Unifying principles of calcium wave propagation - Insights from a three-dimensional model for atrial myocytes

Atrial myocytes in a number of species lack transverse tubules. As a consequence the intracellular calcium signals occurring during each heartbeat exhibit complex spatio-temporal dynamics. These calcium patterns arise from saltatory calcium waves that propagate via successive rounds of diffusion and calcium-induced calcium release. The many parameters that impinge on calcium-induced calcium release and calcium signal propagation make it difficult to know a priori whether calcium waves will successfully travel, or be extinguished. In this study, we describe in detail a mathematical model of calcium signalling that allows the effect of such parameters to be independently assessed. A key aspect of the model is to follow the triggering and evolution of calcium signals within a realistic three-dimensional cellular volume of an atrial myocyte, but with low computational costs. This is achieved by solving the linear transport equation for calcium analytically between calcium release events and by expressing the onset of calcium liberation as a threshold process. The model makes non-intuitive predictions about calcium signal propagation. For example, our modelling illustrates that the boundary of a cell produces a wave-guiding effect that enables calcium ions to propagate further and for longer, and can subtly alter the pattern of calcium wave movement. The high spatial resolution of the modelling framework allows the study of any arrangement of calcium release sites. We demonstrate that even small variations in randomly positioned release sites cause highly heterogeneous cellular responses. This article is part of a Special Issue entitled: 13th European Symposium on Calcium.