Interval analysis of worst-case stationary moments for stochastic chemical reactions with uncertain parameters

The dynamics of cellular chemical reactions are variable due to stochastic noise from intrinsic and extrinsic sources. is the intracellular fluctuations molecular copy numbers caused by probabilistic encounter molecules modeled master equation. noise, on other hand, represents intercellular variation kinetic parameters global factors affecting gene expression. objective this paper propose a theoretical framework analyze combined effect equation with uncertain parameters. More specifically, we formulate semidefinite program compute intervals stationary solution moment equations whose given only partially in form statistics their distributions. derived without approximating governing contrast many existing approaches. Thus, can obtain guaranteed worst possible values moments for all parameter distributions satisfying statistics, which prohibitively hard estimate sample-path simulations since sampling difficult. We demonstrate proposed optimization approach using two examples show that problem gives informative upper lower bounds number