Section: New Results
Abstract Interpretation for Systems Biology
Abstract interpretation is a theory of abstraction that has been introduced for the analysis of programs. In particular, it has proved useful for organizing the multiple semantics of a given programming language in a hierarchy of semantics corresponding to different detail levels, and for defining type systems for programming languages and program analyzers in software engineering. We have investigated the application of these concepts to systems biology formalisms.
More specifically, we consider the Systems Biology Markup Language SBML, and the Biochemical Abstract Machine BIOCHAM with its differential, stochastic, discrete and boolean semantics  . In  , we show how all of these different semantics, except the differential one, can be formally related by simple Galois connections. This provides a simple algebraic setting for relating the different interpretations of biochemical networks, and a formal ground for conducting precise analyses. In particular, we study the inference/checking of protein functions, influence graphs and compartment topology in reaction models.