Computational probe of cavitation events in protein systems

Model Folded Hydrophobic Polymers Reside in Highly Branched Voids

By using advanced data analysis techniques, we characterize the shape of the voids surrounding model polymers of different sizes in water, observed in molecular dynamics simulations. We find that even when the model polymer is folded, the voids are extremely rough, with branches that can extend to over 1 nm away from the polymer. Water molecules in contact with the void retain close-to-bulk properties in terms of local structure. The branches disappear, and the voids start resembling the quasispherical shape predicted by dewetting theory only when they surround particles with a radius ∼1 nm, well above the size occupied by a folded hydrophobic polymer. Our results provide fresh insights into the microscopic origins of the vapor-like interfaces underlying dewetting and drying transitions.

The role of material flexibility on the drying transition of water between hydrophobic objects: a thermodynamic analysis

Liquid water confined between hydrophobic objects of sufficient size becomes metastable with respect to its vapor at separations smaller than a critical drying distance. Macroscopic thermodynamic arguments predicting this distance have been restricted to the limit of perfectly rigid confining materials. However, no material is perfectly rigid and it is of interest to account for this fact in the thermodynamic analysis. We present a theory that combines the current macroscopic theory with the thermodynamics of elasticity to derive an expression for the critical drying distance for liquids confined between flexible materials. The resulting expression is the sum of the well-known drying distance for perfectly rigid confining materials and a new term that accounts for flexibility. Thermodynamic arguments show that this new term is necessarily positive, meaning that flexibility increases the critical drying distance. To study the expected magnitude and scaling behavior of the flexible term, we consider the specific case of water and present an example of drying between thin square elastic plates that are simply supported along two opposite edges and free at the remaining two. We find that the flexible term can be the same order of magnitude or greater than the rigid solution for materials of biological interest at ambient conditions. In addition, we find that when the rigid solution scales with the characteristic size of the immersed objects, the flexible term is independent of size and vice versa. Thus, the scaling behavior of the overall drying distance will depend on the relative weights of the rigid and flexible contributions.

Phase-field approach to implicit solvation of biomolecules with Coulomb-field approximation

A phase-field variational implicit-solvent approach is developed for the solvation of charged molecules. The starting point of such an approach is the representation of a solute-solvent interface by a phase field that takes one value in the solute region and another in the solvent region, with a smooth transition from one to the other on a small transition layer. The minimization of an effective free-energy functional of all possible phase fields determines the equilibrium conformations and free energies of an underlying molecular system. All the surface energy, the solute-solvent van der Waals interaction, and the electrostatic interaction are coupled together self-consistently through a phase field. The surface energy results from the minimization of a double-well potential and the gradient of a field. The electrostatic interaction is described by the Coulomb-field approximation. Accurate and efficient methods are designed and implemented to numerically relax an underlying charged molecular system. Applications to single ions, a two-plate system, and a two-domain protein reveal that the new theory and methods can capture capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states as found in molecular dynamics simulations. Comparisons of the phase-field and the original sharp-interface variational approaches are discussed.

Evaluation of Hydration Free Energy by Level-Set Variational Implicit-Solvent Model with Coulomb-Field Approximation

In this article, we systematically apply a novel implicit-solvent model, the variational implicit-solvent model (VISM) together with the Coulomb-Field Approximation (CFA), to calculate the hydration free energy of a large set of small organic molecules. Because these molecules have been studied in detail by molecular dynamics simulations and other implicit-solvent models, they provide a good benchmark for evaluating the performance of VISM-CFA. With all-atom Amber force field parameters, VISM-CFA is able to reproduce well not only the experimental and MD simulated total hydration free energy but also the polar and nonpolar contributions individually. The correlation between VISM-CFA and experiments is R² = 0.763 for the total hydration free energy, with a root-mean-square deviation (RMSD) of 1.83 kcal/mol, and the correlation to results from TIP3P explicit water MD simulations is R² = 0.839 with a RMSD = 1.36 kcal/mol. In addition, we demonstrate that VISM captures dewetting phenomena in the p53/MDM2 complex and hydrophobic characteristics in the system. This work demonstrates that the level-set VISM-CFA can be used to study the energetic behavior of realistic molecular systems with complicated geometries in solvation, protein–ligand binding, protein–protein association, and protein folding processes.

Solvent fluctuations in hydrophobic cavity-ligand binding kinetics

Water plays a crucial part in virtually all protein-ligand binding processes in and out of equilibrium. Here, we investigate the role of water in the binding kinetics of a ligand to a prototypical hydrophobic pocket by explicit-water molecular dynamics (MD) simulations and implicit diffusional approaches. The concave pocket in the unbound state exhibits wet/dry hydration oscillations whose magnitude and time scale are significantly amplified by the approaching ligand. In turn, the ligand's stochastic motion intimately couples to the slow hydration fluctuations, leading to a sixfold-enhanced friction in the vicinity of the pocket entrance. The increased friction considerably decelerates association in the otherwise barrierless system, indicating the importance of molecular-scale hydrodynamic effects in cavity-ligand binding arising due to capillary fluctuations. We derive and analyze the diffusivity profile and show that the mean first passage time distribution from the MD simulation can be accurately reproduced by a standard Brownian dynamics simulation if the appropriate position-dependent friction profile is included. However, long-time decays in the water-ligand (random) force autocorrelation demonstrate violation of the Markovian assumption, challenging standard diffusive approaches for rate prediction. Remarkably, the static friction profile derived from the force correlations strongly resembles the profile derived on the Markovian assumption apart from a simple shift in space, which can be rationalized by a time-space retardation in the ligand's downhill dynamics toward the pocket. The observed spatiotemporal hydrodynamic coupling may be of biological importance providing the time needed for conformational receptor-ligand adjustments, typical of the induced-fit paradigm.

Level-Set Variational Implicit-Solvent Modeling of Biomolecules with the Coulomb-Field Approximation

Central in the variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett.2006, 96, 087802 and J. Chem. Phys.2006, 124, 084905] of molecular solvation is a mean-field free-energy functional of all possible solute–solvent interfaces or dielectric boundaries. Such a functional can be minimized numerically by a level-set method to determine stable equilibrium conformations and solvation free energies. Applications to nonpolar systems have shown that the level-set VISM is efficient and leads to qualitatively and often quantitatively correct results. In particular, it is capable of capturing capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states as found in molecular dynamics (MD) simulations. In this work, we introduce into the VISM the Coulomb-field approximation of the electrostatic free energy. Such an approximation is a volume integral over an arbitrary shaped solvent region, requiring no solutions to any partial differential equations. With this approximation, we obtain the effective boundary force and use it as the “normal velocity” in the level-set relaxation. We test the new approach by calculating solvation free energies and potentials of mean force for small and large molecules, including the two-domain protein BphC. Our results reveal the importance of coupling polar and nonpolar interactions in the underlying molecular systems. In particular, dehydration near the domain interface of BphC subunits is found to be highly sensitive to local electrostatic potentials as seen in previous MD simulations. This is a first step toward capturing the complex protein dehydration process by an implicit-solvent approach.