Comparison of Dynamical Behaviors Between Monofunctional and Bifunctional Two-Component Signaling Modules

Abstract

Two-component signaling modules exist extensively in bacteria and microbes. These modules can be, based on their distinct network structures, divided into two types: the monofunctional system (denoted by MFS) where the sensor kinase (SK) modulates only phosphorylation of the response regulator (RR), and the bifunctional system (denoted by BFS) where the SK catalyzes both phosphorylation and dephosphorylation of the RR. Here, we analyze dynamical behaviors of these two systems based on stability theory, focusing on differences between them. The analysis of the deterministic behavior indicates that there is no difference between the two modules, that is, each system has the unique stable steady state. However, there are significant differences in stochastic behavior between them. Specifically, if the mean phosphorylated SK level is kept the same for the two modules, then the variance and the Fano factor for the phosphorylated RR in the BFS are always no less than those in the MFS, indicating that bifunctionality always enhances fluctuations. The correlation between the phosphorylated SK and the phosphorylated RR in the BFS is always positive mainly due to competition between system components, but this correlation in the MFS may be positive, almost zero, or negative, depending on the ratio between two rate constants. Our overall analysis indicates that differences between dynamical behaviors of monofunctional and bifunctional signaling modules are mainly in the stochastic rather than deterministic aspect.