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I am reading a journal paper, and in one of their experiments they treated organotypic hippocampal slice cultures with a high potassium solution to depolarize the neuronal membranes:

We found that the medium from control slices, transduced with AAV-CMV-LacZ, incubated in high potassium solution (+20 mM) over 24 hours contained statistically significantly higher IGF1 than that in high sodium solution (+20 mM), consistent with our hypothesis that IGF1 is released from pyramidal neurons in an activity-dependent manner.

I know that increasing extracellular KCl concentrations is commonly used to depolarize neurons in experiments. I have read that the resting neuronal membrane is highly permeable to K+, and that the membrane potential is sensitive to changes in extracellular K+ concentration. Increasing extracellular K+ depolarizes membranes.

This is due to the influx of K+ ions through potassium leak channels (though neurons also have voltage-gated K+ channels, I'm assuming that they have more potassium leak channels).

Under resting conditions, there is a higher concentration of Na+ ions in the extracellular fluid compared to the cytosol of the neuron.

At rest, both the electrical and diffusion forces are driving Na+ towards the inside of the neuron (since the inside of the neuron is more negatively charged compared to the extracellular space).

In the paper, they incubated neurons for 24 hours in serum-free medium plus 20 mM NaCl.

However, increasing extracellular Na+ levels did not depolarize the neuronal membrane (unlike increasing extracellular K+ levels).

Why is this the case? I know that the neuronal membrane contains voltage-gated sodium channels and sodium leak channels. Is it because neurons have a higher number of voltage-gated sodium channels in their membranes compared to sodium leak channels?

I.e. to depolarize the membrane, the Na+ leak channels are not enough, you also need the opening of the voltage-gated Na+ channels.

Any advice is appreciated.

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I would start with the Goldman equation, plug in some reasonable values and experiment with the results. Your reasoning I think comes from a common misconception that involves counting positive charges and forgetting that any solution with sodium or potassium cations comes with an equal balanced number of anions. You're never adding just sodium or potassium; if you did, you'd have enough energy in a small solution to create lightning and the charges would rebalance themselves. Membrane potentials are based on really tiny charge imbalances.

Potassium is high inside cells and low outside; if a cell is only permeable to potassium, that would mean a bit of potassium leaks out, following that concentration gradient. The result is a cell that's a bit negatively charged inside. If you increase the potassium concentration outside to equal the inside, there's no concentration gradient for those ions to travel down, so no membrane potential. If the potassium concentration outside is greater than inside, potassium ions flowing down their concentration gradient results in a positive charge inside the cell.

If there is little sodium conductance, changes in sodium don't affect the membrane potential. If you add a bunch more sodium outside, it will depolarize the cell a little bit if there's some sodium conductance, but as long as most of the conductance is for potassium it's mainly the potassium concentration gradient that matters.

Also, this experiment is just adding 20 mM additional sodium or potassium extracellularly; for potassium that may be doubling the concentration or more. For sodium it's more likely a 10-20% increase.

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