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Mathematics > Optimization and Control

arXiv:1808.08263 (math)
[Submitted on 24 Aug 2018 (v1), last revised 28 Mar 2019 (this version, v2)]

Title:Stability of Metabolic Networks via Linear-In-Flux-Expressions

Authors:Nathaniel J. Merrill, Zheming An, Sean T. McQuade, Federica Garin, Karim Azer, Ruth E. Abrams, Benedetto Piccoli
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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.
Comments: 30 pages, 6 figures
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1808.08263 [math.OC]
  (or arXiv:1808.08263v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1808.08263
Related DOI: https://doi.org/10.3934/nhm.2019006

Submission history

From: Zheming An [view email]
[v1] Fri, 24 Aug 2018 18:41:16 UTC (574 KB)
[v2] Thu, 28 Mar 2019 16:18:15 UTC (56 KB)
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