The emergence of subcellular pacemaker sites for calcium waves and oscillations

Key points Calcium (Ca2+) is fundamental to biological cell function, and Ca2+ waves generating oscillatory Ca2+ signals are widely observed in many cell types. Some experimental studies have shown that Ca2+ waves initiate from random locations within the cell, while other studies have shown that waves occur repetitively from preferred locations (pacemaker sites). In both ventricular myocyte experiments and computer simulations of a heterogeneous model of coupled Ca2+ release units (CRUs), we show that Ca2+ waves occur randomly in space and time when the Ca2+ level is low, but as the Ca2+ level increases, waves occur repetitively from the same sites. Ca2+ waves are self‐organized dynamics of the CRU network, and the wave frequency strongly depends on CRU coupling. Using these results, we develop a theory for the entrainment of random oscillators, which provides a unified explanation for the experimental and computational observations. Abstract  Calcium (Ca2+) waves generating oscillatory Ca2+ signals are widely observed in biological cells. Experimental studies have shown that under certain conditions, initiation of Ca2+ waves is random in space and time, while under other conditions, waves occur repetitively from preferred locations (pacemaker sites) from which they entrain the whole cell. In this study, we use computer simulations to investigate the self‐organization of Ca2+ sparks into pacemaker sites generating Ca2+ oscillations. In both ventricular myocyte experiments and computer simulations of a heterogeneous Ca2+ release unit (CRU) network model, we show that Ca2+ waves occur randomly in space and time when the Ca2+ level is low, but as the Ca2+ level increases, waves occur repetitively from the same sites. Our analysis indicates that this transition to entrainment can be attributed to the fact that random Ca2+ sparks self‐organize into Ca2+ oscillations differently at low and high Ca2+ levels. At low Ca2+, the whole cell Ca2+ oscillation frequency of the coupled CRU system is much slower than that of an isolated single CRU. Compared to a single CRU, the distribution of interspike intervals (ISIs) of the coupled CRU network exhibits a greater variation, and its ISI distribution is asymmetric with respect to the peak, exhibiting a fat tail. At high Ca2+, however, the coupled CRU network has a faster frequency and lesser ISI variation compared to an individual CRU. The ISI distribution of the coupled network no longer exhibits a fat tail and is well‐approximated by a Gaussian distribution. This same Ca2+ oscillation behaviour can also be achieved by varying the number of ryanodine receptors per CRU or the distance between CRUs. Using these results, we develop a theory for the entrainment of random oscillators which provides a unified explanation for the experimental observations underlying the emergence of pacemaker sites and Ca2+ oscillations.