A neuron has a resting membrane potential of −70 mV. The equilibrium potential for K⁺ is −89 mV. What is the electrochemical driving force on potassium, and in which direction will K⁺ flow?
ADriving force = −19 mV; K⁺ flows inward because the inside is more negative than E_K
BDriving force = +19 mV; K⁺ tends to flow outward because V_m is more positive than E_K, meaning the electrical force holding K⁺ inside is insufficient to counteract the concentration gradient
CDriving force = 0; K⁺ is at equilibrium at −70 mV
DDriving force = +19 mV; K⁺ flows inward because the concentration gradient overpowers the electrical gradient
Driving force = V_m − E_K = −70 − (−89) = +19 mV. A positive driving force for a monovalent cation means the net force pushes K⁺ outward. At −89 mV, K⁺ would be perfectly balanced; at −70 mV (less negative), the electrical pull inward is weaker than at equilibrium, so the concentration gradient pushing K⁺ out wins. K⁺ flows out of the cell through open K⁺ channels — this outward current is what maintains the resting membrane potential near (but not equal to) E_K.
Question 2 Multiple Choice
What does the Nernst equilibrium potential E_Na ≈ +67 mV represent for sodium?
AThe membrane voltage required to pump sodium out of the cell against its concentration gradient
BThe voltage at which the concentration gradient driving Na⁺ inward and the electrical gradient driving Na⁺ outward exactly cancel, so there is no net electrochemical force on sodium
CThe resting membrane potential contribution from sodium channels
DThe threshold membrane voltage at which sodium channels open during an action potential
E_Na is the single-ion equilibrium potential: the membrane voltage at which the Na⁺ concentration gradient (pointing inward, because Na⁺ is more concentrated outside) is exactly balanced by the electrical gradient (at +67 mV, the positive interior repels incoming positive ions). At this voltage, Na⁺ has zero net electrochemical driving force. At the resting potential of −70 mV, V_m is far below E_Na, so the driving force (V_m − E_Na = −70 − 67 = −137 mV) is large and negative, meaning Na⁺ is powerfully driven inward whenever Na⁺ channels open.
Question 3 True / False
If the actual membrane potential equals the Nernst equilibrium potential for a given ion, there is no net electrochemical driving force on that ion.
TTrue
FFalse
Answer: True
The equilibrium potential is defined as the membrane voltage at which the concentration gradient and electrical gradient for that ion exactly cancel. At E_ion, the chemical potential difference driving the ion down its concentration gradient is exactly offset by the electrical potential difference, so the net electrochemical driving force is zero and there is no net ion flux. This is the condition the Nernst equation calculates.
Question 4 True / False
The Nernst equation can directly calculate the resting membrane potential of a neuron, since it relates membrane voltage to ion concentration gradients.
TTrue
FFalse
Answer: False
The Nernst equation calculates the equilibrium potential for a single ion in isolation — the voltage that would develop if the membrane were permeable to only that one ion. Real neuron membranes are permeable to multiple ions (K⁺, Na⁺, Cl⁻, and others) simultaneously, and the resting potential reflects all of them weighted by their relative permeabilities. The Goldman equation handles the multi-ion case. The resting potential (≈ −70 mV) falls between E_K (≈ −89 mV) and E_Na (≈ +67 mV), closer to E_K because resting potassium permeability greatly exceeds sodium permeability.
Question 5 Short Answer
Explain why the resting membrane potential of a typical neuron (around −70 mV) is close to E_K (−89 mV) but not equal to it. What determines where between E_K and E_Na the resting potential falls?
Think about your answer, then reveal below.
Model answer: The Nernst equation gives the equilibrium potential for each ion individually. At rest, the membrane is much more permeable to K⁺ than to Na⁺ (due to leak channels), so the resting potential is dominated by K⁺ and falls close to E_K. However, there is a small but non-zero resting Na⁺ permeability that pulls the potential toward E_Na (+67 mV), shifting it from −89 mV toward a less negative value. The Goldman equation formalizes this: the resting potential is a permeability-weighted average of the equilibrium potentials. If P_K >> P_Na, the result is close to E_K but not exactly equal. The Na⁺/K⁺-ATPase pump also makes a small direct contribution by pumping 3 Na⁺ out for every 2 K⁺ in (electrogenic).
This explains why disrupting K⁺ channels affects resting potential more than disrupting Na⁺ channels at rest — the resting potential is fundamentally a potassium equilibrium perturbed by minor sodium permeability. During an action potential, the relationship reverses: sodium permeability spikes and the membrane potential rushes toward E_Na.