Design principles of noise-induced oscillation in biochemical reaction networks: II. coupled positive and negative feedback loops

摘要

According to the chemical reaction network theory, the topology of a certainclass of chemical reaction networks, regardless of the kinetic details, sets alimit on the dynamical properties that a particular network can potentiallyadmit; the structure of a network predetermines the dynamic capacity of thenetwork. We note that stochastic fluctuations can possibly confer a newdynamical capability to a network. Thus, it is of tremendous value tounderstand and be able to control the landscape of stochastic dynamicalbehaviors of a biochemical reaction network as a function of networkarchitecture. Here we investigate such a case where stochastic fluctuations cangive rise to the new capability of noise-induced oscillation in a subset ofbiochemical reaction networks, the networks with only three biochemical specieswhose reactions are governed by mass action kinetics and with the coupling ofpositive and negative feedback loops. We model the networks with the masterequations and approximate them, using the linear noise approximation. For eachnetwork, we read the signal-to-noise ratio value, an indicator of amplified andcoherent noise-induced oscillation, off from the analytically derived powerspectra. We classify the networks into three performance groups based on theaverage values of the signal-to-noise ratio and the robustness. We identify thecommon network architecture among the networks belonging to the sameperformance group, from which we learn that the coupling of negative andpositive feedback loops generally enhance the noise-induced oscillationperformance better than the negative feedback loops alone. The performance ofnetworks also depends on the relative size of the positive and negativefeedback loops; the networks with the bigger positive and smaller negativefeedbacks are much worse oscillators than the networks with only negativefeedback loops.