Theory of epigenetic switching due to stochastic histone mark loss during DNA replication.

How much information does a cell inherit from its ancestors beyond its genetic sequence? What are the epigenetic mechanisms that allow this? Despite the rise in available epigenetic data, how such information is inherited through the cell cycle is still not fully understood. Often, epigenetic marks can display bistable behaviour and their bistable state is transmitted to daughter cells through the cell cycle, providing the cell with a form of memory. However, loss-of-memory events also take place, where a daughter cell switches epigenetic state (with respect to the mother cell). Here, we develop a framework to compute these epigenetic switching rates, for the case when they are driven by DNA replication, i.e. the frequency of loss-of-memory events due to replication. We consider the dynamics of histone modifications during the cell cycle deterministically, except at DNA replication, where nucleosomes are randomly distributed between the two daughter DNA strands, which is therefore implemented stochastically. This hybrid stochastic-deterministic approach enables an analytic derivation of the replication-driven switching rate. While retaining great simplicity, this framework can explain experimental switching rate data, establishing its biological importance as a framework to quantitatively study epigenetic inheritance.