Electrodiffusion dynamics in the cardiomyocyte dyad at nano-scale resolution using the Poisson-Nernst-Planck (PNP) equations

Abstract

During each heartbeat, a voltage wave propagates through the cardiac muscle, triggering action potentials in approximately two billion cardiomyocytes. This electrical activity ensures the coordinated contraction of the heart, which is essential for its pumping function. A key event in this process is the opening of voltage-gated calcium channels in the cell membrane, allowing calcium ions to enter the cardiac dyad and triggering a large-scale release of calcium ions from the sarcoplasmic reticulum through ryanodine receptors. This process is fundamental to cardiac function because calcium subsequently binds to troponin, initiating the conformational changes necessary for myofilament contraction. The cardiac dyad is characterized by a very small volume with steep ionic concentration gradients, which is challenging for detailed mathematical modeling. Traditionally, the dyadic calcium concentration has been approximated using spatially averaged values or modeled with reaction-diffusion equations. However, at the nanometer (nm) and nanosecond (ns) scales, such approximations may be insufficient. At this resolution, the Poisson-Nernst-Planck (PNP) system provides a detailed continuous representation of the underlying electrodiffusion dynamics. Here, we present a nano-scale computational model, representing dyad dynamics using the PNP system. Potassium, sodium, and calcium channels are incorporated in the cell membrane, along with the sodium-calcium exchanger. We demonstrate the formation of the Debye layer in the resting state and highlight how both diffusive and electrical effects are required to maintain this equilibrium. Additionally, we show that cross-species ion interactions in the dyad are electrical, and that diffusion models fail to capture this effect. Finally, we illustrate how the dyad width and diffusion coefficient influence local ionic concentrations and the timing of calcium arrival at the ryanodine receptors. These results provide new insights into the electrodiffusive properties of the dyad and clarify when solving the full PNP system is necessary for accurate modeling.