| A fundamental problem in biology is to understand the complex relationship between genes. From the explosion in data generated by new biological techniques, the last decade has seen a proliferation in the use of mathematics to tackle this complex issue. As many researchers before, we seek to build a mathematical framework to describe gene-gene relationships. Therefore, we have generalized previous work done to describe the pRM, pL and pR promoters in phage lambda to any arbitrary genetic network. This formulation describes the mRNA (x) and protein ( y) concentrations of a gene by the following ODE, x&d2;=af y-3x y&d2;=bx-gy where epsilon, gamma, alpha and beta are constants. Here, we define &phis; using an enzyme kinetic formulation. We then apply this framework to phage lambda. We are able to reproduce (1) N-mediated antitranslation and antitermination, (2) CII sensitivity to RNaseIII and FtsH, (3) CI maintenance of lysogenic state and (4) the lysogenic to lytic switch mediated by RecA. Our results hightlight many of the strengths and weaknesses of applying this framework to different kinds of genetic networks. |
