Neuron X has standard resting permeabilities, and standard intracellular and extracellular concentrations of sodium, potassium, chloride and calcium. When depolarised to +58mV by a strong, excitatory synaptic input, what direction will K+ move across the membrane if its selective channel were opened?

Question

BlackTom AI · Accepted Answer

E_K ≈ -95 mV, so with the membrane at +58 mV K+ will flow out of the cell.

1) Relevant knowledge points and concepts
- Nernst equilibrium potential for K+ (E_K) sets the voltage at which chemical and electrical forces on K+ balance. 
- If membrane potential (Vm) is more positive than E_K, the net electrochemical driving force pushes K+ outwards; if Vm is more negative than E_K, K+ is driven inwards. 
- Nernst equation: E = (RT/zF) ln([out]/[in]) or at 37°C in mV: E = 61.5·log10([out]/[in]) for a monovalent ion.

2) Step-by-step reasoning
- Use typical "standard" mammalian concentrations: [K+]in ≈ 140 mM, [K+]out ≈ 4 mM. z = +1.
- Compute E_K using the temperature-corrected Nernst form.

3) Calculations (intermediate steps)
- log10([K+]out/[K+]in) = log10(4/140) = log10(0.02857) ≈ -1.544
- E_K ≈ 61.5 mV × (-1.544) ≈ -95.0 mV

- Compare Vm to E_K: Vm − E_K = +58 − (−95) = +153 mV. This positive difference indicates a strong outward electrochemical driving force for K+.

4) Why the correct answer is correct
- Because intracellular K+ is much higher than extracellular and E_K is strongly negative (~−95 mV), a membrane potential of +58 mV is far more positive than the equilibrium potential. To reduce the positive charge inside and move Vm toward E_K, positively charged K+ ions leave the cell when K+-selective channels open. Thus net K+ movement is outward.

5) Why other options are incorrect
- "In" would be correct only if Vm were substantially more negative than E_K (i.e., Vm < E_K), so positive K+ would be driven into the cell — not the case here. 
- "No net movement" would require Vm = E_K (≈ −95 mV); at +58 mV there is a large driving force, so net flux is not zero.

Conclusion: The net movement of K+ is Out, which matches the provided correct answer.

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