Spatio-temporal logic for the analysis of biochemical models

Abstract

Process algebra, formal specification, and model checking are all well studied techniques in the analysis of concurrent computer systems. More recently these techniques have been applied to the analysis of biochemical systems which, at an abstract level, have similar patterns of behaviour to concurrent processes. Process algebraic models and temporal logic specifications, along with their associated model-checking techniques, have been used to analyse biochemical systems. In this thesis we develop a spatio-temporal logic, the Logic of Behaviour in Context (LBC), for the analysis of biochemical models. That is, we define and study the application of a formal specification language which not only expresses temporal properties of biochemical models, but expresses spatial or contextual properties as well. The logic can be used to express, or specify, the behaviour of a model when it is placed into the context of another model. We also explore the types of properties which can be expressed in LBC, various algorithms for model checking LBC - each an improvement on the last, the implementation of the computational tools to support model checking LBC, and a case study on the analysis of models of post-translational biochemical oscillators using LBC. We show that a number of interesting and useful properties can be expressed in LBC and that it is possible to express highly useful properties of real models in the biochemistry domain, with practical application. Statements in LBC can be thought of as expressing computational experiments which can be performed automatically by means of the model checker. Indeed, many of these computational experiments can be higher-order meaning that one succinct and precise specification in LBC can represent a number of experiments which can be automatically executed by the model checker.