par Thomas, René
Référence Journal of theoretical biology, 42, 3, page (563-585)
Publication Publié, 1973-12
Article révisé par les pairs
Résumé : This paper is an attempt to formalize in Boolean terms genetic situations, from simple concepts like recessitivity and cis-dominance, to models describing complex control circuits. A primary objective was to provide a language describing in a compact and unambiguous way, systems which become more and more difficult to describe as their complexity is being unravelled. Expression of a gene is given as a binary function of binary variables of three types: • "genetic" variables, which describe the state (so-called normal, or mutated in various ways) of genes or recognition sites (promoters, operators, terminators, etc....); • "environmental" variables such as a temperature shift or the presence of a substance above a threshold concentration; • "internal" variables used for memorizing previous states of the system. Circuit engineers use, for memorization, pairs internal functions (Yt) and variables (yt) such that the value of the variable at time t is the same as that of the associated function at time t - Δt; the value of a variable thus serves as a memory of the value of the associated function in the proceeding period (see Florine, 1964). It was realized during this work that concepts like the expression of a gene and the presence of its product are related to each other essentially in the same way as the internal functions Yt and variables yt. Tabulation of the logic equations as Veitch matrices greatly helps in reducing the algebraic expressions (and, hence, the corresponding verbal expressions) to their simplest form. But the main interest of the Veitch tabulation of the equations is that it gives a clear and exhaustive view of all the states of the system as predicted by the model. This is especially useful for sequential problems; the matrices show which states are stable ones, and how the system proceeds from state to state. The logic equations can also be wired up for simulation, using appropriate delays between switching on or off an internal function and its memorization variable. The language proposed is now currently used by the author for clarification of complex models (e.g. in regulation of bacteriophage λ). © 1973.