A simple quantitative model of neuromodulation, Part I: Ion flow neural ion channels

We develop a simple model of ionic current through neuronal membranes as a function of membrane potential and extracellular ion concentration. The model combines a simplified Poisson-Nernst-Planck (PNP) model of ion transport through individual ion channels with channel activation functions calibrated from ad hoc in-house experimental data. The simplified PNP model is validated against bacterial gramicidin A ion channel data. The calibrated model accounts for the transport of calcium, sodium, potassium, and chloride and exhibits remarkable agreement with the experimentally measured current-voltage curves for the differentiated human neural cells. All relevant data and code related to the ion flow models are available at Werneck et al. (2023).