Resting Membrane Potential & Nernst
Core concepts for deriving the resting membrane potential and calculating equilibrium potentials.
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Questions Covered in This Set
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Typical resting membrane potential of skeletal muscle vs. neuron
Skeletal muscle ≈ −90 mV; neuron ≈ −70 mV (inside negative relative to outside).
What two ingredients are required to generate a membrane potential?
(1) A concentration gradient for an ion (built by the Na⁺/K⁺-ATPase) and (2) a selectively permeable open channel. Either alone gives 0 mV.
Stoichiometry and effect of the Na⁺/K⁺-ATPase
3 Na⁺ out : 2 K⁺ in per ATP. It builds the gradients and, being electrogenic, contributes about −2 to −4 mV directly.
Simplified Nernst equation at 37 °C
E_ion = (61/z) · log₁₀([ion]_out/[ion]_in) mV, where z is valence (+1 K⁺/Na⁺, +2 Ca²⁺, −1 Cl⁻).
Calculate E_K given K⁺ 140 in / 4 out
61 · log(4/140) = 61 · (−1.54) ≈ −94 mV.
Calculate E_Na given Na⁺ 14 in / 140 out
61 · log(140/14) = 61 · (+1) = +61 mV.
Why is the inside of the cell negative at rest?
K⁺ leaks out down its gradient through K⁺ leak channels, but large intracellular anions (proteins, phosphates, DNA) cannot follow, leaving net negative charge inside until electrical pull balances chemical push.
Does building −90 mV change bulk ion concentrations?
No — only ~10⁻¹² mol/cm² of ions move. Membrane potential is a surface phenomenon; the bulk solution stays electroneutral.
What does the Goldman–Hodgkin–Katz (GHK) equation describe?
V_m as a permeability-weighted average of the equilibrium potentials of K⁺, Na⁺, and Cl⁻ (Cl⁻ subscripts flipped because it is an anion).
The master rule of membrane potential
V_m always moves toward the equilibrium potential of whichever ion the membrane is most permeable to; at rest that is K⁺ (P_K:P_Na ≈ 100:1).
