HSF/Nervous system/Action potential

From ViridisWiki

The action potential is a peculiar beast to study. For some, the topic is completely foreign, while for others it's all too familiar. Unfortunately, the concept is difficult to convey in a didactic format, so we students are often left with much to desire even after a full lecture on the subject. Hopefully this brief set of notes will give you all you need to understand how action potentials are generated.

Contents 1 Fundamentals 2 Resting membrane potential 3 Concentrations and membrane potential 4 Currents and membrane potential 5 Action potentials 6 Quiz 6.1 Questions 6.2 Answers 7 Caveats

Fundamentals

• Channels are ion-specific
  • There are sodium channels, potassium channels, etc., which are more or less specific for that ion
• Channels allow ions to flow down their concentration gradients
  • Channels themselves do not dictate the direction of flow
  • This is in contrast to pumps, which drive ions against their concentration gradients
• For action potentials, we're concerned with four types of channels:
  • Leakage sodium channels
  • Leakage potassium channels
  • Voltage-gated sodium channels
  • Voltage-gated potassium channels (also called the delayed rectifier potassium channel)
• All cells have a resting membrane potential
  • For many neurons, this is around -60 mV
  • It is generated mainly by potassium leak channels
• Depolarization vs. hyperpolarization
  • Positive current flowing into the cell (or negative current flowing out of the cell) depolarizes the membrane
  • Positive current flowing out of the cell (or negative current flowing into the cell) hyperpolarizes the membrane

Resting membrane potential

The ratio of the extracellular to intracellular concentration is 140:10 for sodium and 5:140 for potassium approximately. These concentration gradients result from activity of the Na,K-ATPase (sodium-potassium pump), which pumps potassium and sodium against their concentration gradients.

Cell membranes are semipermeable. They are 100 times more permeable to potassium than they are to sodium. These permeabilities result from having more potassium leak channels open than there are sodium leak channels. Because the cell is mostly permeable to potassium at rest, we will consider only potassium here.

The movement of any ion across a membrane is governed by two gradients: 1) electric and 2) chemical. These are collectively called the electrochemical gradient of the ion. When the electric and chemical gradients of an ion are balanced (ie, equal in magnitude and opposite in direction), then the ion is said to be in equilibrium.

Moving ions across a membrane (ie, producing a current) changes the potential across the membrane. For example, injecting a positive current into a cell causes depolarization, as mentioned earlier. Conversely, the movement of positive charges out of a cell causes hyperpolarization. Thus the movement of potassium down its concentration gradient results in membrane hyperpolarization.

The degree to which movement of an ion changes the membrane potential is given by the Nernst equation. This equation takes into account the electric and chemical gradients of an ion and determines what the membrane potential will be if the membrane is permeable only to that ion. For example, in the case of a membrane that is permeable to potassium only, and the concentration gradient for potassium is 140:5 (inside:outside), then the Nernst equation says that the movement of potassium ions will equilibrate when the membrane potential is approximately -90 mV.

To understand why the equilibrium potential for potassium (E_K) is negative, consider the effect of allowing potassium to flow down its concentration gradient. As potassium is more abundant inside than outside the cell, potassium will tend to leave the cell, leaving relative negativity behind. These relative negative charges hyperpolarize the cell, as seen before. Hyperpolarized cells are cells with membrane potentials more negative than the resting membrane potential, which is typically -60 mV. Thus E_K is destined to have a value that is more negative than -60 mV.

The Nernst equation is perfect for membranes that are permeable only to a single ion. But real cells are much more complicated than that. In reality, cell membranes are permeable to a number of ions, including potassium, chloride, and sodium (listed in order of decreasing permeability). So the Nernst equation isn't sufficient for determining the resting membrane potential of a cell that's permeable to more than one ion. For that, we need an equation that takes into account the electric and chemical gradients for multiple membrane-permeable ions: the Goldman-Hodgkin-Katz (constant field) equation.

Using the GHK equation and plugging in the concentration gradients and charge for potassium, chloride, and sodium, we get a reasonable estimate of the true resting membrane potential for a cell: about -60 mV.

If the membrane is mostly permeable to potassium, then why isn't the resting potential equal to E_K? It's because the membrane isn't permeable to only potassium, but also to those other ions. For instance, the equilibrium potential for sodium is somewhere in the range of +50 mV, meaning that even though the membrane is only modestly permeable to sodium at rest, sodium will tend to bring the resting membrane potential away from E_K and slightly towards E_Na. Likewise for E_Cl. The result is a resting membrane potential that is a sort of average of E_K, E_Cl, and E_Na. R_m is closest to E_K because the membrane is most permeable to potassium.

Concentrations and membrane potential

One of the most valuable things you can remember is that the membrane potential is determined by currents. If a positive current is injected into the cell, the membrane potential becomes more positive; the cell is depolarized. If a positive current is leaving the cell, the membrane potential becomes more negative; the cell is hyperpolarized. This is the basis for the effects of potassium and sodium currents on the membrane potential.

An important clinical correlation is hyperkalemia, an increase in plasma potassium concentration. The plasma potassium concentration is an indicator of the concentration of potassium outside of cells. In hyperkalemia, the extracellular environment contains a higher potassium concentration than is found in normal individuals. The result is that the potassium gradient is thrown off from normal. Rather than having, say, 5 mM of potassium outside the cell, an individual has, say, 10 mM. The intracellular potassium concentration is unaffected. As a result, the potassium gradient is diminished compared to a normal individual, resulting in a decreased driving force for potassium to leave the cell. If less potassium is leaving the cell, the cell maintains a hold on more positive charges and is thus depolarized. Therefore an increase in extracellular potassium concentration, such as that seen in hyperkalemia, causes depolarization.

(I should mention that the description above does not attempt to tell the whole story of why hyperkalemia can lead to muscle weakness and cardiac arrest. That'll come later when we delve into cardiac physiology.)

Here's the whole picture in shorthand:

• ↑[K⁺]_out → ↓[K⁺] gradient → ↓driving force for K⁺ to leave the cell
• ↓K⁺ leaves cell → ↑positive charges inside cell → depolarization

By the same reasoning, what happens if I increase the concentration of potassium within the cell? Think about it, then see if this makes sense:

• ↑[K⁺]_in → ↑[K⁺] gradient → ↑driving force for K⁺ to leave the cell
• ↑K⁺ leaves cell → ↓positive charges inside cell → hyperpolarization

Don't continue with the next section until you've got that bit down.

Currents and membrane potential

Don't confuse the addition of a current with a change in concentration. (Whaaa? Confusing, I know. Try to get to the end of this, and I'm confident you'll understand.) As discussed above, injecting a positive current into a cell results in depolarization. So injecting potassium into the cell causes depolarization. Compare this to what we said above: increasing the potassium concentration inside the cell causes hyperpolarization. It seems fishy at first, but it's really all about currents.

When you add a current across the membrane, you're directly altering the membrane potential. Again, as before, injecting a positive current into the cell causes depolarization. Now notice what happens when you don't change the current, but instead change the concentration gradient. If I increase the concentration gradient for potassium, what have I done to the driving force for potassium? Yup, I've increased it. And assuming that there's more potassium inside than outside the cell, won't an increased driving force for potassium cause it to leave the cell more readily? Of course. So increasing the concentration gradient for potassium essentially increases its outward flow. More potassium leaves, causing hyperpolarization.

Action potentials

Action potentials are rapid swings in membrane potential that travel the length of an axon. They're made of a rising phase, falling phase, and undershoot, which are very nicely explained in this Wikipedia article.

The action potential in an unmyelinated axon depends on the movement of charges down the axon. If you inject a positively charged current (the stimulus) into the axon hillock, these charges will propagate down the axon towards the terminus. As the charges go down the center of the axon, some of them are pulled away by the membrane so that the next segment of axon membrane receives fewer positive charges. Since changes in membrane potential are governed by changes in ion currents, if you were to compare the potential at the axon hillock (where the stimulus was applied) to the membrane potential at the terminus, you would see that the change in potential at the hillock is much more than at the terminus. This is because those positively charges ions were lost as the current propagated down the axon. The result is called a graded potential: one that loses its amplitude with distance.

Why does the membrane pull some of the charges away? It's just one of the intrinsic properties of membranes; that is, membranes act as capacitors. The degree to which capacitors can store charge is given by their capacitance. The greater the capacitance, the better the capacitor can store charge. So a membrane with greater capacitance can store more charge, and is thus more able to extract ions away from the center of the axon. Thus greater capacitance means that the graded potential seen in unmyelinated axons will decay more rapidly.

What if you could somehow decrease the capacitance of the axon? If you were to do so, the membrane would be less able to store charge, so it would tend to extract fewer positive charges away from the center of the axon; as a result, more positive charges would be able to participate in the propagation of the graded potential down the axon. Consequently, the potential at the terminus would be higher than that of an axon with increased capacitance.

Before discussing how to change capacitance, first understand how capacitors relate to cell membranes. Capacitors are just plates separated by a space; these plates are where charges are stored. In a cell membrane, the plates are the regions just inside the membrane and just outside the cell membrane where charges are found (charges aren't found in the bilayer because its hydrophobicity restricts the entry of ions). The charges found on either plate are important. One plate contains more positive charges relative to the other plate. So in a membrane, you have two "plates" of opposite charges separated by a space: you have a capacitor.

A capacitor has greater capacitance if it can store charges easily. So if it's easier to add a charge onto the capacitor, then that capacitor has greater capacitance by definition. Imagine the positively charged plate in isolation. How easy is it to add a positive charge to an already positively charged plate? Not very, because like charges repel. But what if you brought the positively charged plate near the negatively charged plate? In doing so, you've basically neutralized the charges. And what's easier? Adding a positive charge to a neutral zone or adding a positive charge to an already positively charged plate? Right: it's much easier to add the positive charge to a zone of relatively neutral charge. The end result is that by bringing the plates closer together, you make it easier to store charge, so the capacitance increases. By separating the plates by a greater distance, you cannot add new charges as easily, so the capacitance decreases.

Now take a moment to recall why we wanted to change the membrane capacitance. Remember, we wanted to increase the amplitude of the potential so that it doesn't completely dissipate by the time it reaches the axon terminus. To do so, we have to ensure that the membrane doesn't pull too many ions away from the center of the axon. This will make more ions available to participate in the graded potential. How do you make the membrane less able to extract ions away? Decrease its ability to store charge, of course; that is, decrease its capacitance. To do so, we need to separate the plates of the capacitor. Nature has accomplished this by adding a layer of fat (myelin) between the inner plate and the outer plate.

Quiz

If you think you've got all that down, try answering these questions:

Questions

1. How does the membrane potential change (ie, de- or hyperpolarization) when the intracellular concentration of sodium is increased?
2. Does injecting a potassium current into the cell cause de- or hyperpolarization?
3. Decreasing the intracellular concentration of which ion (potassium or sodium) would result in membrane depolarization?
4. Decreasing the extracellular potassium concentration has what effect on membrane potential (ie, de- or hyperpolarization)?
5. Would rising the extracellular potassium concentration render a cell more or less excitable?

Answers

1. Hyperpolarization, because you've decreased the driving force for sodium to enter the cell
2. Depolarization, because you're injecting a positive current into the cell
3. Decreasing both (or either) will result in depolarization:
   • ↓[Na⁺]_in → ↑driving force for Na⁺ to enter → depolarization
   • ↓[K⁺]_in → ↓driving force for K⁺ to leave → depolarization
4. Hyperpolarization, because you've increased the driving force for sodium to enter the cell
5. It would make it more excitable, because you've decreased the driving force for potassium to leave, causing membrane depolarization, which makes it easier for the membrane to reach the threshold for action potential generation

Caveats

• I didn't consult a textbook while writing this, so I didn't track down the actual concentrations for sodium and potassium inside and outside the cell. Thus the Nernst values I used may not work out just right, but they're in the right ballpark.
• In the introduction, I said these notes were brief. Well, yeah...