For the next couple of classes I want to discuss the ionic basis of the action potential, which is the mechanism that the nervous system uses for long distance signalling. As you’ll see, the basic principles are similar to those we’ve used in discussing the resting potential, except that during the action potential, the membrane isn’t resting--its potential increases and decreases very rapidly because the membrane actively changes its permeability to different ions. What I’m going to do is first tell you about the history of ideas to explain the action potential, describe a series of experiments conducted by Alan Hodgkin and Andrew Huxley around 1950 that established the modern explanation for the AP, then discuss what cell and molecular biologists have been able to add to their story in the last 40 years.

First, the history. As I previously mentioned, Galvani suggested in 1791 that animals used electrical signals in their nervous system, and this was established conclusively in the mid-1800s by the German/French scientist Dubois-Raymond. However, it wasn’t until the early years of the 20th century that anyone tried to suggest a mechanism for how these signals could be generated, and the first person to do that was Julius Bernstein, whom we’ve already discussed. Bernstein had applied the Nernst equation to the study of the resting potential and concluded that the membrane of nerve cells was selectively permeable only to K⁺ at rest (as we now know, this isn’t exactly true). He knew that the interior of nerve cells was negative with respect to the outside of the cell in resting cells. And he made an effort to measure the change in the membrane potential during an action potential, which normally lasts only a few thousandths of a second. What he was able to show was that the membrane potential became much more positive during the action potential. Bernstein in fact thought that the membrane potential changed from -60 mV or so to 0 mV for a brief time during the AP; i.e., the membrane potential became 60 mV more positive than normal. His explanation for this was that a resting membrane was selective permeable to K⁺, but when the cell was "excited", somehow the membrane became so disorganized that it would allow any ion to pass through it freely; i.e., the permeability for all ions was essentially infinite. The effect of this would be to have what Vm? He published his idea in 1902 and it was the standard explanation of the action potential for 40 years.

Once again Bernstein was partly right and partly wrong. In fact in the same issue of the same journal in which Bernstein published his explanation of the action potential, another scientist named William Overton published a paper that contradicted Bernstein’s basic hypothesis. Overton showed that if he removed Na⁺ ions from the liquid in which he immersed a frog muscle, he abolished the ability of the muscle to conduct Action Potentials. Why does this contradict Bernstein’s hypothesis? Because if Bernstein were right, even with no external Na⁺, when the membrane permeability went to infinity, Na⁺in, K⁺ and Cl^- would rapidly cross the membrane and cause Vm to go to 0. In other words, in Bernstein’s model the action potential shouldn’t depend on the external concentration of any ion. Overton thought that his results implied that the membrane maintained its ability to select among ions during an action potential, but that the permeability for Na⁺ rose dramatically. However, he couldn’t think of an experiment to test whether that was true, and so his idea was passed over and ignored, in favor of Bernstein’s.

That situation persisted until the 1930’s when two important technical advances allowed scientists to measure the membrane potential at rest and during the action potential much more precisely than ever before. The first advance was the rediscovery by J.Z. Young, a British physiologist, of the squid giant axon, a relatively enormous nerve cell. With this axon it was possible to slip a thin copper wire inside it and use the wire as an Intracellular Recording electrode. By comparing the internal charge, as measured by this electrode, with a reference electrode outside the cells, it was possible to get a much more accurate reading of Vm and membrane resistance (which is related to the permeability of the membrane to ions) than ever before.

The first experiments, conducted by the Americans Cole and Curtis, showed that during an action potential the permeability of the membrane increased but did not become infinite as proposed by Bernstein. Moreover, Cole and Curtis and Hodgkin and Huxley soon showed that during the peak of the action potential the membrane potential was actually more positive inside than out, rather than being equal to zero, as predicted by Bernstein. What does this result indicate about membrane permeability to ions during the action potential? It means that the membrane is not infinitely permeable to all ions, but must remain selectively permeable to ions during an AP. At this time, WWII began and these scientists took up war-related research.

After the war, Hodgkin and Katz returned to consider this problem and they basically came up the same idea that Overton had proposed--that the permeability of nerve cells increased greatly to Na⁺ during an action potential. They first showed theoretically that this would cause a big increase in the resting potential, and then they did some experiments to suggest that external [Na⁺] had a large effect on the size of the AP. Their theoretical explanation was based on the GHK equation.

Remember the GHK equation:

For mammalian muscle, P_Na/P_K = 0.02 and K⁺_in = 4 mM; K⁺_out = 140 mM; Na⁺_out = 142 mM; Na⁺_in = 12 mM ; E_Na = +62; E_K = -90 mV

When PNa/PK = 0.02, Vm = -76. Hodgkin & Katz said, suppose we could increase P_Na a lot all of a sudden, and make it 500 times bigger than usual. What would happen to Vm, according to our equation? Work it out for yourself. What would Vm be? (Answer: +43 mV). In other words a big increase P_Na would cause the membrane potential to move away from E_K and close to E_Na. So Hodgkin & Katz reasoned that the peak of the action potential (draw what the "peak" is) should vary according to [Na⁺]_out. They thought that if the peak amplitude was near E_Na, then they could vary E_Na by changing [Na⁺]_out. i.e., if Vm (AP) ~ E_Na = RT/F ln ([Na⁺]_out/[Na⁺]_in )= 58 log [Na⁺]_out - 58 log [Na⁺]_in, then varying [Na⁺]_out should cause the maximum Vm of the AP (action potential) to change. To test this, they varied [Na⁺]_out and measured the max amplitude of the AP. What else should they have tested as a control for their hypothesis?

See Figure 2.6D in Purves et al., Neuroscience

 They got a straight line of positive slope when they plotted maximum Vm (during the AP) vs [Na⁺]_out, but no change when they varied [K⁺]_out or [Cl^-]_out. So they proposed that the Action Potenial could be caused by a sudden, but short-lived increase in the P_Na of the membrane. When P_Na increased, Vm would become positive (a depolarization) and when P_Na decreased, the Vm would return to its normal negative value (a repolarization). This is the sodium theory of Hodgkin & Katz, published in 1949. In the following years, Hodgkin working with Huxley, figured out a way to test this hypothesis. I want to describe the conclusions they reached first, then after that I’ll explain the experiments on which they based their conclusions.

As I drew a minute ago, the Action Potential revealed by the work of Cole and Curtis and Hodgkin and Huxley in the 1930s had several features. Various phases of the AP included resting potential, the rising phase, threshold, the overshoot, the falling phase, the undershoot and the absolute and relative refractory periods. (Explain and define all). They noticed that once a cell’s membrane potential passed the threshold value, the AP was stereotyped. That is, it always had the same amplitude and time course for a given cell. But as long as Vm remained below the threshold, no AP occurred; that is, the AP was all or none, depending on whether the Vm exceeded threshold. The triumph of Hodgkin and Huxley’s work in the late 40s and early 50s is that they provided an explanation for all these features of the AP, and they provided compelling experimental evidence that their explanation was right.

Well, we now think that Hodgkin and Katz were essentially right; that is, that the membrane potential changes during an action potential because the membrane permeability to ions, especially sodium ions, changes. I’ve already given you a mathematical argument, based on the GHK equation, that changes in membrane permeability should cause changes in membrane potential. Hodgkin and Huxley showed that this was exactly true--they measured membrane potential and membrane permeability throughout the course of an action potential and showed that the changes in ionic permeability of the membrane could account for changes in the membrane potential.

Actually, what they measured was not membrane permeability, but membrane conductance, which is a much easier value to determine experimentally. They used something called the parallel conductance model, rather than the GHK equation, because it's easier to compute changes in Vm as a function of changes in conductance. The idea is that anytime the membrane potential isn’t changing, DVm = 0, which is true only if Im = 0 = I_K + I_Na (ignoring I_Cl). And Ohm’s law says V = IR or I =V/R = gV. (Conductance = g is defined as 1/R). Since V for an ion equals the difference between the Vm and the equilibrium potential for the ion, I_ion = g_ion(Vm-E_ion). So I_K + I_Na = 0 = g_K(Vm-E_K) + g_Na (Vm - E_Na).

Rearranging gives

so when g_Na/g_K changes, so does Vm

This is just another way of saying that if something changed g_Na, it would change Vm. What Hodgkin & Huxley showed is that the agent that changes g_Na is Vm itself. That is, an increase in Vm causes an increased in g_Na, which in turn causes a further increase in Vm. This is a self-reinforcing action, or positive feedback--a similar phenomenon is seen in the relationship between reaction rate and heat in gunpowder.

So if Vm increases g_Na, then Vm will increase until what value? (E_Na). Draw a graph of this. That explains the overshoot, but the action potential, as you know, quickly returns to the resting potential. Why? Because g_Na returns to its original value through a process called inactivation. In other words the increase in g_Na is temporary. And this rise and fall in gNa would be enough to cause a rise and fall of Vm. But in addition g_K also changes, it increases during the AP, so that g_Na/g_K is actually smaller after the Action Potential than before, making the Vm more negative than the normal resting potential (the undershoot).

After the g_Na is inactivated it takes a small, but finite, period of time for it to recover to the resting value. During this period, g_Na no longer increases when Vm increases. The consequence is that no matter how much one increases Vm ("depolarizes" the cell), there is no increase in g_Na, and therefore no sodium entry, and therefore no AP. This period when g_Na is locked (compare with closed door--which can be opened) into a non-conducting state is called the absolute refractory period. However, if Vm stays at or below the resting membrane potential for a few milliseconds, g_Na reactivates (unlocks) and the cell returns to its original level of excitability.

Because g_K stays high for a while after the AP, even while g_Na is returning to normal, the resting potential is less than normal, meaning that Vm is farther from threshold than usual. During this period, it is harder than usual to bring the cell to threshold, and this is called the relative refractory period.

I've given you Hodkin & Huxley’s explanation for refractory periods, undershoot and overshoot, and now I want to tackle the tricky notion of why there is a threshold, which is defined as the value of Vm which there is never an AP and above which there always is. The cell acts discontinuously; one doesn’t see a fraction of an action potential. How can this discontinuous behavior arise from continuous variation in the sodium and potassium conductances? It turns out that at the threshold, the influx of sodium (the sodium current into the cell) is exactly balanced by the efflux of potassium (the potassium current out of the cell). When else are those two currents balanced? (at the resting potential). How can it be that the two currents balance at two different values of the resting potential. I’m going to give a semi-quantitave argument for how this might work. Remember that whenever DVm = 0, then Im = 0 = I_K + I_Na or I_Na = - I_K; or g_Na(Vm - E_Na) = -g_K(Vm-E_K). At the resting potential g_Na is small, Vm-E_Na is large, g_K is large and Vm-E_K is small. If the membrane potential is depolarized, then I’ve said that this causes g_Na to get larger. That means that I_Na (equals g_Na x (Vm - E_Na)) will increase; more sodium ions will be entering the cell per given unit of time. But as Vm increases the value of Vm - E_K will get larger, even though g_K stays relatively constant. That means that I_K (= g_K(Vm-E_K)) will also increase when Vm increases, and more K⁺ will exit the cell per unit time. The threshold is the point at which the increase in sodium inflow is exactly balanced by the increase in potassium outflow. Below the threshold, the increase in K⁺ outflow is bigger than the increase in sodium influx, and more positive charge leaves the cell than enters, causing Vm to return to rest. Small depolarizations (below threshold) don’t cause enough of an increase in sodium conductance to cause an AP. At or above threshold, the rate of sodium entry becomes greater than the increased amount of potassium that leaves, and therefore the membrane potential starts to increase (as Vm moves toward E_Na); this in turn causes a further increase in sodium conductance, more rapid movement of Na+ into the cell, a bigger change in Vm and so forth, causing the rapid depolarization of the action potential that lasts until the sodium conductance inactivates.

In summary, the Hodgkin-Huxley explanation is that the AP is caused by a rapid increase in g_Na, that allows Na⁺ to rush into the cell along its electrochemical gradient, followed by a rapid decrease in g_Na (inactivation) and a slower increase in g_K. These latter two events bring the Vm back below zero to near the normal resting potential.

Now Hodgkin and Huxley suspected that the description I just gave you was correct, but they needed a way to test this idea experimentally. To do such a test, they’d have to measure g_K, g_Na and Vm constantly during an AP, a prodigious task they accomplished in 1950 and published in 1952 and 1953. It was a technical and intellectual tour de force because:

a). They thought that g_Na = f (Vm, t) and g_K = f'(Vm, t). So there were 4 variables, Vm, g_Na, g_K, and t; and 3 of them interact and affect each other.

b. The changes occur very rapidly during the initial phase of the AP: DV/Dt >700 V/sec, making it hard to do accurate measurements within short periods of time.

c. There is a capacity current that complicates measurement of ionic currents--essentially the problem you encountered with the "stimulus artifact".

Thus the natural situation is too complex to study as a whole. Hodkin & Huxley decided to simplify the situation by eliminating one of the variables, DV/Dt--i.e., they devised a method to hold Vm constant while measuring g_Na, g_K and t.

To do this they used an apparatus called a voltage clamp that was first designed by K.S. Cole. This is an electronic machine that can shift Vm instantly (within microseconds) and hold it constant at some new value.

They accomplished this as follows.

See Box A, Chapter 3 of Purves et al., Neuroscience

 Using this system they could isolate a large segment of membrane and hold it isopotential so that the action potential occurred throughout the whole piece of membrane at once. The voltage clamp works as follows: Starting at the existing membrane potential of the axon (the "holding potential"), you dial in the desired Vm on the voltage clamp. The Clamp passes current through the positive electrode until the voltage measuring electrodes indicate that Vm = Vcommand (the voltage that you chose and dialed into the voltage clamp). But if you increase Vm, this causes an increase in g_Na of the membrane, which means that there is now an increased likelihood that Na⁺ ions will enter the axon, which will tend to make Vm more positive. However the slight increase in Vm is detected by the Vm-sensing input to the voltage clamp, which now passes current in order to maintain Vm at the holding potential. In this case, it will pass negative current in order to counteract the accumulation of Na⁺ inside the cell. In other words, the electronic feedback circuit removes positive charge and adds negative charge just as fast as Na⁺ enters, keeping Vm constant. Later g_Na declines, Na⁺ stops entering, but then g_K increases and K⁺ starts flowing out of the cell more rapidly, causing Vm to become more negative. Again the machine senses this and passes postive charge to counteract the efflux (outflow) of K⁺ and to hold Vm constant. While all this is going on, the current being passed by the voltage clamp--either positive or negative--is being recorded by a recording device (essentially a fancy current meter). If everything works, then ÆVm = 0, that is the membrane potential is constant, so I_membrane = 0 = I_K + I_Na + I_{other ions} + I_{voltage clamp}, or, rearranging

-I_{voltage clamp} = I_K + I_Na + I_others.

The first figure to consult (Fig. 3.2 in Purves) shows their measurement of the total current crossing the membrane (= I _{voltage clamp}) when the membrane of the squid axon was set to different voltages. Initially there is an inward rush of positive charge followed by a later outflow of positive charge that lasts as long as the membrane is kept at the depolarized voltage. (At very high values of Vm, there is no inward current, it’s all outward. Why?)

While these measurements give the total movement of ion across the membrane (= -I _{voltage clamp}), they don’t tell us whether the inward positive current is because Na⁺ is entering the cell, K⁺ entering the cell or some other ion entering the cell (or Cl^- leaving). So Hodgkin & Huxley had to find a way to separate out the sodium and potassium currents, which they did by removing extracellular Na⁺ and replacing it with an impermeant positive ion, choline. Now when they repeated their measurements, they saw a current that was essentially all caused by the movement of K⁺ ions (Figure 3.4, Purves, middle trace ("Na-free"). If they then assumed that I_total = I_K + I_Na (ignoring the other possible currents), they could also calculate I_Na, by simply subtracting the I_K measured in the absence of sodium from the total current measured in the presence of sodium.

From these measurements of the time course of the sodium and potassium currents, they could compute g_Na and g_K during the action potential, using the version of Ohm’s law that we discussed earlier: I_K = g_K (Vm - E_K) and I_Na = g_Na (Vm - E_Na). Since Vm is held constant throughout the experiment, and E_K and E_Na don’t change, Vm-E_Na and Vm - E_K are constants. So changes in I (current) are directly proportional to changes in g (conductance ~ permeability).

In other words the principle of the voltage clamp is to measure the movement of ions electronically and to calculate the changes in the membrane conductance to particular ions over time from Ohm’s law. Then one changes Vm to some new value, and repeats the experiment. By doing enough measurements of this sort, Hodgkin &Huxley could figure out how g_Na and g_K varied as functions of Vm and time.

The next figure (Fig. 3.7 in Purves et al.) shows g_K and g_Na as continuous functions of time at several different values of Vm. Note the differences between them. At low values of Vm, g_Na increases and remains high, but at higher values of Vm, g_Na increases rapidly (more rapidly as Vm gets larger) and then decreases quickly back to essentially zero, a process they called "inactivation". g_K increases more slowly than g_Na as a function of Vm, but once it reaches its maximum value, g_K stays constant as long as Vm is constant. That is, g_K doesn’t inactivate (at least not in squid axons; there are some cells that have an inactivating g_K).

Hodgkin & Huxley supposed that there were two opposing processes that affected g_Na when Vm was increased. A very fast process (activation) caused the g_Na to increase greatly, while a slower (but still rapid) process called inactivation eventually shut down g_Na and caused a decrease. On the other hand g_K was subject only to an activation process that was relatively slow compared to what was happening to g_Na. H&H further showed that g_Na and g_K returned to their original values if they shifted Vm to some positive value for a while, then shifted it back to the original resting potential. That is, just as g_Na activated and inactivated when Vm was increased, it reactivated when Vm was decreased again. Similarly, g_K went up when Vm was increased and went back down when Vm went down again.

From their measurements of g_Na and g_K as functions of Vm and t, Hodgkin & Huxley derived a series of empirical equations for g_Na and g_K as functions of Vm and used these to compute what would happen to Vm during an AP. They did this by changing t in 0.01 msec increments, recomputing g_Na and g_K, figuring out how that would alter Vm, changing t again, seeing how the new value of Vm would alter g_Na and g_K, and repeated that process over and over. Huxley did the calculations on a manual desk calculator because computers and electronic calculators weren’t available. It took him 3 weeks to compute all the values for one AP (it would take much less than a second today with a computer) . Worse, most of the time they put the wrong parameters into their equation, and they got calculated DVm values that didn’t look anything like a real AP. But the next slide shows one computed AP compared with a real AP (Fig. 3.8B in Purves et al.). The computed AP depends on certain assumptions about the relationship between Vm and g_Na and g_K that I've explained. As you can see, the computed action potential has an amplitude and time course very similar to what happens during a real AP. Because the calculated and measured action potentials are so similar, this provides strong support for their hypothesis that alterations in membrane ionic conductances control changes in Vm during an AP. In other words, the calculations show that voltage-dependent changes in ionic conductance of the membrane can account for all the known features of the Action Potential, which is strong support for the proposal that this is the real cause of the action potential. These calculations allowed them to account for the size and shape of the AP, the increase in membrane permeability during the AP, the absolute and relative refractory periods, the threshold and a variety of other measured characteristics of the AP (I’ve already given you their explanations), all of which indicated that they had found the correct explanation for how action potentials occur.

Now this calculation was based on an unrealistic circumstance of having the whole axon go through an action potential simultaneously. In reality the action potential starts in one place and travels along the axon. So they also computed what would happen during a conducted Action Potential, as shown in the fourth slide (this one's not in the book; you'll have to come to class to see it). Note that Vm is above threshold before g_Na and g_K change at all. Why? That’s because electrical current is flowing along inside the axon from an adjacent region and changing Vm, via a so-called local circuit, which we’ll discuss next time.

To reiterate the important points about action potentials that I’ve made so far:

1.Increasing Vm causes an increase in g_Na, allowing Na⁺ ions to enter the cell rapidly; this influx of a positively charged ion (an inward current) causes a further increase in Vm.

2. Eventually g_Na inactivates so g_Na goes essentially to zero, and no more Na⁺ can enter the cell.

3. Vm also increases g_K, allowing K⁺ to exit the cell (an "outward current").

4. The decrease in g_Na caused by inactivation and the increase in g_K brings Vm back to or below its original value.

5. The return of Vm to a negative value allows g_Na and g_K to recover to their original conditions.

6. A change in membrane potential at one place on the surface of a cell (such as during an AP) can depolarize an adjacent region of the cell and cause it to fire an action potential.