Question
A neuron has mM and mM. Using the Nernst equation at 37°C, find the K⁺ equilibrium potential. Why is the actual resting potential ( mV) less negative than this?
Solution — Step by Step
mV at 37°C, with .
.
, so mV.
The actual resting potential is mV because the membrane has small but nonzero permeability to Na⁺. Sodium leaking in pulls the potential slightly positive of pure . The full expression is the Goldman equation.
Final answer: mV. Resting potential is less negative because of Na⁺ leak permeability.
Why This Works
The Nernst equation assumes the membrane is permeable to only one ion. Real membranes leak multiple ions, so the resting potential is a weighted average of each ion’s equilibrium potential, weighted by its permeability.
Alternative Method
If the question gives you Na⁺ concentrations too, apply Goldman directly instead of Nernst.
Most neural-system numericals come down to unit hygiene and remembering what each gate does at each phase. Draw the action potential graph before reading the question — it saves time.
Common Mistake
Plugging in for K⁺ or forgetting the sign when . K⁺ is monovalent () and the log of a number less than 1 is negative.
Do not confuse passive channels (follow the gradient) with active pumps (fight the gradient). This single distinction clears half of all neural-system doubts.