UC San Diego

Significant progress has been made in the development of genome-scale models of metabolism in the past 15 years. The majority of the efforts have focused on the analysis of the right null space. While the steady state solution space is very important since homeostatic mechanisms are continuously trying to push the system back to a steady state, there are three other subspaces which also have significance. This dissertation approaches metabolic networks with the goal of investigating all four fundamental subspaces of linear systems, particularly the row and column spaces, which determine the dynamic capabilities of networks. First, the key matrices are defined and their general properties and characteristics are identified. The subspaces are analyzed for a simple metabolic network. Next the right null space is explored in a targeted manner using real networks, the cardiomyocyte mitochondria and a genome-scale model of Mycobacterium tuberculosis, focusing on perfectly correlated reaction sets and the biologically interesting implications they may hold. This is followed by the development of analytical methods to define the time scale hierarchy in the column space of the human red cell, human folate metabolism, and yeast glycolysis. These studies are further pursued by investigating various decompositions of the stoichiometric and gradient matrices that are determined by the underlying physico-chemical characteristics. These investigations lead to the identification of key properties of metabolic networks, such as the duality between fluxes and concentrations in dynamic networks. Having established how to decompose these networks, a middle-out integration approach is described for building or reconstructing kinetic networks using '-omic' data streams that are increasingly available. This approach is applied to construct a dynamic model of human red cell metabolism with and without mechanistic integration of allosteric regulatory functions of enzymes, dynamic models of E. coli, as well as a general hepatocyte mitochondria model which can be used for application of these methods, when the appropriate data becomes available. Simulations with the regulated erythrocyte model highlight the importance of active versus inactive states of enzymes and how the binding state of the enzyme exerts control of the flux through competing pathways. The subsequent chapter investigates perturbational analyses and how they can inform functional states and identify pathophysiological conditions. This dissertation culminates in a description of a conceptually new approach to modeling, 'delta' networks, that relaxes data requirements and is focused on identifying the functional differences between different data sets in an effort to understand as much of the four subspaces as possible, not just the right null space. The studies carried out in this dissertation also further support the use of models as data interrogation tools; for data integration, analysis, as well as for the evaluation of data consistency. The developments and advancements made herein take steps towards achieving genome-scale dynamic regulated networks of metabolism, which can in principle be applied to any biological network.