Zero-order ultrasensitivity: A study of criticality and fluctuations under the total quasi-steady state approximation in the linear noise regime

摘要

Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenonin enzyme networks. Here, a substrate is reversibly modified by twoantagonistic enzymes (a "push-pull" system) and the fraction in modified stateundergoes a sharp switching from near-zero to near-unity at a critical value ofthe ratio of the enzyme concentrations, under saturation conditions. ZOU andits extensions have been studied for several decades now, ever since theseminal paper of Goldbeter and Koshland (1981); however, a completeprobabilistic treatment, important for the study of fluctuations in finitepopulations, is still lacking. In this paper, we study ZOU using a modularapproach, akin to the total quasi-steady state approximation (tQSSA). Thisapproach leads to a set of Fokker-Planck (drift-diffusion) equations for theprobability distributions of the intermediate enzyme-bound complexes, as wellas the modified/unmodified fractions of substrate molecules. We obtain explicitexpressions for various average fractions and their fluctuations in the linearnoise approximation (LNA). The emergence of a "critical point" for theswitching transition is rigorously established. New analytical results arederived for the average and variance of the fractional substrate concentrationin various chemical states in the near-critical regime. For the total fractionin the modified state, the variance is shown to be a maximum near the criticalpoint and decays algebraically away from it, similar to a second-order phasetransition. The new analytical results are compared with existing ones as wellas detailed numerical simulations using a Gillespie algorithm.