# Why isn't the resting membrane potential at equilibrium?

There has been a question asked regarding the purpose of ion pumps, and the main answer was that the resting membrane potential isn't in an equilibrium state, so the potassium keeps flowing out. Other sources claim this, too.

But why is this the case? For example(in this case considering only sodium and potassium), wouldn't potassium be forced out the cell when sodium starts to enter, and in the same way that potassium builds up an electric force to match its diffusional force to reach equilibrium, the electric force of potassium get stronger to the point that it can counter sodium's inflow? This would create a new equilibrium, albeit different from potassium's Nernst potential, but still an equilibrium.

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Jul 28, 2022 at 3:05

This would create a new equilibrium, albeit different from potassium's Nernst potential, but still an equilibrium.

The Nernst equation is how you determine the voltage at which an equal number of potassium ions move in each direction across the membrane; that seems to be what you are calling "equilibrium" for potassium. If you have two ions and you'd like them both to have zero net flow, their Nernst potentials must be identical. The Nernst potential depends on relative concentration; the only way to change Nernst potential is to change relative concentration.

The Goldman equation will help you find a different "equilibrium": the voltage at which net total flow of all ions equals zero. This gives you the membrane potential with multiple ions present; however, at this equilibrium, as you've read, individual ions are not at equilibrium; for a typical neuron, you can expect that at the resting potential given by the Goldman equation you will have about equal potassium leaving the cell as sodium entering.

In a typical neuron, there is more potassium and less sodium inside the cell relative to outside.

This makes a negative Nernst potential (=reversal potential) for potassium: to stop net flow of potassium down its concentration gradient and out of the cell, you need negative charge inside.

Similarly, there is a positive Nernst potential for sodium: to stop net flow of sodium down its concentration gradient and into the cell, you need positive charge inside.

The resting membrane potential is a weighted sum of these potentials that are driven by concentration gradients. The relative contribution of different ions to the membrane potential depends on their permeability; the more permeable the membrane is to an ion (through specialized channels), the more important that ion is for setting the overall membrane potential.

For a typical neuron, the resting membrane potential is near the potassium reversal potential, but not quite as negative, due to sodium (and other ions, but for now we can just think in terms of these two).

Let's say, for example, potassium reversal is -90 mV, sodium reversal is +50 mV, and the membrane potential is around -70 mV. The reason it's around -70 mV would be because that's precisely the voltage where as many potassium ions are flowing out of the cell as sodium ions are flowing in.

If pumps keep the concentrations of sodium and potassium constant inside and out, this will stay the same indefinitely: concentrations stay the same means reversal potentials stay the same which means the membrane potential stays the same, as long as ion permeabilities stay the same.

However, with no pump, the sodium concentration inside is rising, and the potassium concentration is falling. That means the reversal potentials won't stay the same. As the potassium concentration in and out becomes more similar, the Nernst potential for potassium drifts towards zero: you don't need any voltage to stop net potassium from flowing if the concentration is equal inside and out. As the sodium concentration in and out becomes more similar, the Nernst potential for sodium drifts towards zero. These potentials are not intrinsic to the ions, they are entirely a function of relative concentrations inside and out. If you lose the relative concentration gradients, you lose the voltage, and, importantly, you lose the ability to influence membrane voltage by changing the permeability of particular ions.

• What I'm curious about is why potassium just leaves the cell without forming an electric gradient (by leaving behind anions) when sodium starts flowing in. Wouldn't potassium eventually be attracted back, match the sodium inflow, disable more sodium from coming in, and reach an actual equilibrium as the resting membrane potential? This is the same way the electric force matches the diffusional force to reach the potassium Nernst equilibrium (which is when we're only considering potassium), but this time also matching the added diffusional force by the sodium inflow. Jul 30, 2022 at 7:09
• @SentientRays At the resting potential, the sodium entering equals potassium leaving; that's what the Goldman equation tells you: what voltage will the cell be at when the charge moving is equal. If 100 potassium ions leave and 100 sodium ions come in, there's no electrical change: +100 - +100 = 0. If enough ions move so that concentrations change (like if a pump isn't keeping them constant), you need to redo your calculations. Jul 30, 2022 at 14:57
• Oh. So then would the reason sodium increases the membrane potential a bit be that there's initially some space for the sodium to go to, therefore making multiple sodium entering equal one potassium ion leaving for a while until it fills up and one sodium equals one potassium? But then, after that other ions will not affect the membrane potential. If calcium enters after potassium and sodium establish themselves, since the cell is in a state where one charge entering one charge leaving, one calcium would kick two ions out and not affect the membrane potential at all. Aug 1, 2022 at 0:52
• @SentientRays Not really following and I don't think anything you are writing is grounded in reality. Use the Nernst and Goldman equations, they tell you everything about what will happen in the cell: Goldman equation tells you what the membrane potential will be, Nernst equation tells you the equilibrium for each ion. Ions will always move according to their Nernst potential relative to the membrane potential. Aug 1, 2022 at 3:42
• Alright. I was just wondering if you could explain the mechanics behind exactly why ions change the membrane potential before reaching the inflow-outflow balance. Aug 1, 2022 at 10:23