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.
Highlights
Biological background Mitochondria are often termed the cell’s powerhouse due to their main function as energy supplier for almost all eukaryotic cells [1]
The calcium diffusion occurs slower than the development of the mitochondrial populations and the constant state is reached later (t = 4100 for the calcium evolution, t = 1900 for the mitochondrial populations)
If we compare the dynamics with those of simple diffusion without any feedback, the resulting calcium evolution induced by mitochondrial swelling is completely different
Summary
Biological background Mitochondria are often termed the cell’s powerhouse due to their main function as energy supplier for almost all eukaryotic cells [1] These double-membrane enclosed organelles play a decisive role in cell death by their ability to trigger apoptosis. The increased permeability leads to an osmotically driven influx of solutes and water into the mitochondrial matrix, which in turn causes swelling [8], [14]. This process culminates in the rupture of the outer membrane [20]. Outer membrane rupture denotes a critical event, since apoptosis is irreversibly triggered by the release of several proapoptotic factors from the intermembrane space [15]
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