Kinetic Model of the Lysogeny/Lysis Switch of Phage λ

A kinetic model of the interactions between operators and regulators is developed to study the stabilities of genetic states and lysogeny/lysis switch in Escherichia coli infected by bacteriophage lambda. Using adiabatic approximation, the kinetic evolutions of mRNA and regulator concentrations can be deduced from operators' equations. Furthermore, the stability of each state of the system is studied. The results show that the lysogenic state switches to the lytic state through two bifurcations: one from a single stable state to a three-point state, and the other from a three-point state to a single stable state. Then we indicate that the property of the lysogeny/lysis switch satisfies the topological characteristics theorem. Finally, the influence of the left operators on the lysogeny/lysis switch is briefly discussed. The results show that the cooperativity of the CI₂ bound to left and right operators makes the lysogenic state more stable.