University of Groningen

Peptide folding in non-aqueous environments investigated with molecular dynamicssimulationsSoto Becerra, Patricia

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Chapter 3

3 Is it possible to reliably sample the accessibleconformational states of peptides? Case study: Betanovaand mutants

Based on: Patricia Soto, Giorgio Colombo, Alan E. Mark. *Characterization of theconformational space of a triple stranded β-sheet forming peptide with molecular dynamicssimulations To be submitted to Proteins.

Abstract

Molecular Dynamics (MD) simulations have been performed on a series of mutants of the 20amino acid peptide Betanova in order to critically assess the ability of MD simulations toreproduce the folding and stability of small β-sheet forming peptides on currently accessibletime scales. Simulations were performed in both water and in 40% methanol solution usingan explicit solvent model. The simulations suggest that all mutants adopt a wide range ofconformations in solution, that the structures are highly flexible and that stabilization ofcompact structures is due to a delicate balance of hydrophobic and polar side chaininteractions. Simulations longer than 100ns, although not sufficient for a completethermodynamic and kinetic description of the system, sample an ensemble of compactconformations characterized by the loss of ordered β-sheet secondary structure. Thissuggests that no significant free energy barrier separates the different conformationsavailable.

25

Peptide folding in non-aqueous environments

3.1 Introduction

Understanding protein folding lies at the heart of protein design techniques. However, beforewe can hope to understand the process of folding in whole proteins we must be able tocharacterize the kinetics and thermodynamics of folding in simple model systems. Thedifficulty is that although much has been learnt in regard to peptide folding via experimentalstudies few if any experimental techniques can be used to follow the process of folding inindividual molecules at atomic resolution.5,94 Molecular Dynamics (MD) simulations incontrast hold the promise of being able to follow the process of folding of individualmolecules in atomic detail. Simulations of protein or peptide folding require, however, that itis possible to follow a system for an appropriate time-scale and sample configurationalspace with appropriate weights. In principle MD simulations are ergodic and shouldeventually sample all the available conformational space with Boltzmann weights. However,in practice, with current computational resources, it is only possible to sample a fewlocalized basins in the free energy surface or, to diffuse over the surface sampling a smallregion of the available conformational space at random. Where the potential energy surfaceis characterized by a limited number of low energy conformations in rapid equilibrium (onthe MD time scale), adequate sampling of the thermodynamically relevant regions ofconformational space can be achieved. In such cases MD simulations have provided highlydetailed information on the nature of alternative states in solution and the dynamics ofspontaneous folding-unfolding.95,125 However, such cases are rare and despite dramaticimprovements over recent years in simulation codes and computer capacity, the ability tosample the time scales relevant to understanding the behavior of biomolecules is extremelylimited. This is especially problematic in the case of in silico protein (un)foldingsimulations.

To date the most successful simulation studies of folding and stability have involved theformation of α-helices. Helices primarily involve local interactions within the polypeptidechain and experimentally are known to fold on a nanosecond time scale,96 which is readilyaccessible in MD simulations. Simulations have provided information on the initial stagesof helix formation including the timescale on which the first helical turn forms and breaks,the energetics of helix formation97 and the nature of possible intermediate states.Nevertheless, the dependence of the mechanism on the force field used remains a seriousissue and except in those cases where repeated folding-unfolding transitions could beobserved, conclusions concerning possible folding intermediates and folding pathways muststill be questioned.

Compared to helix formation, β-sheet formation is more complex. The physical interactionsthat determine the geometry and stability of a β-sheet are non-local and poorly understood.98

In addition, β-hairpins have proved difficult to study experimentally primarily due to theirtendency to aggregate. Nevertheless, β-sheet forming peptides are the subject of intense

26

Chapter 3

research, due to their importance in amyloid fibril formation, a factor in wide variety ofpathological disorders.99,100 Peptides obtained from proteins101,102 or from de novodesign103,104,105 which adopt stable folded structures in solution have been isolated andcharacterized using NMR, fluorescence and other spectroscopic techniques. Critical forsimulation studies, experimental kinetic studies indicate that β-hairpins have folding times inthe range of several microseconds, much longer than the respective helix folding times.Nevertheless, a wide range of computational studies of β−turn as well as β−hairpin formingsequences have been performed in an attempt to address different aspects of the thesesystems, such as β-hairpin formation and hydrophobic interactions,106 stability,107,108

equilibrium distributions,109,110,111 free energy landscapes25 and co-solvent effect on therelative stability of model peptides.112

Triple stranded antiparallel β-sheet peptides, as a next step in complexity from β-hairpins,have also been studied in an attempt to address the problem of how extended β-structuresform and whether a pre-organized β-hairpin motif acts as a template for the interaction of thethird strand.113 The nature of the folded state in solution and the degree of cooperativityduring folding remain issues of debate in these peptides. Betanova,114 a 20-residue peptidedesigned by Serrano and co-workers based on a three-stranded anti-parallel β-sheet template,was suggested to display apparent cooperative two-state folding behavior in chemical andthermal denaturation studies thus making it an attractive model to study folding. Betanovahas also been analyzed by Ansari and coworkers124 who attempted to characterize theconformation and equilibrium folding and unfolding of Betanova using circular dichroism(CD), infrared measurements and FRET techniques. In contrast, they concluded thatBetanova samples an ensemble of compact conformations but did not fold cooperatively. Asimilar conclusion was proposed by Asher and coworkers115 using UV resonance Ramanspectroscopy (UVRR). As an extension of their earlier work, Serrano and co-workers haverecently designed and synthesized a series of mutants of Betanova to demonstrate theirability to rationally alter the stability of the molecule.123 With the backbone of Betanova asstructural template the protein design algorithm PERLA (Protein Engineering RotamerLibrary Algorithm)116 was used to propose both single and multiple mutations that eitherenhanced or reduced the stability of the peptide (see figure 3.1). Changes in the populationof the β-sheet containing conformers of Betanova and mutants were assessed using NMRspectroscopy and far-UV circular dichroism (assuming a two-state model).

27

Peptide folding in non-aqueous environments

Figure 3.1

Average NMR structure of Betanova.114 Residues that were mutated123 are highlighted.

Simulation studies have also been used to analyse the free energy landscape of triplestranded antiparallel β-sheets. Wang and Sung117 studied the folding of three triple-strandedanti-parallel β-sheet peptides (including Betanova) with an all-atom representation of theprotein, a solvent-reference potential and simulation length of 100ns each. According totheir results, the experimentally observed peptide structure may include an ensemble of β-sheet structures. Caflish and coworkers22 performed simulations, in implicit solvent, whichreached the defined folded state of each peptide from different starting conformations butonly in high temperature simulations. In these two studies, the conformational space of thefolded state of the peptide, though simulated for 100 or 200ns, was likely incompletelyexplored because some features, like conformational flexibility, might not be successfullyreproduced by the implicit solvent simulations.

The existing experimental and simulation studies of the folding behavior of Betanova leavesmany open questions unanswered. The system also provides the opportunity to criticallyaddress whether MD simulations can correctly reproduce the conformational behavior ofhighly flexible β-sheet forming peptides. In this study we attempt to investigate thedistribution of the populations sampled during the simulations and the factors that affectstability and flexibility of Betanova and some of the proposed mutants.

28

Chapter 3

3.2 Methods

3.2.1 MD Simulations

In total eleven simulations were performed and analyzed. The parameters used forsimulations of Betanova in water are described by Colombo et al.118 In the protocol to setupthe simulations the only difference respect to this work is that Colombo et al used NVTconditions for the production runs while here NPT conditions were used. The simulations ofBetanova in methanol solution and the mutants of Betanova (see Table 3.1) in water and inmethanol solution were performed as follows: The initial structure for the simulations of thenative Betanova in methanol was the average NMR structure provided by Serrano andcoworkers.114 The initial structures used in the simulations of the various mutants weregenerated from the average NMR structure of Betanova using the software WHATIF.119 Thepeptides were protonated to give a zwitterionic form (with N-terminal NH3

+ and C-terminalCOO- group) in line with the experimental conditions (pH 5.0) at which the peptides werestudied. The total charge on the peptide was +3. The peptide was then solvated in explicitSPC water75,76,77 or SPC water with 40% methanol in line with the experimental conditions.The simulations were performed using periodic boundary conditions in truncated octahedralbox with the minimum distance between the solute and the wall of the box being initially 0.8nm. All simulations were performed using the GROMOS96 43A1 forcefield.65,66 Thetemperature was maintained close to the intended value by weak coupling to an externaltemperature bath83 with a coupling constant of 0.1 ps. In the same way, the density of thesystem was adjusted by weak coupling to an external pressure bath83 (P0 = 1 bar, couplingtime tp = 1.0 ps). The LINCS algorithm84 was used to constrain bond lengths within thepeptide and methanol, allowing a time step of 2 fs. A twin-range cut-off of 0.8/1.4 nm wasused for non-bonded interactions. The SETTLE algorithm120 was used to constrain the bondlengths and the bond angle in water. All simulations and analysis were performed using theGROMACS software package.85,86 To initiate the simulations, the system was first energyminimized. The solvent was then relaxed by simulating the system with the peptidepositionally restrained (50 ps for systems solvated in water and 100 ps for systems solvatedin methanol solution). The whole system was then slowly heated over a period of 5 ps from50 K (initial velocities taken from a Maxwell distribution) to the target temperature. Thesystem was then further equilibrated for 50 ps for systems in water and 150 ps for systems inmethanol solution. New initial velocities where then generated at the target temperature toinitiate the simulations used for acquisition data. According to Serrano and coworkers,123 itwould be expected that mutant LLM has higher population of β-sheet respect to othermutants both in water and in methanol solution, therefore additional simulations of thismutant were performed. These simulations were started from the same initial structure butwith different sets of initial velocities. A summary of the simulations performed is given inTable 3.2.

29

Peptide folding in non-aqueous environments

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-

Table 3.1

Sequence of Betanova and the mutants simulated. The first two mutants have a mutationAsp12Leu (L12) and Asp12Phe (F12). The third mutant has a triple point mutation Val5Leu,Asp12Leu and Thr17Met (LLM). The solvent, temperature and length of each simulationare reported in Table 3.2.

3.2.2 Analysis of the trajectories

Structural properties: The positional root mean square deviation (RMSD) of atoms wascalculated after fitting the nth structure (Rn) to the reference structure (Rref) subsequentlycalculating the RMSD via the equation

RMSD � R n , R ref � �65 1N�k � 1

N � R nk� R refk � 2

where Rnk and Rrefk represent the Cartesian vector of the kth atom (backbone atoms ofresidues 3 to 18 ) of structures n and ref, respectively.

Cluster Analysis: A series of non-overlapping clusters of structures were obtained asdescribed by Daura et al121 by calculating the backbone RMSD between all pairs ofstructures (sampled every 0.04ns) after a best fit rotation. Then, the structure with thelargest number of neighbors that satisfy the condition RSMD < 0.08nm (considered thecentral structure of the cluster) was taken together with the neighbors to form the (first)cluster and eliminated from the pool of structures. This process was repeated until the poolof structures was empty.

Secondary structure: Elements of secondary structure were calculate according to the DSSPalgorithm.122

Side chain contacts: For each conformation defined according to DSSP criteria, contactsbetween the side chains of two non-adjacent residues were defined to exist if the averagedistance between the center of mass of the respective side chains was less than 0.65 nm.'Hydrophobic contacts' correspond to contacts between residues that form the hydrophobiccluster of Betanova, that is, residues 3, 5, 11, 12 and 17 according to López et al.123

30

Chapter 3

Solvent Peptide Total simulation time[ns]

SPC water Betanova 100L12 20F12 20

LLM (LLMw-A) 200LLM (LLMw-B) 100LLM (LLMw-C) 100

40% methanol Betanova 20L12 20F12 20

LLM (LLMm-A) 100LLM (LLMm-B) 100

Table 3.2

A summary of the total simulation times for MD simulations of Betanova and mutants inexplicit solvent (either water or methanol solution) at T=280K.

3.3 Results and discussion

Betanova114 (NH3+ RG - WSVQNGKYTNNGKTTE - GR COO-) was designed by Serrano

and co-workers based on a triple stranded anti-parallel β-sheet template with four residuesper strand and two (natural) residues per turn. The residues from the third to the eighteenthposition were intended to form the desired structural motif and the RG-ends were included toavoid aggregation of the peptide and facilitate solubilisation in polar solvents. Betanovadisplays evidence of cooperative two-state folding behavior in chemical and thermaldenaturation studies and it was initially suggested that 80 to 90% of the molecules adopted atriple stranded β-sheet conformation at 278 K. As such Betanova was considered anattractive model with which to study folding114 computationally. In particular Brooks andcoworkers18 attempted to calculate a two-dimensional folding free energy landscape forBetanova by all atom MD simulations using umbrella sampling techniques and unfoldingconditions. They obtained a funnel-shaped landscape and proposed a folding pathway forBetanova. As part of this work they used the fact that Betanova remained as a triple strandedβ-sheet for 2 ns as "evidence" that the structure proposed by Serrano and coworkers was infact stable in solution. Colombo et al118 based on simulations an order of magnitude longer(4 x 20 ns) claimed in contrast that it was not possible to draw firm conclusions in regard tothe stability of Betanova from simulations as reversible folding could not be demonstrated.Instead they proposed that in solution Betanova sampled a range of conformations that

31

Peptide folding in non-aqueous environments

together could explain the available experimental data. We note that the structuralcharacterization of small peptides such as Betanova using NMR is non-trivial. Serrano andco-workers originally concluded that Betanova formed the desired structure based primarilyon the presence of long-range NOEs between the aromatic protons of Trp 3 and Cγ protonsof Thr 17 and corroborated by the large 3JNHα coupling constant values measured for β−strand residues.114 In their most recent work,123 however, these long range NOEs are nolonger reported and more importantly the β-sheet population of Betanova at 283 K has beenre-estimated based on the chemical shift of Hα Thr11 (∆δHα(Thr11)) to be 9% in water and20% in methanol solution. Taking instead the average of the Hα chemical shifts of Lys9,Tyr10 and Thr11 the estimated β-sheet populations are 8% in water and 26% in methanolsolution.123 These changes dramatically alter the conclusions in regard to the accuracy of theprevious simulation studies. In particular it is clear that the triple stranded structure shouldnot be the dominant conformation in solution.

In figure 3.2, the secondary structure as a function of time as defined by the DSSP criteriafor a simulation of Betanova in water is shown. This simulation of 100 ns in length is acontinuation of the simulation 280 B of Colombo et al. Various snapshots from thetrajectory are shown above the plot. It is clear that while there is intermittent formation ofhairpin like structures the triple stranded structure is only observed in the initial period of thesimulation. This suggests that the previous simulations reported by Colombo et al aredominated by the starting configuration and the conclusions based on those simulations inregard to the stability of Betanova are unreliable. In particular while many of theconfigurations sampled in the trajectories contain β-sheet, a rich variety of other structuresare also evident.

Based on Betanova alone it is difficult to draw definitive conclusions in regard to thestructure of the peptide in solution based either on experiment or simulation studies. For thisreason Serrano and coworkers used the prediction algorithm PERLA116 with an idealizedtriple stranded structure for Betanova as a target to propose both single and multiplemutations that either enhanced or reduced the stability of the peptide123 (see figure 3.1). Therelative stability of the different mutants was determined based primarily on Hα chemicalshifts of residues Lys9, Tyr10 and Thr11 of the different peptides in water and in methanolsolution with respect to a set of reference sequences which were considered to be completelyunfolded or completely folded. In particular, the peptides in which Asn12 is substituted byPhe or Leu were judged more stable than Betanova as were the three triple mutantsinvestigated LLM, YLM, and FLM. It was also argued that at least for the peptide LLM thecombination of the NOE's observed in water and methanol are consistent with the formationof an antiparallel three-stranded β-sheet.

32

Chapter 3

Figure 3.2

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

Figure 3.3 shows the secondary structure as a function of time for two simulations of theLLM mutant in water. The two simulations, LLMw-A and LLMw-B vary only in the initialvelocities yet show dramatically different behavior. In LLMw-A (upper DSSP plot in figure3.3) the triple stranded β-sheet conformation is essentially maintained for the first 75 ns ofthe simulation. There are nevertheless short (<10 ns) periods during which there is loss andreformation of the first or second hairpin. Comparing the first 100 ns of this simulation tothat of Betanova in water (figure 3.2) it would be easy to conclude that the LLM mutant wasthe more stable. However, continuing the simulation to 200 ns we see that once fully lost thetriple stranded structure is not recovered (within 200 ns). We also see that the secondarystructure elements that form do not necessarily correspond to subsets of the triple strandedconformation. This is illustrated by the structures shown above in figure 3.3. For example,between 130 ns and 170 ns there is a region of parallel as opposed to parallel β-sheetinvolving residues 3, 4, 13 and 14. During the last 5 ns of the trajectory there is a region ofβ-sheet involving the N and C-termini and for a short period at around 190 ns a series ofresidues form a transient tight turn and are recognized by DSSP as α-helix. In the simulationLLMw-B in contrast (lowest DSSP plot in figure 3.3) there is an almost immediate loss ofthe triple stranded conformation and at no point in this simulation are any elements ofsecondary structure stable for an extended period. Similar behavior was observed in thesimulation LLMw-C (data not shown). Two other mutants L12 and F12 were alsoexamined. However, in none of the simulations performed did the peptide adopt a singlestable secondary structure pattern.

Figure 3.4 shows the number of clusters as a function of simulation time for the trajectories

33

Peptide folding in non-aqueous environments

in water. The most striking feature of this graph is the obvious difference in the number ofclusters obtained in the different trajectories. For example, after 100 ns, LLMw-B andLLMw-C have more than twice the number of clusters as LLMw-A. This is an indication ofstatistical variation between the trajectories which were all started from the same initialconfiguration. This suggests that a single short trajectory will never be representative of theconformational behavior of this type of peptide. It is also evident that the number ofclusters of each trajectory increases almost linearly with time. This indicates that even thelongest trajectory LLMw-A (200 ns) does not sample all relevant regions of conformationalspace. The three dominant clusters are almost equally populated after 200 ns, roughly 10%each, indicating that the free energy surface is comparatively flat and that the barriersbetween the conformations can be easily overcome during the simulations. The clusters doexhibit elements of secondary structure: the most populated cluster corresponds to anarrangement of parallel β-sheets between residues 3, 4, 13 and 14. This is illustrated infigure 3.3 where the structure at t = 130.58 ns corresponds to the central member of the firstmost populated cluster. The second and third most populated clusters correspond to a triplestranded antiparallel β-sheet. These have a population of less than 10% each. The structureat t = 36.12 ns in figure 3.3 corresponds to the central member of the second most populatedcluster. Since these structures were identified as belonging to different clusters, it is evidentthat the backbone can adopt different conformations even when the overall pattern ofsecondary structure is the same.

Figure 3.3

A plot of the secondary structure as a function of time for the 200 ns trajectory LLMw-Aand 100 ns trajectory LLMw-B. Structures depicted at different times for LLMw-A, fromleft to right: t = 36.12 ns, t = 87.82 ns, t = 130.58 ns, and t = 193.63 ns.

34

Chapter 3

Figure 3.4

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

The distribution of the backbone root mean square deviation (RMSD) values of eachtrajectory with respect to the central member of the most populated cluster of that trajectorywas also calculated. From this it could be seen that each trajectory sampled distinct regionsof configuration space. This is also illustrated in figure 3.5 which shows the RMSD matrixfor the combined trajectory of LLM in water (in total, 400 ns). The maximum difference inRMSD between any two conformations is 0.95 nm. Figure 3.5 shows that although havingthe same initial configuration each simulation evolves towards very different states.Structures between 90 ns and 100 ns in trajectory LLMw-B, for example, have a RMSDvalue of ~0.9 nm with respect to the structures between 1 ns and 75 ns of trajectory LLMw-A. There is also considerable variation between structures sampled in trajectory LLMw-Band in trajectory LLMw-C with the RMSD values between them being on average, higherthan 0.3 nm. Periods during which the three simulations converged were also observed, asindicated by the presence of off-diagonal blocks of low RMSD values.

Overall it is clear that neither reversible folding nor in fact any specific preferredconformation could be reliably identified even with sampling on a 400 ns timescale for theLLM mutant. This makes it impossible to fully characterize their thermodynamics of thispeptide using classical MD and must call into question some of the results of simulationsreported previously. For example, Brooks and coworkers based their conclusion that thetriple stranded conformation proposed by Serrano was close to the global free energy

35

Peptide folding in non-aqueous environments

minimum in the charmm force field on a single 2 ns trajectory of the "folded" state. Thisconfirmed what Brooks and coworkers expected and they had no reason to suspect that thesimulation lead to an overestimation of the stability of the peptide and was a poorrepresentation of the behavior of the peptide in solution. However, it is also very clear thatthe free energy landscape as a whole must be even flatter than that initially predicted.

Figure 3.5

RMSD matrix of the combined trajectory of LLM in water.

The fact that the sampling achieved even within 200 ns (our longest continuous simulation)is still extremely limited imposes severe restrictions on any comparison with experimentaldata since the populations obtained for specific conformations are not statistically reliable.95

For example an attempt was made to relate the distances between specific pairs of protonsduring the simulations using <r-3>-1/3 and <r-6>-1/6 averaging to experimentally observed NOEintensities obtained by NMR. However, significantly different results were obtained for thedifferent trajectories. The degree of sampling that could be achieved in the simulations issimply insufficient to represent adequately the time- and ensemble averaging inherent in theexperimental data. An attempt to relate other NMR observables such as J-coupling constantsand chemical shifts to the results of the simulations was also made. In each case theuncertainty in the experimental data, the uncertainty in calculating the property of interestand the statistical noise in the trajectories meant that reliable conclusions in regard towhether the ensemble sampled in the trajectories was in fact a reasonable representation ofthe peptide in solution could not be made. This also means that the results of Colombo et alwhich showed broad agreement between experimentally observed NOE intensities andaverage inter proton distances must be questioned. It is likely the observed agreementreflects the fact that the systems were still biased by the starting configurations.

36

Native L12 F12 LLM

Structure Triplestranded

β-hairpin 1 β-hairpin 1 Triplestranded

β-hairpin 1 β-hairpin 1 Triplestranded

β-hairpin 1 Parallel β-sheet

Residues 4 to 17 3 to 10 3 to 11 5 to 17 5 to 10 4 to 11 5 to 17 5 to 12 3, 4, 13,14

Turn 7 to 813 to 14

6 to 8 7 to 8 7 to 813 to 14

7 to 8 7 to 8 7 to 813 to 14

7 to 9

W3 - Y10 X X X X

W3 - x12 X X X X

W3 - x17 X

x5 - Y10 X X X X X X

x5 - x12 X X

x5 - x17

Y10 - x17

x12 - x17 X X

S4 - K9 X X

S4 - T11 X X X X X

Q6 - T11 X X X X

Native L12 F12 LLM

Q6 - T16 X

K9 - K15 X

K9 - T16 X X X

K9 - E18 X X

T11 - K15 X

T11 - T16 X X X X

W3 - T16

S4 - Y10 X

S4 - x12

x5 - K9 X

x5 - T11

Q6 - K9

Q6 - Y10 X X

K9 - x17 X X

Y10 - E18 X

T11 - x17 X

x12 - T16 X

Table 3.3

Side chain contacts for the simulations in water. Mutated residues are indicated with an "x" and the number of the residue.Contacts between the side chains of two non-adjacent residues were defined to exist if the average distance between the center ofmass of the respective side chains was less than 0.65 nm.

Native L12 F12 LLM

Structure Triplestranded

β-hairpin 2 β-hairpin 2 β-hairpin2

Triplestranded

β-hairpin 2 β-hairpin 1 β-hairpin 2 β-hairpin 1 β-hairpin 1

Residues 4 to 16 11 to 16 11 to 16 10 to 18 3 to 16 10 to 17 5 to 10 11 to 16 3 to 12 6 to 12

Turn 7 to 813 to 14

13 to 14 13 to 14 13 to 14 7 to 813 to 14

13 to 14 7 to 8 13 to 14 7 to 8 8 to 10

W3 - Y10 X X X X X X

W3 - x12 X X X

W3 - x17 X X X X

x5 - Y10 X X X X X X X

x5 - x12

x5 - x17 X

Y10 - x17 X

x12 - x17 X X X X X X

S4 - K9

S4 - T11 X X X X X

Q6 - T11 X X X X X

Q6 - T16

K9 - K15

K9 - T16 X X X X X

K9 - E18

Native L12 F12 LLM

T11 - K15

T11 - T16 X X X X X X X

W3 - T16 X

S4 - Y10

S4 - x12 X

x5 - K9

x5 - T11 X

Q6 - K9 X

Q6 - Y10

K9 - x17

Y10 - E18

T11 - x17 X X

x12 - T16

Table 3.4

Side chain contacts for the simulations in methanol solution. Mutated residues are indicated with an "x" and the number of theresidue. Contacts between the side chains of two non-adjacent residues were defined to exist if the average distance between thecenter of mass of the respective side chains was less than 0.65 nm.

Chapter 3

Although it is not possible to make a direct comparison between the simulations and theavailable NMR data, the observation from the simulations that Betanova and the mutantsshow fluctuations in secondary structure is in qualitative agreement with the conclusions ofseveral recent experimental studies. For example, Asher and coworkers115 examined thetemperature dependence of the UV Raman spectra of Betanova in solution. They concludedthat between 276 and 355 K the structure of Betanova might best be described as a moltenglobule and that it does not show a two-state cooperative folding mechanism. Ansari andcoworkers124 interpreted the results of a combination of measurements as indicating that thepeptide exists as an ensemble of conformations at all temperatures and denaturantconcentrations, with no significant free energy barrier separating the "folded" and"unfolded" conformations.

From the above discussion it is clear that it is not possible to characterize thermodynamicallythe overall folding behavior of Betanova or its mutants based on the current simulations.The simulations are simply too short to sample a representative fraction configurationalspace. What is evident is that there are localized elements of secondary structure whichreoccur in the simulations. Four distinct elements of secondary structure could be identified(see Table 3.3 and Table 3.4): i) a triple stranded antiparallel β-sheet involving residues 3 to17, ii) a β-hairpin (1) starting at residues 3, 4 or 5 and ending at residues 10, 11 or 12, with aturn involving residues 6 to 9, iii) a β-hairpin (2) starting at residues 10 or 11 and ending atresidues 16, 17 or 18, with a turn between residues 13 and 14, and iv) a segment of parallelβ-sheet between residues 3, 4, 13 and 14 (found only in the simulation LLMw-A).

To illustrate the behavior of specific regions of the sequence a RMSD matrix for selectedresidues of the template structure was calculated for the combined trajectory of LLM inwater (see figure 3.6). Each group of residues was chosen based on the initial assumptionsof Serrano and coworkers.123 Residues 3 to 6 (fragment 1) corresponds to the first strand ofan ideal triple stranded antiparallel β-sheet, residues 9 to 12 (fragment 2) to the secondstrand and residues 15 to 18 (fragment 3) to the third strand. It has been already shown thatin the simulations only a small percentage of the overall population of structures correspondsto this specific secondary structure definition. However, the experimental evidence forclaiming the LLM mutant has a high propensity to form a triple stranded β-sheet (~46% inwater) was based on the backbone chemical shift values of residues of the central strandwhich are primarily determined by local geometry. For fragment 1, the majority of theRMSD values are below 0.2 nm. Fragment 2 has relatively low RMSD values for LLMw-Aand LLMw-C (below ~0.25 nm), but in the case of LLMw-B the RMSD values go up to~0.3 nm. Fragment 3 shows a slightly different pattern: the RMSD values are higher than0.3 nm for the structures of LLMw-B and LLMw-C compared to those in trajectory LLMw-A that exhibit triple stranded conformation, suggesting a considerable deviation of thisfragment from the triple stranded geometry. On the other hand, the RMSD values are below0.15 nm for the first 150 ns of LLMw-A indicating that flexibility in these structures mightdepend on the conformation of fragment 2. Another interesting feature is that structures

41

Peptide folding in non-aqueous environments

between 160 ns and 190 ns of LLMw-A have low RMSD values when compared to LLMw-B and LLMw-C, which may be evidence that for certain conformations fragment 3 isconformationally restricted while fragments 1 and 2 are more mobile.

López de la Paz et al123 proposed that the relative stability of the mutants of Betanova isdetermined mainly by three factors: i) the intrinsic backbone turn propensities, ii) the extentof van der Waals contacts between aliphatic and aromatic side chains in the well orderedregions of the structure, and iii) medium-range electrostatic interactions in the less orderedregions of the structure. To gain further insight in this issue, side-chain contacts werecalculated for each set of structures that exhibit similar secondary structure elements asdefined by the DSSP algorithm (see Table 3.3, for trajectories in water, and Table 3.4, fortrajectories in methanol solution). Facing and diagonal (inter strand) interacting residues aredefined following the template of a triple stranded antiparallel β-sheet suggested forBetanova (see reference 114, figure 1A). Facing residues are residues that face each otherbetween strands according to the template in reference 114, figure 1A. Diagonal residues areresidues that are in relative diagonal orientation between facing strands, according to thetemplate in reference 114, figure 1A. In general, it is observed from the simulations that bothhydrophobic and electrostatic side chain interactions between facing or diagonal interactingresidues are present in each of the conformations. Nevertheless, no clear relationshipbetween the number of side chain contacts and either the mutation itself nor the solventenvironment was found.

For the triple stranded conformations, it was found that the total number of side chaincontacts varies between 7 (for F12 in water, only 1 hydrophobic contact was found) and 9(for LLM in water, 4 hydrophobic contacts), and that there are two pairs of facing interactingside chains: hydrophobic contact between residues 5 and 10 and electrostatic interactionbetween residues 11 and 16. Particularly for the triple stranded conformation of F12 inwater, there is a network of electrostatic interactions between facing residues 4 and 11, 11and 16, and 9 and 18; and between residues 6 and 11, and 9 and 16, in diagonal disposition.The other triple stranded conformations show diagonal interactions between pairs of residues3 and 10, 3 and 17 and/or 12 and 17, which builds a network of interactions that connectsthe whole structure.

For β-hairpin 1 like conformations, the total number of side chain contacts varies between 2(for LLM in methanol solution, 1 hydrophobic contact) and 6 (for Native in water, 2hydrophobic contacts). In this case, it is not possible to identify common features betweensimilar conformations. For β-hairpin 2 like conformations, which were found only in thetrajectories in methanol solution, the total number of side chain contacts varies between 3(for LLM, no hydrophobic contacts) and 10 (for Native, 4 hydrophobic contacts). Theconformation without hydrophobic contacts exhibits two pairs of side chains that interactelectrostatically: residues 9 and 16 in diagonal disposition, and residues 11 and 16, facingeach other.

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Chapter 3

Figure 3.6

RMSD matrix of each fragment of the structure of the mutant LLM: fragment 1 correspondsto residues 3, 4, 5 and 6, fragment 2 corresponds to residues 9, 10, 11 and 12, and fragment 3corresponds to residues 15, 16, 17, 18. The calculation was performed for the combinedtrajectory of LLM in water.

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Peptide folding in non-aqueous environments

These observations imply that similar networks of backbone hydrogen bonds can bestabilized by different, non specific, networks of side chain interactions. This is in contrastto previous studies of β-hairpins where the role of diagonal interactions and their relation tothe hydrophobic cluster was highlighted.106 Triple stranded conformations will be stabilizedboth by hydrophobic and electrostatic interactions of side chains paired either diagonally orfacing each other. β-hairpin 1 like conformations might be intrinsically more stable (thedesign of Betanova was based on a hairpin 1 template114) so that the side chains have morefreedom to arrange and thus the network of interactions is less specific. On the other hand,β-hairpin 2 like conformations require more specific side chain interactions since thetemplate backbone has not been proved experimentally to be stable. Yet, no clear evidence isfound to contrast with the hypothesis proposed by López de la Paz et al.123

Side chain packing observed in the trajectories is consistent with Betanova beingpredominantly compact but poorly structured.123,124 For example in the 100 ns trajectorystarted from the NMR based model of Betanova, around 30% of the trajectory does notcontain secondary structure elements as defined by the DSSP algorithm even though theradius of gyration is on average only 0.75 nm and both hydrophobic contacts (residues 3 and10), and electrostatic interactions (residues 4 and 11, and 9 and 18) are present throughoutthe whole trajectory. In the 400 ns combined trajectory of mutant LLM, more than 50% ofthe structures do not exhibit secondary structure. In solution Betanova and the mutantsinvestigated rapidly interconvert between a range of conformations that are stabilized by adelicate balance between hydrophobic and electrostatic interactions. Structural fluctuationscan easily bring the structure to a compact conformation whose backbone no longer spansthe network of hydrogen bonds that characterizes elements of β-sheet secondary structure,an observation in good qualitative agreement with experimental studies124 which suggest thatthe structure is compact but poor in β-sheet content.

3.4 Conclusions

Our MD simulation studies suggest that Betanova and mutants in solution are best describedin terms of an ensemble of different conformations in equilibrium. The configurationssampled do not correspond strictly to well defined secondary structure elements but are ingeneral compact structures with a folded backbone, extensive hydrogen bonding networksand a diverse range of side chain packing. The conformations are stabilized both byhydrophobic and electrostatic side chain interactions. The side chain - side chaininteractions maintain the structure compact and cause the backbone to twist. Theseobservations are consistent with the most recent experimental observations which suggestthat Betanova like peptides are intrinsically flexible, and that the ideal triple strandedgeometry is only transiently populated.

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Chapter 3

It is clear, however, that any conclusions in regard to the precise behavior of Betanova insolution based on these simulations must be made cautiosly. Even on the extended timescales investigated in this study it has not been possible to accumulate enough statistics todetermine the relative populations of even the most readily accessible states with muchcertainty. At least for this system extracting reliable thermodynamic data from simulations <1µs is not possible.

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