A Convex Approach to Steady State Moment Analysis for Stochastic Chemical Reactions
Provides a theoretically rigorous alternative to approximate methods for quantifying stochastic noise in biomolecular circuit design.
The paper proposes a convex optimization method to rigorously bound steady-state moments of stochastic chemical reactions, demonstrating precise prediction of mean and variance for a protein dimerization example.
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.