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

Abstract

The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Abstract Atrial myocytes in a number of species lack transverse tubules. As a consequence the intracellular calcium signals occurring during each heart beat 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 a low computational overhead. 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. By being able to follow the evolution of a calcium wave in three dimensions, 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.

What Is Required for Neuronal Calcium Waves? A Numerical Parameter Study

“…These data were further used to derive empirical laws that explain the behavior of the observed calcium dynamics in distinct geometric regimes. As a side note and in agreement with [ 26 ], we also show that the higher spatial dimension (as compared to classical 1D cable models) is indeed required to adequately represent even the most basic properties of calcium wave propagation.…”

“… There are regimes in which abortive calcium waves are initiated (closely below threshold density). Such threshold dependency has previously been introduced in [ 26 ]. Our results confirm the existence of such thresholded regimes and are later quantified by deriving empirical laws.…”

“…4 B does not reach such an upper limit (the trace corresponding to a RyR density of 1.0 does reach a limit, but outside the depicted range). One can conclude that a minimal RyR density is required for stable calcium waves (see also [ 26 ]) if the ER is restricted to specific dendritic volumes. Further investigation of this observation showed that this is due to calcium buffering in the cytosol: If the RyR-supported calcium current through the membrane is too small, too much of the released calcium is buffered and there is not enough left to trigger further release through RyR channels.…”

“…One major question is how the cellular and intracellular architecture can shape and regulate calcium signals that are able to propagate over long distances, for instance in the context of synapse-to-nucleus communication. It was shown in [ 26 ] that variations in the activation of Ca 2+ store release through inositol 1,4,5-trisphosphate (IP 3 ) receptors were able to significantly change the calcium wave patterns. Additionally, the distances between distinct IP 3 receptor clusters and the pump strength were shown to control wave stability and instability [ 37 , 38 ].…”

Computational models of atrial cellular electrophysiology and calcium handling, and their role in atrial fibrillation

“…) and even small variations in randomly positioned Ca 2+ ‐release sites causes highly heterogeneous cellular responses (Thul et al . ), further highlighting the importance of the atrial‐specific subcellular structure in modulating Ca 2+ handling abnormalities.…”