Fig. 3: Holimaps for two-node gene networks in steady-state conditions.
From: Holimap: an accurate and efficient method for solving stochastic gene network dynamics
a Illustration of the 2-HM and 4-HM for a two-node gene network, where two genes G1 and G2 regulate each other. Feedback is mediated by cooperative binding of h1 copies of protein P1 to gene G2 and cooperative binding of h2 copies of protein P2 to gene G1. b The two-node network can describe four different feedback loops, according to whether ρui > ρbi or ρui < ρbi for i = 1, 2. c A negative feedback loop with non-cooperative binding (h1 = h2 = 1). d Heat plots of the HDs for the LMA and 4-HM as functions of the binding rates σb1 and σb2. Here the HD represents the Hellinger distance between the real and approximate steady-state distribution of the number of molecules of protein P1. The red curve encloses the true bimodal parameter region computed using FSP, and the orange curve encloses the bimodal region predicted by Holimap. e Comparison of the steady-state distributions of protein P1 computed using FSP, LMA, 2-HM, and 4-HM. f A toggle switch with cooperative binding (h1 = h2 = 2). g Same as (d) but for the toggle switch. The yellow curve encloses the parameter region of deterministic bistability, i.e., the region in which the deterministic rate equations have two stable fixed points and one unstable fixed point. h Same as (e) but for the toggle switch. Here the parameters are chosen so that the system displays deterministic bistability. While we only focus on the distribution of protein P1 in (d), (e), (g), and (h), the distribution of the second protein P2 is also accurately predicted by Holimap (Supplementary Fig. 3). See Supplementary Note 1 for the technical details of this figure. Source data are provided as a Source Data file.
