title: A mathematical model of mitochondrial swelling.
abstract: BACKGROUND
  The permeabilization of mitochondrial membranes is a decisive event in apoptosis or necrosis culminating in cell death. One fundamental mechanism by which such permeabilization events occur is the calcium-induced mitochondrial permeability transition. Upon Ca2+-uptake into mitochondria an increase in inner membrane permeability occurs by a yet unclear mechanism. This leads to a net water influx in the mitochondrial matrix, mitochondrial swelling, and finally the rupture of the outer membrane. Although already described more than thirty years ago, many unsolved questions surround this important biological phenomenon. Importantly, theoretical modeling of the mitochondrial permeability transition has only started recently and the existing mathematical models fail to characterize the swelling process throughout the whole time range.
  
  
  RESULTS
  We propose here a new mathematical approach to the mitochondrial permeability transition introducing a specific delay equation and resulting in an optimized representation of mitochondrial swelling. Our new model is in accordance with the experimentally determined course of volume increase throughout the whole swelling process, including its initial lag phase as well as its termination. From this new model biological consequences can be deduced, such as the confirmation of a positive feedback of mitochondrial swelling which linearly depends on the Ca2+-concentration, or a negative exponential dependence of the average swelling time on the Ca2+-concentration. Finally, our model can show an initial shrinking phase of mitochondria, which is often observed experimentally before the actual swelling starts.
  
  
  CONCLUSIONS
  We present a model of the mitochondrial swelling kinetics. This model may be adapted and extended to diverse other inducing/inhibiting conditions or to mitochondria from other biological sources and thus may benefit a better understanding of the mitochondrial permeability transition.
authors.affiliation: Institute of Biomathematics and Biometry, Helmholtz Zentrum München, German Research Center for Environmental Health, Ingolstädter Landstrasse 1, 85764 Neuherberg, Germany. sabine.eisenhofer@googlemail.com.
authors.forename: Sabine
authors.initials: S
authors.lastname: Eisenhofer
authors.forename: Ferenc
authors.initials: F
authors.lastname: Toókos
authors.forename: Burkhard A
authors.initials: BA
authors.lastname: Hense
authors.forename: Sabine
authors.initials: S
authors.lastname: Schulz
authors.forename: Frank
authors.initials: F
authors.lastname: Filbir
authors.forename: Hans
authors.initials: H
authors.lastname: Zischka