Novel Procedure for Developing Implicit Solvation Models for Peptides and Proteins

N-Terminus of the Third PDZ Domain of PSD-95 Orchestrates Allosteric Communication for Selective Ligand Binding

PDZ domains constitute common models to study single-domain allostery without significant structural changes. The third PDZ domain of PSD-95 (PDZ3) is known to have selective structural features that confer unique modulatory roles to this unit. In this model system, two residues, H372 directly connected to the binding site and G330 holding an off-binding-site position, were designated to assess the effect of mutations on binding selectivity. It has been observed that the H372A and G330T-H372A mutations change ligand preferences from class I (T/S amino acid at position -2 of the ligand) to class II (hydrophobic amino acid at the same position). Alternatively, the G330T single mutation leads to the recognition of both ligand classes. We have performed a series of molecular dynamics (MD) simulations for wild-type, H372A, and G330T single mutants and a double mutant of PDZ3 in the absence and presence of both types of ligands. With the combination of free-energy difference calculations and a detailed analysis of MD trajectories, "class switching" and "class bridging" behavior of PDZ3 mutants, as well as their effects on ligand selection and binding affinities are explained. We show that the dynamics of the charged N-terminus plays a fundamental role in determining the binding preferences in PDZ3 by altering the electrostatic energy. These findings are corroborated by simulations on N-terminus-truncated versions of these systems. The dynamical allostery orchestrated by the N-terminus offers a fresh perspective to the study of communication pathways in proteins.

Conformational Sampling of a Biomolecular Rugged Energy Landscape

The protein structure refinement using conformational sampling is important in hitherto protein studies. In this paper, we examined the protein structure refinement by means of potential energy minimization using immune computing as a method of sampling conformations. The method was tested on the x-ray structure and 30 decoys of the mutant of [Leu]Enkephalin, a paradigmatic example of the biomolecular multiple-minima problem. In order to score the refined conformations, we used a standard potential energy function with the OPLSAA force field. The effectiveness of the search was assessed using a variety of methods. The robustness of sampling was checked by the energy yield function which measures quantitatively the number of the peptide decoys residing in an energetic funnel. Furthermore, the potential energy-dependent Pareto fronts were calculated to elucidate dissimilarities between peptide conformations and the native state as observed by x-ray crystallography. Our results showed that the probed potential energy landscape of [Leu]Enkephalin is self-similar on different metric scales and that the local potential energy minima of the peptide decoys are metastable, thus they can be refined to conformations whose potential energy is decreased by approximately 250 kJ/mol.

MOPED: method for optimizing physical energy parameters using decoys

We present a method called MOPED for optimizing energetic and structural parameters in computational models, including all-atom energy functions, when native structures and decoys are given. The present method goes beyond previous approaches in treating energy functions that are nonlinear in the parameters and continuous in the degrees of freedom. We illustrate the method by improving solvation parameters in the energy function EEF1, which consists of the CHARMM19 polar hydrogen force field augmented by a Gaussian solvation term. Although the published parameters for EEF1 correctly discriminate the native from decoys in the decoy sets of Levitt et al., they fail on several of the more difficult decoy sets of Baker et al. MOPED successfully finds improved parameters that allow EEF1 to discriminate native from decoy structures on all protein structures that do not have metals or prosthetic groups.

Long time dynamics of Met-enkephalin: comparison of explicit and implicit solvent models

Met-enkephalin is one of the smallest opiate peptides. Yet, its dynamical structure and receptor docking mechanism are still not well understood. The conformational dynamics of this neuron peptide in liquid water are studied here by using all-atom molecular dynamics (MD) and implicit water Langevin dynamics (LD) simulations with AMBER potential functions and the three-site transferable intermolecular potential (TIP3P) model for water. To achieve the same simulation length in physical time, the full MD simulations require 200 times as much CPU time as the implicit water LD simulations. The solvent hydrophobicity and dielectric behavior are treated in the implicit solvent LD simulations by using a macroscopic solvation potential, a single dielectric constant, and atomic friction coefficients computed using the accessible surface area method with the TIP3P model water viscosity as determined here from MD simulations for pure TIP3P water. Both the local and the global dynamics obtained from the implicit solvent LD simulations agree very well with those from the explicit solvent MD simulations. The simulations provide insights into the conformational restrictions that are associated with the bioactivity of the opiate peptide dermorphin for the delta-receptor.

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.

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).

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

Using a recently developed statistical mechanics methodology, the solution structures and populations of the cyclic pentapeptide cyclo(D-Pro(1)-Ala(2)-Ala(3)-Ala(4)-Ala(5)) in DMSO are obtained ab initio, i.e., without using experimental restraints. An important ingredient of this methodology is a novel optimization of implicit solvation parameters, which in our previous publication [Baysal, C.; Meirovitch, H. J Am Chem Soc 1998, 120, 800-812] has been applied to a cyclic hexapeptide in DMSO. 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. This methodology, which relies on an extensive conformational search, Monte Carlo simulations, and free energy calculations, is applied here with E(tot) based on the ASPs derived in our previous work, and for comparison also with E(GRO) alone. For both models, entropy effects are found to be significant. For E(tot), the theoretical values of proton-proton distances and (3)J coupling constants agree very well with the NMR results [Mierke, D. F.; Kurz, M.; Kessler, H. J Am Chem Soc 1994, 116, 1042-1049], while the results for E(GRO) are significantly worse. This suggests that our ASPs might be transferrable to other cyclic peptides in DMSO as well, making our methodology a reliable tool for an ab initio structure prediction; obviously, if necessary, parts of this methodology can also be incorporated in a best-fit analysis where experimental restraints are used.

Free energy based populations of interconverting microstates of a cyclic peptide lead to the experimental NMR data

Analysis of nuclear Overhauser enhancement (NOE) intensities data of interconverting microstates of a peptide is a difficult problem in nmr. A new statistical mechanics methodology has been proposed recently, consisting of several steps: (1) potential energy wells on the energy surface of the molecule are identified (the corresponding regions are called wide microstates); (2) each wide microstate is then spanned by a Monte Carlo (MC) or molecular dynamics simulation starting from a representative structure, and the corresponding relative populations are obtained from the free energy calculated with the local states method; and (3) the overall NOEs and 3J coupling constants are obtained as averages over the corresponding contributions of the samples, weighted by the populations. Extending this methodology to cyclic peptides, we are treating here the hexapeptide cyclo(D-Pro1-Phe2-Ala3-Ser4-Phe5-Phe6) in DMSO, which was studied by Kessler et al. using nmr (Journal of the American Chemical Society, 1992, Vol. 114, pp. 4805-4818). They found that at least two structures are required to explain their NOE data, a conclusion also corroborated by our analysis (Journal of the American Chemical Society, 1998, Vol. 120, pp. 800-812) and led to a novel derivation of atomic solvation parameters (ASPs) for DMSO. Thus, the overall interactions within the peptide-solvent system are described approximately by Etot = EGRO + summation operator sigmaiAi, where EGRO is the energy of the GROMOS force field, Ai is the solvent-accessible surface area of atom i, and sigmai is the ASP. In the present paper the validity of these ASPs within the framework of the entire methodology is verified. This requires taking into account 23 microstates. A very good agreement is obtained between experimental and calculated NOEs and 3J coupling constants. The free energy based populations lead to the best results, which means that entropic effects should not be ignored. We have also studied the behavior of the internal angular fluctuations of the proton-proton vectors and discovered that they have a negligible effect on the calculated NOEs; this is due to the relatively concentrated wide microstates spanned by the MC simulations. The applicability of our ASPs to other cyclic peptides in DMSO is being studied in another work and preliminary results are discussed.