Epigenetic cell memory: The gene’s inner chromatin modification circuit
Fig 6
Mutual repression circuit: Robust memory of multiple co-existing gene expression patterns.
(A) Interaction diagram of two mutually repressing and positively autoregulated genes, wherein the product of each gene recruits writers of repressive chromatin modifications to the other gene. Here, X and Z represent the products of the two genes. (B) Block diagram corresponding to the circuit in panel (A). Here, nX and nZ correspond to the number of molecules of X and Z, respectively. (C) Stationary probability distribution π of the system obtained by simulating the reactions listed in Tables E and F in S2 File with the SSA, in which nA, ℓ with ℓ = X, Z represents the number of nucleosomes in each gene with activating histone modifications. In (C), px = pz = p with p = 0, 0.1, 10 and ϵ = 0.48, 0.2. The parameter values of each plot are listed in Tables E and F in S2 File. For all simulations we have μ = 1, μ′ = 0.6, and ϵ′ = 1 (Figs G-I in S2 File show different parameter values). (D) Time trajectories of nA, X and nA, Z starting from nA, X = Dtot and nA, Z = 0, in which nX and nZ are reset to zero at the indicated times (dashed line). Time is normalized with respect to . The parameter values for each panel are listed in Tables G and H in S2 File. In particular, p = 0.15, μ′ = 0.6, μ = 1, ϵ = 1 and ϵ as indicated. In all plots, we assume equal parameters for both chromatin modification circuits. 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 all plots (nA, ℓ, nR, ℓ) ≈ (50, 0) and (nA, ℓ, nR, ℓ) ≈ (0, 50) correspond to the active and repressed state of gene ℓ, with ℓ = X, Z. In the figure, we use green and purple, respectively, to indicate DA,X and DA,Z and related quantities.