A Galois Field Approach to Modelling Gene Expression Regulation

Gene expression is the process by which the cell transforms the information in the DNA to functions, often carried out by proteins. Which genes will be expressed, depends on many factors some internal to the cell and others from the environment around it. This can be considered as a logic function prescribing gene expression in response to the different conditions. Apart from continuous models, the most common formulation of such a function is using Boolean logic. This has the major drawback of restricting analysis to binary valued variable which are not always an appropriate approximation. We propose a multiple-valued logic modelling approach on a Galois field and formulate the regulatory function using the Reed-Muller expansion. Two examples are given that illustrate the application of this approach.