Modeling spiral Ca2+ waves in single cardiac cells: role of the spatial heterogeneity created by the nucleus GENEVIEVE DUPONT, JO& PONTES, AND ALBERT GOLDBETER Unite’ de Chronobiologie The’orique, Faculte’ des Sciences, Universite’ Libre de Bruxelles CP 231, B-1050 Brussels, Belgium DuPont, Genevihe, Jo& Pontes, and Albert Gold- beter. Modeling spiral Ca2+ waves in single cardiac cells: role of the spatial heterogeneity created by the nucleus. Am. J. Physiol. 271 (CeZl PhysioZ. 40): C1390-C1399, 1996.- Excitation-contraction coupling in cardiomyocytes is known to rely on the Ca2+-induced Ca2+ release mechanism. This autoamplification process is also very apparent when voltage- clamped or Ca2+ -overloaded myocytes exhibit fast-propagat- ing Ca2+ waves. Although most of the fronts are planar, some adopt a spiral shape, revealing additional characteristics about the excitability and structure of the cardiac cell (P. Lipp and E. Niggli, Biophys. J. 65: 2272-2276, 1993; J. Engel, M. Fechner, A. Sowerby, S. Finch, and A. Stier, Biophys. J. 66: 1756-1762, 1994). Using a previously developed model for Ca2+ oscillations and waves (A. Goldbeter, G. DuPont, and M. J. Berridge, Proc. lVat1. Acad. Sci. USA 87: 1461-1465, 1990; G. DuPont andA. Goldbeter, Biophys. J. 67: 2191-2204, 1994), we study by numerical simulations different conditions in which spiral Ca2+ waves can occur as a result of the spatial heterogeneity created by the nucleus in a system with geometry resembling that of a myocyte. A region of the cell lacking Ca2+ pools, acting as an obstacle able to break the propagation of planar waves, suffices to initiate a spiral wave; however, this region must be properly placed with respect to the pacemaker. An obstacle behaving as a barrier to diffusion is also able to create the initial bending that can lead to the spiral wave. We study how the occurrence of spiral Ca2+ waves in single cardiomyocytes is influenced by factors such as the stimulus location and the position, shape, and dimen- sions of the obstacle to planar wave propagation. calcium oscillations; calcium-induced calcium temporal patterns; heart cell; myocyte release; spatio- IN MAMMALIAN CARDIOMYOCYTES, Ca2+ signaling is orga- nized in time and space (32, 33). Under physiological conditions, the signal for cardiac contraction is a brief rise in cytosolic Ca2+ just beneath the plasma mem- brane, occurring in a quasi-homogeneous manner. Thus, after electrical activation, the Ca2+ influx elicited by the L-type voltage-gated channels triggers a massive and rapid release of Ca 2+ from the sarcoplasmic reticu- lum (SR) through the ryanodine receptors (RyR). This phenomenon, known as Ca2+-induced Ca2+ release (CICR), is the basis for the excitable behavior and subsequent contraction of the myocytes (14,26,36,39). The CICR mechanism is also very apparent in other less physiological conditions when isolated cardiomyo- cytes spontaneously exhibit periodic Ca2+ waves under voltage clamp (33) or when they are overloaded with Ca2+ (25). In these cases, a localized increase in Ca2+ periodically propagates as a sharp -109pm-wide band through the cell at a velocity of 65-120 pm/s. Two fronts of elevated Ca2+ can sometimes be observed in a cell, given that the length of the myocyte is of the order of 100 urn and the periodicity of the wave is of the order of 1 s (33, 37). Oscillations and waves of cytosolic Ca2+ have been observed in a variety of cell types (8, 9, 27, 31,35) and have become a prototype of spatiotemporal organization at the cellular level (16). Propagating Ca 2+ fronts in cardiomyocytes have un- til recently always been viewed as planar waves, but recent observations performed with confocal micros- copy have demonstrated another pattern of Ca2+ wave propagation that generally occurs when overloading is not too high. In guinea pig cardiomyocytes (25) or in rat myocytes (13), the Ca 2+ front that passes throughout the cell sometimes deviates from a linear propagation and adopts a curved path reminiscent of a spiral wave. This transition from a planar to a spiral wave is most often observed near a cell nucleus, and the newly formed spiral wave can spin around it at a frequency of -1 Hz. The spiral wave in turn initiates a planar wave, which then disappears when it collides with another wave or when it encounters the plasma membrane (25). Numerical simulations have shown that the CICR mechanism can account for the propagation of planar Ca2+ fronts resembling those observed in depolarized or Ca2+-overloaded myocytes (11, 12, 34). On the other hand, spiral Ca2+ waves based on the dynamics of the inositoll,4,5-trisphosphate [Ins( l,4,5)P3] receptor have also been simulated in large square systems (5, 15, 18, 28) to account for the spiral Ca2+ waves sometimes ob- served in Xenopus oocytes, the dimensions of which much exceed those of cardiac myocytes (24). In some of these studies (15,28), the simulated cell was arbitrarily divided into three regions characterized by different initial levels of cytosolic and intravesicular Ca2+; these somewhat artifi- cial differences in initial conditions suffice for the initiation of a spiral wave, which can then rotate indefinitely, because the velocity of the wavefront de- pends on its curvature. Concentric waves encountering appropriately located regions made refractory by tran- sient lowering of the level of cytosolic Ca2+ can generate spiral waves in a more realistic way (5,18). Cl390 0363-6143196 $5.00 Copyright o 1996 the American Physiological Society