Abstract
We present a model that provides a unified framework for studying Ca 2+ sparks and Ca 2+ waves in cardiac cells. The model is novel in combining 1) use of large currents (∼20 pA) through the Ca 2+ release units (CRUs) of the sarcoplasmic reticulum (SR); 2) stochastic Ca 2+ release (or firing) of CRUs; 3) discrete, asymmetric distribution of CRUs along the longitudinal (separation distance of 2 μm) and transverse (separated by 0.4–0.8 μm) directions of the cell; and 4) anisotropic diffusion of Ca 2+ and fluorescent indicator to study the evolution of Ca 2+ waves from Ca 2+ sparks. The model mimics the important features of Ca 2+ sparks and Ca 2+ waves in terms of the spontaneous spark rate, the Ca 2+ wave velocity, and the pattern of wave propagation. Importantly, these features are reproduced when using experimentally measured values for the CRU Ca 2+ sensitivity (∼15 μM). Stochastic control of CRU firing is important because it imposes constraints on the Ca 2+ sensitivity of the CRU. Even with moderate (∼5 μM) Ca 2+ sensitivity the very high spontaneous spark rate triggers numerous Ca 2+ waves. In contrast, a single Ca 2+ wave with arbitrarily large velocity can exist in a deterministic model when the CRU Ca 2+ sensitivity is sufficiently high. The combination of low CRU Ca 2+ sensitivity (∼15 μM), high cytosolic Ca 2+ buffering capacity, and the spatial separation of CRUs help control the inherent instability of SR Ca 2+ release. This allows Ca 2+ waves 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.
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