Distributed delay stabilizes bistable genetic networks

TL;DR

This paper investigates how distributed delays inherent in genetic regulatory networks can significantly stabilize bistable states, with implications for understanding biological switches and designing synthetic genetic circuits.

Contribution

It demonstrates that increasing noise in distributed delays stabilizes metastable states in bistable genetic networks, using stochastic hybrid models and generalized three-states models.

Findings

Distributed delay noise increases metastable state stability.

Mean residence times in metastable states are dramatically increased.

Stability insights can inform synthetic genetic network design.

Abstract

Delay is an inherent feature of genetic regulatory networks. It represents the time required for the assembly of functional regulator proteins. The protein production process is complex, as it includes transcription, translocation, translation, folding, and oligomerization. Because these steps are noisy, the resulting delay associated with protein production is distributed (random). We here consider how distributed delay impacts the dynamics of bistable genetic circuits. We show that for a variety of genetic circuits that exhibit bistability, increasing the noise level in the delay distribution dramatically stabilizes the metastable states. By this we mean that mean residence times in the metastable states dramatically increase. Relevance to Life Sciences. Bistable genetic regulatory networks are ubiquitous in living organisms. Evolutionary processes seem to have tuned such networks so that they switch between metastable states when it is important to do so, but small fluctuations do not cause unwanted switching. Understanding how evolution has tuned the stability of biological switches is an important problem. In particular, such understanding can guide the design of forward-engineered synthetic bistable genetic regulatory networks. Mathematical Content. We use two methods to explain this stabilization phenomenon. First, we introduce and simulate stochastic hybrid models that depend on a switching-rate parameter. These stochastic hybrid models allow us to unfold the distributed-delay models in the sense that, in certain cases, the distributed-delay model can be viewed as a fast-switching limit of the corresponding stochastic hybrid model. Second, we generalize the three-states model, a symbolic model of bistability, and analyze this extension.