Threshold response and bistability in gene regulation by small noncoding RNA.

In this paper, we study through mathematical modelling the combined effect of transcriptional
and translational regulation by proteins and small noncoding RNAs (sRNA) in a genetic feedback motif
that has an important role in the survival of E. coli under stress associated with oxygen and energy
availability. We show that subtle changes in this motif can bring in drastically different effects on the
gene expression. In particular, we show that a threshold response in the gene expression changes to a
bistable response as the regulation on sRNA synthesis or degradation is altered. These results are obtained
under deterministic conditions. Next, we study how the gene expression is altered by additive and multiplicative
noise which might arise due to probabilistic occurrences of different biochemical events. Using
the Fokker-Planck formulation, we obtain steady-state probability distributions for sRNA concentration
for the network motifs displaying bistability. The probability distributions are found to be bimodal with
two peaks at low and high concentrations of sRNAs. We further study the variations in the probability
distributions under different values of noise strength and correlations. The results presented here might be
of interest for designing synthetic network for artificial control.