Stationary Distributions and Metastable Behaviour for Self-regulating Proteins with General Lifetime Distributions

Invariance of Poisson statistics in molecular counts to sequestration mechanisms

“…The function g(x) [h(y )] is the distribution of the marginal free [sequestered] protein. Similar product-form distributions have been reported in [34][35][36].…”

A modified fluctuation test for elucidating drug resistance in microbial and cancer cells

“…on the characteristic system (22). Solving the logistic equation for η = η(t) in ( 22) by separating the variables η and t yields…”

Postponing production exponentially enhances the molecular memory of a stochastic switch

“…The LNA (40) and the mixture approximation (46) to the probability distribution p(x, s, t) are easily recast, by means of the transformation ( 8 40) is used for early, and the WKB-based approximation (46) for the later timepoints; the last two time-points are set to log(2)/(λ − + λ + ) and 10/(λ − + λ + ), where λ ± are the metastable transition rates (63). The model parameters are f s = 0.5 for s ≤ 5; f s = 2.5 for s ≥ 6; B = 4; ε = 0.0125; s max = 20.…”

“…The key insight of [29], on which we expand in this work, is that a stochastic autoregulatory circuit extended by a large delay exhibits a near-deterministic behaviour of the inactive protein (the production of which has been initiated but not yet completed). A classical means of eliminating noise in a stochastic model is to increase its system size/volume [30]; the near-deterministic behaviour in large-volume systems can be described using the linear noise approximation (LNA) [31][32][33][34][35] and the Wentzel-Kramers-Brillouin (WKB) approximation [36][37][38][39][40]. These two approaches are complementary: the LNA applies on finite temporal domains [41]; the WKB approximation covers slow metastable dynamics such as transitions between deterministically stable steady states or to a fixation/extinction point [42].…”