Transition of spiral calcium waves between multiple stable patterns can be triggered by a single calcium spark in a fire-diffuse-fire model

Abstract

Spiral patterns have been found in various nonequilibrium systems. The Ca 2+ -induced Ca 2+ release system in single cardiac cells is unique for highly discrete reaction elements, each giving rise to a Ca 2+ spark upon excitation. We imaged the spiral Ca 2+ waves in isolated cardiac cells and numerically studied the effect of system excitability on spiral patterns using a two-dimensional firediffuse-fire model. We found that under certain conditions, the system was able to display multiple stable patterns of spiral waves, each exhibiting different periods and distinct routines of spiral tips. Lethal arrhythmia, the leading cause of sudden cardiac death, is usually characterized by self-sustained spiral activity, as well as turbulent wavelets after spiral break up. With the motivation of understanding and preventing various cardiac arrhythmias, spiral waves in excitable media have long been the subject of numerous studies from different disciplines. Here, using the Ca 2+ -induced Ca 2+ release (CICR) system in single heart cells as a discrete excitable model, we imaged spiral Ca 2+ waves with high-speed confocal microscope and simulated their nonlinear properties using a well-defined two-dimensional fire-diffuse-fire (FDF) model. The simulation showed that the spiral waves in a single heart cell displayed multiple stable patterns. These spiral patterns exhibited different periods with distinct behavior of spiral centers depending on the initial conditions. When a spiral wave was rotating, a single molecular event of Ca 2+ release in the form of a Ca 2+ spark, which hits the wave at a proper location and timing, was able to trigger a transition between these different patterns. The multistability of spiral waves represents a novel behavior of a discrete excitable media and may have important implications in understanding the arrhythmogenisis in heart cells and the complex behaviors in other discrete biological systems.