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0:06
00:06 We talked about the ionic mechanisms 00:07 of the resting potential and the action potential, 00:10 and now we are going to discuss 00:13 the propagation of the action potential. 00:16 How it is possible for an action potential, 00:18 once initiated, in one part of a nerve cell, 00:21 like the cell body in the spinal cord 00:23 of a motor neuron, to propagate to the terminal regions 00:28 of that motor neuron in the periphery. 00:32 Now, at first pass, propagation of the action potential
2:20
00:35 is really quite simple and all you need to know or remember 00:40 is a little bit about your high school physics. 00:45 And, you remember from high school physics that, 00:48 unlike charges attract each other. 00:52 So here is a very simple representation of a nerve axon. 00:57 This would be the axon, and you see this charge 01:01 distribution across the membrane, with the 01:04 inside of the membrane negative with respect to the outside. 01:07 And that is because of the high concentration
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01:11 of potassium within the cell that tends 01:14 to fuse out and leave negative charge behind. 01:18 Now let’s just assume for the moment 01:20 that we impale this neuron, this axon, 01:23 with an electrode and connect that 01:25 to a suitable stimulus generator that, 01:29 when the switch is closed, will be 01:31 sufficient to de-polarize this particular 01:33 region of the axon and lead to the 01:37 initiation of an action potential. 01:39 So, the switch is closed.
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01:41 The membrane is depolarized, and 01:44 in fact, depolarization is sufficiently large, 01:46 and let’s assume that it is. That will 01:50 initiate that the regenerative positive feedback cycle 01:51 giving rise to an action potential at this particular region. 01:56 Those positive ions, then, are attracted 01:58 to their negative neighbors, so positive ions 02:01 are going to go this way and positive ions 02:03 are going to go this way, 02:05 and now if you simply assume
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02:06 that the movement of that positive charge 02:09 reduces sufficient depolarization in the 02:12 adjacent region to bring this region to threshold, 02:15 initiate a new positive regenerative cycle 02:19 which will lead to a new action potential here, 02:22 new sodium influx which will then depolarize 02:24 adjacent regions and these adjacent regions will, 02:27 in turn, initiate action potential and depolarize 02:31 adjacent regions. So once you initiate this process,
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02:33 it will re go along the axon in a repeated, 02:39 non-decremented fashion. 02:41 Note also, that in principle, 02:45 although it generally does not happen, 02:48 an action potential can propagate in 02:50 both directions along an axon. 02:52 If you initiate an action potential 02:54 in the middle of an axon, that action potential 02:56 will propagate both this way and this way. 02:59 So there’s nothing stopping an action potential 03:01 from propagating in both directions
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along an axon. 03:05 Now, I like to think of this process again in terms 03:07 of thermal analog, let’s just say you were to have a fuse 03:10 that was covered with gunpowder and if you were to ignite 03:15 the fuse in the middle of the fuse, you know, the fuse 03:19 is going to burn in both directions; it’s going to burn 03:21 in this direction and it’s going to burn in this direction. 03:23 Normally, you would light a fuse at one end and it would 03:25 only burn in one direction, but there’s
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nothing, intrinsically, 03:28 that prevents a fuse from burning in either direction. 03:33 Similarly, there’s nothing intrinsically that stops 03:36 an action potential from propagating in both directions. 03:39 So that’s the basic physical properties of propagation 03:45 of action potentials, but there are some subtleties here 03:49 of course, and that’s why we are going to spend the next 03:51 half hour or so talking about them. It turns out that
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03:54 there’s a large variability in the propagation velocity 03:59 of action potentials. So, some action potentials propagate 04:03 at a velocity of 0.1 meters per second and other action 04:10 potentials propagate at a velocity of 100 meters per second, 04:14 0.1 meters per second to 100 meters per second. 04:18 So, that’s a thousand-fold range of propagation velocities. 04:25 So 0.1, I think I indicated in your handout, 04:27 0.1 meters per second, just to put that into
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04:30 English units is how many miles per hour? 04:33 It’s 0.6 miles per hour. 04:37 0.6 miles per hour is pretty slow. 04:39 What do you, what’s normal walking pace? 3? 3? 04:44 So, 0.6 miles per hour is really a 04:46 snail’s pace almost. 04:50 Whereas 100 meters per second is is 580 miles 04:55 per hour; so that’s the speed of a 777. 05:00 So action potentials propagate in one extreme 05:05 a snail’s pace and the other extreme like a 777. 05:09 So you need to be able to explain why that is,
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05:15 and, in order to explain that, you need to consider 05:20 something called the passive properties of membranes. 05:23 They are called passive because they are not dependent 05:25 upon any voltage-dependent channels, like 05:27 voltage-dependent sodium channels, voltage-dependent 05:29 potassium channels. They’re not dependent on any 05:31 pumps or exchangers. They’re strictly a property, 05:36 a physical property of the membrane.
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Not just nerve 05:38 membranes, by the way, but all membranes. 05:41 And there’s two passive properties of the membrane 05:44 that are really important. They are called the 05:46 time-constant and the space-constant. And let’s 05:49 talk about them each individually. But before 05:53 I talk about the time-constant, let me give 05:56 you a thermal analog because I think it is 05:59 useful to, when you talk about propagation 06:01 of action potentials and electric phenomenon
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06:03 to consider temperature phenomenon because 06:06 they’re really very analogous. So, consider 06:09 what would happen if you had a block of mass 06:14 which was, say, initially at 10 degrees. 06:16 Ten degrees. And this podium was a hotplate 06:19 that was 100 degrees, right. 10 degrees. 06:21 100 degrees. And at a time, a certain time, 06:24 you instantly took this block of mass and 06:27 slammed it on the hotplate. And now, ask 06:29 yourself, how would the temperature in this
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06:32 block of mass change as a function of time? 06:38 It would increase. It’s going to get hot, right? 06:42 How hot is it going to get? This is 100 degrees; 06:49 this was initially 10. It’s going to get 06:53 probably 100 degrees. It’s not going to get 06:54 any hotter than 100 degrees. And it’s going 06:56 to increase, but will it increase instantly? 06:58 No, it will not increase instantly, 07:00 and that’s the key point. How will it increase?
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07:05 Slowly. Exponentially, somebody said. 07:11 Inverse exponentially? Let’s just say exponentially. 07:14 It will increase as an exponential function. 07:17 Anyone know what exponential function is? 07:19 You’ve heard about exponential growth, 07:21 so this is exponential function of time. 07:23 It will initially start, the temperature 07:25 will start to increase rapidly, and then 07:27 it will sort of plateau and ultimately
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07:29 get up to 100 degrees. It will be an 07:32 exponential function of time. Now any 07:35 time you have an exponential function 07:37 of time, you can describe an index of 07:41 the speed at which those changes take 07:43 place by something called the time 07:45 constant. Now here is what happens 07:48 in nerve cells. Here is the experimental 07:50 configuration. It’s really the equivalent, 07:54 the neuronal equivalent of putting that
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07:56 block of mass on the hotplate. So one 07:58 electrode is recoding the membrane 08:01 potential. And the membrane potential 08:03 of this cell is -60mV. Right here, right? 08:05 Now another electrode has impaled the cell, 08:08 and that’s connected to this battery. 08:10 Now. Note that this is a small battery. 08:13 So, as a result of closing this switch, 08:16 current is going to flow into the cell, 08:18 and it’s going to depolarize the cell. 08:21 The battery is sufficiently small such
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08:23 that depolarization will not reach threshold. 08:26 This is an important thing. We are NOT talking 08:28 about any action potential here. We are not 08:31 reaching threshold. We are not igniting the 08:33 gunpowder. We are not igniting the gunpowder. 08:36 This block of mass has no gunpowder. Close the 08:40 switch. And what you see is as a result of the 08:46 closure of the switch, the current through the
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08:47 circuit changes instantly, but the membrane 08:52 potential does not. It takes time for the 08:54 membrane potential to change from its initial 08:56 value of -60mV to this new value of -50mV. 09:01 So we adjusted the size of this battery to 09:03 give us a 10 mV change. Now it’s important 09:06 to note that and you see this change, this 09:09 exponential change in the potential doesn’t 09:12 instantly change from -60 to -50. It takes time.
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09:15 Here, about 20 milliseconds before it reaches 09:18 the final value. Now, it’s important to note 09:21 this could occur if you put the negative pole 09:25 of the battery here and connected it this way 09:27 and then you’d get actually a potential that 09:30 would be symmetrical. You’d go from say 09:33 -60 to -70mV just as if you were to take a 09:36 10 degree block of metal and put it on a cold 09:39 plate, which is zero degrees, it’s going to get
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09:42 colder. And, it’s going to get colder as an 09:45 exponential function of distance. 09:47 Totally symmetrical processes. 09:49 So here is the time-constant now. 09:51 The time-constant is defined as, and is denoted 09:54 by the symbol Tau, as the time it takes to get 09:58 to 63% of the final value, so 63% of the final 10:00 value is this -53.7, and it takes 10 msec to get 10:07 to 63%. So the time-constant is an index of how 10:13 rapidly a membrane will respond to a
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stimulus. 10:16 If the time-constant were 20 msec, then the membrane 10:20 potential would take a longer amount of time to build 10:25 up to its final value. If the time-constant was 5 msec, 10:28 then it would, the membrane would change more rapidly. 10:33 So the time is an index, you don’t need to know 10:37 mathematically where it comes from, although there 10:39 is a description in the online course that describes 10:42 the origin of the time-constant, you
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don’t need to 10:45 know where it comes from, you just need to know that 10:48 it’s an index that tells you how a membrane is going 10:52 to respond to a physical stimulus like a depolarization. 10:56 The time-constant is kind of like the 0 to 60 11:00 rating of cars, automobiles, right? So what’s 11:05 the 0 to 60 of a Ferrari? 3½ seconds? What model are 11:12 you talking about? 3½ seconds, something like that, 11:15 pretty much. 3½ seconds to go from
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0 to 60 miles an hour. 11:18 What about a Vespa scooter? Don’t say infinite, infinete, 11:27 infinity? More than 3.5 seconds, right? Let’s be generous 11:33 and say 15, let’s be generous and say 15 seconds. 11:36 So, what’s faster: a Ferrari that has a 0 to 60 of 11:39 3.5 seconds or a Vespa with 15, a 0 to 60 of 15 seconds? 11:44 The Ferrari’s faster. The smaller the 0 to 60, the 11:48 faster the automobile. The smaller the time-constant, 11:52 the faster a membrane responds to a
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stimulus. 11:56 So that’s the time-constant and you could 12:00 actually describe the time-constant in terms 12:02 of mathematical expression. The time-constant, 12:06 which, tau = Rm x Cm. Rm you know about. Rm is 12:20 just the inverse of the permeability. So membranes 12:23 have resistance to ion flow, just like they have permeabilities. 12:26 One is the inverse of the other. So a membrane that 12:29 has a high permeability has a low resistance, and vice versa.
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12:32 Okay. Cm is the membrane capacitance. So membranes, 12:36 as you learned in Physiology and Biochemistry are 12:39 bi-lipid layers, and so there’s a separation. 12:41 They’re capable of separating charge, just like 12:44 a physical device, a capacitor. So, membranes 12:48 have capacitance and they have resistance, and 12:51 the product of the two is equal to the time-constant. 12:53 Okay, so that’s time-constant. 12:56 Now, for space-constant, let’s go back to a
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12:59 thermal analog, again. So, for time-constant we 13:02 talked about a block of mass, for space-constant, 13:05 also called length-constant, we’ll talk about 13:07 a metal rod, like this pointer. So, again, 13:12 100 degrees hotplate, a rod (which has a uniform 13:16 temperature of 10 degrees). And now what we’re 13:18 going to do is put on end of the rod at the 13:21 end of the hotplate and we are going to wait. 13:24 Wait a while, maybe wait 10 15 minutes.
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13:27 And then you need to ask yourself, what will 13:30 be the profile of the temperature change in 13:33 this rod as a function of distance? We’re not 13:36 talking about time now, we’re talking about 13:37 distance. Initially 10 degrees (points to rod), 13:40 100 degrees. So, we do this, we wait a while, 13:44 what will be the temperature at this end of 13:46 the rod (where it touched hotplate)? Close to 100. 13:49 What will be the temperature here (1/3 of the
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13:54 way from hotplate)? Less than? 59.3? 14:00 No, it will be less than 100; we don’t 14:02 know exactly what it will be. We know it 14:04 will be less than 100. What do you know about 14:05 the temperature out here (at the far end from 14:08 the hotplate)? It will be even less than 100, 14:12 and it will be close to ___? It might be close 14:14 to 10. Certainly if this rod was sufficiently 14:15 long, if it went to the other end of the building, 14:16 it would still be 10 because the heat
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is not 14:19 going to propagate. We are going to get loss 14:21 of heat as we go along the rod. So initially 14:24 we are going to be at 100 degrees because that’s 14:26 what the hotplate is, but we’re going to lose 14:27 heat as we go along, and if the rod is long 14:29 enough, we still we be at 10 degrees. Now, 14:33 if you were to make a careful plot of that 14:36 change in temperature as a function of distance, 14:39 you would see a shape that would look like this,
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14:41 what kind of shape is that (high at the hotplate 14:43 and sloping down to the far end)? An exponential 14:44 shape. So, there would be a relationship; there 14:48 would be an exponential decay of the potential 14:50 along the rod. 14:55 So we can do a similar thing in nerve cells. 14:59 So here is the experiment. It is equivalent of 15:01 the one we just did with the rod. Now we record 15:04 from a nerve, not just in the cell body, but at
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15:07 various distances along the axon at 1 mm, 2 mm, 4 mm 15:11 and so forth. We impale the cell with a stimulating 15:15 electrode and adjust the size of the stimulus so that 15:18 the membrane potential is changed from its initial 15:21 value of -60 millivolts to a new value of -50. So this 15:26 is like putting that rod, 10 degrees, at the hotplate 15:30 we made we made it a 100 degrees. Here we made the 15:33 membrane potential, at this point, -50. And now
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15:36 the interesting thing is, that when you sample the 15:39 membrane potential at these more distant regions, 15:42 you see that the membrane potential is not 50 any 15:45 longer. Out here it's -56.3, and out here, it's 15:50 closer to -60, and out here, it’s even closer to -60, 15:53 and further away, it is exactly -60. So, just as 15:56 temperature decays as a function of distance, 15:59 the membrane potential decays as a function 16:02 of distance from the site where that
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stimulus 16:05 was produced. So, this is an exponential function, 16:10 and just as we have an index for exponential 16:12 functions of time, we have an index for exponential 16:16 functions of distance, and this is denoted as lambda. 16:20 And, this is called the space-constant or the 16:24 length-constant as a characteristic feature of axons. 16:30 So, the greater the length constant, the greater 16:33 will be the ability of the potential generated at
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16:36 one place to propagate or spread along the axon. 16:39 So, if we had a space constant of 2, of 2, millimeters, 16:45 for example, then the decay, that would be a lambda 16:49 of two, then the decay would look like this. 16:53 The potential would spread a greater distance 16:56 along the axon. If lambda was only 0.5, then, 17:00 the membrane potential would spread less 17:03 of a distance along the axon. This would be a 17:06 lambda of say 2 here (I can’t make a 2 very well),
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17:09 and this would be a lambda of 0.5, for example, right? 17:15 Now, just as we can write a formula for the time-constant. 17:20 We can also write a formula for the space-constant. 17:27 And that is lambda is equal to and you need 17:37 to know these two formulas the square root 17:40 of d times Rm divided by 4 x Ri. So, 18:01 let’s look at the terms in this equation; 18:03 d is the diameter of the axon. That’s simple. 18:06 The axon is 1 mm in diameter or 10 mm in diameter
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18:12 or 1 micron or 10 microns. That’s the diameter. 18:14 Rm is the same Rm we saw here. It’s the membrane 18:18 resistance. Four is 4, and Ri is a new term. 18:22 Ri is the intracellular resistance. So, there is 18:26 a resistance within the axon for a flow of movement 18:30 of ions. So ions just can’t freely move along the axon. 18:33 They encounter some resistance and that is taken into 18:36 account by this term, Ri. 18:41 Okay, so, now we have equations for the
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18:46 time-constant and the space-constant. How do we put, 18:48 how do we put these two together? Let’s just make a 18:52 simple, very simple diagram of a membrane. 19:02 Put some charges here. Let’s say we have an 19:18 action potential that is generated right here. 19:21 Because of an action potential generated right here, 19:24 the polarity of the membrane now will switch from 19:28 being inside positive compared to what it was before 19:33 being inside negative. Now because of
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this positive 19:36 charge here, this charge will move to adjacent regions. 19:40 The smaller the time-constant, the smaller the time-constant, 19:45 the more rapid will the charge here be able to reach to 19:49 adjacent regions. Therefore the propagation of velocity 19:52 will be proportional, inversely proportional to 19:58 the time-constant. The smaller the time-constant, 20:00 the more rapid will the potential be able move to
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20:02 adjacent regions. The greater the space-constant, 20:09 the greater the distance this charge will be able to 20:12 travel to affect these more distant regions sooner. 20:15 So the propagation velocity, while inversely proportional 20:18 to the time-constant, will be directly proportional 20:22 to the space-constant or lambda. Now because we have 20:27 formulas for both lambda and tau, we can write a new 20:33 equation that incorporates the new phenomenon
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together. 20:36 And that would be 1 over C divided by the diameter, 20:46 4 times Rm times Ri. So the velocity is proportional 20:55 to 1 over C, the square root of the diameter divided 21:00 by 4 times Rm Ri. You just need to do a little 21:02 bit of high school algebra to transform these two 21:05 equations into this equation. So, now we have a 21:12 formula that can help us explain the issue that we 21:17 addressed in the very beginning of the
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lecture, 21:22 which was, “How can one axon propagate information 21:26 at 0.1 meters/sec and another axon propagate an action 21:32 potential at 100 meters/sec?” Myelin, someone wants to 21:37 talk about myelin. Where’s myelin? Do you see any myelin 21:43 in this equation? Let’s look at the equation. Rm, you can 21:49 change Rm. You can change Ri. I don’t really know what 21:54 Rm and Ri, how would you how would you change Rm and Ri. 21:57 Might be hard. What’s easy to do?
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Let’s do something easy. 22:02 Let’s make it just bigger. Let’s just make a bigger axon. 22:06 Make a bigger axon, we make this diameter bigger, then the 22:12 velocity will increase. This is exactly the strategy that 22:16 is very, very common in the nervous system. Larger diameter 22:19 axons have greater propagation velocities. In fact the 22:24 prime example of this is the squid giant axon. Everybody 22:26 know about the squid giant axon? This
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is not the giant 22:31 squid axon; this is the squid giant axon. The giant squid 22:35 probably has a giant, giant axon, but we’re talking 22:38 about the squid giant axon. You all know, everybody here 22:41 has had calamari at one point in their life? 22:43 So, that’s a squid. It’s a mollusk, and it has a 22:46 very pronounced defensive reflex. It has a very 22:49 rapid contraction of its mantle, and that contraction 22:53 is driven by a large axon called the
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squid giant axon. 22:57 It can have propagation velocities 23:00 of about 100 meters/sec, right up there with a 777. 23:05 Uh, and it has a diameter of about 1 mm or so. In fact, 23:10 when people first saw this axon they thought it was a 23:12 blood vessel it was so big. So, that’s one way of 23:16 getting high propagation velocity action potentials 23:20 in nerves. But there’s a price you pay for that 23:24 and that is in this equation. What’s the price
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23:29 you pay? Where are our, where’s our mathematicians? 23:36 You three guys seem to be the mathematicians. 23:42 Algebra, let’s go back to algebra. Let’s look 23:43 at this equation. What happens if you want to 23:47 double the propagation velocity? What do you 23:49 have to do to the diameter? Yes, you have to 23:54 increase it by, how much do you have to increase 23:56 it by if you want to double the diameter?
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23:58 You have to quadruple the diameter if 24:00 you want to double the propagation velocity. 24:03 So the problem you pay is that to get large 24:07 increases in propagation velocity, you have 24:09 to have really big increases in diameter. 24:12 Now, that’s fine for a squid because a squid 24:14 is essentially just a body full of water and 24:19 there’s lots of room for giant axons. 24:21 You could have ten giant axons in there, 24:23 but that’s a problem in the invertebrate
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24:26 nervous system. Now, there is nerve axons 24:29 in the optic tract that take information 24:31 from the eye. They have propagation velocities 24:33 of about 100 meter/sec. It’s important to get 24:36 visual information into the Central Nervous System 24:39 quickly. So they have the same propagation velocities 24:41 as the squid giant axon. But it is estimated, 24:45 it has been estimated that if each of those axons 24:49 were the size of the squid giant axon, the optic nerve
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24:51 alone would take up the volume of the entire brain. 24:56 So that’s not good. It’s a cheap way of doing it, 24:59 but you pay the price. You need to have a big axon. 25:03 So there’s a more expensive way of doing it, 25:05 and the key is here, right in this equation. 25:10 There is one of these parameters that is outside 25:15 of that nasty square root relationship, and that’s 25:17 the capacitance. So, if you could decrease the 25:20 capacitance some way, then you could
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directly 25:23 affect the propagation velocity. 25:26 And how do we do that? Finally, we get to myelin. 25:30 So myelin, what myelin does is it decreases, you coat 25:33 the axon with myelin, and decreases dramatically the 25:37 membrane capacitance and allows the relationship to 25:43 increase dramatically. But there’s a price you pay 25:46 for that. If you coat the axon with myelin, what do 25:50 you do? Well you increase the membrane resistance but
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25:56 what you are doing most significantly is that you’re 26:00 plugging up the pores of the membrane that you need to 26:03 initiate an action potential. So, there’s a way around 26:09 that, of course. The nervous system is no dope, and it 26:12 figured out a way to get around this problem. And what it 26:15 did was to not coat the entire axon with myelin but rather 26:21 just coat parts of the axon with myelin and leave these 26:24 bare regions called nodes. So, here’s a schematic diagram
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26:28 of a nerve axon, the dashed lines, and you see the myelin 26:35 that Dr. Waymire talked about, this these blue structures 26:39 that’s covering the axon. It’s not completely covered. 26:43 There’s bare regions, so what happens here is you get an 26:45 action potential at the node. The potential then spreads 26:50 passively underneath the myelin. It emerges. It spre, 26:57 It spreads with some decrement. The potential spreads 27:00 with some decrement but it emerges at the next node at a
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27:05 potential of depolarization which is still super-threshold. 27:09 So that allows a new action potential, if you will, 27:12 to be initiated at this node, and then the process 27:15 repeats itself: action potential, passive spread, 27:19 action potential, passive spread, action potential, 27:24 passive spread, and so forth, all along the axon. 27:30 And this process occurs much more rapidly than 27:33 it would have if you just had increased the size
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27:36 of the axon. It’s kind of like, let’s go back to 27:41 our thermal analog and finish this up. So, if you 27:45 have un-myelinated axon, it would be like this rod 27:49 that’s covered with gunpowder. If you lit, put 27:53 a little heat there, you’d ignite the gunpowder, 27:56 and it would burn along the rod, right? Well what’s 27:58 happening with myelinated axons is that, the 28:01 equivalent would be to take that rod and put 28:05 some insulation on it, right? Here’s some insulation.
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28:11 And here’s some insulation. So, now we put some 28:15 gunpowder here, and we put some gunpowder here, 28:18 and we put some gunpowder here. And if you ignite 28:21 the gunpowder here, this is going to burn, and 28:24 it’s going to be very hot. The heat then will 28:26 spread under this region where the insulation is, 28:29 there’s no gunpowder. But if this insulation is 28:31 really good, the temperature change produced here 28:33 by the first ignition is going to spread to here
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28:36 and it’s going to ignite this gunpowder and the 28:39 process then will continue along this rod. Right? 28:42 Same thing happens with myelinated axons, but now 28:45 instead of gunpowder we are dealing with sodium, 28:48 voltage dependent sodium channels and propagation 28:50 of the potential.
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