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

Abstract

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. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the "normal velocity" that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit [7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach. Published by AIP Publishing. [http://dx

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“…Theoretical as well as experimental studies investigated first models for such capillary surface waves at planar surfaces [196][197][198]; however, the dynamic response of capillary waves at arbitrary solute interface properties also remains a challenge to future work. In principle, a dynamic model of water on such a continuum level of solvation could help for extended simulation studies by more accurate implicit solvent models [199][200][201].…”

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

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Stochastic level-set method for shape optimisation

“…Having described the deterministic optimisation algorithm of [8,21], the next step is to introduce a stochastic component to this algorithm. Several other stochastic level-set methods have been considered recently [12,13,27], but differ from the approach proposed here in that the noise in this scheme is applied directly only on the boundary Γ, which ensures that the function φ retains its property as a signed-distance function under the stochastic time-evolution.…”