Equation-Free Analysis of Two-Component System Signalling Model Reveals the Emergence of Co-Existing Phenotypes in the Absence of Multistationarity

Abstract

Phenotypic differences of genetically identical cells under the same environmental conditions have been attributed to the inherent stochasticity of biochemical processes. Various mechanisms have been suggested, including the existence of alternative steady states in regulatory networks that are reached by means of stochastic fluctuations, long transient excursions from a stable state to an unstable excited state, and the switching on and off of a reaction network according to the availability of a constituent chemical species. Here we analyse a detailed stochastic kinetic model of two-component system signalling in bacteria, and show that alternative phenotypes emerge in the absence of these features. We perform a bifurcation analysis of deterministic reaction rate equations derived from the model, and find that they cannot reproduce the whole range of qualitative responses to external signals demonstrated by direct stochastic simulations. In particular, the mixed mode, where stochastic switching and a graded response are seen simultaneously, is absent. However, probabilistic and equation-free analyses of the stochastic model that calculate stationary states for the mean of an ensemble of stochastic trajectories reveal that slow transcription of either response regulator or histidine kinase leads to the coexistence of an approximate basal solution and a graded response that combine to produce the mixed mode, thus establishing its essential stochastic nature. The same techniques also show that stochasticity results in the observation of an all-or-none bistable response over a much wider range of external signals than would be expected on deterministic grounds. Thus we demonstrate the application of numerical equation-free methods to a detailed biochemical reaction network model, and show that it can provide new insight into the role of stochasticity in the emergence of phenotypic diversity.

The Architecture of a Prototypical Bacterial Signaling Circuit Enables a Single Point Mutation to Confer Novel Network Properties

“…While bistability provides an explanation for the observed all-or-none behavior based on deterministic steady-state analysis, it is also possible for a monostable network to exhibit bimodal behavior because of slow kinetics and positive feedback, as has been seen in stochastic models [16], [20], [21]. To compare and contrast these mechanisms, we examined the detailed model using both deterministic steady-state analysis and stochastic simulations (Text S1).…”

“…Previous modeling work indicates that two-component systems have the potential to exhibit bimodal behavior as a result of stochastic fluctuations in molecular components [16], [20], [21] as well as bistability [26], [27]. Bistability has been observed experimentally in the MprB/MprA two-component system [28], although additional feedback loops not present in simple two-component signaling architectures may be responsible for the bistability in that system [29].…”

Stability of bacterial toggle switches is enhanced by cell-cycle lengthening by several orders of magnitude

“…Biand multistable regulatory elements introduce heterogeneity in cell populations and allow cells in a multicellular organism to specialize and specify their fate. Although multistability is not required for the emergence of coexisting phenotypes [6], decisions between cell death, survival, proliferation, or senescence are likely associated with bistability. In prokaryotes multistability is regarded as an optimal strategy for adapting to varying environmental conditions [7].…”

Role of functionality in two-component signal transduction: A stochastic study

“…Although deterministic modeling of bacterial signal transduction machinery is known in the literature [7,12,[21][22][23][24], few attempts have been made to study the same using a stochastic framework. In this connection, it is important to mention the theoretical modeling of bacterial two-component systems where stochastic kinetics has been used to study different phenotypic response (graded and all-or-none) [25,26]. In the present work, however, we have developed a mathematical formalism to study signal transduction processes in generic bacterial TCS.…”