Fig. 5.

Phenotype induction. (A) We consider a hypothetical induction experiment in which a TF induces the expression of a slow promoter, such as, for instance, in response to osmotic or heat shock. Here, the external stimulus is assumed to be controlled via a ramp of TF input (or production) rate. Because TF degradation is assumed to be fast, its concentration follows the instantaneous induction rate. (B) The probability distribution of protein obtained from an induction experiment which carries the promoter from the inactive to the induced state displays transient bimodality. Here, the stimulus is assumed to be a ramp between times 10 and 20, as shown in A. (C) The same experiment is carried out in the reverse direction: A decreasing ramp leading from the fully induced to the depleted promoter state also shows transient bimodality which is, however, persistent for much longer times. The resulting probability distribution is reminiscent of the induction history, indicating hysteresis. We also note that, at each time point, the protein distributions obtained from stochastic simulation of the full network (Left) agree well with the predictions of our conditional LNA (Right). (D) We quantify the apparent hysteresis phenomenon associated with an increasing and then decreasing stimulus by comparing the global modes of either distribution, i.e., the most probable protein concentrations, which result in a hysteresis loop. The difference between forward and reverse induction, as predicted by the conditional LNA (solid), is in good agreement with simulation (dotted). Parameter values are given in SI Appendix, Table S4.