Binary Level Set Method for Variational Implicit Solvation Model

TL;DR

This paper introduces a binary level set method to efficiently minimize the variational implicit solvation model's free energy, enabling faster computation of biomolecular interface conformations with complex topology.

Contribution

The paper presents a novel binary level set approach that significantly accelerates the minimization process in the variational implicit solvation model compared to traditional methods.

Findings

The binary level set method achieves comparable accuracy to existing methods.

It reduces computational time for interface minimization.

Numerical experiments validate the method's effectiveness.

Abstract

In this article, we apply the binary level set method to the Variational Implicit Solvent Model (VISM), which is a theoretical and computational tool to study biomolecular systems with complex topology. Central in VISM is an effective free energy of all possible interfaces separating solutes (e.g., proteins) from solvent (e.g., water). Previously, such a functional is minimized numerically by the level set method to determine the stable equilibrium conformations and solvation free energies. We vastly improve the speed by applying the binary level set method, in which the interface is approximated by a binary level set function that only takes value $\pm 1$ on the solute/solvent region, leading to a discrete formulation of VISM energy. The surface area is approximated by convolution of an indicator function with a compactly supported kernel. The VISM energy can be minimized by iteratively "flipping" the binary level set function in a steepest descent fashion. Numerical experiments are performed to demonstrate the accuracy and performance of our method.