Diffusion restrictions surrounding mitochondria: a mathematical model of heart muscle fibers.

Several experiments on permeabilized heart muscle fibers suggest the existence of diffusion restrictions grouping mitochondria and surrounding ATPases. The specific causes of these restrictions are not known, but intracellular structures are speculated to act as diffusion barriers. In this work, we assume that diffusion restrictions are induced by sarcoplasmic reticulum (SR), cytoskeleton proteins localized near SR, and crowding of cytosolic proteins. The aim of this work was to test whether such localization of diffusion restrictions would be consistent with the available experimental data and evaluate the extent of the restrictions. For that, a three-dimensional finite-element model was composed with the geometry based on mitochondrial and SR structural organization. Diffusion restrictions induced by SR and cytoskeleton proteins were varied with other model parameters to fit the set of experimental data obtained on permeabilized rat heart muscle fibers. There are many sets of model parameters that were able to reproduce all experiments considered in this work. However, in all the sets, <5-6% of the surface formed by SR and associated cytoskeleton proteins is permeable to metabolites. Such a low level of permeability indicates that the proteins should play a dominant part in formation of the diffusion restrictions.