##### Department of Mathematics,

University of California San Diego

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### Informal Seminar on Mathematics and Biochemistry-Biophysics

## Shenggao Zhou

#### Department of Mathematics and CTBP, UCSD

## Varitional Implicit Solvation with Poisson-Boltzmann Theory

##### Abstract:

We incorporate the Poisson--Boltzmann (PB) theory of electrostatics into the variational implicit-solvent model (VISM) for the solvation of charged molecules in an aqueous solvent. The principle of VISM is to determine equilibrium solute-solvent interfaces and estimate the molecular solvation free energies by minimizing a mean-field free-energy functional of all possible solute-solvent interfaces. The functional consists mainly of solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic energy. We develop highly accurate numerical methods for solving the dielectric PB equation and for computing the dielectric boundary force. These methods are integrated into a robust level-set method for numerically minimizing the VISM functional. We test and apply our level-set VISM with PB theory to the solvation of some single ions, two charged particles, and two charged plates, and to the solvation of the host-guest system Cucurbit[7]uril and Bicyclo[2.2.2]octane. Our computational results show that VISM with PB theory can capture well the sensitive response of capillary evaporation to the charge in hydrophobic confinement and the polymodal hydration behavior, and can provide accurate estimates of binding affinity of the host-guest system. We also discuss several issues for further improvement of VISM. This is a joint work with Li-Tien Cheng, Joachim Dzubiella, Bo Li, and J. Andrew McCammon.

Organizers: Li-Tien Cheng and Bo Li

### January 9, 2014

### 1:00 PM

### AP&M 5829

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