Fig. 4: Stochastic vs. deterministic waiting times to achieve a target protein value for autoregulatory feedback models.
From: A stochastic vs deterministic perspective on the timing of cellular events
A (left) An illustration of the feedback loop (given in reaction scheme (15)) for positive feedback (PFB) (i.e., ρu < ρb), and (right) negative feedback (NFB) (i.e., ρu > ρb). The schematic was created with BioRender.com. B–E Top panel: MFPT, 〈τ0〉, of the stochastic system (orange) to reach 90% of the steady-state mean, given the system is started from 0 protein molecules, for increasing ρb. The corresponding deterministic waiting times, τd, are shown in green. Middle panel: the corresponding ratio, η = 〈τ0〉/τd, of the stochastic waiting time to the deterministic waiting time, as a function of ρb. Bottom panel: ratio, η = 〈τ0〉/τd, of the MFPT of the stochastic system to the deterministic FPT, to reach 90% of the steady-state mean, given the system is started from 0 protein molecules, as a function of ρb and σu. All parameters along with the mean molecule numbers are given in Supplementary Table 1.
