ORIGINAL PAPER

Low-temperature molecular dynamics simulations of horseheart cytochrome c and comparison with inelastic neutronscattering data

Wojciech Pulawski • Slawomir Filipek • Anna Zwolinska •

Aleksander Debinski • Krystiana Krzysko • Ramon Garduno-Juarez •

Sowmya Viswanathan • Venkatesan Renugopalakrishnan

Received: 30 August 2012 / Revised: 7 November 2012 / Accepted: 16 November 2012 / Published online: 8 December 2012

� European Biophysical Societies’ Association 2012

Abstract Molecular dynamics (MD) simulation com-

bined with inelastic neutron scattering can provide infor-

mation about the thermal dynamics of proteins, especially

the low-frequency vibrational modes responsible for large

movement of some parts of protein molecules. We per-

formed several 30-ns MD simulations of cytochrome c

(Cyt c) in a water box for temperatures ranging from 110 to

300 K and compared the results with those from experi-

mental inelastic neutron scattering. The low-frequency

vibrational modes were obtained via dynamic structure

factors, S(Q, x), obtained both from inelastic neutron

scattering experiments and calculated from MD simula-

tions for Cyt c in the same range of temperatures. The well

known thermal transition in structural movements of Cyt c

is clearly seen in MD simulations; it is, however, confined

to unstructured fragments of loops X1 and X2; movement

of structured loop X3 and both helical ends of the protein is

resistant to thermal disturbance. Calculated and experi-

mental S(Q, x) plots are in qualitative agreement for low

temperatures whereas above 200 K a boson peak vanishes

from the calculated plots. This may be a result of loss of

crystal structure by the protein–water system compared

with the protein crystal.

Keywords Cytochrome c � Molecular dynamics �Inelastic neutron scattering � Dynamic structure factor

Introduction

Cytochrome c (Cyt c) is a 104-residue (MW 12.4 kDa)

heme-containing globular protein of crucial importance in

electron transport in mitochondria (Battistuzzi et al. 2001;

Bertini et al. 2004). A variety of stress stimuli including

growth factor withdrawal, heat shock, and DNA damageVenkatesan Renugopalakrishnan: Dedicated to my father, Varun.

W. Pulawski � S. Filipek � A. Debinski

Faculty of Chemistry, University of Warsaw, ul. Pasteura 1,

02-093 Warsaw, Poland

A. Zwolinska

Faculty of Pharmacy, Medical University of Warsaw,

ul. Banacha 1, 02-097 Warsaw, Poland

A. Zwolinska � K. Krzysko

International Institute of Molecular and Cell Biology,

ul. Trojdena 4, 02-109 Warsaw, Poland

K. Krzysko

Faculty of Physics, CoE BioExploratorium, University

of Warsaw, ul. Zwirki i Wigury 93, 02-089 Warsaw, Poland

R. Garduno-Juarez

Instituto de Ciencias Fısicas, Universidad Nacional Autonoma

de Mexico, 62210 Cuernavaca, Morelos, Mexico

S. Viswanathan

Wellesley Hospital/Partners Healthcare System, Newton,

MA 02462, USA

V. Renugopalakrishnan

Children’s Hospital, Harvard Medical School, 300 Longwood

Ave., Boston, MA 02115, USA

V. Renugopalakrishnan

Department of Chemistry and Chemical Biology, Northeastern

University, Boston, MA 02115, USA

V. Renugopalakrishnan (&)

Children’s Hospital, Harvard Medical School, 20 Shattuck

Street, Boston, MA 02115, USA

e-mail: v.renugopalakrishnan@neu.edu

123

Eur Biophys J (2013) 42:291–300

DOI 10.1007/s00249-012-0874-9

activate the apoptosis intrinsic or mitochondrial pathway in

which Cyt c has an important role. The secondary structure

of Cyt c is highly conserved among species. The redox

potential of the cytochrome family varies over a range of

800 mV from -400 mV for cytochrome C3 to ?400 mV

for cytochrome b559 and hence has been the focus of

research as a candidate protein for the design of biosensors

for detection of such substances as nitric oxide (Kiel 1995;

Verma and Renugopalakrishnan 2004) and superoxide

(Beissenhirtz et al. 2004). The relatively small size of Cyt c

makes its dynamics amenable to study by such techniques

as NMR and computational methods (Garcia and Hummer

1999; Autenrieth et al. 2004; Daidone et al. 2003; Bu and

Straub 2003a, b; Simonson 2002; Parrish et al. 2001; Banci

et al. 1997). The physical integrity of Cyt c under a wide

range of temperature, pressure, and other conditions has

been investigated (Garcia and Hummer 1999; Kumar et al.

2005; Renugopalakrishnan et al. 2005; Prabhakaran et al.

2004; Nordgren et al. 2002) to enable understanding of the

robustness of the molecule at the temperatures and pres-

sures at which it will be used as a biosensor.

Computer simulations of proteins are crucial to under-

standing the details of their dynamics and the link between

structure and function (Karplus et al. 2005; Norberg and

Nilsson 2003). Significant progress has been made in

understanding the dynamic behavior of proteins since the

first application of molecular dynamics simulation to

bovine pancreatic trypsin inhibitor by Karplus and his team

(McCammon et al. 1977). Dynamic events in proteins

occur in the temporal range of femtoseconds to seconds.

The physical properties of globular proteins encompass

picosecond time-scale internal/local fluctuations (Cusack

et al. 1986, 1988) to collective motion involving large

numbers of atoms whose frequencies dominate the

1–100 cm-1 region of the vibrational spectra of proteins,

including the so-called boson peak. The low-frequency

region of the vibrational spectra of proteins (Renugopala-

krishnan and Bhatnagar 1984; Renugopalakrishnan et al.

1985) contains a wealth of information about proteins

dynamics. Unfortunately, because of experimental diffi-

culties, the 1–100 cm-1 frequency region for proteins has

been difficult to study by high-resolution far IR and low-

frequency Raman spectroscopy. Low-frequency modes of

a-chymotrypsin (Brown et al. 1972) and lysozyme (Genzel

et al. 1976) were reported in the early literature, and an

attempt was made to relate the molecular dynamics of

lysozyme with its enzymatic activity (McCammon et al.

1976).

Dynamic fluctuations in proteins on the nanosecond

timescale are now routinely studied in much detail by

molecular dynamics simulations. However, there are very

few experimental data with which the results of MD sim-

ulations can be quantitatively compared; one of these is

inelastic neutron scattering (INS) data (Cusack et al. 1986).

We have used INS to investigate the dynamics of Cyt c

over the temperature range 110–300 K. Nowadays, facili-

tated by the development of state-of-the-art inelastic neu-

tron spectrometers, INS of proteins provides access to the

low-frequency region, e.g., frequencies below 100 cm-1

with good resolution (Cusack et al. 1986; Goupil-Lamy

et al. 1997; Smith 2000; Zaccai 2004; Joti et al. 2004;

Bellissent-Funel 2004) and has therefore emerged as an

important means of probing the picosecond dynamics of

proteins (Kataoka et al. 2003; Connatser et al. 2003).

Despite these developments, interpretation of the INS data

in terms of the dynamic behavior of proteins has remained

underexploited. INS of proteins and its interpretation were

reviewed by Smith (2000) and, more recently, by Gabel

et al. (2002).

Inelastic neutron scattering is an experimental technique

used to study the atomic and molecular motion and mag-

netic properties of condensed matter. It is different from

other neutron scattering methods in that it resolves the

change in kinetic energy that occurs when the neutrons

collide inelastically with the sample. The results are

reported as a quantity named the dynamic structure factor,

S(Q, x), where Q is the scattering vector that measures the

difference between the incoming and the outgoing vector

and x is proportional to the energy transfer experienced by

the sample. When results are plotted as function of x they

can be interpreted in a manner similar to spectra obtained

by conventional spectroscopic techniques.

The dynamic structure factor is often written as

SðQ;xÞ ¼ 12p

R1�1 IðQ; tÞe�ixtdt where IðQ; tÞ ¼ 1

N

PNj¼1

eiQrjðtÞe�iQrjð0Þ� �

is called the intermediate scattering

function and is the spatial Fourier transform of the van

Hove function for a spatially uniform system containing

N scattering point particles (H atoms) and rj is the position

of atom j. When the kinetic energy of the incident neutrons

is conserved in the center-of-mass frame we have elastic

scattering represented by S(Q, 0), that is with x = 0.

In this paper, we present an analysis of 30 ns MD

simulations focusing on changes of mobility of different

parts of Cyt c and their correlation with protein–water

interactions at different temperatures. Furthermore, we

compared experimental INS spectra with data derived from

MD simulations of Cyt c by examining the observed and

calculated dynamic structure factors S(Q, x), where Q and

x are the wave vector and frequency (which can also be

expressed in energy terms), respectively. The experimen-

tally observed neutron spectra expressed as dynamic

structure factors, S(Q, x), as a function of the momentum

and energy transfer (�hQ~; �hx) were compared with those

from MD simulations. The measured dynamic structure

factor, S(Q, x), is the sum of coherent and incoherent

292 Eur Biophys J (2013) 42:291–300

123

contributions. However, because the incoherent scattering

length of hydrogen is an order of magnitude larger than

those of all other elements in Cyt c and the water molecules

associated with it, it is a good approximation to consider

only the contribution of incoherent scattering. Conse-

quently, S(Q, x) can be directly calculated from the

hydrogen-atom trajectories in MD simulations of Cyt c,

including water molecules, and this can give insight into

protein–water interactions.

Experimental methods

Horse heart Cyt c

Horse heart Cyt c was purchased from Sigma–Aldrich in its

oxidized form, after extensive purification by HPLC then

SDS–gel electrophoresis it was directly loaded into the

neutron-scattering sample cell. The molecular weight of

horse heart Cyt c was checked by mass spectrometry to be

12,384 Da and its purity was determined to be C99 %. The

commercial sample had a threshold of hydration of *0.4 g

H2O per g dry protein, and less than 5 % was the reduced

form of Cyt c.

INS spectra of Cyt c

INS experiments were performed at Argonne’s intense

pulsed neutron source (IPNS) which produces 30 sharp

bursts of polychromatic neutrons every second. This time

structure enables the use of a spectrometer equipped with

an array of detectors, distributed over a wide range of

scattering angles, to determine the momentum and energy

transfer from a scattering process by the time-of-flight

technique. A spectrometer that selects a fixed incident

neutron energy (direct-geometry type), for example a

chopper spectrometer, provides progressively improving

energy resolution with increasing x for neutron-energy-

loss scattering whereas a spectrometer that analyzes a fixed

scattered neutron energy (inverse-geometry type), for

example a crystal analyzer spectrometer, has the best res-

olution in the elastic (x = 0) and low-x region. For

polycrystalline or disordered specimens that are predomi-

nantly incoherent scatterers, for example the Cyt c in this

work, the sum of the measured scattering function over a

range of jQ~j enables quantitative comparison of the

dynamic structure factor (weighted by the neutron cross

section and the inverse mass of the elements) obtained

from MD simulations (Price and Skold 1986).

To maximize the instrumental resolution from 0 to

*1,500 cm-1, we measured the S(Q, x) of powder sam-

ples of purified Cyt c by use of both the direct and inverse-

geometry spectrometers, LRMECS and QENS, respec-

tively, at IPNS (Loong et al. 1987). The energy resolution

Dx (full width at half-maximum) of LRMECS varies from

*8 % of the incident energy (E0) in the elastic region to

*4 % near the end of the neutron energy-loss spectrum.

We chose E0 = 240 meV (1 meV is equivalent to

8.066 cm-1) for characterization of the vibrational density

of states at 12 and 300 K in the 500–1,500 cm-1 region.

QE ? NS, on the other hand, provided a Dx of 80 leV

(0.65 cm-1) at the elastic position and a Dx/x of 4–5 % in

the inelastic region up to approximately 1,000 cm-1.

Therefore, the low-energy vibrations were better resolved

by the QENS measurements. The sample (*500 mg) was

placed inside a sealed aluminium or steel container in the

shape of either a thin slab or a thin cylinder which was

mounted on the cold plate of a closed-cycle helium

refrigerator. Sample geometry was chosen to minimize the

multiple-scattering effects viewed by all detectors. To

assess multiple-phonon contributions, measurements were

taken at several temperatures ranging from 110 to 300 K.

Background scattering was subtracted from the data by

means of an empty-container run. Measurements of elastic

incoherent scattering from a vanadium standard provided

detector calibration and intensity normalization.

Theoretical calculations

Molecular dynamics simulation of Cyt c

The three-dimensional model was developed on the basis

of the crystal structure coordinates of horse heart Cyt c,

PDB ID code 1HRC (Bushnell et al. 1990) (Fig. 1).

The protein contains 104 residues with an acetylated

N-terminus and, if the histidine residues are assumed to be

neutral, it has a net charge of ?7. We followed the crystal

structure 1HRC, in which an acetylated N-terminus and

open C-terminus are present. Hydrogen atoms were added

to the crystal structure and the resulting model was placed

in a rectangular periodic box with initial dimensions 6.7,

6.0, and 6.6 nm solvated with approximately 8,000 water

molecules (TIP3P water model; Jorgensen et al. 1983) and

seven chloride ions to ensure neutrality of the investigated

system. For comparison, the crystal periodic box is 5.8,

5.8, and 4.2 nm with four Cyt c molecules inside. The

model was refined by 500 steps of energy minimization

using the conjugate gradient method. Molecular dynamics

(MD) simulations were performed using NAMD software

(Phillips et al. 2005) with the CHARMM 27 force field

(MacKerell et al. 2000) at four different temperatures: 110,

170, 230, and 300 K. The electrostatic interaction was

handled by the particle-mesh Ewald (PME) method

(Essmann et al. 1995). The Lennard-Jones interaction

Eur Biophys J (2013) 42:291–300 293

123

cutoff was used by applying the switching function (Brooks

et al. 1983) with a switching range of 1.0–1.2 nm. Constant

temperature and pressure (1 bar) were achieved by use of a

Langevin thermostat (van Gunsteren and Berendsen 1988).

The SHAKE algorithm (Ryckaert et al. 1977) was applied

to constrain bonds containing hydrogen atoms in protein,

and water molecules were kept rigid with SETTLE

(Miyamoto and Kollman 1992). All MD simulations were

conducted for up to 30 ns with a time step of 0.2 fs and

sampling every 1 ps. Data were collected only from the last

10 ns of each simulation, which describes the most relaxed

system.

Dynamic structure factor calculations by simulations

To perform comparisons of calculated and experimental

dynamic structure factors, we conducted a series of short

molecular dynamics simulations for Cyt c relaxed from

previous 30 ns MD simulations in a periodic box, filled

with water molecules, at 110, 170, 230 and 300 K under

normal pressure (1 bar). A calculation step was set at 1 fs

and the systems were allowed to equilibrate for 100 ps

before production runs. During the production runs the

frames were saved every 10 fs. Because of the huge

number of calculations required for dynamic structure

factor determination we limited the length of our simula-

tions to 10 ps. An all-atom CHARMM force field was used

in NAMD software, as described above.

Dynamic structure factor calculations were performed

using formulas from Tarek and Tobias (2000). For INS

calculations, the hydrogen atoms of the protein and 1 nm of

water protons around protein were used—approximately

5,700 atoms. The intermediate scattering function I(Q, t) was

computed using three scattering vectors, jQ~j = 0.5, 1.0, and

2.0, and then averaged. The incoherent structure factors,

S(Q, E), computed from MD trajectories for different tem-

peratures were plotted in arbitrary units.

Results

The Cyt c structure was stabilized mostly within the first

10 ns of molecular dynamics simulations in a water box for

all analyzed temperatures (Fig. 2) therefore a total length

of 30 ns of each MD simulation is justified. The root mean

square displacement (RMSD) plots of backbone atoms

(Fig. 2a) indicated some instability of the Cyt c structure in

the initial part of the 300 K temperature simulation.

However, during the later stages of simulations the struc-

ture was stable. The RMSD plots for hydrophobic residues

of this protein (Fig. 2b) showed higher values compared

with backbone atoms because the plots include the motion

of the side chains of these residues. Nevertheless, the

overall shape of these plots indicates smooth change to the

most stable structure at each temperature.

Analysis of the data taken from the last 10 ns of each

simulation (the most relaxed structures) revealed an inter-

esting dependence of average values of RMSD on tem-

perature. Although the RMSD of the backbone increases

almost linearly with temperature (a straight line within

standard error bars), the plot for RMSD of hydrophobic

residues indicates a change of a slope at approximately

200 K (Fig. 2c). The standard deviation values for points in

this plot (taken from RMSD data in Fig. 2b) are much

smaller than in the plot for backbone atoms although the

average RMSD values are higher. Such small values of the

standard deviation suggest the plot for hydrophobic resi-

dues is nonlinear, indicating that the hydrophobic residues

are more resistant than the other residues to increasing

temperature at approximately 200 K. However, at higher

temperatures the mobility of hydrophobic residues increa-

ses quickly. The mobility of particular residues of Cyt c at

each temperature around their average positions can be

seen via RMSF (root mean square fluctuation) plots

(Fig. 3). For the lowest temperatures, 110 and 170 K, the

plots are nearly flat without major peaks. However, after

increasing the temperature by 60� to 230 K, large peaks are

observed, especially for three parts of the structure: resi-

dues 22KGGKH26, 41GQAPG45, and 53KNKG56. So the

increased motion of these parts of the Cyt c structure is not

associated with hydrophobicity but rather with the presence

of these regions in X1 and X2 loops, because these residues

Fig. 1 The crystal structure of Cyt c (PDB code 1HRC). The location

of hydrophobic residues is marked in orange on the protein structure.

The heme group and amino acids bound to it are shown in ball-and-stick representation. Three of the four major loops are shown—X1,

X2, and X3

294 Eur Biophys J (2013) 42:291–300

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are located in the loops, namely the 20–35 X1 loop, the

40–57 X2 loop (close to b-sheet), and the 71–85 X3 loop.

Loops X1 and X2 are the most distant parts of Cyt c loosely

connected with the rest of the protein. On increasing the

temperature to 300 K only a small increase in RMSF val-

ues for these regions is observed.

The RMSF of highly flexible parts of the X1 and X2

loops and the rest of protein are shown in Fig. 4a. These

highly flexible parts contribute to the first and second peak

on RMSF plots (Fig. 3). Helices present in the X2 and X3

loops make them more rigid and prevent a change of

mobility at approximately 200 K. Only at 300 K are the

peaks of increased fluctuations visible. N and C-termini of

Cyt c are also structured (they are helical), and these also

have no transition at approximately 200 K, as is clearly

seen in Fig. 3. Such transition is seen only for the first and

second peaks of RMSF. They were collected together and

are shown in Fig. 4a.

The number of hydrogen bonds between Cyt c and water

molecules per amino acid is shown in Fig. 4b. It is shown

separately for unstructured parts of the X1 and X2 loops and

the rest of the protein, as in Fig. 4a. The number of bonds

decreases with increasing temperature and this dependence

is nearly linear for both plots, with no rapid transition. The

increased motion of amino acid residues with elevated

temperature results in reduction of the number of hydrogen

bonds between protein and water for all external parts of

protein in equal proportions. The hydrophobic residues do

not participate in the hydrogen bond network, because

these residues are usually hidden in the interior of proteins,

as in the case of Cyt c, where they are located in the inner

part of all helices in close proximity to heme (Fig. 1).

Therefore, they form, together with the heme prosthetic

group, the most stable part of the protein structure.

Fig. 2 Root mean square displacement (RMSD) of backbone atoms

of cytochrome c (a) and hydrophobic residues of this protein (b).

c Dependence on temperature of average values of RMSD for

backbone atoms and hydrophobic residues of Cyt c (taken from last

10 ns of 30-ns MD simulations)

Fig. 3 The mobility (RMSF—root mean square fluctuations) of

backbone atoms per residue of Cyt c for four different temperatures

Eur Biophys J (2013) 42:291–300 295

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The experimental INS spectra of Cyt c at 110, 170, 230,

and 300 K are shown in Fig. 5. It is observed that the low-

frequency modes at 110 K are much sharper and well

defined than the low-frequency modes at 300 K, and that

there is a gradual but distinct loss of fine structure, espe-

cially in the boson frequency region, \6 meV. There is

qualitative similarity between experimental (Fig. 5a) and

theoretical (Fig. 5b) S(Q, x) plots. The shape and length of

the boson peak is nearly the same for experimental and

calculated plots for the lowest temperature. For 170 K the

calculated peak is smaller than the analogous experimen-

tally derived peak. The experimental boson peak for 170 K

is of the same length as that for 110 K. For the elevated

temperatures 230 and 300 K this peak vanishes in calcu-

lated S(Q, x) plots but is still present in experimental

curves, however, for 300 K the boson peak is the smallest.

Discussion

MD simulations of Cyt c were performed not only for low

temperatures but also for elevated temperatures. Other MD

simulations of Cyt c have been reported in the literature

(Garcia and Hummer 1999; Daidone et al. 2003; Bu and

Straub 2003a; Mao et al. 2001; Bu and Straub 2003b;

Olkhova et al. 2004; Cukier 2004, 2005). Garcia and

Hummer (1999) reported a conformational fluctuations

study of Cyt c at 300, 360, 430, and 550 K, but did not

compare their results with experimental data. However, the

1.5-ns MD simulation of Cyt c was analyzed in terms of

collective motion involving the formation and rupture of

hydrogen bonds. This study showed that at the lowest

temperatures (300 and 360 K) the multiple minima basins

of the trajectory are sampled for a few hundred picosec-

onds, and that at the higher temperatures (430 and 550 K)

the amplitude of the interbasin motion is larger, and that

collective motion occurs at shorter time scales. At all

temperatures (300, 360, 430, and 550 K) Garcia and

Hummer observed that the structural changes correspond to

collective motion of the X loops and coiled regions, and

that relative motion of the a helices occurs as rigid bodies.

It was also shown that large fluctuations in turns and

a helices do not break the hydrogen bonds involved in

forming these structures. However, the transitions at the

40–57 X2 loop occur via intermediate states that enable the

loop to open and a later to fold into a different confor-

mation. In our simulations for lower temperatures, such

motion of this region did not appear and only unstructured

parts of the protein participated in the transition at

approximately 200 K. At 300 K, however, movement of

structured parts of the X2 and X3 loops also started to

increase, but without the loops unfolding.

Research by Prabhakaran et al. (2004) revealed that the

physical integrity of the protein is maintained at high

temperature and pressure. Even though at high temperature

the atomic fluctuations increase threefold–sevenfold

Fig. 4 Comparison of the

properties of the X1 and X2

loops with those of the rest of

Cyt c. a Change of sum RMSF

with temperature. b Change of

an average number of hydrogen

bonds between specific parts of

Cyt c and water per amino acid

with temperature

Fig. 5 Comparison of plots of

S(Q, x) from neutron-scattering

experiments (a) and S(Q, x)

calculated from MD simulations

(b) at four different

temperatures. The horizontalaxis shows neutron energy loss

and is scaled in meV

296 Eur Biophys J (2013) 42:291–300

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(leading to states that are characterized by large fluctua-

tions reminiscent of partial unfolding at the surface

regions), the radius of gyration changes by approximately

10 % only relative to low temperatures and overall integ-

rity is nevertheless maintained. Upon increasing the pres-

sure, the change in fluctuations is minimal and the radius of

gyration decreases by approximately 3 % only. The density

of internal hydrogen bonds is relatively unperturbed as

functions of both temperature and pressure.

In more recent work Singh et al. (2009) performed MD

simulations for two mutants of Cyt c and revealed reduced

conformational flexibility of the protein; however, only

4-ns simulations were conducted. Calculations of free

energy of solvation of Cyt c by use of MD simulations with

explicit solvent were conducted by Karino and Matubayasi

(2011). The new method used, called energy representa-

tion, was performed for up to 20 ns of MD simulations in a

large water box containing approximately 20,000 water

molecules. In other work the effect of an external electric

field on the properties of Cyt c was studied by de Biase

et al. (2009). Two 50 ns simulations were performed, and

the results implied that a conformational change of the Cyt

c structure was involved in modulation of the electron-

transfer reactions. MD was performed by Abel et al. (2010)

who investigated Cyt c unfolding in reverse micelles of

detergent. Their analysis of 10 ns MD simulations revealed

that structural changes observed at the heme level are the

first steps of the process of protein denaturation, as previ-

ously found experimentally in micellar solutions.

Our 30-ns MD simulations of Cyt c for different tem-

peratures revealed that the sudden increase of conforma-

tional flexibility of Cyt c at approximately 200 K is related

to increased thermal motion of unstructured parts of the

protein, namely X1 and the first part of X2 loop. The

motion of loops in individual protein molecules may be

different from that in the Cyt c crystal, in which four

protein molecules interact with each other in a periodic

box. In the crystal, the X1 loop forms two interactions with

the N-terminus of the adjacent protein molecule: Glu21–

Lys8 and Lys25–Glu4. However, in the simulations there

was also a stabilizing interaction, Lys22–Glu104, with the

side chain of the last amino acid of Cyt c (its terminal

carboxyl group interacted with Lys100 which is adjacent in

a helix). This interaction is not present in the crystal

structure, because of the different conformation of Lys22,

but both residues are feasible to create it. At lower tem-

peratures there is no interaction between residues K22 and

E104, as is observed for the crystal; however, with

increasing temperature the ionic interaction occurs spo-

radically at 230 K and at 300 K this salt bridge is nearly

stable (Fig. 6). This interaction, involving the C-terminus

of Cyt c (E104), can result in collective motion of the

C-terminus and X1 loop at elevated temperatures. Their

similar and high flexibility can be seen in the RMSF plot

(Fig. 3). Such collective motion may be beneficial for

recognition of Cyt c by other proteins. The unstructured

part of the X2 loop did not participate in any interactions,

either with adjacent Cyt c in a crystal or within the Cyt c

molecule; it did, however, participate in a thermal transi-

tion at approximately 200 K, in the same way as the X1

loop. The explanation of this effect is that the electrostatic

interactions between charged amino acids are equivalent to

those between charged amino acids and counter ions

present in the solution, especially when charged residues

are located on the protein surface. Such interactions

between charged amino acids break when the temperature

increases and do not preclude unrestricted motion of the

loops.

Linear reduction of the number of hydrogen bonds

between protein and water with increasing temperature

suggests that the dynamic water hydrogen bond network

does not contribute to the protein transition, although

protein–water hydrogen bonds are extremely important for

relaxation of the protein and its assumption of the proper

structure. During the MD simulation the average lifetime of

hydrogen bonds between amino acids and water is only

*1 ps (Tarek and Tobias 2002). This is also observed

during the larger motion of X loops, when hydrogen bonds

between the new position of these loops and water mole-

cules are formed much more quickly compared with the

time scale of backbone motion; despite this, there is a

decrease in the number of hydrogen bonds between the

protein and water molecules, because of the increased

motion of unstructured and flexible loops at approximately

200 K for the protein in solution (Fig. 4). Calculated and

experimental S(Q, x) plots are in qualitative agreement for

lower temperatures whereas for higher temperatures the

boson peak vanishes in calculated plots, an effect that may

be the result of damping of the boson peak on hydration, as

was described by Tarek and Tobias (2001) who, by simu-

lation of dried and hydrated protein (RNase), revealed that

damping of the boson peak propagates through the whole

protein, irrespective of the character of the residues.

Therefore, shrinking of this peak when protein is in solu-

tion (by loss of crystal structure by the protein–water

system in a periodic box and hence an excess of hydration

effects) may be responsible for vanishing of boson peaks at

230 and 300 K in calculated S(Q, x) plots.

The movement of loops and a related thermal transition

at approximately 200 K cannot contribute to the structural

change of hydrophobic residues because there are only a

few of such residues in the loops. The plots of RMSF and,

especially, RMSD of hydrophobic residues against tem-

perature reveal that the hydrophobic protein core sur-

rounding the heme group forms the most stable part of the

Cyt c structure, resisting structural changes induced by

Eur Biophys J (2013) 42:291–300 297

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thermal motion. Hydrophobic residues are also responsible

for the rigidity of the structural fragments of loops and also

N and C-termini of Cyt c, because these helical parts are

bound to the rest of the protein via hydrophobic interac-

tions. Only high temperatures, i.e. much above 200 K, are

able to disrupt such interactions.

Conclusions

Because cytochrome c can be used in sensitive, picomolar

range biosensors to detect NO and CO, knowledge of its

stability under different conditions and of its interactions

with solvent is of crucial importance. The dynamics of this

protein in solution can be different from movements in the

crystal lattice especially at room temperature; at lower

temperatures, however, a protein in water behaves as it

does in a crystal, so experimental and calculated S(Q, x)

plots are similar. Therefore, lack of boson peaks at elevated

temperatures can be explained by damping of this peak by

unrestricted thermal movement of water molecules and a

reduction in the number of hydrogen bonds between

the protein and water. To obtain quantitative agreement

between MD simulations and INS experiments for tem-

peratures higher than 200 K, simulations of Cyt c in the

crystal periodic box with many copies of the protein would

be required. In this work we revealed, by MD simulations,

that the thermal transition at approximately 200 K for Cyt c

is confined to unstructured parts of the X1 and X2 loops

whereas all the structured parts, including the X3 loop and

both helical termini of Cyt c, are stable, and are activated at

high temperatures only. Movement of Cyt c on an electrode

can be between that in solution and that in the crystal; both

types of investigation can, therefore, be useful in under-

standing the modes of action of Cyt c.

Acknowledgments V.R. and S.V. acknowledge the Rothschild

Foundation, NIH, NSF, USAFOSR, and the Wallace H. Coulter

Foundation for support. The authors also wish to acknowledge

Pittsburgh Supercomputing Center for generous allocation of Super-

computer time on TeraGrid through Project Serial Number:

TG-CH090102. V.R. acknowledges neutron beam time at Argonne

National Laboratory, Argonne, IL, USA.

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