Analytical and computational study of the stochastic behavior of a chromatin modification circuit

Abstract

— The property of multicellular organisms that allows cells with the same genetic code to maintain distinct identities for the entire life of the organism is known as epigenetic cell memory (ECM). Recently, chromatin modifications and their effect on the DNA structure, that is, the chromatin state, have appeared to have a key role in ECM. Here, we conduct a stochastic analysis of a chromatin modification circuit to determine the effect of time scale separation among key constituent processes on the extent to which the system can keep a stable steady state in the face of noise. Specifically, from the full set of reactions describing the system, we first obtain a reduced circuit model and determine an analytical expression for both the system stationary probability distribution and the switching time between repressed and active chromatin states. Then, we validate these analytical results with stochastic simulations of the original full set of reactions. Our results show that when the basal decay of all chromatin marks is sufficiently slower with respect to the speed of auto and cross-catalysis and of the recruited erasure of all the marks, the stationary distribution shows bimodality, with two concentrated peaks in correspondence of the active and repressed states, but biased towards the repressed state. In accordance with these results, slower basal decay increases the extent of memory of the active and repressed states, suggesting, more broadly, a critical design principle for long-term memory of gene expression states.