## Ionic Basis of Resting Membrane Potential ### The Goldman-Hodgkin-Katz (GHK) Equation **Key Point:** The resting membrane potential is NOT determined by K⁺ alone. Rather, it is a weighted average of the equilibrium potentials of all permeable ions, weighted by their relative membrane permeabilities. $$V_m = \frac{RT}{F} \ln \left( \frac{P_K[K^+]_{out} + P_{Na}[Na^+]_{out} + P_{Cl}[Cl^-]_{in}}{P_K[K^+]_{in} + P_{Na}[Na^+]_{in} + P_{Cl}[Cl^-]_{out}} \right)$$ ### Why Each Statement Is Correct (Except One) | Statement | Correctness | Explanation | |-----------|-------------|-------------| | Na⁺/K⁺-ATPase pump stoichiometry (3:2) | ✓ Correct | The pump is electrogenic, extruding 3 Na⁺ and importing 2 K⁺, contributing ~−5 to −10 mV to the RMP | | K⁺ dominates RMP due to higher permeability | ✓ Correct | At rest, P_K >> P_Na (approximately 40:1), so K⁺ is the primary determinant, but Na⁺ still contributes ~−5 mV | | Equilibrium potentials: E_K ≈ −90 mV, E_Na ≈ +60 mV | ✓ Correct | Calculated using the Nernst equation with physiological ion concentrations | | RMP = −70 mV determined by K⁺ alone, independent of Na⁺ | ✗ **WRONG** | The RMP is a result of BOTH K⁺ and Na⁺ gradients (and Cl⁻). Na⁺ contributes approximately −5 to −10 mV to the final RMP | **High-Yield:** At rest, the membrane is ~40 times more permeable to K⁺ than Na⁺. If it were infinitely permeable to K⁺ alone, RMP would be exactly −90 mV. Because some Na⁺ permeability exists (~2.5% of K⁺ permeability), the actual RMP is depolarized to −70 mV. **Clinical Pearl:** Conditions that alter the Na⁺ gradient (e.g., Na⁺-K⁺-ATPase inhibition by digoxin, or ischemia) cause depolarization because the Na⁺ contribution to RMP increases. **Mnemonic:** **GHK** = **G**oldman-**H**odgkin-**K**atz — remember it's a weighted average, not a single-ion equation.
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