The resting voltage of a living cell, weighting each ion by how easily it crosses the membrane. Not a single battery but a permeability-weighted vote across K, Na and Cl at once. Rendered, not quoted.
SOURCE Goldman, D.E. (1943) "Potential, Impedance, and Rectification in Membranes," J. Gen. Physiol. 27, 37–60 — the constant-field GHK voltage; with Hodgkin & Katz (1949), J. Physiol. 108, 37 — PubMed 19873371
Each cation is weighted by its permeability P and its concentration ratio. The cell rests where the net current is zero — a compromise, pulled toward whichever ion is most permeable.
Anion twist: chloride (charge −1) enters with its concentrations inverted — inside over outside — versus the cations. That single flip is what makes GHK correct rather than a naive sum. ILLUSTRATIVE PARAMS
This is the baseline the spike departs from. GHK gives the quiet resting voltage; the-hodgkin-huxley sphere shows what happens when voltage-gated Na channels throw PNa upward and Vm lunges toward ENa.
Reduce GHK to one ion and you recover Nernst — the same battery a single-ion sphere assumes. Goldman is Nernst, summed and weighted.
Re-runs the full selfcheck live against this DOM. Confirms the Nernst-reduction and correct anion orientation; flips red if window 6 tampers with chloride's placement.
Mammalian concentrations (mM) and relative permeabilities PK:PNa:PCl.
At rest (PNa=0.04) the vote lands near −67 mV — above EK, dragged there by the small Na and the Cl leak. Raise PNa and Vm climbs toward ENa: a depolarization, computed live.
"The constant-field assumption is a fiction." True — real membranes do not hold a perfectly linear field, ions interact, and single-file pores violate independence. GHK is a tractable approximation, not the last word.
Permeabilities are themselves voltage- and time-dependent; treating them as fixed constants is the model's honest limit. AMBER
"Resting potential just equals EK."
→ Only if PNa=PCl=0. Finite Na/Cl leak pulls it above EK to ~−67 mV.
"Add every ion's Nernst potential up."
→ No — you weight and log a ratio, and the anion's concentrations invert.
"Bigger permeability = bigger voltage."
→ It pulls Vm toward that ion's own Nernst potential, no further.
Flip chloride into the same orientation as the cations (out over in). The resting potential comes out wrong and Cl no longer reduces to ECl — the WITNESS (7) catches it live.