Comparison of simulated and measured calcium sparks in intact skeletal muscle fibers of the frog.

Calcium sparks in frog intact skeletal muscle fibers were modeled as stereotypical events that arise from a constant efflux of Ca(2+) from a point source for a fixed period of time (e.g., 2.5 pA of Ca(2+) current for 4.6 ms; 18 degrees C). The model calculates the local changes in the concentrations of free Ca(2+) and of Ca(2+) bound to the major intrinsic myoplasmic Ca(2+) buffers (troponin, ATP, parvalbumin, and the SR Ca(2+) pump) and to the Ca(2+) indicator (fluo-3). A distinctive feature of the model is the inclusion of a binding reaction between fluo-3 and myoplasmic proteins, a process that strongly affects fluo-3's Ca(2+)-reaction kinetics, its apparent diffusion constant, and hence the morphology of sparks. DeltaF/F (the change in fluo-3's fluorescence divided by its resting fluorescence) was estimated from the calculated changes in fluo-3 convolved with the microscope point-spread function. To facilitate comparisons with measured sparks, noise and other sources of variability were included in a random repetitive fashion to generate a large number of simulated sparks that could be analyzed in the same way as the measured sparks. In the initial simulations, the binding of Ca(2+) to the two regulatory sites on troponin was assumed to follow identical and independent binding reactions. These simulations failed to accurately predict the falling phase of the measured sparks. A second set of simulations, which incorporated the idea of positive cooperativity in the binding of Ca(2+) to troponin, produced reasonable agreement with the measurements. Under the assumption that the single channel Ca(2+) current of a ryanodine receptor (RYR) is 0.5-2 pA, the results suggest that 1-5 active RYRs generate an average Ca(2+) spark in a frog intact muscle fiber.