Potassium concentration cells and resting voltage

A student studies how a concentration difference of potassium ions across a membrane produces an electrical potential. All concentrations below are values chosen for the experiments, not physiological norms, and all measurements are made at 37 °C (310 K), held constant with a water bath.

Experiment 1. A thin artificial lipid bilayer separates two chambers, each filled with 100 mM KCl. Electrodes in each chamber read 0 mV, confirming that the electrodes and the setup introduce no offset. The solution in one chamber is then replaced with 10 mM KCl. The potential stays near 0 mV, because the bare bilayer is almost impermeable to ions. The student then adds valinomycin, a research reagent that shuttles K+ across the bilayer but does not carry Cl-. Within seconds a steady potential of about 61 mV appears, with the 10 mM chamber positive.

Experiment 2. The resting potential of a cultured mammalian cell line is recorded with a microelectrode while external K+ is varied. Internal K+ is taken as 140 mM. External Na+ is 150 mM and internal Na+ is 15 mM, and the cells are slightly permeable to Na+. For each external K+ concentration, the student also calculates E_K, the potential at which K+ has no net flux, using E_K = (RT/F) ln([K+]out/[K+]in), where RT/F is about 26.7 mV at 310 K. This is about 61.5 mV per tenfold concentration ratio for a monovalent ion.

   K+ out (mM)   E_K calc (mV)   measured (mV)
        2            -113.5          -89
        5             -89.0          -77
       10             -70.5          -64
       20             -52.0          -48
       50             -27.5          -26
      100              -9.0           -8

The student notes that the measured values lie close to the calculated E_K at high external K+ and fall away from it at low external K+.