Ab initio prediction of the solution structures and populations of a cyclic pentapeptide in DMSO based on an implicit solvation model

Accurate Structure Prediction and Conformational Analysis of Cyclic Peptides with Residue-Specific Force Fields

Cyclic peptides (CPs) are promising candidates for drugs, chemical biology tools, and self-assembling nanomaterials. However, the development of reliable and accurate computational methods for their structure prediction has been challenging. Here, 20 all-trans CPs of 5-12 residues selected from Cambridge Structure Database have been simulated using replica-exchange molecular dynamics with four different force fields. Our recently developed residue-specific force fields RSFF1 and RSFF2 can correctly identify the crystal-like conformations of more than half CPs as the most populated conformation. The RSFF2 performs the best, which consistently predicts the crystal structures of 17 out of 20 CPs with rmsd < 1.1 Å. We also compared the backbone (ϕ, ψ) sampling of residues in CPs with those in short linear peptides and in globular proteins. In general, unlike linear peptides, CPs have local conformational free energies and entropies quite similar to globular proteins.

Toward structure prediction of cyclic peptides

Cyclic peptides are a promising class of molecules that can be used to target specific protein-protein interactions. A computational method to accurately predict their structures would substantially advance the development of cyclic peptides as modulators of protein-protein interactions. Here, we develop a computational method that integrates bias-exchange metadynamics simulations, a Boltzmann reweighting scheme, dihedral principal component analysis and a modified density peak-based cluster analysis to provide a converged structural description for cyclic peptides. Using this method, we evaluate the performance of a number of popular protein force fields on a model cyclic peptide. All the tested force fields seem to over-stabilize the α-helix and PPII/β regions in the Ramachandran plot, commonly populated by linear peptides and proteins. Our findings suggest that re-parameterization of a force field that well describes the full Ramachandran plot is necessary to accurately model cyclic peptides.

Methods for calculating the absolute entropy and free energy of biological systems based on ideas from polymer physics

The commonly used simulation techniques, Metropolis Monte Carlo (MC) and molecular dynamics (MD) are of a dynamical type which enables one to sample system configurations i correctly with the Boltzmann probability, P(i)(B), while the value of P(i)(B) is not provided directly; therefore, it is difficult to obtain the absolute entropy, S approximately -ln P(i)(B), and the Helmholtz free energy, F. With a different simulation approach developed in polymer physics, a chain is grown step-by-step with transition probabilities (TPs), and thus their product is the value of the construction probability; therefore, the entropy is known. Because all exact simulation methods are equivalent, i.e. they lead to the same averages and fluctuations of physical properties, one can treat an MC or MD sample as if its members have rather been generated step-by-step. Thus, each configuration i of the sample can be reconstructed (from nothing) by calculating the TPs with which it could have been constructed. This idea applies also to bulk systems such as fluids or magnets. This approach has led earlier to the "local states" (LS) and the "hypothetical scanning" (HS) methods, which are approximate in nature. A recent development is the hypothetical scanning Monte Carlo (HSMC) (or molecular dynamics, HSMD) method which is based on stochastic TPs where all interactions are taken into account. In this respect, HSMC(D) can be viewed as exact and the only approximation involved is due to insufficient MC(MD) sampling for calculating the TPs. The validity of HSMC has been established by applying it first to liquid argon, TIP3P water, self-avoiding walks (SAW), and polyglycine models, where the results for F were found to agree with those obtained by other methods. Subsequently, HSMD was applied to mobile loops of the enzymes porcine pancreatic alpha-amylase and acetylcholinesterase in explicit water, where the difference in F between the bound and free states of the loop was calculated. Currently, HSMD is being extended for calculating the absolute and relative free energies of ligand-enzyme binding. We describe the whole approach and discuss future directions.

Non-Markovian noise mediated through anomalous diffusion within ion channels

It is evident from a wide range of experimental findings that ion channel gating is inherently stochastic. The issue of "memory effects" (diffusional retardation due to local changes in water viscosity) in ionic flow has been recently addressed using Brownian dynamics simulations. The results presented indicate such memory effects are negligible, unless the diffusional barrier is much higher than that of free solute. In this paper using differential stochastic methods we conclude that the Markovian property of exponential dwell times gives rise to a high barrier, resulting in diffusional memory effects that cannot be ignored in determining ionic flow through channels. We have addressed this question using a generalized Langevin equation that contains a combination of Markovian and non-Markovian processes with different time scales. This approach afforded the development of an algorithm that describes an oscillatory ionic diffusional sequence. The resulting oscillatory function behavior, with exponential decay, was obtained at the weak non-Markovian limit with two distinct time scales corresponding to the processes of ionic diffusion and drift. This will be analyzed further in future studies using molecular dynamics simulations. We propose that the rise of time scales and memory effects is related to differences of shear viscosity in the cytoplasm and extracellular matrix.

Entropy and free energy of a mobile protein loop in explicit water

Estimation of the energy from a given Boltzmann sample is straightforward since one just has to average the contribution of the individual configurations. On the other hand, calculation of the absolute entropy, S (hence the absolute free energy F) is difficult because it depends on the entire (unknown) ensemble. We have developed a new method called "the hypothetical scanning molecular dynamics" (HSMD) for calculating the absolute S from a given sample (generated by any simulation technique). In other words, S (like the energy) is "written" on the sample configurations, where HSMD provides a prescription of how to "read" it. In practice, each sample conformation, i, is reconstructed with transition probabilities, and their product leads to the probability of i, hence to the entropy. HSMD is an exact method where all interactions are considered, and the only approximation is due to insufficient sampling. In previous studies HSMD (and HS Monte CarloHSMC) has been extended systematically to systems of increasing complexity, where the most recent is the seven-residue mobile loop, 304-310 (Gly-His-Gly-Ala-Gly-Gly-Ser) of the enzyme porcine pancreatic alpha-amylase modeled by the AMBER force field and AMBER with the implicit solvation GB/SA (paper I, Cheluvaraja, S.; Meirovitch, H. J. Chem. Theory Comput. 2008, 4, 192). In the present paper we make a step further and extend HSMD to the same loop capped with TIP3P explicit water at 300 K. As in paper I, we are mainly interested in entropy and free energy differences between the free and bound microstates of the loop, which are obtained from two separate MD samples of these microstates. The contribution of the loop to S and F is calculated by HSMD and that of water by a particular thermodynamic integration procedure. As expected, the free microstate is more stable than the bound microstate by a total free energy difference, Ffree-Fbound=-4.8+/-1, as compared to -25.5 kcal/mol obtained with GB/SA. We find that relatively large systematic errors in the loop entropies, Sfree(loop) and Sbound(loop) are cancelled in their difference which is thus obtained efficiently and with high accuracy, i.e., with a statistical error of 0.1 kcal/mol. This cancellation, which has been observed in previous HSMD studies, is in accord with theoretical arguments given in paper I.

Conformational Templates for Rational Drug Design: Flexibility of cyclo(d-Pro-Ala-Ala-Ala-Ala) in DMSO Solution

Long MD simulations (100 ns) for the important model cyclopentapeptide cyclo(D-Pro1-Ala2-Ala3-Ala4-Ala5) were performed in explicit DMSO solution using both OPLS-AA and AMBER03 force fields. Simulations revealed conformational transitions between two main conformers, a predominant one (population 93-99%) and a minor conformer (population 0.4-6.7%). These results are in excellent agreement with 20 experimental proton-proton distances estimated for this cyclopentapeptide. The previously discussed gamma-turn-like conformation for Ala4 was present only in a minor conformer.

Conformational Flexibility, Internal Hydrogen Bonding, and Passive Membrane Permeability: Successful in Silico Prediction of the Relative Permeabilities of Cyclic Peptides

We report an atomistic physical model for the passive membrane permeability of cyclic peptides. The computational modeling was performed in advance of the experiments and did not involve the use of "training data". The model explicitly treats the conformational flexibility of the peptides by extensive conformational sampling in low (membrane) and high (water) dielectric environments. The passive membrane permeabilities of 11 cyclic peptides were obtained experimentally using a parallel artificial membrane permeability assay (PAMPA) and showed a linear correlation with the computational results with R(2) = 0.96. In general, the results support the hypothesis, already well established in the literature, that the ability to form internal hydrogen bonds is critical for passive membrane permeability and can be the distinguishing factor among closely related compounds, such as those studied here. However, we have found that the number of internal hydrogen bonds that can form in the membrane and the solvent-exposed polar surface area correlate more poorly with PAMPA permeability than our model, which quantitatively estimates the solvation free energy losses upon moving from high-dielectric water to the low-dielectric interior of a membrane.

Optimization of the GB/SA solvation model for predicting the structure of surface loops in proteins

Implicit solvation models are commonly optimized with respect to experimental data or Poisson-Boltzmann (PB) results obtained for small molecules, where the force field is sometimes not considered. In previous studies, we have developed an optimization procedure for cyclic peptides and surface loops in proteins based on the entire system studied and the specific force field used. Thus, the loop has been modeled by the simplified solvation function E(tot) = E(FF) (epsilon = 2r) + Sigma(i) sigma(i)A(i), where E(FF) (epsilon = nr) is the AMBER force field energy with a distance-dependent dielectric function, epsilon = nr, A(i) is the solvent accessible surface area of atom i, and sigma(i) is its atomic solvation parameter. During the optimization process, the loop is free to move while the protein template is held fixed in its X-ray structure. To improve on the results of this model, in the present work we apply our optimization procedure to the physically more rigorous solvation model, the generalized Born with surface area (GB/SA) (together with the all-atom AMBER force field) as suggested by Still and co-workers (J. Phys. Chem. A 1997, 101, 3005). The six parameters of the GB/SA model, namely, P(1)-P(5) and the surface area parameter, sigma (programmed in the TINKER package) are reoptimized for a "training" group of nine loops, and a best-fit set is defined from the individual sets of optimized parameters. The best-fit set and Still's original set of parameters (where Lys, Arg, His, Glu, and Asp are charged or neutralized) were applied to the training group as well as to a "test" group of seven loops, and the energy gaps and the corresponding RMSD values were calculated. These GB/SA results based on the three sets of parameters have been found to be comparable; surprisingly, however, they are somewhat inferior (e.g, of larger energy gaps) to those obtained previously from the simplified model described above. We discuss recent results for loops obtained by other solvation models and potential directions for future studies.

Solvent effect on the synthesis of clarithromycin: a molecular dynamics study

Clarithromycin (6-O-methylerythromycin A) is a 14-membered macrolide antibiotic which is active in vitro against clinically important gram-positive and gram-negative bacteria. The selectivity of the methylation of the C-6 OH group is studied on erythromycin A derivatives. To understand the effect of the solvent on the methylation process, detailed molecular dynamics (MD) simulations are performed in pure DMSO, pure THF and DMSO:THF (1:1) mixture by using the anions at the C-6, C-11 and C-12 positions of 2',4"-[O-bis(TMS)]erythromycin A 9-[O-(dimethylthexylsilyl)oxime] under the assumption that the anions are stable on the sub-nanosecond time scale. The conformations of the anions are not affected by the presence of the solvent mixture. The radial distribution functions are computed for the distribution of different solvent molecules around the 'O-' of the anions. At distances shorter than 5 A, DMSO molecules are found to cluster around the C-11 anion, whereas the anion at the C-12 position is surrounded by the THF molecules. The anion at the C-6 position is not blocked by the solvent molecules. The results are consistent with the experimental finding that the methylation yield at the latter position is increased in the presence of a DMSO:THF (1:1) solvent mixture. Thus, the effect of the solvent in enhancing the yield during the synthesis is not by changing the conformational properties of the anions, but rather by creating a suitable environment for methylation at the C-6 position.

Coordination topology and stability for the native and binding conformers of chymotrypsin inhibitor 2

We demonstrate that the stabilization of the binding region is accomplished at the expense of a loss in the stability of the rest of the protein. A novel molecular mechanics (MM) approach is introduced to distinguish residue stabilities of proteins in a given conformation. As an example, the relative stabilities of folded chymotrypsin inhibitor 2 (CI2) in unbound form, and CI2 in complex with subtilisin novo is investigated. The conformation of the molecule in the two states is almost identical, with an approximately 0.6-A root-mean-square deviation (RMSD) of the Calpha atoms. On binding, the packing density changes only at the binding loop. However, residue fluctuations in the rest of the protein are greatly altered solely due to those contacts, indicating the effective propagation of perturbation and the presence of remotely controlling residues. To quantify the interplay between packing density, packing order, residue fluctuations, and residue stability, we adopt an MM approach whereby small displacements are inserted at selected residues, followed by energy minimization; the displacement of each residue in response to such perturbations are organized in a perturbation-response matrix L. We define residue stability lambda(i) = summation operator((j)L(ij))/ summation operator((j) L(ji)) as the ratio of the amount of change to which the residue is amenable, to the ability of a given residue to induce change. We then define the free energy associated with residue stability, DeltaG(lambda) = -RT ln lambda. DeltaG(lambda) intrinsically selects the residues that are in the folding core. Upon complexation, the binding loop becomes more resistant to perturbation, in contrast to the alpha-helix that favors change. Although the two forms of CI2 are structurally similar, residue fluctuations differ vastly, and the stability of many residues is altered upon binding. The decrease in entropy introduced by binding is thus compensated by these changes.

Determination of conformational equilibrium of peptides in solution by NMR spectroscopy and theoretical conformational analysis: application to the calibration of mean-field solvation models

Peptides occur in solution as ensembles of conformations rather than in a fixed conformation. The existing energy functions are usually inadequate to predict the conformational equilibrium in solution, because of failure to account properly for solvation, if the solvent is not considered explicitly (which is usually prohibitively expensive). NMR data are therefore widely incorporated into theoretical conformational analysis. Because of conformational flexibility, restrained molecular dynamics (with restraints derived from NMR data), which is usually applied to determine protein conformation is of limited use in the case of peptides. Instead, (a) the restraints are averaged within predefined time windows during molecular dynamics (MD) simulations (time averaging), (b) multiple-copy MD simulations are carried out and the restraints are averaged over the copies (ensemble averaging), or (c) a representative ensemble of sterically feasible conformations is generated and the weights of the conformations are then fitted so that the computed average observables match the experimental data (weight fitting). All these approaches are briefly discussed in this article. If an adequate force field is used, conformations with large statistical weights obtained from the weight-fitting procedure should also have low energies, which can be implemented in force field calibration. Such a procedure is particularly attractive regarding the parameterization of the solvation energy in nonaqueous solvents, e.g., dimethyl sulfoxide, for which thermodynamic solvation data are scarce. A method for calibration of solvation parameters in dimethyl sulfoxide, which is based on this principle was recently proposed by C. Baysal and H. Meirovitch (Journal of the American Chemical Society, 1998, Vol. 120, pp. 800--812), in which the energy gap between the conformations compatible with NMR data and the alternative conformations is maximized. In this work we propose an alternative method based on the principle that the best-fitting statistical weights of conformations should match the Boltzmann weights computed with the force field applied. Preliminary results obtained using three test peptides of varying conformational mobility: H-Ser(1)-Pro(2)-Lys(3)-Leu(4)-OH, Ac-Tyr(1)-D-Phe(2)-Ser(3)-Pro(4)-Lys(5)-Leu(6)-NH(2), and cyclo(Tyr(1)-D-Phe(2)-Ser(3)-Pro(4)-Lys(5)-Leu(6)) are presented.

Optimization of solvation models for predicting the structure of surface loops in proteins

A novel procedure for optimizing the atomic solvation parameters (ASPs) sigma(i) developed recently for cyclic peptides is extended to surface loops in proteins. The loop is free to move, whereas the protein template is held fixed in its X-ray structure. The energy is E(tot) = E(FF)(epsilon = nr) + summation operator sigma(i)A(i), where E(FF)(epsilon = nr) is the force-field energy of the loop-loop and loop-template interactions, epsilon = nr is a distance-dependent dielectric constant, and n is an additional parameter to be optimized. A(i) is the solvent-accessible surface area of atom i. The optimal sigma(i) and n are those for which the loop structure with the global minimum of E(tot)(n, sigma(i)) becomes the experimental X-ray structure. Thus, the ASPs depend on the force field and are optimized in the protein environment, unlike commonly used ASPs such as those of Wesson and Eisenberg (Protein Sci 1992;1:227-235). The latter are based on the free energy of transfer of small molecules from the gas phase to water and have been traditionally combined with various force fields without further calibration. We found that for loops the all-atom AMBER force field performed better than OPLS and CHARMM22. Two sets of ASPs [based on AMBER (n = 2)], optimized independently for loops 64-71 and 89-97 of ribonuclease A, were similar and thus enabled the definition of a best-fit set. All these ASPs were negative (hydrophilic), including those for carbon. Very good (i.e., small) root-mean-square-deviation values from the X-ray loop structure were obtained with the three sets of ASPs, suggesting that the best-fit set would be transferable to loops in other proteins as well. The structure of loop 13-24 is relatively stretched and was insensitive to the effect of the ASPs.

Structure and conformational behavior of biopolymers by density functional calculations employing periodic boundary conditions. I. The case of polyglycine, polyalanine, and poly-alpha-aminoisobutyric acid in vacuo

Fully quantum mechanical calculations exploiting periodic boundary conditions (PBC) have been applied to the study of four different regular structures (alpha- and 3(10)-helix, fully extended and repeated gamma-turns) of the infinite polypeptides of glycine, alanine, and alpha-aminoisobutyric acid (Aib) in vacuo. alpha-Helix is predicted to be the most stable conformer for polyalanine and polyglycine, being stabilized over the 3(10)-helix mainly by more favorable dipole-dipole interactions. Contrary to previous suggestions, steric effects and hydrogen-bond strengths are comparable for both helix structures. 3(10)-Helix is preferred for poly-Aib, since in this case alpha-helix is strongly distorted due to unfavorable intrachain repulsions. Extended structures and repeated gamma-turns are much less stable than helix structures for all of the polypeptides examined, mainly due to the absence of favorable long-range interactions. The optimized geometries are in good agreement with the available experimental data and reveal a remarkable dependence on the nature of the residue forming the polypeptides; at the same time the electronic and structural parameters of each residue strongly depend on the secondary structure of the polypeptides.

A Gaussian statistical mechanical model for the equilibrium thermodynamics of barnase folding

Given an all non-hydrogen-atom potential function that implicitly includes solvation effects, it is possible to adjust its parameters to favor the correct native structure for several proteins over decoys produced by ungapped threading. It is also possible to further train it to reproduce the experimental free energy of unfolding in aqueous solution at 298 K for wild-type barnase and 66 mutants. For this, the native state is represented by the crystal structure at a single energy level with a calculated low degeneracy; the denatured state is represented by the extended conformation and a high calculated degeneracy. The same two-state model can be extended to account for the stability of all 67 sequences toward urea denaturation at 298 K by building in a solvation term that depends on urea concentration. With the addition of one more parameter set to give the correct heat capacity of unfolded barnase in solution, it is possible to approximate the experimental thermodynamics of barnase thermal denaturation: melting temperature, width of thermal transition, deltaG, deltaH, deltaS, and deltaCp. This requires a novel sort of statistical mechanical model where the two states each have a Gaussian density of microscopic state distribution as a function of energy.

On the transferability of atomic solvation parameters: Ab initio structural prediction of cyclic heptapeptides in DMSO

A statistical mechanics methodology for predicting the solution structures and populations of peptides developed recently is based on a novel method for optimizing implicit solvation models, which was applied initially to a cyclic hexapeptide in DMSO (C. Baysal and H. Meirovitch, Journal of American Chemical Society, 1998, vol. 120, pp. 800-812). Thus, the molecule has been described by the simplified energy function E(tot) = E(GRO) + summation operator(k) sigma(k)A(k), where E(GRO) is the GROMOS force-field energy, sigma(k) and A(k) are the atomic solvation parameter (ASP) and the solvent accessible surface area of atom k, respectively. In a more recent study, these ASPs have been found to be transferable to the cyclic pentapeptide cyclo(D-Pro(1)-Ala(2)-Ala(3)-Ala(4)-Ala(5)) in DMSO (C. Baysal and H. Meirovitch, Biopolymers, 2000, vol. 53, pp. 423-433). In the present paper, our methodology is applied to the cyclic heptapeptides axinastatin 2 [cyclo(Asn(1)-Pro(2)-Phe(3)-Val(4)-Leu(5)-Pro(6)-Val(7))] and axinastatin 3 [cyclo(Asn(1)-Pro(2)-Phe(3)-Ile(4)-Leu(5)-Pro(6)-Val(7))], in DMSO, which were studied by nmr by Mechnich et al. (Helvetica Chimica Acta, 1997, vol. 80, pp. 1338-1354). The calculations for axinastatin 2 show that special ASPs should be optimized for the partially charged side-chain atoms of Asn while the rest of the atoms take their values derived in our previous work; this suggests that similar optimization might be needed for other side chains as well. The solution structures of these peptides are obtained ab initio (i.e., without using experimental restraints) by an extensive conformational search based on E(GRO) alone and E(*)(tot), which consists of the new set of ASPs. For E(*)(tot), the theoretical values of proton-proton distances, (3)J coupling constants, and other properties are found to agree very well with the nmr results, and they are always better than those based on E(GRO).