions and viscosity in the realistic cellularcircumstance

119872

1198892119909

1198891199052= minusnabla119864 (119909) minus119872120574

119889119909

119889119905

+ 119877 (119905) (5)

Here 119872 is the mass matrix 119864 is the potential energygoverning the solute 120574 is the damping coefficient and 119877(119905)

is a Gaussian white noise force vector that has mean zeroFrom classic theories on Brownian motion it can be

seen that although molecular collisions are random theensemble of these collisions produces a systematic effectThatis to say the molecular random motions exist at thermalequilibrium as a fluctuation Hence one can see that thefrictional force is a correlate of the random force by thefluctuationdissipation theorem [35] This relation can beexpressed by the 120574-dependence of the covariance of 119877

⟨119877 (119905) 119877(1199051015840)

119879

⟩ = 2120574119896119861119879119872120575 (119905 minus 119905

1015840) (6)

where 119896119861is the Boltzmann constant 119879 is the target tempera-

ture and 120575 is the usual Dirac symbolThe Dirac-120575 function is in the form

120575 (119905) =

infin 119905 = 0

0 119905 = 0

int

infin

minusinfin

119891 (119905) 120575 (119905) 119889119905 = 1

(7)

The random force is chosen independently for each stepAnd the covariance matrix is diagonal as hydrodynamicinteractions between particles have been discounted

A physical value of 120574 for each particle can be selectedaccording to Stokesrsquo law for a hydrodynamic particle withradius 119886

119903 Stokesrsquo lawdescribes how the frictional resistance of

a spherical particle in solution varies linearly with its radiusThe practical force magnitude is 6120587120578119886

119903times the particlersquos

velocity where 120578 is the solvent viscosity Stokesrsquo law is oftenapplied to particles of molecular size Therefore the 120574 inLangevin equation can be expressed as

120574 =

6120587120578119886119903

119898

(8)

where119898 is the particlersquos massThe damping coefficient 120574 controls not only the magni-

tude of the frictional force but also the variance of the randomforces It can ensure that the system converges to a Boltzmanndistribution characterized by the temperature 119879 The largerthe value of 120574 the greater the influence of the surroundingfluctuating force Small value of 120574 implies inertial motion In

this study themain objective is to control the temperature sowe need to use small value of 120574The temperature of the systemis maintained via the relationship between 119877(119905) and 120574

For constant pressure and temperature simulations inwhich Langevin dynamics are used to control temperaturethe pressure can be controlled in NAMD with a modifiedNose-Hoover method This method entitled Nose-Hoover[36ndash38] adds a fictive degree of freedom to the physicalsystem with ldquocoordinaterdquo parameter 119909

119905(effectively a scal-

ing parameter [39]) mass 119898119905 and thermodynamic friction

coefficient 120589119905 (This friction coefficient is relative to 119909

119905and

the corresponding momentum 119905) Besides the effective

coordinate mass and friction set (119909119905 119898119905 120589119905) associated with

the fictive thermostat variable a set (119909119901 119898119901 120589119901) associated

with virtual pressure piston (barostat) is also adopted Theeffective equations of motion for a 3-dimensional system canbe expressed as

(119905) = 119881 (119905) + 120589119901119883

119872 (119905) = 119865 (119883 (119905)) minus 119872 (119905) [(1 +

3

119892

) 120589119901+ 120589119905]

V119897 = 3V119897120589119901

119898119901120589119901 (119905) = 3V119897 (119875in minus 119875

0) +

3

119892

(2119881119879119872119881) minus 119898

119901120589119905120589119901

119898119905120589119905 (119905) = 2119881

119879119872119881 +

1205892

119901

119898119901

minus (119892 + 1) 1198961198611198790

(9)

where V119897 is an external volume variable 119892 is the number ofdegrees of freedom in the system 119875

0is the external applied

pressure and 119875in is the internal pressure defined as

119875in =2

3V119897[119864119896minus vir minus (

3V1198972

)

120597119864 (119883 V119897)120597V119897

] (10)

The internal virial vir is proportional to the inner productof the each atomrsquos position vector 119903

119894with the corresponding

force component acting on atom 119894 due to all particles 119865119894

vir = minussum

119894

(119903119879

119894119865119894) (11)

The conserved quantity under these augmented equationsof motion is

119873119875119879

=

1

2

(119881119879119872119881) + 119864 (119883 V119897) +

1

2

(1198981199051205892

119905+ 1198981199011205892

119901)

+ (119892 + 1) 1198961198611198790119909119905+ 1198750V119897

(12)

By this means the magnitude of the system fluctuatesunder specified thermostat and barostats and the system isdriven to steady state at which the average internal pressure119875 is equal to the external applied force 119875

0

3 Results and Discussion

All simulations were performed on a PC with a Pentium4 28GHz dual core processor running Windows operating

4 Mathematical Problems in Engineering

system and using the molecular dynamics program NAMD[40] with CHARMM27 [41] force fields In order to run MDsimulation we need to do the following things

(1) A Protein Data Bank (pdb) file which stores atomiccoordinates andor velocities for the system is neededThe coordinates for starting configurations Barnasewas obtained from the Protein Data Bank (PDB entrycodes 1RNB [42]) which consisted of 110 residues

(2) A Protein Structure File (psf) which contains all ofthe molecule-specific information needed to apply aparticular force field to a molecular system is neededCoordinates of the atoms that were missing in thecrystallographic structure were reconstructed usingthe PSFGEN structure building utility a module ofNAMD

(3) The protein needs to be solvated and put insidewater to more closely resemble the cellular envi-ronment The protein was solvated in a cubic boxconsisting of TIP3 water molecules [43] with periodicboundary conditions The system was neutralizedby adding ions (Clminus) at physiological concentrationusing VMDrsquos solvate and autoionize plugins [44]

(4) We need a force field parameter file A force field is amathematical expression of the potential which atomsexperience in the system A CHARMM forcefieldparameter file contains all of the numerical constantsneeded to evaluate forces and energies given a PSFstructure file and atomic coordinatesThe CHARMMparameters are available for download from the web-site httpwwwcharmmorg

(5) Create the simulation script in which we specified allthe options that NAMD should adopt in running asimulation NAMD parses its configuration file usingthe Tcl scripting language

(i) First we specify the files that contain the molec-ular structure and initial conditions Setting theTcl variable temperaturemakes it easy to changethe target temperature for many options TheoutputName prefix will be used to create all ofthe trajectory output and restart files generatedby NAMD run

(ii) Next is the parameter file itself and the optionsthat control the nonbonded potential functionsThese are mostly specified by the CHARMMforce field In force-field parameters the cut-off distance was specified to 12 A Electrostaticinteractions were calculated using the ParticleMesh Ewald (PME) summation scheme Turnon switching for the van der Waals interactionswhich were calculated with a switching functionfrom 10 A to 12 A SHAKE method [45] wasused for constraining the bonds with hydrogenThe number of time steps between each outputwas 2 fs Set up the temperature and pressurecontrollersThe Langevinwas turned on and thevalue of the Langevin damping coefficient was

set to 5ps The value of the Langevin temper-ature was set equal to the target temperaturefor the simulation of temperature control Thepressure control of the system was set to 1 atm

(6) The system was subjected to energy minimizationfor 1000 steps by steepest descents and subsequentlyequilibrated for 500 ps and then the equilibratedsystem was subjected to molecular dynamics simu-lations for 2 ns each at five different temperaturesnamely 300K 400K 500K 550K and 600K Thecoordinates were saved at every 500 time steps

31 Global Structural Stability MD simulations generatean ensemble of conformations and thus include valuableinformation of the protein dynamics In the following wepresent a detailed analysis of the four molecular dynamicstrajectories in water generated for the protein of BarnaseThe RMSD of the backbone atoms of the protein from thestarting structure over the course of simulation may be usedas a measure of the conformational stability of a proteinduring the simulation The plots of RMSD of the proteinversus time at different temperatures are shown in Figure 1(a)The plots show that the MD simulation of enzyme at 300K isvery stable throughout the simulation time In the trajectoryrun at 400K the backbone RMSD increases slightly from thestarting conformation which fluctuates between 11 A and17 A during the simulation The average value of RMSD isabout 120 A in 400K simulation slightly above the valueof 096 A for the 300K structure simulation The curvecorresponding to the 500K simulation fluctuates more anddisplays a sharp rise (173 A) about 662 ps after that RMSDincreases further and oscillates between 236 A and 371 A forthe remainder of the simulation At 600K the RMSD rises toabout 3 A over the first 200 ps of the simulation and reachesa value of 378 A at around 900 ps Therefore it records adescent to about 256 A at 1184 ps and another sharp rise to416 A after 1295 psThe rise in RMSD indicates large changesto the protein structure and some disruption of the tertiarystructure of the protein

32 Structural Flexibility Following molecular dynamicssimulations at multiple temperatures it was of interest todetermine which general regions of the Barnase polypeptidechain exhibit hypersensitivity to thermal stress The resultsare shown in Figure 1(b) There is a relatively small bump-like peak for the structure at 300K At 400K the loopsbetween 120573-sheet1 and 120573-sheet2 120573-sheet2 and 120573-sheet3 showsignificant increase together with the N- and C-terminalsThe interesting finding is a dramatic increase in RMSF valuesbetween residues 5 and 7 at 500K which implies the begin-ning of the unfolding process for the N-terminal loop regionand the N-terminal of 120572-helix1 region As the temperatureincreases these above-mentioned peaks generally becomemore pronounced This pattern is especially noted in the600K simulation As can be seen most of the changesoccurred in the loop region N-terminal and C-terminalTheregular secondary structure regions such as 120572-helix and 120573-sheet showed much less mobility during the simulationsThe

Mathematical Problems in Engineering 5

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

RMSD

(Aring)

300K400K

500K600K

(a)

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100 110Residue number

RMSF

(Aring)

300K400K

500K600K

(b)

Figure 1 Time evolution (a) Backbone RMSD of Barnase at different temperatures (b) RMSFs as a function of residue number of Barnaseat different temperatures The color-coding scheme is as follows 300K (red) 400K (blue) 500K (magenta) and 600K (cyan)

curves observed for four temperature simulations exhibitedmore or less similarly distributed fluctuations Only at hightemperature simulations most of the residues become highlymobile therefore the curve shows a lot more fluctuationThis is due to the loss of secondary structure at these hightemperatures These observations clearly reveal the differentbehavior of the residues of Barnase molecule in response toincreasing thermal stress and give an indication of the regionsof the Barnase polypeptide chain which are most sensitive orresponsive to heating

33 Secondary Structure Analysis At high temperature sim-ulations dramatically increased RMSD values were observedfor the loop regions and both terminal regions in Barnasewhich indicate these regions extensive local conformationalchanges upon thermal unfolding A close analysis of the timeevolution of the secondary structure (Figure 2) can presentfurther information about its structural flexibilities

Figure 2(a) reveals that 120572-helices 120573-sheets and loopsobserved within Barnase structure are maintained stablythroughout the whole simulation period at 300K Theoverall conformation hydrophobic core compactness andsecondary structural elements are all stable and there is nowater penetration into the protein The simulation at 300Kalso appears to agree well with the stability of the RMSDand RMSF curves (Figure 1) In case of 400K simulationthe structure exhibits slight deviation from starting structureThere is a high degree of similarity between the graphscorresponding to the simulations at 300K and 400K Onlymarginal structural fluctuations were observed and no sig-nificant structural changes

At 500K protein structure fluctuation is significantlymore pronounced In this time period the dominant struc-tural change was the expansion of the protein in responseto the temperature increase and the packing density in thethree hydrophobic cores decreased During the simulationthe edge residues particularly those at or near theN-terminalpart of 120572-helix1 are less stable and unfold first At 2 nssimulation 120572-helix1 maintains a regular shape 120572-helix2 was

perturbed but mostly at the termini 120572-helix 3 was graduallyunfolded after 1687 ps 1205723 was lost completely Among thefive 120573-sheets the first obvious observation is that 120573-sheet1of the structure is partially unfolded after 959 ps and ashortening of 120573-sheet1 is observed for residues 50 51 and56 A similar shortening also occurs at 1205732 1205733 and 1205734 forresidues 71 75 91 and 96 As shown in Figure 2(c) it is foundthat the 120573-sheet began to unfold at the edges and associatedturns and the center of the sheet is mostly stronger thanthe edges In addition the loops and turns unfold to variousdegrees However in spite of these important fluctuationsin the protein it appears that the main chain still showsessentially the same overall fold as in the native structureandmost native secondary structure elements remain presentuntil the end of simulation (Figure 3)

When the temperature is increased to 550K the structureof the protein shows a continuous and progressive unfoldingThe N terminus begins to unfold during the first 250 psThis is followed by partial denaturation of 120572-helix1 the 120572-helix1 lost one turn at the N-terminal about 1000 ps andmoved away from the rest of the protein during most ofthe simulation 120572-helix3 was unfolded in the beginning ofthe simulation In the 120573-sheet its disruption starts at theedges of the 120573-sheet and near the irregular element of the120573-sheet1 (120573-bulge at residues 53 and 54) it is promoted byan increase in the twist and an influx of water moleculesand the 120573-sheet1 lost mostly about 850 ps Actually fromthe time dependence of secondary structure as well as theoverlap view of tertiary structure (Figure 3) we can find thatcentral 120573-sheet3 seems to be the most stable in five 120573-sheetsMeanwhile rearrangements of secondary structural elementswere observed along with the simulation and additional 120572-helix and 120573-sheet developed in the structure However thesenonnative interactions were not stable enough as they wouldbe disrupted over time When the temperature was raisedto 600K unfolding began almost immediately Destructionof the native protein structure occurred very fast as alsoindicated by the RMSF and RMSD values (Figure 1) Theprotein was highly coiled in the early stage simulation and

6 Mathematical Problems in Engineering

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

(a)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

(b)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(c)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(d)

Figure 2 Time evolution of secondary structure in unfolding trajectory at different temperatures for Barnase (a) 300K (b) 400K (c) 500K(d) 550K The different secondary elements are presented in a color code format indicated at the bottom of the figure

only a few rearrangement secondary structures remained inthe protein The MD trajectories can provide a detailed viewof the conformational transitions in the early stage of thermalunfolding Figure 3 shows snapshots of protein Barnase fromthe different temperature trajectories The correspondingsnapshots at 300K are also shown as references

34 Intramolecular Contacts

341 Hydrogen Bonding Pattern Hydrogen bond is oneof the factors influencing the thermal stability of proteinIn the hydrogen bond calculations a distance cutoff of

30 A and an angle cutoff of 20∘ were applied The averagenumbers of hydrogen bonds are 29 24 17 and 18 for the300K 400K 500K and 600K simulations respectivelyThus as the simulation temperature is increased there is aconcomitant decrease in number of intact hydrogen bondsThis is reasonable as the structures become more distorted asthe simulation temperature is raised It is also evident fromthe plot (Figure 4) that although the number of hydrogenbonds varies in different temperature it is steadily maintainedthroughout the simulations except for 600K simulationThe interesting finding is the rapid increase of hydrogenbonding number along with the simulation at 600K after

Mathematical Problems in Engineering 7

300K 05ns 10ns 15ns

400K 05ns 10ns 15ns

500K 05ns 10ns 15ns

600K 50ps 05ns 10ns

Figure 3 Snapshots from the thermal unfolding simulations of BarnaseThe structures are made with the VMD program 120572-helices and 3ndash10helices are shown as ribbons 120573-sheets as arrows and the rest are shown as loops

94 psDue to a large distortion of regular secondary structuralelements and unpacking of the hydrophobic cores someof water molecules are inserted in hydrophobic cores andparticipate in hydrogen bonds as both donors and acceptorswith the main-chain polar groups This observation suggeststhe gradual destabilization of the protein in concert withincreasing thermal stress

342 Salt Bridge Analysis To further probe the stabil-ity behavior of Barnase under thermal stress we ana-lyzed another important intramolecular contact namely saltbridge Charged residues in globular proteins frequently formsalt bridges The electrostatic contribution of salt bridge hasbeen suggested to be important for protein stability Further-more the statistical analysis of salt bridges from mesophilic

and thermophilic organisms has shown a higher frequencyof complex salt bridges in thermophilic proteins suggestingthat they have a special role in thermostabilization

In the structure of Barnase nine salt bridges Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27 Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 and Glu60-Lys62 can be identified with the help of VMD Interestinglyamong these salt bridges there are four salt bridge networksNetworks of ionic interactions occur when more than twoionic residues interact and an increased occurrence has beensuggested to be essential in explaining the enhanced thermalstability of protein [46] In order to estimate the behaviorof unfolding under thermal stress the lifetimeoccupancy ofthese pairs were analyzed in detail In dynamic simulation at300K these bridges were found to be stable during the periodof 20 ns Figure 5 shows the distance as a function of time in

8 Mathematical Problems in Engineering

05

101520253035404550

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(a)

05

1015202530354045

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(b)

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(c)

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time(ps)

Num

ber o

f hyd

roge

n bo

nds

(d)

Figure 4 Time evolution of hydrogen bonds of the protein at four different temperatures (a) 300K (b) 400K (c) 500K (d) 600K

protein unfolding trajectory among these salt bridges Fromthe profiles it was found how changes in these salt bridgenetwork interactions are correlated with the initial eventsassociated with tertiary structure unfolding in response tothermal stress

The salt bridge network of Asp8-Arg110-Asp12 is locatedin the main hydrophobic core1 which is formed by thepacking of 120572-helix1 against the 120573-sheet and it is thought tobe the major stabilizing element of Barnase In hydrophobiccore1 the two residues Asp8 and Asp12 located in 120572-helix1could form salt bridge with Arg110 located in C-terminalThe C-terminal is docked to 120572-helix1 in the simulationand this stable docking is dominated by strong electrostaticinteractions between Arg110 and two acidic residues on thehelix Asp8 andAsp12 An interesting finding is that theAsp8-Arg110-Asp12 double salt bridge is not stable very much inthe native structure of Barnase As shown in Figure 5(a) thesalt bridge network of Asp8-Arg110-Asp12may be kept withina short distance in solution after 600 ps at 400K When thetemperature is increased to 500K the salt bridgeAsp8-Arg110was maintained within a relatively short distance duringthe 1750 ps simulation while the salt bridge Asp12-Arg110was maintained within a relatively short distance only about400 ps during the whole simulation and the two residues fellapart eventually after 600 ps

The rupture of the double salt bridge initiates the separa-tion of the 120572-helix1 and 120573-sheet The side chain of lle109 has

moved away from the aromatic ring of Phe7 and the Asp8Asp12 Then some water moves into the center of the corethe inward motion of Lys98 is coupled to the Arg110 outwardmotion of the side chain The exterior strands of the 120573-sheetwere solvated by water molecules that replace some of thehydrogen bonds between 120573-sheets 4 and 5 The break of twosalt bridges lead to the increase in accessible surface areaand partial penetration of the water molecules and thus core1undergoes a partial opening

In the 550K simulation ruptures and restorations ofthe salt bridge Asp8-Arg110 were observed along the firsthalf of unfolding simulations and the Asp8 and Arg110 sidechains begin to recover during the 1110 to 1890 ps periodTheseparation of theAsp12 andArg110 side chains begins at initialstage of simulation and the side chains of two residues camewithin a relatively short distance during the 381 to 1005 psand 1099 to 1500 ps period of the simulation but they fellapart eventually The denaturation of the N-terminal part of120572-helix1 (Phe7) the unfolding of the edges of the 120573-sheet thedenaturation of the C-terminal (Ile109) and the separatingmotion of loop1 (which contributes the Leu20 and Tyr24sidechains to core1) contribute significantly to the unfoldingof the main hydrophobic core1 Meanwhile accompanyingthe solvation of hydrophobic core upon thermal unfolding120572-helix1 and strands of the 120573-sheet also undergo dramaticstructural distortion changes again

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

system and using the molecular dynamics program NAMD[40] with CHARMM27 [41] force fields In order to run MDsimulation we need to do the following things

(1) A Protein Data Bank (pdb) file which stores atomiccoordinates andor velocities for the system is neededThe coordinates for starting configurations Barnasewas obtained from the Protein Data Bank (PDB entrycodes 1RNB [42]) which consisted of 110 residues

(2) A Protein Structure File (psf) which contains all ofthe molecule-specific information needed to apply aparticular force field to a molecular system is neededCoordinates of the atoms that were missing in thecrystallographic structure were reconstructed usingthe PSFGEN structure building utility a module ofNAMD

(3) The protein needs to be solvated and put insidewater to more closely resemble the cellular envi-ronment The protein was solvated in a cubic boxconsisting of TIP3 water molecules [43] with periodicboundary conditions The system was neutralizedby adding ions (Clminus) at physiological concentrationusing VMDrsquos solvate and autoionize plugins [44]

(4) We need a force field parameter file A force field is amathematical expression of the potential which atomsexperience in the system A CHARMM forcefieldparameter file contains all of the numerical constantsneeded to evaluate forces and energies given a PSFstructure file and atomic coordinatesThe CHARMMparameters are available for download from the web-site httpwwwcharmmorg

(5) Create the simulation script in which we specified allthe options that NAMD should adopt in running asimulation NAMD parses its configuration file usingthe Tcl scripting language

(i) First we specify the files that contain the molec-ular structure and initial conditions Setting theTcl variable temperaturemakes it easy to changethe target temperature for many options TheoutputName prefix will be used to create all ofthe trajectory output and restart files generatedby NAMD run

(ii) Next is the parameter file itself and the optionsthat control the nonbonded potential functionsThese are mostly specified by the CHARMMforce field In force-field parameters the cut-off distance was specified to 12 A Electrostaticinteractions were calculated using the ParticleMesh Ewald (PME) summation scheme Turnon switching for the van der Waals interactionswhich were calculated with a switching functionfrom 10 A to 12 A SHAKE method [45] wasused for constraining the bonds with hydrogenThe number of time steps between each outputwas 2 fs Set up the temperature and pressurecontrollersThe Langevinwas turned on and thevalue of the Langevin damping coefficient was

set to 5ps The value of the Langevin temper-ature was set equal to the target temperaturefor the simulation of temperature control Thepressure control of the system was set to 1 atm

(6) The system was subjected to energy minimizationfor 1000 steps by steepest descents and subsequentlyequilibrated for 500 ps and then the equilibratedsystem was subjected to molecular dynamics simu-lations for 2 ns each at five different temperaturesnamely 300K 400K 500K 550K and 600K Thecoordinates were saved at every 500 time steps

31 Global Structural Stability MD simulations generatean ensemble of conformations and thus include valuableinformation of the protein dynamics In the following wepresent a detailed analysis of the four molecular dynamicstrajectories in water generated for the protein of BarnaseThe RMSD of the backbone atoms of the protein from thestarting structure over the course of simulation may be usedas a measure of the conformational stability of a proteinduring the simulation The plots of RMSD of the proteinversus time at different temperatures are shown in Figure 1(a)The plots show that the MD simulation of enzyme at 300K isvery stable throughout the simulation time In the trajectoryrun at 400K the backbone RMSD increases slightly from thestarting conformation which fluctuates between 11 A and17 A during the simulation The average value of RMSD isabout 120 A in 400K simulation slightly above the valueof 096 A for the 300K structure simulation The curvecorresponding to the 500K simulation fluctuates more anddisplays a sharp rise (173 A) about 662 ps after that RMSDincreases further and oscillates between 236 A and 371 A forthe remainder of the simulation At 600K the RMSD rises toabout 3 A over the first 200 ps of the simulation and reachesa value of 378 A at around 900 ps Therefore it records adescent to about 256 A at 1184 ps and another sharp rise to416 A after 1295 psThe rise in RMSD indicates large changesto the protein structure and some disruption of the tertiarystructure of the protein

32 Structural Flexibility Following molecular dynamicssimulations at multiple temperatures it was of interest todetermine which general regions of the Barnase polypeptidechain exhibit hypersensitivity to thermal stress The resultsare shown in Figure 1(b) There is a relatively small bump-like peak for the structure at 300K At 400K the loopsbetween 120573-sheet1 and 120573-sheet2 120573-sheet2 and 120573-sheet3 showsignificant increase together with the N- and C-terminalsThe interesting finding is a dramatic increase in RMSF valuesbetween residues 5 and 7 at 500K which implies the begin-ning of the unfolding process for the N-terminal loop regionand the N-terminal of 120572-helix1 region As the temperatureincreases these above-mentioned peaks generally becomemore pronounced This pattern is especially noted in the600K simulation As can be seen most of the changesoccurred in the loop region N-terminal and C-terminalTheregular secondary structure regions such as 120572-helix and 120573-sheet showed much less mobility during the simulationsThe

Mathematical Problems in Engineering 5

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

RMSD

(Aring)

300K400K

500K600K

(a)

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100 110Residue number

RMSF

(Aring)

300K400K

500K600K

(b)

Figure 1 Time evolution (a) Backbone RMSD of Barnase at different temperatures (b) RMSFs as a function of residue number of Barnaseat different temperatures The color-coding scheme is as follows 300K (red) 400K (blue) 500K (magenta) and 600K (cyan)

curves observed for four temperature simulations exhibitedmore or less similarly distributed fluctuations Only at hightemperature simulations most of the residues become highlymobile therefore the curve shows a lot more fluctuationThis is due to the loss of secondary structure at these hightemperatures These observations clearly reveal the differentbehavior of the residues of Barnase molecule in response toincreasing thermal stress and give an indication of the regionsof the Barnase polypeptide chain which are most sensitive orresponsive to heating

33 Secondary Structure Analysis At high temperature sim-ulations dramatically increased RMSD values were observedfor the loop regions and both terminal regions in Barnasewhich indicate these regions extensive local conformationalchanges upon thermal unfolding A close analysis of the timeevolution of the secondary structure (Figure 2) can presentfurther information about its structural flexibilities

Figure 2(a) reveals that 120572-helices 120573-sheets and loopsobserved within Barnase structure are maintained stablythroughout the whole simulation period at 300K Theoverall conformation hydrophobic core compactness andsecondary structural elements are all stable and there is nowater penetration into the protein The simulation at 300Kalso appears to agree well with the stability of the RMSDand RMSF curves (Figure 1) In case of 400K simulationthe structure exhibits slight deviation from starting structureThere is a high degree of similarity between the graphscorresponding to the simulations at 300K and 400K Onlymarginal structural fluctuations were observed and no sig-nificant structural changes

At 500K protein structure fluctuation is significantlymore pronounced In this time period the dominant struc-tural change was the expansion of the protein in responseto the temperature increase and the packing density in thethree hydrophobic cores decreased During the simulationthe edge residues particularly those at or near theN-terminalpart of 120572-helix1 are less stable and unfold first At 2 nssimulation 120572-helix1 maintains a regular shape 120572-helix2 was

perturbed but mostly at the termini 120572-helix 3 was graduallyunfolded after 1687 ps 1205723 was lost completely Among thefive 120573-sheets the first obvious observation is that 120573-sheet1of the structure is partially unfolded after 959 ps and ashortening of 120573-sheet1 is observed for residues 50 51 and56 A similar shortening also occurs at 1205732 1205733 and 1205734 forresidues 71 75 91 and 96 As shown in Figure 2(c) it is foundthat the 120573-sheet began to unfold at the edges and associatedturns and the center of the sheet is mostly stronger thanthe edges In addition the loops and turns unfold to variousdegrees However in spite of these important fluctuationsin the protein it appears that the main chain still showsessentially the same overall fold as in the native structureandmost native secondary structure elements remain presentuntil the end of simulation (Figure 3)

When the temperature is increased to 550K the structureof the protein shows a continuous and progressive unfoldingThe N terminus begins to unfold during the first 250 psThis is followed by partial denaturation of 120572-helix1 the 120572-helix1 lost one turn at the N-terminal about 1000 ps andmoved away from the rest of the protein during most ofthe simulation 120572-helix3 was unfolded in the beginning ofthe simulation In the 120573-sheet its disruption starts at theedges of the 120573-sheet and near the irregular element of the120573-sheet1 (120573-bulge at residues 53 and 54) it is promoted byan increase in the twist and an influx of water moleculesand the 120573-sheet1 lost mostly about 850 ps Actually fromthe time dependence of secondary structure as well as theoverlap view of tertiary structure (Figure 3) we can find thatcentral 120573-sheet3 seems to be the most stable in five 120573-sheetsMeanwhile rearrangements of secondary structural elementswere observed along with the simulation and additional 120572-helix and 120573-sheet developed in the structure However thesenonnative interactions were not stable enough as they wouldbe disrupted over time When the temperature was raisedto 600K unfolding began almost immediately Destructionof the native protein structure occurred very fast as alsoindicated by the RMSF and RMSD values (Figure 1) Theprotein was highly coiled in the early stage simulation and

6 Mathematical Problems in Engineering

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

(a)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

(b)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(c)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(d)

Figure 2 Time evolution of secondary structure in unfolding trajectory at different temperatures for Barnase (a) 300K (b) 400K (c) 500K(d) 550K The different secondary elements are presented in a color code format indicated at the bottom of the figure

only a few rearrangement secondary structures remained inthe protein The MD trajectories can provide a detailed viewof the conformational transitions in the early stage of thermalunfolding Figure 3 shows snapshots of protein Barnase fromthe different temperature trajectories The correspondingsnapshots at 300K are also shown as references

34 Intramolecular Contacts

341 Hydrogen Bonding Pattern Hydrogen bond is oneof the factors influencing the thermal stability of proteinIn the hydrogen bond calculations a distance cutoff of

30 A and an angle cutoff of 20∘ were applied The averagenumbers of hydrogen bonds are 29 24 17 and 18 for the300K 400K 500K and 600K simulations respectivelyThus as the simulation temperature is increased there is aconcomitant decrease in number of intact hydrogen bondsThis is reasonable as the structures become more distorted asthe simulation temperature is raised It is also evident fromthe plot (Figure 4) that although the number of hydrogenbonds varies in different temperature it is steadily maintainedthroughout the simulations except for 600K simulationThe interesting finding is the rapid increase of hydrogenbonding number along with the simulation at 600K after

Mathematical Problems in Engineering 7

300K 05ns 10ns 15ns

400K 05ns 10ns 15ns

500K 05ns 10ns 15ns

600K 50ps 05ns 10ns

Figure 3 Snapshots from the thermal unfolding simulations of BarnaseThe structures are made with the VMD program 120572-helices and 3ndash10helices are shown as ribbons 120573-sheets as arrows and the rest are shown as loops

94 psDue to a large distortion of regular secondary structuralelements and unpacking of the hydrophobic cores someof water molecules are inserted in hydrophobic cores andparticipate in hydrogen bonds as both donors and acceptorswith the main-chain polar groups This observation suggeststhe gradual destabilization of the protein in concert withincreasing thermal stress

342 Salt Bridge Analysis To further probe the stabil-ity behavior of Barnase under thermal stress we ana-lyzed another important intramolecular contact namely saltbridge Charged residues in globular proteins frequently formsalt bridges The electrostatic contribution of salt bridge hasbeen suggested to be important for protein stability Further-more the statistical analysis of salt bridges from mesophilic

and thermophilic organisms has shown a higher frequencyof complex salt bridges in thermophilic proteins suggestingthat they have a special role in thermostabilization

In the structure of Barnase nine salt bridges Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27 Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 and Glu60-Lys62 can be identified with the help of VMD Interestinglyamong these salt bridges there are four salt bridge networksNetworks of ionic interactions occur when more than twoionic residues interact and an increased occurrence has beensuggested to be essential in explaining the enhanced thermalstability of protein [46] In order to estimate the behaviorof unfolding under thermal stress the lifetimeoccupancy ofthese pairs were analyzed in detail In dynamic simulation at300K these bridges were found to be stable during the periodof 20 ns Figure 5 shows the distance as a function of time in

8 Mathematical Problems in Engineering

05

101520253035404550

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(a)

05

1015202530354045

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(b)

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(c)

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time(ps)

Num

ber o

f hyd

roge

n bo

nds

(d)

Figure 4 Time evolution of hydrogen bonds of the protein at four different temperatures (a) 300K (b) 400K (c) 500K (d) 600K

protein unfolding trajectory among these salt bridges Fromthe profiles it was found how changes in these salt bridgenetwork interactions are correlated with the initial eventsassociated with tertiary structure unfolding in response tothermal stress

The salt bridge network of Asp8-Arg110-Asp12 is locatedin the main hydrophobic core1 which is formed by thepacking of 120572-helix1 against the 120573-sheet and it is thought tobe the major stabilizing element of Barnase In hydrophobiccore1 the two residues Asp8 and Asp12 located in 120572-helix1could form salt bridge with Arg110 located in C-terminalThe C-terminal is docked to 120572-helix1 in the simulationand this stable docking is dominated by strong electrostaticinteractions between Arg110 and two acidic residues on thehelix Asp8 andAsp12 An interesting finding is that theAsp8-Arg110-Asp12 double salt bridge is not stable very much inthe native structure of Barnase As shown in Figure 5(a) thesalt bridge network of Asp8-Arg110-Asp12may be kept withina short distance in solution after 600 ps at 400K When thetemperature is increased to 500K the salt bridgeAsp8-Arg110was maintained within a relatively short distance duringthe 1750 ps simulation while the salt bridge Asp12-Arg110was maintained within a relatively short distance only about400 ps during the whole simulation and the two residues fellapart eventually after 600 ps

The rupture of the double salt bridge initiates the separa-tion of the 120572-helix1 and 120573-sheet The side chain of lle109 has

moved away from the aromatic ring of Phe7 and the Asp8Asp12 Then some water moves into the center of the corethe inward motion of Lys98 is coupled to the Arg110 outwardmotion of the side chain The exterior strands of the 120573-sheetwere solvated by water molecules that replace some of thehydrogen bonds between 120573-sheets 4 and 5 The break of twosalt bridges lead to the increase in accessible surface areaand partial penetration of the water molecules and thus core1undergoes a partial opening

In the 550K simulation ruptures and restorations ofthe salt bridge Asp8-Arg110 were observed along the firsthalf of unfolding simulations and the Asp8 and Arg110 sidechains begin to recover during the 1110 to 1890 ps periodTheseparation of theAsp12 andArg110 side chains begins at initialstage of simulation and the side chains of two residues camewithin a relatively short distance during the 381 to 1005 psand 1099 to 1500 ps period of the simulation but they fellapart eventually The denaturation of the N-terminal part of120572-helix1 (Phe7) the unfolding of the edges of the 120573-sheet thedenaturation of the C-terminal (Ile109) and the separatingmotion of loop1 (which contributes the Leu20 and Tyr24sidechains to core1) contribute significantly to the unfoldingof the main hydrophobic core1 Meanwhile accompanyingthe solvation of hydrophobic core upon thermal unfolding120572-helix1 and strands of the 120573-sheet also undergo dramaticstructural distortion changes again

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

RMSD

(Aring)

300K400K

500K600K

(a)

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100 110Residue number

RMSF

(Aring)

300K400K

500K600K

(b)

Figure 1 Time evolution (a) Backbone RMSD of Barnase at different temperatures (b) RMSFs as a function of residue number of Barnaseat different temperatures The color-coding scheme is as follows 300K (red) 400K (blue) 500K (magenta) and 600K (cyan)

curves observed for four temperature simulations exhibitedmore or less similarly distributed fluctuations Only at hightemperature simulations most of the residues become highlymobile therefore the curve shows a lot more fluctuationThis is due to the loss of secondary structure at these hightemperatures These observations clearly reveal the differentbehavior of the residues of Barnase molecule in response toincreasing thermal stress and give an indication of the regionsof the Barnase polypeptide chain which are most sensitive orresponsive to heating

33 Secondary Structure Analysis At high temperature sim-ulations dramatically increased RMSD values were observedfor the loop regions and both terminal regions in Barnasewhich indicate these regions extensive local conformationalchanges upon thermal unfolding A close analysis of the timeevolution of the secondary structure (Figure 2) can presentfurther information about its structural flexibilities

Figure 2(a) reveals that 120572-helices 120573-sheets and loopsobserved within Barnase structure are maintained stablythroughout the whole simulation period at 300K Theoverall conformation hydrophobic core compactness andsecondary structural elements are all stable and there is nowater penetration into the protein The simulation at 300Kalso appears to agree well with the stability of the RMSDand RMSF curves (Figure 1) In case of 400K simulationthe structure exhibits slight deviation from starting structureThere is a high degree of similarity between the graphscorresponding to the simulations at 300K and 400K Onlymarginal structural fluctuations were observed and no sig-nificant structural changes

At 500K protein structure fluctuation is significantlymore pronounced In this time period the dominant struc-tural change was the expansion of the protein in responseto the temperature increase and the packing density in thethree hydrophobic cores decreased During the simulationthe edge residues particularly those at or near theN-terminalpart of 120572-helix1 are less stable and unfold first At 2 nssimulation 120572-helix1 maintains a regular shape 120572-helix2 was

perturbed but mostly at the termini 120572-helix 3 was graduallyunfolded after 1687 ps 1205723 was lost completely Among thefive 120573-sheets the first obvious observation is that 120573-sheet1of the structure is partially unfolded after 959 ps and ashortening of 120573-sheet1 is observed for residues 50 51 and56 A similar shortening also occurs at 1205732 1205733 and 1205734 forresidues 71 75 91 and 96 As shown in Figure 2(c) it is foundthat the 120573-sheet began to unfold at the edges and associatedturns and the center of the sheet is mostly stronger thanthe edges In addition the loops and turns unfold to variousdegrees However in spite of these important fluctuationsin the protein it appears that the main chain still showsessentially the same overall fold as in the native structureandmost native secondary structure elements remain presentuntil the end of simulation (Figure 3)

When the temperature is increased to 550K the structureof the protein shows a continuous and progressive unfoldingThe N terminus begins to unfold during the first 250 psThis is followed by partial denaturation of 120572-helix1 the 120572-helix1 lost one turn at the N-terminal about 1000 ps andmoved away from the rest of the protein during most ofthe simulation 120572-helix3 was unfolded in the beginning ofthe simulation In the 120573-sheet its disruption starts at theedges of the 120573-sheet and near the irregular element of the120573-sheet1 (120573-bulge at residues 53 and 54) it is promoted byan increase in the twist and an influx of water moleculesand the 120573-sheet1 lost mostly about 850 ps Actually fromthe time dependence of secondary structure as well as theoverlap view of tertiary structure (Figure 3) we can find thatcentral 120573-sheet3 seems to be the most stable in five 120573-sheetsMeanwhile rearrangements of secondary structural elementswere observed along with the simulation and additional 120572-helix and 120573-sheet developed in the structure However thesenonnative interactions were not stable enough as they wouldbe disrupted over time When the temperature was raisedto 600K unfolding began almost immediately Destructionof the native protein structure occurred very fast as alsoindicated by the RMSF and RMSD values (Figure 1) Theprotein was highly coiled in the early stage simulation and

6 Mathematical Problems in Engineering

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

(a)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

(b)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(c)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(d)

Figure 2 Time evolution of secondary structure in unfolding trajectory at different temperatures for Barnase (a) 300K (b) 400K (c) 500K(d) 550K The different secondary elements are presented in a color code format indicated at the bottom of the figure

only a few rearrangement secondary structures remained inthe protein The MD trajectories can provide a detailed viewof the conformational transitions in the early stage of thermalunfolding Figure 3 shows snapshots of protein Barnase fromthe different temperature trajectories The correspondingsnapshots at 300K are also shown as references

34 Intramolecular Contacts

341 Hydrogen Bonding Pattern Hydrogen bond is oneof the factors influencing the thermal stability of proteinIn the hydrogen bond calculations a distance cutoff of

30 A and an angle cutoff of 20∘ were applied The averagenumbers of hydrogen bonds are 29 24 17 and 18 for the300K 400K 500K and 600K simulations respectivelyThus as the simulation temperature is increased there is aconcomitant decrease in number of intact hydrogen bondsThis is reasonable as the structures become more distorted asthe simulation temperature is raised It is also evident fromthe plot (Figure 4) that although the number of hydrogenbonds varies in different temperature it is steadily maintainedthroughout the simulations except for 600K simulationThe interesting finding is the rapid increase of hydrogenbonding number along with the simulation at 600K after

Mathematical Problems in Engineering 7

300K 05ns 10ns 15ns

400K 05ns 10ns 15ns

500K 05ns 10ns 15ns

600K 50ps 05ns 10ns

Figure 3 Snapshots from the thermal unfolding simulations of BarnaseThe structures are made with the VMD program 120572-helices and 3ndash10helices are shown as ribbons 120573-sheets as arrows and the rest are shown as loops

94 psDue to a large distortion of regular secondary structuralelements and unpacking of the hydrophobic cores someof water molecules are inserted in hydrophobic cores andparticipate in hydrogen bonds as both donors and acceptorswith the main-chain polar groups This observation suggeststhe gradual destabilization of the protein in concert withincreasing thermal stress

342 Salt Bridge Analysis To further probe the stabil-ity behavior of Barnase under thermal stress we ana-lyzed another important intramolecular contact namely saltbridge Charged residues in globular proteins frequently formsalt bridges The electrostatic contribution of salt bridge hasbeen suggested to be important for protein stability Further-more the statistical analysis of salt bridges from mesophilic

and thermophilic organisms has shown a higher frequencyof complex salt bridges in thermophilic proteins suggestingthat they have a special role in thermostabilization

In the structure of Barnase nine salt bridges Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27 Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 and Glu60-Lys62 can be identified with the help of VMD Interestinglyamong these salt bridges there are four salt bridge networksNetworks of ionic interactions occur when more than twoionic residues interact and an increased occurrence has beensuggested to be essential in explaining the enhanced thermalstability of protein [46] In order to estimate the behaviorof unfolding under thermal stress the lifetimeoccupancy ofthese pairs were analyzed in detail In dynamic simulation at300K these bridges were found to be stable during the periodof 20 ns Figure 5 shows the distance as a function of time in

8 Mathematical Problems in Engineering

05

101520253035404550

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(a)

05

1015202530354045

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(b)

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(c)

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time(ps)

Num

ber o

f hyd

roge

n bo

nds

(d)

Figure 4 Time evolution of hydrogen bonds of the protein at four different temperatures (a) 300K (b) 400K (c) 500K (d) 600K

protein unfolding trajectory among these salt bridges Fromthe profiles it was found how changes in these salt bridgenetwork interactions are correlated with the initial eventsassociated with tertiary structure unfolding in response tothermal stress

The salt bridge network of Asp8-Arg110-Asp12 is locatedin the main hydrophobic core1 which is formed by thepacking of 120572-helix1 against the 120573-sheet and it is thought tobe the major stabilizing element of Barnase In hydrophobiccore1 the two residues Asp8 and Asp12 located in 120572-helix1could form salt bridge with Arg110 located in C-terminalThe C-terminal is docked to 120572-helix1 in the simulationand this stable docking is dominated by strong electrostaticinteractions between Arg110 and two acidic residues on thehelix Asp8 andAsp12 An interesting finding is that theAsp8-Arg110-Asp12 double salt bridge is not stable very much inthe native structure of Barnase As shown in Figure 5(a) thesalt bridge network of Asp8-Arg110-Asp12may be kept withina short distance in solution after 600 ps at 400K When thetemperature is increased to 500K the salt bridgeAsp8-Arg110was maintained within a relatively short distance duringthe 1750 ps simulation while the salt bridge Asp12-Arg110was maintained within a relatively short distance only about400 ps during the whole simulation and the two residues fellapart eventually after 600 ps

The rupture of the double salt bridge initiates the separa-tion of the 120572-helix1 and 120573-sheet The side chain of lle109 has

moved away from the aromatic ring of Phe7 and the Asp8Asp12 Then some water moves into the center of the corethe inward motion of Lys98 is coupled to the Arg110 outwardmotion of the side chain The exterior strands of the 120573-sheetwere solvated by water molecules that replace some of thehydrogen bonds between 120573-sheets 4 and 5 The break of twosalt bridges lead to the increase in accessible surface areaand partial penetration of the water molecules and thus core1undergoes a partial opening

In the 550K simulation ruptures and restorations ofthe salt bridge Asp8-Arg110 were observed along the firsthalf of unfolding simulations and the Asp8 and Arg110 sidechains begin to recover during the 1110 to 1890 ps periodTheseparation of theAsp12 andArg110 side chains begins at initialstage of simulation and the side chains of two residues camewithin a relatively short distance during the 381 to 1005 psand 1099 to 1500 ps period of the simulation but they fellapart eventually The denaturation of the N-terminal part of120572-helix1 (Phe7) the unfolding of the edges of the 120573-sheet thedenaturation of the C-terminal (Ile109) and the separatingmotion of loop1 (which contributes the Leu20 and Tyr24sidechains to core1) contribute significantly to the unfoldingof the main hydrophobic core1 Meanwhile accompanyingthe solvation of hydrophobic core upon thermal unfolding120572-helix1 and strands of the 120573-sheet also undergo dramaticstructural distortion changes again

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

(a)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

(b)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ue

Secondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(c)

0 250 500 750 1000 1250 1500 1750 2000

0

10

20

30

40

50

60

70

80

90

100

110

Times (ps)

Resid

ueSecondary structure

120572-HelixTurn310 helix

Coil120573-Sheet120573-Bridge

(d)

Figure 2 Time evolution of secondary structure in unfolding trajectory at different temperatures for Barnase (a) 300K (b) 400K (c) 500K(d) 550K The different secondary elements are presented in a color code format indicated at the bottom of the figure

only a few rearrangement secondary structures remained inthe protein The MD trajectories can provide a detailed viewof the conformational transitions in the early stage of thermalunfolding Figure 3 shows snapshots of protein Barnase fromthe different temperature trajectories The correspondingsnapshots at 300K are also shown as references

34 Intramolecular Contacts

341 Hydrogen Bonding Pattern Hydrogen bond is oneof the factors influencing the thermal stability of proteinIn the hydrogen bond calculations a distance cutoff of

30 A and an angle cutoff of 20∘ were applied The averagenumbers of hydrogen bonds are 29 24 17 and 18 for the300K 400K 500K and 600K simulations respectivelyThus as the simulation temperature is increased there is aconcomitant decrease in number of intact hydrogen bondsThis is reasonable as the structures become more distorted asthe simulation temperature is raised It is also evident fromthe plot (Figure 4) that although the number of hydrogenbonds varies in different temperature it is steadily maintainedthroughout the simulations except for 600K simulationThe interesting finding is the rapid increase of hydrogenbonding number along with the simulation at 600K after

Mathematical Problems in Engineering 7

300K 05ns 10ns 15ns

400K 05ns 10ns 15ns

500K 05ns 10ns 15ns

600K 50ps 05ns 10ns

Figure 3 Snapshots from the thermal unfolding simulations of BarnaseThe structures are made with the VMD program 120572-helices and 3ndash10helices are shown as ribbons 120573-sheets as arrows and the rest are shown as loops

94 psDue to a large distortion of regular secondary structuralelements and unpacking of the hydrophobic cores someof water molecules are inserted in hydrophobic cores andparticipate in hydrogen bonds as both donors and acceptorswith the main-chain polar groups This observation suggeststhe gradual destabilization of the protein in concert withincreasing thermal stress

342 Salt Bridge Analysis To further probe the stabil-ity behavior of Barnase under thermal stress we ana-lyzed another important intramolecular contact namely saltbridge Charged residues in globular proteins frequently formsalt bridges The electrostatic contribution of salt bridge hasbeen suggested to be important for protein stability Further-more the statistical analysis of salt bridges from mesophilic

and thermophilic organisms has shown a higher frequencyof complex salt bridges in thermophilic proteins suggestingthat they have a special role in thermostabilization

In the structure of Barnase nine salt bridges Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27 Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 and Glu60-Lys62 can be identified with the help of VMD Interestinglyamong these salt bridges there are four salt bridge networksNetworks of ionic interactions occur when more than twoionic residues interact and an increased occurrence has beensuggested to be essential in explaining the enhanced thermalstability of protein [46] In order to estimate the behaviorof unfolding under thermal stress the lifetimeoccupancy ofthese pairs were analyzed in detail In dynamic simulation at300K these bridges were found to be stable during the periodof 20 ns Figure 5 shows the distance as a function of time in

8 Mathematical Problems in Engineering

05

101520253035404550

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(a)

05

1015202530354045

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(b)

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(c)

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time(ps)

Num

ber o

f hyd

roge

n bo

nds

(d)

Figure 4 Time evolution of hydrogen bonds of the protein at four different temperatures (a) 300K (b) 400K (c) 500K (d) 600K

protein unfolding trajectory among these salt bridges Fromthe profiles it was found how changes in these salt bridgenetwork interactions are correlated with the initial eventsassociated with tertiary structure unfolding in response tothermal stress

The salt bridge network of Asp8-Arg110-Asp12 is locatedin the main hydrophobic core1 which is formed by thepacking of 120572-helix1 against the 120573-sheet and it is thought tobe the major stabilizing element of Barnase In hydrophobiccore1 the two residues Asp8 and Asp12 located in 120572-helix1could form salt bridge with Arg110 located in C-terminalThe C-terminal is docked to 120572-helix1 in the simulationand this stable docking is dominated by strong electrostaticinteractions between Arg110 and two acidic residues on thehelix Asp8 andAsp12 An interesting finding is that theAsp8-Arg110-Asp12 double salt bridge is not stable very much inthe native structure of Barnase As shown in Figure 5(a) thesalt bridge network of Asp8-Arg110-Asp12may be kept withina short distance in solution after 600 ps at 400K When thetemperature is increased to 500K the salt bridgeAsp8-Arg110was maintained within a relatively short distance duringthe 1750 ps simulation while the salt bridge Asp12-Arg110was maintained within a relatively short distance only about400 ps during the whole simulation and the two residues fellapart eventually after 600 ps

The rupture of the double salt bridge initiates the separa-tion of the 120572-helix1 and 120573-sheet The side chain of lle109 has

moved away from the aromatic ring of Phe7 and the Asp8Asp12 Then some water moves into the center of the corethe inward motion of Lys98 is coupled to the Arg110 outwardmotion of the side chain The exterior strands of the 120573-sheetwere solvated by water molecules that replace some of thehydrogen bonds between 120573-sheets 4 and 5 The break of twosalt bridges lead to the increase in accessible surface areaand partial penetration of the water molecules and thus core1undergoes a partial opening

In the 550K simulation ruptures and restorations ofthe salt bridge Asp8-Arg110 were observed along the firsthalf of unfolding simulations and the Asp8 and Arg110 sidechains begin to recover during the 1110 to 1890 ps periodTheseparation of theAsp12 andArg110 side chains begins at initialstage of simulation and the side chains of two residues camewithin a relatively short distance during the 381 to 1005 psand 1099 to 1500 ps period of the simulation but they fellapart eventually The denaturation of the N-terminal part of120572-helix1 (Phe7) the unfolding of the edges of the 120573-sheet thedenaturation of the C-terminal (Ile109) and the separatingmotion of loop1 (which contributes the Leu20 and Tyr24sidechains to core1) contribute significantly to the unfoldingof the main hydrophobic core1 Meanwhile accompanyingthe solvation of hydrophobic core upon thermal unfolding120572-helix1 and strands of the 120573-sheet also undergo dramaticstructural distortion changes again

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

300K 05ns 10ns 15ns

400K 05ns 10ns 15ns

500K 05ns 10ns 15ns

600K 50ps 05ns 10ns

Figure 3 Snapshots from the thermal unfolding simulations of BarnaseThe structures are made with the VMD program 120572-helices and 3ndash10helices are shown as ribbons 120573-sheets as arrows and the rest are shown as loops

94 psDue to a large distortion of regular secondary structuralelements and unpacking of the hydrophobic cores someof water molecules are inserted in hydrophobic cores andparticipate in hydrogen bonds as both donors and acceptorswith the main-chain polar groups This observation suggeststhe gradual destabilization of the protein in concert withincreasing thermal stress

342 Salt Bridge Analysis To further probe the stabil-ity behavior of Barnase under thermal stress we ana-lyzed another important intramolecular contact namely saltbridge Charged residues in globular proteins frequently formsalt bridges The electrostatic contribution of salt bridge hasbeen suggested to be important for protein stability Further-more the statistical analysis of salt bridges from mesophilic

and thermophilic organisms has shown a higher frequencyof complex salt bridges in thermophilic proteins suggestingthat they have a special role in thermostabilization

In the structure of Barnase nine salt bridges Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27 Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 and Glu60-Lys62 can be identified with the help of VMD Interestinglyamong these salt bridges there are four salt bridge networksNetworks of ionic interactions occur when more than twoionic residues interact and an increased occurrence has beensuggested to be essential in explaining the enhanced thermalstability of protein [46] In order to estimate the behaviorof unfolding under thermal stress the lifetimeoccupancy ofthese pairs were analyzed in detail In dynamic simulation at300K these bridges were found to be stable during the periodof 20 ns Figure 5 shows the distance as a function of time in

8 Mathematical Problems in Engineering

05

101520253035404550

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(a)

05

1015202530354045

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(b)

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(c)

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time(ps)

Num

ber o

f hyd

roge

n bo

nds

(d)

Figure 4 Time evolution of hydrogen bonds of the protein at four different temperatures (a) 300K (b) 400K (c) 500K (d) 600K

protein unfolding trajectory among these salt bridges Fromthe profiles it was found how changes in these salt bridgenetwork interactions are correlated with the initial eventsassociated with tertiary structure unfolding in response tothermal stress

The salt bridge network of Asp8-Arg110-Asp12 is locatedin the main hydrophobic core1 which is formed by thepacking of 120572-helix1 against the 120573-sheet and it is thought tobe the major stabilizing element of Barnase In hydrophobiccore1 the two residues Asp8 and Asp12 located in 120572-helix1could form salt bridge with Arg110 located in C-terminalThe C-terminal is docked to 120572-helix1 in the simulationand this stable docking is dominated by strong electrostaticinteractions between Arg110 and two acidic residues on thehelix Asp8 andAsp12 An interesting finding is that theAsp8-Arg110-Asp12 double salt bridge is not stable very much inthe native structure of Barnase As shown in Figure 5(a) thesalt bridge network of Asp8-Arg110-Asp12may be kept withina short distance in solution after 600 ps at 400K When thetemperature is increased to 500K the salt bridgeAsp8-Arg110was maintained within a relatively short distance duringthe 1750 ps simulation while the salt bridge Asp12-Arg110was maintained within a relatively short distance only about400 ps during the whole simulation and the two residues fellapart eventually after 600 ps

The rupture of the double salt bridge initiates the separa-tion of the 120572-helix1 and 120573-sheet The side chain of lle109 has

moved away from the aromatic ring of Phe7 and the Asp8Asp12 Then some water moves into the center of the corethe inward motion of Lys98 is coupled to the Arg110 outwardmotion of the side chain The exterior strands of the 120573-sheetwere solvated by water molecules that replace some of thehydrogen bonds between 120573-sheets 4 and 5 The break of twosalt bridges lead to the increase in accessible surface areaand partial penetration of the water molecules and thus core1undergoes a partial opening

In the 550K simulation ruptures and restorations ofthe salt bridge Asp8-Arg110 were observed along the firsthalf of unfolding simulations and the Asp8 and Arg110 sidechains begin to recover during the 1110 to 1890 ps periodTheseparation of theAsp12 andArg110 side chains begins at initialstage of simulation and the side chains of two residues camewithin a relatively short distance during the 381 to 1005 psand 1099 to 1500 ps period of the simulation but they fellapart eventually The denaturation of the N-terminal part of120572-helix1 (Phe7) the unfolding of the edges of the 120573-sheet thedenaturation of the C-terminal (Ile109) and the separatingmotion of loop1 (which contributes the Leu20 and Tyr24sidechains to core1) contribute significantly to the unfoldingof the main hydrophobic core1 Meanwhile accompanyingthe solvation of hydrophobic core upon thermal unfolding120572-helix1 and strands of the 120573-sheet also undergo dramaticstructural distortion changes again

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

05

101520253035404550

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(a)

05

1015202530354045

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(b)

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Num

ber o

f hyd

roge

n bo

nds

(c)

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time(ps)

Num

ber o

f hyd

roge

n bo

nds

(d)

Figure 4 Time evolution of hydrogen bonds of the protein at four different temperatures (a) 300K (b) 400K (c) 500K (d) 600K

protein unfolding trajectory among these salt bridges Fromthe profiles it was found how changes in these salt bridgenetwork interactions are correlated with the initial eventsassociated with tertiary structure unfolding in response tothermal stress

The salt bridge network of Asp8-Arg110-Asp12 is locatedin the main hydrophobic core1 which is formed by thepacking of 120572-helix1 against the 120573-sheet and it is thought tobe the major stabilizing element of Barnase In hydrophobiccore1 the two residues Asp8 and Asp12 located in 120572-helix1could form salt bridge with Arg110 located in C-terminalThe C-terminal is docked to 120572-helix1 in the simulationand this stable docking is dominated by strong electrostaticinteractions between Arg110 and two acidic residues on thehelix Asp8 andAsp12 An interesting finding is that theAsp8-Arg110-Asp12 double salt bridge is not stable very much inthe native structure of Barnase As shown in Figure 5(a) thesalt bridge network of Asp8-Arg110-Asp12may be kept withina short distance in solution after 600 ps at 400K When thetemperature is increased to 500K the salt bridgeAsp8-Arg110was maintained within a relatively short distance duringthe 1750 ps simulation while the salt bridge Asp12-Arg110was maintained within a relatively short distance only about400 ps during the whole simulation and the two residues fellapart eventually after 600 ps

The rupture of the double salt bridge initiates the separa-tion of the 120572-helix1 and 120573-sheet The side chain of lle109 has

moved away from the aromatic ring of Phe7 and the Asp8Asp12 Then some water moves into the center of the corethe inward motion of Lys98 is coupled to the Arg110 outwardmotion of the side chain The exterior strands of the 120573-sheetwere solvated by water molecules that replace some of thehydrogen bonds between 120573-sheets 4 and 5 The break of twosalt bridges lead to the increase in accessible surface areaand partial penetration of the water molecules and thus core1undergoes a partial opening

In the 550K simulation ruptures and restorations ofthe salt bridge Asp8-Arg110 were observed along the firsthalf of unfolding simulations and the Asp8 and Arg110 sidechains begin to recover during the 1110 to 1890 ps periodTheseparation of theAsp12 andArg110 side chains begins at initialstage of simulation and the side chains of two residues camewithin a relatively short distance during the 381 to 1005 psand 1099 to 1500 ps period of the simulation but they fellapart eventually The denaturation of the N-terminal part of120572-helix1 (Phe7) the unfolding of the edges of the 120573-sheet thedenaturation of the C-terminal (Ile109) and the separatingmotion of loop1 (which contributes the Leu20 and Tyr24sidechains to core1) contribute significantly to the unfoldingof the main hydrophobic core1 Meanwhile accompanyingthe solvation of hydrophobic core upon thermal unfolding120572-helix1 and strands of the 120573-sheet also undergo dramaticstructural distortion changes again

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(a)

02468

10121416

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(2)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(b)

02468

1012141618

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

(1)

0123456789

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(2)

(c)

05

10152025303540

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(1)

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

Oxy

gen-

nitro

gen

dista

nce (

Aring)

(2)

400K500K550K

400K500K550K

(d)

Figure 5 Continued

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

02468

101214161820

0 200 400 600 800 1000 1200 1400 1600 1800 2000Time (ps)

400K500K550K

Oxy

gen-

nitro

gen

dist

ance

(Aring)

(e)

Figure 5 Oxygen-nitrogen distance of salt bridges plots Time evolution of distance between selected atoms during simulation (a) Distancebetween (1)Asp8-Arg110 and (2)Arg110-Asp12 which form salt bridge network in the core1 (b) Distance between (1)Asp54-Lys27 and Lys27-Glu73 these residues form salt bridges close to the core2 (c) Distance between (1) Arg83-Asp75 and (2) Asp75-Arg87 (d) (1) Lys66-Asp93and (2) Asp93-Arg69 and (e) Glu60-Lys62 these above-mentioned atom pairs form salt bridge close to the core3

The salt bridge network of Asp54-Lys27-Glu73 was foundto be stable at 300K and 400K simulations (Figure 5(b)) andthey can hold the stable conformation of the spatial neighbor-hood When the temperature rose to 500K the salt bridge ofAsp54-Lys27 was maintained within 4 A except for transientseparation at about 1344 ps while another salt bridge ofLys27-Glu73 only maintained the short distance from 400 psto 600 ps and they were clearly separated from each otherafter about 650 ps At 550K Glu73 could sometimes interactwith Arg83 located in loop4 and Arg87 located in 120573-sheet3during the simulation The disruption of salt bridge Lys27-Glu73 means the loss of interaction between 120573-sheet2 and120572-helix2 then the sliding motion of loop4 is coupled to themovement of120573-sheet2 which results in a slight increase in the120573-sheet twist Ala30 Leu42 and Ile51 side chains move awayfrom the center of core2 The above-mentioned movementand the loss of native hydrogen bonds between 120573-sheet1 and120573-sheet2 result in the separation of core2 from the rest ofthe protein Concomitant with these changes there was anobviously unfolding in the hydrophobic core2 (Figure 3)

The double salt bridges between Arg83 Arg87 and Asp75were found to be very stable up to 500K simulation (Fig-ure 5(c))This salt bridge network is close to the hydrophobiccore3 and provides a moderate stable spike holding theconformation of loop4 120573-sheet2 and 120573-sheet3 Moreoverduring the course of thermal simulation at 550K the saltbridge of Asp75-Arg87 located in the middle of 120573-sheet2 and120573-sheet3 as expected was found to be more stable than thesalt bridge of Asp75-Arg83 which is located in between 120573-sheet2 and loop4 The two residues Asp75 and Arg83 camewithin a short distance during the first 1400 ps simulationlater they were completely separated Since the presenceof salt bridge network Asp75-Arg83-Arg87 and interstrandhydrogen bonds simulation suggests that the most stableinteraction appears in 120573-sheet2 and 120573-sheet3

Another salt bridge network Lys66-Asp93-Arg69 is alsoclose to the core3 In the network the two residues Lys66

and Arg69 are all located in loop3 and the residue Asp93is located in the 120573-turn connecting strands3 and 4 Itis evident from the plot that salt bridge Asp93-Arg69 ismaintained throughout the simulation (within 40 A) withoutany transient separation from 300K to 500K (Figure 5(d))Increasing the temperature to 550K results in Asp93-Arg69side chain contact breaks after 1750 ps and does not reformIn contrast the stability of Lys66-Asp93 is not very stable athigh temperature The Lys66 side chain transiently separatesfrom the Asp93 side chain during about the 1300 to 1400 psperiod at 400K simulation However the occupied time ofsimulation for this salt bridge descended to about 50 withan average distance of 5 A at 500K The rupture of Lys66-Asp93 and several hydrogen bonds between 120573-sheet3 and120573-sheet4 are coupled to the separating motion of 120573-sheet4and 120573-sheet5 from the rest of the 120573-sheet and the packingwas looser than in the native state (Figure 3) In the 550Ksimulations Lys66-Asp93 is stable only for 500 ps or so duringthe initial simulation The presence of salt bridge networksArg83-Asp75-Arg87 and Lys66-Asp93-Arg69 has stabilizedthe native state of hydrophobic core3 at elevated tempera-tures Compared with other hydrophobic cores core3 is thelast one to unfold For the stability of core3 against thermalunfolding from the time dependence of secondary structureas well as the overlap view of tertiary structure (Figures 2 and3) we can also find that the central three 120573-sheets 1205732 1205733 and1205734 seem to be the most stable in protein which provide thekey stabilization interactions within hydrophobic core

Finally there is salt bridge Glu60-Lys62 located in theouter domain of hydrophobic core3 and the two residues areall located in loop3 Loop residues showed increasedmobilityrelative to sheet or helical residues (Figure 1(b)) The saltbridge of Glu60-Lys62 could not be well-formed as it wasdisrupted in the beginning and recovered for a while in themiddle of simulation along the four temperature simulations(Figure 5(e)) On the other hand Glu60 preferred to form saltbridge with the neighboring residue Arg59 There occurred

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

a positioning switch of the side chain of Glu60 from Lys62 toArg59 in the simulation leading to the departure of Glu60from Lys62 Meanwhile due to the fluctuation of the loopregion the backbone conformation and the tertiary packingof the loop were considerably influenced

On the basis of these results we concluded that surfacesalt bridge does stabilize the native state of the protein atelevated temperatures and the complex salt bridge contri-bution to the overall protein stability is more than the indi-vidual pairs Several experiments also confirm that hyper-thermophilic proteins generally possess not only an increasednumber of surface salt bridges but also an increased numberof salt bridge networks [15 47ndash49]

4 Conclusion

We have here investigated the electrostatic stability of nonco-valent interactions in the context of temperature adaptationof Barnase by using MD simulations The results show thathydrogen bond is very sensitive to heat while salt bridgeis comparatively stable Nine salt bridges have been identi-fied (Asp8-Arg110 Asp12-Arg110 Asp54-Lys27 Glu73-Lys27Asp75-Arg83 Asp75-Arg87 Asp93-Arg69 Asp93-Lys66 andGlu60-Lys62) as critical salt bridges These salt bridgesare of fundamental importance in maintaining the struc-tural integrity of the protein structure Among these ninepairs two salt bridge networks (Arg83-Asp75-Arg87 andLys66-Asp93-Arg69) have been found to be extremely stablethroughout the simulation up to 500K Two salt bridgenetworks located in core3 outer domain add more stabilitytowards thermostable core3 region The strength and thenumber of salt bridges present in a protein and whether theyare involved in networks or not are important for the overallstructural stabilityTheir presence can have a large impact onthe structural integrity modulating molecular plasticity Thepresent study attempts to gain a deeper understanding of thenoncovalent intramolecular interaction factors conferringthermostability of Barnase It can offer a general pictureof the first steps of unfolding and may help to designbiotechnologically improved thermostable proteins

Acknowledgments

This work was supported in part by the FundamentalResearch Funds for the Central Universities under Grant noJUSRP111A46 and the National Natural Science Foundationof China under Grant no 61170119 Ming Li thanks thesupports in part by the National Natural Science Foundationof China under the Project Grant nos 61272402 61070214and 60873264

References

[1] S Robic M Guzman-Casado J M Sanchez-Ruiz and SMarqusee ldquoRole of residual structure in the unfolded state ofa thermophilic proteinrdquo Proceedings of the National Academyof Sciences of the United States of America vol 100 no 20 pp11345ndash11349 2003

[2] A Razvi and J M Scholtz ldquoLessons in stability from ther-mophilic proteinsrdquo Protein Science vol 15 no 7 pp 1569ndash15782006

[3] S Kumar and R Nussinov ldquoHow do thermophilic proteins dealwith heatrdquo Cellular and Molecular Life Sciences vol 58 no 9pp 1216ndash1233 2001

[4] K A Luke C L Higgins and P Wittung-Stafshede ldquoTher-modynamic stability and folding of proteins from hyperther-mophilic organismsrdquo FEBS Journal vol 274 no 16 pp 4023ndash4033 2007

[5] MMGromihaM C Pathak K Saraboji E A Ortlund and EA Gaucher ldquoHydrophobic environment is a key factor for thestability of thermophilic proteinsrdquo Proteins vol 81 no 4 pp715ndash721 2013

[6] A Szilagyi and P Zavodszky ldquoStructural differences betweenmesophilic moderately thermophilic and extremely ther-mophilic protein subunits results of a comprehensive surveyrdquoStructure vol 8 no 5 pp 493ndash504 2000

[7] S Basu and S Sen ldquoDo homologous thermophilic-mesophilicproteins exhibit similar structures and dynamics at optimalgrowth temperatures Amolecular dynamics simulation studyrdquoJournal of Chemical Information andModeling vol 53 no 2 pp423ndash434 2013

[8] A D Meruelo S K Han S Kim and J U Bowie ldquoStructuraldifferences between thermophilic and mesophilic membraneproteinsrdquo Protein Science vol 21 no 11 pp 1746ndash1753 2012

[9] E Papaleo M Olufsen L de Gioia and B O BrandsdalldquoOptimization of electrostatics as a strategy for cold-adaptationa case study of cold- and warm-active elastasesrdquo Journal ofMolecular Graphics and Modelling vol 26 no 1 pp 93ndash1032007

[10] A V Gribenko M M Patel J Liu S A McCallum C Wangand G I Makhatadze ldquoRational stabilization of enzymes bycomputational redesign of surface charge-charge interactionsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 106 no 8 pp 2601ndash2606 2009

[11] J M Vinther S M Kristensen and J J Led ldquoEnhancedstability of a protein with increasing temperaturerdquo Journal of theAmerican Chemical Society vol 133 no 2 pp 271ndash278 2011

[12] P Durrschmidt J Mansfeld and R Ulbrich-Hofmann ldquoDif-ferentiation between conformational and autoproteolytic sta-bility of the neutral protease from Bacillus stearothermophiluscontaining an engineered disulfide bondrdquo European Journal ofBiochemistry vol 268 no 12 pp 3612ndash3618 2001

[13] C N Pace H Fu K L Fryar et al ldquoContribution of hydropho-bic interactions to protein stabilityrdquo Journal of Molecular Biol-ogy vol 408 no 3 pp 514ndash528 2011

[14] G I Makhatadze V V Loladze D N Ermolenko X Chenand S T Thomas ldquoContribution of surface salt bridges toprotein stability guidelines for protein engineeringrdquo Journal ofMolecular Biology vol 327 no 5 pp 1135ndash1148 2003

[15] J H Missimer M O Steinmetz R Baron et al ldquoConfigura-tional entropy elucidates the role of salt-bridge networks inprotein thermostabilityrdquo Protein Science vol 16 no 7 pp 1349ndash1359 2007

[16] A SThomas and A H Elcock ldquoMolecular simulations suggestprotein salt bridges are uniquely suited to life at high tempera-turesrdquo Journal of the American Chemical Society vol 126 no 7pp 2208ndash2214 2004

[17] J Chen H M Yu C C Liu J Liu and Z Y Shen ldquoImprovingstability of nitrile hydratase by bridging the salt-bridges in

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Mathematical Problems in Engineering

specific thermal-sensitive regionsrdquo Journal of Biotechnologyvol 164 pp 354ndash362 2012

[18] J Li Y Matsumura M Shinjo M Kojima and H Kihara ldquoAstable 120572-helix-rich intermediate is formed by a single mutationof the 120573-sheet protein src SH3 at pH 3rdquo Journal of MolecularBiology vol 372 no 3 pp 747ndash755 2007

[19] S P He Z T Ding and F Liu ldquoOutput regulation of aclass of continuous-time Markovian jumping systemsrdquo SignalProcessing vol 93 no 2 pp 411ndash419 2013

[20] S He and F Liu ldquoRobust stabilization of stochastic Markovianjumping systems via proportional-integral controlrdquo Signal Pro-cessing vol 91 no 11 pp 2478ndash2486 2011

[21] S P He and F Liu ldquoFinite-time Hinfin control of nonlinearjump systems with time-delays via dynamic observer-basedstate feedbackrdquo IEEE Transactions on Fuzzy Systems vol 20 no4 pp 605ndash614 2012

[22] C Cattani A Ciancio and B Lods ldquoOn a mathematical modelof immune competitionrdquo Applied Mathematics Letters vol 19no 7 pp 678ndash683 2006

[23] C Cattani and A Ciancio ldquoSeparable transition density inthe hybrid model for tumor-immune system competitionrdquoComputational and Mathematical Methods in Medicine vol2012 Article ID 610124 6 pages 2012

[24] G Strittmatter J Janssens COpsomer and J Botterman ldquoInhi-bition of fungal disease development in plants by engineeringcontrolled cell deathrdquo BioTechnology vol 13 no 10 pp 1085ndash1089 1995

[25] S Agarwal B Nikolai T Yamaguchi P Lech and N V SomialdquoConstruction and use of retroviral vectors encoding the toxicgene barnaserdquo Molecular Therapy vol 14 no 4 pp 555ndash5632006

[26] S Leuchtenberger A Perz C Gatz and J W Bartsch ldquoCondi-tional cell ablation by stringent tetracycline-dependent regula-tion of barnase inmammalian cellsrdquoNucleic Acids Research vol29 no 16 article e76 2001

[27] J L Ivanova E F Edelweiss O G Leonova T G Balandin VI Popenko and S M Deyev ldquoApplication of fusion protein 4D5scFv-dibarnasebarstar-gold complex for studying P185HER2receptor distribution in human cancer cellsrdquo Biochimie vol 94no 8 pp 1833ndash1836 2012

[28] T Konuma T Kimura S Matsumoto et al ldquoTime-resolvedsmall-angle X-ray scattering study of the folding dynamics ofbarnaserdquo Journal of Molecular Biology vol 405 no 5 pp 1284ndash1294 2011

[29] J Yin D Bowen and W M Southerland ldquoBarnase thermaltitration via molecular dynamics simulations detection ofearly denaturation sitesrdquo Journal of Molecular Graphics andModelling vol 24 no 4 pp 233ndash243 2006

[30] A Caflisch andM Karplus ldquoMolecular dynamics simulation ofprotein denaturation solvation of the hydrophobic cores andsecondary structure of barnaserdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 91 no5 pp 1746ndash1750 1994

[31] A Li and V Daggett ldquoMolecular dynamics simulation of theunfolding of barnase characterization of the major intermedi-aterdquo Journal of Molecular Biology vol 275 no 4 pp 677ndash6941998

[32] A Langham and Y N Kaznessis ldquoMolecular simulations ofantimicrobial peptidesrdquoMethods in Molecular Biology vol 618pp 267ndash285 2010

[33] T Darden D York and L Pedersen ldquoParticle mesh Ewald an119873sdotlog(119873)method for Ewald sums in large systemsrdquoThe Journalof Chemical Physics vol 98 no 12 pp 10089ndash10092 1993

[34] T Schlick Molecular Modeling and Simulation An Interdisci-plinary Guide InterdisciplinaryAppliedMathematics SpringerNew York NY USA 2nd edition 2010

[35] R Kubo ldquoThe fluctuation-dissipation theoremrdquo Reports onProgress in Physics vol 29 no 1 article 306 pp 255ndash284 1966

[36] W G Hoover ldquoCanonical dynamics equilibrium phase-spacedistributionsrdquo Physical Review A vol 31 no 3 pp 1695ndash16971985

[37] S Nose ldquoA molecular dynamics method for simulations in thecanonical ensemblerdquo Molecular Physics vol 52 no 2 pp 255ndash268 1984

[38] G J Martyna D J Tobias and M L Klein ldquoConstant pres-sure molecular dynamics algorithmsrdquo The Journal of ChemicalPhysics vol 101 no 5 pp 4177ndash4189 1994

[39] D Frenkel and B Smit Understanding Molecular SimulationsFrom Algorithms to Applications Academic Press San DiegoCalif USA 2nd edition 2002

[40] L Kale R Skeel M Bhandarkar et al ldquoNAMD2 greaterscalability for parallel molecular dynamicsrdquo Journal of Compu-tational Physics vol 151 no 1 pp 283ndash312 1999

[41] A D MacKerell Jr D Bashford M Bellott et al ldquoAll-atomempirical potential for molecular modeling and dynamicsstudies of proteinsrdquo Journal of Physical Chemistry B vol 102 no18 pp 3586ndash3616 1998

[42] S Baudet and J Janin ldquoCrystal structure of a barnase-d(GpC)complex at 19 A resolutionrdquo Journal of Molecular Biology vol219 no 1 pp 123ndash132 1991

[43] W L Jorgensen J Chandrasekhar J D Madura R W Impeyand M L Klein ldquoComparison of simple potential functions forsimulating liquidwaterrdquoThe Journal of Chemical Physics vol 79no 2 pp 926ndash935 1983

[44] W Humphrey A Dalke and K Schulten ldquoVMD visualmolecular dynamicsrdquo Journal of Molecular Graphics vol 14 no1 pp 33ndash38 1996

[45] J-P Ryckaert G Ciccotti and H J C Berendsen ldquoNumericalintegration of the cartesian equations of motion of a systemwith constraints molecular dynamics of n-alkanesrdquo Journal ofComputational Physics vol 23 no 3 pp 327ndash341 1977

[46] M Olufsen E Papaleo A O Smalas and B O Brandsdal ldquoIonpairs and their role in modulating stability of cold- and warm-active uracil DNA glycosylaserdquo Proteins vol 71 no 3 pp 1219ndash1230 2008

[47] G Pappenberger H Schurig and R Jaenicke ldquoDisruptionof an ionic network leads to accelerated thermal denatura-tion of D-glyceraldehyde-3-phosphate dehydrogenase from thehyperthermophilic bacteriumThermotogamaritimardquo Journal ofMolecular Biology vol 274 no 4 pp 676ndash683 1997

[48] K S P Yip T J Stillman K L Britton et al ldquoThe structureof Pyrococcus furiosus glutamate dehydrogenase reveals a keyrole for ion-pair networks in maintaining enzyme stability atextreme temperaturesrdquo Structure vol 3 no 11 pp 1147ndash11581995

[49] N Dhaunta K Arora S K Chandrayan and P GuptasarmaldquoIntroduction of a thermophile-sourced ion pair network inthe fourth betaalpha unit of a psychophile-derived triosephos-phate isomerase from Methanococcoides burtonii significantlyincreases its kinetic thermal stabilityrdquo Biochimica et BiophysicaActa vol 1834 no 6 pp 1023ndash1033 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of