Evolution of cardiac calcium waves from stochastic calcium sparks.
We present a model that provides a unified framework for studying Ca2+ sparks and Ca2+ waves in cardiac cells. The model is novel in combining 1) use of large currents (approximately 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 longitudinal (separation distance of 2 microm) and transverse (separated by 0.4-0.8 microm) directions of the cell; and 4) anisotropic diffusion of Ca2+ and fluorescent indicator to study the evolution of Ca2+ waves from Ca2+ sparks. The model mimics the important features of Ca2+ sparks and Ca2+ waves in terms of the spontaneous spark rate, the Ca2+ wave velocity, and the pattern of wave propagation. Importantly, these features are reproduced when using experimentally measured values for the CRU Ca2+ sensitivity (approximately 15 microM). Stochastic control of CRU firing is important because it imposes constraints on the Ca2+ sensitivity of the CRU. Even with moderate (approximately 5 microM) Ca2+ sensitivity the very high spontaneous spark rate triggers numerous Ca2+ waves. In contrast, a single Ca2+ wave with arbitrarily large velocity can exist in a deterministic model when the CRU Ca2+ sensitivity is sufficiently high. The combination of low CRU Ca2+ sensitivity (approximately 15 microM), high cytosolic Ca2+ buffering capacity, and the spatial separation of CRUs help control the inherent instability of SR Ca2+ release. This allows Ca2+ 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.
Izu
L T
LT
Department of Medicine, University of Maryland School of Medicine, Baltimore, Maryland 21201, USA. lizu@umaryland.edu
Wier
W G
WG
Balke
C W
CW
D000818:Animals; D055592:Biophysical Phenomena; D001703:Biophysics; D002021:Buffers; D020013:Calcium Signaling / Q000502:physiology*; D066298:In Vitro Techniques; D007700:Kinetics; D016014:Linear Models; D008955:Models, Cardiovascular; D009206:Myocardium / Q000166:cytology / Q000378:metabolism*; D017711:Nonlinear Dynamics; D012519:Sarcoplasmic Reticulum / Q000378:metabolism; D013269:Stochastic Processes
D002021:Buffers