An abstraction theory for qualitative models of biological systems

Multi-valued networks are an important qualitative modelling approach used widely by the biological community. In this paper we consider developing an abstraction theory for multi-valued networks that allows the state space of a model to be reduced while preserving key properties of the model. This is important as it aids the analysis and comparison of multi-valued networks and in particular, helps address the well-known problem of state space explosion associated with such analysis. We consider developing techniques for efficiently identifying abstractions and so provide a basis for the automation of the abstraction task. We illustrate the theoretical results and techniques developed by considering two detailed case studies based on existing biological models in the literature: (1) the regulation of tryptophan biosynthesis in Escherichia coli; and (2) the lysis–lysogeny switch in the bacteriophage λ.