On the Relation between Boolean Methods and the Theory of Finite Markov Chains

Abstract

One of the objectives of these lectures is to compare the different theoretical methods available to persons wishing to make models of genetic regulatory processes. This might be done in two ways. On the one hand, we may select some concrete system, analyze it by the various theoretical techniques, and then compare the results. The trouble with this approach is that in constructing a model for analysis by any technique, there is a certain freedom allowed to the model builder in translating the qualitative aspects of a concrete system into the language of the theoretical method. For example, in a Boolean representation a system may sometimes be described using either logical AND or logical OR, depending on whether or not some substance is absolutely necessary for the occurence of an effect ; the selection of either logical function is at the discretion of the model builder. And in constructing a deterministic, kinetic model of the same system, we may decide to use quadratic kinetics rather than, say, cubic kinetics. Since the conclusions drawn depend on the particular theoretical representation, it is not always clear whether different predictions made by different approaches are the result of something inherent in the methods or whether they result from the particulars of each model.

This lecture follows closely the recent article Rigney, D. Bull. CI. Sc. Acad. Rpy. Belg. 63, 516–533 (1977) Markov Chain Analysis of operon — type genetic control Networks and its Relation to the Boolean Formalism of Thomas.