Bifurcation Analysis for Phage Lambda with Binding Energy Uncertainty

In a phage λ genetic switch model, bistable dynamical behavior can be destroyed due to the bifurcation caused by inappropriately chosen model parameters. Since the values of many parameters with biologicalsignificance often cannot be accurately acquired, it is thus of fundamental importance to analyze how and towhich extent the system dynamics is influenced by model parameters, especially those parameters pertainingto binding energies. In this paper, we apply a Jacobian method to investigate the relation between bifurcationand parameter uncertainties on a phage λ OR model. By introducing bistable range as a measure of system robustness, we find that RNA polymerase binding energies have the minimum bistable ranges among all thebinding energies, which implies that the uncertainties on these parameters tend to demolish the bistabilitymore easily. Moreover, parameters describing mutual prohibition between proteins Cro and CI have finitebistable ranges, whereas those describing self-prohibition have infinity bistable ranges. Hence, the former aremore sensitive to parameter uncertainties than the latter. These results help to understand the influence ofparameter uncertainties on the bifurcation and thus bistability