Reverse turns in blocked dipeptides are intrinsically unstable in water

cl. Mol. Riol. (1990) 216, 7833796

Reverse Turns in Blocked Dipeptides Intrinsically Unstable in Water

are

Douglas J. Tobias, Scott F. Sneddon and Charles L. Brooks III Department of Chemistry Carnegie Mellon University Pittsburgh, PA 15213, IJ.S.A. (Received

12 March

1990; accepted 18 June 1990)

We have carried out molecular dynamics simulations to study the conformational equilibria of two blocked dipeptides, Ac-Ala-Ala-NHMe and trans-Ac-Pro-Ala-NHMe, in water (AC, amino-terminal blocking group COCH,; NHMe, carboxy-terminal blocking group NHCH,). Using specialized sampling techniques we computed free-energy surfaces as functions of a conformation co-ordinate that corresponds to hydrogen-bonded reverse turns at small values and to extended conformations at large values. The free-energy difference between hydrogen-bonded reverse turn conformations and extended conformations, determined from the equilibrium constants for reverse turn unfolding, is approximately -5 kcal/mole for Ac-Ala-Ala-NHMe, and - 10 kcal/mole for Ac-Pro-Ala-NHMe. These results demonstrate that reverse turns in blocked dipeptides are intrinsically unstable in water. That is, in the absence of strongly stabilizing sequence-specific inter-residue interactions involving sidechains and/or charged terminal groups, the extended conformations of small peptides are highly favored in solution. By thermodynamically decomposing the free-energy differences, we found that the peptide-water entropy is the primary reason for the exceptional stability of the extended conformations of both peptides, and that the differences between the two peptides are primarily due to differences in the peptide-water interactions. In addition, we assessed the “proline effect” on the conformational equilibria by comparing the differences in configurational entropies between the reverse turn and extended conformations of the two peptides. As expected, the extended conformation of the Pro-Ala peptide is destabilized by reduced configurational entropy, but the effect is negligible in the blocked dipeptides. Finally, we compared our results with the results of several other experimental studies to identify some of the specific interactions that may be responsible for stabilizing reverse turns in small peptides in solution.

1. Introduction

In addition to their structural significance in folded proteins, reverse turns are also thought to be important in the initial stages of protein folding (Lewis et al., 1971; Zimmerman & Scheraga, 1977a; Dyson et al., 1988). This hypothesis is supported by the fact that turns in short linear peptides (with as few as 3 residues) can be sufficiently stable in aqueous solution to be detected by nuclear magnetic resonance (n.m.r.t) spectroscopy (Montelione et al., 1984; Williamson et al., 1986; Dyson et al., 1988). The observation showing that turns in short linear peptides exist and can be quite stable in aqueous solution implies that they must also exist in polypeptide chains under folding conditions (Dyson et al., 1988). Once formed, turns can direct the folding

Reverse turns (also known as tight turns, /I turns, /I bends, hairpin bends, etc.), are regions of polypeptides involving four consecutive residues where the chain changes direction by almost 180 degrees. Reverse turns are important secondary structural elements in folded proteins (Chou & Fasman, 1977; Richardson, 1981). In their survey of highresolution X-ray atomic co-ordinates of 29 proteins, Chou & Fasman (1977) found that 32% of the residues (counting 4/turn) were involved in reverse turns. Large sections of folded proteins can be described as sequence-adjacent stretches of repetitive secondary structure (helices or strands of fi sheet) in the protein interior joined by reverse turns near the protein surface (Richardson, 1981). Most proteins have a compact, globular shape rather than a loose, extended structure because of the chain reversals produced by /? turns (Chou & Fasman, 1977).

f Abbreviations used: n.m.r., nuclear magnetic resonance; AC, amino-terminal blocking group COCH,; NHMe, carboxy-terminal blocking group XHCK3; p.m.f., potential of mean force. 783

002%2836/90/230783-14

$03.00/0

0 1990 Academic Press Limited

784

D. J. Tobias

process by greatly reducing the conformational space available to the folding polypeptide chain, and by bringing together residues that are distant in sequence (Zimmerman & Scheraga, 1977a). Wright et al. (1988) remarked that the observation of significant populations of turns in small (4 to 6 residues) peptides is surprising. Indeed, the factors that contribute to the stability of turns in small these peptides in water are not obvious. However, factors must be elucidated in order to appreciate fully the possible role of turn formation in the early stages of the folding process. As we see it,, the relative stabiity of secondary structures (compared to extended structures) in short peptides is the sum of five contributions: (1) first, the relative energies of the backbone conformations need to be considered. How stable is the backbone conformation of t,he folded secondary structure compared to the extended conformations? (2) If backbone amide hydrogen bonds are present, as for example in helices, fi sheets, and in some reverse turns, what is their contribution t.o the stability of the folded st,ructure? (3) Side-chain interactions, such as salt bridges, hydrogen bonds, and hydrophobic interactions or steric interactions, are also important. (4) In small unblocked peptides, electrostatic interactions of the charged terminal groups with each other or with charged side-chains or the backbone peptide units could contribute to the relative stability of folded and unfolded structures. (5) The changes in the peptide-solvent interactions that accompany changes in the peptide conformations must be considered. The observation that stable secondary structures form in some short peptide sequences but not in others (Montelione et al., 1984; of Dyson et al.; 1988) clearly shows that the stability the folded structures is not simply due to one or two factors alone, such as backbone conformation preferences and/or the presence of backbone hydrogen bonds. Furthermore. the various factors are obviously coupled, and they must be considered t’ogether in order to understand the relative stability of various structures in a given peptide sequence. For example, specific favorable side-chain and/or terminal group interactions could stabilize structure that do not have optimal backbone conformations and hydrogen bonds. The situation is obviously quite complicated, and can only be understood by considering the relat,ive importance of the various factors in comparative studies of particular peptide sequences. Our purpose in the present work is to decouple the sequence-specific extrinsic factors (( 3) and (4)) from the intrinsic factors (( 1 ), (2) and (5)) bv studying blocked Ala-Ala and Pro-Ala dipeptides ;n water. explicit Computer simulations incorporating solvent models can complement experimental studies of conformational equilibria of small peptides in solution. Detailed microscopic information is not available from n.m.r. experiments, since the relevant observables such as the chemical shift and coupling constant are population-weighted accessible conformations. averages over all

et al.

Therefore, it is difficult semi-quantitatively to assess the relative importance of the various individual factors affecting turn stability using n.m.r. methods. Assuming that the potential energy functions are reliable, computer simulations can yield the microscopic detail that is lacking from the experimental studies. Once an appropriate “folding/ co-ordinate” is defined?, specialized unfolding sampling techniques can be used t)o generate specific ensembles of configurations, and t,o calcula,te a variety of average properties along that co-ordinate. Most importantly, free-energy surfaces as functions of t.he folding/unfolding co-ordinate can be computed, and therefore the relative stabilities of the folded and unfolded species can be quantitativelv determined. Furthermore, the information contained in the trajectories may be utilized t,o characterize thermodynamically and microscopically the factors affecting those stabilities. Tn this paper, we report the results of molecular dynamics simulations of reverse turn formation in the blocked dipeptide AC-Ala Ala-NHMe (As is the amino-terminal blocking group COCH,. and NHMe is the carboxy-terminal blocking group NHCH,)f; in aqueous soltltion. By carrying out simulations in a realistic model for water, we can explicitly investigate the effects of the solvent on the peptide conformational equilibrium. We chose the Ala-Ala sequence for study because its backbone conformational preferences should be generally representative of all of the remaining amino acids (excluding glycine), in the absence of side-chain-specific interactions. We studied the folding/unfolding of Ac-AlaAla-NHMe by defining the one-dimensional rraction co-ordinate, r(Oc,J-Hc,)), as the distance between the Ac carbonyl oxygen and the NHMe amide hydrogrrl (see Fig. I), and carrying out a series of simulations of the peptide wit.h that distance constrained at different, values. As we shall show below. the reaction co-ordinate we define is a foltling/nnfoltling coordinate since, at, small values of r(O(, ,-H,,,) the peptide forms a reverse turn, at large values it is extended, and intermediate values of r(0,1)-mHc4)) smoothly connect the folded and unfolded states. Of course. there are other possible one-dimensional reaction co-ordinates, for example the C(,,--N(,, distance. which we could use to simulat,e reverse turn folding/unfolding. However. we are interestBed in studying t’he role of t,he amide hydrogen bond in use reverse turns. therefore we stabilizing T(O~~)-H~~)) because at small values it definitely corresponds to hydrogen-bonded turns. while other clhoices of the co-ordinate might) not. Since proline is t Throughout, this paper we shall refer to t,hr reverse turn conformation as the “folded“ state. the extjrnded wnformation as the “unfolded” state. and the interconversion of these two states HS “folding/unfolding“. 1 Throughout this paper we will use the abbreviations and symbols for the description of the conformation of polypeptide chains from the IUPA(I-IUR Commission on 13iochemical Nomenclature (IITPA(‘-TL!R. 1!470).

Reverse Turns in Blocked Dipeptides

785

stability of reverse turn conformations and hydrogen bonds, and the “proline effect” on reverse turn conformational equilibria, of short linear peptides in water.

2. Methods (a) Construction

of the folding~unfolding

co-ordinate

We studied the folding/unfolding of reverse turns in Ac-Ala-Ala-NHMe and Ac-Pro-Ala-NHMe hy carrying out series of simulations with the peptides constrained near particular values of the r(O(,,-H(,,) distance. We initially built each peptide in hydrogen-bonded. ideal type I conformations (&z -6O”, ti2 z -3O”, 43 z -90” and 11/3z 0” (Chou & Fasman, 1977), except & z -90” for the proline-containing peptide), with r(O(,)-HJ z 2.0 A (1 A = @l nm)t. We chose type I primarily because it is the most common type in proteins (Chou & Fasman, 1977). Then we minimized the energy of each peptide using the CHARMM potential energy function and parameters (all of the energy minimizations and molecular dynamics simulations described herein were carried out using the CHARMM program (Brooks et al.. 1983)). with the addition of a harmonic constraint potent,ial, (J*(r):

T:*(r) = K(r-r,)Z, Figure 1. Pseudo-atom representations of the model peptides used in this study. The upper drawing shows Ac-Ala-Ala-NHMe in a type I reverse turn conformation. reaction co-ordinate, with the folding/unfolding r(O(,,-Ho,), indicated. The lower drawing shows Ac-ProAla-NHMe in an extended conformation.

by far the most prevalent residue at position 2 of reverse turns in proteins (Chou & Fasman, 1978), we are also interested in the effects that proline at position 2 has on the stability of reverse turns. We carried out a parallel study of the peptide trans-AcPro-Ala-NHMe to see if reverse turns with proline at the second position are intrinsically more stable than others in water. We expected that, since the of proline is restricted conformational space compared to other residues, the unfolded form of the proline-containing peptide should have less configurational entropy (Matthews et al., 1987), and hence should be destabilized, leading to a more stable turn compared to Ac-Ala-Ala-NHMe. We will compare the relative stabilities, and estimates of the configurational entropies, of the folded and unfolded forms of Ac-Ala-Ala-NHMe and Ac-Pro-Ala-NHMe, on reverse turn effect” to assess the “proline formation. This paper illustrates how computer simulations can complement experimental studies of the folding of small peptides in solution. The experimental work of Montelione et al. (1984), Williamson et al. (1986) and Dyson et al. (1988) led to important conclusions regarding the effects of side-chain and reverse interactions on turn terminal-group stability, and furthermore, the sequence requirements for formation of reverse turns, in solutions of short peptides. The results of our theoretical study lead us t’o conclusions regarding the intrinsic

(1)

where the force constant K = k,T/26r2. e.g. 6r is the deviation from the reference distance rO, at which the constraint energy is ,&T/2 (in the present work, we used 6r = @3 to @5 8) and IL, is the Boltzmann constant. The constraint potential is supposed to keep the separation r(Oclj-Hc4)) near TV during the course of minimization (or dynamics). At the end of the energy minimizations, both peptides were still in hydrogen-bonded type I turn conformations, with T(O~,)-H~,)) x 2.0 i\. From t’hese 2 minimized peptides, we generated 2 new structures with larger T(O~,)-H& values by increasing the value of r0 and repeating the minimizations. We repeated this procedure, generating each new pair of structures from t,he most recently generated pair, until we had 2 sets of 12 peptides with v(O~~)-H++)) in the range 1% to 11..5.A. We will show below that small values of r(O(,,-H(,,) correspond to hydrogen-bonded, ideal type I reverse turns, intermediate values to turns without hydrogen bonds, and large values to extended conformations. Finally. to prepare for the simulations, each structure was placed in the renter of a rectangular box of water molecules, and solvent, molecules that overlapped with the peptide were removed. Simulation of these systems with the corresponding constraint potentials generates configurations along the hydrogen-bonded reverse turn folding/unfolding coordinate. from which a variety of properties can be computed. including the free energy as a function of do,,,-Hpt,).

(b) Free-energy

surfaces

via umbrella

sam,pling

Using equilibrium statistical mechanics, one can calculate the free energy, W(r) (also known as the potential of mean force, or p.m.f.), as a function of a reaction coordinate r, once the normalized probability density, p(r), t We use the numbers I t,o 4 to label the residues in reverse turns, e.g. 1 refers to the first residue of a turn, etc.

D. J.

Tobias et al.

is known for that co-ordinate in the canonical ensemble (Landau & Lifschitz, 1969; Northrup et al., 1982), e.g.: W(r) = --/I-’

In P(T),

(2) where p= l/k,T, k, is the Boltzmann constant, 7’ is the absolute temperature, and p(r’) dr’ is the probability of finding the system in a configuration where the coordinate r is between T’ and r’+dr’. In t,he language of thermodynamics, W(r) is the reversible work, or the Helmholtz free energy in the canonical ensemble, required to change the co-ordinate to r from a reference value where the free energy is defined to be zero. In principle, p(r) could be computed from a single computer simulation if all configurations corresponding to the full range of possible values of the co-ordinate r could be adequately sampled. However, in practice this is generally not possible, since the system tends to get trapped in wells on the potential energy surface, and transitions between wells across high-energy barriers are usually rare during the course of a simulation. For example. in a tripeptide simulation, the system could get trapped in the broad minimum where the 4 central backbone dihedral angles are in the extended p region of the Ramachandran map and, during the course of a simulation of reasonable length on a present-day supercomputer, & and ti3 might never make transitions to the CIregion to sample reverse turn conformations. This problem can be circumvented by using a specialized sampling technique known as umbrella sampling. In the umbrella sampling procedure (Valleau & Torrie, 1977; Northrup et al., 1982), an auxiliary “umbrella” potential U*(r) is added to the potential energy function of the system to bias the sampling toward a desired range of r values. By carrying out a series of simulations in which U*(r) is systematically varied, statistics are gathered in a series of overlapping “windows” centered around different values of r. The resulting biased probability distributions, p*(r), are subsequently corrected to remove the effects of U*(r) using (Northrup et al., 1982): p(r) = e~“*c’)(e-~u*n)~*(r),

(3)

where ( ) denotes a canonical ensemble average. Thus, with eqn (2), the corrected p.m.f. for the ith window. W,(r):

W,(r) =-p-l

lnp:(r)-UT(r)-Cir

(4) Ci = (e-flui*(*) ) is a different constant for each window. The Wi from overlapping windows are matched

where

to determine the differences in the Ci and form a continuous p.m.f. However, the resulting p.m.f. contains an additive constant C. Thus, the absolute vertical location of the overall W(r) computed using this procedure is unknown. Since we will restrict ourselves to a discussion of the shapes of the surfaces, and free-energy differences, the abolute vertical locations are not. important. Finally, we note that the formalism used to calculate the p.m.f. values rontains no approximations. Errors in the p.m.f. arise from finite sampling of the distributions and statistical uncertainties in the averages. (c) Equilibrium

constants

The relative stability of 2 particular conformations may be determined by calculating the difference between 2 point,s on a p.m.f. However, when the relative stability of 2 states is desired, the free-energy difference between ensembles of conformations must be computed. For example, in a calorimetric study of thermal denaturation, one does not measure the free-energy difference between a

single folded structure and a single unfolded structure. Rather, a difference between ensembles of folded and unfolded structures, the folded and unfolded states, is measured. Thus, if one wants to know the relative stability of 2 states, X and Y, which correspond to 2 distributions of conformations (e.g. there are many extended conformations, with different r(%,-Hd values, which we would say correspond to the unfolded state), then one should compute the free-energy difference, AAXY. from the equilibrium constant for the conversion of X to Y 1 Kxy: eq AAXY = A(Y)-A(X)

= -k,T

In K:J.

(5)

The equilibrium constant is simply the ratio of the mole fractions of X and Y. zx and xy, which can be determined from the p.m.f.: e -flW(r)&. 5Y .-

KXY=??E eq xx

(6)

e - bw(*)& sX

The integrations in eqn (6) are over the ranges of T values corresponding to either X or Y. Although eqn (6) is a working definition of K:T, one should be careful about’ interpreting equilibrium constants and relative free energies computed from it because the results are often quite sensitive to the choice of the ranges of integration, which is arbitrary. (d) GonJigwutior~

eatropy

Once the p.m.f. has been computed, eqn (2) can be inverted t,o yield the probability density: p(r) = (‘e-nW(r).

(7)

In eqn (7), W(r) is the p.m.f. obtained using umbrella sampling, and C is the normalization constant. The probability density may now be used t,o calculate the configurational entropy for the stable conformations, identified as peaks in p(r) or wells in W(r), along the co-ordinate r. The configurational entropy for the conformation X, Sf, due to fluctuations about X on the solventaveraged p.m.f., is related to p(r) by (Karplus & Kushick, 1981): P

,S’t(=-k,

(8)

p(r) In p(r) dr. JX

The integration in eqn (8) is over the range of r values spanned by the peak in p(r) corresponding to the conformation X. (e) Decomposition

of the free-energy

surfaces

We will be using free-energy differences between points on the p.m.f. values to discuss the relative stabilities of particular conformations along the reaction co-ordinate. In addition, we can decompose these free-energy differences into peptide-peptide and peptide-solvent contributions to gain a more microscopic understanding of the relative stabilities. Now we show how we carrv out the thermodynamic decomposition using our simulation data. The Helmholtz free-energy difference between 2 systems with particular values, rl and r2, of the coordinate r may be written: AA = W(r,)-

W(r,)

= AE-TAS,

where AE’ and AS are the differences in internal

(9) energy

Reverse Turns in Blocked Dipeptides and entropy, respectively. The internal energy difference is equal to the difference in the average potential energies: AE = (UP,))-(U(r,)). Since the potential

787

(10)

degrees of freedom were allowed to fluctuate. The coordinates of each system were stored every 10 time-steps for the calculation of the p.m.f. values and other average quantities, which are presented and discussed below.

(11)

3. Results

energy may be written:

U = Uuu+ li,, + U,, ,

where O;,, U,,, and U,, are peptide-peptide, peptidesolvent and solvent-solvent interaction energies, respectively, we can express the internal energy difference as the sum of 3 average interaction energy differences: AE = (AU”,)+(AU,,)+(AU,,).

(12)

Now; using eqns (10) to (12), we can rewrite eqn (9) as: AA = (AU”:‘,,)+(AU,,)+(AU,,)-TAS.

(13)

The ent,ropy difference is composed of differences in t,he peptide configurational entropy, and the solvent-peptide and solvent-solvent entropies. Yu & Karplus (1988) have shown that the solvent-solvent energy and entropy contributions exactly cancel each other in the solvation free energy. Furthermore, as we shall show below, the configurational entropies computed from the free-energy surfaces are actually quite small. Thus, we neglect the configurational contribution in our final decomposition: AA = (A~J~i,,)--AU,,)-TAS,,,

(14) where - TAS,, is the peptide-solvent entropy difference. If we can calculate all of the terms in eqn (14), we can explain the relative stability between 2 peptide conformations in solution in terms of differences in the peptidepeptide, peptide-solvent interactions. It is straightforward to compute all of the average interaction energies, but it is difficult bo calculate the entropy difference, directly from the simulation data. Since the entropy change is the only missing term in eqn (14) it can be obtained indirectly as the difference between AA and the remaining terms. (f) Details of the simulations We carried out molecular dynamics simulations on each of the solvated peptide systems that were constructed and

constrained as described above. Each system consisted of 1 peptide molecule and 233 to 238 water molecules in a rectangular box with periodic boundary conditions. We used the 3-site TIP3P model described by Jorgensen et al. (1983) for water. The box dimensions were 2L x L x L, where L = 155516 A, to give approximate agreement with the experimentally observed water density at room temperature (1.0 g cme3), after the solute volume was subtracted from the box volume. The non-bonded energies and forces were smoothly truncated at 115 A (using a van der Waals’ switching function and an electrostatic shifting function (Brooks et al., 1983)) based on atomic centers, according to the minimum image convention (Allen & Tildesley, 1989). The Verlet (1967) algorithm was used to integrate Newton’s equations of motion (with a time-step of 1.5 fs). Each of the simulations consisted of 10,000 steps (15 ps) of equilibration and 20,000 steps (30 ps) of data collection. The non-bonded interactions were processed using a listbased algorithm (Verlet, 1967), and the lists were updated every 20 steps. The velocities were periodically reassigned from a Maxwell-Boltzmann distribution to maintain temperatures of approximately 300 K. The SHAKE constraint algorithm (Ryckaert et al., 1977) was used to keep the water molecules rigid, and to maintain rigid N-H bonds in the peptide molecules. All of the remaining

In this section we present our results for the free-energy surfaces and probability densities as functions of the reaction co-ordinate, as well as various other thermodynamic quantities derived from them. In addition to computing the freesurfaces, we have further analyzed our energy

trajectories

to determine

tions were generated

what peptide conforma-

by the constrained

molecular

dynamics simulations. We present the results of this analysis first, so that we can identify regions of the reaction mations

co-ordinate with in the remainder

particular peptide of the paper.

confor-

of peptide conformations along pathway the folding/unfolding

(a) Characterization

We will use the joint probability densities of the pairs of dihedral angles +2, 1+9~and $3, es, and average values of the distance between the AC and NHMe methyl carbons, r(C;,,-C&,), to characterize the peptide backbone conformations observed during several constrained simulations along the folding/unfolding pathway. We can thus verify that certain regions of the reaction co-ordinate r(O(,,-H++,) do indeed correspond to reverse turn and extended peptide conformations. Furthermore, we can characterize the reverse turns in terms of their dihedral

angle preferences.

In addition,

we will

use the averages and root mean square (r.m.s.) fluctuations of the distance between the O(,, and Nc4) atoms, WC,,- N,,,), and the angle between the Ctl)-Oo) and NC,,-H(,, bond vectors, @CO, NH), to describe the hydrogen bonding in the folded peptides. In Figures 2 and 3 we show the normalized probability densities for 42, ti2 and &, $s from two sets of three simulations of Ac-Ala-Ala-NHMe and Ac-Pro-Ala-NHMe, respectively. In Table 1 we list the most probable values of the dihedral angles, along with the average values of r(Otl,-Hc,,), rK$-C:d ~(O~I~-N~~~)>and @CO, NH), from the six simulations. First, we consider the data from the r,, = 1.8 A simulations. The average value of r(CT,,-C&,) from the simulation of Ac-Ala-Ala-NHMe was 5.4 + 0.3 A. Roth the dZ, $* and 43, *a pairs remained in the c1 region of the Ramachandran map throughout that simulation (see Fig. 2). The most probable values of the dihedral angles from that simulation were $2, $2 = -6O”, -40” and &, es = -80”. -40”. In the simulation of Ac-Pro-Ala-NHMe, both pairs of dihedral angles also remained in the a region, their most probable values were &, IL, = - 60”, - 20” and 43, *3 = -8O”, -4O”, and the average value of r(CT,,-C&J was 6.0 + 0.2 A. The average C;;,-C& distances for both peptides fall in the middle of the range of values (4 to 8 A) found for bends in pro-

788

et al.

D. J. Tobias

Figure 2. Kormalized joint probability densities of the dihedral angle pairs 42, 1(12and 43, ti3 for Ac-Ala-Ala-NHMe. The upper 2 distributions are from the r,, = 6.5 L%simulation, 2 from the r0 = 1.8 a simulation.

teins (Chou & Fasman, 1977). The probability densities in Figures 2 and 3 show that, according to the classification scheme of Chou & Fasman (1977), both peptides remained in ideal type I reverse turn throughout their respective conformations simulations. By looking at the averages and fluctuations of the Oc1)-Nc4) distance from the r. = 18 A simulations, we can determine whether or not the reverse turns were hydrogen bonded during the simulations. We use the definition of Chou & Fasman (1977), which states that reverse turns are hydrogen bonded if r(O~r)-N& 5 3.5 A. By considering the average

the middle

2 from the rO = 3.5 L%simulation,

and the bottom

distance together with the average of the angle between the C~lj-O~lj and Nc4)-Hc4) bond vectors, &CO, NH), we can assess the quality of the hydrogen bonds. With the peptide model used in our simulations, optimal linear amide hydrogen bonds have r(Oc1)-Nc4)) = 2.9 A and @CO, NH) = 180” (Sneddon et al., 1989). From the r,, = 1.8 A simulations, the average values of r(0(,)-Nt4)) were 2.95 + 0.15 A for Ac-Ala-Ala-NHMe and 2.98 50.15 A for Ac-Pro-Ala-NHMe. Thus, both peptides maintained l-4 hydrogen bonds throughout the course of those simulations. The average values of &CO, NH), 146( + 15)” for the Ala-Ala

Table 1 Peptide Peptide

ro

Ala-Ala

1.8 35 6.5 1.8 30 65

Pro-Ala


conformational

characteristics

along the folding

42

*2

43

*Ln

(r(CT,,-C&,,))

-60 -60 -100 -60 -80 -60

-40 -60 120 -20 60 120

-80 -80 -80 -80 -100 -80

-40 -60 120 -40 -40 140

54 kO.3 54 + 03 9.0 f 0.6 6.OkO.2 8.3 +02 9.5 +@6

co-ordinate (r(Oc,,-N,,,)) 3.0fO.2 40 & 0.4 6.7 +@3 3.0+@2 47 +0.2 6.7 +0.3

(@(CO, NH))

TYP

146+15

I I Extended I IV Extended

145f8

Definitions of the numerical quantities are given in the text. Distances are tabulated in A, angles in degrees. Tabulated are the standard deviations in the average quantities. The entries in the type column denote either reverse turn types 1981) or extended conformations.

uncertainties (Richardson,

Reverse Turns

Figure 3. Normalized The unner 2 distributions

2 fro;Ithe

joint probability

densities of the dihedral angle pairs 4*, I)~ and 43, tj3 for Ac-Pro-Ala-KHMe.

are from the T,, = 65 A simulation,

r0 = 1.8 A simulation.

789

in Blocked Dipeptides

the middle

2 from the T,, = 3.0 A simulation.

and the bottom

”

peptide and 145( f 8)” for the Pro-Ala peptide, show that the hydrogen bonds in both peptides are significantly bent. However, the small fluctuations in the distances and angles show that the hydrogen bonds are quite rigid. In fact, the reverse turn hydrogen bonds are about as close to optimal as is possible, given the constraints of the backbone connectivity and the presence of the r(O(,)-H(,J constraint potential. The average values of the Ot1)-Ht4) distance from the r,, = 1.8 A simulations were 2.1+02 for both peptides. Looking at the biased T(O(~)-H& probability distributions (not shown), we saw that the peptides actually spent most of the time with r(O(,)-H(,)) values in the range I.8 to 2.8 a during those simulations. Thus, we can say that small values of the reaction co-ordinate (r(O(,,-H(,,) E 1.8 to 2.8 A) correspond to hydrogen-bonded reverse turn peptide conformations. Next, we examine the data from simulations with intermediate values of r,, (35 A for Ac-AlaAla-NHMe and 3.0 tf for Ac-Pro-Ala-NHMe). Both and &, tig of the Ala-Ala peptide were 4% $2 still in the a region of the 4, $ map during the r. = 3.5 A simulation (see Fig. 2). The most probable values were $J~, 11/2= -6O”, -60” and &, $I~ = - SO”, - 60”, the average value of r(Ct,-CT+) was

5.4 + @8 A, and the average Ocl)-N++) separation was 4.0+@4 A. Thus, the peptide was still in a type I reverse conformation, but it no longer had a l-4 hydrogen bond. During the r. = 3.0 A simulation of the Pro-Ala peptide, the 42, $Z pair was in the /l region, while the 43, e3 pair was in the LYregion (see Fig. 3). The large average CT,,-CT+ distance, EG3f0.2 8, suggests that the Pro-Ala peptide was not in bend conformations during that simulation. However, when we studied the Ac-Pro-Ala-NHMe trajectory using molecular graphics, we saw that all of the peptide structures contained chain “reversals” of ~100 to 180” in spite of their large Cyl,-CT+ distances. The most probable values of the dihedral angles, t2, ti2 = -SO”, BO”, and &,$I~ = - lOO”, -4O”, fall into the miscellaneous bend category, type IV (Chou & Fasman, 1977). The average value of r(O(,, -NC,,), 47 kO2 8, shows that the distorted Ac-Pro-Ala-NHMe bend was not l-4 hydrogen-bonded. The average values of the O(,,-H,, distance from the r,, = 6.5 A simulations were 3.7 +@4 A for Ac-Ala-Ala-NHMe and 4.0 kO.2 A for Ac-Pro-Ala-NHMe. From the biased r(Ofl)-Hc4) probability distributions, we saw that both peptides mostly had r(O(,,-H,,) values in the range 3 to 5 A during those simulations. Therefore, that range of values of the reaction co-ordinate

790

D. J. Tobias

corresponds to type I bends without l-4 hydrogen bonds in Ac-Ala-Ala-NHMe, and distorted bend-like structures in Ac-Pro-Ala-NHMe. Finally, we consider the data from the r. = 65 A simulations. The average Cl;,-C”,, distances from those simulations were 9.0 f 66 B for Ac-Ala-AlaNHMe and 9.5f.66 for Ac-Pro-Ala-NHMe. These values are characteristic of those seen for extended structures in proteins (Zimmerman et al., 1977). Figures 2 and 3 show that both pairs of 4, + angles were in the /I region of the Ramachandran map for both peptides throughout the simulations. The most probable values were 42, ti2 = -lo@‘, 126” and 43, $3 = -8O”, 120” for the Ala-Ala peptide, and 42, $2 = -6O”, 120” and &, $3 = -8O”, 140” for the Pro-Ala peptide. Thus, the extended conformations of both peptides are like sections of /I strand, with successive CO bond vectors pointing in opposite directions. The average values of the O(,,-H(,, distance from the r,, = 65 A simulations were 66 + 0.3 A for Ac-Ala-Ala-NHMe and 6.6 + 0.4 A for Ac-Pro-Ala-NHMe. The biased r(O(,,-H(,,) probability distributions (not shown) demonstrate that both peptides mostly had T(O~,,-H& values in the range 60 to 7.5 A during those simulations. Consequently, we can identify values of the reaction co-ordinate greater than -6 A with extended peptide conformations. densities, (b) Free-energy surfaces, probability entropies and equilibrium constants conjgurational

In Figure 4 we show the free-energy surfaces as functions of the reaction co-ordinate r(O(,,-H(,,) for the Ala-Ala and Pro-Ala peptides. Each curve was obtained by splicing together the Wi from 12 simulations. We joined the Wi from neighboring windows at the r(O(r)-H(+) values where the p:(r) intersected. Because the intersection between neighboring windows was quite large, most of the data used to compute the free energies came from the peaks of the distributions, and the statistical errors were therefore quite small. We obtained the statist,ical uncertainties as error-propagated standard deviations in the free energies computed from blocks of 100 configurations. The uncertainties ranged from 0.1 to 95 kcal/mole (1 cal = 4184 J) for values to 1.5 kcal/mole at most of the r(O(,)-H& the endpoints. Since we will discuss only the qualitative features of the p.m.f. values and quantities derived from them, these relatively small statistical uncertainties will not affect our conclusions. While the absolute vertical placement of the curves is arbitrary, we set them both to zero at r(O(,)-H& = 2.6 A. The p.m.f. values in Figure 4 have several features in common. First of all, each curve rises sharply with decreasing r(O(,)-H(+) below 2 A, due to the van der Waals’ repulsion between the Ocl) and Hc4) atoms at small separations. Secondly, each curve exhibits another steep wall due to bond angle distortions in the extended structures at large r(O(,,-H(,,) values. The bond angles of the rigid

et

al.

61

I

-12’ 0

2

4 6 O-H distance (8)

8

IO

Figure 4. Free-energy surfaces (potentials of mean co-ordinate, force) as functions of the reaction r(O(,,--Kc,,). The continuous curve is for Ac-Ala-AlaNHMe and the broken curve is for Ac-Pro-Ala-NHMe. Both curves were arbitrarily set to zero at T(O,,~-H~,~) = %6 8.

proline residue in the Pro-Ala peptide become distorted at r(O(,,-H,,) z 7 A, while those in the more flexible Ala-Ala peptide do so at r(Oll)-H& z 9 A. The locations and shapes of these large r(O(,,-H,,) walls are of little interest to us, they merely indicate the ends of the stable basins immediately preceding them on the folding coordinate. Finally, the overall topology of both surfaces is similar: there is little or no stable minimum in the hydrogen-bonded reverse turn region around r(O(,, -H,,,) % 2.5 A, the free energy is monotonically decreasing in the non-hydrogenbonded bend region around r(O(,)-H& x 3 to 5 A, and there is a deep well in the region around r(Ocl)-Hc4)) x 65 A, corresponding to the manifold of stable extended conformations. The nonhydrogen-bonded bends are lower in free energy than the hydrogen-bonded bends, and the extended conformations of both peptides are several kcal/ mole lower in free energy than any of the reverse turn conformations. Thus, our free energy surfaces show that reverse turns in the blocked Ala-Ala and Pro-Ala peptides, both with and without l-4 hydrogen bonds, are unstable with respect to the extended conformations in water?. A comparison of the two curves in Figure 4 t Strictly speaking, stability refers to the curvature of and stable conformations are on the free-energy surface, e.g. the hydrogen-bonded Pro-Ala turn, and the extended conformations of both peptides. We will occasionally loosen the definition of stability and use the concept of relative stability to refer to the relative free energies of different conformations. Thus, when we say one conformation is more (or less) stable than another, we mean that it is lower (or higher) in free energy. the free-energy

surface,

those corresponding to local minima

Reverse Turns in Blocked Dipeptides 1.6,

I .2t

1::; 0

2

__.--__ fi!I i! ;I ;! ;i;!!! ;! ;;; !!! ;; i!! 1

1

4 6 O-H distance CL)

8

IO

Figure 5. Normalized probability densities of the reaction co-ordinate, r(O(,,-H(,,). The continuous curve is for Ac-Ala-Ala-NHMe and the broken curve is for Ac-ProAla-NHMe. The inset shows an expansion of the hydrogen-bonded reverse turn region.

reveals some important differences between the AlaAla and Pro-Ala peptides. First, the free-energy surface for the Pro-Ala peptide has a shallow minimum centered around r(Ot,)-HC4J cz 2.5 A, corresponding to a slightly stable hydrogen-bonded turn, whereas there is no such minimum for the Ala-Ala peptide. The barrier to unfolding the ProAla turn is approximately 65 kcal/mole, which is less than thermal energy at 300 K (kBT x 66 kcal/ mole). Secondly, the hydrogen-bonded turn conformations in the Pro-Ala peptide are much less stable, relative to extended conformations, than in the Ala-Ala peptide: the free energy difference between hydrogen-bonded turn and extended conformations 10 kcal/mole for Ac-Pro-Alais approximately NHMe, while it is about 5 kcal/mole for Ac-Ala-AlaNHMe. Furthermore, in the non-hydrogen-bonded bend region, the Ala-Ala p.m.f. is much flatter than the Pro-Ala p.m.f.; neither p.m.f. has a stable minimum in that region. Finally, the well corresponding to stable extended conformations of the Pro-Ala peptide is much narrower, and occurs at than that of the smaller O,, )- H(,, separations, Ala-Ala peptide. The stable extended conformations of Ac-Ala-Ala-NHMe exist over a range of values of the folding co-ordinate, r(O(,,-Ho,) x 6 to 9 A, whereas those of Ac-Pro-Ala-NHMe are highly localized around r( O,,,- H& z 6.5 A. This is a manifestation of the greater rigidity of the proline residue, which restricts the conformational space of the extended Pro-Ala peptide, and, as we will show below, lowers its configurational entropy, compared to the Ala-Ala peptide. The normalized probability densities, computed from the p.m.f. values shown in Figure 4 using equation (7), are shown in Figure 5. Figure 5 also shows that the distribution of extended conforma-

791

tions for Ac-Pro-Ala-NHMe is very sharp and narrow, and it is centered at r(Ot,)-HC,J z 6.5 A, while for Ac-Ala-Ala-NHMe it is much broader, and is centered at r(OC,)-HC,)) z 7.2 A. Thus, the conformational space for the extended Pro-Ala peptide is much more restricted compared to that of the AlaAla peptide. In addition, the inset of the Figure shows that there is a very small peak centered at r(OC,)-HC,)) z 2.6 A in the probability density for the Pro-Ala peptide, corresponding to a small number of stable reverse turn conformations. In contrast, there is no such peak in the probability density for Ac-Ala-Ala-NHMe. When we apply equation (8) to the probability densities in Figure 5, we find that the configurational entropy of the extended Pro-Ala peptide is Sz” = 0.0006 cal/mol K, and for the AlaAla peptide is SE” = 6003 cal/mol K. The configurational entropy of the reverse turn conformations is zero for Ac-Ala-Ala-NHMe and negligible for AcPro-Ala-NHMe. Therefore, the contribution of the configurational entropy to the free-energy difference between the folded and unfolded conformations is - TS%‘, which is equal to -0.2 kcal/mole for Ac-Pro-Ala-NHMe and - 68 kcal/mole for Ac-AlaAla-NHMe, at 300 K. To determine quantitatively the relative stabilities of reverse turn and extended conformations, we computed the equilibrium constants for unfolding the turns using equation (6). We chose the range r(OC,)-HC,J < 3.0 A for the hydrogen-bonded turns and r(OC,)-HC4)) > 41 A for the extended conformations. This choice gave K,, = 4995 for unfolding Ac-Ala-Ala-NHMe and K,, = 1.8 x lo7 for Ac-ProAla-NHMe. The corresponding free energies for unfolding the hydrogen turns were -5.1 kcal/mole for the Ala-Ala peptide and - 160 for the Pro-Ala peptide. We also computed the same quantities for unfolding all turn structures (not just hydrogenbonded turns) by using the range r(OC1)-HC4)) < 4.1 A for the turns. The expanded range yielded K,, = 1057 or -4.2 kcal/mole of free energy for unfolding Ac-Ala-Ala-NHMe, and K,, = 17,205 or - 5.9 kcal/mole for Ac-Pro-Ala-NHMe. The former unfolding free energies are very similar to the values we get if we simply take the differences between points on the p.m.f.s corresponding to the centers of the distributions of the turn and extended conformations. The latter value, obtained by considering an expanded range for the folded state, is essentially unchanged for Ac-Ala-Ala-NHMe, but is significantly different for Ac-Pro-Ala-NHMe. This is because the p.m.f. for the Pro-Ala peptide has a steep negative slope beyond r(OC,)-HC,)) = 3.0 A, which introduces a greater number of low energy conformations into the folded state population. The use of equilibrium constants to obtain free-energy differences from our p.m.f.s is difficult because there is no folded state minimum on the Ala-Ala p.m.f., and only a slight minimum at r(OC,)-HC,J < 3.0 A on the Pro-Ala p.m.f. Thus, the choice of integration limits used in equation (6) is arbitrary, since the separation of folded and unfolded populations is unclear. Qualitatively, our results show t,hat the

792

D. J. Tobias

shapes of the wells of extended conformations on the p.m.f.s are of little consequence in determining the relative stabilities of the folded and unfolded dipeptides when reasonable definitions of the folded and unfolded states are used. However, as is demonstrated by our “looser” definition of “folded”, the quantitative details of the free-energy differences are quite sensitive to the choice of the limits of integration. (c) Decomposition

of the unfolding

unfolding

=

Table 2 Ijecumposition

of the unfolding

*free energies

Prre-energy terms are defined in t,he text, and tshulated here in kcal/molr. Tabulated uncertainties were determined from the standard deviations in the averages by error propagation.

free energies

In order to understand why the hydrogen-bonded reverse turn conformations of our model peptides are unstable relative to extended conformations in water, and why the free energy difference between t,he hydrogen-bonded turns and extended structures is much greater for the Pro-Ala peptide, we consider the thermodynamic decomposition (see eqn (14)) of the “unfolding” free energy, AAunfolding: AA

et al.

A extd -A t”r”

(15)

For Ac-Ala-Ala-NHMe, we take Aextd = W(6.8 A) and A,,,, = W(2.2 A), and for Ac-Pro-Ala-NHMe, A extd = W(6.5 A) and A,,,, = W(2.3 8). We chose the above definition for AAunfolding because it allows us to use the thermodynamic decomposition in equation (14). We will see that the definition is useful because these unfolding free energies are very similar to the free-energy differences computed from t,he equilibrium constants. Furthermore, we will show below that differences in other thermodynamic quantit’ies computed between structures with distributions of r(OC,)-HC,)) values are very similar to those computed between particular r(OC,)-HC,)) values. We present the unfolding free energies and their thermodynamic decompositions according to equation (14) in Table 2. The uncertainties in the internal energy differences (and hence the solvent peptide-solvent entropy differences) listed in Table 2 were computed as standard deviations in averages over blocks of 106 configurations. The uncertainties therefore reflect the widths of the distributions of the interaction energies, but they probably do not indicate the repeatability of the tabulated averages. For lack of a better measure of the “errors” in t’he internal energies, we report the uncertainties. The unfolding free energy for the Ala-Ala peptide is - 56 kcal/mole; -6.6 kcal/mole of that is the average peptide-peptide interaction energy differis the average peptide-water ence , 9.8 kcal/mole interaction energy difference, and - 8.2 kcal/mole is the peptide-water entropy difference. Thus, changes in peptide-peptide energy and peptide-water entropy strongly favor unfolding the Ala-Ala bend, while changes in peptide-water energy strongly oppose it. The unfolding free energy of the Pro-Ala - 16.3 kcal/mole, is more than twice that peptide, of the Ala-Ala peptide, with - 1.6 kcal/mole due to peptide-peptide interactions, - 26 kcal/mole due to peptide-water energy, and -6.7 kcal/mole to the peptide-water entropy. In contrast to the

Ala-Ala peptide folding, that of t’he Pro-Ala is only slight’ly favored by changes in peptide-peptide interactions, and it is slightly favored rather than opposed by changes in the peptide-water energy. However. the peptide-water entropy st)rongly opposes turn formation in both the Pro-Ala and Ala-Ala peptides. By separately considering each interaction energy contribution, we can partially develop a qualitative microscopic interpretation of the unfolding thermodynamics. We begin with the peptide-peptide interna. energy differences. The average peptidepeptide interaction energy difference is negative for both peptides, and is mainly eletrostatic (the average elect’rostatic energy difference is -6.9 kcal/ mole for Ac-Ala-Ala-NHMe and -2.8 kcal/mole for Ac-Pro-Ala-NHMe). We can rationalize the electrostatic stabilization of the extended conformations in terms of the orientation of the peptide unit dipoles. In the hydrogen-bonded type I turns there is only one favorable dipole-dipole interaction: the dipoles of the first and third peptide units, which are held in proximity by the hydrogen bond, are aligned favorably at an angle, which is. on the average, approximately 35”. In the extended conformat)ion of the Ala-Ala peptide, the dipole in each peptide unit is stabilized by an oppositely aligned dipole in an adjacent peptide unit, so that the peptide-peptide electrostatic stabilization is maximized by unfolding. Because the Pro residue is missing an NH group. the first peptide unit in the Pro-Ala peptide has a smaller dipole moment than that of the AlaAla peptide, and the net gain in electrostatic stabilization upon unfolding is correspondingly smaller. We can use similar physical arguments to explain partially the peptide-water intern&on energies. The Ala-Ala peptide-water average interaction energy difference is due almost entirely to the 9.7 kcal/mole electrostatic contribution. For the Pro-Ala peptide, the electrostatic contribution is onlv 67 kcal/mole, while the van der Waals’ contrb&on is -2.7 kcal/mole. In the hydrogen-bonded type I Ala-Ala turn, all three peptide unit dipoles are basically pointing in the same direction, giving the turn an appreciable net dipole moment. Since the adjacent peptide unit dipoles point in opposite directions in the extended conformation, they effeetively cancel one another, and the net dipole moment of the extended Ala-Ala peptide is small. Thus, when the Ala-Ala turn unfolds, its net dipole moment decreases and its interaction energy wit,h the polar solvent water therefore increases. The

Reverse Turns in Blocked Dipeptides Pro-Ala turn also has a net dipole moment, but it is smaller than that of the Ala-Ala peptide because of the missing NH group in the Pro residue. Moreover, the cancelling of the net dipole moment in the extended conformation is much less complete for the Pro-Ala peptide, again because of the NH group. Consequently, t,he decrease in the net dipole moment upon unfolding, and the corresponding increase in the peptide-water interaction energy, are much smaller for the Pro-Ala peptide. Before leaving this section, we want to show that we get results for the int’eraction thermodynamics similar to those for the free-energy differences, when we consider ensembles of reverse turn and extended conformations with distributions of r(OC,)-HC,)) values, rather than those with single r(OC,,-HC,,) values. Since the comparison is very similar for both peptides, we use the Ala-Ala peptide as an example. Tn the last< section we showed that reverse turn and extended conformations were sampled throughout t.he r,, = 1.8 and 6.5 .& simulations, respectively. If we use all the configurations saved from those simulations, rather than just those with r(OC,,-HC,,) = 2.2 and 6.8 A, we find AE,, = -5.7 +5.1 kcal/mole, At/:,, = 9.0 f 11.0, and - TAS,, = - 8.3 + 12.1 kcal/ mole. These results are quite similar to those in Table 2. and would lead us to the same conclusions. However, the r0 = 6.5 A simulation only covers a subset, r(OC1)-HC4)) z 6 t’o 7.5 A, of the full range of extended conformations of the Ala-Ala peptide, r(O,,,-H(,,) c 6 to 9 8. Therefore, we should also check the results from the r0 = 8.5 A. which covers t)he range. ,r(OC1,- H(,,) z 7.5 to 9 8, according to the biased probability distribution. Using all of the configurations from the r0 = 8.5 a simulation, we find AK,, = -5.4 + 4.9 kcallmole. A&, = 6.7 + 1@6 kcal/mole. and - 7’AS,, = - 6.2 k 11.7 kcal/ mole. Again, these result’s are qualitatively similar t,o, and would lead to t’he same conclusions as. the results given in Table 2.

4. Discussion (a) Intrinsic

stability of reverse

turns

in solution

In this paper we have presented results from molecular dynamics simulations that suggest that reverse turns in blocked dipeptides are intrinsically unstable in water. This conclusion is based on the solvent-averaged free-energy surfaces computed from our simulations of Ac-Ala-Ala-NHMe and Ac-Pro-Ala-NHMe in water, which show that reverse turn structures, either with or without l-4 hydrogen bonds, are much higher (several kcal/ mole) in free energy than extended structures. We believe that our conclusions generally apply to both types of hydrogen-bonded turns, even though only type I turns were sampled during our simulations. Energy minimizations of our model peptides, in the gas phase, show that the hydrogen-bonded type I and type II turn structures have very similar energies (D. J. Tobias, S. F. Sneddon & C. I,. Brooks, unpublished results). Since both types of turns

793

should also have similar interactions with the solvent, they should have similar free energies in solution. The only appreciable free-energy contribution that is missing from our p.m.f.s is an entropy of mixing term (Karplus et al., 1987), arising from the interconversion of type.1 and type II turns. For two distinct conformations, type T and type 11, this contribution is - k,T In 2, which is -04 kcal/mole at 300 K. Therefore, we expect that adding in type TT conformations would not appreciably change our p.m.f.s or our conclusions. We use the concept of “intrinsic stability” to refer to the conformational equilibria of peptides in which the only variables affecting stabilit,y are the backbone conformational preferences. the presence or absence of a l-4 hydrogen bond, and the solvent. We chose the Ac-Ala-Ala-NHMe peptide for study in order to decouple the intrinsic factors affecting stability from “extrinsic” sequence-specific factors such as side-chain to side-chain, side-chain to backbone, or side-chain to terminal group interactions. The Ala-Ala peptide is typical of most, possible dipeptides in the sense that it is subject, to the same conformational restrictions as all dipeptides with residues containing a B carbon. The only intrinsic factor that we did not evaluate in this study is the additional conformation flexibility allowed in glycine-containing peptides. Indeed, we (*hose the Ac-Pro-Ala-NHMe peptide for studv because the prevalence of proline at position 2 oi reverse turns in proteins suggests that the geometry and rigidity of the proline residue might play a special role in affecting intrinsic turn stability. In fact. it’ turns out that, although the hydrogen-bonded Pro-Ala turn corresponds to a relative minimum in the free energy while the Ala-Ala turn does not, the Pro-Ala turn is more unstable (higher in free energy) wit,h respect to extended conformations t’han is t’he AlaAla turn. Our thermodynamic decomposit)ions of the “unfolding” free energies into peptide-peptide and peptide-water contributions show why hydrogenbonded reverse turn conformations of Ac-Ala-AlaNHMe and Ac-Pro-Ala-NHMe are unstable with respect to extended conformations. and why the Pro-Ala turn is more unstable. The extended conformations of both the Ala-Ala and Pro-Ala peptides are stabilized by favorable dipole-dipole interactions between adjacent peptide units: the stabilization is much greater for the Ala-Ala peptide. The common factor destabilizing the turn conformations of both peptides is the peptide-solvent entropy. The turn conformation of the Ala-Ala peptide is strongly stabilized by peptide-water dipole-dipole interactions. while that of the Pro-Ala peptide is not. That is the main reason why the magnitude of the free-energy difference between the turn and extended conformations for the Pro-Ala peptide is much greater than that of the Ala-Ala peptide. Our results show that a hydrogen-bond between the CO group of the first residue and the NH group of the fourth residue is not an important factor stabilizing reverse turns in solution. In fact, we

794

D. J. Tobias et al.

found that the hydrogen-bonded turn conformations of Ac-Ala-Ala-NHMe and Ac-Pro-Ala-NHMe are actually higher in free energy than turn conformations without hydrogen bonds. Apparently, the l-4 hydrogen bond is not an important factor in stabilizing turns in proteins either. Only about half the turns found in the survey of protein structures by Chou & Fasman (1977) were hydrogen-bonded. The insignificance of the l-4 hydrogen bond as a stabilizing interaction in reverse turns is not too surprising. Since reverse turns typically occur at the surfaces of proteins, the amide groups of the first and fourth residues are exposed, and are therefore capable of hydrogen bonding to the solvent as well as to each other (Richardson, 1981). Moreover, since the free energy of forming ideal, linear amide hydrogen bonds in water is roughly zero (Sneddon et al.. 1989), there is little potential for stabilization of turns by formation of the 1-4 hydrogen bond. Our results show that the presence of the peptide backbone actually makes the l-4 amide hydrogen bond unstable. We can see this by considering the folding/ unfolding co-ordinate r(O(,,-H(,,) to be a hydrogen bonding co-ordinate (at small values a l-4 hydrogen bond is formed, and at large values it is broken), and comparing our free-energy surfaces with the free-energy profile of Sneddon et al. (1989) for hydrogen bond formation in water. The free-energy surface of Sneddon et al. (1989) shows that, although the free energy of forming a linear hydrogen bond between two formamide molecules is approximately zero, there is roughly a 2 kcal/mole barrier to breaking it. Our Ac-Ala-Ala-NHMe freeenergy surface shows that when the conformational constraints and intra- and intermolecular interactions of the additional one peptide unit, two a carbons, and four methyl groups are added, the hydrogen bonding free-energy profile changes corn pletely: the free energy of forming the hydrogen bond is large and positive, and there is no barrier to breaking it Our principal result, that reverse turns are intrinsically unstable in water, is surprising given the oftt quoted results of Zimmerman & Scheraga (1977a,b, 1978a.b,c) and Zimmerman et al. (1977). Those workers used vacuum conformational energy calculations? with an approximate statistical mechanical theory to compute the relative “free energies” and probabilities of blocked dipeptide conformations. They found good agreement between the theoretical bend probabilities and the observed bend probabilities in several proteins for most of the dipeptide sequences they examined, including Ala-Ala and Pro-Ala. In addition, they found that some of the low-energy dipeptide structures identified in their

7 We note that the potential energy function used by Scheraga and co-workers was parameterized using protein crystallographic data (Momany et al., 1975). Therefore, their “vacuum” conformatlonal energy surfaces correspond, in principle, to p.m.f.s in the crystalline environment,.

calculations were similar to those seen in crystals of cyclic and linear oligopeptides. On the basis of the agreement between the theoretical and observed turn probabilities, and the observation that the stable conformations of many dipeptides were combinations of single-residue energy minima. Zimmerman & Scheraga (1977a,b, 1978a,b,c) and Zimmerman et al. (1977) concluded that shortrange, local (intra-residue) interactions are the primary forces stabilizing turns in proteins. In other words, they claimed that for most dipeptide sequences, medium- and long-range inter-residue interactions and the solvent play a minor role compared t,o intra-residue interactions in determining bend stability. Zimmerman & Scheraga (1977a) also concluded that “bends may exist in segments of the protein chain (under folding conditions in water), as a result of local interactions before the native structure is formed”. We cannot, dispute their claim that local interactions are important in stabilizing bends in proteins. However, sina thev did not account for the presence of solvent in their calculations, we believe that their methods and conclusions, and the conclusions of other workers using similar methods, should be applied cautiously to the subject of conformational equilibria of short peptides in solution. Our argument is based on the results of our work on blocked dipept.ides, and the results of earlier theoretical studies of a blocked monopeptide, incorporating explicit models for water. Several theoretical studies of the “alanine dipepGde”, Ac-Ala-NHMe, have shown that the conformational equilibria of blocked monopeptides are quite different in a vacuum and in water (Mezei et al., 1985: Pettitt & Karplus, 1985; Brady Sr Karplus, 1985; Anderson 8 Hermans, 1988). Although there are differences in the quantitative details of their predictions, available theoretical studies of the alanine dipeptide in water show that preferences single-residue conformational are profoundly affected by the solvent water. Are these solvent-modified intra-residue interactions additive, e.g. can we predict the stable conformations of Ac-Ala-Ala-NHMe in solution using superpositions of the alanine dipeptide results! If short-range; intra-residue interactions are as important for stabilizing

peptide

conformations

in solution

as they

are

thought to be in a vacuum and proteins (Zimmerman & Scheraga, 1977a,b, 1978u.b,c: Zimmerman et nl., 1977), then, on the basis of the alanine dipeptide results, we would expect to see stable LXX,c$, /Ia and pp conformations of Ac-AlaAla-NHMe in solution. However, it is clear from our results that, since there is only one stable solution conformation of Ac-Ala-Ala-NHMe (the extended interactions are not /3/I structure), intra-residue additive in solution. This “non-additivity” is a manifestation of the fact that aqueous solvation thermodynamics are complicated functions of solute (Tobias &, Brooks, 1990). size and shape Consequently, a knowledge of the stable conforma-

tions of blocked monopeptides

(in a vacuum or in

Reverse Turns in Blocked Dipeptides solution) cannot be confidently used to predict the stable conformations of blocked dipeptides (or other small peptides) in solution. We claim that reverse turn conformations of short, linear peptides are intrinsically unstable in water. However, many experimental studies have shown that significant populations of reverse turns exist in solution for some small peptides with particular sequences. For example, experimental studies of small peptides in solution have shown that the following types of interaction stabilize reverse turns: a hydrogen bond between the side-chain CO group of Asn or Asp at position 1 and the backbone NH group at position 3 (Montelione et al., 1984; Williamson et al., 1986); hydrophobic interactions between apolar side-chains (Azzena & Luisi, 1986); electrostatic interactions between the positively charged N-terminal group of residue 1 and the negatively charged unprotonated side-chain of Asp at position 4 (Dyson et al., 1988); and salt bridges between side-chains (Otter et al., 1989). Therefore, we believe that sequence-specific extrinsic interactions involving the side-chains and/or terminal groups must be responsible for stabilizing reverse turns in those peptides. We are currently using molecular dynamics simulations to evaluate the importance of such interactions on the stability of folded structures in small peptides in solution (D. J. Tobias, J. E. Mertz & C. L. Brooks, unpublished results).

795

similar, Matthews et al. (1987) concluded that the increased thermostability of the A82P mutant was due to a change in the backbone configurational entropy. Initially, we thought that the additional entropic stabilization would make the Pro-Ala turn intrinsically more stable than the Ala-Ala turn. It turns out that the entropic stabilization due to the “proline effect” is too small to be important for Ac-Pro-AlaNHMe. The unfolding free energy is much more negative for Ac-Pro-Ala-NHMe than for Ac-AlaAla-NHMe because the reverse turn conformations of the Pro-Ala peptide lack the strong stabilization that those of the Ala-Ala peptide have due to favorable peptide-water interactions. Evidently, the advantages of having proline at position 2 of turns are realized only when favorable extrinsic interactions are possible. Then the geometry and rigidity of the proline residue leads to “better” interactions, and hence greater stabilization of reverse turns, than would be achieved by other amino acids.

This work was partially supported by an NIH grant to C.L.B. (GM37554). D.J.T. was supported by an NIH predoctoral training grant, and S.F.S. by the Office of Naval Research graduate fellowship program. The Pittsburgh Supercomputer Center and Cray Research, Inc. generously provided the computer time. We are grateful to Dr Joseph McDonald for assistance in preparing the Figures.

(b) The proline effect In this final section we analyze in greater detail the effects of proline on the peptide conformational equilibria. During our comparison of the free-energy surfaces and probability distributions for Ac-AlaAla-NHMe and Ac-Pro-Ala-NHMe we noted that the distribution of extended conformations of the Pro-Ala peptide is much narrower than that of the Ala-Ala peptide. We attributed this observation to the greater conformational rigidity of proline compared to the other amino acids. This “proline effect” on the distributions of conformations is manifested in the difference in configurational entropies of unfolding between the Ala-Ala and Pro-Ala peptides. We determined above that the contribution of the configurational entropy to the free-energy difference between extended and reverse conformations is -0.2 kcal/mole for Ac-Ala-AlaNHMe and - 0.8 kcal/mole for Ac-Pro-Ala-NHMe. Thus, the folded conformations of the Pro-Ala peptide are stabilized relative to those of the AlaAla peptide by 0.6 kcal/mole due to the difference in configurational entropies. This result is very similar to a result from an experimental study by Matthews et al. (1987) of the reversible thermal denaturation of wild-type T4 lysozyme and the Ala82 -+Pro(A82P) mutant enzyme. Matthews et cd. (1987) determined that the difference in unfolding free energy between the A82P and wild-type enzymes was 0.8 kcal/mole at pH 6. Since the X-ray crystal structures of the two proteins were very

References Allen, M. P. & Tildesley, D. J. (1989). Computer Simulation of Liquids, pp. 24-25. Oxford University Press, Oxford. Anderson, A. & Hermans, J. (1988). Microfolding: Conformational Probability Map for the Alanine Dipeptide in Water from Molecular Dynamics Simulations. Proteins, 3, 262-265. Azzena, U. & Luisi, P. L. (1986). Models of Thioredoxin Hairpin Structures: Conformational Properties of /?-turn Containing Sequences. Biopolymers, 25, 555-570. Brady, J. & Karplus, M. (1985). Configuration Entropy of the Alanine Dipeptide in Vacuum and in Solution: A Molecular Dynamics Study. J. Am. (Them. Sot. 107, 6103-6105. Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S. & Karplus, M. (1983).

CHARMM: A Program for Macromolecular Energy, Minimization

and Dynamics Calculations.

J. Comput.

Chem. 4, 187-217.

Chou, P. Y. & Fasman, G. D. (1977). P-Turns in Proteins. J. Mol. Biol. 115, 135-175. Ckou, I’. Y. & Fasman, G. D. (1978). Empirical Predictions of Protein Conformation. Annu. Rev. Biochem. 47, 251-276. Dyson, H. J., Rance, M., Houghten, R. A., Lerner, R. A. 8r Wright, P. E. (1988). Folding of Immunogenic Peptide Fragments of Proteins in Water. I. Sequence Requirements for the Formation of a Reverse Turn. J. Mol. Biol. 201, 161-200. IUPAC-IUB Commission on Biochemical Nomenclature (1970). J. Mol. Biol. 52, 1-17.

D. J. Tobias
J.

Chem.

Phys. 79, 926-935.

Karplus, M., Ichiye, T. & Pettitt, B. M. (1987). ConJiguraBiophys. J. 52, tional Entropy of Native Proteins. 108331085. Karplus, M. & Kushick, J. N. (1981). Method of Estimating the Configurational Entropy of Macromolecules. Macromolecules, 14, 325-332. Landau, L. D. & Lifschitz, E. M. (1960). Statistid Physics, 2nd edit., pp. 343-353, Pergamon, New York. Lewis, P. pu’., Momany, F. A. & Scheraga, H. A. (1971). Folding of Polypeptide Chains in Proteins: A Proposed Mechanism for Folding. Proc. Nat. Acad.

Sci., U.S.A. 68, 2293-2297. Matthews, B. W., Nicholson, H. & Becktel. W. J. (1987). Enhanced Protein Thermostability from Sitedirected Mutations that Decrease the Entropy of Unfolding. Proc. Nat. Acad. Sci., U.S.A. 84. 66636667. Mezei, M., Mehrotra, P. K. & Beveridge, D. L. (1985). Monte Carlo Determination of the Free Energy and Internal Energy of Hydration for the Ala Dipeptide at 25°C. J. Am. Chem. Sot. 107, 2239-2245. Momany, F. A., McGuire, R. F., Burgess, A. W. bz Scheraga, H. A. (1975). Energy Parameters for Polypeptides. VII. Geometric Parameters, Partial Atomic Charges, Eonbonded Interactions, Hydrogen Bond Interactions, and Intrinsic Torsional Potentials for the Naturally Occurring Amino Acids. J. Ph,ys. Chem. 79, 2361-2381. Montelione, G. T.. Arnold. E., Meinwald. Y. C.. Stimson. E. R., Denton, J. B., Huang, S.-G., Clardy, ,J. & Scheraga, H. 4. (1984). Chain-folding Imtiation in Ribonuclease A: Conformational Structures Analysis of trans.Ac-Asn-Pro-Tyr-NHMr and transAc-Tyr-Pro-Asn-KHMe in Water and in the Solid State. J. Am. Chem. Sot. 106, 7946-7958. Northrup, S. H., Pear, M. R., Lee, C-P.. McCammon. ,J. A. & Karplus, M. (1982). Dynamical Theory of Activated Processes in Globular Proteins. Proc. Sa,t. A

cad. Sri., lJ.S. A. 79, 4035-4039.

Otter,

A., Scott, P. G., Liu, X. & Kotovych, G. (1989). A ‘H and i3C NMR Study on the Role of Salt Bridges in the Formation of a Type-l /l-turn in ,li-acetyl-I,.I. Riomol. Struct. AsJ)-1,.C:lu-L-Lys-L-Ser-NH,. Dynam. 7, 455-476. Pettitt, B. M. & Karplus. M. (1985). The Potential of Mean Force Surface for the Alanine Dipeptida in Aqueous Solution: A Theoretical Approach. Chem. Phys.

Letters,

121, 194-201.

Richardson. ,J. S. (1981). The Anatomy and Taxonomy of Protein Structure. Advan. Protein Chrm. 34. 1677339. Ryckarrt. ,J .-P.. Ciccotti, G. & Berendsen. H. J. C. (1977).

et, al

Numerical Integration of the Cartesian Equations of Motion for a System with Constraints: Molecular Phys. 23. Dynamics of n-alkanes. ./. Comput. 327-341.

Sneddon. S. F., Tobias, D. ?J. & Brooks. C. L., III (1989). Thermodynamics of Amide Hydrogen Bond Formation in Polar and Apolar Solvents. I. Mol. Biol.

209,

817-820.

Tobias. D. tJ. & Brooks, C. L., III (1990). The Thermodynamics of Solvophobir Effects: A Molecular Dynamics Study of n-butane in Carbon Tetrachloride and Water. I. Chem. Phys. 92, 2582-2592. Valleau, J. P. & Torrie. G. M. (1977). A Guide to Monte Carlo for Statistical Mechanics: 2. Byways. Tn &atistica/ Mechanics. part A (Berne. B. .I ed.), pp. 169-194. Plenum New York. Verlet. L. (1967). Computer “Experiments” on (Yassical Fluids. T. Thermodynamical Properties of T,ennard *Jones Molecules. Phys. Rev. 159, 98103. Williamson, M. P., Hall, M. J. & Handa, B. K. (1986). ‘H PITMR Assignment and 2” Structure of a Herpes Simplex Virus Glycoprotein D-l Antigenic Domain.

JCw. J.

Kiochemj.

158, 527-536.

Wright. 1’. E., J)yson. H. J. & Lerner. R. A. (1988). Conformation of Peptide Fragments in Aqueous for Initiation of Protein Solution: Implications Folding. Biochemistry, 27, 7167-7175. Yu. H.-A. & Karplus. M. (1988). A Thermodynamic Analysis of Solvation. J. C%em. Phys. 89. 2366-2379. Zimmerman. S. S. & Scheraga. H. A. (1977a). TAocal Interactions in Bends of Proteins. Proc. Nat. ilca,d. Sci.. rT.A.A. 74. 4126-4129. Zimmerman, S. S. & Scheraga, H. A. (19776). Influence of Local lntjerartions on Protein Structure. 1. Conformational Energy Studies of ,~-acetyl-,V’-nlrth~lamides of Pro-X and X-Pro Dipeptides. B%opoZy7rwr.s.

17. 81 I-843. Zimmerman. S. S. & Scheraga, H. A. (1978a). Influence of Tocal Interactions on Protein Structure. IT. Clanformational Energy Studies of N-acetyl-N’-methylamides of Ala-X and X-Ala Dipeptides. Hiopolymws,

18, 1849-1869. Zimmerman, S. S. & Scheraga, H. A. (1978b). Influence of Tocal Interactions on Protein Structure. III. Conformational Energy Studies of N-acetyl-Ll;‘-methylamides of Gly-X and X-Gly Dipeptides. Riopolymers.

18, 187lLl884. Zimmerman. S. S. & Scheraga, H. ,4. (1978c). TnAuence of T,ocal Interactions on Protein Structure. TV. Conformational Energy Studies of N-acetyl-lN’-methylof Dipeptides. amides Ser-X and Ser-Pro Biopolywcers, 18, 188551890. Zimmerman, S. S., Shipman, L. L. & Scheraga, H. A. (1977). Bends in Globular Proteins: A Statistical Mechanical Analysis of the Conformational Space of Dipeptides and Proteins. J. Phys. Chem. 81,614-622.