Inferring initial state of the ancestral network of cellular fate decision: a case study of phage lambda

Gene regulatory networks (GRNs) describe how gene expression is controlled by interactions among DNA and proteins. The decision network controlling prophage induction in phage lambda has served as a paradigm for studying decision control of cellular fate, which has broad implications for understanding phenomena such as embryo development, tissue regeneration, and tumorigenesis. The phage-lambda GRN dictates whether the phage enters the lytic mode or the lysogenic mode. In this work, we study the evolutionary origin of this GRN and explore the initial architecture of the proto-GRN, from which the modern GRN is evolved. Specifically, we examined the model of proto-GRN of phage-lambda containing one operator, from which the modern GRN with three operators evolved. We constructed 9 network architectures of the proto-GRNs by different combinations of the three operators O_R3, O_R2, O_R1 and the three different genomic locations. We quantified the full stochastic behavior of each of these networks through exact computation of their steady-state probability landscapes using the Accurate Chemical Master Equation(ACME) algorithm. We further analyzed changes in the copy numbers of the two key proteins CI and Cro during prophage induction upon UV irradiation at different dosages. By examining the dynamic changes of the protein copy numbers upon different UV irradiations, our results show that the network in which O_R1 located at the second site is the most probable architecture for the ancestral phage-lambda network. Our work can be extended for further analysis of the evolutionary trajectories of this cellular fate decision network.