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

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 Escherichia coli.

Transcript degradation and noise of small RNA-controlled genes in a switch activated network inEscherichia coli

“…While iron deprivation induces the expression of RyhB through derepression by Fur, RyhB was reported to downregulate Fur, albeit indirectly ( 21 ), thereby establishing a double-negative feedback loop. A double-negative feedback motif may give rise to bistable behavior in the case of two transcription factors negatively regulating each other ( 22 ), suggesting similar behavior could be observed for the mixed sRNA-transcription factor motif ( 24 , 53 ). The notion of bimodal behavior has also been considered in the case of the sRNA MicF, which forms a double negative feedback loop with the global transcription factor Lrp ( 54 ).…”

“…RyhB was reported to inhibit Fur production in a mixed double-negative feedback loop configuration ( 21 ), suggesting the possibility of bistable behavior similar to that found in double-negative feedback motifs involving two transcription factors ( 22 , 23 ). Bistability in a mixed double-negative feedback loop involving a sRNA and a transcription factor has been observed in a stochastic numerical analysis, but only in a limited region of parameter space ( 24 ).…”

Functional characteristics of gene expression motifs with single and dual strategies of regulation

“…A more recent study [26] combines mathematical modeling with single cell experiments to establish that microRNA-regulated gene expression results in lower intrinsic noise as compared to the case of unregulated gene expression. We compute the CV of the protein levels of a target gene in the steady state of the four-gene motif using the FD relation (10). The CV is considerably lower than that in the case of the genetic toggle ( figure 5).…”

“…matrix, C ij = δx i δx j (i, j = 1, 2, · · · , N), with C ii (i = 1, 2, · · · , N) denoting the variance, can be calculated using the FD relation (10). Under the LNA, the mean value of x i is given by the deterministic steady state value so that the CV associated with x i can be computed.…”

“…The connectivity structure of these networks reveals the existence of a number of gene expression motifs or substructures, e.g., positive and negative feedback loops, single input modules and feed forward loops. In recent years, similar motifs have been identified in genome-scale regulatory networks with dual strategies of regulation, i.e., the regulatory interactions include both transcriptional and post-transcriptional regulation [6,7,8,9,10,11]. Amongst the various types of motifs, the positive feedback loop has the potential for the generation of multistability, i.e., the coexistence of more than one stable steady state for the same parameter values.…”