In a two-compartment model of a cell with a K +- and Cl --permeable membrane and a 10-fold excess of K + in the inside compartment, how would the membrane potential change if all K + ions were replaced by Cl - ions?

Question

BlackTom AI · Accepted Answer

The Nernst equation gives the equilibrium membrane potential for a single permeant ion: E = (RT / zF) ln([out] / [in]). For biological conditions at 37°C this is often written E ≈ (61.5 mV / z) log10([out]/[in]).

1) Relevant knowledge points and concepts
- The Nernst equation relates concentration ratio of a permeant ion to the membrane potential (Vm = Vinside − Voutside for our sign convention).
- The ionic valence z determines the sign: cations (z = +1) and anions (z = −1) produce potentials of opposite sign for the same concentration ratio.
- A 10-fold concentration difference is log10([out]/[in]) = log10(0.1) = −1.

2) Step-by-step reasoning
- Case with K+ (z = +1) and 10× more inside: E_K = (61.5 mV / +1) × (−1) = −61.5 mV. So the inside is negative relative to outside.
- If every K+ is replaced by Cl−, the concentration ratio is the same (10× inside), but z = −1 for Cl−.

3) Intermediate calculation steps
- For Cl−: E_Cl = (61.5 mV / −1) × (−1) = +61.5 mV.
- Algebraically, changing the sign of z flips the sign of E for the same [out]/[in].

4) Why the correct answer is correct
- Replacing a permeant cation with a permeant anion reverses the direction of charge movement that generates the equilibrium potential. The magnitude remains the same for a 10-fold gradient, but the sign inverts: negative → positive.

5) Why other options are incorrect
- "No potential would be generated": incorrect because a permeant ionic gradient always generates a diffusion potential.
- "It would not change": incorrect; switching ion charge changes the sign of Vm.
- "It would double" / "It would be reduced by half": incorrect because magnitude remains the same for the same 10-fold ratio; only the sign changes.

6) Conclusion
- Therefore the membrane potential would become positive, confirming the provided answer.

In a two-compartment model of a cell with a K +- and Cl --permeable membrane and a 10-fold excess of K + in the inside compartment, how would the membrane potential change if all K + ions were replaced by Cl - ions?单项选择题

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