InSilico ProportionalIntegral Moment Control of Stochastic Gene Expression
Abstract
The problem of controlling the mean and the variance of a species of interest in a simple gene expression is addressed. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a simple PI controller that satisfies certain sufficient conditions. Controlling both the mean and variance however requires an additional control input, e.g. the mRNA degradation rate, and local robust tracking of mean and variance is proved to be achievable using multivariable PI control, provided that the reference point satisfies necessary conditions imposed by the system. Even more importantly, it is shown that there exist PI controllers that locally, robustly and simultaneously stabilize all the equilibrium points inside the admissible region. The results are then extended to the mean control of a gene expression with protein dimerization. It is shown that the moment closure problem can be circumvented without invoking any moment closure technique. Local stabilization and convergence of the average dimer population to any desired reference value is ensured using a pure integral control law. Explicit bounds on the controller gain are provided and shown to be valid for any reference value. As a byproduct, an explicit upperbound of the variance of the monomer species, acting on the system as unknown input due to the moment openness, is obtained. The results are illustrated by simulation.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.12293
 arXiv:
 arXiv:1810.12293
 Bibcode:
 2018arXiv181012293B
 Keywords:

 Mathematics  Optimization and Control;
 Electrical Engineering and Systems Science  Systems and Control;
 Quantitative Biology  Molecular Networks
 EPrint:
 28 pages