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Single Mol. 1 (2000) 2, 123-128 RESEARCH PAPER MoleculesSingle

Static and Dynamical Propertiesof Single Poly(Ethylene Glycol) MoleculesInvestigated by Force Spectroscopy

Ferry Kienberger, Vassili Ph. Pastushenko, Gerald Kada, Hermann J. Gruber,Christian Riener, Hansgeorg Schindler and Peter Hinterdorfer

Institute for Biophysics, University of LinzAltenbergerstr. 69, A-4040 Linz, Austria

Correspondence toDr. Peter HinterdorferInstitute for Biophysics, University of LinzAltenbergerstr. 69, A-4040 Linz, AustriaPhone +43(732)2468-9265Fax +43(732)2468-822e-mail peter.hinterdorfer@jk.uni-linz.ac.at

submitted 02 May 2000published 23 Jun 2000

Abstract

Molecular recognition force spectroscopy was employed toprobe the mechanical and dynamical features ofpoly(ethylene glycol) (PEG). His6 was covalently coupled toAFM tips via PEG for the specific recognition of NTA on thesurface. Force-extension profiles of single moleculesobtained in force-distance cycles were fitted with anextended Worm Like Chain (WLC) model with a quality of thefit sdata-fit / sdata of 1.3. The fit revealed a persistence lengthLP of 3.8 ± 0.02 Å and an enthalpic correction term K0 of1561 ± 33 pN. Amplitude-distance cycles were recordedwith dynamical force microscopy. Fitting with the dampedlinear oscillator model, using values for the persistencelength and the nonlinear spring constant from force-distancecycles, yielded a fit quality sdata-fit / sdata of 1.5. Force-distance cycles calculated from amplitude-distance cyclesby integration nicely agreed with simultaneously measuredforce-distance cycles, and even yielded an improved signalto noise ratio. This shows that no dissipative andirreversible processes occur and that the force extensionprofile of PEG is determined by purely elastic behavior.

Introduction

Force spectroscopy using the atomic force microscope(AFM) [1] is a powerful single molecule method to measurespecific ligand-receptor interaction forces [2,3,4], to studythe elastic properties of polymers [5,6,7], and to investigateunfolding-refolding of proteins [8,9,10,11]. Controlledexternal pulling forces and pulling force-profiles are appliedto single molecules by the AFM cantilever that alsosimultaneously detects the molecule response. Here, weinvestigate the static and dynamical properties ofpoly(ethylene glycol) (PEG) by using contact mode anddynamic force microscopy (DFM) [12,13], respectively.

PEG is a water soluble, nontoxic polymer with a widerange of applications in surface technology and clinicalresearch [14]. It prevents surface adsorption of proteinsand vesicles [15], and also supports membrane fusion [16].We [4,17,18,19] and others [20, 21] have used short PEGderivatives with functional groups at their ends as tethers tocovalently couple ligands to AFM tips. The ligand on the AFMtip is specifically bound to receptors on the surface so thatPEG physically connects tip and surface. The elastic anddynamical properties of PEG are analyzed by subsequentlyapplying defined pulling force cycles. In order to obtaininformation up to high loading forces we used the ligand-receptor pair His6-NTA as specific holding point because itshows a large interaction force [22,23].

Experimental

Contact Mode AFM

A Nanoscope IIIa (Digital Instruments, Santa Barbara, CA)with a commercial fluid cell was used in the conventionalforce calibration mode. Force-distance measurements wererecorded in force-distance cycles at 0.9 Hz vertical scan rate

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and 100 – 300 nm z-amplitude. The measurements werecarried out in PBS buffer (phosphate buffered saline)containing 100 µM Ni2+. Spring constants of Si3N4 (Park,Sunnyvale, CA) and magnetically coated (Molecular Imaging,Phoenix, AZ) cantilevers were calibrated with the thermalnoise method [24]. Spring constants of 17 pN/nm (nominalvalue 20 pN/nm) and 123 pN/nm (nominal value 100pN/nm) were obtained, respectively, from the integral of theresonance peak in the power spectral density plot[25,26,23].

Macmode AFM

For dynamic force microscopy (DFM) experiments we used aMacmode PicoSPM magnetically driven dynamic forcemicroscope (Molecular Imaging, Phoenix, AZ) with aconvential fluid cell to acquire amplitude-distance cycles.Amplitude-distance cycles were recorded at 0.9 Hz verticalscan rate and 300 nm z-amplitude. The free peak to peaktip oscillation amplitude was 6 nm at 5 kHz drivingfrequency. Measurements were performed in PBS containing100 µM Ni2+.

Sample Preparation

In order to get high stretching forces of PEG, a specific,single pair His6-NTA recognition system was used in thisstudy. His6 was covalently coupled to AFM tips viaheterobifunctional polyethylene glycol (PEG) derivative of 18units with an amine - and a thiol-reactive end [27,23]. NTAwas embedded into a self-assembled monolayer that wascovalently bound to a gold surface. Details of NTA-fatty acidsynthesis, surface- and tip- preparation are describedelsewhere [23].

Data Analysis

Force-distance cycles were analyzed using Matlab(MathWorks Inc., Natick, MA) similar to [28]. AFM forcemeasures were calibrated using the slope of the cantileveron a hard surface and values of cantilever spring constantsdetermined with the thermal noise method. The zero pointof the force-axis was determined by the horizontal part inthe very beginning of the PEG stretching curve. Real tip-to-surface distances were obtained by subtracting the bendingof the cantilever according to Hook’s law from arbitrarilymeasured z-positions. After that, the length axis of eachforce-distance curve was normalized by the length at 130pN force. This normalization allowed to construct anensemble curve with force-distance curves of different PEGlengths.

The ensemble curve was fitted with the extended WLCequation [29] using the least square method. The quality ofthe fit was defined by the ratio sdata-fit / sdata, where sdata-fit is

the standard deviation between the ensemble curve and thefit, and sdata is the standard deviation of the data in thebeginning of the ensemble curve. The standard deviationsdata-fit was used to calculate variances of the fit parameters.

Amplitude-distance cycles were simultaneouslyacquired with the force-distance cycles. The length axis ofthe force-distance cycle was transformed as describedabove and also used for the amplitude-distance cycles. Afterthis, the length axis of each amplitude-distance cycle wasnormalized by the length at 30 % amplitude reduction andan ensemble curve of amplitude-distance curves of differentPEG lengths was generated. The ensemble curve was fittedwith a damped linear oscillator model [30] combined withthe Marko-Siggia WLC equation [31] using the least squaremethod. The standard deviation between data and fit, sdata-

fit, and the quality of the fit, sdata-fit / sdata , were calculatedas described above.

Fig. 1. Single molecule force-distance curve. (A) Raw datafrom a force-distance cycle with 100 nm z-amplitude at 0.9Hz, measured in PBS containing 100 µM Ni2+. An AFM tipcontaining a polyethylene glycol (PEG) crosslinker to which aHis6 is bound is approached (trace) and subsequentlyretracted (retrace) from NTA-groups on the surface and thecantilever deflection angle is measured as a function of thetip-surface separation. The attractive force signal in theretrace (pixels 100 – 270) arises from the molecularrecognition of His6 on the AFM tip to NTA on the surface,which leads to a nonlinear stretching of the PEG moleculeduring the retrace by the increasing load. (B) Molecularrecognition is blocked in the presence of 200 mM imidazolin buffer and the recognition event in the retracedissappears.

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Results and Discussion

Force-distance Cycle

The elastic behavior of polyethylene glycol (PEG) wasanalyzed by stretching single molecules in force-distancecycles. For this, we used a specific His6-NTA recognitionsystem to get well defined stretching of PEG up to highforces. His6 molecules, covalently coupled to PEGmolecules on the AFM tip, specifically ligate NTA moleculesembedded in a monolayer on the surface [23]. Due to thedilute surface density of PEG on the tip only one of theligands has access to the receptors on the surface inaverage (‘single tool tip’) [4,17,23].

A typical single molecule recognition event recorded in aforce-distance cycle is shown in Fig. 1A. His6-NTA binding isevident from the attractive force signal in the retrace. Itsnonlinear shape reflects the viscoelastic properties of thePEG molecule. PEG is stretched up to a certain critical force(unbinding force) until the His6-NTA connection dissociatesand the cantilever jumps back to the resting position (Fig.1A, pixel 270). In the presence of the blocking agentimidazol no His6-NTA recognition was found and retracelooked like trace (Fig. 1B). This gives confidence that themeasured interaction forces arise from specific His6-NTAbinding.

Fig. 2. Ensemble force-distance curve. 86 single force-distance curves were normalized to unit length andsuperimposed. Fitting with the extended WLC model (solidline) yields the persistence length LP and the enthalpiccorrection term K0. The quality of the fit, sdata-fit / sdata , is1.3, indicating a very good agreement between model andexperimental data.

For further characterization of the force-extension profile,retraces of 86 force-distance cycles were superimposed andplotted upside-down (Fig. 2). The apparent length of thestretched polymers varied as a result from the lengthdistribution of the PEG molecules used and the differentrelative surface positions of PEG and NTA in force-distancecycles. Therefore the length axis was normalized at thelength of a certain force (130 pN). The ensemble curve of

the single molecule stretching profiles (Fig. 2, dots) wasfitted with an extended Worm Like Chain (WLC) model [29]

F zBL

B k Tl

l l with lz

LF

KPB i

i

i( ) = =

-( )- + +

é

ë

êê

ù

û

úú

= -=å, ( )

1

4 1

142

2

7

0 0

a (1)

where F reflects the applied force, z the actual length, kB theBoltzmann constant, T the temperature, LP the persistencelength, K0 the enthalpic correction, L0 the contour length,and ai the polynomial factors. The contour length L0 is theoverall length scale in the force extension curve. Thepersistence length LP determines the slope in the low-forceregime and the curvature in the mid-force regime, while theenthalpic correction K0 determines the slope in the high-force regime. From fitting the ensemble curve (Fig. 2, solidline) we obtained a persistence length LP of 3.8 ± 0.02 Åand an enthalpic correction term K0 of 1561 ± 33 pN. Thequality of the fit, sdata-fit / sdata , was 1.3, indicating that theextended WLC model is an appropriate model to describethe stretching behavior of PEG. If the WLC applies exactly,the effective persistence length LP,eff should be independentof the applied force F [29,31], according to

( )L FBFP eff, .= (2)

Applying this analysis (Fig. 3) to the ensemble curve fromFig. 2 indeed reveals a constant value of LP,eff of 3.8 Å, withan experimental error of 0.36 Å. Apparently, the extendedWLC model describes the stretching profile of PEG very well.

Fig. 3. Persistence length in dependence of loading force.For each point of the ensemble force-distance curve theeffective persistence length was calculated (dots). Themean value of the calculated persistence length was 3.8 Å(solid line) with a SD of 0.36 Å (dashed lines).

Furthermore, the persistence length of PEG was notdependent on the loading rate (force velocity) of theexperiment. This agrees with the consideration, thatrotational isomeric state transitions of PEG [32] are muchfaster than the time scales of our experiments. In therotational isomeric state approximation (RIS model), thepersistence length of PEG was estimated to be in the orderof 3.7 Å [32] which is close to our measured value. Theextension profile of much longer PEG linkers [7] was slightly

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different compared to our data. Fitting these data with anextended Freely Jointed Chain model (FJC model) yielded aKuhn length of 7 Å [7]. Since the Kuhn length in the FJCmodel is two times the persistence length in the WLC model[32], this value is in fair agreement with our value.

Fig. 4. Single molecule amplitude-distance curve. (A) Rawdata from an amplitude-distance cycle with 300 nm z-amplitude at 0.9 Hz and a peak to peak amplitude of 6 nmat an oscillation frequency of 5 kHz, measured in PBS with100 µM Ni2+. The inverse of the amplitude is plotted againstthe tip-surface separation. The oscillation amplitudedecreases upon tip-surface contact until it is completelydamped on the hard substrate (pixels 0 to 300). Duringcantilever retraction the free oscillation amplitude is fullyrecovered (pixels 370 to 460). The additional dampingsignal in the retrace (pixels 370 to 460) reflects themolecular recognition of His6 on the tip to NTA on thesurface. (B) Molecular recognition is blocked with 200 mMimidazol in buffer and the recognition signal in the retrace isabsent.

Amplitude-Distance Cycle

Dynamic force microscopy (DFM) [12,13] opens thepossibility to perform single molecule pulling experiments inwhich the tip is oscillated at the same time as the moleculeis pulled. We recorded the DFM oscillation amplitudealongside traditional force curves. Therefore, amplitude-distance cycles and force-distance cycles were recordedsimultaneously in a buffer solution. In an amplitude-distancecycle (Fig. 4), the free tip oscillation amplitude decreases in

the trace upon tip-surface contact due to the tip-surfaceinteraction until full damping is achieved. The amplitudeincreases again when the tip is retracted from the surface.Figure 4A shows the DFM mode signature of a His6-NTArecognition event which is an additional, characteristicdamping signal in the retrace. This amplitude reductionarises from the increasing spring constant of the PEGcrosslinker during the stretching process. With increasingload the binding complex finally dissociates at a criticalforce value (unbinding force) and the free tip oscillationamplitude fully recovers. In the presence of imidazol therecognition event is missing due to the block of the specificHis6-NTA interaction bond (Fig. 4 B).

Fig. 5. Ensemble amplitude-distance curve. 58 singleamplitude-distance cycles were normalized andsuperimposed (dots). Fitting with the damped linearoscillator model combined with the Marko-Siggia WLC model(solid line) resulted in a very good agreement with the data,quantified by the ratio sdata-fit / sdata = 1.5. The persistencelength needed for the Marko-Siggia WLC model was takenfrom the optimal fit of the ensemble force-distance curve.

58 retraces of amplitude-distance cycles weresuperimposed after transformation of the length axis intoreal tip-to-surface distances (Fig. 5). The ordinate wastransformed into relative amplitude reduction values and thelength axis was normalized to the length of a certainamplitude reduction level (0.3). The reduction of theoscillation amplitude can be described by a damped linearharmonic oscillator, yielding the amplitude of oscillation independence of the spring constant of the PEG molecule[30]

A kW

Q

PEG( )( )

=

- +

1

2 2 2 22W W (3)

with the following notations:

w01 2

= ( )k mLEV/

,

eigenfrequency of the cantilever,

w k k mLEV PEG01 2

= +( ) / ,

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mod i fi ed ei g enfr eq uenc y due t o t he l oad of t he P E G mol ec ul e,

Q=w

b0 ,

quality factor, b, coefficient reflecting dissipative processes

of the cantilever in liquid,

W=ww0

normalized driving frequency, and

Ww

= 0

0w ,

the normalized modified eigenfrequency. The free tiposcillation peak to peak amplitude was 6 nm at wdrive = 5

kHz and the resonance frequency of the used cantilever waswres = 7.5 kHz with a quality factor Q = 1.7 [30]. The only

unknown parameter, the spring constant of the PEGmolecule, kPEG , is dependent on the length extension z. Itcan be calculated by the derivative of the Marko-Siggia WLCformula [31] according to

( )( )

k zdF z

dz

k T

L LzLPEG

B

P

= = -æ

èç

ö

ø÷ +

é

ëêê

ù

ûúú

-

0 0

3

05 1 1. (4)

Since the persistence length is known from the ensembleforce-distance cycle, the only remaining fit parameter is thecontour length. The fit is in a very good agreement with theexperimental data (Fig. 5, solid line) yielding a quality of thefit sdata-fit / sdata of 1.5. Apparently, the dynamical behavior of

the PEG molecule is solely determined by its springconstant kPEG(z).

Additional evidence that the elastic behavior of PEGdominates the dynamical oscillation regime without anydissipative process was obtained from calculating a force-distance cycle out of an amplitude-distance cycle. In theabsence of dispersion or dissipation, dynamic forcemicroscopy (DFM) operates by sensing the change ininterfacial stiffness, S(z). If the tip motion is small enoughin amplitude so that S(z) remains constant over a swing,then

( )( )

S z kA

A zLEV= -æ

èç

ö

ø÷

0 1 (5)

[33,34,11], where A0 is the free oscillation amplitude, A(z)is the amplitude at a distance z from the surface and kLEV isthe spring constant of the cantilever. Assuming aconservative regime in which the Hook’s law is valid, theforce curves should be reproduced by integrating eq 5

( )F z kA

A zdz CLEV=- -

æ

èç

ö

ø÷ +ò

0 1( ) (6)

[11], where C is the force at the point where integration isstarted. Force-distance cycles, calculated from amplitude-distance cycles were compared with simultaneouslymeasured force-distance cycles. The dashed line in Figure 6shows that the calculated force-distance cycle according toeq 6 is in good agreement with the measured force data(Fig. 6, solid line) with an even enhanced signal to noise

ratio for the calculated curve [11]. This finding implies thatdissipation does not give a significant contribution in thereversible regions of an amplitude-distance cycle of PEG.

Fig. 6. Calculation of a force-distance cycle from anamplitude-distance cycle. An amplitude-distance cycle and aforce-distance cycle were simultaneously acquired in buffersolution. The amplitude-distance cycle was integratedaccording eq. 6 (dashed line) and compared with themeasured force-distance cycle (solid line). An excellentagreement is observed.

Conclusions and Perspectives

We have used the well defined receptor-ligand system NTA-His6 to investigate the mechanical and dynamicalproperties of single PEG molecules. Force-extensionprofiles, acquired in force-distance cycles, were welldescribed by an extended WLC equation, yielding thepersistence length which characterizes the mechanicalbehavior of the molecule in the static regime. Dynamicalproperties of single PEG molecules at kHz frequencies wereobtained in amplitude-distance cycles. Damping of thecantilever in liquids due to dissipative processes is given bythe quality factor Q in the damped linear oscillator model.The response of the PEG molecule to the externally drivenoscillation agreed well with the damped harmonic oscillatormodel by calculating the nonlinear spring constant of PEGwith the Marko-Siggia WLC equation using the persistencelength from force-distance cycles. Therefore, the oscillatoryresponse upon stretching the PEG molecule in the range offrequencies and amplitudes used can be explained just bythe static measured persistence length and nonlinear springconstant. In addition, the calculation of a force-distancecycle from an amplitude-distance cycle showed that nodissipative processes occur, suggesting that the elasticbehavior dominates the pulling curve and no irreversibleprocesses contribute. Furthermore, measuring amplitude-distance cycles and calculating force-distance cycles byintegration offers an enhanced signal to noise level and

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thus gives the possibility to get a better force resolution inpulling experiments.

Acknowledgement We thank M. Trieb and H.-G. Knaus forproviding us with the octapeptide NH3-His6-Gly-Cys-CONH2.This work was supported by the Austrian ScienceFoundation projects P12801/2-MED, the Austrian Ministeryof Science project GZ200.026/2-Pr/4/98, and the EC-BIOTECHNOLOGY program project ERBBIO4CT960592.

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