Stochastic analysis of bistability in coherent mixed feedback loops combining transcriptional and post-transcriptional regulations

TL;DR

This paper investigates the bistability in mixed feedback loops involving transcriptional and post-transcriptional regulation, combining deterministic and stochastic models to analyze stability, transition lifetimes, and biological implications.

Contribution

It provides a theoretical and numerical analysis of bistability in coherent mixed feedback loops, highlighting the role of stochastic fluctuations and parameter dependencies.

Findings

Bistability exists under specific parameter ranges.

State lifetimes depend strongly on transcription rates.

The sRNA dominated state's duration decreases sigmoidally with repressor transcription rate.

Abstract

Mixed feedback loops combining transcriptional and post-transcriptional regulations are common in cellular regulatory networks. They consist of two genes, encoding a transcription factor and a small non-coding RNA (sRNA), which mutually regulate each other's expression. We present a theoretical and numerical study of coherent mixed feedback loops of this type, in which both regulations are negative. Under suitable conditions, these feedback loops are expected to exhibit bistability, namely two stable states, one dominated by the transcriptional repressor and the other dominated by the sRNA. We use deterministic methods based on rate equation models, in order to identify the range of parameters in which bistability takes place. However, the deterministic models do not account for the finite lifetimes of the bistable states and the spontaneous, fluctuation-driven transitions between them. Therefore, we use stochastic methods to calculate the average lifetimes of the two states. It is found that these lifetimes strongly depend on rate coefficients such as the transcription rates of the transcriptional repressor and the sRNA. In particular, we show that the fraction of time the system spends in the sRNA dominated state follows a monotonically decreasing sigmoid function of the transcriptional repressor transcription rate. The biological relevance of these results is discussed in the context of such mixed feedback loops in {\it Escherichia coli}.