Stochastic model of IP3-induced Ca2+ spiking of HEK293 cells

Mathematical theory that accounts for the stochastic character of spike sequences of IP3-induced Ca2+ signalling calculates the probability distributions of the features of the [Ca2+]i time course, their moments and correlations. Including slow feedback from [Ca2+]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 (IP3R) 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 Ca2+-induced Ca2+ release (CICR) and the measured non-linear IP3-dependency of the open probability as part of the dynamic feedback. Our theory can calculate spike amplitude distributions, correlation coefficients (Cc) 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 Ccs 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 Ccs, which indicate feedback that decreases the open probability of IP3R 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.Author summary: Ca2+ is a versatile second messenger. Ca2+ signals show stochastic spike timing and large cell variability despite their signal transmission function. Spike train properties, which are not subject to cell variability and thus define the system, are related to noise. Hence, the first step in theoretical comprehension must be a stochastic theory. This study reports on progress in developing that theory and on experimental results. The application to Ca2+ signals in HEK293 cells meets basic expectations and, in part, explains the surprising results on ISI-amplitude correlations. The measured anticorrelation requires us to expand our ideas on feedback during spiking and the corresponding stochastic theory. Once we understand the role of fluctuations, we may also derive deterministic approximations for simulating averages.