On an ODE-PDE coupling model of the mitochondrial swelling process

Sabine Eisenhofer; Messoud A. Efendiev; Mitsuharu Ôtani; Sabine Schulz; Hans Zischka

doi:10.3934/dcdsb.2015.20.1031

Article Contents

2015, Volume 20, Issue 4: 1031-1057. Doi: 10.3934/dcdsb.2015.20.1031

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On an ODE-PDE coupling model of the mitochondrial swelling process

1.
Institute of Computational Biology, Helmholtz Center Munich, Ingolstädter, Landstrasse 1, 85764 Neuherberg
2.
Helmholtz Zentrum München, Institute of Computational Biology, Ingolstädter Landstrasse1, D-85764 Neuherberg,
3.
Department of Applied Physics, Waseda University, 3-4-1, Okubo, Tokyo, 169-8555
4.
Institute of Molecular Toxicology and Pharmscology, Helmholtz Center Munich, Ingolstädter, Landstrasse 1, 85764 Neuherberg

Received: May 31, 2013

Revised: July 31, 2014

Published: May 2015

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Abstract

Mitochondrial swelling has huge impact to multicellular organisms since it triggers apoptosis, the programmed cell death. In this paper we present a new mathematical model of this phenomenon. As a novelty it includes spatial effects, which are of great importance for the in vivo process. Our model considers three mitochondrial subpopulations varying in the degree of swelling. The evolution of these groups is dependent on the present calcium concentration and is described by a system of ODEs, whereas the calcium propagation is modeled by a reaction-diffusion equation taking into account spatial effects. We analyze the derived model with respect to existence and long-time behavior of solutions and obtain a complete mathematical classification of the swelling process.

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Mathematics Subject Classification: Primary: 35B40, 35K57, 37N25; Secondary: 92B05.

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