##### Department of Mathematics,

University of California San Diego

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### Informal Seminar on Mathematics and Biochemistry-Biophysics

## Zhongming Wang

#### UCSD \\ Biochemistry and Mathematics

## A Level-Set Variational Implicit-Solvent Approach to Hydrophobic Interactions

##### Abstract:

Hydrophobic interactions drive relatively apolar molecules to stick together in an aqueous solution. Such interactions are crucial to the structure, dynamics, and function of biological systems. The implicit (or continuum) solvent approach is an efficient way to model such interactions. In this talk, I will first describe a class of variational implicit-solvent models for solvation. Central in these models isÂ a free-energy functional of all possibleÂ solute-solvent interfaces, coupling both non-polar and polar contributions.Â Minimization of this free-energy functional determines equilibrium solute-solvent interfaces which conceptually replace solvent accessible surfaces (SAS) or solvent excluded surfaces (SES). I will then describe a level-set method for capturing equilibrium solute-solvent interfaces. In our level-set method, a possible solute-solvent interface is represented by the zero level set (i.e., the zero level surface) of a function and is evolved to reduce the free energy of the system, eventually intoÃƒï¿½Ã‚Â an equilibrium solute-solvent interface. ThisÃƒï¿½Ã‚Â method is applied to the study of a large concave wall in water, together with a small solute molecule. Our level-set calculations determine the solute-solvent interface locations and free energies very accurately compared with molecular dynamics simulations that have been previously reported. We also capture the bimodal behavior of the potential of mean force of the underlying hydrophobic interactions. In addition, we find the curvature correction to the surface tension has a significant influence on the solute-solvent interface profile in the concave region. All these demonstrate that our mean-field approach and numerical techniques are capable of efficiently and accurately describing hydrophobic interactions with significant geometric influences. This is joint work with Li-Tien Cheng, Piotr Setny, Joachim Dzubiella, Bo Li, and J. Andrew McCammon.

Organizer: Li-Tien Cheng and Bo Li

### January 27, 2009

### 1:00 PM

### AP&M 5829

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