Figure 5.

A mutually repressive network with an additional element. (A) The homeobox-containing transcription factor Xom mediates the repression of Gsc by Xbra. The gene network can be abstracted into a general network consisting of M, A, B and C as illustrated. (B) Ordinary differential equations describing the dynamics of the network in (A). k_a, k_b and k_c are respectively the rates of synthesis of A, B and C. α and γ are the cooperativities of repression by A and C, ε and μ are the cooperativities of induction by B and M, respectively. kd_a, kd_b and kd_c are the decay rate constants. The dynamics of A and B are similar to those in Additional file 1 and show bistability. (C) Simulations were performed with k_a = k_b = 5 and α = γ = 3 (μ = 1, kd_a = kd_b = kd_c = 1). Threshold values of M, which are colour-coded, are plotted in the parameter plane (k_c, ε). k_c and ε determine how the value of C changes over time. There are two areas in the parameter plane where the system is bistable with a threshold. With smaller values of k_c and ε (area 1), B is on and A is off with low M, and vice versa with high M at steady state. With larger values of k_c and ε (area 2), A is on and B is off with low M, and vice versa with high M at steady state. (D) Typical examples (black dots in (C)) of steady state values of A and B plotted against M. Left panel, (k_c, ε) = (4, 2.5). Right panel, (k_c, ε) = (12, 9). If smaller values of k_c and ε are favoured in nature, the above observation may explain why at steady state and with low activin Xbra (which corresponds to B) is on and Gsc (which corresponds to A) is off, and vice versa with high activin.