##### Department of Mathematics,

University of California San Diego

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### Math 218 - Seminars on Mathematics for Complex Biological Systems

## Mauricio del Razo Sarmina

#### Univ. of Amsterdam, Netherlands

## Multiscale Molecular Kinetics by Coupling Markov State Models and Reaction Diffusion Dynamics

##### Abstract:

A novel approach to simulate simple protein-Âligand systems at large timeÂ and lengthÂ-scales is to couple Markov state models (MSMs) of molecular kinetics with particle-Âbased reactionÂ-diffusion (PBRD) simulations; this approach is named MSM/RD. Current formulations of MSM/RD lack an underlying mathematical framework to derive coupling schemes; they are limited to protein-Âligand systems, where the ligand orientation and conformation switching are not taken into account; and they lack multiÂparticle extensions. In this work, we develop a general MSM/RD framework by coarseÂ-graining molecular dynamics into hybrid switching diffusion processes, a class of stochastic processes that integrate continuous dynamics and discrete events into the same process. With this MSM/RD framework, it is possiÂble to derive MSM/RD coupling schemes as discretizations of the underlying equations. It also allows conformation switching and the inclusion of all the rotational degrees of freedom. Given enough data to parametrize the model, it is capable of modeling proteinÂ-protein interactions over large timeÂ and lengthÂ-scales, and it can be extended to hanÂdle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two proteinÂ-protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules.

Organizers: Li-Tien Cheng, Bo Li, and Ruth Williams

### September 30, 2021

### 2:00 PM

(Contact Bo Li at bli@math.ucsd.edu for the Zoom info)

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