The AChR is permeable to sodium and potassium ions only and has a reversal potential of 0mV.

However the Nernst potentials for sodium and potassium ions is ~ +60mV and -88mV respectively. Taking a simple average of these two potentials would give an expected AChR reversal potential of -14mV; but that is not what we see.

My question is whether the reversal potential is pulled up to zero because of a greater conductivity to sodium than potassium ions, and if so, how the AChR selectivity filter achieves this.



Short answer


There are differences in Na+ versus K+ permeability, but you have it backward: potassium is actually slightly more permeable; however, these differences are not the only factors influencing the reversal potential, and also, the reversal potential for a nAChR need not be exactly 0 mV.

tl;dr to the long answer

You need to sum before taking ratios rather than take a difference of ratios when computing a reversal potential for multiple ions together.

Before we get into the weeds...

In most sources you will hear something like the reversal potential for a nonspecific ligand-gated channel like nAChR is "about 0 mV" - this is going to vary in different cell types, in different conditions, with different recent activity levels, with different versions of the receptor, etc.

What's important to remember in all this is that -14 mV is also about 0 mV... In the context of excitable cells, what is most important is the reversal potential relative to the threshold for firing a spike or activating other channels. That said, I'm not actually saying the reversal potential for nAChR is actually -14 mV, there are a couple other factors missing...

What you are missing

The big one you are missing is that the concentrations of the ions matter, not just their ratios. For the reversal potential of a single ion, all we really care about is the ratio inside and out, which is found in the Nernst equation.

Averaging the reversal potential for two major ion species, like you have done, gives you a pretty good ballpark estimate (afterall, -14 mV is also about 0 mV!).

To get the actual reversal, however, you'll need the Goldman Equation.

We can simplify the Goldman equation for just Na+ and K+ in fairly standard conditions to something like:

$61.5 \mathrm{mV} * log_{10}(\frac{P_{Na} [Na^+_{out}] + P_{K} [K^+_{out}]]}{P_{Na} [Na^+_{in}] + P_{K} [K^+_{in}]]}$)

If the permeabilities are both :=1, and the concentrations of Na and K are equal and opposite, then indeed you will get zero. However, if that was true, you would also have equal and opposite reversal potentials for Na and K alone in the cell: in the numbers you gave, that isn't the case.

I'm not sure what numbers you used exactly, but I'll use my own example. If potassium is 5mM out, 140 mM in, the reversal potential will be -85.6 mV for potassium. If sodium is 140 mM out, 12 mM in, the reversal potential will be 63.1 mV for sodium (you can check my math with the Nernst equation).

If you combine these numbers in the Goldman equation above, you will get -1.2 mV: closer to zero than your -14 mV estimate.

They are so close because the ratio (140+5)/(12+140) is a lot smaller than the difference of the ratios (5/140) and (140/12): order of operations matters.

This is assuming identical permeabilities

However, the permeabilities aren't actually identical

There are many papers measuring relative permeabilities in nAChRs, I just chose one randomly as an example (happened to be the first Google Scholar result).

Nutter and Adams 1995 found the relative permeability of several monovalent and divalent cations, with Na as a reference:

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Therefore, potassium is actually slightly more permeable than sodium. However, there are also other important ions that could contribute, even if they are found at lower concentrations than either sodium or potassium, and the example ion concentrations you find in a textbook might not apply in the systems you are studying. A source that says nAChRs are only permeable to sodium and potassium really just means that they are not permeable to another other important high-concentration ion: chloride. They are also simplifying things a bit for you, which is okay.

If I use the Goldman equation quickly with these data, I get a reversal potential (with just Na and K, ignoring other ion species) of -5.9 mV: still "about 0 mV" and still closer than your original -14 mV estimate.

But how are different ions with the same charge showing different permeabilities?

This is better off as a separate question, and probably easier to address with a more extreme case, like in selective sodium or potassium channels. However, like in those channels, in channels that we call "non-specific", the particular arrangement of amino acid residues (especially charged ones) at the pore can favor particular ions because those ions differ slightly in size.

Nutter, T. J., & Adams, D. J. (1995). Monovalent and divalent cation permeability and block of neuronal nicotinic receptor channels in rat parasympathetic ganglia. The Journal of general physiology, 105(6), 701-723.

  • $\begingroup$ I'm really happy with this answer! I hadn't really appreciated the importance of the magnitude of ion concentration as opposed to just their ratios in setting membrane potential. Thanks for taking the effort to correct my misconception:) $\endgroup$ – ogu01 May 30 '18 at 22:03
  • 1
    $\begingroup$ @ogu01 I really like the simplicity of the Goldman equation: sort of the "F=ma" of neuroscience and other disciplines where excitable membranes are important; I think it's really helpful as a student of these sorts of topics to just sort of "play" with it and make up your own scenarios and test them out. This will help the concepts make better sense. Best of luck to you! $\endgroup$ – Bryan Krause May 30 '18 at 22:07

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