The emergence of subcellular pacemaker sites for calcium waves and oscillations

Calcium (Ca(2+)) waves generating oscillatory Ca(2+) signals are widely observed in biological cells. Experimental studies have shown that under certain conditions, initiation of Ca(2+) 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 Ca(2+) sparks into pacemaker sites generating Ca(2+) oscillations. In both ventricular myocyte experiments and computer simulations of a heterogeneous Ca(2+) release unit (CRU) network model, we show that Ca(2+) waves occur randomly in space and time when the Ca(2+) level is low, but as the Ca(2+) 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 Ca(2+) sparks self-organize into Ca(2+) oscillations differently at low and high Ca(2+) levels. At low Ca(2+), the whole cell Ca(2+) 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 Ca(2+), 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 Ca(2+) 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 Ca(2+) oscillations.