Oxygen control of intracellular distribution of mitochondria in muscle fibers.

Mitochondrial density in skeletal muscle fibers is governed by the demand for aerobic ATP production, but the heterogeneous distribution of these mitochondria appears to be governed by constraints associated with oxygen diffusion. We propose that each muscle fiber has an optimal mitochondrial distribution at which it attains a near maximal rate of ATP consumption (RATPase ) while mitochondria are exposed to a minimal oxygen concentration, thus minimizing reactive oxygen species (ROS) production. We developed a coupled reaction-diffusion/cellular automata (CA) mathematical model of mitochondrial function and considered four fiber types in mouse extensor digitorum longus (EDL) and soleus (SOL) muscle. The developed mathematical model uses a reaction-diffusion analysis of metabolites including oxygen, ATP, ADP, phosphate, and phosphocreatine (PCr) involved in energy metabolism and mitochondrial function. A CA approach governing mitochondrial life cycles in response to the metabolic state of the fiber was superimposed and coupled to the reaction-diffusion approach. The model results show the sensitivity of important model outputs such as the RATPase , effectiveness factor (η) and average oxygen concentration available at each mitochondrion to local oxygen concentration in the fibers through variation in the CA model parameter θdet , which defines the sensitivity of mitochondrial death to the oxygen concentration. The predicted optimal mitochondrial distributions matched previous experimental findings. Deviations from this optimal distribution corresponding to higher CA model parameter values (a more uniform mitochondrial distribution) lead to lower aerobic rates. In contrast, distributions corresponding to lower CA model parameter values (a more asymmetric distribution) lead to an increased exposure of mitochondria to oxygen, usually without substantial increases in aerobic rates, which would presumably result in increased ROS production and thus increased risks of cytotoxicity.

The formation and functional consequences of heterogeneous mitochondrial distributions in skeletal muscle.

Diffusion plays a prominent role in governing both rates of aerobic metabolic fluxes and mitochondrial organization in muscle fibers. However, there is no mechanism to explain how the non-homogeneous mitochondrial distributions that are prevalent in skeletal muscle arise. We propose that spatially variable degradation with dependence on O(2) concentration, and spatially uniform signals for biogenesis, can account for observed distributions of mitochondria in a diversity of skeletal muscle. We used light and transmission electron microscopy and stereology to examine fiber size, capillarity and mitochondrial distribution in fish red and white muscle, fish white muscle that undergoes extreme hypertrophic growth, and four fiber types in mouse muscle. The observed distributions were compared with those generated using a coupled reaction-diffusion/cellular automata (CA) mathematical model of mitochondrial function. Reaction-diffusion analysis of metabolites such as oxygen, ATP, ADP and PCr involved in energy metabolism and mitochondrial function were considered. Coupled to the reaction-diffusion approach was a CA approach governing mitochondrial life cycles in response to the metabolic state of the fiber. The model results were consistent with the experimental observations and showed higher mitochondrial densities near the capillaries because of the sometimes steep gradients in oxygen. The present study found that selective removal of mitochondria in the presence of low prevailing local oxygen concentrations is likely the primary factor dictating the spatial heterogeneity of mitochondria in a diversity of fibers. The model results also suggest decreased diffusional constraints corresponding to the heterogeneous mitochondrial distribution assessed using the effectiveness factor, defined as the ratio of the reaction rate in the system with finite rates of diffusion to that in the absence of any diffusion limitation. Thus, the non-uniform distribution benefits the muscle fiber by increasing the energy status and increasing sustainable metabolic rates.

Influence of reaction and diffusion on spatial organization of mitochondria and effectiveness factors in skeletal muscle cell design.

A mathematical model is developed to analyze the influence of chemical reaction and diffusion processes on the intracellular organization of mitochondria in skeletal muscle cells. The mathematical modeling approach uses a reaction-diffusion analysis of oxygen, ATP, and ADP involved in energy metabolism and mitochondrial function as governed by oxygen supply, volume fraction of mitochondria, and rates of reaction. Superimposed upon and coupled to the continuum species material balances is a cellular automata (CA) approach governing mitochondrial life cycles in response to the metabolic state of the cell. The effectiveness factor (η), defined as the ratio of reaction rate in the system with finite rates of diffusion to those in the absence of any diffusion limitation is used to assess diffusional constraints in muscle cells. The model shows the dramatic effects that the governing parameters have on the mitochondrial cycle of life and death and how these effects lead to changes in the distribution patterns of mitochondria observed experimentally. The model results showed good agreement with experimental results on mitochondrial distributions in mammalian muscle fibers. The η increases as the mitochondrial population is redistributed toward the fiber periphery in response to a decreased availability of oxygen. Modification of the CA parameters so that the mitochondrial lifecycle is more sensitive to the oxygen concentration caused larger mitochondrial shifts to the edge of the cell with smaller changes in oxygen concentration, and thus also lead to increased values of η. The present study shows that variation in oxygen supply, muscle activity and mitochondrial ATP supply influence the η and are the important parameters that can cause diffusion limitations. In order to prevent diffusion constraints, the cell resorts to shifts in their mitochondrial population towards the cell periphery, thus increasing η.