Absolute concentration robustness controllers for stochastic chemical reaction network systems

German Enciso (May 7, 2020)

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Abstract

In this work, we provide a systematic control of a given biochemical reaction network through a control module reacting with the existing network system. This control module is designed to confer so-called absolute concentration robustness (ACR) to a target species in the controlled network system. We show that when the deterministic network system is controlled with the ACR controller, the concentration of a species of interest has a steady state at the desired value for any initial amounts, and it converges to the value under some mild conditions. For the stochastic counterparts of reaction network systems, we further show that when the abundance of the control species is high enough, the ACR controller can be utilized to make a target species approximately follow a Poisson distribution centered at the desired value. For this framework, we use the deficiency zero theorem (Anderson et al, 2010) in chemical reaction network theory and multiscaling model reduction methods. This control module also brings robust perfect adaptation, which is a highly desirable goal of the control theory, to the target species against transient perturbations and uncertainties in the model parameters.