Calculating biological behaviors of epigenetic states in the phage lambda life cycle.

The biology and behavior of bacteriophage lambda regulation have been the focus of classical investigations of molecular control of gene expression. Both qualitative and quantitative aspects of this behavior have been systematically characterized experimentally. Complete understanding of the robustness and stability of the genetic circuitry for the lysis-lysogeny switch remains an unsolved puzzle. It is an excellent test case for our understanding of biological behavior of an integrated network based on its physical, chemical, DNA, protein, and functional properties. We have used a new approach to non-linear dynamics to formulate a new mathematical model, performed a theoretical study on the phage lambda life cycle, and solved the crucial part of this puzzle. We find a good quantitative agreement between the theoretical calculation and published experimental observations in the protein number levels, the lysis frequency in the lysogen culture, and the lysogenization frequency for mutants of O(R). We also predict the desired robustness for the lambda genetic switch. We believe that this is the first successful example in the quantitative calculation of robustness and stability of the phage lambda regulatory network, one of the simplest and most well-studied regulatory systems.