Functional analysis of chemical systems in vivo using a logical circuit equivalent IV. Simulation of cellular control systems using a hybrid computing system

There are two types of mathematical analysis in biological research; one is continuous, a mathematical model of the differential equations of kinetics, and the other finite mathematics relying on a switching circuit model or automaton theory. In this paper a unification of these two types is attempted by introducing binary parameters or variables into the differential equations of kinetics and using a hybrid computing system. The method is applied to the kinetics of formation of repressor and messenger RNA of the enzyme β-galactosidase of Escherichia coli. Simplification of the hybrid system yields the switching circuit model of a preceding paper. In this way a unification of the qualitative logical considerations and quantitative mathematical analysis is suggested. The concept of parametric interaction or informational correlation, discussed in detail as a theory of flexible throttle in a preceding paper, is further explored. Considering a “process analogue” of kinetics having a flexible throttle and also flexibility under on-off control, we can integrate finite mathematics and continuous analysis.