The Goldman-Hodgkin-Katz Equation

by Greg Crowther

This song helps students understand the Goldman-Hodgkin-Katz (GHK) equation, which calculates a cell's membrane potential based on ion concentrations and permeances. It was written for BBIO 351 at the University of Washington Bothell. Since the GHK equation can be written in many ways (depending on the ions considered, temperature, etc.), this song does not promote one particular version over the others; rather, it focuses attention on the "ratio of sums of permeance-weighted concentrations," which is often hard to understand.

Ideally, this song should sound reminiscent of early They Might Be Giants, with John Linnell singing lead.

Take the log of the ratio of the sums of permeance-weighted concentrations.
That's the part that's the heart of the famous Goldman-Hodgkin-Katz equation.
There's no denyin' several ions have an impact on the cell's membrane potential,
But the P is how you see if the effect of any one is strong or gentle.
Yes, the P is how you if the effect of any one is strong or gentle.

• MP3 (demo)

• music video

• sheet music (with melody play-back)

Songs like this one can be used during class meetings and/or in homework assignments. Either way, the song will be most impactful if students DO something with it, as opposed to just listening.

An initial, simple follow-up activity could be to answer the study questions below. A more extensive interaction with the song might entail (A) learning to sing it, using an audio file and/or sheet music as a guide, and/or (B) illustrating it with pictures, bodily poses, and/or bodily movements. The latter activity could begin with students identifying the most important or most challenging content of the song, and deciding how to illustrate that particular content.

(1) How is the GHK equation similar to and different from the Nernst equation?

(2) In a typical "resting" neuron, which permeance is higher, P_K+ or P_Na+? What does this tell us about the resting potential of this neuron?

(3) During the rising phase of an action potential, which permeance is higher, P_K+ or P_Na+? What does this tell us about the membrane potential during this phase?

(4) The P's in this song stand for permeances. Are permeances the same as permeabilities?

(5) Are the extracellular ion concentrations in the numerator of the GHK equation, or the denominator, or both?

(6) Considering the specific content covered by this song, is there anything important that is missing, unclear, or misleading? If so, what?