Compositional Techniques and Tools for Constructing and Analysing Boolean Networks

Abstract

Boolean networks are an important qualitative modelling approach that are widely used in biological modelling. In particular, attractor analysis (i.e. finding key cyclic behaviour) has been a crucial tool for analysing biological systems. The practical application of Boolean networks is limited by the state space explosion problem. To address this, researchers have considered applying compositional analysis techniques to Boolean networks. Recently, a new compositional framework for constructing and analysing Boolean networks was developed at Newcastle University. This framework provides a foundation for both engineering Boolean networks and decomposing them to aid analysis. While the initial results for this framework are interesting, its practical application currently has some important limitations: the definition of a composition is too restrictive, and it lacks support for compositional attractor analysis. In this thesis, we set out to address these practical limitations of the existing compositional framework for Boolean networks. We significantly strengthened and extended this compositional framework by developing a new general structure for compositions and by providing new results and techniques to compositionally identify the attractors of a Boolean network. Our attractor analysis approach is based on using strongly connected components to identify potential cyclic behaviour, taking into account the interference arising from a composition, and then merging these cyclic behaviour using an important new property called interference alignment. We began by identifying attractors in a composition involving a set of two BNs and a set of three BNs. However, it became clear that extending the results to multiple Boolean networks with multiple entities to be merged was constrained by the complexity of the existing compositional framework. Therefore, a new generalised version of a composition was developed and the compositional attractor analysis techniques were then extended to this new compositional approach. To support the practical applications of our techniques of compositionally identifying the attractors, a prototype support tool was developed. This involved developing a new algorithmic approach based on the underlying theoretical results we have developed. During the development of the tool, two small case studies were undertaken to gain insight into its practical application. The final tool was implemented, and its performance was evaluated by using a series of compositional tests. Moreover, the tool’s performance was compared to the performance of three mature tools from the literature, and the results were very promising