Mathematical modelling in the post-genome era: understanding genome expression and regulation—a system theoretic approach

This paper introduces a mathematical framework for modelling genome expression and regulation. Starting with a philosophical foundation, causation is identified as the principle of explanation of change in the realm of matter. Causation is, therefore, a relationship, not between components, but between changes of states of a system. We subsequently view genome expression (formerly known as ‘gene expression’) as a dynamic process and model aspects of it as dynamic systems using methodologies developed within the areas of systems and control theory. We begin with the possibly most abstract but general formulation in the setting of category theory. The class of models realised are state-space models, input–output models, autoregressive models or automata. We find that a number of proposed ‘gene network’ models are, therefore, included in the framework presented here. The conceptual framework that integrates all of these models defines a dynamic system as a family of expression profiles. It becomes apparent that the concept of a ‘gene’ is less appropriate when considering mathematical models of genome expression and regulation. The main claim of this paper is that we should treat (model) the organisation and regulation of genetic pathways as what they are: dynamic systems. Microarray technology allows us to generate large sets of time series data and is, therefore, discussed with regard to its use in mathematical modelling of gene expression and regulation.