A reaction-diffusion analysis of energetics in large muscle fibers secondarily evolved for aerobic locomotor function

Abstract

The muscles that power swimming in the blue crab, Callinectes sapidus, grow hypertrophically, such that in juvenile crabs the cell diameters are <60 microm, whereas fibers of the adult crabs often exceed 600 microm. Thus, as these animals grow, their muscle fibers greatly exceed the surface area to volume ratio and intracellular diffusion distance limits of most cells. Previous studies have shown that arginine phosphate (AP) recovery in the anaerobic (light) fibers, which demonstrate a fiber size dependence on anaerobic processes following contraction, is too slow to be restricted by intracellular metabolite diffusive flux, in spite of the fiber's large size. By contrast, the aerobic (dark) fibers have evolved an intricate network of intracellular subdivisions that maintain an effectively small ;metabolic diameter' throughout development. In the present study, we examined the impact of intracellular metabolite diffusive flux on the rate of post-contractile AP resynthesis in the dark muscle, which has a much higher aerobic capacity than the light muscle. AP recovery was measured for 60 min in adults and 15 min in juveniles following burst contractile activity in dark fibers, and a mathematical reaction-diffusion model was used to test whether the observed aerobic rates of AP resynthesis were fast enough to be limited by intracellular metabolite diffusion. Despite the short diffusion distances and high mitochondrial density, the AP recovery rates were relatively slow and we found no evidence of diffusion limitation. However, during simulation of steady-state contraction, which is an activity more typical of the dark fibers, there were substantial intracellular metabolite gradients, indicative of diffusion limitation. This suggests that high ATP turnover rates may lead to diffusion limitation in muscle even when diffusion distances are short, as in the subdivided dark fibers.