Characterizations of sharp solute-solvent interfaces in hydrophobic environments via cylindrical coordinates

TL;DR

This paper develops a novel approach to characterize sharp solute-solvent interfaces in hydrophobic environments by transforming the problem into an ODE boundary value problem, improving computational tractability and understanding of interface behavior.

Contribution

It introduces an innovative method to compute saddle solute-solvent interfaces as an ODE boundary value problem, enhancing numerical efficiency and analysis.

Findings

Effective numerical method for saddle interface computation

Analysis of interface variation with molecular distance

Reduction of PDE to ODE in cylindrical coordinates

Abstract

This paper characterizes sharp solute-solvent interfaces in hydrophobic environments, and there are three major ingredients. The first is the variational implicit solvent model (VISM) which establishes the free energy functional of arbitrary solvation states. The minimization of this functional yields a PDE which characterizes both the stable and saddle solute-solvent interfaces. The second is a solute system consisting of two Gay-Berne ellipsoidal hydrophobic molecules. The cylindrical coordinates reduce the corresponding PDE to an ODE which is more traceable, increasing the computability of the solute-solvent interfaces under solvation effects. The third, which is the innovative part of this paper, transforms the computation of sharp solute-solvent interfaces into an ODE boundary value problem. We introduce an effective method for numerically computing saddle interfaces. This remains a hard problem in previous research. Besides, we address some qualitative results and study how the interface varies with respect to the distance between the two Gay-Berne ellipsoidal hydrophobic molecules.