Prediction of multiple dry-wet transition pathways with a mesoscale variational approach.

Water fluctuates in a hydrophobic confinement, forming multiple dry and wet hydration states through evaporation and condensation. Transitions between such states are critical to both thermodynamics and kinetics of solute molecular processes, such as protein folding and protein-ligand binding and unbinding. To efficiently predict such dry-wet transition paths, we develop a hybrid approach that combines a variational implicit solvation model, a generalized string method for minimum free-energy paths, and the level-set numerical implementation.

Coupling Monte Carlo, Variational Implicit Solvation, and Binary Level-Set for Simulations of Biomolecular Binding.

We develop a hybrid approach that combines the Monte Carlo (MC) method, a variational implicit-solvent model (VISM), and a binary level-set method for the simulation of biomolecular binding in an aqueous solvent. The solvation free energy for the biomolecular complex is estimated by minimizing the VISM free-energy functional of all possible solute-solvent interfaces that are used as dielectric boundaries. This functional consists of the solute volumetric, solute-solvent interfacial, solute-solvent van der Waals interaction, and electrostatic free energy.

Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics.

Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multimethod approach to predict the (un)binding kinetics for a generic ligand-pocket model.

Tailoring the Variational Implicit Solvent Method for New Challenges: Biomolecular Recognition and Assembly.

Predicting solvation free energies and describing the complex water behavior that plays an important role in essentially all biological processes is a major challenge from the computational standpoint. While an atomistic, explicit description of the solvent can turn out to be too expensive in large biomolecular systems, most implicit solvent methods fail to capture "dewetting" effects and heterogeneous hydration by relying on a pre-established (i.e.

"Martinizing" the Variational Implicit Solvent Method (VISM): Solvation Free Energy for Coarse-Grained Proteins.

Solvation is a fundamental driving force in many biological processes including biomolecular recognition and self-assembly, not to mention protein folding, dynamics, and function. The variational implicit solvent method (VISM) is a theoretical tool currently developed and optimized to estimate solvation free energies for systems of very complex topology, such as biomolecules. VISM's theoretical framework makes it unique because it couples hydrophobic, van der Waals, and electrostatic interactions as a functional of the solvation interface.

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations.

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition.

Identification of protein-ligand binding sites by the level-set variational implicit-solvent approach.

Protein–ligand binding is a key biological process at the molecular level. The identification and characterization of small-molecule binding sites on therapeutically relevant proteins have tremendous implications for target evaluation and rational drug design. In this work, we used the recently developed level-set variational implicit-solvent model (VISM) with the Coulomb field approximation (CFA) to locate and characterize potential protein–small-molecule binding sites.

LS-VISM: A software package for analysis of biomolecular solvation.

We introduce a software package for the analysis of biomolecular solvation. The package collects computer codes that implement numerical methods for a variational implicit-solvent model (VISM). The input of the package includes the atomic data of biomolecules under consideration and the macroscopic parameters such as solute-solvent surface tension, bulk solvent density and ionic concentrations, and the dielectric coefficients.

Variational Implicit Solvation with Poisson-Boltzmann Theory.

We incorporate the Poisson-Boltzmann (PB) theory of electrostatics into our variational implicit-solvent model (VISM) for the solvation of charged molecules in an aqueous solvent. In order to numerically relax the VISM free-energy functional by our level-set method, we develop highly accurate methods for solving the dielectric PB equation and for computing the dielectric boundary force. We also apply our VISM-PB theory to analyze the solvent potentials of mean force and the effect of charges on the hydrophobic hydration for some selected molecular systems.

Heterogeneous Hydration of p53/MDM2 Complex.

Water-mediated interactions play critical roles in biomolecular recognition processes. Explicit solvent molecular dynamics (MD) simulations and the variational implicit-solvent model (VISM) are used to study those hydration properties during binding for the biologically important p53/MDM2 complex. Unlike simple model solutes, in such a realistic and heterogeneous solute-solvent system with both geometrical and chemical complexity, the local water distribution sensitively depends on nearby amino acid properties and the geometric shape of the protein.

Variational Implicit-Solvent Modeling of Host-Guest Binding: A Case Study on Cucurbit[7]uril|.

The synthetic host cucurbit[7]uril (CB[7]) binds aromatic guests or metal complexes with ultrahigh affinity compared with that typically displayed in protein-ligand binding. Due to its small size, CB[7] serves as an ideal receptor-ligand system for developing computational methods for molecular recognition. Here, we apply the recently developed variational implicit-solvent model (VISM), numerically evaluated by the level-set method, to study hydration effects in the high-affinity binding of the B2 bicyclo[2.

Motion of a Cylindrical Dielectric Boundary.

The interplay between geometry and electrostatics contributes significantly to hydrophobic interactions of biomolecules in an aqueous solution. With an implicit solvent, such a system can be described macroscopically by the dielectric boundary that separates the high-dielectric solvent from low-dielectric solutes. This work concerns the motion of a model cylindrical dielectric boundary as the steepest descent of a free-energy functional that consists of both the surface and electrostatic energies.

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.

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.

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.

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.

Coupling the Level-Set Method with Molecular Mechanics for Variational Implicit Solvation of Nonpolar Molecules.

We construct a variational explicit-solute implicit-solvent model for the solvation of molecules. Central in this model is an effective solvation free-energy functional that depends solely on the position of solute-solvent interface and solute atoms. The total free energy couples altogether the volume and interface energies of solutes, the solute-solvent van der Waals interactions, and the solute-solute mechanical interactions.

Interfaces and hydrophobic interactions in receptor-ligand systems: A level-set variational implicit solvent approach.

A model nanometer-sized hydrophobic receptor-ligand system in aqueous solution is studied by the recently developed level-set variational implicit solvent model (VISM). This approach is compared to all-atom computer simulations. The simulations reveal complex hydration effects within the (concave) receptor pocket, sensitive to the distance of the (convex) approaching ligand.

Application of the level-set method to the implicit solvation of nonpolar molecules.

A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model [Dzubiella, Swanson, and McCammon, Phys. Rev. Lett.