Molecular Dynamics Simulations of Cyclic and Linear DPDPE

J. Phys. Chem. 1996, 100, 2555-2563

2555

Molecular Dynamics Simulations of Cyclic and Linear DPDPE: Influence of the Disulfide Bond on Peptide Flexibility Yan Wang and Krzysztof Kuczera*,† Departments of Chemistry and Biochemistry, UniVersity of Kansas, 2010 Malott Hall, Lawrence, Kansas 66045 ReceiVed: September 11, 1995; In Final Form: NoVember 7, 1995X

Three 1 ns simulations of the solvated DPDPE peptide have been performed, one for the cyclic and two for the linear forms. The trajectories allow us to describe the conformations explored by DPDPE and DPDPE(SH)2 in aqueous solution on the 1 ns time scale, to quantify the conformational constraints imposed by the presence of the disulfide bond by comparing the conformational flexibility of the cyclic and acyclic peptides, evaluate several physical properties (NMR vicinal coupling constants, diffusion coefficients, and dipole moments of the peptides), and to suggest relations between the calculated properties and biological function. The cyclic peptide, while retaining the general structural features found previouslysthe presence of a hydrophobic and a hydrophilic face and a parallel arrangement of peptide dipoles, explores four major conformers during the 1 ns simulation. In two independent simulations, started from an extended and a cycliclike structure, the linear peptide is found to be about twice as structurally flexible as the cyclic form. Both DPDPE(SH)2 trajectories converge to essentially the same final structure, a type IV β-turn. This indicates both that a stable, representative conformation of the linear peptide has been found and that the cyclic-like structure is unfavorable when the disulfide bond is not present.

Introduction Disulfide bonds perform a wide range of biological functions. In proteins disulfides stabilize native three-dimensional structures,1,2 influence folding,3 and participate in a number of biochemical reactions.4,5 In short peptides, such as conotoxin,6 endothelin,7 oxytocin, and vasopressin,8 disulfide bridges are believed to stabilize the conformations important for biological activity. For this reason, disulfide bonds have been utilized in peptide drug design to constrain the peptides to their high affinity conformations for their receptors.9 The goal of this work is to study the role of the disulfide bond in determining structure, flexibility, physical properties, and biological function of one such peptide, the opioid DPDPE (Tyr-D-Pen-Gly-Phe-D-Pen). Since the discovery that enkephalins are agonists of opioid receptors in 1975,10 efforts have been undertaken to develop enkephalin analogues as analgesic drugs. The selectivity for the different receptors, µ, δ, and κ, was found to depend on the flexibility and topography of the opioid peptides.11-13 DPDPE, designed with topographical and conformational constraints,9 is a highly specific δ opioid. DPDPE has been the object of a large number of studies, including low-energy conformational search,14,15 molecular mechanics with NMR constraints,16 quenched molecular dynamics,17 molecular dynamics simulations,18-21 X-ray crystallography,22 and NMR. DPDPE has been utilized as a standard δ-opioid peptide in the past decade.23 Most of the previous conformational studies of DPDPE focused on the conformational search of an isolated molecule, with solvation effects modeled by employing a dielectric constant of about 80.9,14,16,17,20,21,24 These studies, combined with structure-activity relationship analyses,15,23,25-28 suggested that several conformational features were essential for δ-selectivity: the presence of the two aromatic side chains on Tyr1 and Phe4 on the same side of the disulfide-bridged ring, interaction between the disulfide moiety and the phenyl groups, † X

E-mail address: [email protected]. Abstract published in AdVance ACS Abstracts, January 15, 1996.

0022-3654/96/20100-2555$12.00/0

the g- conformation of Phe,4 and the t conformation of Tyr1 side chains.26 In the most advanced studies so far, Pettitt et al.18,19,29 performed molecular dynamics simulations of the DPDPE zwitterion with explicit water molecules, using Ewald summation to avoid effects of truncating nonbonded interactions. In a 200 ps simulation of solvated DPDPE the backbone of the peptide was found to be quite rigid, with only one reorientation at the Gly; conformational transitions were found for the aromatic Phe and Tyr side chains, while peptide groups were arranged in parallel, favoring solvation.18 Further simulations indicated that inclusion of explicit salt could influence the conformational preference of the Tyr side chain,19 while the backbone conformation of DPDPE remained essentially unchanged.29 Relatively little attention has been devoted to the acyclic analogue of DPDPE(SH)2. This molecule exhibits similar radioligand-binding affinity ratios to DPDPE and a biological potency that is comparable to but lower than that of DPDPE.30 Recent studies indicate that DPDPE(SH)2 can permeate membranes more readily than DPDPE, presumably due to enhanced flexibility.30-32 The conformational preferences of DPDPE(SH)2 are largely unknown. A molecular mechanics study of DPDPE(SH)2 with NMR constraints suggests that the membranebound conformation of this peptide is a β-turn involving D-Pen2 and Gly3, with Tyr1 and Phe4 side chains on opposite sides of the molecule.30 In this paper we present three 1 ns length molecular dynamics simulations of the DPDPE zwitterion and its acyclic analogue, solvated by 875 explicit water molecules at 300 K. The goals of our study are (1) to investigate the conformations explored by DPDPE and DPDPE(SH)2 in aqueous solution on the 1 ns time scale, (2) to quantify the conformational constraints imposed by the presence of the disulfide bond by comparing the conformational flexibility of the cyclic and acyclic peptides, (3) to evaluate some observable physical properties of the studied peptides, including diffusion coefficients, dipole moments, and NMR vicinal coupling constants, and (4) to attempt to relate the calculated properties to biological function. © 1996 American Chemical Society

2556 J. Phys. Chem., Vol. 100, No. 7, 1996

Wang and Kuczera

TABLE 1: DPDPE Conformers Explored in the Molecular Dynamics Simulations conformers of cyc-DPDPE residue tyr1

D-pen2

gly3 phe4

D-pen5 S-S bridge

distances (Å) O1/N4 N1/OH1 N1/O4 N1/C5 ring1/N1 ring1/CR3 ring1/S2 ring1/S5 ring4/CR3 ring4/S2 ring4/S5 ring1/ring4 S2/S5

lin-DPDPE

torsion 1 2 3 4 angle 0-20 ps 160-260 ps 260-380 ps 380-1000 ps range ψ ω χ1 χ2 φ ψ ω φ ψ ω φ ψ ω χ1 χ2 φ χ21 χ22 S-S χ52 χ51

144 -177 -168 63 112 40 -180 -118 43 -179 -148 -61 175 -158 83 104 174 160 -128 117 -63 7.2 7.8 11.5 11.6 5.1 7.4 6.7 7.2 7.2 8.6 7.9 9.2 2.0

133 -178 -169 65 106 51 -166 -80 -65 -175 -90 -33 172 -159 73 100 174 103 -147 167 -51 7.7 7.7 11.7 11.9 5.0 7.9 6.6 7.6 7.3 9.9 8.1 13.7 2.0

132 -178 -167 68 105 52 -172 -85 -61 -176 -90 -53 172 -162 70 97 171 79 110 -176 50 7.6 7.4 11.4 12.2 4.9 7.9 6.6 8.0 7.4 9.7 7.8 13.3 2.0

128 -179 -168 68 103 53 -171 -85 -64 -175 -93 -44 172 -63 114 91 171 78 110 -176 49 7.6 7.6 11.5 12.1 5.0 8.1 6.6 8.1 5.3 9.4 8.0 11.9 2.0

Additionally, to further study the rate of conformational space exploration of DPDPE, we calculate the fluctuation metric and force metric from our trajectories.33,34 Methods The three simulations performed here are further denoted as cyc-DPDPE, lin-DPDPE, and cyl-DPDPE. Simulation cycDPDPE involved the disulfide-bridged DPDPE peptide and started from conformation 2′ from ref 16, one of the lowest energy structures obtained by energy minimization with NMR constraints in a continuum solvent model. The remaining two simulations involved the acyclic analogue DPDPE(SH)2 and started from two different initial structuressan extended conformer in simulation lin-DPDPE and a cycliclike conformer (analogous to 2′ from ref 16) in simulation cyl-DPDPE. In each case the peptide was energy minimized in vacuum with harmonic constraints on the torsional angles in order to obtain a relaxed structure close to the starting coordinates and consistent with our potential energy function. Each energy-minimized peptide was placed in a preequilibrated truncated octahedral water cell based on a cube of edge a ) 37.86 Å and containing 906 TIP3P water molecules.35 The final simulation systems obtained by deletion of water molecules overlapping the peptides contained 875 waters. The overall number of atoms was thus 2708 for cyc-DPDPE and 2710 for cyl- and lin-DPDPE. The systems were heated to about 300 K by performing molecular dynamics interspersed with random atomic velocity assignments over 10 ps. This was followed by a 10 ps equilibration simulation in which the

(30 (20 (22 (27 (30 (30 (20 (40 (40 (20 (32 (35 (20 (25 (35 (35 (22 (20 (20 (22 (20 (0.8 (0.5 (1.2 (1.0 (0.3 (1.4 (1.2 (1.3 (0.5 (0.7 (0.7 (2.6 (0.1

av value

cyl-DPDPE range

-180, 125 (35 180 (20 -170 (23 63 (35 100 (35 -140, 170, 40, -140 (40 180 (20 60 to 180 ) -180 to -60 130 to +180 ) -180 to -120 180 (20 -120 (60 -80 to 180 ) -180 to -60 180 (20 -167, -60 (25 60, 110 (35 100 (40 165 (25

(23

176 4.5-9.0 7.9

av value

-63

(0.5 7.9

4.8-14.0 5.5-15.5

5.2 (0.3 8.0, 9.1, 8.0, 9.1 (1.0 6.6 (1.3 7.8-19.0 7.4 ( 0.8, 5.2 ( 1.2 9.9, 5.2 (2.2 6.6 ( 1.2, 10.1 ( 0.9 7.5-16.7 6.7-14.2

range

125 (40 180 (20 -170 (23 63 (35 100 (35 40, -140 (40 180 (20 80 to 180 ) -180 to 180 130 to -80 ) -180 to 100 180 (20 -110 (40 -120 to 70 180 (20 -60 (25 110 (35 100 (40 165 (25

(23 4.7-9.0 4.8-13.7 5.5-15.0

5.2 8.0, 9.1 6.6

(0.5 (0.3 (1.0 (1.3

4.3-16.3 7.2 ( 0.8, 5.2 ( 1.2 9.1, 4.9 (2.6 8.2 (1.3 8.0-15.5 3.2-12.6

velocities were rescaled to bring the system temperature to 300 K. Finally, unperturbed molecular dynamics trajectories of 1 ns length were generated for the three systems. Coordinates were saved every 0.05 ps. The average temperatures were 300 ( 5 K for cyc- and cyl-DPDPE and 302 ( 5 K for lin-DPDPE. The molecular dynamics simulations were performed using the Verlet algorithm with a time step of 2 fs, with SHAKE constraints applied to all bonds involving hydrogen atoms. The CHARMM version 22 all-hydrogen parameter set was used in our calculations, with parameters for penicillamine adopted from those of cysteine and leucine residues. A nonbonded cutoff distance of 12.0 Å was used, with van der Waals terms smoothly eliminated by a switching function between 10 and 12 Å and electrostatic interactions removed at 12 Å by shifting.36 The dielectric constant was set to 1.0. The calculations were performed using the program CHARMM36 version 22. A 1 ns simulation of one of the solvated peptide systems took about 3 weeks of CPU time on an IBM RS/6000 Model 375 computer. Results and Discussion Conformations Explored. The conformations explored by the simulated peptides are identified and analyzed below. To describe the different conformers, we use the values of the backbone and side chain dihedrals as well as distances between functional groups. The results are summarized in Table 1 and in Figures 1-3. DPDPE. Qualitatively, the time evolution of the DPDPE structure consists of several periods of fluctuations around a temporary average position, interspersed with relatively fast

Molecular Dynamics Simulations of DPDPE

Figure 1. Structures of cyclic DPDPE: (a) initial conformation adopted from conformer 2′ in ref 16; (b) conformer 4, average structure from 380-1000 ps of simulation cyc-DPDPE (C, white; N, dark grey, O, black; S, light grey; H atoms not shown for clarity).

transitions involving significant changes of the average. Some gradual structural adjustments also occur during the periods of mainly fluctuation-like motion (see Table 1 and Figures 1 and 2). Such behavior has been found previously.18 Thanks to this property of the trajectory, calculating separate average structures of cyc-DPDPE over the time intervals between transitions s020, 160-260, 260-380, and 380-1000 pssgives four welldefined conformers, denoted as conformations 1, 2, 3, and 4, respectively. In the fluctuation-type motions cyc-DPDPE dihedral angles typically oscillate with a 30° amplitude during a period of several hundreds of picoseconds, while the dihedral transitions typically involve angle changes by more than 60° occurring on time scales below 1 ps. Torsional angles ω, S-S, χ11, χ21, χ51, χ22, and χ52 are the most rigid and oscillate within (20° of their average values. The small movement of the χ dihedrals in Pen2 and Pen5 is caused by the proximity of the disulfide bridge and the steric hindrance of the penicillamine β-methyl groups. χ11 appears to be constrained by the large aromatic tyrosine ring. On the other hand the φ and ψ dihedrals around residue Gly3 can explore the widest range of values and exhibit fluctuation amplitudes of 40° around their temporaray average values. The time evolution of the cyc-DPDPE structure is described in Table 1 and Figure 1. In the first 160 ps ψ3 and φ4 exhibit synchronized transitions resulting in a reorientation of the peptide carbonyl group in Gly3, aligning it roughly parallel to the other peptide carbonyls. Accompanying this movement are more gradual transitions of χ22 and χ52 at the opposite end of the 14-membered ring, demonstrating the flexibility of the disulfide moiety. The adjustment of the backbone dihedrals increases the separation between the aromatic ring of Phe4 from the Tyr1 ring and the Pen2 methyl groups. The parallel peptide dipoles, initial glycine flip, and increased separation of aromatic rings relative to the starting structure have been found in previous simulations with explicit water.18 Aromatic ring distances ranging from 6 to 15 Å have been reported in other studies.14-16,21,28,37 The transition from conformation 2 to 3 consists of the synchronized transitions of the S-S from -147° to +110° and χ51 from -51° to +50° at about 260 ps. This changes the S-S bond helicity from the left- to right-handed.38 The final conformation which DPDPE explores in our simulation is attained through a rotation of the χ41 dihedral from the t to gregion, which moves the Phe4 side chain toward the C3R and closer to the ring of Tyr1 and the methyl groups on Pen2 (Table 1). The time series of most of the energy componentsspeptide internal deformations, peptide intramolecular nonbonded interactions, and peptide-water interactionssdo not exhibit any statistically significant systematic change during the 1 ns cycDPDPE simulation. The only exception is the dihedral angle deformation energy term, which changes from 32 kcal/mol down

J. Phys. Chem., Vol. 100, No. 7, 1996 2557 to 27 kcal/mol at ∼260 ps. The time of this energy jump coincides with the transition between conformers 2 and 3 of DPDPE, involving reorientations of the χ51 and S-S dihedrals. The transition brought the conformation of the disulfide bond to one of the six most populated disulfide conformations.38 We conclude that the 2 f 3 transition releases about 5 kcal/mol of torsional strain and that the conformations without this strain, i.e., conformations 3 and 4, should be the most favorable structures of DPDPE in aqueous solution. Due to the dihedral energy changes found in the cyc-DPDPE trajectory, it appears probable that the initial dynamics of DPDPE during 0-260 ps does not represent the intrinsic equilibrium structural fluctuations of the peptide but rather nonequilibrium relaxation from a strained initial structure. The final two conformations of DPDPE exhibit the general features found in the previous simulations in aqueous and saline solutionssthe roughly parallel orientation of the peptide dipoles18 and the concentration of hydrophobic groups, rings of Tyr and Phe and β-methyls of Penson one side of the 14-membered ring.16,18,19 Due to these effects DPDPE presents a “polar face” and and a “hydrophobic face” to its environment. Other features of our simulation in accord with other studies are the distance between the tyrosine and phenylalanine ringssbetween 12 and 14 Åsin conformers 2-4 (11 Å is found in the crystal structure22) the proximity of the Tyr1 phenyl ring to the disulfide moiety16 and the Pen2 methyl groups, and the occupancy of t and g- conformers of χ11 and χ41, respectively.18,19 A careful comparison reveals that the most stable structures found in our cyc-DPDPE trajectory differ in a number of details from previously reported structures of DPDPE. Conformer 1 is already different from the starting structure (conformer 2′ of ref 16) due to a Gly3 carbonyl flip during the equilibration period. A similar dihedral flip was found at the start of the 250 ps aqueous simulation.18 Of the four conformers explored in the cyc-DPDPE trajectory, structures 2-4 persisted for 100 ps or more. These conformers are different from those determined by other authors14,15,17-19,20,21 in terms of the backbone dihedrals. Within trajectory fluctuations, a number of dihedral angles from our simulation structures agree with conformers previously proposed; e.g., our conformer 4 is essentially the same as conformer 2 reported in ref 16. In most cases the specific combinations of dihedral angle values that define a DPDPE conformer are somewhat different between our structures and those reported previously. However, the conformations explored by individual dihedrals are the same. Thus, we find that the same sets of values of individual dihedrals occur in the low-energy structures of Hruby et al.16 and in our simulation. Although our simulation of DPDPE is 1 ns in length, the longest of those reported so far, we cannot be certain that we have sampled all relevant conformations of the peptide. One indication of incomplete conformational sampling is the deviation between the calculated and observed NMR coupling constants (see below). Another indication that the peptide has not reached the limits of available conformational space is that each conformer has been sampled only once, with no recurrence such as that found in ref 39. Two conclusions of general importance may be drawn from our cyc-DPDPE simulation. First, our simulation confirms that many conformations are available to the cyclic peptide DPDPE, a fact that is believed to be of crucial importance for the biological function of the peptide. Second, it appears that methods using different potential energy functions and approaches of varying levels of sophistication, from unconstrained

2558 J. Phys. Chem., Vol. 100, No. 7, 1996

Wang and Kuczera

Figure 2. Time series of selected dihedral anglessψ3, φ3, and ψ4sin the simulations of the cyclic (cyc-DPDPE) and linear (cyl-DPDPE, linDPDPE) peptides.

Figure 3. Superposition of five structures from the final 100 ps of the two independent simulations of the linear DPDPE(SH)2 peptide (a) linDPDPE and (b) cyl-DPDPE. S atoms displayed as grey spheres; H atoms not shown for clarity.

conformational search14,17,20,21,24 and energy minimization with NMR constraints16,26 to simulations with explicit water (this work and ref 18) and salt19,29 lead to qualitatively similar structures of cyclic the peptide. To better understand the role of the explicit water molecules, a 1 ns simulation of DPDPE with solvent modeled by a continuous medium with a dielectric constant of 80 was performed. In this trajectory the transition of ring4 from the t to g- conformation was also found; the remaining dihedrals performed oscillations around their initial values with amplitudes larger than in the explicit water trajectories. The dihedrals around Gly3 underwent several changes of 60° amplitude, but the residence time in these perturbed states was less than 50 ps. These observations are in accord with previous molecular mechanics studies.16 On the other hand, the continuum solvent simulations give a more puckered structure to the 14-membered

ring, leading to a dipole moment lower by more than 20 D than the explicit water simulations (see Dipole Moments). Our simulation was started from a low-energy structure obtained with NMR constraints. The structures found in the simulations have a number of features common with low-energy states found in other modeling studies. Most of the calculated and observed NMR coupling constants are in accord (see below). These facts suggest that the conformations explored in the cycDPDPE simulation are low free energy, representative structures, rather than unstable, transient states. On the other hand, although our simulation of DPDPE is 1 ns in length, the longest of those reported so far, we cannot be certain that we have sampled all relevant conformations of the peptide. One indication that the peptide has not reached the limits of available conformational space is that each conformer has been sampled only once, with no recurrence such as that found in ref 39. Another indication of incomplete conformational sampling is that the agreement between the calculated and observed NMR coupling constants, although good, is not perfect (see below). Approaches such as ours and those of refs 18 and 29, based on direct molecular dynamics simulations of the peptide in water, have the advantage of accurately modeling the solvation effects and yielding not only stable structures of the solute but also residence times in a given structure and pathways for conformational transitions as well as the possibility of evaluating a wide range of physical properties. The disadvantage of direct simulations is the slow rate of exploration of conformational space in the necessarily finite trajectories. This leads to such problems as dependence of results on the starting structure and

Molecular Dynamics Simulations of DPDPE trapping in local minima on the potential energy surface.33,34 A number of approaches search conformational space more effectively than direct simulations, but they do not provide much information besides identification of low-energy structures.40,41 DPDPE(SH)2. The conformations explored by DPDPE(SH)2 in the cyl-DPDPE and lin-DPDPE are described in Table 1 and Figures 2 and 3. As expected, DPDPE(SH)2 is more flexible than the cyclic DPDPE. Our simulations show both qualitative and quantitative differences in dynamics of the two forms of the opioid peptide. Qualitatively, in addition to the superposition of short time fluctuations and transitions which was the main feature in the cyc-DPDPE trajectory, for cyl-DPDPE and linDPDPE we additionally observe long-term, large-amplitude structural changes. These occur over several hundreds of picoseconds and involve dihedral shifts by up to 180°. The latter feature of DPDPE(SH)2 flexibility appears to be related to the presence of Gly in the peptide, since it is exhibited by ψ3, φ3, and ψ4 (see Figure 2). Quantitatively, the flexibility difference can be seen in the greater number of dihedral angle transitions and in larger ranges explored by most torsional angles in the acyclic peptide simulations. Based on an analysis of time evolution of all dihedral angles, the linear peptide undergoes about twice as many dihedral angle transitions as the cyclic form in 1 ns. Figure 2 shows three examples of evolution of those dihedrals that exhibit the largest mobility difference between the cyclic and linear peptides. In fact, DPDPE(SH)2 is so flexible that average structures from just 20 ps trajectory fragments have unrealistic internal geometries, making individual conformers of the peptide difficult to characterize. Therefore for DPDPE(SH)2 we do not give average conformations as we did for DPDPE. Instead, in Table 1 we present two types of information. For dihedrals exhibiting restricted fluctuations superimposed on sharp transitions we list the temporary average values in the order of occurrence and the range of local oscillations in periods between transitions. For the gradually changing dihedrals, we give the ranges they explore. The simulation of lin-DPDPE explores a larger number of transiently stable states than cyl-DPDPE. In both simulations the dihedrals undergoing the largest number of sharp transitions are ψ1, ψ2, χ41, and χ42. The ranges of the values assumed by the gradually varying dihedrals ψ3, φ3, and ψ4 are also greater in lin-DPDPE than in cyl-DPDPE (Figure 2). Two interesting observations can be made on the basis of our simulations of the acyclic peptide DPDPE(SH)2. The first is that the cylDPDPE trajectory quickly moves away from its starting structure. This indicates that structures similar to the disulfidebridged one are strained, unfavorable conformers for the acyclic peptide and will not be significantly populated. The second observation is that the two independent simulations of the acyclic peptide DPDPE(SH)2 converge to essentially the same family of structures that differ only in χ51, ψ3, and ψ4 dihedrals (Table 1 and Figures 2 and 3). The linear peptide occupies the same region of conformational space in the last 450 ps of the linand cyc-DPDPE trajectories. In the two simulations, the average values over this time period are essentially identical for all dihedrals except χ51, ψ3, and ψ4. The difference in the averge dihedral value of χ51 (175° for lin-DPDPE; -63° for cylDPDPE) is reflected in different distances from S5 to other groups. The difference in ψ3 and ψ4 between lin-DPDPE and cyl-DPDPE leads to different orientations of the amide group linking Gly3 and Phe4 residues. Because the two DPDPE(SH)2 simulations are completely independent, started from markedly different coordinates, we believe that the conformational regions explored by lin- and cyl-DPDPE in the last 450 ps are highly

J. Phys. Chem., Vol. 100, No. 7, 1996 2559 representative, stable structures for DPDPE(SH)2 in aqueous solution. These conformations are shown in Figure 3. The DPDPE(SH)2 structures explored in the final 450 ps of simulations lin-DPDPE and cyl-DPDPE can be classified as type IV β-turns,42 with the backbone tracing a skewed “S” shape. No intramolecular hydrogen bonds are formed in these structures, with O‚‚‚N distances above 5 Å. Such conformations have been suggested for DPDPE16 and for membrane bound conformations of DPDPE(SH)2.30 The two aromatic rings do not tend to approach one another in the ayclic simulations. This appears to be the result of the influence of explicit water molecules on the backbone structure (see below). In the β-turn conformation of DPDPE(SH)2, the aromatic rings are on the opposite sides of the S, close to the mean backbone plane. Two hydrophobic centers are formed due to proximity between the Tyr1 ring and the Pen2 β-methyls and between the Phe4 ring and C3R. Such aggregation of hydrophobic groups is expected to be favorable in aqueous solution. The final stable structures of DPDPE(SH)2 from the lin-DPDPE and cyc-DPDPE simulations have the Phe4 side chain in the g- conformation. The Phe4 g- conformer is also found in conformation 4 of our cycDPDPE trajectory and in the simulations of Pettitt et al.18,19,29 Thus, it appears that the g- orientation is favorable for the Phe4 side chain in both linear and cyclic DPDPE. In agreement with chemical intuition, almost all dihedrals involved in the DPDPE 14-membered ring experience greater variation in the DPDPE(SH)2 simulations compared to DPDPE. The only exception is χ51, which samples both the g- and g+ conformers in the cyc-DPDPE trajectory, while remaining solely in the t region for lin-DPDPE and solely in g- for cyl-DPDPE. As has been stated in the previous section, the χ51 dihedral mobility in cyc-DPDPE appears to be related to the choice of a strained starting structure rather than to some intrinsic flexibility in this coordinate. In our DPDPE(SH)2 simulations we do not find a tendency for the oppositely charged peptide termini to approach and form a salt link. This result does not appear to be an artifact of the 12 Å nonbonded cutoff used, since the N1‚‚‚C5 distance remains below 12 Å for more than half of the simulation time and approaches 6-8 Å for short periods. It thus appears that structures with the salt link are not favored in aqueous solution. Similar observations were found in simulations of DPDPE without nonbonded cutoffs.18 In a 1 ns simulation of the acyclic peptide DPDPE(SH)2 in which the solvent was modeled by a continuum with a dielectric constant of 80, we observed significantly increased mobility of the ψ dihedrals around Gly3 relative to the explicit water trajectories. The χ dihedrals on Tyr1 and Phe4 also exhibited more transitions. The distance of the two aromatic rings of about 6.7 Å, which is very close to the results of ref 16 but much smaller than those found in the explicit water simulations. As in the case of cyclic DPDPE, the dipole moment of DPDPE(SH)2 was underestimated in the continuum model. Thus, lack of explicit solvent leads to excessive flexibility and both gross and subtle changes in average structure. Our simulations offer the most extensive study of structural and dynamical properties of DPDPE in solution performed to date, involving the longest trajectories with the largest number of water molecules, and are the first to investigate both cyclic and linear peptides. In all three DPDPE simulations no recurrence of conformations was found, suggesting that conformational sampling is probably incomplete. We cannot thus completely rule out that some unexplored stable conformations of the peptides exist that exhibit properties different from the one sampled so far. Assuming that this is not the case, the two

2560 J. Phys. Chem., Vol. 100, No. 7, 1996

Wang and Kuczera

TABLE 2: NMR Vicinal Coupling Constants (Hz). Comparison of the Experimental Data from Ref 16 for 3J HNCrH and from Ref 26 for Jrβ and Molecular Dynamics Simulation Results residue 3J

DPDPE exptl

cyc-DPDPE

lin-DPDPE

cyl-DPDPE

8.1 4.2 8.5 6.8 8.4

10.2 ( 1.1 6.5 ( 2.6 7.1 ( 1.7 8.2 ( 2.0 8.5 ( 2.1

9.8 ( 1.4 5.6 ( 3.5 5.8 ( 3.4 9.1 ( 1.8 9.2 ( 1.8

9.8 ( 1.4 5.3 ( 3.3 5.4 ( 3.7 9.3 ( 1.7 8.8 ( 2.0

6.5 9.0

3.6 ( 0.8 6.9 ( 3.2

3.6 ( 0.8 6.0 ( 3.1

3.6 ( 0.8 9.3 ( 1.2

HNCRH

D-Pen2 Gly3

Phe4 D-Pen5 JR-Pro-R-β Tyr1 Phe4 JR-Pro-S-β Tyr1 Phe4

9.5 6.0

9.5 ( 0.4 5.7 ( 2.9

9.5 ( 0.4 6.7 ( 3.0

9.5 ( 0.5 3.4 ( 1.2

main conclusions from our simulations are (a) that cyclic-like structures are relatively unstable for the linear peptide, while a stable family of β-turn structures was found the exist and (b) that the linear peptide is significantly more flexible than the cyclic form. Because of incomplete conformational sampling, we cannot reliably estimate the relative stability of the initial cyclic-like structure and the final β-turn in the cyl-DPDPE simulation. We can only observe that the cyclic-like structure persisted for less than 100 ps and the β-turn family of structures for almost 500 ps in the 1 ns trajectory, suggesting that the latter conformations are more stable than the former. We are currently working to obtain an improved, qualitative estimate of the population ratio of these two states using conformational free energy simulations. Generally, a pentapeptide has a large number of possible conformations, with the vast majority being unstable, high free energy structures and only a small fraction corresponding to stable, low free energy conformations. It would be highly unlikely that two independent simulations of DPDPE(SH)2 starting from arbitrary and significantly different conformations should converge to the same family of unstable structures. Rather, the convergence of the two simulations suggests that the β-turn conformational regions explored by lin- and cylDPDPE in the last 450 ps correspond to highly representative, low free energy structures for DPDPE(SH)2 in aqueous solution. Within the β-turn family of structures, the acyclic peptide still exhibits significant conformational flexibility, mainly in dihedrals surrounding Gly3 (Figure 2), in both lin- and cyl-DPDPE trajectories. In contrast, fluctuations within a single conformational state are found for the cyclic peptide in the final 620 ps of the cyc-DPDPE trajectory. The difference in flexibility between the linear and cyclic forms thus tends to increase as the peptides move from the somewhat arbitrary starting structures to the more representative final states. Within our 1 ns trajectories we thus see a systematically greater flexibility of the linear peptide. Physical Properties of the Simulation Systems. Molecular dynamics trajectories contain the detailed time evolution of positions and velocities of all atoms in a molecular system. Trajectories can thus be used to calculate various physical properties that depend on atomic coordinates and velocities.43 In this section we describe the results of calculating NMR vicinal coupling constants 3JHN-CRH and JRβ, dipole moments, and translational and rotational diffusion constants for DPDPE and DPDPE(SH)2. Wherever possible, we try to compare simulation results to experimental data and discuss the biological significance of the observable values. The calculated properties are summarized in Tables 2 and 3. Vicinal Coupling Constants. The 3JHN-CRH vicinal coupling constants are calculated from the time series of θ dihedrals

TABLE 3: Physical Properties of the Solvated Peptides and the Force Metric of the Simulation Systems cyc-DPDPE water vacuum,  ) 1 continuum,  ) 80 Dt, 10-5 cm2 s-1 Dr, rad2 ns-1 τc ps τΩ, ps DΩ, ps-1 DF, ps-1

lin-DPDPE

cyl-DPDPE

Dipole moment, D 64 ( 3 50 ( 11 10.2 ( 1.8 7.2 ( 2.2 52 ( 5 35 ( 17

56 ( 9 6.9 ( 2.7 30 ( 14

Translational Diffusion 4.1 ( 0.2 2.0 ( 0.3

3.8 ( 0.1

Rotational Diffusion 1.36 ( 0.06 1.46 ( 0.08 122 ( 5 114 ( 6

1.48 ( 0.05 113 ( 4

Ergodic Measures 620 320 0.16 0.31

280 0.36 0.33

between the H-N-CR and N-CR-H planes using the Karplus equation 3

J ) A′ cos2 θ - β′ cos θ + C′

with A′, B′, and C′ taken from the Bystrov parametrization.44 The 3JH-CR-Cβ-H coupling constants are calculated according to ref 45. Due to the fact that dihedral angles sample a range of values during the simulations, we obtain a distribution of calculated J values, which we can characterize by giving its average and standard deviation. Table 2 gives the averages and standard deviations of coupling constants from the three molecular dynamics trajectories as well as the 3JHN-CRH values measured by Hruby et al.16 for DPDPE and 3JH-CR-Cβ-H given in ref 26. There are no published experimental results for free DPDPE(SH)2. Out of nine J constants for DPDPE, seven calculated values agree with experimental observations within the standard deviations and one within two standard deviations. The only real discrepancy between calculated and experimental values is that for the Tyr 3JH-CR-Cβ-Pro-R-H, describing the Tyr side chain orientation. The connection between coupling constants and dihedral angles is indirect, through the Karplus equation which involves empirical parameters determined under a number of approximations. In our molecular dynamics simulations the peptide samples several conformations by moving freely, without NMR constraints. In view of these facts, the agreement between calculated and observed J constants is quite good, although not perfect. The similarity of the observed and calculated coupling constants suggests a corresponding similarity of the underlying structuresswe expect that the set of structures sampled in the simulation should overlap with, but not be identical to, the set of conformations found under experimental conditions. This suggests that conformational sampling is probably incomplete in the 1 ns cyc-DPDPE simulation. The vicinal coupling constants 3JHN-CRH of DPDPE(SH)2 calculated from the lin- and cyl-DPDPE simulations are presented in Table 2. The similarity of the corresponding coupling constants from the two trajectories is another illustration of the similarity of the structures of the acyclic peptide found in our two independent trajectories. Dipole Moments. The time series of the classical dipole moments b µ were calculated according to

b µ (t) )

∑

qi b r i(t)

atoms i

ri is the position of the ith where qi is the partial charge and b atom. The partial atomic charges qi used in evaluating dipole moments were the same as those employed in energy calcula-

Molecular Dynamics Simulations of DPDPE

J. Phys. Chem., Vol. 100, No. 7, 1996 2561

tions. Partial charges appearing in empirical potential functions of the CHARMM type are both parameters optimized to reproduce nonbonded interaction energies of molecules and measures of the molecular static charge distribution.36 Table 3 gives the average dipole moments and standard deviations calculated from the three 1 ns molecular dynamics trajectories. The peptides have large average dipole moments: 64 D for cyclic DPDPE and 50-56 D for acyclic DPDPE(SH)2. Interestingly, only about 25-30% of the total dipole moment is due to the charged termini, the rest resulting from positioning and orientation of other polar groups, CdO, N-H, and O-H. Our results indicate that cyclic DPDPE has a higher dipole moment than the acylic form; it appears that the disulfide bond constrains the dipole moment of DPDPE to a relatively high value, “locking in place” its favorable solvation. In 1 ns simulations of the studied peptides in a dielectric continuum, dipole moments of about 10 D were found when a dielectric constant  ) 1 was used and about 40 D for  ) 80. The large dipole moments of the simulated peptides are thus clearly due to solvation in general and solvation by explicit water in particular. The increased flexibility of the acyclic DPDPE(SH)2 is evident in the enhanced dipole moment fluctuations in cyl- and lin-DPDPE simulations (Table 3). The dipole moment varies in the 30-70 D range for DPDPE(SH)2 and in the 58-68 D range for DPDPE. The availability of structures with low dipole moment for the acyclic peptide explains why DPDPE(SH)2 can bind to membranes more easily than DPDPE.30 The dipole moment time series does not show any correlation with torsional angle or distance transitions. Therefore, the changes of the dipole moments appear to be due to the gradual component of conformational change. The species with the higher dipole momentscyclic DPDPEsis more strongly solvated than DPDPE(SH)2, in accord with standard correlations between dipole moment and solubility. On the other hand, the unconstrained linear DPDPE(SH)2 exhibits more favorable intramolecular interactions than cyclic DPDPE. Diffusion Coefficients. The translational diffusion coefficients Dt of the peptides are calculated from the expression46

Dt ) 〈∆r2(t)〉/6t

(1)

where ∆r(t) is the displacement of the center of mass in time t and 〈...〉 denotes an average over starting structures. Analogously, the rotational diffusion coefficients Dr (equal to onethird of the trace of the diffusion tensor), are evaluated from47

Dr ) 〈∆θ2(t)〉/6t

(2)

where ∆θ(t) is the angle of rotation of the molecule-fixed frame during time t. Analysis of the principal components of the moment of inertia shows that all three systems can be approximated as prolate ellipsoids with Ixx < Iyy ≈ Izz and Ixx/Izz ratios of 0.4-0.5, 0.30.4, and 0.2-0.3 for cyc-, cyl-, and lin-DPDPE, respectively. The calculated translational diffusion coefficients decrease with increasing deviation from spherical shape, in agreement with hydrodynamic theory.48 The more compact cyclic DPDPE molecule has a higher translational diffusion coefficient than the linear peptide (Table 3), while the most elongated linDPDPE exhibits slowest diffusion. The Dt for cyl-DPDPE is intermediate between the other two simulations, with which it shares conformations. The different translational diffusion coefficients calculated from the lin- and cyl-DPDPE simulations illustrate the differences in structures explored along the trajectories. The reported Dt values are obtained from the slopes

of 〈∆r2(t)〉 vs t plots, with t in the 0-100 ps range, where plots from three simulations are approximately linear. These values represent averages over the complete trajectories. The different conformers found in the simulation exhibit different translational diffusion coefficients, which can be found by averaging ∆r2 over the appropriate trajectory fragment. Thus, Dt of DPDPE exhibits a significant decrease at 260 ps corresponding to the reorientation around the S-S bond, while the value of Dt for lin-DPDPE increases after 195 ps, which can be interpreted as the time scale of peptide folding from the extended structure to the β-turn. The rotational diffusion coefficients Dr and the rotational correlation times τc ) 1/6Dr of the linear and cyclic peptides are given in Table 3. The rotational correlation times found in the three simulations are in the 110-120 ps range and are indistinguishable within the statistical errors. The correlation functions 〈∆θ2(t)〉 markedly deviate from linear behavior for t > 100 ps, because the peptdies are not rigid bodies; we compute Dr from the slope of 〈∆θ2(t)〉 for times t < 25 ps. A number of amino acid agonists react with their respective receptors at rates approaching the diffusion limit.49 Dt can thus be related to the rate constants of diffusion controlled reactions.50,51 The overall tumbling rate obtained from rotational diffusion is the rate at which the different functional groups of a ligand explore all possible orientations. This quantity can thus influence the rate of ligand binding to an acceptor site, in which relative positioning of functional groups plays a role. Measures of Self-Averaging. Molecular dynamics simulations yield trajectories of finite length, which sample limited regions of conformational space. Interesting methods of estimating the rate of conformational space explorationsthe generalized ergodic measures (GEMs)shave recently been proposed.33,34,52 These methods enable the determination of time scales on which different system properties become selfaveraging, i.e., when time-averaged properties of all individual atoms converge to the same value.33 Self-averaging is a necessary, though not sufficient condition for ergodicity, for both homogeneous and heterogeneous systems.34,52 We have computed the nonbonded force fluctuation metrics Ω(t) for each of the three trajectories cyc-, cyl-, and lin-DPDPE, and the nonbonded force matric d(t) between the two DPDPE(SH)2 simulationsscyl- and lin-DPDPE. From the longtime part of the decays of Ω(0)/Ω(t) = DΩt, d(0)/d(t) = DFt, we extract the diffusion coefficients: DΩ, measuring the rate of exploration of conformational space within each trajectory, and DF, measuring the rate of convergence of averages from the two DPDPE(SH)2 trajectories.33 Alternatively one may view τΩ ) 100/DΩ as the time required for a trajectory to effectively sample conformational space and τF ) 100/DF as the time needed for two independent trajectories to converge to the same conformational region.33 The calculations are summarized in Table 3. The results indicate that DPDPE explores its conformational space at about half the rate of DPDPE(SH)2, in qualitative agreement with estimates based on counting dihedral transitions (see Conformations Explored). According to the GEM analysis, the time scales needed for effective sampling are about 600 ps for DPDPE and about 300 ps for DPDPE(SH)2. This suggests that our 1 ns trajectory lengths are of the appropriate order of magnitude to explore representative regions of conformational space of the studied systems. On the basis of the nonbonded force metric d(t), we can see that the convergence of the two DPDPE(SH)2 trajectories occurs at a rate similar to that of space exploration within each trajectory. The decay of d(t) gives 300 ps as the time scale for the lin- and cyl-DPDPE trajectories to

2562 J. Phys. Chem., Vol. 100, No. 7, 1996 reach the same conformational region, which is consistent with the time scale of the conformational change found in Conformations Explored. Conclusions We have performed three 1 ns simulations of the solvated DPDPE peptide, one for the cyclic and two for the linear forms. The trajectories allow us to investigate the conformations explored by DPDPE and DPDPE(SH)2 in aqueous solution on the 1 ns time scale, quantify the conformational constraints imposed by the presence of the disulfide bond by comparing the conformational flexibility of the cyclic and acyclic peptides, evaluate NMR vicinal coupling constants, diffusion coefficients, and dipole moments of the peptides, and suggest relations between the calculated properties and biological function. Both forms of the peptide explore a number of conformations in solution. The cyclic peptide dynamics is characterized by periods of fluctuations around a temporary average position, occurring on a time scale of 100 ps, interspersed with much faster transitions involving significant changes of the average. In the cyclic DPDPE simulalion, which is the most extensive reported so far, we find four major conformers in the 1 ns cyclic DPDPE trajectory. Starting with an initial structure proposed from energy minimization with NMR constraints,16 the peptide undergoes a flip around the S-S bond, several conformational transitions at the glycine residue, and side chain reorientations. The structural transitions occurring along the trajectory lead to relief of conformational strain and to improved solvation. For the acyclic DPDPE(SH)2 peptide our simulations provide the first definite structures based on two independent 1 ns trajectories, starting from an extended (lin-DPDPE) and a cycliclike structure (cyl-DPDPE). The linear peptide was significantly more flexible than the cyclic form, exhibiting approximately twice the number of dihedral angle transitions, involving mainly side chains and the glycine residue backbone. The motion DPDPE(SH)2 was qualitatively different from that of cyclic DPDPEsbesides the superposition of =100 ps fluctuations around an average structure and fast transitions we additionally detected long-term, large-amplitude structural changes. These “creeping” transitions occur over several hundreds of picoseconds and involve dihedral shifts by up to 180°. The most interesting observation from the DPDPE(SH)2 simulations was that the two independent trajectories converged to essentially the same final structure, a family of type IV β-turn structures. Because of the large differences in initial structures of the two trajectories, we believe that this common final conformation is a representative stable state of DPDPE(SH)2. The cyl-DPDPE trajectory quickly moved away from its starting structure, suggesting that conformations similar to the disulfide-bridged one are not highly populated in the acyclic peptide, which may explain the lower biological potency of DPDPE(SH)2. Because of the large differences in initial structures of the two trajectories, we believe that this common final conformation is a representative stable state of DPDPE(SH)2. For cyclic DPDPE good overall agreement was found between the calculated and experimentally observed NMR vicinal coupling constants, indicating that the structures sampled in the simulation are similar to those found under experimental conditions. The calculated NMR coupling constants of DPDPE(SH)2 are a prediction which can be compared with experimental data when they become available. Both the cyclic and linear forms of DPDPE exhibit high dipole moments in solution. In accord with the relatively low structural flexibility of the cyclic peptide, its dipole exhibits small fluctuations,

Wang and Kuczera appearing to be “locked” at a high value. In contrast, the dipole moment of the linear DPDPE exhibits large fluctuations in magnitude. The more compact cyclic peptide has a higher translational diffusion coefficient than the more elongated linear form. However, the linear and cyclic forms exhibit similar overall tumbling rates in solution. The differences in structure, flexibility, polarity, and mobility of the cyclic and linear forms of DPDPE can be used to explain the higher membrane permeability of the linear peptide. We have found that using the generalized ergodic measures of Straub and Thirulamai is helpful in estimating lengths of simulations needed for exploration of conformational space within one trajectory and of convergence to similar structures between two trajectories. From the nonbonded force exploration metric we obtain time scales of configuration space exploration of 600 ps for cyclic DPDPE and 300 ps for thelinear form, suggesting that our 1 ns simulation is of the correct order of magnitude, and should be able to capture representative structures of the simulated peptides. The estimate that linear DPDPE should exhibit approximately 2 times higher structural flexibility than the cyclic form obtained from ergodic measures is in agreement with results from more standard methods such as counting dihedral angle transitions. The 300 ps time scale for convergence of the two independent linear DPDPE trajectories obtained from the nonbonded force metric is similar to the rate of structural convergence found by analyzing dihedral time series. Since the three generated 1 ns trajectories continue to explore new conformations and no recurrence of previously visited structures is found, the conformational sampling appears to be incomplete. In order to better explore conformational space, to obtain a more detailed picture of structural changes induced by S-S bond dissociation and to differentiate between relaxational and fluctuational motions, we will continue the studies of this interesting peptide using conformational free energy simulations. Acknowledgment. K.K. would like to gratefully acknowledge Martin Karplus for stimulating his interest in computer simulations of biological molecules. This work was supported in part by the University of Kansas General Research Fund and by the Kansas Institute for Theoretical and Computational Science. Figures 1 and 3 were created using the program MOLSCRIPT.53 References and Notes (1) Thornton, J. M. J. Mol. Biol. 1981, 151, 261-287. (2) Creighton, T. E. J. Phys. Chem. 1985, 89, 2452-2459. (3) Creighton, T. E., Ed. Protein folding; W. H. Freeman: New York, 1992. (4) Holmgren, A. Annu. ReV. Biochem. 1985, 54, 237-271. (5) Creighton, T. E. Bioessays 1988, 8, 57-63. (6) Nishiuchi, Y.; Sakakibara, S. FEBS Lett. 1982, 148, 260-262. (7) Yanagisawa, M.; Kurihara, H.; Kimura, S.; Tomobe, Y.; Kobayashi, M.; Mitsui, Y.; Yazaki, Y.; Goto, K.; Masaki, T. Nature 1988, 332, 441415. (8) Hruby, V. J.; Smith, C. W. In The Peptides: Analysis, Synthesis, Biology; Udenfriend, S., Meienhofer, J., Eds.; Academic Press: London, 1987; pp 77-197. (9) Mosberg, H. I.; Hurst, R.; Hruby, V. J.; Gee, K.; Yamamura, H. I.; Galligan, J. J.; Burks, T. F. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 58715874. (10) Hughes, J.; Smith, T. W.; Kosterlitz, H. W.; Forthergill, L. A.; Morgan, B. A.; Morris, H. R. Nature 1975, 258, 577-580. (11) Hruby, V. J. Opioid Peptides: Medicinal Chemistry; Rapaka, R. S., Barnett, G., Hawks, R. L., Eds.; National Institute on Drug Abuse Research Monograph 69; NIDA: Rockville, MD, 1986; pp 128-147. (12) Udenfriend, S., Meienhoferr, J., Eds. The peptides, analysis, synthesis, biology. Opioid peptides: Biology, Chemistry, and Genetics; Academic Press: Orlando, FL, 1984; Vol. 6, pp 147-189.

Molecular Dynamics Simulations of DPDPE (13) Schiller, P. W. The peptides. analysis, synthesis, biology. Opioid peptides: Biology, Chemistry, and Genetics; Acdemic Press: Orlando, FL, 1984; Vol. 6, pp 219-268. (14) Froimowitz, M.; Hruby, V. J. Int. J. Peptide Protein Res. 1989, 34, 89-96. (15) Nikiforovich, G. V.; Hruby, V. J.; Prakash, O.; Gehrig, C. A. Biopolymers 1991, 31, 941-955. (16) Hruby, V. J.; Kao, L.-F.; Pettitt, B. M.; Karplus, M. J. Am. Chem. Soc. 1988, 110, 3351-3359. (17) Pettitt, B. M.; Matsunaga, T.; Al-Obeidi, F.; Gehrig, C.; Hruby, V. J.; Karplus, M. Biophys. J. 1991, 60, 1540-1544. (18) Smith, P. E.; Dang, L. X.; Pettitt, B. M. J. Am. Chem. Soc. 1991, 113, 67-73. (19) Smith, P. E.; Pettitt, B. M. Biopolymers 1992, 32, 1623-1629. (20) Wilkes, B. C.; Schiller, P. W. J. Comput.-Aided Mol. Des. 1991, 5, 293-302. (21) Chew, C.; Villar, H. O.; Loew, G. H. Mol. Pharm. 1991, 39, 502510. (22) Flippen-Anderson, J. L.; Hruby, V. J.; Collins, N.; George, C.; Cudney, B. J. Am. Chem. Soc. 1994, 116, 7523-7531. (23) Misicka, A.; Lipkowski, A. W.; Horvath, R.; Davis, P.; Porreca, F.; Yamamura, H. I.; Hruby, V. J. Int. J. Pept. Protein Res. 1994, 44, 8084. (24) Froimowitz, M. Biopolymers 1990, 30, 1011-1025. (25) Haaseth, R. C.; Sobczyk-Kojiro, K.; Medzihradsky, F.; Smith, C. B.; Mosberg, H. I. Int. J. Pept. Protein Res. 1990, 36, 139-146. (26) Mosberg, H. I.; Sobczyk-Kojiro, K.; Subramanian, P.; Crippen, G. M.; Ramalingam, K.; Woodard, R. W. J. Am. Chem. Soc. 1990, 112, 822829. (27) Misicka, A.; Nikiforovich, G.; Lipkowski, A. W.; Horvath, R.; Davis, P.; Kramer, T. H.; Yamamura, H. I.; Hruby, V. J. Bioorg. Med. Chem. Lett. 1992, 2, 547-552. (28) Qian, X.; Ko¨ve´r, K. E.; Shenderovich, M. D.; Lou, B.-S.; Misika, A.; Zalewska, T.; Horvath, R.; Davis, P.; Bilsky, E. J.; Porreca, F.; Yamamura, H. I.; Hruby, V. J. J. Med. Chem. 1994, 37, 1746-1575. (29) Smith, P. E.; Marlow, G. E.; Pettitt, B. M. J. Am. Chem. Soc. 1993, 115, 7493-7498. (30) Matsunaga, T. O.; Collins, N.; Ramaswami, V.; Yamamura, S. H.; O’Brien, D. F.; Hruby, V. J. Biochemistry 1993, 32, 13180-13189. (31) Ramaswami, V.; Haaseth, R. C.; Matsunaga, T. O.; Hruby, V. J.; O’Brien, D. F. Biochim. Biophys. Acta 1992, 1109, 195-202. (32) Brownson, E. A.; Abbruscato, T. J.; Gillespie, T. J.; Hruby, V. J.; Davis, T. P. J. Pharmacol. Exp. Ther. 1994, 270 (2), 675-680.

J. Phys. Chem., Vol. 100, No. 7, 1996 2563 (33) Thirumalai, D.; Mountain, R. D. Phys. ReV. A 1990, 42, 45744587. (34) Straub, J. E.; Rashkin, A. B.; Thirumalai, D. J. Am. Chem. Soc. 1994, 116, 2049-2063. (35) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926-935. (36) Brooks, B. R.; Bruccoleri, R.; Olafson, B.; States, D.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187-217. (37) Nikiforrovich, G. V.; Golbraikh, A. A.; Shenderovich, M. D.; Balodis, J. Int. J. Pept. Protein Res. 1990, 36, 209-218. (38) Srinivasan, N.; Sowdhamini, R.; Ramakrishnan, C.; Balaram, P. Int. J. Pept. Protein Res. 1990, 36, 147-155. (39) Tobias, D. J.; Mertz, J. E.; Brooks, C. L., III. Biochemistry 1991, 30, 6054-6058. (40) Bruccoleri, R. E.; Karplus, M. Biopolymers 1990, 29, 1847-1862. (41) Roitberg, A.; Elber, R. J. Chem. Phys. 1992, 95, 9277. (42) Lewis, P. N.; Momany, F. A.; Scheraga, H. A. Biochim. Biophys. Acta 1973, 303, 211-229. (43) Brooks, C. L., III; Karplus, M.; Petitt, B. M. Proteins; John Wiley and Sons: New York, 1988. (44) Bystrov, V. F. Prog. Nucl. Magn. Reson. Spectrosc. 1976, 10, 4181. (45) de Leeuw, C.; amd Altona, F. A. A. M. Int. J. Pept. Protein Res. 1982, 20, 120-125. (46) McQuarrie, D. A. Statistical Mechanics; Harper & Row: New York, 1976. (47) McConnell, J. Rotational Brownian Motion and Dielectric Theory; Academic Press: London, 1980. (48) Cantor, C. R.; Schimmel, P. R. Biophysical Chemistry: Techniques for the Study of Biological Structure and Function; W. H. Freeman: New York, 1980; Vol. II. (49) Pratt, W. B., Taylor, P., Eds.; Principles of Drug Action; Churchill Livingstone Inc.: New York, 1990. (50) Burgen, A. S. V. J. Pharm. Pharmacol. 1966, 18, 137. (51) Alberty, R. A.; Hammes, G. G. J. Phys. Chem. 1958, 62, 154. (52) Straub, J. E.; Thirumalai, D. Proteins: Structure, Funct., Genet. 1993, 15, 360-373. (53) Kraulis, P. J. J. Appl. Crystallogr. 1991, 24, 946-950.

JP952669B