title: DIFFUSED SOLUTE-SOLVENT INTERFACE WITH POISSON-BOLTZMANN ELECTROSTATICS: FREE-ENERGY VARIATION AND SHARP-INTERFACE LIMIT.
abstract: A phase-field free-energy functional for the solvation of charged molecules (e.g., proteins) in aqueous solvent (i.e., water or salted water) is constructed. The functional consists of the solute volumetric and solute-solvent interfacial energies, the solute-solvent van der Waals interaction energy, and the continuum electrostatic free energy described by the Poisson-Boltzmann theory. All these are expressed in terms of phase fields that, for low free-energy conformations, are close to one value in the solute phase and another in the solvent phase. A key property of the model is that the phase-field interpolation of dielectric coefficient has the vanishing derivative at both solute and solvent phases. The first variation of such an effective free-energy functional is derived. Matched asymptotic analysis is carried out for the resulting relaxation dynamics of the diffused solute-solvent interface. It is shown that the sharp-interface limit is exactly the variational implicit-solvent model that has successfully captured capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states of underlying biomolecular systems as found in experiment and molecular dynamics simulations. Our phase-field approach and analysis can be used to possibly couple the description of interfacial fluctuations for efficient numerical computations of biomolecular interactions.
authors.affiliation: Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA.
authors.forename: B O
authors.initials: BO
authors.lastname: Li
authors.affiliation: Department of Mathematics, Fudan University, 220 Handan Road, Yangpu District, Shanghai, 200433, P. R. China, and Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Liu
keywords: Poisson–Boltzmann theory; diffused solute-solvent interface; matched asymptotic analysis; sharp-interface limit; variational implicit-solvent model