This is the MATLAB source code permitting to replicate the simulations presented in an article that is presently under peer-review for publication. Download all files into the same folder. Details regarding the operation of the scripts and functions are presented briefly below and in detail as comments at the beginning of the scripts/functions as well as throughout the code. These simulations are optimally run in MATLAB version 2019a on a PC with the Windows 10 operating system, an Intel Core i7 processor and 64 GB of RAM.Use in terms of the Creative Commons CC-BY license (Attribution 4.0 International) and, regarding the functions from the "DistMesh" package (see below), under the terms of the GNU General Public License version 2.

Cardiac ephaptic coupling, a mechanism mediated by negative electric potentials occurring in the narrow intercellular clefts of intercalated discs, can influence action potential propagation by modulating the sodium current. Intercalated discs are highly tortuous due to the mingling of plicate and interplicate regions. To investigate the effect of their convoluted structure on ephaptic coupling, we refined our previous model of an intercalated disc and tested predefined folded geometries, which we parametrized by orientation, amplitude and number of folds. Ephaptic interactions (assessed by the minimal cleft potential and amplitude of the sodium currents) were reinforced by concentric folds. With increasing amplitude and number of concentric folds, the cleft potential became more negative during the sodium current transient. This is explained by the larger resistance between the cleft and the bulk extracellular space. In contrast, radial folds attenuated ephaptic interactions and led to a less negative cleft potential due to a decreased net cleft resistance. In conclusion, despite limitations inherent to the simplified geometries and sodium channel distributions investigated as well as simplifications regarding ion concentration changes, these results indicate that the folding pattern of intercalated discs modulates ephaptic coupling.

Ion channels on the membrane of cardiomyocytes regulate the propagation of action potentials from cell to cell and hence are essential for the proper function of the heart. Through computer simulations with the classical monodomain model for cardiac tissue and the more recent extracellular-membrane-intracellular (EMI) model where individual cells are explicitly represented, we investigated how conduction velocity (CV) in cardiac tissue depends on the strength of various ion currents as well as on the spatial distribution of the ion channels. Our simulations show a sharp decrease in CV when reducing the strength of the sodium (Na+) currents, whereas independent reductions in the potassium (K1 and Kr) and L-type calcium currents have negligible effect on the CV. Furthermore, we find that an increase in number density of Na+ channels towards the cell ends increases the CV, whereas a higher number density of K1 channels slightly reduces the CV. These findings contribute to the understanding of ion channels (e.g. Na+ and K+ channels) in the propagation velocity of action potentials in the heart.

The basic building blocks of the electrophysiology of cardiomyocytes are ion channels integrated in the cell membranes. Close to the ion channels there are very strong electrical and chemical gradients. However, these gradients extend for only a few nano-meters and are therefore commonly ignored in mathematical models. The full complexity of the dynamics is modelled by the Poisson-Nernst-Planck (PNP) equations but these equations must be solved using temporal and spatial scales of nano-seconds and nano-meters. Here we report solutions of the PNP equations in a fraction of two abuttal cells separated by a tiny extracellular space. We show that when only the potassium channels of the two cells are open, a stationary solution is reached with the well-known Debye layer close to the membranes. When the sodium channels of one of the cells are opened, a very strong and brief electrochemical wave emanates from the channels. If the extracellular space is sufficiently small and the number of sodium channels is sufficiently high, the wave extends all the way over to the neighboring cell and may therefore explain cardiac conduction even at very low levels of gap junctional coupling.

No abstract