Robustness, Stability and Efficiency of Phage lambda Gene Regulatory Network: Dynamical Structure Analysis

Based on the recently developed dynamical structure theory for complex networks and the seminal work of Shea and Ackers in the 1980’s, we formulate a transparent and concise mathematical framework for the gene regulatory network controlling phage λ life cycles, which naturally includes the stochastic effect. The dynamical structure theory states that the dynamics of a complex network is determined by its four elementary components: The dissipation (analogous to degradation) and stochastic force, the driving force determined by a potential and the transverse force. The potential may be interpreted as a landscape for the phage development in terms of attractive basins, saddle points, peaks and valleys. The dissipation gives rise to the adaptivity of the phage in the landscape defined by the potential: The phage always has the tendency to approach the bottom of the nearby attractive basin. The stochastic fluctuation gives the phage the ability to search around the potential landscape by passing through saddle points.