Sensitivity analysis of reaction-diffusion constraints in muscle energetics

Theoretical and experimental studies of aerobic metabolism on a wide range of skeletal muscle fibers have shown that while all fibers normally function within the reaction control regime, some fibers operate near the transition region where reaction control switches to diffusion control. Thus, the transition region between reaction and diffusion control may define the limits of muscle function, and analysis of factors that affect this transition is therefore needed. In order to assess the role of all important model parameters, a sensitivity analysis (SA) was performed to define the parameter space where muscle fibers transition from reaction to diffusion control. SA, performed on a previously developed reaction-diffusion model, shows that the maximum rate for the ATPase reaction (V(max,ATPase)), boundary oxygen concentration in the capillary supply (O ₂⁰), the mitochondrial volume fraction (ε(mito)), and the diffusion coefficient of oxygen (DO ₂) are the most sensitive parameters affecting this transition to diffusion control. It is demonstrated that fibers are not limited by diffusion for slow reactions (V(max,ATPase)  < 25 mM/min), high oxygen supply for the capillaries (O ₂⁰ ≥ 35 µM), and large amounts of mitochondria (ε(mito) ≥ 0.1). These conditions are applicable to muscle cells spanning a very broad range of animals. Within the diffusion-controlled region, the overall metabolic rate and ATP concentrations have much higher sensitivity to the diffusion coefficient of oxygen than to the diffusion coefficients of the other metabolites (ATP, ADP, P(i)).