Absolute protein-protein association rate constants from flexible, coarse-grained Brownian dynamics simulations: the role of intermolecular hydrodynamic interactions in barnase-barstar association.

Theory and computation have long been used to rationalize the experimental association rate constants of protein-protein complexes, and Brownian dynamics (BD) simulations, in particular, have been successful in reproducing the relative rate constants of wild-type and mutant protein pairs. Missing from previous BD studies of association kinetics, however, has been the description of hydrodynamic interactions (HIs) between, and within, the diffusing proteins. Here we address this issue by rigorously including HIs in BD simulations of the barnase-barstar association reaction. We first show that even very simplified representations of the proteins--involving approximately one pseudoatom for every three residues in the protein--can provide excellent reproduction of the absolute association rate constants of wild-type and mutant protein pairs. We then show that simulations that include intermolecular HIs also produce excellent estimates of association rate constants, but, for a given reaction criterion, yield values that are decreased by ∼35-80% relative to those obtained in the absence of intermolecular HIs. The neglect of intermolecular HIs in previous BD simulation studies, therefore, is likely to have contributed to the somewhat overestimated absolute rate constants previously obtained. Consequently, intermolecular HIs could be an important component to include in accurate modeling of the kinetics of macromolecular association events.

Computational sampling of a cryptic drug binding site in a protein receptor: explicit solvent molecular dynamics and inhibitor docking to p38 MAP kinase.

An increasing number of structural studies reveal alternative binding sites in protein receptors that become apparent only when an inhibitor binds, and correct prediction of these situations presents a significant challenge to computer-aided drug design efforts. A striking example is provided by recent crystal structures of the p38 MAP kinase, where a 10A movement of the Phe169 side-chain creates a new binding site adjacent to the ATP binding site that is exploited by the diaryl urea inhibitor BIRB796. Here, we show that this binding site can be successfully and repeatedly identified in explicit-solvent molecular dynamics (MD) simulations of the protein that begin from an unliganded p38 crystal structure. Ligand-docking calculations performed on 5000 different structural snapshots generated during MD indicate that the conformations sampled are often surprisingly competent to bind the inhibitor BIRB796 in the crystallographically correct position and with docked energies that are generally more favorable than those of other positions. Similar docking studies with an ATP-binding site-directed inhibitor suggest that it may be possible to develop hybrid inhibitors that target both the ATP and cryptic binding sites simultaneously. Intriguingly, both inhibitors are occasionally found to dock correctly even with p38's "DFG" motif in the "wrong" conformation and BIRB796 can successfully dock, albeit infrequently, without significant displacement of the Phe169 side-chain; this suggests that the inhibitor might facilitate the latter's conformational change. Finally, two quite different conformations of p38's DFG motif are also sampled for extended periods of time during the simulations; these may provide new opportunities for inhibitor development. The MD simulations reported here, which total 390 ns in length, therefore demonstrate that existing computational methods may be of surprising utility in predicting cryptic binding sites in protein receptors prior to their experimental discovery.

Parametrization of Backbone Flexibility in a Coarse-Grained Force Field for Proteins (COFFDROP) Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of All Possible Two-Residue Peptides.

Recently, we reported the parametrization of a set of coarse-grained (CG) nonbonded potential functions, derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acid pairs and designed for use in (implicit-solvent) Brownian dynamics (BD) simulations of proteins; this force field was named COFFDROP (COarse-grained Force Field for Dynamic Representations Of Proteins). Here, we describe the extension of COFFDROP to include bonded backbone terms derived from fitting to results of explicit-solvent MD simulations of all possible two-residue peptides containing the 20 standard amino acids, with histidine modeled in both its protonated and neutral forms. The iterative Boltzmann inversion (IBI) method was used to optimize new CG potential functions for backbone-related terms by attempting to reproduce angle, dihedral, and distance probability distributions generated by the MD simulations. In a simple test of the transferability of the extended force field, the angle, dihedral, and distance probability distributions obtained from BD simulations of 56 three-residue peptides were compared to results from corresponding explicit-solvent MD simulations. In a more challenging test of the COFFDROP force field, it was used to simulate eight intrinsically disordered proteins and was shown to quite accurately reproduce the experimental hydrodynamic radii (Rhydro), provided that the favorable nonbonded interactions of the force field were uniformly scaled downward in magnitude. Overall, the results indicate that the COFFDROP force field is likely to find use in modeling the conformational behavior of intrinsically disordered proteins and multidomain proteins connected by flexible linkers.

Molecular Dynamics Simulations of 441 Two-Residue Peptides in Aqueous Solution: Conformational Preferences and Neighboring Residue Effects with the Amber ff99SB-ildn-NMR Force Field.

Understanding the intrinsic conformational preferences of amino acids and the extent to which they are modulated by neighboring residues is a key issue for developing predictive models of protein folding and stability. Here we present the results of 441 independent explicit-solvent MD simulations of all possible two-residue peptides that contain the 20 standard amino acids with histidine modeled in both its neutral and protonated states. (3)J(HNHα) coupling constants and δ(Hα) chemical shifts calculated from the MD simulations correlate quite well with recently published experimental measurements for a corresponding set of two-residue peptides. Neighboring residue effects (NREs) on the average (3)J(HNHα) and δ(Hα) values of adjacent residues are also reasonably well reproduced, with the large NREs exerted experimentally by aromatic residues, in particular, being accurately captured. NREs on the secondary structure preferences of adjacent amino acids have been computed and compared with corresponding effects observed in a coil library and the average ß-turn preferences of all amino acid types have been determined. Finally, the intrinsic conformational preferences of histidine, and its NREs on the conformational preferences of adjacent residues, are both shown to be strongly affected by the protonation state of the imidazole ring.

Computer Simulations of the Bacterial Cytoplasm.

Ever since the pioneering work of Minton, it has been recognized that the highly crowded interior of biological cells has the potential to cause dramatic changes to both the kinetics and thermodynamics of protein folding and association events relative to behavior that might be observed in dilute solution conditions. One very productive way to explore the effects of crowding on protein behavior has been to use macromolecular crowding agents that exclude volume without otherwise strongly interacting with the protein under study. An alternative, complementary approach to understanding the potential differences between behavior in vivo and in vitro is to develop simulation models that explicitly attempt to model intracellular environments at the molecular scale, and that thereby can be used to directly monitor biophysical behavior in conditions that accurately mimic those encountered in vivo. It is with studies of this type that the present review will be concerned. We review in detail four published studies that have attempted to simulate the structure and dynamics of the bacterial cytoplasm and that have each explored different biophysical aspects of the cellular interior. While each of these studies has yielded important new insights, there are important questions that remain to be resolved in terms of determining the relative contributions made by energetic and hydrodynamic interactions to the diffusive behavior of macromolecules and to the thermodynamics of protein folding and associations in vivo. Some possible new directions for future generation simulation models of the cytoplasm are outlined.

Striking Effects of Hydrodynamic Interactions on the Simulated Diffusion and Folding of Proteins.

Successful modeling of the processes of protein folding and aggregation may ultimately require accurate descriptions of proteins' diffusive characteristics, which are expected to be influenced by hydrodynamic effects; a comprehensive study of the diffusion and folding of 11 model proteins with an established simulation model extended to include hydrodynamic interactions between residues has therefore been carried out. Molecular simulations that neglect hydrodynamic interactions are incapable of simultaneously reproducing the expected experimental translational and rotational diffusion coefficients of folded proteins, drastically underestimating both when reasonable hydrodynamic radii are employed. In contrast, simulations that include hydrodynamic interactions produce diffusion coefficients that match very well with the expected experimental values for translation and rotation and also correctly capture the significant decrease in translational diffusion coefficient that accompanies protein unfolding. These effects are reflected in folding simulations of the same proteins: the inclusion of hydrodynamic interactions accelerates folding by 2-3-fold with the rate enhancement for the association of secondary structure elements exhibiting a strong sensitivity on the sequence-distance between the associating elements.