##### Department of Mathematics,

University of California San Diego

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### Math 218: Seminar on Mathematics for Complex Biological Systems

## Bo Li

#### Department of Mathematics and qBio Ph.D. program, UCSD

## Variational Implicit Solvation and Fast Algorithms for Molecular Binding and Unbinding

##### Abstract:

Ligand-receptor binding and unbinding are fundamental molecular processes, whereas water fluctuations impact strongly their thermodynamics and kinetics. We develop a variational implicit-solvent model (VISM) and a fast binary level-set method to calculate the potential of mean force and the molecule-water interfacial structures for dry and wet states. Monte Carlo simulations with our model and method provide initial configurations for efficient molecular dynamics simulations. Moreover, combined with the string method and stochastic simulations of ligand molecules, our hybrid approach enables the prediction of the transition paths and rates for the dry-wet transitions and the mean first-passage times for the ligand-pocket binding and unbinding. Without any explicit description of individual water molecules, our predictions are in a very good, qualitative and semi-quantitative, agreement with existing explicit-water molecular dynamics simulations.

This talk reviews a series of works done in collaboration with L.-T. Cheng, S. Zhou, Z. Zhang, S. Liu, H.-B. Cheng, J. Dzubiella, C. Ricci, and J. A. McCammon.

### January 25, 2024

### 2:00 PM

APM 5829

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