Cooperativity leads to temporally-correlated fluctuations in the bacteriophage lambda genetic switch

Cooperative interactions are widespread in biochemical networks, providing the nonlinear response that underlies behavior such as ultrasensitivity and robust switching. We introduce a temporal correlation function-the conditional activity-to study the behavior of these phenomena. Applying it to the bistable genetic switch in bacteriophage lambda, we find that cooperative binding between binding sites on the prophage DNA lead to non-Markovian behavior, as quantified by the conditional activity. Previously, the conditional activity has been used to predict allosteric pathways in proteins; here, we show that it identifies the rare unbinding events which underlie induction from lysogeny to lysis.