Isolating intrinsic noise sources in a stochastic genetic switch

Abstract

The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be unrepressed, leaving three possible promotor states. This model is analysed in its bistable regime in which the deterministic limit exhibits two stable fixed points and an unstable saddle, and the case of small noise is considered. On small time scales, the stochastic process fluctuates near one of the stable fixed points, and on large time scales, a metastable transition can occur, where fluctuations drive the system past the unstable saddle to the other stable fixed point. To explore how different intrinsic noise sources affect these transitions, fluctuations in protein production and degradation are eliminated, leaving fluctuations in the promotor state as the only source of noise in the system. Perturbation methods are then used to compute the stability landscape and the distribution of transition times, or first exit time density. To understand how protein noise affects the system, small magnitude fluctuations are added back into the process, and the stability landscape is compared to that of the process without protein noise. It is found that significant differences in the random process emerge in the presence of protein noise.

25 pages, 5 figures

Cited by in corpus (18)

• WKB theory of large deviations in stochastic populations
• Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches
• Breakdown of fast-slow analysis in an excitable system with channel noise
• Dynamic behavior of stochastic gene expression models in the presence of bursting
• Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments
• Metastability in a stochastic neural network modeled as a velocity jump Markov process
• Bistable switching asymptotics for the self regulating gene
• Genetic Toggle Switch in the Absence of Cooperative Binding: Exact Results
• Metastable behavior in Markov processes with internal states
• Model reduction for slow-fast stochastic systems with metastable behaviour
• Quantitative Analysis of a Transient Dynamics of a Gene Regulatory Network
• Stochastic gene expression conditioned on large deviations
• Construction of stochastic hybrid path integrals using "quantum-mechanical'' operators
• Synchronization of stochastic hybrid oscillators driven by a common switching environment
• Spin coherent states and stochastic hybrid path integrals
• Two-scale large deviations for chemical reaction kinetics through second quantization path integral
• Distribution of population averaged observables in stochastic gene expression
• Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs