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Epigenetic cell memory: The gene’s inner chromatin modification circuit

Fig 4

Time scale separation parameters ϵ, ϵ′ and μ′ control bimodality, time to memory loss, and reactivation time in the chromatin modification circuit.

(A)-(B) Stationary probability distributions π of (n^A, n^R) for the chromatin modification circuit in Fig 3A obtained by simulating the reactions listed in Fig 2 with the SSA. (A) Effect of ϵ and μ′ on the distribution: in the left side plots ϵ = 0.19, 0.02 and μ′ = 1. In the right side plots, μ′ = 1, 0.1 and ϵ = 0.19. (B) Effect of the input stimulus on the distribution: here, ϵ = 0.12 and μ′ = 0.8. In the top plots, u^A = 0, 1, and in the bottom plots and u^R = 0, 1 (Fig R shows different values of μ′ and ϵ). The parameter values for each panel are listed in Table A in S1 File. In all simulations, ϵ = 1 and μ = 1 (Figs S and T in S1 File show different values) and we decrease ϵ by decreasing (similar results can be obtained if we vary as shown in Fig Q in S1 File). (C) Time trajectories of n^R starting from a repressed chromatin state n^A = 5, , as ϵ and μ′ are varied. Simulations are stopped when n^R = 6 for the first time. (D) Time trajectories of n^A starting from an active chromatin state n^A = 45, , as ϵ and μ′ are varied. Simulations are stopped when n^A = 6 for the first time. In all plots of (C)-(D), time is normalized according to , ϵ = 0.36, 0.12, μ′ = 1, 0.5, μ = 1, and ϵ′ = 1 (Fig V in S1 File shows different values of ϵ′). The parameter values are listed in Table B in S1 File. (E) Effect of ϵ′ on the stationary probability distribution π. We set ϵ = 0.12, μ′ = 1, μ = 1 and ϵ′ = 1, 0.001 from left to right (Fig U in S1 File shows different values of ϵ′). The parameter values for each panel are listed in Table P in S1 File. (F) Time trajectories of the system starting from n^R = 45, n^A = 5 and applying an input u^A that, at steady state, leads to a unimodal distribution in the proximity of the active state n^A = D_tot. The parameter values are listed in Table C in S1 File. In particular, u^A = 3.2, μ′ = 0.1, ϵ = 0.24, 0.16, μ = 1 and ϵ′ = 1 (Fig W in S1 File shows different parameter values). In all plots, and simulations are obtained by implementing the set of reactions listed in Fig 2 with the SSA [51]. In all simulations, . In our model, parameters ϵ and ϵ′ quantify the time scales of basal and recruited erasure rates of all modifications relative to those of auto and cross-catalysis. Similarly, parameters μ and μ′ quantify the time scales of erasure rates (basal and recruited) of repressive histone modifications and DNA methylation, respectively, relative to those of activating histone modifications. Mathematical definitions are found in Eq (2). In all plots (n^A, n^R) ≈ (50, 0) corresponds to the active state and (n^A, n^R) ≈ (0, 50) corresponds to the repressed state. In each panel of (C), (D), and (F), the number of trajectories plotted is 10.

doi: https://doi.org/10.1371/journal.pcbi.1009961.g004