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

Fig 5

Positive autoregulation allows robust temporal extension of memory of the active chromatin state.

(A) Diagram of a positively autoregulated gene where the gene’s product X recruits writers of D^A. A simplified representation of the chromatin modification circuit is introduced, in which the the labels are not represented. (B) Block diagram corresponding to the circuit in panel (A). Here, . Furthermore, is the input and n^X, the number of molecules of X, is the output, which feeds back on by increasing its value. (C) Input/output steady state characteristics for the pair, with , for different values of p_x obtained from simulations of system Eqs (1) in S2 File with as initial conditions. The parameter values are listed in Table A in S2 File. In particular, ϵ′ = 1, μ = 1, μ′ = 0.7, ϵ = 0.1. (D) Stationary probability distribution π obtained by simulating the reactions listed in Table B in S2 File with the SSA. As before, . The parameter values of each plot are listed in Table B in S2 File. In particular, p_x = 0, 0.1, 10, ϵ′ = 1, μ = 1, μ′ = 0.5, ϵ = 0.12 (Figs B and C in S2 File show different parameter values). (E) Time trajectories obtained by simulating the reactions listed in Table C in S2 File with the SSA with no inputs and starting with initial conditions n^A = 45, and n^X = p_x n^A. Simulations are stopped the first time at which n^A = 6. In all plots, time is normalized according to , ϵ = 0.36, μ′ = 0.5, μ = 1, ϵ′ = 1, and p_x = 0, 0.2, 5. The parameter values of each panel are listed in Table C in S2 File. In each panel, the number of trajectories plotted is 10. (F) Time trajectories of system of reactions listed in Table D in S2 File with the SSA starting from the active chromatin state (n^A = 45, n^D = 5 and n^X = 45). At the indicated times, n^X is reset artificially to zero (dashed lines). The parameter values for each simulation are listed in Table D in S2 File. In particular, p_x = 1, μ′ = 0.1, μ = 1, ϵ′ = 1 and ϵ = 0.4, 0.02. For both values of ϵ, the system is bistable. In our model, ϵ, defined in Eq (2), is a non-dimensional parameter that quantifies the time scales of basal erasure rate of all modifications relative to those of auto and cross-catalysis. In the figure, we use green to indicate the activating modification and related quantities.

doi: https://doi.org/10.1371/journal.pcbi.1009961.g005