Adaptation Mechanisms in Phosphorylation Cycles By Allosteric Binding and Gene Autoregulation

Abstract

In this article, we study adaptation mechanisms in a class of phosphorylation cycles where allosteric binding and gene autoregulation mechanisms regulate the phosphorylation processes. We show that both mechanisms enable a robust setpoint regulation of the regulator metabolite in the presence of constant, as well as periodic, external stimuli. The allosteric binding mechanism without the presence of gene autoregulation can serve as an integral controller. Furthermore, we show that the incorporation of a gene autoregulation mechanism enables the gene expression system to act as a genetic oscillator, which allows for the adaptation mechanism to periodic external stimuli. These results provide a theoretical explanation to the cell homeostasis under quasi-constant environmental conditions, as well as periodic, biological rhythms.

Stochastic filtering for multiscale stochastic reaction networks based on hybrid approximations

“…Such an autoregulation mechanism (where the gene product auto-regulates its own gene expression) is very common in living cells, which occurs over 40% of known E. coli's transcription factors [49]. Moreover, it has various biological functions, including speeding up the response time of gene expression [50], inducing genetic oscillators [51], and achieving adaptation to periodic external stimuli [52]. The model considered in this subsection involves five species: the protein monomer (denoted by S 1 ), the dimer (also the transcription factor, denoted by S 2 ), the mRNA (S 3 ), the unbound DNA (S 4 ), and the bound DNA (also the activated state, denoted by S 5 ); moreover, it has eight reactions:…”