Equilibria and control of metabolic networks with enhancers and inhibitors

Zheming An; Nathaniel J. Merrill; Sean T. McQuade; Benedetto Piccoli; Zheming An; Nathaniel J. Merrill; Sean T. McQuade; Benedetto Piccoli

doi:10.3934/mine.2019.3.648

Mathematics in Engineering

2019, Volume 1, Issue 3: 648-671. doi: 10.3934/mine.2019.3.648

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Research article Special Issues

Equilibria and control of metabolic networks with enhancers and inhibitors

1.
Center for Computational and Integrative Biology, Rutgers Camden. Camden NJ USA
2.
Joseph and Loretta Lopez chair professor of Mathematics

Received: 12 February 2019 Accepted: 30 June 2019 Published: 01 August 2019

Linear-In-Flux-Expressions (briefly LIFE) methodology models metabolism by using correlations among fluxes of metabolic networks and reducing the number of model parameters. These correlations are calculated for an equilibrium state and developed to include tools from the fields of network flows, compartmental systems, Markov chains, and control theory. LIFE methodology was developed with pharmacology simulators in mind, and the present study advances this goal, by focusing on the control of metabolic networks and inclusion of enhancers and inhibitors. We consider two control problems on metabolic networks: 1. The optimization of intakes from the outside environment to drive the system to a desired state, and 2. The inclusion of inhibitors and enhancers and their optimization. Simulations are included to test the approach on these more complex networks.
- systems biology,
- flows on graphs,
- control,
- ordinary differential equations
Citation: Zheming An, Nathaniel J. Merrill, Sean T. McQuade, Benedetto Piccoli. Equilibria and control of metabolic networks with enhancers and inhibitors[J]. Mathematics in Engineering, 2019, 1(3): 648-671. doi: 10.3934/mine.2019.3.648

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Abstract

Linear-In-Flux-Expressions (briefly LIFE) methodology models metabolism by using correlations among fluxes of metabolic networks and reducing the number of model parameters. These correlations are calculated for an equilibrium state and developed to include tools from the fields of network flows, compartmental systems, Markov chains, and control theory. LIFE methodology was developed with pharmacology simulators in mind, and the present study advances this goal, by focusing on the control of metabolic networks and inclusion of enhancers and inhibitors. We consider two control problems on metabolic networks: 1. The optimization of intakes from the outside environment to drive the system to a desired state, and 2. The inclusion of inhibitors and enhancers and their optimization. Simulations are included to test the approach on these more complex networks.

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