Characterization of the conformational space of a triple-stranded β-sheet forming peptide with molecular dynamics simulations

Characterization of the Conformational Space of a Triple-Stranded �-Sheet Forming Peptide With MolecularDynamics SimulationsPatricia Soto1* and Giorgio Colombo2

1Groningen Biomolecular Sciences and Biotechnology Institute (GBB), Department of Biophysical Chemistry, University ofGroningen, Groningen, The Netherlands2Istituto di Chimica del Riconoscimento Molecolare, CNR, Milano, Italy

ABSTRACT Molecular dynamics (MD) simula-tions have been performed on a series of mutants ofthe 20 amino acid peptide Betanova in order tocritically assess the ability of MD simulations toreproduce the folding and stability of small �-sheet–forming peptides on currently accessible time-scales. Simulations were performed in both waterand in 40% methanol solution, using an explicitsolvent model. The simulations suggest that all mu-tants adopt a wide range of conformations in solu-tion, that the structures are highly flexible, and thatstabilization of compact structures is due to a deli-cate balance of hydrophobic and polar side-chaininteractions. Simulations longer than 100 ns, al-though not sufficient for a complete thermodynamicand kinetic description of the system, sample anensemble of compact conformations characterizedby the loss of ordered �-sheet secondary structure.This suggests that no significant free energy barrierseparates the different conformations available.Proteins 2004;57:734–746. © 2004 Wiley-Liss, Inc.

Key words: Betanova; peptide folding; molecular dy-namics simulation

INTRODUCTION

Understanding protein folding lies at the heart of pro-tein design techniques. However, before we can hope tounderstand the process of folding in whole proteins, wemust be able to characterize the kinetics and thermodynam-ics of folding in simple model systems. The difficulty is thatalthough much has been learned in regard to peptidefolding via experimental studies, few, if any, experimentaltechniques can be used to follow the process of folding inindividual molecules at atomic resolution.1,2 Moleculardynamics (MD) simulations, in contrast, hold the promiseof being able to follow the process of folding of individualmolecules in atomic detail. Simulations of protein orpeptide folding require, however, that it be possible tofollow a system for an appropriate timescale and sampleconfigurational space with appropriate weights. In prin-ciple, MD simulations are ergodic and should eventuallysample all the available conformational space with Boltz-mann weights. However, in practice, with current compu-tational resources, it is only possible to sample a fewlocalized basins in the free energy surface or to diffuse over

the surface sampling a small region of the availableconformational space at random. Where the potentialenergy surface is characterized by a limited number oflow-energy conformations in rapid equilibrium (on the MDtimescale), adequate sampling of the thermodynamicallyrelevant regions of conformational space can be achieved.In such cases, MD simulations have provided highlydetailed information on the nature of alternative states insolution and the dynamics of spontaneous folding–unfold-ing.3 However, such cases are rare, and despite dramaticimprovements over recent years in simulation codes andcomputer capacity, the ability to sample the timescalesrelevant to understanding the behavior of biomolecules isextremely limited. This is especially problematic in thecase of in silico protein (un)folding simulations.

To date, the most successful simulation studies of fold-ing and stability have involved the formation of �-helices.Helices primarily involve local interactions within thepolypeptide chain and experimentally are known to fold ona nanosecond timescale,4 which is readily accessible in MDsimulations. Simulations have provided information onthe initial stages of helix formation, including the time-scale on which the first helical turn forms and breaks,5 theenergetics of helix formation,6 and the nature of possibleintermediate states.7 Nevertheless, the dependence of themechanism on the force field used remains a serious issue,and except in those cases where repeated folding–unfolding transitions could be observed, conclusions con-cerning possible folding intermediates and folding path-ways must still be questioned.

Compared to helix formation, �-sheet formation is morecomplex. The physical interactions that determine thegeometry and stability of a �-sheet are nonlocal and poorlyunderstood.8 In addition, �-hairpins have proved difficultto study experimentally primarily due to their tendency toaggregate. Nevertheless, �-sheet forming peptides are thesubject of intense research, due to their importance inamyloid fibril formation, a factor in a wide variety of

*Correspondence to: Patricia Soto, Groningen Biomolecular Sci-ences and Technology Institute, Department of Biophysical Chemis-try, University of Groningen, Nijenborgh 4, 9747 AG Groningen, TheNetherlands. E-mail: [email protected]

Received 8 April 2004; Accepted 20 May 2004

Published online 29 July 2004 in Wiley InterScience(www.interscience.wiley.com). DOI: 10.1002/prot.20236

PROTEINS: Structure, Function, and Bioinformatics 57:734–746 (2004)

© 2004 WILEY-LISS, INC.

pathological disorders.9,10 Peptides obtained from pro-teins11,12 or from de novo designs13–15 that adopt stablefolded structures in solution have been isolated and charac-terized using NMR, fluorescence, and other spectroscopictechniques. Critical for simulation studies, experimentalkinetic studies indicate that �-hairpins have folding timesin the range of several microseconds, much longer than therespective helix folding times. Nevertheless, a wide rangeof computational studies of �-turn– as well as �-hairpinforming sequences, have been performed in an attempt toaddress different aspects of the these systems, such as�-hairpin formation and hydrophobic interactions,16 stabil-ity,17,18 equilibrium distributions,3,19,20 free energy land-scapes,21 and cosolvent effect on the relative stability ofmodel peptides.22

Triple-stranded, antiparallel �-sheet peptides, as a nextstep in complexity from �-hairpins, have also been studiedin an attempt to address the problem of how extended�-structures form and whether a preorganized �-hairpinmotif acts as a template for the interaction of the thirdstrand.23 The nature of the folded state in solution and thedegree of cooperativity during folding remain issues ofdebate in these peptides. Betanova,24 a 20-residue peptidedesigned by Serrano and coworkers based on a three-stranded, antiparallel �-sheet template, was suggested todisplay apparent cooperative two-state folding behavior inchemical and thermal denaturation studies, thus makingit an attractive model to study folding. Betanova has alsobeen analyzed by Ansari and coworkers,25 who attemptedto characterize the conformation and equilibrium foldingand unfolding of Betanova using circular dichroism (CD),infrared measurements, and fluorescence resonance en-ergy transfer (FRET) techniques. In contrast, they con-cluded that Betanova sampled an ensemble of compactconformations but did not fold cooperatively. A similarconclusion was proposed by Boyden and Asher26 using UVresonance Raman spectroscopy (UVRR). As an extensionof their earlier work, Serrano, Lopez de la Paz et al.27 haverecently designed and synthesized a series of mutants ofBetanova to demonstrate their ability to rationally alterthe stability of the molecule. With the backbone of Bet-anova as structural template, the protein design algorithmPERLA (Protein Engineering Rotamer Library Algo-rithm)28 was used to propose both single and multiplemutations that either enhanced or reduced the stability ofthe peptide (see Fig. 1). Changes in the population of the�-sheet containing conformers of Betanova and mutantswere assessed using NMR spectroscopy and far-UV CD(assuming a two-state model).

Simulation studies have also been used to analyze thefree energy landscape of triple-stranded, antiparallel�-sheets. Wang and Sung29 studied the folding of 3 triple-stranded, antiparallel �-sheet peptides (including Bet-anova) with an all-atom representation of the protein, asolvent-reference potential, and simulation length of 100ns each. According to their results, the experimentallyobserved peptide structure may include an ensemble of�-sheet structures. Ferrara and Caflisch30 performed simu-lations, in implicit solvent, that reached the defined foldedstate of each peptide from different starting conforma-

tions. Impressive simulation times have been achieved(10’s of microseconds) by combining trajectories run atdifferent temperatures and from different starting condi-tions that allow an analysis of the shape of the free energylandscape. Nevertheless, in the weighting process, pre-knowledge of the native structure is required. Therefore,results are highly biased and do not allow sampling ofother, equally relevant regions of the conformational space.

Betanova24 (NH3� RG - WSVQNGKYTNNGKTTE - GRCOO�) was designed by Serrano and coworkers based on atriple-stranded, antiparallel �-sheet template with 4 resi-dues per strand and 2 (natural) residues per turn. Theresidues from the 3rd to the 18th position were intended toform the desired structural motif, and the RG-ends wereincluded to avoid aggregation of the peptide and facilitatesolubilization in polar solvents. Betanova displays evi-dence of cooperative, two-state folding behavior in chemi-cal and thermal denaturation studies, and it was initiallysuggested that 80–90% of the molecules adopted a triple-stranded �-sheet conformation at 278 K. As such, Bet-anova was considered an attractive model with which tostudy folding24 computationally. In particular, Bursulayaand Brooks31 attempted to calculate a two-dimensional(2D) folding free energy landscape for Betanova by all-atom MD simulations using umbrella sampling techniquesand unfolding conditions. They obtained a funnel-shapedlandscape and proposed a folding pathway for Betanova.As part of this work, they used the fact that Betanovaremained a triple-stranded �-sheet for 2 ns as “evidence”that the structure proposed by Serrano and coworkers wasin fact stable in solution. Colombo et al.,32 based onsimulations an order of magnitude longer (4 � 20 ns),claimed, in contrast, that it was not possible to draw firmconclusions in regard to the stability of Betanova fromsimulations, as reversible folding could not be demon-strated. Instead, they proposed that, in solution, Betanovasampled a range of conformations that together couldexplain the available experimental data. We note that thestructural characterization of small peptides such as Bet-anova using NMR is nontrivial. Serrano and coworkersoriginally concluded that Betanova formed the desired

Fig. 1. Average NMR structure of Betanova.24 Residues that weremutated27 are highlighted.

CONFORMATIONAL SPACE OF A 3-STRANDED �-SHEET 735

structure based primarily on the presence of long-rangenuclear Overhauser effects (NOEs) between the aromaticprotons of Trp 3 and C� protons of Thr17, and corroboratedby the large 3JNH� coupling constant values measured for�-strand residues.24 In their most recent work,27 however,these long-range NOEs are no longer reported, and moreimportantly, the �-sheet population of Betanova at 283 Khas been re-estimated based on the chemical shift of H�Thr11 [��H�(Thr11)] to be 9% in water and 20% inmethanol solution. Taking instead the average of the H�chemical shifts of Lys9, Tyr10, and Thr11, the estimated�-sheet populations are 8% in water and 26% in methanolsolution.27 These changes dramatically alter the conclu-sions in regard to the accuracy of the previous simulationstudies. In particular, it is clear that the triple-strandedstructure should not be the dominant conformation insolution.

The existing experimental and simulation studies of thefolding behavior of Betanova leave many open questionsunanswered. The system also provides the opportunity tocritically address whether MD simulations can correctlyreproduce the conformational behavior of highly flexible�-sheet forming peptides. In this study, we attempt toinvestigate the distribution of the populations sampledduring the simulations, and the factors that affect stabilityand flexibility of Betanova and some of the proposedmutants.

METHODSMD Simulations

In total, 11 simulations were performed and analyzed.The parameters used for simulations of Betanova in waterare described by Colombo et al.32 In the protocol to set upthe simulations, the only difference with respect to thiswork is that Colombo et al. used NVT conditions for theproduction runs, while, here, NPT conditions were used.The simulations of Betanova in methanol solution and themutants of Betanova (see Table I) in water and in metha-nol solution were performed as follows: The initial struc-ture for the simulations of the native Betanova in metha-nol was the average NMR structure provided by Serranoand coworkers.24 The initial structures used in the simula-tions of the various mutants were generated from theaverage NMR structure of Betanova using the softwareWHATIF.33 The peptides were protonated to give a zwitte-rionic form (with N-terminal NH3� and C-terminal COO�

group) in line with the experimental conditions (pH 5.0) at

which the peptides were studied. The total charge on thepeptide was �3. Counterions were not added, because,from our own experience, the presence of such chargeswould bring more artifacts into the simulation box of sucha small molecule than a proper modeling of the chemicalenvironment. These artifacts are particlarly problematicwhen electrostatics is calculated with the cutoff methodand the simulation time length is on the order of nanosec-onds. The peptide was then solvated in explicit simplepoint charge model (SPC) water34–36 or SPC water with40% methanol in line with the experimental conditions.The simulations were performed using periodic boundaryconditions in a truncated octahedral box, with the mini-mum distance between the solute and the wall of the boxbeing initially 0.8 nm. All simulations were performedusing the GROMOS96 43A1 force field.37,38 The same forcefield, or closely related ones, has been extensively used tosuccesfully simulate the behavior of �-hairpins in solu-tion.17,19,20,22,39 The temperature was maintained close tothe intended value by weak coupling to an externaltemperature bath40 with a coupling constant of 0.1 ps. Inthe same way, the density of the system was adjusted byweak coupling to an external pressure bath40 (P0 1 bar,coupling time tp 1.0 ps). The LINCS algorithm41 wasused to constrain bond lengths within the peptide andmethanol, allowing a timestep of 2 fs. A twin-range cutoffof 0.8/1.4 nm was used for nonbonded interactions. TheSETTLE algorithm42 was used to constrain the bondlengths and the bond angle in water. All simulations andanalyses were performed using the GROMACS softwarepackage.43,44 To initiate the simulations, the system wasfirst energy minimized. The solvent was then relaxed bysimulating the system with the peptide positionally re-strained (50 ps for systems solvated in water, and 100 psfor systems solvated in methanol solution). The wholesystem was then slowly heated over a period of 5 ps from50 K (initial velocities taken from a Maxwell distribution)to the target temperature. The system was then furtherequilibrated for 50 ps for systems in water and 150 ps forsystems in methanol solution. New initial velocities wherethen generated at the target temperature to initiate thesimulations used for acquisition data. According to Ser-rano,Lopez de la Paz et al.,27 it would be expected thatmutant LLM has higher population of �-sheet with respectto other mutants both in water and in methanol solution;therefore, additional simulations of this mutant wereperformed. These simulations were started from the sameinitial structure but with different sets of initial velocities.A summary of the simulations performed is given in TableII.

An additional test was performed to check the effect ofour MD protocol on the conformational behavior observed.A trajectory of the LLM mutant (40 ns) was performedusing a reaction-field scheme for the electrostatics. Afterthe first 8 ns of the trajectory, the secondary structure islost and never recovered again. This result gave us confi-dence in that the trajectories are mimicking the solutionbehavior of the peptides but not simulation artifacts.

TABLE I. Sequence of Betanova and mutantsa as designedby Serrano, Lopez de la Paz, and Coworkers27

Peptide Sequence (mutations are showed in bold)

Betanova NH3� RG - WSVQNGKYTNNGKTTE - GR COO-L12 NH3� RG - WSVQNGKYTLNGKTTE - GR COO-F12 NH3� RG - WSVQNGKYTFNGKTTE - GR COO-LLM NH3� RG - WSLQNGKYTLNGKTME - GR COO-aThe first two mutants have a mutation Asp12Leu (L12) and Asp12Phe(F12). The third mutant has a triple-point mutation Va15Leu,Asp12Leu, and Thr17Met (LLM). The solvent, temperature, andlength of each simulation are reported in Table II.

736 P. SOTO AND G. COLOMBO

Analysis of the TrajectoriesStructural properties

The positional root-mean-square deviation (RMSD) ofatoms was calculated after fitting the nth structure (Rn) tothe reference structure (Rref), subsequently calculatingthe RMSD via the equation

RMSDRn, Rref� � �1N�

k1

N

Rnk � Rrefk�2, (1)

where Rnk and Rrefk represent the Cartesian vector of thekth atom (backbone atoms of residues 3–18) of structures nand ref, respectively.

Cluster analysis

A series of nonoverlapping clusters of structures wereobtained as described by Daura et al.45 by calculating thebackbone RMSD between all pairs of structures (sampledevery 0.04 ns) after a best fit rotation. Then, the structurewith the largest number of neighbors that satisfy thecondition RSMD � 0.08 nm (considered the central struc-ture of the cluster) was taken, together with the neighbors,to form the (first) cluster and eliminated from the pool ofstructures. This process was repeated until the pool ofstructures was empty.

Secondary structure

Elements of secondary structure were calculate accord-ing to the DSSP algorithm.46

Side-chain contacts

For each conformation defined according to DSSP crite-ria, contacts between the side-chains of 2 nonadjacentresidues were defined to exist if the average distancebetween the center of mass of the respective side-chainswas less than 0.65 nm. “Hydrophobic contacts” correspondto contacts between residues that form the hydrophobiccluster of Betanova, that is, residues 3, 5, 11, 12, and 17,according to Serrano, Lopez de la Paz et al.27

RESULTS AND DISCUSSION

In Figure 2, the secondary structure as a function oftime, as defined by the DSSP criteria for a simulation ofBetanova in water, is shown. This simulation of 100 ns inlength is a continuation of the simulation 280 B of Colomboet al.32 Various snapshots from the trajectory are shownabove the plot. It is clear that while there is intermittentformation of hairpin-like structures, the triple-strandedstructure is only observed in the initial period of thesimulation. This suggests that the previous simulationsreported by Colombo et al. are dominated by the startingconfiguration, and the conclusions based on those simula-tions in regard to the stability of Betanova are unreliable.In particular, while many of the configurations sampled inthe trajectories contain �-sheets, a rich variety of otherstructures is also evident.

Based on Betanova alone, it is difficult to draw definitiveconclusions in regard to the structure of the peptide insolution based either on experiment or simulation studies.For this reason Serrano and coworkers used the predictionalgorithm PERLA28 with an idealized triple-stranded struc-ture for Betanova as a target to propose both single andmultiple mutations that either enhanced or reduced thestability of the peptide27 (see Fig. 1). The relative stabilityof the different mutants was determined based primarilyon H� chemical shifts of residues Lys9, Tyr10, and Thr11of the different peptides in water and in methanol solutionwith respect to a set of reference sequences that wereconsidered to be completely unfolded or completely folded.In particular, the peptides in which Asn12 is substitutedby Phe or Leu were judged more stable than Betanova, aswere the 3 triple mutants investigated—LLM, YLM, andFLM. It was also argued that at least for the peptide LLM,the combination of the NOEs observed in water andmethanol are consistent with the formation of an antipar-allel, three-stranded �-sheet.

Figure 3 shows the secondary structure as a function oftime for 2 simulations of the LLM mutant in water. The 2simulations, LLMw-A and LLMw-B, vary only in theinitial velocities yet show dramatically different behavior.In LLMw-A (upper DSSP plot in Fig. 3), the triple-stranded �-sheet conformation is essentially maintainedfor the first 75 ns of the simulation. There are neverthelessshort (�10 ns) periods during which there is loss andreformation of the first or second hairpin. Comparing thefirst 100 ns of this simulation to that of Betanova in water(Fig. 2), it would be easy to conclude that the LLM mutantwas the more stable. However, continuing the simulationto 200 ns, we see that once fully lost, the triple-strandedstructure is not recovered (within 200 ns). We also see thatthe secondary structure elements that form do not neces-sarily correspond to subsets of the triple-stranded confor-mation. This is illustrated by the structures shown inFigure 3. For example, between 130 ns and 170 ns, there isa region of parallel, as opposed to antiparallel, �-sheetinvolving residues 3, 4, 13, and 14. During the last 5 ns ofthe trajectory, there is a region of �-sheet involving the N-and C-termini, and for a short period at around 190 ns, aseries of residues form a transient tight turn and arerecognized by DSSP as �-helix. In the simulation LLMw-B,

TABLE II. Summary of Total Simulation Times for MDSimulations of Betanova and Mutants in Explicit Solvent

(Either Water or Methanol Solution) at T � 280 K

Solvent PeptideTotal Simulation

Time [ns]

SPC water Betanova 100L12 20F12 20LLM (LLMw-A) 200LLM (LLMw-B) 100LLM (LLMw-C) 100

40% methanol Betanova 20L12 20F12 20LLM (LLMm-A) 100LLM (LLMm-B) 100


in contrast (lowest DSSP plot in Fig. 3), there is an almostimmediate loss of the triple-stranded conformation, and atno point in this simulation are any elements of secondarystructure stable for an extended period. Similar behaviorwas observed in the simulation LLMw-C (data not shown).Two other mutants, L12 and F12, were also examined.

However, in none of the simulations performed did thepeptide adopt a single stable secondary structure pattern.

Figure 4 shows the number of clusters as a function ofsimulation time for the trajectories in water. The moststriking feature of this graph is the obvious difference inthe number of clusters obtained in the different trajecto-

Fig. 2. A plot of the secondary structure as determined using the DSSP algorithm for the 100-ns trajectoryof Betanova. Structures are depicted at different times, from left to right: t 4.92 ns; t 24.12 ns; and t 81.68ns.

Fig. 3. A plot of the secondary structure as a function of time for the 200-ns trajectory LLMw-A and 100-ns Trajectory LLMw-B. Structures aredepicted at different times for LLMw-A, from left to right: t 36.12 ns; t 87.72 ns; t 130.58 ns; and t 193.63 ns.


ries. For example, after 100 ns, LLMw-B and LLMw-Chave more than twice the number of clusters as LLMw-A.This is an indication of statistical variation between thetrajectories, which were all started from the same initialconfiguration. This suggests that a single short trajectorywill never be representative of the conformational behav-ior of this type of peptide. It is also evident that thenumber of clusters of each trajectory increases almostlinearly with time. This indicates that even the longesttrajectory LLMw-A (200 ns) does not sample all relevantregions of conformational space. The 3 dominant clustersare almost equally populated after 200 ns, roughly 10%each, indicating that the free energy surface is compara-tively flat, and that the barriers between the conforma-tions can be easily overcome during the simulations. Theclusters do exhibit elements of secondary structure: Themost populated cluster corresponds to an arrangement ofparallel �-sheets between residues 3, 4, 13, and 14. This isillustrated in Figure 3, where the structure at t 130.58ns corresponds to the central member of the first mostpopulated cluster. The second and third most populatedclusters correspond to a triple-stranded antiparallel�-sheet. These have a population of less than 10% each.The structure at t 36.12 ns in Figure 3 corresponds to thecentral member of the second most populated cluster.Since these structures were identified as belonging todifferent clusters, it is evident that the backbone can adoptdifferent conformations even when the overall pattern ofsecondary structure is the same.

The distribution of the backbone RMSD values of eachtrajectory with respect to the central member of the mostpopulated cluster of that trajectory was also calculated.From this, it could be seen that each trajectory sampleddistinct regions of configurational space. This is alsoillustrated in Figure 5, which shows the RMSD matrix for

the combined trajectory of LLM in water (in total, 400 ns).The maximum difference in RMSD between any twoconformations is 0.95 nm. Figure 5 shows that althoughhaving the same initial configuration, each simulationevolves toward very different states. Structures between90 ns and 100 ns in trajectory LLMw-B, for example, havea RMSD value of 0.9 nm with respect to the structuresbetween 1 ns and 75 ns of trajectory LLMw-A. There is alsoconsiderable variation between structures sampled intrajectory LLMw-B and in trajectory LLMw-C, with theRMSD values between them being, on average, higherthan 0.3 nm. Periods during which the 3 simulationsconverged were also observed, as indicated by the presenceof off-diagonal blocks of low RMSD values.

Overall, it is clear that neither reversible folding nor, infact, any specific preferred conformation could be reliablyidentified even with sampling on a 400-ns timescale for theLLM mutant. This makes it impossible to fully character-ize the thermodynamics of this peptide using classical MDsimulation and must call into question some of the resultsof simulations reported previously. For example, Bursu-laya and Brooks31 based their conclusion that the triple-stranded conformation proposed by Serrano and cowork-ers was close to the global free energy minimum in theCHARMM force field on a single 2 ns trajectory of the“folded” state. This suggests that their work led to anoverestimation of the stability of the peptide and was apoor representation of the behavior of the peptide insolution. It is also very clear that the free energy landscapeas a whole must be even flatter than that initially pre-dicted.

The fact that the sampling achieved, even within 200 ns(our longest continuous simulation), is still extremelylimited imposes severe restrictions on any comparisonwith experimental data, since the populations obtained for

Fig. 4. The number of clusters as a function of the simulation length for the trajectories in water.


specific conformations are not statistically reliable.3 Forexample, an attempt was made to relate the distancesbetween specific pairs of protons during the simulationsusing �r�3��1/3 and �r�6��1/6, averaging to experimentallyobserved NOE intensities obtained by NMR in the mostrecent work of Serrano, Lopez de la Paz et al.27 However,significantly different results were obtained for the differ-ent trajectories. The degree of sampling that could beachieved in the simulations is simply insufficient to repre-sent adequately the time- and ensemble-averaging inher-ent in the experimental data. An attempt to relate otherNMR observables such as J-coupling constants and chemi-cal shifts to the results of the simulations was also made.In each case, the uncertainty in the experimental data, theuncertainty in calculating the property of interest, and thestatistical noise in the trajectories meant that reliableconclusions in regard to whether the ensemble sampled inthe trajectories was in fact a reasonable representation ofthe peptide in solution could not be made. This also meansthat the results of Colombo et al.32 that showed broadagreement between experimentally observed NOE intensi-ties and average interproton distances must be ques-tioned. It is likely that the observed agreement reflects thefact that the systems were still biased by the startingconfigurations.

Although it is not possible to make a direct comparisonbetween the simulations and the available NMR data, the

observation from the simulations that Betanova and themutants show fluctuations in secondary structure is inqualitative agreement with the conclusions of severalrecent experimental studies. For example, Boyden andAsher26 examined the temperature dependence of the UVRaman spectra of Betanova in solution. They concludedthat between 276 and 355 K, the structure of Betanovamight best be described as a molten globule, and that itdoes not show a two-state cooperative folding mechanism.Ansari and coworkers25 interpreted the results of a combi-nation of measurements as indicating that the peptideexists as an ensemble of conformations at all temperaturesand denaturant concentrations, with no significant freeenergy barrier separating the “folded” and “unfolded”conformations.

From the above discussion, it is clear that it is notpossible to characterize thermodynamically the overallfolding behavior of Betanova or its mutants based on thecurrent simulations. The simulations are simply too shortto sample a representative fraction of configurationalspace. What is evident is that there are localized elementsof secondary structure that reoccur in the simulations.Four distinct elements of secondary structure could beidentified (see Tables III and IV): (1) a triple-stranded,antiparallel �-sheet involving residues 3–17; (2) a �-hair-pin (�-hairpin 1) starting at residues 3, 4, or 5 and endingat residues 10, 11, or 12, with a turn involving residues

Fig. 5. RMSD matrix of the combined trajectory of LLM in water.


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6–9; (3) a �-hairpin (�-hairpin 2) starting at residues 10 or11 and ending at residues 16, 17, or 18, with a turnbetween residues 13 and 14; and (4) a segment of parallel�-sheet between residues 3, 4, 13, and 14 (found only in thesimulation LLMw-A).

To illustrate the behavior of specific regions of thesequence, an RMSD matrix for selected residues of thetemplate structure was calculated for the combined trajec-tory of LLM in water (see Fig. 6). Each group of residueswas chosen based on the initial assumptions of Serranoand coworkers.24 Residues 3–6 (fragment 1) correspondsto the first strand of an ideal triple-stranded antiparallel�-sheet, residues 9–12 (fragment 2) to the second strand,and residues 15–18 (fragment 3) to the third strand. It hasbeen already shown that, in the simulations, only a smallpercentage of the overall population of structures corre-sponds to this specific secondary structure definition.However, the experimental evidence for claiming the LLMmutant has a high propensity to form a triple-stranded�-sheet ( 46% in water) was based on the backbonechemical shift values of residues of the central strand,which are primarily determined by local geometry. Forfragment 1, the majority of the RMSD values are below 0.2nm. Fragment 2 has relatively low RMSD values forLLMw-A and LLMw-C (below 0.25 nm), but in the case ofLLMw-B, the RMSD values go up to 0.3 nm. Fragment 3shows a slightly different pattern: The RMSD values are 0.3 nm for the structures of LLMw-B and LLMw-Ccompared to those in trajectory LLMw-A that exhibittriple-stranded conformation, suggesting a considerabledeviation of this fragment from the triple-stranded geom-etry. On the other hand, the RMSD values are below 0.15nm for the first 150 ns of LLMw-A, indicating thatflexibility in these structures might depend on the confor-mation of fragment 2. Another interesting feature is thatstructures between 160 ns and 190 ns of LLMw-A have lowRMSD values when compared to LLMw-B and LLMw-C,which may be evidence that for certain conformations,fragment 3 is conformationally restricted, while fragments1 and 2 are more mobile.

Serrano, Lopez de la Paz et al.27 proposed that therelative stability of the mutants of Betanova is determinedmainly by 3 factors: (1) the intrinsic backbone turn propen-sities; (2) the extent of van der Waals contacts betweenaliphatic and aromatic side-chains in the well-orderedregions of the structure; and (3) medium-range electro-static interactions in the less ordered regions of thestructure. To gain further insight in this issue, side-chaincontacts were calculated for each set of structures thatexhibit similar secondary structure elements as defined bythe DSSP algorithm (see Table III for trajectories in water,and Table IV for trajectories in methanol solution). Facingand diagonal (interstrand) interacting residues are de-fined following the template of a triple-stranded, antiparal-lel �-sheet suggested for Betanova (see Serrano and cowork-ers, Fig. 1A24 and Fig. 7 in this article). Facing residuesare residues that face each other between strands accord-ing to the template in Figure 1A.24 Diagonal residues areresidues that are in relative diagonal orientation betweenfacing strands, according to the template in Serrano and

Fig. 6. RMSD matrix of each fragment of the structure of the mutantLLM: (a) fragment 1 corresponds to residues 3, 4, 5, and 6; (b) fragment 2corresponds to residues 9, 10, 11, and 12; and (c) fragment 3 corre-sponds to residues 15, 16, 17, and 18. The calculation was performed forthe combined trajectory of LLM in water. The pattern of RMSD valuesdiffers for each fragment and shows that the 3 segments are highlyflexible. There is no clear correlation between the flexibility of the fragmentand the presence of elements of secondary structure.


coworkers’ Figure 1A.24 In general, it is observed from thesimulations that both hydrophobic and electrostatic side-chain interactions between facing or diagonal interactingresidues are present in each of the conformations. Never-theless, no clear relationship between the number ofside-chain contacts and either the mutation itself or thesolvent environment was found.

For the triple-stranded conformations, it was found thatthe total number of side-chain contacts varies between 7(for F12 in water, only 1 hydrophobic contact was found)and 9 (for LLM in water, 4 hydrophobic contacts), and thatthere are two pairs of facing interacting side-chains:hydrophobic contact between residues 5 and 10, andelectrostatic interaction between residues 11 and 16. Par-ticularly for the triple-stranded conformation of F12 inwater, there is a network of electrostatic interactionsbetween facing residues 4 and 11, 11 and 16, and 9 and 18,and between residues 6 and 11, and 9 and 16, in diagonaldisposition. The other triple-stranded conformations showdiagonal interactions between residue pairs 3 and 10, 3and 17, and/or 12 and 17, which builds a network ofinteractions that connects the whole structure.

For �-hairpin 1–like conformations, the total number ofside-chain contacts varies between 2 (for LLM in methanolsolution, 1 hydrophobic contact) and 6 (for Native in water,2 hydrophobic contacts). In this case, it is not possible toidentify common features between similar conformations.For �-hairpin 2–like conformations, which were found onlyin the trajectories in methanol solution, the total numberof side-chain contacts varies between 3 (for LLM, no

hydrophobic contacts) and 10 (for Native, 4 hydrophobiccontacts). The conformation without hydrophobic contactsexhibits 2 pairs of side-chains that interact electrostati-cally: residues 9 and 16 in diagonal disposition, andresidues 11 and 16, facing each other.

These observations imply that similar networks of back-bone hydrogen bonds can be stabilized by different, nonspe-cific networks of side-chain interactions. This is in contrastto previous studies of �-hairpins, where the role of diago-nal interactions and their relation to the hydrophobiccluster was highlighted.16 Triple-stranded conformationswill be stabilized both by hydrophobic and electrostaticinteractions of side-chains paired either diagonally orfacing each other. �-Hairpin 1–like conformations mightbe intrinsically more stable (the design of Betanova wasbased on a hairpin 1 template24) so that the side-chainshave more freedom to arrange; thus, the network ofinteractions is less specific. On the other hand, �-hairpin2–like conformations require more specific side-chain inter-actions, since the template backbone has not been provedexperimentally to be stable. Yet no clear evidence is foundto contrast with the hypothesis proposed by Serrano,Lopez de la Paz et al.27

Side-chain packing observed in the trajectories is consis-tent with Betanova being predominantly compact butpoorly structured.25,27 For example, in the 100-ns trajec-tory started from the NMR-based model of Betanova,around 30% of the trajectory does not contain secondarystructure elements as defined by the DSSP algorithm,even though the radius of gyration is on average only 0.75

Fig. 7. Scheme that follows the template used for Betanova.24 Residues that have been mutated aremarked with an “x.” The definition of facing and diagonal side-chain contacts follows the geometry heresuggested. As an example, facing (dash-dot-dotted line) and diagonal (dashed line) contacts for residue T11are depicted.


nm and both hydrophobic contacts (residues 3 and 10), andelectrostatic interactions (residues 4 and 11, and 9 and 18)are present throughout the whole trajectory. In the 400-nscombined trajectory of mutant LLM, more than 50% of thestructures do not exhibit secondary structure. In solution,Betanova and the mutants investigated rapidly intercon-vert between a range of conformations that are stabilizedby a delicate balance between hydrophobic and electro-static interactions. Structural fluctuations can easily bringthe structure to a compact conformation, whose backboneno longer spans the network of hydrogen bonds thatcharacterizes elements of �-sheet secondary structure, anobservation in good qualitative agreement with experimen-tal studies25 that suggest that the structure is compact butpoor in �-sheet content.

CONCLUSIONS

Our MD simulation studies suggest that Betanova andmutants in solution are best described in terms of anensemble of different conformations in equilibrium. Theconfigurations sampled do not correspond strictly to well-defined secondary structure elements but are in generalcompact structures with a folded backbone, extensivehydrogen-bonding networks, and a diverse range of side-chain packing. The conformations are stabilized both byhydrophobic and electrostatic side-chain interactions. Theside-chain–side-chain interactions maintain the structurecompactness and cause the backbone to twist. Theseobservations are consistent with the most recent experi-mental observations, which suggest that Betanova-likepeptides are intrinsically flexible, and that the idealtriple-stranded geometry is only transiently populated.

It is clear, however, that any conclusions in regard to theprecise behavior of Betanova in solution based on thesesimulations must be made cautiously. Even on the ex-tended timescales investigated in this study, it has notbeen possible to accumulate enough statistics to determinethe relative populations of even the most readily accessiblestates with much certainty. At least for this system,extracting reliable thermodynamic data from simula-tions � 1 �s is not possible.

ACKNOWLEDGMENTS

Our thanks to Prof. Alan E. Mark for very insightfuldiscussions, and to Drs. L. Serrano and M. Lopez de la Paz forhelpful discussions to understand the experimental data.

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Documents

Characterization of the conformational space of a triple-stranded β-sheet forming peptide with molecular dynamics simulations