Dynamics of a genetic toggle switch at the nucleotide and codon levels

Abstract

We study the dynamics of a model stochastic two-gene switch at the nucleotide and codon levels. First, we show that its stability, the mean lifetime of the noisy attractors, differs from that of a model where transcription and translation elongation are modeled as single-step delayed events, indicating the need of detailed models to study the dynamics of switches. Next, we vary the coupling between the two genes by varying the affinity of repressor proteins to the promoters and measure the mutual information between the two proteins times series. We find that there is a degree of coupling that maximizes information propagation between the two genes. This is explained by the effects of the coupling on mean and entropy of RNA and protein numbers of each gene, as well as correlation, 2-tuple entropy between the two proteins numbers, and, finally, the stability of the noisy attractors. We also find that increasing the rate of translation initiation increases the correlation between RNA and protein numbers and between the two proteins, due to increased stability of the noisy attractors. Increasing the rate of transcription or decreasing RNA degradation causes opposite effects to the correlation between RNA and proteins of each gene and the stability of the noisy attractors. Finally, we add a sequence-dependent transcription pause site and show that both its probability of occurrence, as well as its mean time length, affects the dynamics of the switch, further demonstrating the dependence of the dynamics of this circuit on sequence level events. © 2011 American Physical Society.