Probability of induction by a single large burst and quasi-steady state.

Abstract

<p>(A)Two typical single-cell time traces of permease levels. The first shows induction by a single full dissociation event of the repressor from the operon (left), while the second shows a failure to induce (right). (B) The large burst size in the presence of positive feedback is remarkably prolonged compared with the case without positive feedback. (C) Successful probability of induction by a complete dissociation event as a function of the extracellular inducer concentration. (D-G) Probability of induction within different time windows starting from uninduced cells (blue) or induced cells (red); we determined the stochastic threshold through mathematical fitting in the form of for these curves. The deterministic threshold is approximately 20(<i>molec.</i>), while the stochastic thresholds are larger and decrease when the time window is extended. The extracellular inducer concentration, <i>I</i>_<i>e</i>, is set to 40<i>μ</i>M.</p