The OR control system of bacteriophage lambda. A physical-chemical model for gene regulation

A quantitative model has been developed for processes in the bacteriophage lambda that control the switchover from lysogenic to lytic modes of growth. These processes include the interactions of cI repressor and cro proteins at the three DNA sites of the right operator, OR, the binding of RNA polymerase at promoters PR and PRM, the synthesis of cI repressor and cro proteins, and the degradative action of recA during induction of lysis. The model is comprised of two major physical-chemical components: a statistical thermodynamic theory for relative probabilities of the various molecular configurations of the control system; and a kinetic model for the coupling of these probabilities to functional events, including synthesis of regulatory proteins cI and cro. Using independently evaluated interaction constants and rate parameters, the model was found capable of predicting essential physiological characteristics of the system over an extended time. Sufficiency of the model to predict known physiological properties lends credence to the physical-chemical assumptions used in its construction. Several major physiological characteristics were found to arise as "system properties" through the non-linear, time-dependent, feedback-modulated combinations of molecular interactions prescribed by the model. These include: maintenance of the lysogenic state in the absence of recA-mediated cI repressor degradation; induction of lysis and the phenomenon of subinduction; and autogenous negative control of cro. We have used the model to determine the roles, within the composite system, of several key molecular processes previously characterized by studies in vitro. These include: co-operativity in cI repressor binding to DNA; interactions between repressors and RNA polymerase (positive control); and the monomer-dimer association of cI repressor molecules. A major role of cI repressor co-operativity is found to be that of guaranteeing stability of the lysogenic state against minor changes in cI repressor levels within the cell. The role of positive control seems to be that of providing for a peaked, rather than monotonic, dependence of PRM activity on cI repressor level, while permitting PR activity to be a step function. The model correlates an immense body of studies in vivo and in vitro, and it makes testable predictions about molecular phenomena as well as physiological characteristics of bacteriophage lambda. The approach developed in this study can be extended to include more features of the lambda system and to treat other systems of gene regulation.