Why the lysogenic state of phage lambda is so stable: a mathematical modeling approach.
We develop a mathematical model of the phage lambda 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 (gammacI) is slightly increased from its normal value (gammacI approximately 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 gammacI until gammacI approximately 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 lambda switch are discussed, as well as possible experimental tests of the model.
Santillán
Moisés
M
Centre for Nonlinear Dynamics, McGill University, H3G 1Y6 Montreal, Quebec, Canada. moyo@esfm.ipn.mx
Mackey
Michael C
MC
D010582:Bacteriophage lambda / Q000737:chemistry* / Q000235:genetics; D001665:Binding Sites; D003198:Computer Simulation; D004268:DNA-Binding Proteins / Q000737:chemistry*; D012321:DNA-Directed RNA Polymerases / Q000737:chemistry*; D004789:Enzyme Activation; D005812:Genes, Switch; D007700:Kinetics; D008242:Lysogeny; D008956:Models, Chemical; D009875:Operator Regions, Genetic; D011401:Promoter Regions, Genetic; D011485:Protein Binding; D017434:Protein Structure, Tertiary; D012097:Repressor Proteins / Q000737:chemistry*; D012680:Sensitivity and Specificity; D014764:Viral Proteins; D054334:Viral Regulatory and Accessory Proteins
D004268:DNA-Binding Proteins; D012097:Repressor Proteins; D014764:Viral Proteins; D054334:Viral Regulatory and Accessory Proteins; C016649:phage repressor proteins; D012321:DNA-Directed RNA Polymerases