TY - JOUR

T1 - Interval analysis of worst-case stationary moments for stochastic chemical reactions with uncertain parameters

AU - Sakurai, Yuta

AU - Hori, Yutaka

N1 - Funding Information:
This work was supported in part by JSPS KAKENHI Grant Numbers JP16H07175 , JP18H01464 , and JP21H01355 . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Marcello Farina under the direction of Editor Ian R. Petersen.
Publisher Copyright:
© 2022 Elsevier Ltd

PY - 2022/12

Y1 - 2022/12

N2 - The dynamics of cellular chemical reactions are variable due to stochastic noise from intrinsic and extrinsic sources. The intrinsic noise is the intracellular fluctuations of molecular copy numbers caused by the probabilistic encounter of molecules and is modeled by the chemical master equation. The extrinsic noise, on the other hand, represents the intercellular variation of the kinetic parameters due to the variation of global factors affecting gene expression. The objective of this paper is to propose a theoretical framework to analyze the combined effect of the intrinsic and the extrinsic noise modeled by the chemical master equation with uncertain parameters. More specifically, we formulate a semidefinite program to compute the intervals of the stationary solution of uncertain moment equations whose parameters are given only partially in the form of the statistics of their distributions. The semidefinite program is derived without approximating the governing equation in contrast with many existing approaches. Thus, we can obtain guaranteed intervals of the worst possible values of the moments for all parameter distributions satisfying the given statistics, which are prohibitively hard to estimate from sample-path simulations since sampling from all possible uncertain distributions is difficult. We demonstrate the proposed optimization approach using two examples of stochastic chemical reactions and show that the solution of the optimization problem gives informative upper and lower bounds of the statistics of the stationary copy number distributions.

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

KW - Biomolecular systems

KW - Markov process

KW - Mathematical optimization

KW - Uncertain dynamical systems

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U2 - 10.1016/j.automatica.2022.110647

DO - 10.1016/j.automatica.2022.110647

M3 - Article

AN - SCOPUS:85139827325

SN - 0005-1098

VL - 146

JO - Automatica

JF - Automatica

M1 - 110647

ER -