Amide I two-dimensional infrared spectroscopy of β -hairpin peptidesAdam W. Smith and Andrei Tokmakoff Citation: The Journal of Chemical Physics 126, 045109 (2007); doi: 10.1063/1.2428300 View online: http://dx.doi.org/10.1063/1.2428300 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/126/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Discriminating trpzip2 and trpzip4 peptides’ folding landscape using the two-dimensional infrared spectroscopy: Asimulation study J. Chem. Phys. 140, 055101 (2014); 10.1063/1.4863562 Simulation of vibrational energy transfer in two-dimensional infrared spectroscopy of amide I and amide II modesin solution J. Chem. Phys. 129, 055101 (2008); 10.1063/1.2961020 Phosphorylation effect on the GSSS peptide conformation in water: Infrared, vibrational circular dichroism, andcircular dichroism experiments and comparisons with molecular dynamics simulations J. Chem. Phys. 126, 235102 (2007); 10.1063/1.2738472 Signatures of β-sheet secondary structures in linear and two-dimensional infrared spectroscopy J. Chem. Phys. 120, 8201 (2004); 10.1063/1.1689637 Self-trapping of the amide I band in a peptide model crystal J. Chem. Phys. 117, 2415 (2002); 10.1063/1.1487376

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Amide I two-dimensional infrared spectroscopy of �-hairpin peptidesAdam W. Smith and Andrei TokmakoffDepartment of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

�Received 8 September 2006; accepted 5 December 2006; published online 31 January 2007�

In this report, spectral simulations and isotope labeling are used to describe the two-dimensional IRspectroscopy of �-hairpin peptides in the amide I spectral region. 2D IR spectra of Gramicidin S,PG12, Trpzip2 �TZ2�, and TZ2-T3*T10*, a dual 13C� isotope label, are qualitatively described by amodel based on the widely used local mode amide I Hamiltonian. The authors’ model includesmethods for calculating site energies for individual amide oscillators on the basis of hydrogenbonding, nearest neighbor and long-range coupling between sites, and disorder in the site energy.The dependence of the spectral features on the peptide backbone structure is described usingdisorder-averaged eigenstates, which are visualized by mapping back onto the local amide I sites.�-hairpin IR spectra are dominated by delocalized vibrations that vary by the phase of adjacentoscillators parallel and perpendicular to the strands. The dominant �� band is sensitive to the lengthof the hairpin and the amount of twisting in the backbone structure, while the �� band is composedof several low symmetry modes that delocalize along the strands. The spectra of TZ2-T3*T10* areused to compare coupling models, from which we conclude that transition charge coupling issuperior to transition dipole coupling for amide groups directly hydrogen bound across the �strands. The 2D IR spectra of TZ2-T3*T10* are used to resolve the redshifted amide I band andextract the site energy of the labeled groups. This allows the authors to compare several methods forcalculating the site energies used in excitonic treatments of the amide I band. Gramicidin S isstudied in dimethyl sulfoxide to test the role of solvent on the spectral simulations. © 2007American Institute of Physics. �DOI: 10.1063/1.2428300�

I. INTRODUCTION

�-hairpin secondary structure is common in proteins,and represents a subunit of larger, antiparallel �-sheet motifs.�-hairpin peptides are small enough to be subject to rigoroussimulation methods, while containing a complex network ofweak stabilizing interactions known to guide protein foldingprocesses. Recent work has sought to study these systems inisolation in order to describe the factors that stabilize nativestructure1,2 and guide structural isomerization duringfolding.3–7 These efforts have led to a clearer description ofthe stabilizing role of mesoscopic structural features such asthe four to six residue turn region and the packing together ofhydrophobic side chains.1–7

In spite of the variety of methods used to characterizestructure and stability, it has been difficult to obtain residue-level information about the folding dynamics of these sys-tems. Their fast folding times �100 ns–10 �s� make the di-rect observation of folding events inaccessible to NMR.Optical methods are fast enough but offer more qualitativestructural information. For example, UV fluorescence spec-troscopy is useful for reporting on the solvent environmentof side chain chromophores.6,8 UV circular dichroism andinfrared spectroscopy report on larger scale structure and canbe especially informative for peptide systems with a well-defined structural morphology.5,9 More detailed insight canbe gained from comprehensive mutation studies, which canbe carried out at several important sites to determine theeffect of side chains at specific parts of the structure.1,10

The introduction of two-dimensional infrared �2D IR�

spectroscopy11 of amide I vibrations12 has provided a newtechnique that increases structural information while retain-ing the high time resolution required for folding studies. 2DIR spectroscopy reveals vibrational couplings within theamide I band, which depend on the spatial configuration andbonding of peptide units within the protein backbone. Onthis basis, 2D IR has been used to reveal the backbone con-figurations of di- and tripeptides.13,14 However, because ofthe excitonic nature of the amide I transition,15,16 the struc-tural interpretation for larger systems is generally focused onlarge-order secondary structure. For instance, the pair ofamide I peaks characteristic of antiparallel � sheets has beenused to observe the thermal unfolding of proteins and pep-tides with 2D IR and related spectroscopies.17,18 When com-bined with site-specific isotope labeling of the amide I group,2D IR spectroscopy provides a more local probe of couplingsand peptide configurations.14,19,20 This approach offers a wayto probe individual amide groups within a larger peptide atequilibrium and during a folding event. One unique advan-tage of 2D IR spectroscopy over traditional Fourier trans-form infrared �FTIR� measurements is that it can distinguishhomogeneous and inhomogeneous contributions to the spec-tral line shape.21 In this way, a 2D IR spectrum can be usedto describe the structural heterogeneity of the peptide, whichleads to the broad line shapes observed in infraredexperiments.19,22,23

The interpretation of protein amide I 2D IR spectra relieson a spectroscopic model, the development and parameter-ization of which is an active area of research.13,24–26 Since ab

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initio calculation of the vibrational spectra of proteins is dif-ficult to scale up to biologically relevant proteins, approxi-mate methods are used to reproduce the band positions andline shapes.15,25,27,28 One approach is to use semiempiricalsimulations combined with a Hessian matrix reconstructionto calculate amide I frequencies and intensities.24 Anothermethod performs full quantum mechanical simulations ofpeptide fragments from which local interactions areextracted.29,30 An alternate approach that is commonly usedand is easily transferable to very large systems is based on alocal mode Hamiltonian that treats couplings between amideI vibrations of the individual peptide units.13,15,16,25,28,31 Inthis model, a protein structure is used to parametrize thediagonal and off-diagonal elements �site energies and cou-plings�, and the energy eigenvalues and transition momentsobtained from this Hamiltonian are used to compare to thespectroscopy. The site energy of these oscillators has beenshown to be dependent on hydrogen bonding to the amideunit.32,33 More generally, it is dependent on electrostatic in-teractions with the surrounding solvent, which forms the ba-sis for a number of site energy models.34–36 Transition dipolecoupling was originally used to calculate couplings betweenoscillators.37 More accurate models now go beyond the di-pole approximation to include higher-order electrostatic in-teractions for through space couplings, and assign through-bond interactions between adjacent peptide units fromab initio calculations.13,25,38 We have recently evaluated anumber of local amide Hamiltonian models and concludedthat site energy variation and the disorder in site energies thatarise from structural variation or fluctuations in the peptideand surrounding solvent are the crucial elements to simulat-ing protein 2D IR spectra.22,23

In this report, we model the 2D IR spectra of three �hairpins and describe the local mode symmetry of the amideI eigenstates. The spectroscopic model draws on a straight-forward combination of methods for choosing site energies,nearest neighbor coupling, and long-range coupling.28 Thespectral simulations are used to prepare eigenstate visualiza-tions according to the participation ratio and relative vibra-tional phase of each local site. The symmetry of the eigen-states allows us to describe the main spectral features presentin the 2D IR data. The salient features in a �-hairpin 2D IRspectrum are the �� and �� diagonal peaks with the cross-peak ridge connecting the two frequency regions. Thesemodes have been characterized in detail in the context of �sheets.39–42 The �� peak �1635–1645 cm−1� consists ofamide I sites oscillating in phase with the amide group acrossthe strand and out of phase with their in-strand neighbor. The�� peak �1665–1680 cm−1� involves in-phase oscillationsalong the strand. These peaks are sensitive to hairpin struc-ture and stability including twisting of the �-sheetstrands.41–43

We perform our studies on three types of �-hairpin pep-tides with well-defined folded structures. The tryptophan zip-per trpzip2 �TZ2� �Ref. 44� and PG12 �Ref. 45� are tightlyfolded de novo designed peptides that differ in the �-turntype, relative stability, and degree of twisting in the �strands. Spectra of a TZ2 13C� isotopomer are used to studythe influence of isotope labeling on the amide I eigenstates

and 2D IR spectroscopy. Gramicidin S, a cyclic �-hairpinpeptide,46 is chosen to test the transferability of amide I spec-troscopic models to nonaqueous solvents. A comparison ofthe spectroscopy and vibrational modes of these peptides of-fers insight into the generality of spectral assignments andamide I modeling for � hairpins.

II. EXPERIMENT

A. Samples and preparation

The TZ2 �SWTWENGKWTWK-NH2� and PG12�RYVEV-D-Pro-GKKILQ-NH2� samples were synthesizedand purified by the MIT Biopolymers Laboratory. Both pep-tides were synthesized using standard9–fluorenylmethoxycarbonyl protocols as C-terminal amides,purified with high performance liquid chromatography, andtested for purity using matrix-assisted laser desorption/ionization-time-of-flight mass spectrometry. To prepare forinfrared measurements, the samples were repeatedly lyo-philized against 50 mM �TZ2� or 20 mM �PG12� DCl inD2O to remove residual trifluoroacetic acid, which exhibits astrong IR transition at 1673 cm−1. The PG12 solution con-sisted of a 10 mM deuterated acetate buffer at pH 3.85�pD=4.25�. TZ2 was dissolved in a 50 mM deuterated phos-phate buffer at pH 7.0 �pD=7.4�. The peptide concentrationfor the infrared measurements was approximately 12 mg/ml��7 mM� for TZ2 and 25 mg/ml ��17 mM� for PG12.Gramicidin S �cyclo�-Val-Orn-Leu-D-Phe-Pro-�2� was ob-tained from Professor Glenn Jones of Holy Cross College,Worchester, MA, and used without further purification. Forinfrared measurements, it was dissolved indimethylsulfoxide-d6 �DMSO� �Cambridge Isotope Labs� ata concentration of 25 mg/ml ��22 mM�. TZ2-T3*T10* wassynthesized and purified by Anaspec Inc. �San Jose, CA�using L-threonine-1-13C �Icon Isotopes, Summit, NJ� at resi-dues Thr3 and Thr10. Experimental sample conditions werethe same as for the unlabeled TZ2. For TZ2, TZ2-T3*T10*,and PG12, the sample temperature was held to 25 °C. TheGramicidin S spectrum was taken at room temperature��22 °C�.

B. Spectroscopy

Infrared measurements were done in a temperature con-trolled sample cell consisting of two 25�1 mm2 CaF2 win-dows separated by a 50 �m Teflon spacer. FTIR spectra werecollected on a Mattson Infinity FTIR spectrometer. Bufferbackground and sample spectra were taken at 0.5 cm−1 reso-lution and averaged for 64 scans.

The 2D IR instrument and methods used have been de-scribed in detail previously.21 Briefly, a series of three 90 fs,6.0 �m laser pulses drive and probe transitions that are reso-nant with the pulse spectrum, including the peptide amide I�i=1↔0 and �i=2↔1 transitions, as well as the two quan-tum combination bands ��i+� j =2↔�i=1�. The data shownin this report are absorptive 2D IR spectra which correlatethe excitation and detection frequencies.21 The excitation��1� axis is obtained by a numerical Fourier transform of �1,the time delay between the first and second probe pulses. Thesignal is collected for �1 delays up to 2000 fs in the rephas-

045109-2 A. W. Smith and A. Tokmakoff J. Chem. Phys. 126, 045109 �2007�

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ing geometry and 1500 fs in the nonrephasing geometry. Forthe data shown in this report, the waiting time ��2�, which isthe delay between the second and third pulses, is set to zero.To obtain the detection axis, �3, we overlap the emitted sig-nal field with a local oscillator pulse, with the time delaybetween them designated as �3. In practice, we set �3=0 andsend the overlapped signal and local oscillator through thespectrometer and onto a 64-channel mercury-cadmium-telluride array detector. The grating acts to Fourier transform�3 to produce the �3 axis.21 Spectra are collected in theZZYY polarization geometry.

To find the zero times between the probe pulses, we firstmeasure the cross correlation between pulses 1, 2, and 3,which gives a temporal resolution on the order of ±10 fs.After the data are collected, we run a least squares fittingroutine to match the slices in �1 with the dispersed pumpprobe. The �3 timing is found by setting the �1 and �2 equalto zero and scanning the local oscillator timing until the sig-nal matches the dispersed pump probe. The numerical Fou-rier transform of the �1 axis is done using a triangle apodiza-tion function with zero padding.

III. CALCULATIONS

A. Calculation of 1D and 2D IR spectra

Spectral calculations were done using a local amide IHamiltonian �LAH� formalism, which is commonly used todescribe protein and peptide amide I spectroscopy.15,16,28,31,47

The LAH treats the amide I vibrations as a set of N coupledoscillators in the basis of the amide I oscillators of the pep-tide residues. The zero-order vibrational frequency of eachamide group is included as a diagonal matrix element withthe coupling to other groups included in the off-diagonalmatrix elements. Amide I site energies are influenced by thehydrogen bonding of the amide group, which can be de-scribed in terms of the electric field of the surroundings act-ing on the amide I coordinate.34–36 Long-range couplings aredominated by electrostatic interactions, and neighboringgroups along the � strand are dominated by coupling throughthe peptide backbone.

The matrix elements of the LAH are assigned on thebasis of previously determined hairpin structures. The NMRstructure of TZ2 was obtained from the Protein Data Bank�ID lle1�.44 We used the first of the 20 available structures forall calculations shown here. The structure of PG12 was pro-vided by Professor Samuel Gellman at UW-Madison. It wasdetermined using experimental NMR constraints to guide amolecular dynamics �MD� simulation. The structure ofGramicidin S has not been measured experimentally becauseit has not been possible to produce a high quality crystalsample. We used the crystal structure of a Gramicidin S ana-log, where the ornithine side chains were capped withm-bromobenzoic acid.48

To choose site energies we employed a heuristic modelthat is based on hydrogen bonding geometries.15 Startingfrom a zero-order frequency ��0=1688 cm−1�, the energy ofa particular site ��n� is redshifted if the amide oxygen par-ticipates in a hydrogen bond to an amide proton or to asolvent hydrogen bond donor ���CO,n�. An additional red-

shift is included if the amide proton is hydrogen bound toanother amide oxygen or to a solvent hydrogen bond accep-tor ���NH,n�,32

�n = �0 − ��NH,n − ��CO,n.

The frequency shifts are

��CO,n,b = 30 cm−1 � �2.6 − rO�n�¯H�b�/Å� ,

��NH,n = 10 cm−1.

Here rO�n�¯H�b� is the hydrogen bonding distance in ang-stroms. For groups with hydrogen bonds to solvent we set��CO,n=20 cm−1.32 For intramolecular hydrogen bonds,rO�n�¯H�b� is obtained from the experimentally determinedstructure. If the amide oxygen or proton does not participatein a hydrogen bond, we estimate that the long-range solventcontribution to the site energy is ��CO,n=10 cm−1.32 For thepresent systems, this only occurs for Gramicidin S in DMSO,where there is no solvent proton available to H bond with theamide oxygen.

Vibrational couplings take into account through bondand through space interactions. Coupling terms between eachnearest neighbor pair along the peptide chain, �n,n+1, are ob-tained from an amide I coupling map parametrized as a func-tion of the dihedral angles using density functional theory�DFT� calculations on glycine dipeptide.38 The ab initio pa-rametrization inherently treats all through bond and throughspace interactions. All other couplings are calculated usingtransition charge coupling �TCC�, which was developed as ahigher-order treatment of the electrostatics compared to thetransition dipole coupling �TDC� model.13 Similar ap-proaches have been used recently by several groups to simu-late amide I infrared spectra of a variety of peptide and pro-tein systems.19,28,47,49

Calculation of 2D IR spectra requires knowledge of thetwo quantum states in the LAH. The 2� site energies areassigned as 2�n−A, where the anharmonicity A is set to16 cm−1.15 The couplings between the 2� states are the sameas the one-quantum coupling terms, but are harmonicallyscaled by �2.15 The linear and 2D IR spectra were calculatedusing the transition dipole moments and energy eigenvaluesof the vibrational eigenstates obtained from diagonalizing theLAH. The methods for this calculation involved an eigen-state summation over one-dimensional �1D� or 2D Lorentz-ian line shapes ��=9.0 cm−1�, and have been described indetail elsewhere.23,41

As we have demonstrated recently,23 it is not possible toproperly simulate amide I 2D IR spectroscopy without ac-counting for disorder in the site energies. We incorporatedthe effect of static disorder in the spectral calculations byadding random Gaussian disorder to the calculated site ener-gies. This approximation is based on the recent work ofGanim and Tokmakoff, where they found that the dominantsource of disorder is in the site energies and that the disorderin coupling due to structural fluctuations has a negligibleeffect on the spectroscopy.23 A similar observation was alsomade by Hahn et al.24 For each spectral calculation �i� aGaussian weighted random number was subtracted from theoriginal site energy,

045109-3 2D IR spectroscopy of peptides J. Chem. Phys. 126, 045109 �2007�

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�n,i = �n − �i.

The standard deviation of the random site energy distributionwas chosen based on qualitative agreement with the experi-mental 2D IR data and was set to =12 cm−1. For each ofthe systems, 10 000 disorder realizations were averaged togive the final calculated spectra. The methods used in thedisorder calculation of 1D and 2D spectra are describedelsewhere.23

B. Visualization of vibrational modes

To develop an interpretation of the vibrational modes indifferent spectral regions in terms of peptide backbone struc-ture, we visualize the calculated eigenstates by projectingthem back onto the peptide local modes. This visualizationscheme adapts a method used by Dijkstra and Kroester, andChung and Tokmakoff, in which the magnitude and phase ofeach amide group is color coded onto a grid.22,28 Each localamide group corresponds to a box in the grid. The color ofthe box �red or blue� reflects the phase of the oscillator, whilethe depth of color encodes the amplitude of that group in thevibrational eigenstate.

Since disorder is crucial to reproducing the amide I spec-troscopy, the visualizations are performed on disorder-averaged vibrational eigenstates. The eigenvectors obtainedfor a calculation without site energy perturbations ��i=0�are used as reference eigenstates. For each disorder realiza-tion, the overlap integral between the realization andreference eigenvectors is calculated, and maximum over-lap is used to sort the eigenstates. The eigenvectors fromeach disorder step are binned and averaged to create thevisualizations.

IV. RESULTS

A. TZ2

TZ2 is an excellent candidate for the purposes of inves-tigating structure-spectroscopy relationships in � hairpins.Previous investigations of TZ2 have demonstrated its excep-tional stability and resistance to structural change.5,6,17,44

Through fluorescence measurements it was shown that bothhigh temperatures and a chemical denaturant were necessaryto completely dissociate the side chain contacts.6 Initial 2DIR work also showed that the hydrogen bond network main-tains some degree of native structure at high, typically dena-turing temperatures.17 TZ2 is an important benchmark be-cause it is well characterized experimentally and isaccessible to a wide range of theoretical methods and com-putational methodologies.6,50,51

The amide I FTIR spectrum of TZ2, shown in Fig. 1together with a diagram of the structure, has two distinguish-ing features: a band maximum at 1636 cm−1 and the promi-nent shoulder near 1673 cm−1.4,6 As describedpreviously17,40–42,52 and shown in detail below, the eigen-states giving rise to the intense low frequency peak involvein-phase vibration of amide oscillators directly across thestrand and in-phase vibration of backbone nearest neighbors.The spectral feature is thus termed the �� peak and the con-tributing vibrations are collectively termed the �� modes.

Neighboring oscillators within the high frequency eigen-states comprising the shoulder around 1673 cm−1 vibrate inphase with each other. Consequently, we designate the shoul-der as the �� peak, with its constituent �� vibrational modes.The 2D IR spectrum of TZ2 is shown in Fig. 1. Along thediagonal axis there are two well-resolved positive peaks, cor-responding to the �� and �� peaks inferred from the FTIRspectrum. The negative diagonal peaks corresponding to the�� and �� overtone transitions are also resolvable, althoughthe �� overtone peak is quite intense and blurs out the crosspeaks around �1=�� and �3=��. The ridge extending out to�1=�� and �3=�� is the result of the cross-peak intensitymixing with that of the positive diagonal peaks. As reportedpreviously, the presence of these two coupled vibrationalmodes in the 2D IR spectrum and the resultant Z-shapedcontour profiles are a direct indication of antiparallel �-sheetsecondary structure.17,42,53

FIG. 1. �Color� �A� Experimental amide I spectra of TZ2 �left�. 2D IRcontour lines are at ±80% of the band maximum for this and all other 2D IRspectra in this paper. Simulated amide I spectra �right�. The simulated FTIRspectrum is plotted in red and the underlying eigenstates prior to incorpo-rating Gaussian disorder are plotted as lines with the intensities weighted bythe relative strength of the transition moment, �2. �B� Stick and ribbondiagrams. Ribbon diagrams made with MOLMOL software. Ellipses overlaythe peptide stick diagram to highlight how the local peptide amide groupsmap on to the box plots below. The color scheme of the ellipses is that sameas the ��=1633 cm−1 eigenstate. �C� Selected eigenstates from the spectralsimulation.

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Figure 1 shows the calculated 1D and 2D IR spectra ofTZ2 alongside the experimental data. The line shape param-eters used in the simulation �=12 cm−1 and �=9 cm−1�were chosen to fit the experimental diagonal and antidiago-nal linewidths, respectively. The spectral simulation repro-duces the experimental �� positive peak width and position.The calculated overtone peak intensity is much smaller thanthe experiment, although the slope of the node between thefundamental and overtone peaks agrees quite well. The in-tensity in the �1=�� and �3=�� regions of the spectrum isalso similar in the experiment and the simulation. The mostsignificant discrepancy between the spectra is the amplitudeof the �� diagonal peak relative to the �� diagonal feature.The 2D IR simulation underestimates the �� amplitude byalmost half. This mismatch could be due to a number offactors, besides the model. One possibility is that the extraintensity is from either the Asn6 side chain or C-terminalamide groups, which are known to absorb near this fre-quency in neutral pH solutions.54 Calculations includingthese additional amide oscillators improve the comparisonwith experiment, as detailed in the supplementary material.55

From the calculations on TZ2, there are two intenseeigenstates that carry over 50% of the total amide I oscillatorstrength and are pictured in Fig. 1. One of the states is local-ized on oscillators 4,5,7 and 8 �1633 cm−1�, while the otheris localized on oscillators 2,3,9, and 10 �1634 cm−1�. Thereason for the separation into two modes on either end of thehairpin is the high degree of twisting, which disrupts thesymmetry that in an ideal � hairpin would delocalize the lowenergy mode across the peptide. The two modes are not re-solved because of their near degenerate frequencies. Both ofthe modes contribute to the �� region—so called because theoscillators are in phase across the strand and the transitiondipole of these modes points perpendicular to the � strand.The high frequency region generally contains highly mixedvibrational states. The two eigenstates with the highest en-ergy and significant intensity show phase symmetry similarto that expected for ideal �� modes, where the neighboringoscillators on the same strand are vibrating in phase and thetwo strands are out of phase.28,41 In this case, the modes aredelocalized over the entire hairpin. While the agreement be-tween spectral calculations remains largely qualitative, wefind that the description of the eigenstates is robust. As dem-onstrated in the supplementary material,55 the symmetry andlocal mode distribution of the dominant eigenstates are rela-tively insensitive to minor changes in site energy and cou-pling models.

B. TZ2-T3*T10*

Backbone 13C�= 16O isotope labeling introduces an�40 cm−1 redshift to the amide I� vibration. The techniquehas been used extensively for peptide and protein FTIRspectroscopy,56,57 although its application to �-hairpin pep-tides is limited.19,58 This is due not only to the relativelysmall number of systems, but also because many of the iso-tope labeled amino acids in the primary sequence of well-studied hairpin peptides are difficult to obtain commercially.We chose to study a pairwise 13C label of TZ2 at the C� atom

of Thr3 and Thr10 for two purposes. First, the spectroscopyof the dual label ensures that the shift of the isotope labeledpeak relative to the amide I maximum is sensitive to cou-pling between the oscillators. Studying the two closelyspaced oscillators provides a test of coupling models. Forexample, TCC predicts the Thr3-Thr10 coupling to be6 cm−1, while the TDC model predicts it to be over 12 cm−1.The other reason to choose this isotope combination is be-cause it will isolate a spectral signature directly related to theThr3-Thr10 interstrand hydrogen bond contacts.

The experimental FTIR and 2D IR spectra of TZ2-T3*T10* are shown in Fig. 2. The FTIR spectrum of theisotope labeled peptide shows a shoulder near 1613 cm−1 anda well-resolved diagonal peak in the 2D IR spectrum. Theamide I maximum shifts from 1636 to 1640 cm−1, while the�� band contracts to the red, becoming less prominent in theFTIR spectrum and unresolved in the 2D IR spectrum. Whilea distinct cross peak is not observed, it is present as ridgeselongated along �3=�� and ��, and can be seen in a �1

=1610 cm−1 slice through the 2D spectrum.The parameters from the spectral calculation of the un-

labeled compound were transferred without modification ex-cept the site energy of residues 3 and 10, which were red-shifted by 33 cm−1 to obtain agreement with the experiment.This empirical isotope shift is lower than the 39 cm−1 shiftestimated by the difference in the reduced mass of a

FIG. 2. �Color� �A� Experimental amide I spectra of TZ2-T3*T10* �left�.Simulated amide I spectra �right�. The simulated FTIR spectrum is plotted inred and the underlying eigenstates are calculated and plotted as in Fig. 1. �B�Selected eigenstates from the spectral simulation. The boxes around the 13C�labeled Thr3 and Thr10 amide groups are in bold. Particularly notable is thesplitting of the two �� bands by 23 cm−1. The isotope shift deduced for thelabeled oscillators based on the site energy model is 34 cm−1.

045109-5 2D IR spectroscopy of peptides J. Chem. Phys. 126, 045109 �2007�

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12Cv

16O oscillator compared to 13Cv

16O. It is also lowerthan the reported 44 cm−1 shift based on a DFT �B3LYP/6-31+G** level� calculation of N-methylacetamidein vacuum.19 As discussed in Sec. V C, we suspect that theunusually small shift is due to our original site energy model,rather than a fundamental disagreement with the earlier pre-dictions.

The calculated eigenstates of the T3*T10* isotope la-beled compound can be used to examine the nature of theredshifted amide I vibration. From the phase plot in Fig. 2,we see that the 1610 cm−1 eigenstate is localized on the 2, 3,9, and 10 amide groups, with most of the intensity on thelabeled groups 3 and 10. This localization of the 13C shifted�� vibration to the residues near the peptide terminal regioncauses the eigenstate at 1633 cm−1, or the unlabeled �� vi-bration, to localize on residues 4, 5, 7, and 8. Thus, while the1610 cm−1 peak reports on the cross-strand hydrogen bondsnear the N and C termini, the amide I spectral maximumdirectly probes the hydrogen bond pair near the turn region.In other words, the effect of the T3*T10* isotope labels is toremove the near degeneracy of the two �� modes of theunlabeled peptide. As expected, the 1610 cm−1 mode is anasymmetric stretch of the labeled oscillators 3 and 10; thecalculations suggest that the weak symmetric vibration of thelabeled oscillators at 1610 cm−1 is coincident with the strong�� transition.

C. PG12

We also investigate the amide I spectroscopy of a 12residue de novo hairpin peptide designed by Syud et al.45

The PG12 hairpin structure is stabilized by a D-Pro enhancedtype II� � turn, and has been optimized for stability. In fact,the structure has proven reliable enough to be used as a tem-plate for the design of larger three and four stranded �-sheetpeptides.59 A previous infrared spectroscopy study of thispeptide was done to systematically analyze the stability ofPG12 by varying the length of the peptide, substituting anL-Pro residue into the turn region, and testing it against cy-clic hairpin analogs.60

The FTIR spectrum of PG12 is shown in Fig. 3, and issimilar to that reported in the previous work.60 The amide Imaximum, or �� peak, is centered at 1640 cm−1, while theshoulder, or �� peak, appears near 1670 cm−1. The energy ofthe �� mode of PG12 is about 4 cm−1 higher than that ofTZ2. Other resolvable features include the peak at1613 cm−1, which was previously assigned to the D-Pro resi-due �P.60 Two other weak features at 1588 and 1705 cm−1

are attributed to the side chain carbonyl vibrations of Gln12and Glu4, respectively.54

The 2D IR spectrum displays positive diagonal peaksthat correspond to the peaks in the FTIR spectrum. The ��

peak is resolved in the 2D IR spectrum, but its spectral po-sition and intensity relative to the �� peak differ from that ofTZ2. The cross-peak ridge is clearly visible, but lacks theprominence of the ridge in the TZ2 2D IR spectrum. Theseeffects are primarily caused by interference with intensityfrom the broad �1660 cm−1 peak corresponding to disor-dered peptide structure. We submit this interpretation based

on comparison to the high temperature spectrum of TZ2,17

where disorder has been thermally introduced to the system.Coupling of the proline to the remainder of the backboneamides is observed through interference effects that lead toextended �3=�� and �� ridges. Also, the negative ridge ob-served for ��1�1600 cm−1; �3=1620 cm−1� arises from thecross peak between the �P and �� resonances.

While significant differences with experiment exist, thespectral simulations of PG12 have many similar features. Inthe simulated 2D IR spectrum, the frequencies and relativeintensities of the �� and �� peaks agree, as do the intensityand profile of the positive diagonal cross-peak ridge. On theother hand, the correct relative intensity of the �� and ��

peaks is not captured well in the simulated 1D absorptionspectrum. For the spectral calculations, the D-Pro peak near1613 cm−1 was produced by empirically shifting the site en-ergy of amide group 5 by 40 cm−1. In order to reproduce theinhomogeneous linewidth of this peak it was necessary toreduce the width of the disorder to =6 cm−1. Other siteswere left with =12 cm−1, yet the simulated 1640 cm−1

positive diagonal peak is significantly narrower than the ex-periment. This suggests that the disorder varies from the turn

FIG. 3. �Color� �A� Experimental amide I spectra of PG12 �left�. Simulatedamide I spectra �right�. The simulated FTIR spectrum is plotted in red andthe underlying eigenstates are calculated and plotted as in Fig. 1. �B� Stickand ribbon diagrams. �C� Selected eigenstates from the spectral simulation.

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to the ends of the hairpin, and is consistent with a tightlyfolded turn and fraying ends of the hairpin. This was alsoobserved in TZ2 by Wang et al., who showed that the 2D IRmeasured homogeneous and inhomogeneous linewidths ofresidues Trp2 and Gly7 are significantly different.19

The eigenstate visualizations in Fig. 3 show that the1609 cm−1 peak is largely located on the site 5 �Val5-Pro6�amide group, but that there is visible intensity on neighbor-ing oscillators. Because the off-diagonal intensity in thesimulated 2D IR spectrum does not match the experiment,we suspect that the calculated couplings near the turn regionare inaccurate. This means that the vibration may, in fact, bemore localized on site 5 than the simulations suggest. Look-ing at the other eigenstates we see that the �� vibration isdelocalized across the entire hairpin, with most of the inten-sity on the groups not involved in the 1609 cm−1 vibration.The �� modes are highly mixed, although the 1667 cm−1 vi-bration does show the expected �� phase pattern on oscilla-tors 1–3 and 8–11.61

D. Gramicidin S

Gramicidin S is an antimicrobial peptide that inducescell death by aggregating in and disrupting the outermembrane.61 No crystal structure of unmodified GramicidinS has been measured, but early NMR and spectroscopicwork showed that it does form an antiparallel pleated sheet,connected by two type II’ � turns.46,62 Recent crystal struc-tures of trichloroacetyl and m-bromobenzoyl Gramicidin Sconfirm the earlier structure models.48 Gramicidin S is notwater soluble, but it can be dissolved in DMSO, for whichthe FTIR spectrum has been reported previously.63

The FTIR and 2D IR spectra of Gramicidin S are pre-sented in Fig. 4. The amide I peak in the FTIR spectrum is1661 cm−1 while the high frequency shoulder appears near1680 cm−1, which correspond to the �� and �� bands, respec-tively. The most striking difference with the earlier systemsis that the center frequency is blueshifted and the width ofthe amide I band is narrower. These effects can both be at-tributed to weaker interactions with the DMSO solvent.Similar shifts in frequency and linewidth are observed for theamide I vibration of N-methylacetamide.64

The simulated amide I spectra of Gramicidin S areshown in Fig. 4. The linewidth parameters ��=9 cm−1, =12 cm−1� and coupling model are the same as were used forPG12 and TZ2. The coupling and line shape parameters arechosen to give a consistent comparison to the simulations ofthe other hairpin spectra in this report. As can be seen, thecalculated spectrum overestimates the ��−�� splitting byabout 10 cm−1. The dominant eigenstates do have the sameoscillator phase pattern as in the previous system. The onlyassumption made in transferring these calculations to thenonhydrogen bonding DMSO solvent is that site energiesshow a weaker solvent redshift. The qualitative agreementwe observe suggests that electrostatic site energy modelsshould be transferable to different peptide environments.

V. DISCUSSION

A. Previous IR studies of � hairpins

As recently as ten years ago, there were very few stable�-hairpin peptides that could be studied in aqueous environ-ments. The model systems that did exist were difficult tostudy with infrared spectroscopy because the required ex-perimental concentrations would lead to significant aggrega-tion over the time scale of the experiments. Consequently,applications of infrared spectroscopy to study � hairpinswere rare. Only in the last five to seven years has there beena widespread use of FTIR methods to study hairpin structure,stability, and folding.5–7,51,65–67 Much of this work has takenadvantage of the distinctive amide I line shape exemplifiedby the systems presented in this report. FTIR spectroscopy ofhairpin peptides has been used most frequently to comparethe relative stability of �-hairpin systems. This work has ledto a greater understanding of the stabilizing role of the � turnand the amino acid sequences that enhance this stability. Thethermal melting transition has also been investigated exten-sively with FTIR techniques, including transient temperaturejump studies to investigate folding kinetics.7,68 These studieshave helped us develop a description of thermal denatur-ation, including insight into the structural regions that con-tribute significantly to the folding rate.

In spite of these advances, the detailed interpretation of

FIG. 4. �Color� �A� Experimental amide I spectra of Gramicidin S �left�.Simulated amide I spectra �right�. The simulated FTIR spectrum is plotted inred and the underlying eigenstates are calculated and plotted as in Fig. 1. �B�Stick and ribbon diagrams. �C� Selected eigenstates from the spectralsimulation.

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the amide I spectral features remains somewhat ambiguous.Generally, the structural interpretation of these data had beenfocused on the stability of the cross-strand hydrogen bondcontacts. For example, a number of reports have focused onthe low frequency �1615–1645 cm−1� region. Often, thisconsists of using the presence of a low frequency peak sim-ply as a marker of �-hairpin structure.6,65 Other groups haveused band deconvolution to assign a low frequency peak tothe turn region as well as to distinguish the carbonyl groupshydrogen bound across the strand from those hydrogenbound to solvent.66 Another method of interpretation is basedon electrostatic coupling methods used in this report. Forexample, the high frequency region has been used to quan-tify �-hairpin stability5 and was the basis for previous inter-pretations of the 2D IR spectroscopy of TZ2.17 The vibra-tional spectroscopy of TZ1 was recently studied using an abinitio fragmentation method.29

B. Testing coupling models

Isotope labeling is often employed in vibrational spec-troscopy to clarify spectral assignments and decongest broadvibrational bands. Spectra of the isotope labeled TZ2 peptidecan be used to investigate the way that vibrational couplingis treated in spectral models. For TZ2, the TDC calculatedcoupling between amide groups 3 and 10 is 12.9 cm−1, whilethe TCC model predicts a value of 6.3 cm−1. This large dif-ference in predicted coupling does not produce significantdifferences between the TCC and TDC simulated amide Iline shapes of unlabeled TZ2. While largely a result of spec-tral congestion, this insensitivity is also because the othermatrix elements are not as sensitive to coupling models. Onthe other hand, when the two models are used to calculatethe spectroscopy of the isotope labeled compound, whereinteraction between Thr3 and Thr10 can be spectrally iso-lated from the main amide I band, there is a marked differ-ence. Specifically, the TDC calculation predicts that the fre-quency of the peak corresponding to the isotope labeledamide groups is 1607 cm−1, while the calculated frequencyin the TCC model is 1613 cm−1—equal to the experimentalvalue.

In order to help isolate coupling effects from the originalchoice of site energy, we can also compare the differencebetween the redshifted peak and the amide I maximum in thepositive diagonal region of the 2D IR spectra. By finding themaxima of the two peaks we can compute the frequencysplitting between the two peaks on the 2D IR surface. Thevalue obtained from the experimental 2D IR spectrum is37.5 cm−1. For the TCC simulated 2D IR spectrum, the valueis 36.8 cm−1, while the TDC simulation gives a difference of47.4 cm−1. This suggests that the TDC coupling model over-estimates the strength of coupling between hydrogen bondedamide groups, although the test cannot be absolutely defini-tive because of uncertainties in the original site energymodel.

The discrepancy between the two models can be under-stood in terms of the limits of the dipole approximation,which is expected to break down as the distance between thedipoles approaches their length.35,69 If we approximate the

size of the amide I dipole to be the distance from the amideproton to the amide oxygen ��3.15 �, we see that it is veryclose to the distance between cross-strand amide groups 3and 10 ��3.73 �. This effect was the primary motivationfor the incorporation of the DFT parameterization to simulatenearest neighbor coupling.13 Here we have shown that forpeptides in tight �-strand registry, the TDC approximationbreaks down appreciably.

Generally speaking, there are still questions that remainregarding the accuracy of the existing coupling models. In allof the calculated spectra, the relative ratio of diagonal tocross-peak amplitudes and strong horizontal cross-peakridges suggests that the relative magnitude of the couplingsrelative to the site energy variation still is somewhat high.This is an issue that remains to be resolved in the parametri-zation of amide I coupling and site energy models so thatquantitative agreement to experiment can be achieved.

C. Assignment of site energies

Recently, two single isotope labeled variations of TZ2have been used to study the line broadening dynamics of theTrp2 and Gly7 residues using 2D IR spectroscopy.19 Hoch-strasser and co-workers found that the 13C labeled Trp2amide I vibration is more inhomogeneous than that of Gly7.Further insights were gained by comparing the separationbetween the positive and negative diagonal peaks to explorethe anharmonicity of the 13C labeled amide I vibration. Theauthors also concluded that the amide I frequency of Gly7 is�16 cm−1 lower than that of Trp2, demonstrating that thezero-order site energies are not degenerate. By assuming a47 cm−1 redshift of the amide I vibration upon 13C substitu-tion, a site energy is assigned to amide groups 2 and 7�1658.5 and 1645 cm−1, respectively�. Based on a symmetryargument, the authors also posit that the site energy of sitesGlu5 and Gly7 should be the same; however, this seemsunreasonable since the hydrogen bond geometry and solventexposure of sites 5 and 7 are very different. The symmetryargument does, however, seem applicable to the Trp residues2, 4, 9, and 11 that have the same side chain environment aswell as the carbonyl oxygen hydrogen bound to solventrather than across the strand.

The TZ2 isotope presented in this work can similarlylead to a reasonable approximation for the site energies ofresidues 3 and 10. Assuming an amide I 13C isotope shift of42 cm−1 �see Ref. 56� and adding that to the empirical siteenergy used to calculate the TZ2-T3*T10* eigenstates in Fig.2 gives a value of 1666 cm−1 for Thr3 and 1668 cm−1 forThr10. We can draw on these values to obtain a rough ap-proximation for the site energies of Glu5 and Lys8, whichhave very similar local geometries and hydrogen bondingpartners. Our site energy assignments combined with thosefrom the previous study19 are summarized in Fig. 5. Onlythree main chain amide group site energies are left unas-signed: Ser1, Lys12, and Asn6. These predictions show con-siderably more site-to-site variation than the heuristic model.The alternating pattern can be understood in terms of anadditional redshift to sites with solvent exposed oxygen at-oms, and has been recognized by other groups.24,29,66

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The pattern in the empirically obtained site energies canbe compared to other methods for assigning TZ2 site ener-gies. Ganim and Tokmakoff have recently used electrostaticmethods for calculating site energies and introducing disor-der by using snapshots from MD trajectories in explicitsolvent.23 The site energy shift is calculated from the electricfield or electrostatic potential of the solvent and solute atomsacting on the individual amide I sites. The site energies ofGanim and Tokmakoff obtained for the electric field site en-ergy model of Schmidt et al.36 are compared to our heuristicand deduced TZ2 site energies in Fig. 5. The MD basedmethod predicts a strong alternation in site energies betweenadjacent oscillators which arises from additional redshift tosolvent exposed oscillators. A similar alternation of site en-ergies, albeit with smaller variation, was observed by Hahnet al. in calculations of �-hairpin amide I spectra from MDsimulations using an electrostatic potential model.24

The 2D IR spectral simulations of TZ2 using the samecoupling model but treating site energy disorder from MDsimulation23 leads to a somewhat better agreement with ex-periment than this heuristic model with Gaussian randomdisorder.55 Since off-diagonal disorder was observed to beinsignificant, this observation suggests that site-specific dis-order plays an important role in modeling the experiment.This would be expected in the case that the TZ2 turn istightly folded, while the ends are frayed.

To better understand the influence of these site energyassignments we have compared the calculated linear and 2DIR spectra of TZ2 and eigenstate visualizations for four dif-ferent site energy models.55 The heuristic site energy modelused in this report has little variation in site energies, andrequires relatively large Gaussian disorder to reproduce theexperimental amide I linewidth. The spectrum calculated byusing empirical site energies deduced from the TZ2 isoto-pomers shows little change in the shape of the IR and 2D IRspectra, or in the nature of the underlying eigenstates. Thecalculated TZ2 2D IR spectra using site energies obtainedfrom MD simulations have a broader than observed site en-

ergy distribution with a particularly high �� frequency. Fi-nally, we calculate results by modifying the heuristic modelto add an additional −20 cm−1 shift for solvent exposed os-cillators. This draws on the fact that on average water willmake two hydrogen bonds to the peptide CO, and the obser-vation that the site energy shift is additive in the number ofhydrogen bonds to water.70 This reproduces the large alter-nating shift of site energies; however, there is little differencein the shape of the calculated 2D IR spectrum when com-pared to only one hydrogen bond allowed to solvent. We notehere that the new eigenstates do not differ greatly from thoseshown in Fig. 1. The degree of delocalization does depend onthe site energy assignments, but the underlying symmetry isretained. This allows us to conclude that the eigenstate analy-sis used to interpret the structure-spectrum relationships inthe Results sections remains valid even with differences inthe assignment of site energies.

Finally, we note that the calculations above do not takeinto account amide oscillators of the amino acid side chains.In the supplementary material55 we show a spectrum calcu-lated by using empirical site energies and including the Asn6side chain amide group and the terminal �Lys12-NH2� amidegroup. The additional oscillators do improve the qualitativeagreement to experiment through more defined �� diagonaland cross peaks.

D. Comparison to previous work

There have been two previous studies of the simulated2D IR spectroscopy of �-hairpin peptides.19,24 In both stud-ies, site energies are reported using semiempiricalcalculations19,24 and electric field projections within MDtrajectories.24 The site energies of the strand regions showremarkably similar patterns to those we posit from the iso-tope labeled systems. Specifically, there is a consistent10 cm−1 redshift for site energies of amide groups with car-bonyl groups pointing out toward the solvent relative togroups whose carbonyl group points in toward the opposing� strand. If a heuristic site energy model is further devel-oped, it must be able to account for this effect.

In the earlier reports, the �� band was attributed prima-rily to oscillators in the � strands, which is consistent withthe present interpretation.19,24 The phase relationships we as-sign to the local sites are also consistent with previouswork.19,71 In the 2D IR simulation of the 16-residue GB1hairpin, Hahn et al. showed that the eigenstates at the highfrequency region of the spectrum are localized on the hairpinturn residues.24 Wang et al. made a similar observation basedon the spectral distribution of the local modes.19 For thesimulations shown in Fig. 1, the eigenstates in the �� spectralregion are highly delocalized, and there is no clear evidencethat the residues in the turn region preferentially contributeto the high frequency eigenstates. In the case of the GB1hairpin, the site energies in the turn region are much higherthan those in the � strands, and thus unsurprisingly contrib-ute more to the high frequency eigenstates. The difference inthe spectral interpretation is reasonable as the GB1 hairpincomprises a large type I � turn stabilized by unique sidechain hydrogen bonds, while the TZ2 turn is a tight, type I�

FIG. 5. Site energy plot for TZ2 using several different models. The solidred trace shows the site energies as calculated from the heuristic model usedto simulate the spectra in this report. The blue trace shows the site energiescalculated by projecting the electric field onto each amide unit �Ref. 23�.The green squares are estimates based on isotope labels in this report andcyan diamonds are from the earlier study �Ref. 19�. The black circles areestimates based on structural similarities with isotope labeled sites. For theremaining dashed black trace, site energies were assigned from the heuristicmodel. The bar on the left of the graph shows the width �2� of the Gauss-ian disorder used in the spectral simulations.

045109-9 2D IR spectroscopy of peptides J. Chem. Phys. 126, 045109 �2007�

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� turn.44 The TZ2 spectral contribution calculated by Wanget al. is unexpected as they set the site energy of Gly7 andGlu5 to 1645 cm−1 leaving only Asn13 �side chain� and Asn6to account for the spectral intensity.19 Further isotope label-ing schemes could help us resolve these issues; however, thisis further evidence that the �� eigenstates are highly mixedstates whose structural origins are difficult to model withcurrent methods.

E. Effect of twist on hairpin spectra

Spectral simulations and eigenstate analysis resolvestructural details by relating gross features in the amide Ispectrum to the relative participation of the local amidegroups in the underlying eigenstates. This type of analysiscan be used to compare PG12 to TZ2 and explain the struc-tural basis for the subtle differences in their respective spec-tra. The low frequency amide I maximum, or �� peak, forTZ2 is 1636 cm−1, while that of PG12 is 1640 cm−1, a dif-ference of about 4 cm−1. When we compare the eigenstates�Figs. 1�c� and 2�c�� we see that the �� modes of TZ2 arelargely localized on four oscillators, while those of PG12extend across the sheet. The difference in the delocalizationis largely a result of the relative degree of twist in the �strands. Less twist leads to stronger coupling between theamide groups near the turn and those near the termini, whichcauses the vibration to delocalize further along the strands.As the vibration delocalizes along the direction of the �strands, there is a corresponding blueshift in the amide I ��

maximum. The frequency shift of the amide I band as afunction of hairpin length was demonstrated in earlier spec-tral modeling of ideal hairpins by Cheatum et al.41 The ef-fects of twist on hairpin spectroscopy have been more di-rectly investigated in an ab initio computational study byBour and Keiderling.43

VI. CONCLUSION

We have investigated the amide I vibrational spectros-copy of several �-hairpin peptides and performed spectralsimulations for each system to connect distinct spectral fea-tures to peptide structure. The general features in a �-hairpin2D IR spectrum are the �� and �� diagonal peaks with thecross-peak ridge connecting the two frequency regions. The�� peak consists of amide I sites oscillating out of phasewith their in-strand neighbor and in phase with the amidegroup across the strand. For 12–16 residue hairpin peptideswe expect the �� frequency to be in the range of1635–1645 cm−1. The �� peak is sensitive to both thestrength of the cross-strand coupling and the delocalizationof the vibration along the direction of the strands. The ��

region, or shoulder in the FTIR spectrum, is a much morecomplicated set of vibrations. The symmetry of these vibra-tions is less well defined, but is generally delocalized overthe entire hairpin and consists of amide I oscillations largelyin phase along the direction of the strand. The cross-peakridge extending from the positive �� peak can also be used asa marker of coupling strength and can help identify the ��, ��

doublet when it is not well resolved in the 2D IR spectrum.The 2D IR spectrum of TZ2-T3*T10* shows that local ��

modes can be spectrally isolated and are a good probe ofcross-strand hydrogen bond contacts. However, isotope la-beling must be interpreted carefully, since the isotope in-duced shift of a subset of oscillators within the hairpin alsoalters the nature of the remaining delocalized amide I modes.

The amide I model used in this report is a useful tool toanalyze the spectroscopy and pattern of eigenstates to deducestructure level details including stability and the relative de-gree of twist in the � strands. The heuristic method of choos-ing site energies based on the hydrogen bond geometries ofthe amide group qualitatively reproduces the features in thespectrum. As discussed in the previous section, however,there is evidence that the heuristic model does not properlyaccount for the difference between inward pointing amidecarbonyl groups and those pointing out toward the solvent.Studies of site energy shifts and heterogeneity drawing onMD simulations will continue to be an important tool forbuilding empirical site energy models. Calculations on thebasis of MD simulation also offer an approach to revealingas yet unanswered questions about the importance of ac-counting for motional narrowing in the spectroscopy.

The 2D IR spectrum of TZ2-T3*T10* compared to simu-lations suggests that TCC is superior to TDC when account-ing for the electrostatic coupling of the amide I vibrations.The coupling model used in this report overall gives qualita-tive agreement with the data. Experimental data generallyhave diagonal peaks that are more inhomogeneous and cross-peak ridges that are less pronounced, which indicates thatfurther refinements are needed to obtain quantitative agree-ment. It is possible that such improvements may require ex-plicitly treating the anharmonic couplings to other amide vi-brations of the peptide.72 The spectral simulation ofGramicidin S also suggests that the model is transferable toother solvents, and perhaps more significantly, to the uniqueenvironments of amide groups buried within folded proteins.

We have shown that a combination of 2D IR spectros-copy, isotope labeling, and spectral modeling has revealedinformation about site energy distributions, coupling models,and hairpin structure and stability. Such insight is essential asvibrational spectroscopy is increasingly being applied tosolve complex problems in protein folding and other ques-tions in biopolymer physics.

ACKNOWLEDGMENTS

The authors would like to thank Professor Sam Gellmanfor providing structures of PG12 and providing samplesearly in the investigations. The authors also would like tothank Professor Glenn Jones for providing samples ofGramicidin S as well as guidance early in the studies. Thiswork was supported by the NSF �CHE-0316736 and CHE-0616575� and the David and Lucile Packard Foundation.

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