In the absence of RecA-mediated cleavage of the repressor, the λ prophage is exceptionally stable. We develop a stochastic model that predicts the stability of such epigenetic states from affinities of the molecular components. We find that the stability, in particular, depends on the maximum possible cI protein production, and on the number of translated cro proteins per transcribed mRNA. We apply the model to the behavior of recently published mutants of $O_{\mathrm{R}}$ and find, in particular, that a mutant that overexpress cro behaves in a different way than what was predicted, thus suggesting that the current view of the $O_{\mathrm{R}}$ switch is incomplete. The approach described here should be generally applicable to the stability of expressed states.

• Received 9 January 2002

DOI:https://doi.org/10.1103/PhysRevE.65.051914