Resting potentials, equilibrium potential, and action potentials

Mr. Strapps says “I put the “rest” in resting potential.”

Transmembrane proteins

There are 3 types of transporters which appear in the mammalian neuron that are important to this unit:

1. Sodium/potassium (Na+/K+) pump2. Sodium channels and potassium channels3. Voltage-gated sodium channels and voltage-

gated potassium channels

Remember these three proteins as you read on.

The Na+/K+ pump

The main importance of the Na+/K+ pump for neurons is to maintain specific concentrations of sodium and potassium on either side of the neuron’s cell membrane. It does this by pumping three Na+ out of the cell for every two K+ that it pumps into the cell.

The Na+/K+ pump and concentration gradients

As can be seen on the previous slide, the The Na+/K+ pump uses ATP (energy) to do its work. The pump requires energy because it is pumping against a concentration gradient; that is, it is pumping Na+ from inside the cell, where it is at a low concentration, to outside the cell, where it is already at a high concentration. The pump does the reverse for potassium.

As can be seen on the previous slide, there is a high concentration of K+ inside the nerve cell, and a low concentration outside.

Conversely, there is a high concentration of Na+ outside the cell, and a low concentration inside.

Remember diffusion: if given the chance, solute particles in a high concentration area will tend to diffuse towards an area of low concentration, thus evening out the concentrations of either area.

Therefore, if we think of sodium and potassium as people, we can imagine that sodium “wants” to enter the cell, and potassium “wants” to leave.

In order to get from where they are to where they “want” to be, both sodium and potassium need to pass through the cell membrane.

Sodium channels and potassium channels

These are not voltage gated channels. These are channels which are open all the time, and simply allow sodium and potassium to flow down their concentration gradients: sodium flows into the cell, and potassium flows out.

KEEP THIS IN MIND:

Neither the Na+/K+ pump nor the channels mentioned in previous slides ever closes or stops working. No matter what happens, even in the middle of an action potential, they are always doing what they do.

Equilibrium potential (Ek)

• (As shown on Slide 11) The Na+/K+ pump maintains an extracellular K+ concentration of 5mM and an intracellular concentration of 150mM

• It also maintains an extracellular Na+ concentration of 150mM and an intracellular

Na+ concentration of 15mM.

So, what is Ek, and what does it have to do with resting potentials?

• Remember, we’ve already explained that sodium is always diffusing into the cell, and potassium is always diffusing out of the cell because of their concentration gradients.

• But remember, if potassium (for example) is flowing out of the cell, that means that it’s leaving behind negatively charged proteins and ions that can’t pass through the membrane like potassium.

Look at this picture again, and notice that, when sodium diffuses through the membranedown its concentration gradient, it’s leaving behind a net negative charge, and it’s bringing with it a positive charge. The same is true for sodium. It’s easier to think aboutthis if you look at just sodium or potassium individually.

Now, think about this, and look at the previous slide again if it helps. If there’s a positive charge on the side of the membrane with a low potassium concentration, and a negative charge on the side with a high potassium concentration, doesn’t that mean that potassium will be repelled from the (low concentration) positive side?

Weird…

Yes, it is weird, because we’re saying that the side of the membrane with a lower concentration of potassium - a positively charged ion – actually has a more positive charge than the side with a high potassium concentration. The same is true for sodium.

You can think of potassium (and sodium) as being influenced by two opposing forces. On the one hand, potassium tends to flow out of the cell because of diffusion, but on the other hand, it tends to stay in the cell due to like charges.

Eventually, these two opposing forces will reach an equilibrium, meaning they will oppose each other to the point that there is zero net movement of potassium into or out of the cell (I remind you again, the same can be said for sodium). The voltage across the membrane at this point is called the equilibrium potential (Ek).

Scientists have devised a formula to calculate the equilibrium potential of a given solute across a semi-permeable membrane:

E k = 62mV * log outside cell ______________________

inside cell

Remember, we use the original concentrations (as shown in slide 15) in our equation, because it takes almost no concentration change to cause a significant change in membrane voltage.

If we insert our known concentrations for potassium and sodium (as shown on slide 11), we get the following values:

Epotassium = -92mV

Esodium = +62

The negative voltage for potassium means the intracellular space has a relatively negative charge, and the extracellular space has a relatively positive charge. The reverse is true for the positive voltage for sodium.

All well and good, but….

Yes, so far we’ve been looking at sodium and potassium individually. But won’t things change when you’ve got sodium diffusing into the cell and potassium diffusing out?

Yes, things do change. Instead of the membrane having an Ek value equal to that which we would expect if the membrane were permeable to potassium only or sodium only, we get a value in between. Since the membrane is permeable to both, we get an Ek value somewhere between the two.

And the number is…

-70mV

(Pause for sustained, raucous applause.)

This is the normal resting potential for the average mammalian neuron. So, we can tell from the negative voltage that our neurons have a relatively positive charge external to the cell and negative internal to the cell – as long as the cell is at rest (i.e. not stimulated).

Not so fast!.....

Aha. Yes, as I’m sure you were thinking, the resting Ek value for a membrane that’s permeable to both potassium and sodium should fall right in the middle between the sodium Ek value and the potassium Ek value, right? And that gives us a value of about -15mV. So why is our resting potential -70mV?

Well, it turns out that our neuronal membranes are actually more permeable to potassium than to sodium. Therefore, we have an Ek value closer to that of potassium than sodium.

So, here’s what we know so far…

1 The Na+/K+ pump maintains a relatively high intracellular concentration of potassium and a relatively low intracellular concentration of sodium.

2 Our neurons are more permeable to potassium than sodium, which is why we have a resting membrane potential of -70mV.

Now we’re ready to learn about ACTION POTENTIALS

Here’s the membrane of an axon at rest:

Suddenly, there’s an influx of Na+. This influx raises the charge of the internal environment of the membrane, thus raising the membrane potential from -70mV to a higher (i.e. less negative) value.

The change in voltage causes activation channels on voltage-gated sodium channels (not the same channels that maintain Ek, which are open all the time) to open up. Sodium flows down its concentration gradient – into the cell.

The more sodium flows into the cell, the more the voltage increases, which causes more sodium channels to open, which causes even more sodium to flow into the cell….

and so on.

Eventually, the inflowing sodium raises the membrane voltage enough to cause activation gates on voltage-gated potassium channels to open. Meanwhile, the inactivation channels on the voltage-gated sodium channels close, thus drastically reducing the flow of sodium into the cell.

So, now we have positively charged potassium ions flowing out of the cell, which causes the internal cellular environment to return to a relatively negative charge.

In fact, the inside of the cell develops such a negative charge that it is now more relatively negative than it was when the membrane was at rest. We call this hyperpolarization. This prevents any sudden stimulus (i.e. a new influx of Na+) from triggering a new action potential… at least until the sodium/potassium pump is able to restore the membrane to its regular resting state.

So, we end up with the sodium influx of an action potential at one patch of membrane triggering an action potential at the next patch of membrane – but not at the preceding patch of membrane, because it’s now hyperpolarized:

And don’t forget that, in vertebrate neurons, action potentials only occur at the Nodes of Ranvier. This “leapfrogging” of action potentials from node to node is called saltatory conduction, and it speeds the progress of the action potential down the axon.