Lac Operon Random Sub-single Molecule Dynamics And Its Function

Through modern single-molecule methodology, one can now follow individual proteins in action and observe phenotype switching of a single bacterial cell triggered by a single-molecule event. Here we put forward a stochastic, chemical dynamic model for Lac operon in action based on recent experimental measurements. A unique feature of the dynamics is the interplay between a positive feedback and single-molecule fluc-tuations, giving rise to a bimodal distribution of the permease with intermediate inducer concentrations. We show that single-molecule binding/unbinding not only triggers the stochastic phenotype switching in a reasonable time scale, but also significantly extend the range of extracellular inducer concentrations at which the bistablility ocurrs. In contrast, the range is very narrow when present only the positive feedback but without the single-molecule fluctuations. Also the stochastic threshold within the quasi-steady-state time scale would significantly deviate from that predicted from the correspond-ing deterministic model. On the other hand, although it is known theoretically and experimentally that stochasticity could generate bimodal distribution only by itself in some cases even without positive feedback, the fluctuations must be quite slow and one should wait for an extremely long time even to see the bistability and phenotype switch-ing. This might be the reason why in many real cases, the cell has positive feedback as well as single-molecule fluctuations as the Lac operon. Furthermore, bistability will become quite indistinct when the maximum transcription activity either increases or de-creases, converting the hysteretic response of the system to an ultrasensitive graded-like response.