Voltage mapping in subcellular nanodomains using electro-diffusion modeling.

Voltage distribution in sub-cellular micro-domains such as neuronal synapses, small protrusions, or dendritic spines regulates the opening and closing of ionic channels, energy production, and thus, cellular homeostasis and excitability. Yet how voltage changes at such a small scale in vivo remains challenging due to the experimental diffraction limit, large signal fluctuations, and the still limited resolution of fast voltage indicators. Here, we study the voltage distribution in nano-compartments using a computational approach based on the Poisson-Nernst-Planck equations for the electro-diffusion motion of ions, where inward and outward fluxes are generated between channels. We report a current-voltage (I-V) logarithmic relationship generalizing Nernst law that reveals how the local membrane curvature modulates the voltage. We further find that an influx current penetrating a cellular electrolyte can lead to perturbations from tens to hundreds of nanometers deep, depending on the local channel organization. Finally, we show that the neck resistance of dendritic spines can be completely shunted by the transporters located on the head boundary, facilitating ionic flow. To conclude, we propose that voltage is regulated at a subcellular level by channel organization, membrane curvature, and narrow passages.