Modelling oscillations of calcium and endoplasmic reticulum transmembrane potential

Intracellular calcium oscillations provide a natural clock that may be of crucial importance for the timing of many cellular processes. Elucidating of the mechanisms underlying these oscillations is of particular interest. The theoretical description presented here extends existing models of calcium oscillations by allowing for two types of proteins differing in their calcium-binding properties. This model reflects experimental findings by considering both a fast calcium-binding process to low-affinity protein binding sites such as found in the N-domains of calmodulin or troponin C and a class of high-affinity calcium binding proteins with slow binding kinetics (e.g., parvalbumin or the C-domains of calmodulin and troponin C). Furthermore, recalling that calcium is mainly stored in small subcompartments of the ER, it is argued that only a small fraction of its overall volume participates in the rapid release and uptake of calcium. The effect of the size of this fraction is studied. The hypothesis saying that any electric potential difference across the ER membrane would be dissipated by the highly permeant ions is critically examined by an analytical estimation based on the electroneutrality condition and by numerical integration of the complete model equations. It is predicted theoretically that the transmembrane potential of the ER calcium stores, which is up to now virtually impossible to determine in experiment, builds up in the millivolt range at physiological concentrations of monovalent ions. The phenomenology of oscillations is studied by numerical integration. The model reproduces experimentally observed values of frequency and amplitude as well as the typical spike-like shape of oscillations. The model reveals also the time course of a shift of the bound Ca2+ population from the low-affinity binding sites to the high-affinity binding sites.