Stochastic modeling of gene activation and applications to cell regulation

Transcription factors (TFs) are key regulators of gene expression. Based on the classical scenario in which the TF search process switches between one-dimensional motion along the DNA molecule and free Brownian motion in the nucleus, we study the arrival time of several TFs to multiple binding sites. In the presence of a TF influx and competitive binding ligands, we derive the probability that a fixed number of target sites are simultaneously bound. We obtain analytic expressions for this probability as a function of the mean number of TFs. When there are multiple binding sites, because this probability is a sigmoidal curve, our analysis shows that a bistable regime is possible, which can be interpreted as a genetic switch, occurring without requiring cooperative binding (change in the binding probability depending on the previous bounds). Finally, we use our model to analyze fly embryo patterning and show that bicoid can induce a sharp hunchback concentration, resulting in the formation of a sharp boundary and stripes. To conclude, we have proposed here a general mechanism that allows cells to read a morphogenetic gradient. Thus activating the transcription of an auto-activated TF can lead to the conversation of a broad gradient of morphogens into a sharp boundary.