Stochastic modeling of epigenetic memory

Here, we review mathematical models of epigenetic memory, focusing on chromatin modifications as key mechanisms to achieve long-term maintenance of epigenetic states. After reviewing the main stochastic modeling frameworks, we focus on stochastic models of chromatin modifications to analyze residence time in memory states, which underpins the long-term maintenance of epigenetic information. We review these concepts through increasingly complicated chromatin modification circuits, including histone modifications, DNA methylation, and their combination.