A control theoretical approach to gene regulation raises quantitative constraints for dynamic homeostasis in stochastic gene expression

Cell phenotype dynamic homeostasis contrasts with the inherent randomness of intracellular reactions. Although feedback control of master regulatory genes (MRG) is a key strategy for maintaining gene network expression ranges limited, understanding the quantitative constraints and corresponding mechanisms enabling such a dynamic stability under noise remains elusive. Here we model MRG expression as a stochastic process and downstream genes as sensors which response conditionally induce MRG activity. We show that at homeostatic regime: i. the trajectories of the MRG expression levels can be adjusted towards specific ranges using both the exact solutions of the stochastic model and the exact stochastic simulation algorithm (SSA); ii. there exists a sampling rate which optimizes the feedback control of the MRG activity, and non-optimal controls resulting in alternative homeostatic dynamics; iii. the feedback control of MRG activity leads to updates which intensities and time intervals are non-linearly related; iv. the ON state probability of an MRG promoter has dynamics confined within a narrow domain. Our results help to understand the quantitative constraints underpinning dynamic homeostasis despite randomness, the mechanisms underlying alternative, non-optimal, homeostatic regimes, and may be useful for theoretically prototyping therapies aiming at gene networks modulation.