Epigenetic cell memory, the inheritance of gene expression patterns across subsequent cell divisions, is a critical property of multi-cellular organisms. It was observed in a simulation study by our collaborators that the stochastic dynamics and time-scale differences between establishment and erasure processes in chromatin modifications (such as histone modifications and DNA methylation) can have a critical effect on epigenetic cell memory. In this work, we provide a mathematical framework to rigorously validate and extend beyond these computational findings. Viewing our stochastic model of a chromatin modification circuit as a singularly perturbed, finite state, continuous time Markov chain, we extend beyond existing theory in order to characterize the leading terms in the series expansions of stationary distributions and mean first passage times. In particular, we provide an algorithm to determine the orders of the poles of mean first passage times, character
 ize the
 limiting stationary distribution and the limiting mean first passage times in terms of a reduced Markov chain. We also determine how changing erasure rates affects system behavior. The theoretical tools developed in this paper not only allow us to set a rigorous mathematical basis for the computational findings of our prior work, highlighting the effect of chromatin modification dynamics on epigenetic cell memory, but they can also be applied to other singularly perturbed Markov chains beyond the applications in this paper, especially those associated with biochemical reaction networks.

This talk is based on joint work with Simone Bruno, Felipe A. Campos, Domitilla Del Vecchio, and Ruth J. Williams.