In a two-compartment model of a cell with a K +-permeable membrane and a 10-fold excess of K + in the inside compartment, how would K + ions flow across the membrane?

Question

BlackTom AI · Accepted Answer

Because K+ concentration is ten times higher inside, there is a chemical driving force pushing K+ out of the inside compartment through a K+-permeable membrane. The relevant concepts are diffusion down a concentration gradient, the development of an opposing electrical gradient (membrane potential), and the Nernst equilibrium when chemical and electrical forces balance.

Step-by-step reasoning:
1. Start with concentrations: [K+]inside = 10 × [K+]outside. This creates a net chemical (diffusive) flux of K+ from inside → outside.
2. As K+ leaves, the inside loses positive charge relative to the outside, so the inside becomes negative. This electrical gradient attracts K+ back inward and opposes further efflux.
3. Net movement continues until the electrical force exactly balances the chemical gradient; at that point the electrochemical potential difference = 0 and no net flux occurs (although individual ions still move both ways thermally).

Quantitative check (Nernst equation at physiological temperature, 37°C):
E_K = (61.5 mV / z) × log10([K+]out / [K+]in), with z = +1 for K+.
With a 10-fold inside excess: [K+]out/[K+]in = 0.1, so
E_K = 61.5 mV × log10(0.1) = 61.5 mV × (−1) = −61.5 mV.
A negative inside potential of about −61.5 mV would be the equilibrium; until that potential is reached, net K+ flows out.

Why the correct choice is right:
- It states net flow from inside to outside, which is exactly the direction driven by the initial concentration gradient.

Why the other options are incorrect:
- “Both directions, but negligible”: thermal bidirectional motion exists, but the net flux is not negligible until an opposing voltage builds.
- “There would be no flow”: false because concentrations differ.
- “Both directions at equal molar quantities”: only true at electrochemical equilibrium (specific membrane potential); initially not true.
- “Flow from outside to inside”: opposite of the concentration-driven direction.

Conclusion: Net K+ ions would flow from the inside compartment to the outside compartment, matching the provided correct answer.

In a two-compartment model of a cell with a K +-permeable membrane and a 10-fold excess of K + in the inside compartment, how would K + ions flow across the membrane?单项选择题

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