A Complex Control Circuit
Temperate bacteriophages can display in a stable way two essentially different behaviours. In the immune state, a gene (cI) produces a repressor which prevents expression of all the other viral genes; in the non-immune state the typically viral functions are expressed. The choice between the two pathways and the establishment of one of them have much in common with cell determination and differentiation. This choice depends on a complex control system, in fact one of the most intricate nets of regulation known in some detail. Our paper provides a formal description and partial analysis of this regulatory net. It is shown that even for relatively simple known models, this kind of analysis uncovers predictions which had previously remained hidden. Some of these predictions were checked experimentally. The experimental part chiefly deals with the efficiency of lysogenization by thermoinducible lambda phage carrying mutations in one or more of the regulatory genes, N, cro and cII. Although N− mutations are widely known for preventing efficient integration, and both N− and cII mutations for preventing efficient establishment of immunity, it is shown that, as predicted by a simple model, both N− and cII− phage efficiently lysogenize at low temperature if they are in addition cro−. In contrast with λ N− cro+, λ N− cro− is not propagated as a plasmid at low temperature, precisely because it establishes immunity too efficiently. Genetic control circuits are described in terms of sets of logic equations, which relate the state of expression of genes or of chemical reactions (functions) to input (genetic and environmental) variables and to the presence of gene and reaction products (internal, or memorization variables). From the set of equations, one derives a matrix which shows the stable stationary states (if any) of the system, and from which one can derive the pathways (temporal sequences of states) consistent with the model. This kind of analysis is complementary to the more widely used analysis based on differential equations; it allows one to analyze in less detail more complex systems. The language might be used as well, mutatis mutandis, in fields very different from genetics. The last part of the discussion deals with the role of positive feedback loops in our specific problem (establishment and maintenance of immunity in temperate bacteriophages) and in developmental genetics in general. As a generalization of an old idea, it is suggested that cell determination (for a given character) depends on a set of genes whose interaction constitutes a positive feedback loop. Such a system has two stable stationary states: which one is chosen will usually depend on additional controls grafted on the loop.