Ca(2+)-activation kinetics modulate successive puff/spark amplitude, duration and inter-event-interval correlations in a Langevin model of stochastic Ca(2+) release

Abstract

Through theoretical analysis of the statistics of stochastic calcium (Ca(2+)) release (i.e., the amplitude, duration and inter-event interval of simulated Ca(2+) puffs and sparks), we show that a Langevin description of the collective gating of Ca(2+) channels may be a good approximation to the corresponding Markov chain model when the number of Ca(2+) channels per Ca(2+) release unit (CaRU) is in the physiological range. The Langevin description of stochastic Ca(2+) release facilitates our investigation of correlations between successive puff/spark amplitudes, durations and inter-spark intervals, and how such puff/spark statistics depend on the number of channels per release site and the kinetics of Ca(2+)-mediated inactivation of open channels. When Ca(2+) inactivation/de-inactivation rates are intermediate-i.e., the termination of Ca(2+) puff/sparks is caused by an increase in the number of inactivated channels-the correlation between successive puff/spark amplitudes is negative, while the correlations between puff/spark amplitudes and the duration of the preceding or subsequent inter-spark interval are positive. These correlations are significantly reduced or change signs when inactivation/de-inactivation rates are extreme (slow or fast) and puff/sparks terminate via stochastic attrition.

Keywords: Ca(2+) puffs; Ca(2+) sparks; Langevin equation; Markov chain.