From discrete to continuous and back: Abstractions and mesoscopic phenomena in cells

We discuss the interplay between stochasticity and multistability in bio-molecular networks. The resulting cell-level stochastic behavior reflects the fundamentally discrete and random nature of the underlying molecular processes. These ideas are illustrated on the well studied example of the lac operon. We first describe the switching behavior predicted by a differential-equation based model and then show how cell-level stochastic behavior emerges. Finally we point out that the observed macroscopic behavior may not be enough to determine both the dynamic and stochastic parameters.