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Why the Lysogenic State of Phage Is So Stable: A Mathematical Modeling Approach

Moisés Santillán ^* and Michael C. Mackey 

^* Centre for Nonlinear Dynamics, McGill University, H3G 1Y6 Montreal, Quebec, Canada; and Departments of Physiology, Physics & Mathematics and Centre for Nonlinear Dynamics, McGill University, H3G 1Y6 Montreal, Quebec, Canada

Correspondence: Address reprint requests to Moisés Santillán, Depto. de Física, Esc. Sup. de Física y Matemáticas, Inst. Politécnico Nal. 07738 México D.F., México. Tel.: +52-55-57296000 ext. 55319; Fax: +52-55-57296000 ext. 55051; E-mail: moyo{at}esfm.ipn.mx.

We develop a mathematical model of the phage lysis/lysogeny switch, taking into account recent experimental evidence demonstrating enhanced cooperativity between the left and right operator regions. Model parameters are estimated from available experimental data. The model is shown to have a single stable steady state for these estimated parameter values, and this steady state corresponds to the lysogenic state. When the CI degradation rate (_cI) is slightly increased from its normal value (_cI 0.0 min^-1), two additional steady states appear (through a saddle-node bifurcation) in addition to the lysogenic state. One of these new steady states is stable and corresponds to the lytic state. The other steady state is an (unstable) saddle node. The coexistence these two globally stable steady states (the lytic and lysogenic states) is maintained with further increases of _cI until _cI 0.35 min^-1, when the lysogenic steady state and the saddle node collide and vanish (through a reverse saddle node bifurcation) leaving only the lytic state surviving. These results allow us to understand the high degree of stability of the lysogenic state because, normally, it is the only steady state. Further implications of these results for the stability of the phage switch are discussed, as well as possible experimental tests of the model.

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