Abstract
Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding is achieved, we still lack a comprehensive theory. To achieve this goal it is necessary to reliably predict the temporal evolution of calcium spike sequences for a given stimulus. Here, we propose a modelling framework that allows us to quantitatively describe the timing of calcium spikes. Using a Bayesian approach, we show that Gaussian processes model calcium spike rates with high fidelity and perform better than standard tools such as peri-stimulus time histograms and kernel smoothing. We employ our modelling concept to analyse calcium spike sequences from dynamically-stimulated HEK293T cells. Under these conditions, different cells often experience diverse stimulus time courses, which is a situation likely to occur in vivo. This single cell variability and the concomitant small number of calcium spikes per cell pose a significant modelling challenge, but we demonstrate that Gaussian processes can successfully describe calcium spike rates in these circumstances. Our results therefore pave the way towards a statistical description of heterogeneous calcium oscillations in a dynamic environment.
Highlights
Transient changes in the intracellular calcium (Ca2+) concentration have long been associated with the activation of plasma membrane receptors [1]
They demonstrate that the slopes obtained from individual cells are concentrated close to 1 and exhibit a significantly smaller variability for the inhomogeneous Gamma (IG) compared to the inhomogeneous Poisson (IP) and inhomogeneous inverse Gaussian (IIG)
In this work we have developed a mathematical framework to quantitatively describe the heterogeneous timing of Ca2+ spikes in a cell population subject to time-varying stimulation
Summary
Transient changes in the intracellular calcium (Ca2+) concentration have long been associated with the activation of plasma membrane receptors [1]. Ca2+ oscillations are usually observed as sequences of spikes of the intracellular Ca2+ concentration. A prominent feature of Ca2+ spike sequences is that they are random. Ca2+ spikes only occur with some probability that generally changes over time. There are distributions of inter-spike intervals (ISIs) for agonist induced Ca2+ oscillations in HEK293 cells and spontaneous Ca2+ oscillations in astrocytes, microglia and PLA cells instead of a single value [15]. When astrocytes are transiently stimulated with ATP three times, with a recovery period between stimuli, the observed Ca2+ spikes display any number of response patterns, from no spikes to three [16]. To elucidate the principles that govern the translation of extracellular cues into changes of the intracellular Ca2+ concentration requires faithfully capturing the stochasticity in Ca2+ spike generation
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