##### Department of Mathematics,

University of California San Diego

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### Stochastic Systems seminar, Math 288D

## Ruth Williams

#### UCSD

## Comparison Theorems for Stochastic Chemical Reaction Networks

##### Abstract:

Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this talk we describe theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. We illustrate our results with applications to models of chromatin regulation and enzymatic kinetics.

This talk is based on joint work with Simone Bruno, Felipe Campos, Domitilla Del Vecchio and Yi Fu.

### February 2, 2023

### 1:00 PM

Via Zoom (email Professor Williams for zoom information)

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