Mathematical analysis of an in vivo model of mitochondrial swelling

Messoud Efendiev; Mitsuharu Otani; Hermann J. Eberl

doi:10.3934/dcds.2017176

Mathematical analysis of an in vivo model of mitochondrial swelling

Messoud Efendiev^*, Mitsuharu Otani, Hermann J. Eberl

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We analyze the effect of Robin boundary conditions in a mathematical model for a mitochondria swelling in a living organism. This is a coupled PDE/ODE model for the dependent variables calcium ion contration and three fractions of mitochondria that are distinguished by their state of swelling activity. The model assumes that the boundary is a permeable membrane', through which calcium ions can both enter or leave the cell. Under biologically relevant assumptions on the data, we prove the well-posedness of solutions of the model and study the asymptotic behavior of its solutions. We augment the analysis of the model with computer simulations that illustrate the theoretically obtained results.

Original language	English
Pages (from-to)	4131-4158
Number of pages	28
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	37
Issue number	7
DOIs	https://doi.org/10.3934/dcds.2017176
Publication status	Published - 2017 Jul 1

Keywords

Longtim dynamics
Mitochondria
Partial and complete swelling
PDE/ODE coupling
Robin boundary conditions

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2017176

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title = "Mathematical analysis of an in vivo model of mitochondrial swelling",

abstract = "We analyze the effect of Robin boundary conditions in a mathematical model for a mitochondria swelling in a living organism. This is a coupled PDE/ODE model for the dependent variables calcium ion contration and three fractions of mitochondria that are distinguished by their state of swelling activity. The model assumes that the boundary is a permeable membrane', through which calcium ions can both enter or leave the cell. Under biologically relevant assumptions on the data, we prove the well-posedness of solutions of the model and study the asymptotic behavior of its solutions. We augment the analysis of the model with computer simulations that illustrate the theoretically obtained results.",

keywords = "Longtim dynamics, Mitochondria, Partial and complete swelling, PDE/ODE coupling, Robin boundary conditions",

author = "Messoud Efendiev and Mitsuharu Otani and Eberl, {Hermann J.}",

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T1 - Mathematical analysis of an in vivo model of mitochondrial swelling

AU - Efendiev, Messoud

AU - Otani, Mitsuharu

AU - Eberl, Hermann J.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We analyze the effect of Robin boundary conditions in a mathematical model for a mitochondria swelling in a living organism. This is a coupled PDE/ODE model for the dependent variables calcium ion contration and three fractions of mitochondria that are distinguished by their state of swelling activity. The model assumes that the boundary is a permeable membrane', through which calcium ions can both enter or leave the cell. Under biologically relevant assumptions on the data, we prove the well-posedness of solutions of the model and study the asymptotic behavior of its solutions. We augment the analysis of the model with computer simulations that illustrate the theoretically obtained results.

AB - We analyze the effect of Robin boundary conditions in a mathematical model for a mitochondria swelling in a living organism. This is a coupled PDE/ODE model for the dependent variables calcium ion contration and three fractions of mitochondria that are distinguished by their state of swelling activity. The model assumes that the boundary is a permeable membrane', through which calcium ions can both enter or leave the cell. Under biologically relevant assumptions on the data, we prove the well-posedness of solutions of the model and study the asymptotic behavior of its solutions. We augment the analysis of the model with computer simulations that illustrate the theoretically obtained results.

KW - Longtim dynamics

KW - Mitochondria

KW - Partial and complete swelling

KW - PDE/ODE coupling

KW - Robin boundary conditions

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M3 - Article

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

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Mathematical analysis of an in vivo model of mitochondrial swelling

Abstract

Keywords

ASJC Scopus subject areas

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