Mathematical Modeling of Mitochondrial Swelling
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Beschreibung
The mathematical models considered in this book can help to understand the swelling of mitochondria. For the first time, it presents new mathematical models of mitochondrial swelling that take into account, in particular, spatial effects. The results presented here could make it possible to predict properties of the underlying biological mechanisms. Taking into account that mitochondria could move within a cell, lead to a PDE-PDE model. The book discusses the well-posedness and long-term dynamics of solutions, depending on boundary conditions reflecting the in vitro and in vivo cases. These analytical and numerical results have inspired colleagues from the Institute of Pharmacology and Toxicology of the Helmholtz Center Munich to design new experiments justifying the theoretical and numerical results that are obtained. The book is intended for graduates students and researchers with a solid mathematical background and an interest in cell biology.
The mathematical models considered in this book can help to understand the swelling of mitochondria. For the first time, it presents new mathematical models of mitochondrial swelling that take into account, in particular, spatial effects. The results presented here could make it possible to predict properties of the underlying biological mechanisms. Taking into account that mitochondria could move within a cell, lead to a PDE-PDE model. The book discusses the well-posedness and long-term dynamics of solutions, depending on boundary conditions reflecting the in vitro and in vivo cases. These analytical and numerical results have inspired colleagues from the Institute of Pharmacology and Toxicology of the Helmholtz Center Munich to design new experiments justifying the theoretical and numerical results that are obtained. The book is intended for graduates students and researchers with a solid mathematical background and an interest in cell biology.
Presents new mathematical models of mitochondrial swelling that take into account, for the first time, the spatial effects Proves both the well-posedness of the models under consideration and extensively describes the long-term dynamics with regard to the model data, which is very rarely achieved for such a class of degenerate parabolic type systems (ODE-PDE coupling) Provides mathematical models that can help to understand the swelling of mitochondria
Autor*in
Messoud Efendiev
Themen in »Mathematical Modeling of Mitochondrial Swelling«
35B40 35K45 37N25 swollen mitochondria calcium evolution apoptosis boundary conditions spreading calcium wave reaction-diffusion equations large-time asymptotics well-posedness swelling dynamics classification of limiting profiles degenerate diffusion
Stimmen zu »Mathematical Modeling of Mitochondrial Swelling«
“The mathematical models considered in this book can help to understand the swelling of mitochondria. These models take, for the first time, the spatial effects into account. … This book is intended for graduate students and researchers with a solid mathematical back-ground and interest in cell biology.” (Titus Petrila, zbMATH 1406.92003, 2019)
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