A Bayesian approach to modelling heterogeneous calcium responses in cell populations

• Published in: PLoS computational biology Vol. 13; no. 10; p. e1005794
• Main Authors: Tilūnaitė, Agne, Croft, Wayne, Russell, Noah, Bellamy, Tomas C, Thul, Rüdiger
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01-10-2017; Public Library of Science (PLoS)
• Subjects: Action Potentials - drug effects; Action Potentials - physiology; Artificial intelligence; Bayes Theorem; Bayesian analysis; Biology and Life Sciences; Calcium; Calcium - metabolism; Calcium ions; Calcium Signaling - drug effects; Calcium Signaling - physiology; Calcium signalling; Carbachol - pharmacology; Cellular signal transduction; Cholinergic Agonists - pharmacology; Earthquakes; Engineering and Technology; Funding; Gaussian process; HEK293 Cells; Histograms; Humans; Information processing; Life sciences; Medicine and Health Sciences; Methods; Modelling; Models, Biological; Neural networks; Neurosciences; Partial differential equations; Physical Sciences; Physiological aspects; Signal transduction; Single-Cell Analysis - methods; Spikes; Studies; Time Factors; United Kingdom > UK; England
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1005794

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.