Membrane Transport 🧬
Ion channels, pumps, and the Goldman-Hodgkin-Katz membrane potential
Physics & equations
Goldman-Hodgkin-Katz (GHK) equation gives the membrane potential when multiple ion species are permeable:
Vm = (RT/F) · ln[(PNa[Na⁺]out + PK[K⁺]out + PCl[Cl⁻]in) / (PNa[Na⁺]in + PK[K⁺]in + PCl[Cl⁻]out)]
Nernst equation for a single ion X of valence z: EX = (RT/zF) · ln([X]out/[X]in)
The Na⁺/K⁺-ATPase pump actively moves 3 Na⁺ out and 2 K⁺ in per ATP cycle, maintaining the resting concentration gradients: [Na⁺] 145 mM outside / 12 mM inside; [K⁺] 4 mM / 140 mM; [Cl⁻] 120 mM / 4 mM (typical mammalian neuron).