Numerical simulation of Ca(2+) 'sparks' in skeletal muscle

A three-dimensional model of Ca2+ diffusion and binding was developed to simulate numerically the laser scanning confocal microscope images of Ca2+ "sparks" in skeletal muscle. The model was built on an idealized biological structure of the sarcomere within a myofibril and included the Ca 2+ binding sites troponin, parvalbumin, the sarcoplasmic reticulum (SR) Ca2+ pump, and binding of Ca 2+ by the dye fluo-3 with the spatial distributions of troponin and the SR Ca2+ pump restricted to correspond approximately to those in the myofibril of a muscle fiber. The diffusion of free dye (D) and calcium dye (CaD), as well as that of Ca2+ was considered in the model. The differential equation system for diffusion and binding was solved numerically by the finite difference method with a graded discretization network using a computer program coded in Fortran and run on a multiprocessor computer system. Excellent agreement was found in the comparison of the numerical and analytical solutions of the diffusion process under the condition of no binding reactions. Simulated laser scanning confocal images of the calculated distribution of [CaD] were generated by three-dimensional discrete convolution of the results from the diffusion and binding simulation and a Gaussian kernel representing the theoretical point spread function of a confocal microscope. In addition to successfully simulating the stereotyped experimentally measured "sparks", the model has been used to evaluate the effects of changes in the diffusion coefficients of D and CaD and of changes of binding properties of the binding sites on the properties of the "sparks". The difference in the appearance of the "sparks" viewed from different relative positions has also been simulated. The results of the simulation by the model indicate that both the kinetic properties of the binding sites and the diffusion parameters of free and Ca2+-complexed dye have significant effects on the properties of Ca2+ "sparks".