Yuta Sakurai

Yuta Sakurai, Yutaka Hori

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.

Yuta Sakurai, Yutaka Hori

The predictive ability of stochastic chemical reactions is currently limited by the lack of closed form solutions to the governing chemical master equation. To overcome this limitation, this paper proposes a computational method capable of predicting mathematically rigorous upper and lower bounds of transient moments for reactions governed by the law of mass action. We first derive an equation that transient moments must satisfy based on the moment equation. Although this equation is underdetermined, we introduce a set of semidefinite constraints known as moment condition to narrow the feasible set of the variables in the equation. Using these conditions, we formulate a semidefinite program that efficiently and rigorously computes the bounds of transient moment dynamics. The proposed method is demonstrated with illustrative numerical examples and is compared with related works to discuss advantages and limitations.