Department of Mathematics, University of California Irvine, Irvine, CA 92614, USA.
J R Soc Interface. 2020 May;17(166):20200031. doi: 10.1098/rsif.2020.0031. Epub 2020 May 13.
In this work, we design a type of controller that consists of adding a specific set of reactions to an existing mass-action chemical reaction network in order to control a target species. This set of reactions is effective for both deterministic and stochastic networks, in the latter case controlling the mean as well as the variance of the target species. We employ a type of network property called absolute concentration robustness (ACR). We provide applications to the control of a multisite phosphorylation model as well as a receptor-ligand signalling system. For this framework, we use the so-called deficiency zero theorem from chemical reaction network theory as well as multiscaling model reduction methods. We show that the target species has approximately Poisson distribution with the desired mean. We further show that ACR controllers can bring robust perfect adaptation to a target species and are complementary to a recently introduced antithetic feedback controller used for stochastic chemical reactions.
在这项工作中，我们设计了一种控制器，它由在现有的质量作用化学反应网络中添加一组特定的反应组成，以控制目标物种。该组反应对于确定性和随机网络都是有效的，在后一种情况下，它可以控制目标物种的均值和方差。我们利用一种称为绝对浓度鲁棒性（ACR）的网络特性。我们将该方法应用于控制多部位磷酸化模型和受体配体信号系统。对于这个框架，我们使用化学反应网络理论中的所谓零缺陷定理以及多尺度模型降阶方法。我们表明，目标物种具有所需均值的近似泊松分布。我们进一步表明，ACR 控制器可以为目标物种带来稳健的完美适应，并且与最近引入的用于随机化学反应的对偶反馈控制器互补。
