-73.14
mV
-73.14
mV
The Goldman Equation Calculator computes the resting membrane potential of a cell by considering the concentration gradients and relative permeabilities of the major ions: potassium (K⁺), sodium (Na⁺), and chloride (Cl⁻). Unlike the Nernst equation which considers only one ion, the Goldman-Hodgkin-Katz (GHK) equation accounts for all permeable ions simultaneously, providing a more realistic estimate of membrane potential.
This calculator is essential in neuroscience and cell physiology for understanding how ion concentrations and channel permeabilities determine the resting potential and how changes in these parameters affect cell excitability during action potentials, synaptic transmission, and disease states.
The Goldman-Hodgkin-Katz voltage equation is:
Vm = (RT/F) × ln((PK[K⁺]o + PNa[Na⁺]o + PCl[Cl⁻]i) / (PK[K⁺]i + PNa[Na⁺]i + PCl[Cl⁻]o))
Note that Cl⁻ inside and outside are swapped compared to the cations because chloride has a negative charge. R = 8.314 J/(mol·K), F = 96,485 C/mol. At 37°C, RT/F ≈ 26.7 mV. The result is in millivolts, with typical resting values near -70 mV for neurons.
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With typical neuronal ion concentrations and permeabilities, the resting membrane potential is approximately -73 mV, close to the K⁺ equilibrium potential because PK dominates at rest.
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During an action potential, Na⁺ permeability increases dramatically (PNa = 20 here). The membrane potential swings positive toward the Na⁺ equilibrium potential, reaching about +46 mV.
At rest, the membrane is most permeable to K⁺, which has a high intracellular and low extracellular concentration. K⁺ flows outward down its concentration gradient, leaving behind negative charges. The resulting potential (-60 to -90 mV) is close to the K⁺ equilibrium potential. The slight Na⁺ permeability pulls it somewhat positive of the pure K⁺ potential.
The Nernst equation calculates the equilibrium potential for a single ion. The Goldman equation considers multiple ions simultaneously, weighted by their relative permeabilities. It is more physiologically accurate because real membranes are permeable to several ions. When permeability to one ion dominates, the Goldman equation reduces to the Nernst equation for that ion.
Chloride is an anion (negative charge), so its contribution to the membrane potential is opposite to that of cations. To account for this, intracellular Cl⁻ appears in the numerator and extracellular Cl⁻ in the denominator, which is reversed compared to the cations. This is mathematically equivalent to multiplying the Cl⁻ term by -1 inside the logarithm.
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