Modelling and analysis of structure in cellular signalling systems

Cellular signalling is an important area of study in biology. Signalling pathways are well-known abstractions that explain the mechanisms whereby cells respond to signals. Collections of pathways form signalling networks, and interactions between pathways in a network, known as cross-talk, enables further complex signalling behaviours. Increasingly, computational modelling and analysis is required to handle the complexity of such systems. While there are several computational modelling approaches for signalling pathways, none make cross-talk explicit. We present a modular modelling framework for pathways and their cross-talk. Networks are formed by composing pathways: different cross-talks result from different synchronisations of reactions between, and overlaps of, the pathways. We formalise five types of cross-talk and give approaches to reason about possible cross-talks in a network. The complementary problem is how to handle unstructured signalling networks, i.e. networks with no explicit notion of pathways or cross-talk. We present an approach to better understand unstructured signalling networks by modelling them as a set of signal flows through the network. We introduce the Reaction Minimal Paths (RMP) algorithm that computes the set of signal flows in a model. To the best of our knowledge, current algorithms cannot guarantee both correctness and completeness of the set of signal flows in a model. The RMP algorithm is the first. Finally, the RMP algorithm suffers from the well-known state space explosion problem. We use suitable partial order reduction algorithms to improve the efficiency of this algorithm.

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