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Sodium-potassium pumps pump two potassium ions in and three sodium ions out. That means that it creates space for one more ion. Eventually, it's going to be filled. The concentration will be fine, as it would be 3 sodium out and 3 potassium in (because one potassium ion flowed in), or 2 potassium in and 2 sodium out (as three goes out and one comes in).

However, sodium-potassium pumps supposedly change the membrane potential by pumping more positive ions out than in. Wouldn't this be nullified if another ion comes in to take its place?

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    $\begingroup$ I’m voting to close this question because it: 1) contains multiple questions; 2) shows no evidence of prior research; 3) is unclear; and 4) appears to based on an assumption that seems to reveal a lack of basic understanding of chemistry — if so, this is best rectified by taking an chemistry course or an online equivalent (e.g. from Khan Academy). $\endgroup$
    – tyersome
    Aug 9, 2022 at 16:19

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There is no special "empty space" due to the action of these pumps. Ions are very, very small and even in liquid there are always gaps between molecules/ions/atoms. If you dissolve a bunch of salt in a glass of water, the volume doesn't change noticeably, but even if you measure carefully you find it actually decreases. That's because water molecules surround the ions and take up a bit less space than they would in a pure solution.

Additionally, sodium, potassium, other ions, water, etc. can all cross membranes by a variety of mechanisms. For charged ions, they cross the membrane primarily through ion channels though also through transports, some of which use ion concentration gradients to move other things (see https://en.wikipedia.org/wiki/Cotransporter).

Though flow through these channels is indeed somewhat random, in aggregate you can predict how much ions will move. It isn't as though a random ion will "replace" a sodium ion that has moved, rather, all ions will have net flow according to their concentration gradient and any electrical gradient across the membrane. You can determine the direction of net flow for given ion using the Nernst equation.

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  • $\begingroup$ Well ... this does not apply to ammonium sulphate, and is one reason for the popularity of nomograms. Try dissolving 50g ammonium sulphate in 100ml water, for example, or try dissolving 30 g SDS (sodium dodecyl sulphate) in 100 ml water: in both cases there is a very considerable increase in volume. (In my experience, a very common mistake in biochem labs is to dissolve 30g SDS in 100 ml water, ignore volume changes, and assume this is 30% (w/v) solution: it isn't (the final volume is considerable greater than 100ml). $\endgroup$
    – user338907
    Aug 9, 2022 at 19:40
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    $\begingroup$ What I actually meant by "empty space" is how much ions can enter before before potassium flow and sodium flow equalize, and did not mean actual space (don't really know why I termed it that way). I can imagine a pump leaving one charge worth of "empty space (that is, one ion is needed until potassium and sodium flow equalize. This obviously isn't exact, but is true on average)", therefore slowing down potassium flow a tiny bit (less diffusional force), and allowing sodium to build up in the cell (one sodium ion on average), nullifying the pump's contribution to the membrane potential. $\endgroup$
    – Sentient Rays
    Aug 10, 2022 at 7:51
  • $\begingroup$ @SentientRays The pump's contribution to membrane potential is fairly minimal, a couple mV perhaps. If you want to use a water analogy, think about it as pushing some water to one end of the pool; there's nothing preventing it from flowing back, yet you can have slightly more water on that side indefinitely if you keep pushing. I've repeated this a few times to you now, but use the Nernst equation and Goldman equation; have a look at them and play around with possible values to input. These are the important things. $\endgroup$
    – Bryan Krause ♦
    Aug 10, 2022 at 16:13
  • $\begingroup$ Related questions I've answered: biology.stackexchange.com/questions/88730/… biology.stackexchange.com/questions/81570/… biology.stackexchange.com/questions/95192/… $\endgroup$
    – Bryan Krause ♦
    Aug 10, 2022 at 16:16
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Your question implies that proteins are like metal tubes (i.e., constant shape and form). This, however, is a bad assumption since there really is no "empty" space. Proteins have active sites and their movement is a highly chemical process; they often change shapes (e.g. hemoglobin) as well. Additionally, proteins are really "smart" (i.e., highly specific) and won't accept different ions. This "space" you refer to is very small, diagrams are misleading in that sense. You can look up 3D renders of proteins and quickly realize that they are difficult to understand. There is always the possibility of taking in different ions. This can definitely affect cell metabolism and function not because the cell cannot get rid of the unwanted material (homeostasis), but because when they do, they expel the material onto neighboring cells.

I am sure my answer is probably unsatisfying because you've asked too many questions under one post making it difficult to focus in on one topic. Try researching each question on your own first and if you do not find a satisfying answer, you can always ask a question in this forum :)

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