Modeling And Analysis Of Genetic Regulatory Network Of Lambda Phage Infecting Escherichia Coli

The system of phage λ infecting Escherichia coli(E. coli) is an excellent model for synthetic biology and system biology, and also a well-known paradigm to investigate principle of genetic regulation network occurring at the molecular level, so it’s very important to deeply research the genetic regulation network. The phage λ is a temperate bacteriophage that infects the bacterial species E. coli. After infection, the phage λ will enter either one of two different pathways: Lysogeny or Lysis. The lysogenic state of wild-type(denoted WT) phage λ is extremely stable even more stable than its genome. The lysogenic state is maintained by a highly concentration of CI2 repressor protein, which has been demonstrated by several experiments and theoretical models. Several studies have found that some mutations also have bistability and switching property. However, the stabilities of lysogenic states and other property in λ mutations are still required to investigate because of lacking experiment and theoretical study.In this work, a model base on theory of differential equation was built to describe the biological behavior and life rule of WT phage λ and its mutants by taking into account the important modules and interactions between regulators and operators. The theoretical results partly agree with experimental findings. Subsequently, we investigated the influence of cooperative binding of CI2 to the second site(denoted OR2) and the first site(denoted OR1) in right operator and found that the cooperativity is required for bistability appearance. This cooperativity also plays an important role in the maintenance of high stability of lysogenic state in WT system. Furthermore, we investigated the role of cooperativity between the right operator(denoted OR) and the left operator(denoted OL) in the WT phage λ and found that it plays an important role for building and maintenance of the lysogenic state. Finally, the entropies of WT and mutant systems were used to explain the stabilities of stationary states from physical viewpoint. We observed that the saddle point has the largest entropy. The entropy of lysis is larger than that of lysogeny. The results agree with our hypothesis. On the basis of above observation, we proved that why the lysogeny is so stable from the physical view and offered a demonstration of Erwin Schrodinger’s point that life live for negentropy.Our work also provides a new theoretical proof, research method and enlightenment for study of gene regulatory network. In some aspects, it can saves time and money for the experimental researchers.