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Analysis of a Mathematical Model for the Glutamate/Glutamine Cycle in the Brain

Bulletin of Mathematical Biology volume 81, pages 4251–4270 (2019)Cite this article

Abstract

Our aim in this article is to study the well-posedness and properties of a system with delay which is related with brain glutamate and glutamine kinetics. In particular, we prove the existence and uniqueness of nonnegative solutions. We also give numerical simulations and compare their order of magnitude with experimental data.

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Affiliations

  1. Laboratoire de Mathématiques et Applications, UMR CNRS 7348, SP2MI, Equipe DACTIM-MIS, Université de Poitiers, Boulevard Marie et Pierre Curie - Téléport 2, 86962, Chasseneuil Futuroscope Cedex, France

    A. Perrillat-Mercerot, C. Guillevin, A. Miranville & R. Guillevin

  2. Laboratoire Signalisation et Transports Ioniques Membranaires, ERL CNRS 7003, Equipe 4CS, CHU de Poitiers, Université de Poitiers, 2 Rue de la Milétrie, 86021, Poitiers, France

    N. Bourmeyster

  3. CHU de Poitiers, 2 Rue de la Milétrie, 86021, Poitiers, France

    C. Guillevin & R. Guillevin

Authors
  1. A. Perrillat-Mercerot
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  2. N. Bourmeyster
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  3. C. Guillevin
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  4. A. Miranville
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  5. R. Guillevin
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Corresponding author

Correspondence to A. Miranville.

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Perrillat-Mercerot, A., Bourmeyster, N., Guillevin, C. et al. Analysis of a Mathematical Model for the Glutamate/Glutamine Cycle in the Brain. Bull Math Biol 81, 4251–4270 (2019). https://doi.org/10.1007/s11538-019-00647-4

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  • DOI: https://doi.org/10.1007/s11538-019-00647-4

Keywords

  • Brain glutamate/glutamine cycle
  • Substrate kinetics
  • System with delay
  • Regularity
  • Well-posedness
  • Linear stability
  • Simulations

Mathematics Subject Classification

  • 34A34
  • 35B09
  • 35Q92