ncts

Cellular chemical reactions exhibit stochastic fluctuations due to the low-copy-number nature of molecules within a single cell. These fluctuations are effectively modeled as a jump process, with the dynamics of the copy number distribution governed by the chemical master equation (CME). Currently, many methods rely on ad-hoc approximations of the CME to analyze the stochastic kinetics of such chemical reactions.In this talk, I will present an optimization-based approach for computing theoretically guaranteed bounds on the moments of copy number distributions. Specifically, I will show that the stochastic moments lie within a convex set defined by linear matrix inequalities and affine equations. This formulation enables the use of semidefinite programming, a type of conic optimization, to systematically explore the upper and lower bounds of these moments, offering rigorous quantification of stochastic kinetics without approximating the governing equation. The effectiveness of the proposed technique will be demonstrated through various examples of stochastic biomolecular reactions.