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


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.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:autocatalysis, glycolysis, compositional analysis, tradeoff
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Control and Dynamical Systems
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Doyle, John Comstock
Thesis Committee:
  • Doyle, John Comstock (chair)
  • Murray, Richard M.
  • Marsden, Jerrold E.
  • El-Samad, Hana
Defense Date:18 August 2009
Record Number:CaltechTHESIS:02262010-130618704
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5559
Deposited By: Gentian Buzi
Deposited On:31 Mar 2010 16:30
Last Modified:08 Nov 2019 18:08

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