Evolution of cardiac calcium waves from stochastic calcium sparks

We present a model that provides a unified framework for studying Ca2+ spar ks and Ca2+ waves in cardiac cells. The model is novel in combining 1) use of large currents (similar to 20 pA) through the Ca2+ release units (CRUs) of the sarcoplasmic reticulum (SR); 2) stochastic Ca2+ release (or firing) of CRUs; 3) discrete, asymmetric distribution of CRUs along the longitudina l (separation distance of 2 mum) and transverse (separated by 0.4-0.8 mum) directions of the cell; and 4) anisotropic diffusion of Ca2+ and fluorescen t indicator to study the evolution of Ca2+ waves from Ca2+ sparks. The mode l mimics the important features of Ca2+ sparks and Ca2+ waves in terms of t he spontaneous spark rate, the Ca2+ wave velocity, and the pattern of wave propagation. Importantly, these features are reproduced when using experime ntally measured values for the CRU Ca2+ sensitivity (similar to 15 muM). St ochastic control of CRU firing is important because it imposes constraints on the Ca2+ sensitivity of the CRU. Even with moderate (similar to5 muM) Ca 2+ sensitivity the very high spontaneous spark rate triggers numerous Ca2waves. In contrast, a single Ca2+ wave with arbitrarily large velocity can exist in a deterministic model when the CRU Ca2+ sensitivity is sufficientl y high. The combination of low CRU Ca2+ sensitivity (similar to 15 muM), hi gh cytosolic Ca2+ buffering capacity, and the spatial separation of CRUs he lp control the inherent instability of SR Ca2+ release. This allows Ca2+ wa ves to form and propagate given a sufficiently large initiation region, but prevents a single spark or a small group of sparks from triggering a wave.