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

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 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 principal system processes on the extent to which the system can keep a stable steady state in the face of noise. To this end, we first obtain a reduced circuit model and determine an analytical expression for both the 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 auto and cross-catalysis and 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 extends the memory of the active and repressed states, suggesting, more broadly, a critical design principle for long-lasting memory of gene expression states.