(34b) Positive Feedback, Nuclear Transport, and Noise in Gene Expression

A positive feedback loop represents a prevalent network motif that can lead to bistability and hysteresis in metabolic, developmental and synthetic transcriptional networks. Deterministic models of gene expression suggest that an ultrasensitive open-loop response is a necessary condition for bistable gene expression. However, stochastic models indicate that positive feedback can lead to bimodal gene expression even when the open-loop response is linear and graded, provided gene expression is sufficiently noisy. We have previously experimentally demonstrated this using the synthetic tet-OFF system in budding yeast, but could not quantitatively account for the measured expression distributions. Here, we present data demonstrating that a stochastic model is capable of quantitatively describing a noise-induced, bimodal, all-or none response in positive feedback. We also find multiple transcription factor binding sites lead to noisier gene expression and hence a bimodal response. In addition, three time scales, the stability of the transcription factor, the nuclear import rate of the transcription factor, and the frequency of random bursts of mRNA encoding the transcription factor, determine the overall response of the positive feedback loop. Interestingly, a weakly transported, unstable transcription factor results in a robust bimodal response provided the frequency of cell division is on order the burst frequency of mRNA production. Finally, we comment on the prevalence of the key features of noise-induced bimodal expression ? transcriptional positive feedback loops, multiple binding sites for the transcription factor, unstable transcription factor, weak nuclear localization signal ? in natural organisms.