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Analysis of autocatalytic networks in biology

Buzi, Gentian and Topcu, Ufuk and Doyle, John C. (2011) Analysis of autocatalytic networks in biology. Automatica, 47 (6). pp. 1123-1130. ISSN 0005-1098.

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Autocatalytic networks, in particular the glycolytic pathway, constitute an important part of the cell metabolism. Changes in the concentration of metabolites and catalyzing enzymes during the lifetime of the cell can lead to perturbations from its nominal operating condition. We investigate the effects of such perturbations on stability properties, e.g., the extent of regions of attraction, of a particular family of autocatalytic network models. Numerical experiments demonstrate that systems that are robust with respect to perturbations in the parameter space have an easily "verifiable" (in terms of proof complexity) region of attraction properties. Motivated by the computational complexity of optimization-based formulations, we take a compositional approach and exploit a natural decomposition of the system, induced by the underlying biological structure, into a feedback interconnection of two input–output subsystems: a small subsystem with complicating nonlinearities and a large subsystem with simple dynamics. This decomposition simplifies the analysis of large pathways by assembling region of attraction certificates based on the input–output properties of the subsystems. It enables numerical as well as analytical construction of block-diagonal Lyapunov functions for a large family of autocatalytic pathways.

Item Type:Article
Related URLs:
URLURL TypeDescription
Buzi, Gentian0000-0002-8724-3405
Doyle, John C.0000-0002-1828-2486
Additional Information:© 2011 Elsevier Ltd. Received 1 February 2010; revised 21 January 2011; accepted 2 February 2011. Available online 21 March 2011. This work was supported by the NIH (award# R01 GM078992A), the Institute of Collaborative Biotechnologies from the U.S. Army Research Office (UCSB award# KK9150, ARO prime award# W911NF-09-D-0001), and AFOSR (FA9550-08-1-0043). The material in this paper was partially presented at the 2010 American Control Conference, June 30–July 2, 2010, Baltimore, Maryland, USA. This paper was recommended for publication in revised form by Associate Editor Elling Jacobsen under the direction of Editor Frank Allgöwer.
Funding AgencyGrant Number
NIHR01 GM078992A
Army Research Office (ARO)KK9150
Army Research Office (ARO)W911NF-09-D-0001
Air Force Office of Scientific Research (AFOSR)FA9550-08-1-0043
Subject Keywords:Autocatalytic pathways; Glycolysis; Quantitative analysis; Compositional analysis; Nonlinear systems
Issue or Number:6
Record Number:CaltechAUTHORS:20110624-104150056
Persistent URL:
Official Citation:Gentian Buzi, Ufuk Topcu, John C. Doyle, Analysis of autocatalytic networks in biology, Automatica, Volume 47, Issue 6, Special Issue on Systems Biology, June 2011, Pages 1123-1130, ISSN 0005-1098, DOI: 10.1016/j.automatica.2011.02.040. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24202
Deposited By: Tony Diaz
Deposited On:24 Jun 2011 18:52
Last Modified:09 Mar 2020 13:18

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