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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 Δ V ∼130 mV 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 1 μF cm -2 , experimentally reported radii a = 8,000, 12,000 and 40,000 nm respectively and ephaptic axial distance w = 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 D Na = 1.3 × 10 9 and D Cl = 2 × 10 9 nm 2 s -1 . Stable, concordant computational solutions were confirmed exploring ≤1,600 nm mesh sizes and Δ t ≤0.08 ms 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 2000 ms 99.9% recovery times, with 720 or 360 ms 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, ∼40 ms) can determine physical limits to, electrodiffusive contributions to ephaptic recovery., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Morris, Bardsley, Salvage, Jackson, Matthews and Huang.)

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Jæger, Edwards, Giles and Tveito.)

Understanding the role of axons in neuronal information processing is a fundamental task in neuroscience. Over the last years, sophisticated patch-clamp investigations have provided unexpected and exciting data on axonal phenomena and functioning, but there is still a need for methods to investigate full axonal arbors at sufficient throughput. Here, we present a new method for the simultaneous mapping of the axonal arbors of a large number of individual neurons, which relies on their extracellular signals that have been recorded with high-density microelectrode arrays (HD-MEAs). The segmentation of axons was performed based on the local correlation of extracellular signals. Comparison of the results with both, ground truth and receiver operator characteristics, shows that the new segmentation method outperforms previously used methods. Using a standard HD-MEA, we mapped the axonal arbors of 68 neurons in <6 h. The fully automated method can be extended to new generations of HD-MEAs with larger data output and is estimated to provide data of axonal arbors of thousands of neurons within recording sessions of a few hours.

Axons convey information in neuronal circuits via reliable conduction of action potentials (APs) from the axon initial segment (AIS) to the presynaptic terminals. Recent experimental findings increasingly evidence that the axonal function is not limited to the simple transmission of APs. Advances in subcellular-resolution recording techniques have shown that axons display activity-dependent modulation in spike shape and conduction velocity, which influence synaptic strength and latency. We briefly review here, how recent methodological developments facilitate the understanding of the axon physiology. We included the three most common methods, i.e., genetically encoded voltage imaging (GEVI), subcellular patch-clamp and high-density microelectrode arrays (HD-MEAs). We then describe the potential of using HD-MEAs in studying axonal physiology in more detail. Due to their robustness, amenability to high-throughput and high spatiotemporal resolution, HD-MEAs can provide a direct functional electrical readout of single cells and cellular ensembles at subcellular resolution. HD-MEAs can, therefore, be employed in investigating axonal pathologies, the effects of large-scale genomic interventions (e.g., with RNAi or CRISPR) or in compound screenings. A combination of extracellular microelectrode arrays (MEAs), intracellular microelectrodes and optical imaging may potentially reveal yet unexplored repertoires of axonal functions.

Fibrotic myocardial remodeling is typically accompanied by the appearance of myofibroblasts (MFBs). In vitro , MFBs were shown to slow conduction and precipitate ectopic activity following gap junctional coupling to cardiomyocytes (CMCs). To gain further mechanistic insights into this arrhythmogenic MFB-CMC crosstalk, we performed numerical simulations in cell-based high-resolution two-dimensional tissue models that replicated experimental conditions. Cell dimensions were determined using confocal microscopy of single and co-cultured neonatal rat ventricular CMCs and MFBs. Conduction was investigated as a function of MFB density in three distinct cellular tissue architectures: CMC strands with endogenous MFBs, CMC strands with coating MFBs of two different sizes, and CMC strands with MFB inserts. Simulations were performed to identify individual contributions of heterocellular gap junctional coupling and of the specific electrical phenotype of MFBs. With increasing MFB density, both endogenous and coating MFBs slowed conduction. At MFB densities of 5-30%, conduction slowing was most pronounced in strands with endogenous MFBs due to the MFB-dependent increase in axial resistance. At MFB densities >40%, very slow conduction and spontaneous activity was primarily due to MFB-induced CMC depolarization. Coating MFBs caused non-uniformities of resting membrane potential, which were more prominent with large than with small MFBs. In simulations of MFB inserts connecting two CMC strands, conduction delays increased with increasing insert lengths and block appeared for inserts >1.2 mm. Thus, electrophysiological properties of engineered CMC-MFB co-cultures depend on MFB density, MFB size and their specific positioning in respect to CMCs. These factors may influence conduction characteristics in the heterocellular myocardium.