Fig. 3: Stochastic vs. deterministic waiting times to reach a target mRNA value for the telegraph model.
From: A stochastic vs deterministic perspective on the timing of cellular events
A A schematic of the telegraph model as given by the reaction scheme in Eq. (13). The schematic was created with BioRender.com. B Piecewise-deterministic approximation of the stochastic model (Eq. (14)) versus the deterministic model. (left) For large λ values, the approximate MFPT, 〈τ0〉, (orange cross) of the telegraph process to reach target N (grey dashed line) is smaller than the deterministic FPT, 〈τd〉, (green cross). The deterministic reaction rate equation is shown in purple. Model parameters are λ = 2, μ = 0.5, K = 625, so that the steady-state mean mRNA copy number is 500. We also have that ρ = 0.6, so that the target N = 300. (right) For small values of λ, the approximate MPFT of the stochastic model (orange cross) is larger than that of the deterministic model (green cross). Model parameters used are λ = 0.3, μ = 0.5, K = 1333, and ρ = 0.6. C Deterministic FPTs, τd (green), and stochastic MFPTs, 〈τ0〉 (orange; computed using FSP), as a function of the switching off rate μ, for three different λ values: λ = 10 (left), λ = 1 (middle), λ = 0.1 (right). In each plot, we vary μ from 0 to 100, while keeping the steady-state mean mRNA number fixed at 100; this involves varying K accordingly. The target N is set to 80% of the steady-state mean.
