Numerical methods to determine calcium release flux from calcium transients in muscle cells

Several methods are currently in use to estimate the rate of depolarization-induced calcium release in muscle cells from measured calcium transients. One approach first characterizes calcium removal of the cell. This is done by determining parameters of a reaction scheme from a fit to the decay of elevated calcium after the depolarizing stimulus. In a second step, the release rate during depolarization is estimated based on the fitted model. Using simulated calcium transients with known underlying release rates, we tested the fidelity of this analysis in determining the time course of calcium release under different conditions. The analysis reproduced in a satisfactory way the characteristics of the input release rate, even when the assumption that release had ended before the start of the fitting interval was severely violated. Equally good reconstructions of the release rate time course could be obtained when the model used for the analysis differed in structure from the one used for simulating the data. We tested the application of a new strategy (multiple shooting) for fitting parameters in nonlinear differential equation systems. This procedure rendered the analysis less sensitive to ill-chosen initial guesses of the parameters and to noise. A locally adaptive kernel estimator for calculating numerical derivatives allowed good reconstructions of the original release rate time course from noisy calcium transients when other methods failed.