Structural Characterization of r-Helices of Implicitly Solvated Poly-Alanine†

Vernon A. Couch,* Neal Cheng, Krishnan Nambiar, and William Fink*Department of Chemistry, UniVersity of California, DaVis, California 95616

ReceiVed: September 14, 2005; In Final Form: December 22, 2005

The structural characteristics ofR-helices in poly-alanine-based peptides have been investigated via moleculardynamics simulation with the goal of understanding the basic features of peptide simulations within the contextof a model system, classical molecular dynamics with generalized Born (GB) solvation, and to shed insightinto the formation and stabilization ofR-helices in short peptides. The effects of peptide length, terminalcharges, proline substitution, and temperature on theR-helical secondary structure have been studied. Thesimulations have shown that distinct secondary structure begins to develop in peptides with lengths approaching10 residues while ambiguous structures occur in shorter peptides. The helical content of peptides with lengthsg10 amino acids is observed to be nearly constant up to (Ala)40. Interestingly, terminal charges and prolinein the second position from the N-terminus alter the secondary structure locally with little effect on the overallR-helical content of the peptide. The free energy profile of helix formation was also investigated. A largeincrease in free energy accompanying the formation of helices with more than two consecutive hydrogenbonds in the (i, i + 4) pattern was observed while the free energy increases linearly with additional hydrogenbonds. Values for the change in enthalpy and entropy of helix nucleation and propagation are reported.Additionally the results obtained from the GB model are compared to explicit solvent simulations of twosynthetic alanine-based peptides.

Introduction

Since its discovery theR-helix has played an important rolein understanding the structure of proteins.1 The R-helix is acommon motif in proteins, and increasingly smallR-helicalpeptides are being utilized as drugs such as HIV fusioninhibitors.2 The ability to predict secondary and tertiary structurein peptides and proteins is of fundamental importance tounlocking the mysteries of protein structure and function butare also important in the development of smaller, cheaper, andmore readily synthesized peptide-based pharmaceuticals. Simplechemical modifications and amino acid substitutions have beenshown to dramatically impact the helical content of shortalanine-based synthetic peptides in aqueous solution.3,4 Detailedknowledge of the interactions stabilizing helices in aqueoussolution will facilitate the rational design of peptides that foldwith predetermined secondary structure.

The purpose of this study is to characterize theR-helicalproperties of alanine-based peptides within the context ofclassical generalized Born molecular dynamics simulations,5 toinvestigate some of the factors thought to contribute to helixstabilization, and to evaluate the predictive and qualitative valueof the model. In particular we have investigated the effect oflength on helical content as well as terminal charges and prolinesubstitution in the first turn of the helix. Additionally implicitand explicit solvent simulations of synthetic peptides incorporat-ing these features are compared.

Positive charge, such as a protonated terminal amine, at theN-terminus of R-helices can interact unfavorably with thepositive end of the helix dipole destabilizingR-helical structure.6

Similarly negative charges at the C-terminus are expected tobe destabilizing. Experiments in aqueous solution have shownthat residues with negatively charged side chains can stabilizethe helix when located at the N-terminus.7-9 Gas-phase experi-ments have also shown that appropriately placed charges at thetermini stabilize helices in a vacuum.10-12 We have investigatedboth charged and neutral species to determine the extent of thiseffect within the context of the model. However, the acetyl andamide groups placed at the N- and C-termini not only neutralizethe charges at the termini but can act as additional hydrogenbonding donor and acceptor groups. The regular (i, i + 4)hydrogen bonding pattern leaves the first three backbone amidegroups and the last three backbone carbonyls without hydrogenbonding partners. Presta and Rose13 have suggested that residuesthat can provide additional hydrogen bonds to the unpairedamide and carbonyl groups of the peptide backbone areimportant factors in determining the location and stabilizationof R-helices. An acetyl group at the N-terminus can act as anN-capping residue and has been shown to increase the helicalcontent of short peptides in solution.4,7 Hydrogen bondingpatterns for the acetyl group have been investigated within thecontext of the hypothesis of Presta and Rose.

In the body ofR-helices, proline is known to be a helix-breaking residue due to the pyrrolidine ring, which stericallyhinders adjacent residues, and its lack of an available amideproton for hydrogen bonding.14 Despite this, proline has beenfound to have a high affinity for the second position from theN-terminus,15 and has been successfully utilized in syntheticpeptides of high helical content3. The structure of the pyrrolidinering in proline fixes theφ dihedral to anR-helical conformationand limits the flexibility of theψ dihedral.14 As a result thereshould be less entropic cost for proline to adopt a helicalconformation compared to other amino acids.15 It has also beensuggested that proline occurs in this position not because of its

† Originally submitted for the "Jack Simons Festschrift", published asthe December 22, 2005, issue ofJ. Phys. Chem. A(Vol. 109, No. 50).

* Authors to whom correspondence should be addressed. E-mail:vacouch@ucdavis.edu; whfink@ucdavis.edu.

3410 J. Phys. Chem. B2006,110,3410-3419

10.1021/jp055209j CCC: $33.50 © 2006 American Chemical SocietyPublished on Web 02/01/2006

helix-initiating propensity but rather as a result of its helix-breaking character where it acts as a helix-demarcating resi-due.13,14 We have investigated the effect of proline on thesecondary structure in both charged and neutral peptides.

Due to the importance of secondary structure formation insmall peptides many experimental and theoretical studies ofR-helix formation and stabilization in small peptides have beenreported. Many factors play a role in helix stabilization includingthe propensity of particular amino acids to adopt helicalconformations, the position of the amino acid, side chain andtermini protonation, and the sequence of amino acids withinthe peptide. This complexity of interactions makes it difficultto determine a set of parameters for the amino acids that canbe fed into an appropriate helix-coil theory to predict the helicalcharacteristics of an arbitrary peptide. Typically the helicalcontent of aqueous peptides is monitored experimentally viacircular dichroism measurements at 222 nm characteristic ofR-helices,16 and in the gas-phase ion mobility experiments candiscern helical structure.10 When the circular dichroism ismonitored over a range of temperatures a thermal unfoldingcurve can be generated and fit to the van’t Hoff equation toobtain thermodynamic data for the helix-coil transition.17

Experimental results are often fit to Zimm-Bragg (ZB)18 orLifson-Roig (LR)19 helix-coil theories to obtain thermody-namic and structural information. The effects of variousperturbations on the secondary structure of short peptides suchas amino acid substitution,3,4,7-9 temperature jump experi-ments,20 and sequence changes12 have been probed with theseand other methods.

Similarly molecular dynamics and Monte Carlo simulationscarried out at different temperatures can be fit to the van’t Hoffequation21 or to LR or ZB helix-coil theories22-27 to obtainthermodynamic data by monitoring helical parameters such asthe backbone dihedrals or helical hydrogen bonding. Replicaexchange molecular dynamics (REMD) simulations particularlylend themselves to this type of analysis, since an ensemble ofstructures at various temperatures is simultaneously gener-ated.23,24 Additional simulation methods such as umbrellasampling have been applied to helix formation in short peptides.Tobias and Brooks28 utilized umbrella sampling to generate apotential of mean force (PMF) for the helix to extendedtransition for peptides of the form Ac-Ala3-NHMe along thecoordinate corresponding to the distance between the carbonyloxygen and amide hydrogen of the first and fifth residues, the(1,5) helical hydrogen bond distance. The extension of thismethod is difficult since there are numerous (i, i + 4) hydrogenbonding pairs. The peptide growth method is one possibleextension where thermodynamic integration is used to calculatethe change in free energy as new residues are added to thepeptide.29 We introduce a new method to determine thermody-namic quantities that is similar to both these methods. Bygeneration of a PMF along an abstract coordinate correspondingto sequential helical hydrogen bonds, or sequential helicalresidues, and performing a two-step linear regression of thesePMFs obtained at different temperatures, the enthalpy andentropy of both helix nucleation and propagation can beobtained.

Methods

Simulations. Four sets of model compounds with formulasI, (Ala)n; II, Ac-(Ala)n-NH2; III, Ala-Pro-(Ala)n-2; and IV, Ac-Ala-Pro-(Ala)n-2-NH2 were simulated withn ) 5, 7, 10, 15,20, 30, and 40. Groups I and III have charged terminal residues,while groups II and IV have been neutralized via acetylation

and amidation at the N- and C-termini, respectively. Moleculardynamics (MD) simulations allow us to study systems that arenot accessible to experimentalists due to solubility and syntheticconcerns. These systems were chosen to eliminate the ambiguityassociated with water soluble peptides containing amino acidswith charged side chains that may themselves influence thesecondary structure.

Each peptide was constructed in a fullyR-helical conforma-tion using the xleap module of Amber 7.12 The simulations wererun using the sander module with the ff99 force field and thegeneralized Born solvation model at 300 K, with a dielectricconstant of 78.5 corresponding to that of water. Each peptidewas equilibrated for 15 ps, followed by 15 ns of productionwith a 1 fs time step. Additionally, temperature effects wereexamined via simulations of (Ala)15 at temperatures of 200, 250,300, 350, 400, and 500 K.

To compare the effects of both implicit and explicit solvation,two experimentally studied peptides3 differing in only oneresidue, but with very different helical propensities in solution,were chosen. The synthetic peptides Asn-Pro-Glu-(Ala)2-Lys-(Ala)3-Gly-Arg-NH2 and Gln-Pro-Glu-(Ala)2-Lys-(Ala)3-Gly-Arg-NH2, denoted p1 and p2, were simulated at 300 K for atotal of 15 ns using both generalized Born and explicit solvent.The explicit solvent simulations included 1874 and 2134 TIP3Pwaters for p1 and p2, respectively.

Analysis. The R-helix can be defined by the regular patternof hydrogen bonds between the carbonyl of theith residue andthe amide group of thei + 4 residue. Similarly, the (φ, ψ)backbone dihedrals of the peptide chain, which must lie withina certain range to maintain a helical structure, can also definethe R-helix. Both helical parameters, the backbone dihedralangles and the (i, i + 4) hydrogen bonds, were used to monitorthe R-helical structure over the MD trajectories. For a givenconfiguration each residuei was considered to be in anR-helicalconformation, Hi, if the (φ, ψ) dihedrals were within(25° ofthe ideal angles of approximately (-60°, -40°). The ideal angleswere determined from the statistical analysis of Ramachandranplots to contain the majority of amino acids found inR-helicesin proteins.31 Similarly, a hydrogen bond between the carbonylO of theith residue with the amide N of thei + 4 residue wasconsidered present if the O-N distance was less than 4 Å.21

Using these criteria, we define the following counting functions

To calculate the helical content of each configuration the numberof helical residues or hydrogen bonds is then summed, dividedby the maximum possible (which is given by (Nr - 2) and (Nr

- 4), respectively, whereNr is the number of residues), andmultiplied by 100 to obtain the percentR-helicity. This givesus

where the sum is fromi ) 2 to (Nr - 1) residues andi ) 1 to(Nr - 4) hydrogen bonds, respectively. The percent helicity canbe calculated at each time step or averaged over every few timesteps to follow the secondary structure dynamically. Alterna-

Hi ) {1 (-85 e φ e -35) and (-65 e ψ e -15)0, otherwise

(1)

Hi ) {1 d(Oi-Ni+4) e 4.0 Å0 otherwise

(2)

%H ) 100Σ Hi/(Nr - 2) (dihedrals) (3)

%H ) 100Σ Hi/(Nr - 4) (hydrogen bonds) (4)

R-Helices of Implicitly Solvated Poly-Alanine J. Phys. Chem. B, Vol. 110, No. 7, 20063411

tively, an average over the entire production phase of thesimulation can be used to compare the helical propensities ofdifferent peptides. The average percent helicity was calculatedfrom

where the sum is over all configurations,Nconfig.A probability distribution of the number of hydrogen bonds

per configuration was similarly calculated by counting hydrogenbonds, binning according to the number of bonds per config-uration, and normalizing. This distribution can be used to obtainthe average percent helicity from

where the sum is over all configurations,NH-bondsis the numberof hydrogen bonds present in the configuration, andP(NH-bonds)is the probability ofNH-bonds occurring. The same probabilitymay be used to express a potential of mean force (PMF),W,for the coordinate corresponding toNH-bonds, the total numberof hydrogen bonds per configuration,21 according to

Aside from calculating global properties from the two helicalparameters it is also possible to determine a helical probability,⟨%Hi⟩, for each residue or hydrogen bond,i, by simply averaging%Hi over all configurations. This provides a map of the regionsof the peptide that tend to be more or lessR-helical, andcomparisons of the local structure between different peptidescan be examined.

The percent helicity measured from dihedrals tends tooverestimate the actual helical content of the peptide, sinceresidues can adoptR-helical configurations without being in anR-helical segment. Similarly, the percent helicity measuredaccording to the hydrogen bonds does not distinguish isolatedhydrogen bonds in the (i, i + 4) scheme (turn structures) fromthose in genuineR-helical segments. To address the issue ofR-helix segment length, PMFs were constructed from thedistribution of consecutive hydrogen bonds and the distributionof consecutiveR-helical residues according to

whereP(Ns) is the distribution ofR-helical segments of lengthNs. Ns can be related to the number of consecutive (i, i + 4)hydrogen bonds orR-helical residues. If we consider a 5 residuepeptide in a completelyR-helical configuration, then there wouldbe Nres ) 3 residues in helical conformations (excluding bothterminal residues since the (φ, ψ) dihedrals cannot be simul-taneously defined) corresponding toNH-bond ) 1 (i, i + 4)hydrogen bond between the first and fifth residues, leading tothe relation

with this initial segment being of length zero. However, thePMF corresponding to the distribution of consecutive hydrogenbonds suggested the relation

Motivated by its form, the PMF,W of eq 8, was then fittedusing linear regression to the customary expression from helix-coil theory19

Here we take∆G ) W(Ns), the result calculated by the PMFexpression of eq 8.∆Gs is the free energy associated with addinga hydrogen bond to the helix, and∆Gnuc is the free energyrequired to initiate theR-helix. With the appropriate definitionof Ns, the resulting linear equation has slope equal to∆Gs andintercept equal to∆Gnuc. Through the use of PMFs fromsimulations at different temperatures,∆Gs and ∆Gnuc can bedecomposed into their respective entropic and enthalpic terms.The free energy can thus be expressed as

When ∆Gs versusT is plotted and through the use of linearregression, the PMF slopes can be fitted to a line with slope-∆Ss and intercept∆Hs. Similarly, ∆Hnuc and ∆Snuc can bedetermined from a least-squares fit of∆Gnuc versusT. Due tothe nature of the PMF rather than plotting∆G versusNs ) Ncon,the number of consecutive units satisfying the condition ofclassification as beingR-helical, ∆G versusNs ) (Ncon - 3)was used for the hydrogen bonds andNs ) (Ncon - 5) was usedfor the dihedrals (see Discussion and Results sections).

To investigate further the differences between the dihedraland hydrogen bonding measurements of the percent helicity forthe shorter peptides a clustering analysis was performed on thepeptides of length 5 using the NMRClust program.32 Clusteringwas also performed on the peptides of length 15 to obtain a setof structures representative of the ensemble obtained from thesimulation. Of the 150 000 structures collected over the MDtrajectory for each peptide, 1500 structures were selectedsequentially (i.e., every 100th structure) for clustering. Thepopulation of each cluster represents the weight,wi, of thatcluster within the ensemble. Along with the secondary structureassignments of the representative structures obtained from thedssp program,17 the average percent helicity,⟨%H⟩dssp, wascalculated according to

wherewi is the weight of theith cluster andfH is the helixfraction. The summation in eq 13 is ideally taken over allclusters but in practice was truncated to the first 10 clusters.The ⟨%H⟩dsspwas compared to the⟨%H⟩ values obtained fromeq 5 to verify that the clusters accurately represent the totalensemble.

Results and Discussion

Percent Helicity. The percent helicity as a function of lengthfor each of the four sets of peptides is illustrated in Figure 1. Ineach case the behavior of the longer peptides, 10 or more aminoacids, is similar reaching an equilibrium value of approximately40% and 30% for the dihedral and hydrogen bond measures,respectively, as calculated from eqs 3 and 4. The differentsubstitutions show little global effect on the overall helicalcontent of the longer peptides. The 15 residue peptides (Ala)15,Ac-(Ala)15-NH2, Ala-Pro-(Ala)13, and Ac-Ala-Pro-(Ala)13-NH2

resulted in⟨%H⟩ values of 37.9, 43.4, 40.9, and 43.4 fromdihedral measures and 33.8, 36.1, 35.1, and 37.7 from hydrogenbond measures, respectively. The percent helicity of variousalanine-based peptides have been determined experimentallyfrom circular dichroism data. The 15 residue peptide CH3CO-A5QA4QA2GY-NH2 was reported to be 42% helical, in goodagreement with the dihedral measure obtained for Ac-(Ala)15-NH2.8 However, the peptide NH2-X-AKA 4KA4KA2GY-CONH2

⟨%H⟩ ) Σ %H/Nconfig (5)

⟨%H⟩ ) 100Σ NH-bondsP(NH-bonds)/(Nr - 4) (6)

W(NH-bonds) ) -RT ln{P(NH-bonds)} (7)

W(Ns) ) -RT ln{P(Ns)} (8)

Ns) NH-bond- 1 ) Nres- 3 (9)

Ns ) NH-bond- 3 ) Nres- 5 (10)

∆G ) Ns∆Gs + ∆Gnuc (11)

∆G ) Ns(∆Hs - T∆Ss) + (∆Hnuc - T∆Snuc) (12)

⟨%H⟩dssp) 100(Σ wifH)/(Σ wi) (13)

3412 J. Phys. Chem. B, Vol. 110, No. 7, 2006 Couch et al.

was found to be 23% percent helical when X) Ala and theN-terminus is charged, and when X) acetyl the percent helicityis reported as 58%.7 These values are roughly 10% below thevalues obtained for the zwitterionic peptide, model I, and 10%above the value obtained for the acetylated peptide, model II.The peptide X-HN-A4EA3KA4YR-CONH2 was found to be 17%helical when X) hydrogen, and 32% helical when X) acetyl.4

Finally, the peptide APAEA2KA3GR-CONH2 was reported tobe only 2.4% helical, which is an order of magnitude smallerthan the value observed for model III peptides of similarlengths.3 Gas-phase ion mobility experiments on the peptideAc-A3G12K were observed to be 26% helical at 213 K and 38%at 391 K.12 The experimental results suggest that the valuesobtained from the simulations are reasonable, although thegeneralized Born (GB) model appears less sensitive to thesubstitutions than experiment.

In contrast the 5 residue peptides, which correspond to asingle helical turn with one hydrogen bond, exhibit vastlydiffering behaviors among the set. Model I (Figure 1A) hasdivergent percent helicity measurements in this length regime.Although the single (1, 5) hydrogen bond occurs with afrequency of 45%, the dihedral measurement shows a very lowR-helical content of 27%. This indicates the presence ofpredominantly turn structures and that the residues in a singleturn have more torsional degrees of freedom than residues withinan extended helix. The other peptides show a significant increasein the frequency of the (1, 5) hydrogen bond (61% for model IIand 80% for models III and IV) with moderate increases in thedihedral measurements (36% for models II and III and 40% formodel IV). From this we see that removing charges from thetermini increases the propensity to form the (1, 5) bond,increasing the likelihood of helix initiation, that proline reducesthe conformational degrees of freedom in the first loop of thehelix, helping to secure the fairly mobile N-terminus to anR-helical structure, and that both substitutions (i.e., model IV)can work together to further increase the helical propensity. Thatthe difference persists for the very short peptides indicates that

the substitutions have a short range of action with little globaleffect on the secondary structure of the larger peptides.

Hydrogen Bonds per Conformation. The probability dis-tribution of the number of helical hydrogen bonds per config-uration (Figure 2A) is increasingly Gaussian in form as peptidelength increases and is centered about the constant helix fractionof 0.33 or 33%, consistent with the average percent helicitycalculated from eq 4. The associated PMF,Wof eq 7, illustratesthe deviation of the shorter peptides to a higher helix fraction(Figure 2B). As the peptide length increases the probability ofbecoming fully helical diminishes, the PMF becomes increas-ingly quadratic, and the system maintains with high probabilityapproximately one-third of the possible helical hydrogen bonds.The various substitutions studied showed little effect on thedistribution of hydrogen bonds for the longer peptides, furtherconfirming the local nature of the effect of the substitutions onthe overall helical content. Figure 2C shows the probabilitydistribution of the number of hydrogen bonds per configurationfor each model of length 40 residues. The maximum of eachdistribution occurs at the same helix fraction with little variationin the standard deviation. The probability distribution for modelI (Figure 2D) of length 40 was fit to a normalized Gaussiandistribution34 of the form

wherex is, in this case, the helix fraction,σ is the standarddeviation, andµ is the mean.µ was taken to be 0.33 asdetermined from the percent helicity, andσ was determined fromthe full-width at half-maximum to be 0.06.

Helical Probability. The helical probability per residue orper hydrogen bond is a measure of the frequency with whichparticular residues or hydrogen bonds are inR-helical conforma-tions. This allows us to locate within the peptide those regionsmore likely to beR-helical and allows us to see the effect ofthe substitutions on the local structure of the peptide. TheN-terminus of the model I peptides is significantly less helical

Figure 1. Average percent helicity vs peptide length for (A) model I, (Ala)n (zwitterion), (B) model II, Ac-(Ala)n-NH2 (neutral), (C) model III,Ala-Pro-(Ala)n-2 (proline containing zwitterion), and (D) model IV, Ac-Ala-Pro-(Ala)n-2-NH2 (proline containing neutral). Solid lines and dashedlines indicate dihedral and hydrogen bond measures, respectively.

P(x;µ,σ) ) (2π)-1/2 exp{-0.5*(x - µ)2/σ2} (14)

R-Helices of Implicitly Solvated Poly-Alanine J. Phys. Chem. B, Vol. 110, No. 7, 20063413

than the remaining residues as seen from the hydrogen bondingprofile shown in Figure 3A. The C-terminus appears to be lessaffected by the charge but shows a small decrease in helicalprobability. The plot for model I is binodal, with a loss ofhelicity in the central region of the peptide, indicating thathydrogen bonds are most likely to occur in the regions adjacent

to the termini and away from the center of the peptide. Thisbehavior is also observed in the larger peptides but withincreasingly irregular patterns of high and low helical probabilityas peptide length increases. This differentiation into distinctdomains with different hydrogen bonding patterns indicates theemergence of tertiary structure. Figure 3B shows that the modelII peptides, with neutral termini, exhibit the opposite behavioras in the case of model I. Here an increase in helicity in theterminal regions compared to the residues in the body of thepeptide is observed. Unlike model I both the N- and C-terminiare affected to a similar extent, and there is a nearly constanthelical probability in the body of the peptide.

When proline is substituted in the second position of thezwitterion form, model III, as shown in Figure 3C, there is anincrease in the helicity of the N-terminus while the C-terminusremains unenhanced as in the case of model I. Interestingly,enhancement is observed for the second, rather than the first,(i, i + 4) hydrogen bond for all peptide lengths. Additionally,the helical probability per residue shows a distinct increase inhelicity for Pro-2 and Ala-3, indicating more rigid backbonedihedrals near the N-terminus (Figures 3B and 3F). Again wesee a lower probability to form hydrogen bonds in the centerof the peptide, an apparent characteristic of the zwitterionpeptides that is absent from both neutral models. Model IV,shown in Figure 3D, with neutral termini and proline in thesecond position, exhibits the greatest enhancement at theN-terminus among all models. The enhancement of the first andsecond (i, i + 4) hydrogen bonds is similar to that observed inmodels II and III, respectively, illustrating how both substitutionswork. Proline with reduced torsional degrees of freedompromotes the second (i, i + 4) hydrogen bond in the helix whilethe acetylation promotes the first. The C-terminus of the modelIV peptides exhibit very similar behavior to the model IIpeptides.

The helical probability per residue (Figures 3E-H) showsthat the residues immediately following the N-terminus are mostlikely to haveR-helical dihedral values, and consequently theN-terminus is the most likely position for helix nucleation.Models I and II have decreasing helical probability as weprogress toward the C-terminus. Conversely, models II and IVshow a constant helical probability throughout the body of thepeptide. In all cases the two residues preceding the C-terminusshow a significant decrease in helical probability, indicatingmore flexibility in the C-terminal region.

R-Helix Segment Length.The fact that hydrogen bonds mustoccur in succession to formR-helices is not satisfactorilyaddressed by simply monitoring the number of hydrogen bondsoccurring over the molecular dynamics (MD) trajectory. Theconstruction of a potential of mean force (PMF) along thecoordinate corresponding to the number of consecutive hydrogenbonds or consecutive helical residues based upon the criteriaof eqs 1 and 2 has yielded very interesting results into thestability of R-helices (Figure 4). It is clear that although smallchanges in the percent helicity and helical probability perhydrogen bond were observed, the PMF is essentially the samefor each peptide regardless of length or substitution. The primaryeffect of the substitutions is to reduce the free energy of helixnucleation. This is consistent with our findings that thesubstitutions have rather local effects, at least concerningsecondary structural content, by increasing the probability ofhelix nucleation particularly near the N-terminus. The observed∆∆Gnuc, compared to model I, are approximately-0.3, -0.1,and-0.3 kcal/mol for models II-IV, respectively. It appearsthat the vast majority of the hydrogen bonds occur alone or in

Figure 2. (A) Normalized distribution of the number of hydrogenbonds per configuration for the model I peptides of various lengths.(B) Potential of mean force generated from the distributions in part A.(C) The distribution of the number of hydrogen bonds for each modelof length 40 residues. (D) Gaussian fit to the distribution for model I,again for 40 residues. In parts B-D thex-axis has been scaled accordingto the maximum number of hydrogen bonds to represent the helixfraction.

3414 J. Phys. Chem. B, Vol. 110, No. 7, 2006 Couch et al.

groups of 2, as indicated by the jump in the PMF at threeconsecutive bonds (Figures 4A and 4B), followed by a linearregion out to large segment lengths where sampling becomesrelatively poor. This seems to indicate that there is minimalenergetic or entropic cost to the formation of individual (i, i +4) hydrogen bonds, but the formation of extendedR-helices isenergetically unstable at room temperature.

The PMF of the number of consecutive (i, i + 4) hydrogenbonds at different temperatures (Figure 5A) were used todetermine the enthalpy and entropy of helix formation. Themultiple regression of PMFs from different temperature simula-tions yielded∆Hnuc ) -0.53( 0.40 kcal/mol and∆Snuc ) -8.1( 1.0 cal/(mol K), and∆Hs ) -1.21 ( 0.08 kcal/mol perhydrogen bond and∆Ss ) -5.26 ( 0.22 cal/(mol K) perhydrogen bond. Figure 5 illustrates∆G obtained from eq 12overlaid with the PMFs used in the fit. The values of∆Hs and∆Ss correspond to a melting temperatureTm ) 230 K for theinfinite chain. The poor sampling of short helical segments attemperatures of 200 and 250 K corresponds to the freezing ofthe helix as it becomes thermodynamically stable. This leadsto large errors in the estimate of∆Gnuc, and simulations at thesetemperatures were dropped from the fit.

To validate this approach the percent helicity calculated fromeq 4 was fit to the van’t Hoff equation. Assuming a two-statemodel the helix-coil equilibrium constant can be approximated

asKeq ) fH/(1 - fH) where fH is the helix fraction and equals⟨%H⟩/100. At equilibrium we can write lnKeq ) (-∆H/RT) +(∆S/R). A plot of ln KEq vs 1/T results in a line with slope-∆H/R and intercept∆S/R.24 This analysis resulted in∆H )-1.18 ( 0.17 kcal/mol per residue and∆S ) -5.15 ( 0.47cal/(mol K) per residue, which agrees with∆Hs and ∆Ss towithin 2%. Not only do we see good agreement between thevalues of∆H and∆S, this comparison illustrates the connectionbetween the percent helicity measurements and the PMFsobtained from eq 8.

Interestingly, nucleation appears to occur with three consecu-tive hydrogen bonds as seen from the large increase in the PMFcorresponding to∆Gnuc. The PMFs of consecutive hydrogenbonds and consecutive helical residues (based on dihedralcriterion) show nearly exact correspondence when thex-axis isshifted by three hydrogen bonds and five residues, respectively,illustrating the relationship between the number of hydrogenbonds and the number of helical residues. From this we seethat∆Hs and∆Ss also represent the enthalpic and entropic costof adding an additional helical residue and that the jump in thePMF seen with the hydrogen bonds can be related to the perresidue PMF by∆Gnuc ) 5*∆Gs (Figure 5B).

The value of ∆Hs is in excellent agreement with bothcomputationally and experimentally derived values ranging from-0.6 to-1.3 kcal/mol per residue, with the most probable and

Figure 3. Helical probability,⟨%Hi⟩, for models I-IV of length 15. Parts A-D represent the helical probability per (i, i + 4) hydrogen bond formodels I-IV respectively, and parts E-H represent the corresponding helical probability per residue.

R-Helices of Implicitly Solvated Poly-Alanine J. Phys. Chem. B, Vol. 110, No. 7, 20063415

accepted value near-1 kcal/mol per residue.17,21,22,23,28Recentreplica exchange molecular dynamics (REMD) simulations andthermal unfolding experiments have estimated∆Ss at -2 cal/(mol K) per residue,21,23less than half of our value. To compare∆Gnuc we calculated the Zimm-Bragg helix nucleation param-

eter σ. From our value of∆Gnuc we obtain a value forσ of0.042 using the expressionσ ) exp(-∆Gnuc/RT).19 This valueis an order of magnitude larger than the typical value rangereported forσ of 0.001-0.004,20 leading to an underestimateof the free energy of nucleation by a factor of 2. Although thefree energy of nucleation is underestimated according toaccepted values ofσ, the exact meaning ofσ within theparticular interpretation of Zimm-Bragg helix-coil theory isambiguous at best. Larger values ofσ are often encountered inpeptide simulations22-24,26,28 and are required to interpretexperimental data such as temperature jump experiments.20 Onereason∆Gnuc may be underestimated is the differing definitionof the reference state, which in the case of the present work isnot an extended coil state but rather a turn structure containing(i, i + 4) hydrogen bonds prior to complete nucleation.

Comparing Models. Having discussed the results for thegeneralized poly-alanine chain within the context of generalizedBorn molecular dynamics simulations, it is of interest to considerhow implicitly and explicitly solvated models differ. Thequestion of which features of short aqueous peptides arecorrectly represented by GB simulations is unclear, and we takeup this subject now. Although asparagine and glutamine differby only one side chain CH2 group, circular dichroism (CD)experiments have shown that p1, with Asn at N1, is 5 timesmore helical than p2, with Gln at N1, with %H values of 24.4%and 4.8% respectively3. Explicit simulations of p1 result in⟨%H⟩values of 46% for both dihedral and hydrogen bond criterion,while p2 results in⟨%H⟩ of 29% and 35% for dihedral andhydrogen bond criteria, respectively. Although explicitly sol-vated simulations of both peptides exhibit a much greater helicalcontent than determined from CD data, the difference betweenthe⟨%H⟩ values obtained for p1 and p2 are similar to experimentwith ∆(%H) ) ⟨%Hp1⟩ - ⟨%Hp2⟩ ) 20 (experiment), 17(dihedrals), 11 (hydrogen bonds). Generalized Born simulations,however, have very similar⟨%H⟩ values of 47% (dihedrals) and46% (hydrogen bonds) for p1, and⟨%H⟩ values of 46%(dihedrals) and 43% (hydrogen bonds) for p2. The generalized

Figure 4. PMF of the number of consecutive hydrogen bonds atT )300 K calculated from eq 8. (A) The PMF of each model with peptidelength 15 residues along an abstract coordinate defining successivehydrogen bonds using the criterion of eq 2. (B) The same PMF as inpart A for model I peptides from length 10 to 40 residues. (C) ThePMF of each model with peptide length 15 residues along an abstractcoordinate defining successive helical residues based upon the criterionof eq 1. (D) The same PMF as in part C for model I peptides fromlength 10 to 40 residues.

Figure 5. (A) PMF of R-helix segment length based on hydrogenbonds,W(Ns) of eq 8, for (Ala)15 at each temperature used in the fittingprocedure. (B) PMF ofR-helix segment length as a function ofconsecutive helical dihedral angles and hydrogen bonds. The solid linesin parts A and B indicate the values predicted from eq 12.

3416 J. Phys. Chem. B, Vol. 110, No. 7, 2006 Couch et al.

Born simulations seem unable to differentiate p1 and p2 andresult in percent helicities very similar to that of p1 in explicitsolvent.

To further understand the apparent shortcomings of GB, wecan examine PMFs,W(Ns), obtained from eq 8 using thedistributions of consecutive helical residues as determined bythe hydrogen bond criterion and the dihedral angle criterion forp1 and p2 with explicit and implicit solvation.W(Ns) calculatedfrom eq 8 for p1 (Figures 6A and 6C) with similar features andrelatively small deviations is quite similar for both GB andexplicit solvent simulations.W(Ns) for p2 (Figures 6B and 6D),in contrast, exhibits appreciable deviations between the twosolvation models. These findings suggest that the GB solvationmodel adequately describes p1 but not p2. However, this resultis very interesting because we can use both solvation modelstogether to better understand the behavior of various peptidesand to discern the interactions stabilizing or destabilizingsecondary structure. Although GB screens the interaction ofcharges according to the dielectric of the medium, in the absenceof explicit peptide-solvent interactions, one would expectelectrostatic interactions to dominate. Hence, the generalizedBorn method sees little difference in the electrostatic propertiesof Asn and Gln at the N-terminus, resulting in similar helicalpropensities. In explicit solvent the peptide-solvent interactionsapparently involving the Gln side chain result in a strongdestabilization of the second, third, and fourth hydrogen bonds.A destabilization absent in the GB simulations as can be seenfrom the helical probability illustrated in Figure 7, where partA shows the results for p1 and part B for p2.

From this we can conclude that the generalized Bornsimulation can adequately describe some aqueous peptides butcertainly not all. In cases where GB fails to give an adequatedescription, the results can be useful in differentiating thebehavior observed in more realistic simulations. A full analysisof the helical propensities and interactions of Asn versus Glnat the N1 position is the subject of a future report.

Clustering. The clustering analysis of models I-IV of length5 residues yielded structures consistent with the helical measure-ments. The most populous clusters are shown in Figure 8, andeach is a remarkably similar turn structure with 1 (i, i + 4) and1 (i, i + 3) hydrogen bond. Most interesting are the relativepopulations of each structure. Model II with proline and chargedtermini has a relative population of 53% for this structure whilemodel IV with proline and neutral termini has a population ofonly 11%, indicating that salt bridging between the termini is amajor factor in structural determination at such short lengths.The dssp program requires at least four nonterminal residuesto classifyR-helical secondary structure, making a comparisonto the ⟨%H⟩ measurements via eq 13 irrelevant.

The clustering of model peptides I-IV of length 15 residuesyielded much more informative results than that of the 5 residuepeptides. Figure 9 illustrates the representative structures of themost populous clusters.

Zwitterionic peptides, models I and III, exhibit a turn in thecenter of the helix resulting from the interaction of the chargedtermini, which causes the peptide to fold to bring the terminitogether in space. The first three most populous clusters ofmodel I exhibit this structural characteristic, which accountsfor 26% of the 1500 structures analyzed. However, extendedhelices are also observed but with a much lower frequency ofoccurrence. These findings are in agreement with the helicalprofile (Figure 3) where a drop in helicity in the center ofthe peptide was observed for models I and III. In the case ofmodel I the N-terminus is extended, directing the charged amino

group away from the short helical segment immediatelyfollowing the turn near the center of the peptide. In contrastthe most populous structure for model III has the N-terminusmuch more closely associated with the preceding helical segmentwhile the C-terminal regions of both models I and III are verysimilar.

Figure 6. Comparison of explicit solvent and generalized Bornsimulations. PMF of eq 8 generated from the distribution of consecutive(i, i + 4) hydrogen bonds for (A) p1, Asn-Pro-Ala-Glu-(Ala)2-Lys-(Ala)3-Gly-Arg-NH2, and (B) p2, Gln-Pro-Ala-Glu-(Ala)2-Lys-(Ala)3-Gly-Arg-NH2. The same PMF generated from the distribution ofconsecutive helical residues for (C) p1 and (D) p2. Triangles indicateexplicit solvent results, and squares represent the GB results.

R-Helices of Implicitly Solvated Poly-Alanine J. Phys. Chem. B, Vol. 110, No. 7, 20063417

The peptides with neutral termini exhibitR-helical structuresthat extend the length of the peptide, consistent with the nearlyconstant helical profile for the interior residues of models IIand III (Figure 3). Additionally, the N- and C-termini areparticipating in the helix with both the N-capping acetyl groupand the C-terminal amide forming hydrogen bonds to unpairedbackbone amide and carbonyl groups in accord with thepredictions of Presta and Rose.13 Figure 10 illustrates theprobability distribution of distances of the acetyl oxygen andbackbone amide nitrogens and shows a high probability ofhydrogen bonding with residues 2, 3, and 4. The stabilizationof such hydrogen bonds, at least within the context of these

simulations, is unclear, since we have determined that∆G ispositive for the addition of hydrogen bonds to the helix.However, the determining factor in the sign of∆G is theentropic cost of adopting anR-helical configuration upon bondformation. At the termini it is not necessary for the terminal orcapping groups to maintain a strict helical conformation, sincethese residues must be helix-breaking simply due to the factthat they are located at the termini. If we consider the majorityof helix-initiating events to occur at the N-terminus and thatthere is very little entropic penalty for the N-cap to form ahydrogen bond, then there should be a reduction in∆Gnuc nearlyequal to∆Hs. In fact we see a∆∆Gnuc of only one-quarter of∆Hs, indicating the predominant effect to be due to the favorableinteraction of the acetyl group with the helix dipole opposed tothe additional hydrogen bond.

Conclusion

This study has shown that within the context of classicalgeneralized Born molecular dynamics simulations theR-helixis not inherently stable at room temperature, although it is acommon secondary structural motif in equilibrium with turn andextended structures. In all cases of peptide length greater than10 residues the percent helicity was observed to be ap-proximately 30% with an increasingly Gaussian distribution ofhelical hydrogen bonds centered about this mean as peptidelength increases. This result coupled with the ambiguous percenthelicity measurements for peptides of lengths less than 10residues and the new definition of the helix nucleus leads tothe conclusion that trueR-helical secondary structure is notlikely to occur in peptides less than 10 residues with an absoluteminimum length of 7 residues necessary for nucleation.

The helix-initiating step occurs via a turn structure intermedi-ate with the formation of both helical hydrogen bonds and thetransition of several residues to anR-helical conformation. Therelatively large frequency with which one and two consecutive(i, i + 4) hydrogen bonds are observed implies the rapidformation and dissociation of pre-helix structures with relativelyfew nucleating events. From examining the PMF correspondingto sequential helical hydrogen bonds,W(Ns) of eq 8, we haveobserved that helix initiation occurs when three consecutivehydrogen bonds form and that this corresponds to five consecu-tive residues adoptingR-helical dihedral conformations. It istypical to assume that a single (i, i + 4) hydrogen bond withthe three nonterminal residues in helical dihedral conformationsis a sufficient definition of helix nucleation; however, the currentsimulations suggest that up to two helical hydrogen bonds canform without the entropic loss associated with the residuesforming a highly regular structure.

The substitutions studied were found to have little effect onthe overall form of the PMF with primary influence on the free

Figure 7. Helical probability per hydrogen bond,⟨%Hi⟩, for (A) p1and (B) p2 from implicitly solvated (squares) and explicitly solvated(triangles) simulations.

Figure 8. Cartoon representations of the most populous cluster formodels I-IV (parts A-D) from simulations of peptides of length 5residues.

Figure 9. Cartoon representations of the most populous cluster formodels I-IV (parts A-D) from simulations of peptides of length 15residues.

Figure 10. Probability distribution of the acetyl oxygen and backboneamide nitrogen distance for the residues 2 through 6, where residue 1is taken as the first alanine not the acetyl group.

3418 J. Phys. Chem. B, Vol. 110, No. 7, 2006 Couch et al.

energy of nucleation. This lack of sensitivity to substitution isalso present in the percent helicity measurements, whichexhibited the greatest difference between models for shortpeptides, with little effect on larger peptides, indicating a shortrange of action. However, the helical profile of each model wassignificantly altered by the substitutions with primary effect onthe N-terminus and, to a lesser extent, the residues in the bodyof the peptide. Incorporation of proline into the second positionwith an acetyl N-capping group showed the greatest increaseamong the models studied in the frequency with which the firsttwo helical hydrogen bonds form, increasing the likelihood ofhelix formation at the N-terminus. We conclude that proline inthe second position supports helical structure by limiting thedihedral conformational degrees of freedom, as observed fromthe helical probability per residue. The removal of charge fromthe termini has a profound effect on theR-helical secondarystructure and the tertiary structure observed from the clusteringanalysis. The fact that the replacement of positive charge witha polar group at the N-terminus has a limited range of action isin agreement with the conclusions of A° qvist6 that the effect ofthe helix dipole is primarily localized in the last, or in this casethe first, turn of the helix.

Acknowledgment. We thank April Voss for her helporganizing this paper.

References and Notes

(1) Pauling, L.; Corey, R. B.; Branson, H. R.Proc. Natl. Acad. Sci.U.S.A.1951, 37, 205.

(2) Wild, C. T.; Shugars, D. C.; Greenwell, T. K.; McDanal, C. B.;Matthews, T. J.Proc. Natl. Acad. Sci. U.S.A.1994, 91, 9770.

(3) Forood, B.; Feliciano, E. J.; Nambiar, K. P.Proc. Natl. Acad. Sci.U.S.A.1993, 90, 838.

(4) Forood, B.: Reddy, H. K.; Nambiar, K. P.J. Am. Chem. Soc.1994,116, 6935.

(5) Ponder, J. W.; Case, D. A.AdV. Protein Chem.2003, 66, 27.(6) A° qvist, J.; Luecke, H.; Quiocho, F. A.; Warshel, A.Proc. Natl.

Acad. Sci. U.S.A.1991, 88, 2026.

(7) Doig, A. J.; Baldwin, R. L.Protein Sci.1995, 4, 1336.(8) Cochran, D. A. E.; Penel, S.; Doig, A. J.Protein Sci.2001, 10,

463.(9) Cochran, D. A. E.; Penel, S.; Doig, A. J.Protein Sci.2001, 10,

1305.(10) Jarrold, M. F.Annu. ReV. Phys. Chem.2000, 51, 179.(11) Kinnear, B. S.; Hartings M. R.; Jarrold, M. F.J Am. Chem. Soc.

2001, 123, 5660.(12) Breaux, G. A.; Jarrold, M. F.J. Am. Chem. Soc.2003, 125, 10740.(13) Presta, L. G.; Rose, G. D.Science1988, 240, 1632.(14) Polinsky, A.; Goodman, M.; Williams, K. A.; Deber, C. M.

Biopolymers1992, 32, 399.(15) Richardson, J. S.; Richardson, D. C.Science1988, 240, 1648.(16) Hirst, J. D.; Brooks, C. L, III.J. Mol. Biol. 1994, 243, 173.(17) Scholtz, J. M.; Marquesee, S.; Baldwin, R. L.; York, E. J.; Stewart,

J. M.; Santoro, M.; Bolen, D. W.Proc. Natl. Acad. Sci. U.S.A.1991, 88,2854.

(18) Zimm, B. H.; Bragg, J. K.J. Phys. Chem.1959, 31, 526.(19) Qian, H.; Schellman, J. A.J. Phys. Chem.1992, 96, 3987.(20) Thompson, P. A.; Eaton, W. A.; Hofrichter, J.Biochemistry1997,

36, 9200.(21) Jas, G. S.; Kuczera, K.Biophys. J.2004, 87, 3786.(22) Sung, S.; Wu, X.Proteins: Struct., Funct., Genet.1996, 25, 202.(23) Ohkubo, Y. Z.; Brooks, C. L., III.Proc. Natl. Acad. Sci. U.S.A.

2003, 100, 24, 13916.(24) Sorin, E. J.; Pande, V. S.Biophys. J.2005, 88, 2472.(25) Mitsutake, A.; Okamoto, Y.J. Chem. Phys.2000, 112, 10638.(26) Shental-Bechor, D.; Kirca, S.; Ben-Tal, N.; Haliloglu, T.Biophys.

J. 2005, 88, 2391.(27) Young, W. S.; Brooks, C. A., III.J. Mol. Biol. 1996, 259, 560.(28) Tobias, D. J.; Brooks, C. L., III.Biochemistry1991, 30, 6059.(29) Wang, L.; O’Connell, T.; Tropsha, A.; Hermans, J.Proc. Natl. Acad.

Sci. U.S.A.1995, 92, 10924.(30) Case, D. A.; Pearlman, D. A.; Caldwell, J. W.; Cheatham, T. E.,

III.; Wang, J.; Ross, W. S.; Simmerling, C. L.; Darden, T. A.; Merz, K.M.; Stanton, R. V.; Cheng, A. L.; Vincent, J. J.; Crowley, M.; Tsui, V.;Gohlke, H.; Radmer, R. J.; Duan, Y.; Pitera, J.; Massova, I.; Seibel, G. L.;Singh, U. C.; Weiner P. K.; Kollman, P. A.AMBER 7; University ofCalifornia: San Francisco, CA, 2002.

(31) Hovmoller, S.; Zhou, T.; Ohlson, T.Acta Crystallogr., Sect. D2002,58, 768.

(32) Kelley, L. A.; Gardner, S. P.; Sutcliffe, M.J. Protein Eng.1996,9, 1063.

(33) Kabsch, W.; Sander, C.Biopolymers1983, 22, 2577.(34) Bevington, P. R.; Robinson, D. K.Data Reduction and Error

Analysis for the Physical Sciences; McGraw-Hill: San Fransisco, CA,1992.

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