Is the Goldman-Hodgkin-Katz equation universally true?

TL;DR

This paper challenges the universality of the Goldman-Hodgkin-Katz equation by demonstrating that the assumption of a uniform electric field within ion channels is often invalid, which could significantly alter the interpretation of electrophysiological data.

Contribution

It introduces a new framework based on electrodialysis tools that accounts for non-uniform electric fields, contrasting with the traditional GHK approach assuming uniformity.

Findings

Electric field within ion channels is not always uniform.

Different modeling approaches yield drastically different results.

The new framework bridges electrophysiology and electrodialysis communities.

Abstract

No. Eighty years ago, the two seminal works by Goldman [J. Gen. Phys. 27, 37 (1943)] and by Hodgkin-Katz [J. of Physio 108, 37 (1949)] derived the foundational framework for interpreting electro-physiological measurements in what is commonly termed the Goldman-Hodgkin-Katz (GHK) theory for the membrane potential. Both seminal papers postulate a constant/uniform electric field within the ion channel. Using a uniform electric field allows for a simple, straightforward calculation of the ionic fluxes and the transmembrane potential, which yields the famous GHK potential. The use of this framework is so widely accepted that one can find a plethora of works that no longer cite the original works and GHK has perhaps become the universal and indisputable descriptor of the underlying physics and biology. In recent works [Phys. Rev. Lett. 134, 228401 (2025) and Phys. Rev. E 111, 064408 (2025)], we revisited GHK and its assumption of a uniform field. Non-approximated numerical simulations showed that the electric field is not always uniform. To understand this discrepancy, it is important to understand that the governing equations can be solved using two different approaches: the GHK approach of assuming a constant electric field or postulating that the system is electroneutral. Each approach yields drastically different non-commutative results. The purpose of this report is to provide a non-mathematical summary of the results and to inform the broader community that GHK is not as universal as previously thought. We will discuss these two newer works, with some emphasis on how they can potentially revolutionize the interpretation of electro-physiological measurements. Importantly, we show that this new framework, which utilizes the mathematical tools developed by the electrodialysis community, also serves as a bridge linking the electrophysiology community and the electrodialysis community.