Identification of novel properties of metabolic systems through null-space analysis

Abstract

Metabolic models provide a mathematical description of the complex network of biochemical reactions that sustain life. Among these, genome-scale models capture the entire metabolism of an organism, by encompassing all known biochemical reactions encoded by its genome. They are invaluable tools for exploring the metabolic potential of an organism, such as by predicting its response to different stimuli and identifying which reactions are essential for its survival. However, as the understanding of metabolism continues to grow, so too has the size and complexity of metabolic models, making the need for novel techniques that can simplify networks and extract specific features from them ever more important. This thesis addresses this challenge by leveraging the underlying structure of the network embodied by these models. Three different approaches are presented. Firstly, an algorithm that uses convex analysis techniques to decompose flux measurements into a set of fundamental flux pathways is developed and applied to a genome scale model of Campylobacter jejuni in order to investigate its absolute requirement for environmental oxygen. This approach aims to overcome the computational limitations associated with the traditional technique of elementary mode analysis. Secondly, a method that can reduce the size of models by removing redundancies is introduced. This method identifies alternative pathways that lead from the same start to end product and is useful for identifying systematic errors that arise from model construction and for revealing information about the network’s flexibility. Finally, a novel technique for relating metabolites based on relationships between their concentration changes, or alternatively their chemical similarity, is developed based on the invariant properties of the left null-space of the stoichiometry matrix. Although various methods for relating the composition of metabolites exist, this technique has the advantage of not requiring any information apart from the model’s structure and allowed for the development of an algorithm that can simplify models and their analysis by extracting pathways containing metabolites that have similar composition. Furthermore, a method that uses the left null-space to facilitate the identification of un-balanced reactions in models is also presented.