Stability of metabolic networks via Linear-in-Flux-Expressions

Nathaniel J. Merrill; Zheming An; Sean T. McQuade; Federica Garin; Karim Azer; Ruth E. Abrams; Benedetto Piccoli; Nathaniel J. Merrill; Zheming An; Sean T. McQuade; Federica Garin; Karim Azer; Ruth E. Abrams; Benedetto Piccoli

doi:10.3934/nhm.2019006

Networks and Heterogeneous Media

2019, Volume 14, Issue 1: 101-130. doi: 10.3934/nhm.2019006

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Stability of metabolic networks via Linear-in-Flux-Expressions

1.
Center for Computational and Integrative Biology, Rutgers Camden. Camden NJ, USA
2.
Researcher, Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, GIPSA-lab. Grenoble, France
3.
Bill & Melinda Gates Medical Research Institute, 245 Main Street Kendall Square. Cambridege, MA 02142, USA
4.
Senior scientist, Translational Informatics, Sanofi. Bridgewater NJ, USA
5.
Joseph and Loretta Lopez chair professor of Mathematics, Center for Computational and Integrative Biology, Rutgers Camden. Camden NJ, USA

Received: 01 June 2018
Primary: 92C42, 05C21; Secondary: 93B99, 34H99

The methodology named LIFE (Linear-in-Flux-Expressions) was developed with the purpose of simulating and analyzing large metabolic systems. With LIFE, the number of model parameters is reduced by accounting for correlations among the parameters of the system. Perturbation analysis on LIFE systems results in less overall variability of the system, leading to results that more closely resemble empirical data. These systems can be associated to graphs, and characteristics of the graph give insight into the dynamics of the system.
This work addresses two main problems: 1. for fixed metabolite levels, find all fluxes for which the metabolite levels are an equilibrium, and 2. for fixed fluxes, find all metabolite levels which are equilibria for the system. We characterize the set of solutions for both problems, and show general results relating stability of systems to the structure of the associated graph. We show that there is a structure of the graph necessary for stable dynamics. Along with these general results, we show how stability analysis from the fields of network flows, compartmental systems, control theory and Markov chains apply to LIFE systems.
- Systems biology,
- flows in graphs,
- systems theory,
- control,
- ordinary differential equations
Citation: Nathaniel J. Merrill, Zheming An, Sean T. McQuade, Federica Garin, Karim Azer, Ruth E. Abrams, Benedetto Piccoli. Stability of metabolic networks via Linear-in-Flux-Expressions[J]. Networks and Heterogeneous Media, 2019, 14(1): 101-130. doi: 10.3934/nhm.2019006

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Abstract

The methodology named LIFE (Linear-in-Flux-Expressions) was developed with the purpose of simulating and analyzing large metabolic systems. With LIFE, the number of model parameters is reduced by accounting for correlations among the parameters of the system. Perturbation analysis on LIFE systems results in less overall variability of the system, leading to results that more closely resemble empirical data. These systems can be associated to graphs, and characteristics of the graph give insight into the dynamics of the system.

This work addresses two main problems: 1. for fixed metabolite levels, find all fluxes for which the metabolite levels are an equilibrium, and 2. for fixed fluxes, find all metabolite levels which are equilibria for the system. We characterize the set of solutions for both problems, and show general results relating stability of systems to the structure of the associated graph. We show that there is a structure of the graph necessary for stable dynamics. Along with these general results, we show how stability analysis from the fields of network flows, compartmental systems, control theory and Markov chains apply to LIFE systems.

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