# A Convex Approach to Steady State Moment Analysis for Stochastic Chemical Reactions

## TL;DR

This paper introduces a convex optimization method to accurately compute steady state moments of molecular counts in stochastic chemical reactions, aiding in biomolecular circuit design.

## Contribution

It presents a novel convex semi-algebraic set framework for bounding moments, enabling precise predictions with semidefinite programming.

## Key findings

- Accurately predicts mean and variance of protein copy numbers.
- Provides a rigorous convex optimization approach for stochastic moment analysis.
- Demonstrates effectiveness on a protein dimerization example.

## Abstract

Model-based prediction of stochastic noise in biomolecular reactions often resorts to approximation with unknown precision. As a result, unexpected stochastic fluctuation causes a headache for the designers of biomolecular circuits. This paper proposes a convex optimization approach to quantifying the steady state moments of molecular copy counts with theoretical rigor. We show that the stochastic moments lie in a convex semi-algebraic set specified by linear matrix inequalities. Thus, the upper and the lower bounds of some moments can be computed by a semidefinite program. Using a protein dimerization process as an example, we demonstrate that the proposed method can precisely predict the mean and the variance of the copy number of the monomer protein.