Mathematical Modeling of Non-Selective Channels: Estimating Ion Current Fractions and Their Impact on Pathological Simulations

Abstract

Currents through non-selective ion channels are often mathematically modeled as an Ohmic current. In such models, quantifying the contributions of different contributing ion species is not easily possible. We present a method to adapt Ohmic descriptions using the Goldman-Hodgkin-Katz equation in order to describe every ion species' contribution to the total channel current. We use our method to adapt a model of Channelrhodopsin-2, a light-gated cation non-selective channel, and test our adaption in single cell and 1-dimensional tissue strand simulations of ventricular tachycardia. Resulting contribution ratios of sodium, potassium and proton currents match expectations and correlate well with previously published data. Simulations of optical defibrillation for ventricular tachycardia show that our model predicts a detrimental outcome in ischaemia-like pathological settings that are missed by the original (Ohmic) model.