Stability and multi-attractor dynamics of a toggle switch based on a two-stage model of stochastic gene expression

Abstract

A toggle switch consists of two genes that mutually repress each other. This regulatory motif is active during cell differentiation and is thought to act as a memory device, being able to choose and maintain cell fate decisions. In this contribution, we study the stability and dynamics of a two-stage gene expression switch within a probabilistic framework inspired by the properties of the Pu/Gata toggle switch in myeloid progenitor cells. We focus on low mRNA numbers, high protein abundance and monomeric transcription factor binding. Contrary to the expectation from a deterministic description, this switch shows complex multi-attractor dy- namics without autoactivation and cooperativity. Most importantly, the four attractors of the system, which only emerge in a probabilistic two-stage description, can be identified with committed and primed states in cell differentiation. We first study the dynamics of the system and infer the mechanisms that move the system between attractors using both the quasi-potential and the probability flux of the system. Second, we show that the residence times of the system in one of the committed attractors are geometrically distributed and provide an analytical expression of the distribution. Most importantly we find that the mean residence time increases linearly with the mean protein level. Finally, we study the implications of this distribution for the stability of a switch and discuss the influence of the stability on a specific cell differentiation mechanism. Our model explains lineage priming and proposes the need of either high protein numbers or long term modifications such as chromatin remodeling to achieve stable cell fate decisions. Notably we present a system with high protein abundance that nevertheless requires a probabilistic description to exhibit multistability, complex switching dynamics and lineage priming.

to appear in the Biophysical Journal

References in corpus (7)

• Analytical distributions for stochastic gene expression
• Genetic Toggle Switch Without Cooperative Binding
• Absolute Rate Theories of Epigenetic Stability
• Self consistent proteomic field theory of stochastic gene switches
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• Emergence of switch-like behavior in a large family of simple biochemical networks
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Cited by in corpus (9)

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• Dichotomous noise models of gene switches
• The Limiting Dynamics of a Bistable Molecular Switch With and Without Noise
• Discrete Flux and Velocity Fields of Probability and Their Global Maps in Reaction Systems
• Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations
• Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks
• Strong order-one convergence of the Euler method for random ordinary differential equations driven by semi-martingale noises
• A new generalization of Parrondo's games to three players and its application in genetic switches