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

• Published in: Frontiers in physiology 2024-01, Vol.14, p.1280151-1280151
• Main Authors: Morris, Joshua A, Bardsley, Oliver J, Salvage, Samantha C, Jackson, Antony P, Matthews, Hugh R, Huang, Christopher L-H
• Format: Article
• Language: English
• Subjects: action potential propagation; cardiomyocytes; electrodiffusion; ephaptic conduction; Physiology; sodium channels
• ISSN: 1664-042X; 1664-042X
• DOI: 10.3389/fphys.2023.1280151

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, the initially quiescent neighbouring cardiomyocyte. However, sustainable ephaptic transmission requires subsequent complete 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. 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 Δ ∼130 mV AP upstroke at physiological (37°C) temperatures. This incorporated Nernst-Planck formalisms into equations for the time-dependent spatial concentration gradient profiles. Mammalian atrial, ventricular and purkinje cardiomyocyte ephaptic junctions were modelled by closely apposed circularly symmetric membranes, specific capacitance 1 μF cm , experimentally reported radii 8,000, 12,000 and 40,000 nm respectively and ephaptic axial distance = 20 nm. This enclosed an ephaptic space containing principal ions initially at normal extracellular [Na ] = 153.1 mM and [Cl ] = 145.8 mM, respective diffusion coefficients = 1.3 10 and = 2 10 nm s . Stable, concordant computational solutions were confirmed exploring ≤1,600 nm mesh sizes and Δ ≤0.08 ms stepsize intervals. The corresponding membrane voltage profile changes across the initially quiescent membrane were obtainable from computed, graphically represented and -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 2000 ms 99.9% recovery times, with 720 or 360 ms high limits from doubling ventricular radius or halving diffusion coefficient. Varying , and and markedly affected recovery time-courses with logarithmic and double-logarithmic relationships, Varying exerted minimal effects. We thereby characterise the properties of, and through comparing atrial, ventricular and purkinje recovery times with interspecies background cardiac cycle durati