Self-Organized Criticality Underlies Arrhythmogenic Calcium Waves in Cardiac Myocytes

Abstract

In cardiac myocytes, calcium (Ca)-induced Ca release can give rise to propagating Ca waves that promote cardiac arrhythmias. To understand the mechanism underlying the transition from localized Ca sparks to global Ca waves, we developed a mathematical model of a spatially-distributed network of diffusively coupled Ca release units (CRUs) comprised of junctional/longitudinal sarcoplasmic reticulum and dyadic/cytoplasmic spaces with physiologically realistic dimensions. As total Ca was increased in the model, Ca spark cluster sizes initially exhibited an exponential distribution, which transitioned to a scale-free power-law (f-β) distribution near the threshold at which random Ca sparks transitioned to Ca waves. The power-law relationship indicates that Ca release patterns in the CRU network are governed by a dynamical mechanism called self-organized criticality, the same process underlying many natural world phenomena such as avalanches and earthquakes. We tested this prediction experimentally in saponin-permeabilized cardiac myocytes. As free Ca, buffered with 0.5 mM EGTA, was increased, Ca spark cluster size transitioned from an exponential distribution to a power-law distribution at a free Ca concentration of 400 nM. Consistent with self-organized criticality, this Ca concentration was near the threshold for spark-to-wave transition since fully propagating waves were observed above 400 nM Ca. Below this concentration, Ca was released mostly as individual sparks, and spark cluster sizes followed an exponential rather than power-law distribution. In conclusion, our findings provide both theoretical and experimental evidence that the transition from Ca sparks to arrhythmogenic Ca waves in cardiac myocytes is mediated by the dynamical process of self-organized criticality, common to many natural phenomena. This provides a theoretical framework for developing interventions which modulate the Ca spark-to-wave transition threshold as a potential therapeutic strategy for preventing arrhythmias.