A group of neurons expresses a pump which actively transports Vz2- into the cell, and also expresses a limited number of Vz2- leak channels in the cell membrane. Which voltage would most closely represent EVz in these neurons?

Question

BlackTom AI · Accepted Answer

Because Vz is a divalent anion (charge z = −2), its equilibrium potential is set by the Nernst equation. A pump that actively accumulates Vz2− inside the cell produces a much higher intracellular concentration than extracellular, so the chemical gradient tends to drive Vz2− out of the cell. To balance that outward chemical flux at equilibrium, the electrical gradient must pull Vz2− back in — which requires the inside of the cell to be positive relative to outside. Therefore EVz will be a positive membrane potential.

1) Relevant knowledge points
- Nernst equation: Eion = (RT/zF) ln([out]/[in]) or (at 37°C) E(mV) = (61.5/z) · log10([out]/[in]).
- Sign of z matters: for an anion (negative z) a higher [in] than [out] produces a positive E.
- A limited number of leak channels doesn’t change the Nernst prediction for that ion’s equilibrium potential; it only affects how closely the membrane potential approaches that value.

2) Step-by-step reasoning and calculation
- Use the 37°C form: E(mV) = (61.5/z)·log10([out]/[in]).
- For Vz2−, z = −2, so E = 61.5/(−2) · log10([out]/[in]) = −30.75 · log10([out]/[in]).
- If the pump creates an intracellular concentration about 20× extracellular (a plausible value for an actively transported ion), then [out]/[in] = 1/20 = 0.05.
- Compute log10(0.05) = −1.3010.
- Then E = −30.75 × (−1.3010) = +40.0 mV.

3) Why this is correct
- The positive sign arises because Vz is an anion concentrated inside; the electrical gradient needed to oppose the chemical gradient is inward (inside positive).
- The quantitative result (+40 mV) follows directly from the Nernst equation using a reasonable 20:1 intracellular:extracellular ratio produced by the pump.

4) Why other choices would be wrong (brief)
- Any negative EVz would contradict that an anion is higher inside (that would require higher outside concentration).
- EVz = 0 would imply equal concentrations inside and outside.
- Very large positive values (≫ +60 mV) would require unrealistically huge concentration gradients.

5) Conclusion
These considerations and the Nernst calculation give EVz ≈ +40 mV, confirming the correct answer: a. 40mV.

A group of neurons expresses a pump which actively transports Vz2- into the cell, and also expresses a limited number of Vz2- leak channels in the cell membrane. Which voltage would most closely represent EVz in these neurons?Single choice

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