Bistability and hysteresis in epigenetic regulation of the lactose operon. Since Delbrück, a long series of ignored models.

Bistability is the capacity of a system to switch in an "all-or-none" manner between alternative steady states. This powerful concept originates from the analysis of non-linear equations driving open systems. It is one of the various patterns of regulation associated with a particular class of dynamic structures that Glansdorff and Prigogine baptised "dissipative structures". The idea of discontinuous transitions between alternative states was first formulated much earlier, by Delbrück, in 1949. Cohn and Horibata and Novick and Weiner confirmed that such transitions occur in experiments on the lactose operon carried out ten years later. Modelling with non-linear differential equations made it possible to simulate the dynamic behaviour of the lac operon, and modelling by asynchronous logical analysis elucidated the determinant role played by positive feedback circuits in the emergence of multistationarity. Nevertheless, these studies were largely ignored until the recent demonstration of the hysteretic nature of the bistable transition between alternative states of the lac operon. As originally suggested by Delbrück, the pattern of lactose consumption adopted by the bacterium is controlled epigenetically rather than genetically: the true key determinant is the direction of change of an environmental variable with respect to the structural components of the operon.