Treffer: Ionic flux calculation by an extended Goldman-Hodgkin-Katz equation accounting for nonlinear ion channel electrostatics.

The Goldman-Hodgkin-Katz (GHK) equations have been widely used to model ion channel kinetics in computational models of integrated cellular systems. However, they are derived based on a constant electric field, making them have low accuracy in predicting 'macroscopic' ion channel kinetics – ionic fluxes, electric currents, and membrane potentials. This paper revisits and extends the GHK equations to account for nonlinear electrostatics. A numerical scheme is then presented and analyzed to yield a computable extended GHK equation for calculating ionic fluxes in terms of a set, $ {\mathcal {S}} $ S , of 'microscopic' electrostatic potential values. Furthermore, one finite element iterative method and a Python software package are developed to solve a Poisson-Nernst-Planck ion channel model and applied to the generation of dataset $ {\mathcal {S}} $ S . Numerical results demonstrate significant differences between the extended and classical GHK equations and confirm the importance of considering charge effects in calculating ionic fluxes. [ABSTRACT FROM AUTHOR]