Dewetting-controlled binding of ligands to hydrophobic pockets

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.

Yukawa-Field Approximation of Electrostatic Free Energy and Dielectric Boundary Force

A Yukawa-field approximation of the electrostatic free energy of a molecular solvation system with an implicit or continuum solvent is constructed. It is argued through the analysis of model molecular systems with spherically symmetric geometries that such an approximation is rational. The construction extends non-trivially that of the Coulomb-field approximation which serves as a basis of the widely used generalized Born model of molecular electrostatics. The electrostatic free energy determines the dielectric boundary force that in turn influences crucially the molecular conformation, stability, and dynamics. An explicit formula of such forces with the Yukawa-field approximation is obtained using local coordinates and shape differentiation.

Physical Modeling of Aqueous Solvation

We consider the free energies of solvating molecules in water. Computational modeling usually involves either detailed explicit-solvent simulations, or faster computations, which are based on implicit continuum approximations or additivity assumptions. These simpler approaches often miss microscopic physical details and non-additivities present in experimental data. We review explicit-solvent modeling that identifies the physical bases for the errors in the simpler approaches. One problem is that water molecules that are shared between two substituent groups often behave differently than waters around each substituent individually. One manifestation of non-additivities is that solvation free energies in water can depend not only on surface area or volume, but on other properties, such as the surface curvature. We also describe a new computational approach, called Semi-Explicit Assembly, that aims to repair these flaws and capture more of the physics of explicit water models, but with computational efficiencies approaching those of implicit-solvent models.

Pathway and mechanism of drug binding to G-protein-coupled receptors

How drugs bind to their receptors--from initial association, through drug entry into the binding pocket, to adoption of the final bound conformation, or "pose"--has remained unknown, even for G-protein-coupled receptor modulators, which constitute one-third of all marketed drugs. We captured this pharmaceutically critical process in atomic detail using the first unbiased molecular dynamics simulations in which drug molecules spontaneously associate with G-protein-coupled receptors to achieve final poses matching those determined crystallographically. We found that several beta blockers and a beta agonist all traverse the same well-defined, dominant pathway as they bind to the β(1)- and β(2)-adrenergic receptors, initially making contact with a vestibule on each receptor's extracellular surface. Surprisingly, association with this vestibule, at a distance of 15 Å from the binding pocket, often presents the largest energetic barrier to binding, despite the fact that subsequent entry into the binding pocket requires the receptor to deform and the drug to squeeze through a narrow passage. The early barrier appears to reflect the substantial dehydration that takes place as the drug associates with the vestibule. Our atomic-level description of the binding process suggests opportunities for allosteric modulation and provides a structural foundation for future optimization of drug-receptor binding and unbinding rates.

Hybrid MC-DFT method for studying multidimensional entropic forces

Entropic force has been a focus of many recent theoretical studies because of its fundamental importance in solution thermodynamics and its close relevance to a broad range of practical applications. Whereas previous investigations are mostly concerned with the potential energy as a one-dimensional function of the separation, here we propose a hybrid method for studying multidimensional systems by combining Monte Carlo simulation for the microscopic configurations of the solvent and the density functional theory for the free energy. We demonstrate that the hybrid method predicts the potential of mean force between a test particle and various concave objects in a hard-sphere solvent in excellent agreement with the results from alternative but more expensive computational methods. In particular, the hybrid method captures the entropic force between asymmetric particles and its dependence on the particle size and shape that underlies the "lock and key" interactions. Because the same molecular model is used for the theory and simulation, we expect that the hybrid method provides a new avenue to efficient computation of entropic forces in complex molecular systems.

Dielectric Boundary Force in Molecular Solvation with the Poisson-Boltzmann Free Energy: A Shape Derivative Approach

In an implicit-solvent description of molecular solvation, the electrostatic free energy is given through the electrostatic potential. This potential solves a boundary-value problem of the Poisson-Boltzmann equation in which the dielectric coefficient changes across the solute-solvent interface-the dielectric boundary. The dielectric boundary force acting on such a boundary is the negative first variation of the electrostatic free energy with respect to the location change of the boundary. In this work, the concept of shape derivative is used to define such variations and formulas of the dielectric boundary force are derived. It is shown that such a force is always in the direction toward the charged solute molecules.

Level-Set Minimization of Potential Controlled Hadwiger Valuations for Molecular Solvation

A level-set method is developed for the numerical minimization of a class of Had-wiger valuations with a potential on a set of three-dimensional bodies. Such valuations are linear combinations of the volume, surface area, and surface integral of mean curvature. The potential increases rapidly as the body shrinks beyond a critical size. The combination of the Hadwiger valuation and the potential is the mean-field free-energy functional of the solvation of non-polar molecules in the recently developed variational implicit-solvent model. This functional of surfaces is minimized by the level-set evolution in the steepest decent of the free energy. The normal velocity of this surface evolution consists of both the mean and Gaussian curvatures, and a lower-order, "forcing" term arising from the potential. The forward Euler method is used to discretize the time derivative with a dynamic time stepping that satisfies a CFL condition. The normal velocity is decomposed into two parts. The first part consists of both the mean and Gaussian curvature terms. It is of parabolic type with parameter correction, and is discretized by central differencing. The second part has all the lower-order terms. It is of hyperbolic type, and is discretized by an upwinding scheme. New techniques of local level-set method and numerical integration are developed. Numerical tests demonstrate a second-order convergence of the method. Examples of application to the modeling of molecular solvation are presented.

Hydration in discrete water. A mean field, cellular automata based approach to calculating hydration free energies

A simple, semiheuristic solvation model based on a discrete, BCC grid of solvent cells has been presented. The model utilizes a mean field approach for the calculation of solute-solvent and solvent-solvent interaction energies and a cellular automata based algorithm for the prediction of solvent distribution in the presence of solute. The construction of the effective Hamiltonian for a solvent cell provides an explicit coupling between orientation-dependent water-solute electrostatic interactions and water-water hydrogen bonding. The water-solute dispersion interaction is also explicitly taken into account. The model does not depend on any arbitrary definition of the solute-solvent interface nor does it use a microscopic surface tension for the calculation of nonpolar contributions to the hydration free energies. It is demonstrated that the model provides satisfactory predictions of hydration free energies for drug-like molecules and is able to reproduce the distribution of buried water molecules within protein structures. The model is computationally efficient and is applicable to arbitrary molecules described by atomistic force field.

How Can Hydrophobic Association Be Enthalpy Driven?

Hydrophobic association is often recognized as being driven by favorable entropic contributions. Here, using explicit solvent molecular dynamics simulations we investigate binding in a model hydrophobic receptor-ligand system which appears, instead, to be driven by enthalpy and opposed by entropy. We use the temperature dependence of the potential of mean force to analyze the thermodynamic contributions along the association coordinate. Relating such contributions to the ongoing changes in system hydration allows us to demonstrate that the overall binding thermodynamics is determined by the expulsion of disorganized water from the receptor cavity. Our model study sheds light on the solvent-induced driving forces for receptor-ligand association of general, transferable relevance for biological systems with poorly hydrated binding sites.

Water in cavity-ligand recognition

We use explicit solvent molecular dynamics simulations to estimate free energy, enthalpy, and entropy changes along the cavity-ligand association coordinate for a set of seven model systems with varying physicochemical properties. Owing to the simplicity of the considered systems we can directly investigate the role of water thermodynamics in molecular recognition. A broad range of thermodynamic signatures is found in which water (rather than cavity or ligand) enthalpic or entropic contributions appear to drive cavity-ligand binding or rejection. The unprecedented, nanoscale picture of hydration thermodynamics can help the interpretation and design of protein-ligand binding experiments. Our study opens appealing perspectives to tackle the challenge of solvent entropy estimation in complex systems and for improving molecular simulation models.

Role of electrostatics in modulating hydrophobic interactions and barriers to hydrophobic assembly

Hydrophobic effects continue to be an active area of research due to implications for a wide range of physicochemical phenomena. Molecular dynamics simulations have been used extensively in the study of such effects using various water potential models, with few studies addressing the differences between models. In particular, studies considering the explicit treatment of water polarizability are underrepresented in the literature. We present results from molecular dynamics simulations that systematically compare the dependence of large-scale hydrophobic effects on the water model. We consider three common nonpolarizable models (SPC/E, TIP3P, and TIP4P) and two common polarizable models (TIP4P-FQ and SWM4-NDP). Results highlight the similarities and differences of the different water models in the vicinity of two large hydrophobic plates. In particular, profiles of average density, density fluctuations, orientation, and hydrogen bonding show only minor differences among the water models studied. However, the potential of mean force for the hydrophobe dimerization is significantly reduced in the polarizable water systems. TIP4P-FQ shows the deepest minimum of approximately -54(+/-3) kcal/mol compared to -40(+/-3), -40(+/-2), -42(+/-3), and -45(+/-5) kcal/mol for TIP4P, TIP3P, SPC/E, and SWM4-NDP (all relative to the dissociated state). We discuss the relationship between hydrophobic association and the strength of water-water interactions in the liquid phase. Results suggest that models treating polarizability (both implicitly and explicitly) influence a stronger driving force toward hydrophobic assembly. Implications of these results, as well as prospectives on future work, are discussed.