Mathematical theory that accounts for the stochastic character of spike sequences of IP 3 -induced Ca 2+ signalling calculates the probability distributions of the features of the Ca 2+ i time course, their moments and correlations. Including slow feedback from Ca 2+ i to components of the pathway poses a challenge to stochastic modelling. Here, we present a stochastic model that takes this feedback into account, allows for a non-linear dependency of the open probability of the Inositol 1,4,5-trisphosphate receptor channel (IP 3 R) on the feedback variable and the inclusion of more than one feedback with different relaxation time scales. We use this novel modelling approach to describe the effect of ER depletion by non-linear rate expressions for Ca 2+ -induced Ca 2+ release (CICR) and the measured non-linear IP 3 -dependency of the open probability as part of the dynamic feedback. Our theory can calculate spike amplitude distributions, correlation coefficients (C c ) of interspike intervals (ISIs) and amplitudes, simulate ISI distributions and calculate their moments. We apply it to experiments with HEK293 cells. We find very good agreement between theoretical ISI distributions and their moments with experimental results. Many measured C c s show positive values in accordance with the ideas formulated by our theory. Surprisingly, most ISI-amplitude correlations are weak despite the decay of negative feedback during the ISI, which affects spike probability. We even find negative values of C c s, which indicate feedback that decreases the open probability of IP 3 R with increasing ISI. The components of the pathway causing this anticorrelation have not yet been identified. Our data suggest that they involve components that are subject to cell variability.
Azzoni et al. (2025) studied this question.