Which ONE of the following factors DOES NOT contribute significantly to the resting membrane potential?

Question

BlackTom AI · Accepted Answer

Goldman-Hodgkin-Katz (GHK) formalism and the Nernst equation define the resting membrane potential as arising from ionic concentration gradients and selective membrane permeabilities, not from membrane capacitance.

1) Relevant knowledge points and concepts
- Nernst equation: Eion = (RT/zF) ln([out]/[in]) gives equilibrium potentials for individual ions (e.g., EK ≈ −90 mV, ENa ≈ +60 mV with typical mammalian concentrations).
- GHK equation: Vm is a weighted logarithmic sum of ion concentrations weighted by relative permeabilities (P): Vm ≈ (RT/F) ln((PK[K+]out + PNa[Na+]out + PCl[Cl-]in) / (PK[K+]in + PNa[Na+]in + PCl[Cl-]out)).
- Na+/K+ ATPase maintains the concentration gradients that produce the Nernst potentials.
- Membrane capacitance stores charge and affects temporal dynamics (tau = Rm·Cm) but not the steady-state (DC) voltage.

2) Step-by-step reasoning
- Calculate representative Nernst values (37°C, 61.5 mV·log10 form):
  EK ≈ 61.5·log10(5/140) ≈ 61.5·(−1.447) ≈ −89 mV.
  ENa ≈ 61.5·log10(145/15) ≈ 61.5·0.986 ≈ +61 mV.
- Use GHK to show Vm depends on PK vs PNa. Example: if PK >> PNa (typical), Vm ≈ −65 to −75 mV. For instance, let PK=1, PNa=0.05:
  Numerator = 1·5 + 0.05·145 = 12.25; Denominator = 1·140 + 0.05·15 = 140.75;
  Ratio = 12.25/140.75 ≈ 0.087 → Vm ≈ 61.5·log10(0.087) ≈ −65 mV.
- The Na+/K+ pump is essential because, without it, gradients would dissipate. Relative impermeability (low passive ionic leak except through selective channels) is essential to preserve gradients. Relative permeability to Na determines how much ENa pulls Vm toward positive values.

3) Why the correct answer is correct
- Capacitance affects how quickly Vm can change (charging/discharging), not the steady-state value. In steady state capacitive current is zero; Vm is set by ionic electrochemical equilibrium and conductances, so membrane capacitance does not contribute significantly to the resting membrane potential.

4) Why other options are incorrect
- Ion concentration gradients produced by Na+/K+ ATPase: essential, directly set equilibrium potentials.
- Relative impermeability of the membrane to ion movement: necessary to maintain gradients and prevent rapid equilibration.
- Relative permeability to sodium: changes the weighting in GHK and therefore shifts Vm.

Conclusion: therefore "Capacitance of the neuronal membrane" does not contribute significantly to the resting membrane potential, matching the provided correct answer.

Which ONE of the following factors DOES NOT contribute significantly to the resting membrane potential?Single choice

Similar Questions

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