Predicting Systems-Level Behavior from Biochemically Realistic Algebraic Models

Abstract

An important goal of systems biology is to develop quantitative models that explain how specifc molecular features give rise to systems-level properties. Metabolic and regulatory pathways that contain multifunctional enzymes are especially interesting to study from this perspective because they have frequently been observed to exhibit robustness|the ability for a system to perform its proper function even as levels of its components change. This thesis reports a series of models that were developed to elucidate the basis for robust control in biochemical systems (both with and without bifunctional enzymes). All models were analyzed using steady-state massaction kinetics and algebraic techniques that do not require assignment of numerical values to parameters in the models. A comprehensive compendium of reaction networks involving a bifunctional regulatory enzyme acting on a monomeric substrate was constructed. Algebraic analysis of the reaction network compendium identifed three forms of robustness that can arise in systems with bifunctional enzymes and correlated each type of robustness with particular mechanisms. Robustness was found to be highly sensitive to biochemical details, as subtle changes in mechanism often altered the type of robustness or eliminated robust behavior altogether. Extensive mechanistic, structural, and kinetic data were used to develop detailed models of two systems in which robustness has been experimentally demonstrated. Regulation of isocitrate dehydrogenase (IDH) by a bifunctional kinase/phosphatase partitions carbon flux in Escherichia coli between the full tricarboxylic acid cycle and the glyoxylate bypass, an anapleurotic pathway for growth on two-carbon substrates. Combined algebraic and numerical analysis of the model, which reflects recent structural information about the bifunctional enzyme, indicated that robustness in IDH regulation is due to both bifunctionality of the kinase/phosphatase and homodimerization of IDH. In the yeast Saccharomyces cerevisiae the high-osmolarity glycerol (HOG) pathway is controlled by a three-component phospho-relay that must ensure consistent repression of the HOG pathway in low-osmolarity conditions. Algebraic modeling elucidated the mechanistic basis for this robustness and suggested that robustness is due more to the biochemistry of the response regulator Ssk1 than of the histidine kinase Sln1. Additionally, minimal steady-state models of two processes important to histone coding (multisite heterotypic modification and heterochromatin spreading) were constructed and analyzed. The present work characterizes the mechanistic basis for robustness in several important model systems and lays the groundwork for discriminating between enzymatic mechanisms using simple steady-state measurements of substrate modification forms. The results highlight the importance of biochemical realism in systems-level modeling and illustrate the power of algebraic methods to enable broad, parameter-independent predictions.