Nernst-Planck-Gaussian modelling of electrodiffusional recovery from ephaptic excitation between mammalian cardiomyocytes.

Abstract

Introduction: In addition to gap junction conduction, recent reports implicate possible ephaptic coupling contributions to action potential (AP) propagation between successive adjacent cardiomyocytes. Here, AP generation in an active cell, withdraws Na+ from, creating a negative potential within, ephaptic spaces between the participating membranes, activating the initially quiescent neighbouring cardiomyocyte. However, sustainable ephaptic transmission requires subsequent complete recovery of the ephaptic charge difference. We explore physical contributions of passive electrodiffusive ion exchange with the remaining extracellular space to this recovery for the first time. Materials and Methods: Computational, finite element, analysis examined limiting, temporal and spatial, ephaptic [Na+], [Cl-], and the consequent Gaussian charge differences and membrane potential recovery patterns following a ΔV∼130mV AP upstroke at physiological (37°C) temperatures. This incorporated Nernst-Planck formalisms into equations for the time-dependent spatial concentration gradient profiles. Results: Mammalian atrial, ventricular and purkinje cardiomyocyte ephaptic junctions were modelled by closely apposed circularly symmetric membranes, specific capacitance 1μF cm-2, experimentally reported radii a = 8,000, 12,000 and 40,000nm respectively and ephaptic axial distance w = 20nm. This enclosed an ephaptic space containing principal ions initially at normal extracellular [Na+] = 153.1mM and [Cl-] = 145.8 mM, respective diffusion coefficients D Na = 1.3 109 and D Cl = 2 109 nm2s-1. Stable, concordant computational solutions were confirmed exploring ≤1,600nm mesh sizes and Δt≤0.08ms stepsize intervals. The corresponding membrane voltage profile changes across the initially quiescent membrane were obtainable from computed, graphically represented a and w-dependent ionic concentration differences adapting Gauss's flux theorem. Further simulations explored biological variations in ephaptic dimensions, membrane anatomy, and diffusion restrictions within the ephaptic space. Atrial, ventricular and Purkinje cardiomyocytes gave 40, 180 and 2000ms 99.9% recovery times, with 720 or 360ms high limits from doubling ventricular radius or halving diffusion coefficient. Varying a, and D Na and D Cl markedly affected recovery time-courses with logarithmic and double-logarithmic relationships, Varying w exerted minimal effects. Conclusion: We thereby characterise the properties of, and through comparing atrial, ventricular and purkinje recovery times with interspecies in vivo background cardiac cycle duration data, (blue whale ∼2000, human∼90, Etruscan shrew, ∼40ms) can determine physical limits to, electrodiffusive contributions to ephaptic recovery.