Goldman-Hodgkin-Katz equation, reverse electrodialysis, and everything in between

Area of Science:

• Physical Chemistry
• Biophysics
• Nanotechnology

Background:

• The Goldman-Hodgkin-Katz (GHK) equation is a long-standing model for ion transport in biological systems.
• It is widely used in interpreting experiments and simulations involving ion channels and nanopores.
• However, the GHK model has inherent inconsistencies under certain conditions, particularly when the Debye length is small.

Purpose of the Study:

• To re-examine the mathematical derivation of the GHK equation.
• To identify and address the internal inconsistencies within the GHK model.
• To develop a new, internally consistent model for ion transport that satisfies electroneutrality.

Main Methods:

• Revisiting the mathematical derivation of the GHK equation.
• Identifying the incorrect assumption of a constant electric field in the GHK model.
• Leveraging insights from reverse electrodialysis (RED) to derive a new model.

Main Results:

• The GHK model's assumption of a constant electric field is shown to be incorrect, leading to errors in electroneutrality.
• A new, internally consistent model is derived that does not assume a constant electric field and satisfies electroneutrality.
• The new model aligns with non-approximated numerical simulations and offers a more robust framework for ion transport analysis.

Conclusions:

• The GHK equation, while historically significant, possesses internal inconsistencies that limit its accuracy.
• The newly derived model provides a mathematically sound and internally consistent framework for ion transport.
• This work offers a new paradigm for interpreting ion transport experiments in charge-selective systems.