Control Theoretic Analysis of Autocatalytic Networks in Biology with Applications to Glycolysis

Citation

Buzi, Gentian (2010) Control Theoretic Analysis of Autocatalytic Networks in Biology with Applications to Glycolysis. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MHMV-9M59. https://resolver.caltech.edu/CaltechTHESIS:02262010-130618704

Abstract

Metabolic networks in the cell break down food and resources to create useful energy and components. At the same time they use those same components and energy in the process, thus making autocatalysis an unavoidable part of core metabolism. The simplest and most widely studied autocatalytic network is the glycolytic pathway. It is common to every cell of living organisms, from bacteria to humans. Its special autocatalytic structure, like the structure of many similar autocatalytic networks, makes the pathway hard to control and can lead to instabilities.

In this thesis, we study autocatalytic metabolic networks, specifically glycolysis, to investigate fundamental performance tradeoffs in these network topologies. We hypothesize that instabilities in glycolysis are a result of performance tradeoffs that stem from the structure of the pathways and a conservation law, mathematically described by a special form of the Bode Sensitivity Integral. We show that pathway size and intermediate metabolite consumption adversely affect the performance of the pathway, while reversibility of chemical reactions improves performance. We establish tight bounds for the feedback control gains that guarantee stability of pathways of arbitrary size and arbitrary parameter values for the intermediate reactions.

In addition, we investigate effects of perturbations in metabolite concentrations through the estimation of invariant subsets of the region of attraction around nominal operating conditions. To this end we use a numerical procedure composed of system theoretic characterizations and optimization-based formulations. For large, computationally intractable systems we employ a different technique based on the underlying biological structure, which offers a natural decomposition of the system into a feedback interconnection of two input-output subsystems. This decomposition simplifies the analysis and leads to analytical construction of Lyapunov functions for a large family of autocatalytic pathways.

The results of our analysis reveal fundamental tradeoffs between performance and robustness, energy efficiency, pathway evolvability and computational complexity in these networks.

Thesis Files