Geometry-dependent instabilities in electrically excitable tissues

Little is known about how individual cells sense the macroscopic geometry of their tissue environment. Here we explore whether long-range electrical signaling can convey information on tissue geometry to influence electrical dynamics of individual cells. First, we studied an engineered electrically excitable cell line where all voltage-gated channels were well characterized. Cells grown in patterned islands of different shapes showed remarkably diverse firing patterns under otherwise identical conditions, including regular spiking, period-doubling alternans, and arrhythmic firing. A Hodgkin-Huxley numerical model quantitatively reproduced these effects, showing how the macroscopic geometry affected the single-cell electrophysiology via the influence of gap junction-mediated electrical coupling. Qualitatively similar geometry dependent dynamics were experimentally observed in human induced pluripotent stem cell (iPSC)-derived cardiomyocytes. The cardiac results urge caution in translating observations of arrhythmia in vitro to predictions in vivo where the tissue geometry is very different. We present simulation results and scaling arguments which explore how to extrapolate electrophysiological measurements between tissues with different geometries and different gap junction couplings.