Determining the Stability of Genetic Switches: Explicitly Accounting for mRNA Noise

Abstract

Cells use genetic switches to shift between alternate gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Here, we study the dynamics of switching in a generic-feedback on/off switch. Unlike protein-only models, we explicitly account for stochastic fluctuations of mRNA, which have a dramatic impact on switch dynamics. Employing the WKB theory to treat the underlying chemical master equations, we obtain accurate results for the quasi-stationary distributions of mRNA and protein copy numbers and for the mean switching time, starting from either state. Our analytical results agree well with Monte Carlo simulations. Importantly, one can use the approach to study the effect of varying biological parameters on switch stability.

Modeling the effect of transcriptional noise on switching in gene networks in a genetic bistable switch

“…In this model, the transition between the inactive and active states of the promoter gene is no longer constant but is controlled by protein number n via positive feedback, the protein thereby inducing its own expression. This two-state model with positive feedback is identical to the model treated by Assaf et al [16]. This two-state positive feedback switch has been shown to describe biological switching experimentally [17].…”

“…In our present study, we consider the same model for the positive feedback network as discussed in [16] but propose a different theoretical method that employs the stochastic semi-classical path integral technique to explicitly account for the mRNA noise along with protein fluctuations. This semi-classical method has been used earlier to calculate rare event statistics in reaction diffusion systems [25] and it has been applied to various epidemiological stochastic models [24,26,27].…”

“…To account for the stochastic behavior of the genetic switches, Assaf et al [16] used this simple model and employed two coupled chemical master equations that can describe the probability distribution functions, Ṗ m,n and Qm;n of having m mRNAs and n proteins at time t with the promoter DNA being in the inactive and active state, respectively. They used the WKB approximation method [18] to obtain a quasi-stationary solution to the master equation.…”

“…Recently, it has been shown that including mRNA noise in master equations plays a strong role in determining switching rates [13,14]. Employing the WKB theory [15] to treat the underlying chemical master equations, Assaf et al [16] provided a theoretical framework to obtain the quasistationary probability distributions of mRNA/protein copy numbers for a genetic network with positive feedback and also to calculate the mean switching time from either of these active/ inactive states.…”

Exploiting Stochasticity for the Control of Transitions in Gyre Flows

“…More importantly, these methods can also accurately predict the expected switching time of particles between distinct basins of attraction. This framework has been used to describe a variety of physical and biological phenomena including extinction of diseases [10] or species [11] in populations, and switching between gene states [12] or magnetization states [13]. We use these techniques to predict the average time required to switch from one gyre to the next in an ocean environment.…”