Calcium spiking with cumulative refractoriness - statistics of the fluctuations and implications for Calcium signaling

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Calcium is an important signalling molecule which is used in all eukaryotic cells. Calcium signals consist of random local processes (puffs), whose interaction generates global concentration changes (spikes, waves). We can observe both the local events and the global waves in a single experiment. This opportunity to watch the emergence of macroscopic events from microscopic processes renders the system interesting for Physics in general. Calcium signalling exhibits large cell-to-cell variability in many features but also shows properties conserved across the cell population. We would like to understand the relation between microscopic and macroscopic phenomena – puffs and spikes, and how signalling is possible in the face of cell variability and randomness. Calcium spikes have been described as a sequence of events (a point process) with statistically independent intervals between subsequent events (a renewal process). However, the spike generation is subject to an adaptation process, which cannot be captured on the basis of independent inter-event intervals. In this project, we will develop theoretical models for calcium puffs and spikes including cumulative adaptation processes, which are described by a refractory variable. In the analysis of one of our models (multidimensional integrate-and-fire model), we will use methods from theoretical neuroscience developed for neural spiking with pronounced interval correlations. In a parallel approach, we will use discrete stochastic models based on waiting time distributions and develop new analytical methods for their analysis. In addition to addressing the role of variability in calcium signalling, we hope to understand the relation between cell variability and the conserved properties of the cells.