Dynamics of DNA methylation and persistence of epigenetic memory

DNA methylation is a process by which cells can regulate gene expression. Recent experiments have used synthetic read-write molecules that bind to methylated sites and then methylate nearby unmethylated ones to create a positive feedback [1]. Additionally, methylated sites turn over to unmethylated sites at a constant rate. The feedback allows the methylation to persist, despite the turnover, giving rise to ‘memory’. We examine a theoretical model of this process by considering a one-dimensional lattice where each site can either be methylated (1) or unmethylated (0). Unlike the canonical Ising model, this model has asymmetric interactions since 1s can convert a 0 to a 1 but not vice versa. We compute the steady state number of methylated sites for interactions ranging from nearest neighbour to infinite range, for which we obtain an analytic solution. As the feedback is increased, while the turnover rate is kept constant, we find that the average steady state methylation jumps from zero to a non zero value, reminiscent of a phase transition. We also compute the relaxation time to the steady state and analyze how it depends on the strength of the feedback and the range of interactions.

References:

[1] Park M, Patel N, Keung AJ, Khalil AS, Cell. 2019;176(1-2):227-238.e20