Okay, I think we're ready to put all this together now and have a computational model that explains the action potential. So, what we have here is a precise alignment of the voltage and time-dependent changes in sodium and potassium conductance relative to the action potential. I want you to spend a little bit of time thinking about this figure, figure 3.8, and considering the alignment of these conductance changes with what we see in membrane potential. And the conclusion of such a thought process is that the action potential is indeed explained by the voltage in time-dependent changes and permeability of the neuronal membrane to potassium and to sodium. Now, let's look first at the sodium conductance and how it's aligned to the action potential. There is a sharp rise in sodium conductance that occurs in time with the rise in membrane potential during what we call the rising phase of the action potential. In fact, the rising phase is explained by this rapid increase in sodium conductance. Now, we haven't explained yet how that itself got started. but we'll come to that in the next tutorial. For now, I'll simply state, that some external stimulus was applied to this experimental situation, or if we can imagine, a real neuron or a real axon in a real brain, some stimulus in the form of incoming electrical signaling activity potentially can depolarize that cell and produce this explosive increase in sodium conductance. That explains the rising phase of the action potential. But, again, let's notice that the increase in sodium conductance is short lived. Soon thereafter, there's this falling phase which we call inactivation [SOUND] of the sodium conductance, and in terms of the membrane potential, that can be recorded, this is called the falling phase of the action potential. So, we have the rising phase on the up slope and now the falling phase on the down slope. Now, this sodium channel on activation, I know I'm getting ahead of myself just a little bit with respect to the tutorial notes, but it does allow us to explain an important phenomenon called the refractory period. So, there's a period of time during which it's not possible to generate another action potential and that's called the absolute refractory period. That's happening during this time of sodium channel inactivation because in order to generate another action potential, these sodium conductances need to be reset back to 0. So, this inactivation has to be removed in order for another action potential to fire. So, the period of time during which these sodium channels are progressing through their inactivation state is, in fact, the period of time that we call the absolute refractory period. Alright, so let's now turn to the potassium conductance. The potassium conductance is delayed relative to the onset of the sodium conductance, but it's also sustained for a longer period of time. And this sustained conductance for potassium allows potassium to flow out of the cell, and that means positive charge is leaving the inside of the cell. This delayed outward current or delayed potassium efflux, contributes now to the falling phase of the action potential. And notice, that at the conclusion of the falling phase of the action potential, the membrane potential actually undershoots the resting membrane level by just a small degree. So, this is called the undershoot, and is explained by the ongoing influx of potassium ions. Now, when we first considered the ionic basis of the action potential in principle, it was sufficient to say that the resting membrane potential is approximated by the Nernst equilibrium potential for potassium. Now we can state that that's not exactly the case. The Nernst equilibrium potential for potassium is actually much closer to the [UNKNOWN] of this undershoot. The actual resting membrane potential, I'll call it V rest. In this case, is about minus 65 millivolts, not quite where the Nernst equilibrium potential for potassium would be, because there are other complications, other ionic fluxes that we haven't taken the time to consider and, and that's okay. we can simply state that the resting membrane is not an ideal membrane permeable only to potassium. If it were, then V rest would be precisely Ek, but there is a small offset, and that allows us to explain this undershoot. Now, we've been emphasizing the time-dependencies of these conductances. I don't want to overlook their voltage dependencies. So, as the action potential is in its following phase and undershoot phase, this membrane is now becoming hyper-polarized relative to rest. And as it does so, the potassium conductance trails back down towards its starting point. So, as the membrane is hyper-polarizing and returning towards rest and undershooting rests, the potassium conductance is shutting down. Okay, will these considerations allow us to consider just a couple of other aspects? the action potential behavior that are worth noting. We've talked some about this concept of threshold. now, I think we can approach this in a bit more of a formal way. We know that there is something like a threshold. We saw that a couple tutorials ago where when exceeded, there is a runaway positive feedback cycle where membrane depolarization leads to increased sodium permeability. So, sodium rushes into the cell, and that leads to even further depolarization. This is the rising phase of the action potential. Well, that's accomplished when we stimulate the axon, or when the axon and the neuron receive the stimulation from some other source, such that the threshold for generating this positive feedback cycle is exceeded. So, we might call that a super threshold depolarization. Now, we can also move the cell in the depolarizing direction away from rest and not hit threshold for [UNKNOWN] action potential. That would be what we might call the subthreshold depolarization. So, what's the difference? What's the difference between a depolarization that achieves threshold and one that doesn't? Well the difference is whether that depolarization crosses threshold, and threshold therefore can be defined as the membrane potential when the sodium current is exactly equal to the potassium current. That is, it's a tipping point where just as much potassium is able to leave the cell as sodium entering the cell. Now, because the sodium conductance opens so much more quickly than the potassium conductance depolarizations of the sufficient magnitude are certain to trigger an action potential. Because we know that it's possible for so much more sodium to enter the cell than potassium leaving the cell that were driving this cycle past threshold and generating the rising phase of the action potential. Another way to conceptualize this is to consider the regenerative nature of the action potential. We've been talking about this fast positive cycle where sodium is entering the cell leading to further depolarization and the opening to even more sodium permeability channels that increased sodium current can further depolarize the member until the point at which that conductance begins to inactivate. So, this is a picture of exceeding threshold, and running this fast positive cycle. But we also have a slower negative cycle. And this is set into motion as the membrane begins to depolarize and the permeability channels for potassium begin to open up more slowly. But as they do, potassium channels are opening, potassium is leaving the cell and this leads to more of a negative feedback promoting the repolarization and eventually, the undershoot of the membrane potential. Now, it's interesting, it is not, that the negative cycle is slow and the positive cycle is fast. this, this temporal dependency ensures that the action potential can be an explosive event. That is, the rising phase can happen unimpeded by this more slow negative phase. However, the negative phase eventually does dominate. Yes, the sodium conductance is beginning to inactivate, but the potassium conductance will drive the membrane back to resting levels and even below rest and to undershoot. So, the slow negative cycle seems to be nature's way of ensuring a rapid signaling event, that is an action potential of a short duration. Now, there are action potentials in nature that can be longer because other ion channels are involve but are canonical action potential that we find in axons and in neurons is of this sort. A sharp rising phase followed by a sharp falling phase with an undershoot. Now, this slow negative cycle also allows us to explain the rest of the refractory period. I mentioned that the absolute refractory period is when sodium conductances are in their inactive state, and it's not possible to trigger a second action potential until that inactivation state is removed. However, there is a relative refractory period that will be present as long as we continue to have this slow negative cycle turning away, which is to say the membrane potential is an undershoot. Now, during that time, it is possible to trigger a second action potential, because the sodium permeability channels are ready to fire again. However with undershoot, there is therefore a need for a slightly stronger stimulus that can overcome that undershoot and bring the membrane potential to threshold in order to fire an action potential. That's why this refractory period is said to be relative. Well, together then, this fast positive cycle, this slow negative cycle allows us to understand the shape and the duration of the action potential, and it also raises some interesting philosophical points, I think. It suggests that there is a limit to the speed of processing in the nervous system and that limit is defined by the width of the action potential. Of course, that limit is actually an aggregate of the billions of action potentials that are happening all the time in neural circuits and neural systems. But in principal, there is a limit to what can be defined as the moment. In fact, the aggregate consequence of this action potential width is that our brain is perpetually living in the past. We are processing right now information that just happened a few tens or perhaps even hundredths of milliseconds ago. No, I'm not talking about memory, I'm talking about the brain working on the incoming flow of information. And because of the width of the action potential and, as we'll see in a few sessions, the delay that comes with synaptic transmission, it takes some time to elaborates our thoughts and our perceptions and our emotions. So, from that standpoint, we would seem to be at something of a disadvantage, living in a world in real time knowing that our brain is living perhaps a few hundreds of milliseconds in the past. But brains are wonderful organs. One of the best things they can do is predict the future. In fact, our brains are constantly updating our model about the future, so that we can anticipate that actions that happen in real-time in the world. So, even though the width of the action potential imposes a bit of the delay, in our neural processing, we make up for that delay by being able to predict behavior in the future. Well, enough of that philosophy for the moment. I think we're ready to wrap this up and I'll leave you with a study question which you can find at the bottom of your tutorial and you can find it online in our next slide. So, consider this regenerative nature of the action potential, this fast positive cycle and the slower negative cycle. And I want you to think about why is the action potential a spike, that sometimes the term that neurophysiologists use to describe the action potential. Which of these factors listed below do you think is the best explanation for the short duration of a typical neuronal action potential? Okay, I'll see you with the next tutorial.
