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0:08
00:08 Today, we're going to continue our 00:10 discussion 00:11 about action 00:12 potentials and resting potentials, 00:14 getting a little more detail. 00:15 The history 00:16 of nerve action potentials, and the way 00:19 in which they are involved in the 00:21 information encoding and propagation in 00:24 the nervous system, goes back more than 00:27 80 years ago 00:28 with the development of modern-day 00:32 electronic instrumentation techniques, 00:34 amplifiers and the like. And these
0:37
00:36 studies, that would provide really fundamental 00:39 insights, were done on a seemingly 00:42 unpromising looking species. Anybody 00:46 recognize this animal? So horseshoe crab. 00:49 So if you spent any time on the east 00:51 coast of the United States, this animal 00:55 has been around for a 100 million years. 00:57 It's been called a living fossil. It was 01:00 inhabiting earth before the dinosaurs, so 01:03 it's a very primitive creature, but 01:05 nevertheless this primitive creature
1:07
01:07 like all, and like all, animals have 01:09 nerve cells and resting potentials and 01:12 action potentials. And what these 01:14 investigators did 80 years ago was to 01:16 place electrodes on the surface of the 01:20 nerve; these are so-called extracellular 01:22 recording techniques. And this is just 01:24 one example of many different types of 01:26 extracellular, so-called extracellular, 01:29 recording techniques because we can put
1:31
01:31 electrodes on the surface of an 01:33 excitable membrane and measure 01:35 reflections of the potential changes 01:38 that are taking place across the 01:39 membrane. Anybody tell me the names of 01:42 some other extracellular recording 01:44 techniques that are heavily utilized in 01:47 medicine? EKG? Right put electrodes or the 01:54 chest and you can measure the electrical 01:56 activity to heart. I'll give you a hint: 01:58 they all start with E, and they all
2:00
end 02:00 in G. EEG? Put electrodes on the scalp and 02:05 you measure brain electrical activity. 02:08 EMG? Put electrodes on the muscle you 02:12 measure electrical activity of muscle. That's 02:17 three; there's more than three. 02:21 What if I were to put two electrodes 02:24 right here? EOG? Electro ocula gram. What 02:35 if I were to put electrodes on the 02:37 eyeball itself? Electroretinogram...electro 02:42 ret...what was that? EIG? (audience
2:45
laughter) 02:46 Maybe; that's the good one. Electroretino... 02:49 electroretinogram. So you'll hear 02:52 about these throughout your careers, but 02:54 it's all basically the same 02:56 phenomenology. You put electrodes on the 02:58 surface of the structure that you're 03:00 interested in. There's electrical 03:02 activity of some sort underneath and 03:04 these electrodes pick it up. So here's 03:06 what happened when you put these 03:07 electrodes on the surface of the optic
3:09
03:09 nerve, and you connect these electrodes 03:11 through some recording device. And this 03:14 recording device will also be connected 03:15 to a speaker, so we can actually HEAR 03:18 what happen. So if you make a light very 03:21 dim, as the case here. 03:22 So this has 03:23 different buttons here. You can make a 03:24 dim light, and a brighter light, depending 03:26 upon where you put your cursor. And you 03:28 can do this on the online sylla…, online
3:31
03:30 syllabus. The dim light, you don't see 03:32 anything on a recording device, but if 03:35 you make that light a little brighter <sound of repeated spike-like events>, now all of 03:38 a sudden, you see the light changed <sound of repeated spike-like events>, and you record these <sound of repeated spike-like events> 03:42 events on the recording device, these 03:46 little blip or spike-like events. And 03:48 what's interesting here is that, when you
3:50
03:50 turn the light on so it's a little bit 03:52 brighter <sound of faster repeated spike-like events> and brighter <sound of even faster repeated spike-like events>, what you see is 03:58 that the frequency 04:00 or number of the spike-like events changes 04:05 as a function of the intensity of the 04:07 illumination. These insights are 04:09 applicable not just to how the nerve 04:11 system of a horseshoe crab works, but how 04:13 our nervous system works, as well.
4:15
04:14 There's 04:16 three principles that come from these 04:18 recordings and I don't even need to say them; 04:20 I think you know them already. So what's 04:22 principle number one? What can you say 04:23 about these nerve impulses or action 04:26 potentials? One thing is about the timing. 04:29 Note this is a one-second duration 04:31 stimulus. You can say that these events 04:37 are very brief, right? This is a one- second
4:41
04:41 time scale here, so these events 04:43 are very brief. You can't tell how brief 04:45 they are, but you already know they're 04:46 about a millisecond or so in duration, 04:49 right? Second, you can see, as these 04:54 investigators did, that these action 04:57 potentials or impulses are elicited in 04:59 an all-or-nothing fashion, either you 05:01 have an impulse or you don't have an 05:03 impulse. You never see half an impulse, 05:04 right? So they're elicited in an
5:08
05:07 all-or-nothing fashion and, as you also 05:09 know, they are propagated in at all in 05:12 nothing fashion. So an action potential 05:14 listed here at the eye is going to be 05:16 propagated to the central nervous system 05:18 in an undecremented fashion. And, then, the 05:22 third principle that emerged from these 05:24 studies is the principle of frequency 05:27 coding in the nervous system. The greater 05:30 the intensity of the stimulus <sound
5:30
of repeated spike-like events><sound of faster repeated spike-like events><sound of even faster repeated spike-like events> here a 05:32 visual stimulus, the greater is the 05:35 frequency the firing of 05:38 nerve impulses. 05:40 Okay, so we have to move from these 05:42 extracellular recordings which are, they are very 05:45 informative but at the same time they're 05:46 relatively crude, to the intracellular 05:48 recordings I introduced you to the
5:50
05:50 technique on Monday. Here is an idealized 05:54 nerve cell. You learned about some of the 05:55 features of this with Dr. Waymire. 05:57 You're going to learn more later on. You 05:59 have this micro electrode which is no 06:01 more than a thin piece of glass tubing, 06:02 stretch under heat, filled with a 06:04 conducting solution, and when it's in the 06:07 extracellular environment, the potential 06:09 that's recorded is zero (0) because the
6:12
06:12 extracellular environment is ISO 06:14 potential. So the oscilloscope records zero (0) 06:17 take the electrode, and you penetrate the 06:20 cell so that the inside tip of the 06:21 electrode is now inside the cell, and now 06:24 there's this sharp reflection on the 06:26 recording device. And this is the 06:29 so-called resting potential. Its 06:31 characteristic of all cells in the body. 06:32 Nerve cells have as well as all other 06:35 cells, but we'll see nerve cells are
6:37
06:37 special, as are other excitable membranes 06:40 like muscle cells, new muscle, skeletal 06:42 muscle, and cardiac muscle cells, in that 06:45 they're capable of changing their 06:46 resting potential: nerve cells for the 06:49 process of encoding and transmitting 06:51 information and then muscle cells through 06:53 the process of producing a contraction. 06:55 Now how do you actually trigger an 06:58 action potential? We talked about that in 06:59 the last lecture. You can impale a neuron
7:02
07:02 with another electrode and artificially 07:04 stimulate it. We'll see just next week 07:07 that's the physiological way that nerve 07:09 cells are stimulated are through synapses, 07:12 excitatory synaptic connections we've 07:15 already heard a little bit about them, 07:16 I won’t say much more. So here is showing 07:20 a strategy for stimulating a neuron. We’re 07:24 going to show two examples with a 07:26 stimulating electrode. The stimulating
7:29
07:29 electrode is going to be connected to a 07:30 battery, and the battery in turn can be 07:32 connected to the circuit in two 07:34 different ways. course when you put a 07:35 battery into a device you can put the 07:38 battery in the device so just a negative 07:40 pole is going one way or you can connect 07:42 it so that the positive pole is going 07:44 one way, right? You know they've got a 07:46 little plus and a minus, and you’ve got to 07:48 make sure you get it right for the
7:49
07:49 circuit to work. We got to get it right 07:51 in a nerve cell as well when you get 07:52 two different kinds of responses 07:54 depending upon whether you puts a 07:55 battery this way or you put the battery 07:57 this way. So the pole the battery is 07:59 connected as shown here, and by the way 08:01 just the terminology for batteries is 08:03 the big plate is always the positive 08:05 plate, it's not particularly important to 08:07 you, you know that already.
8:09
08:09 So what do you think would happen if we 08:12 record the membrane potential which is 08:13 initially going to be minus 60 08:15 millivolts? We impale the other, the other 08:18 electrode, into the cell, and we connect 08:20 it to a battery. What's going to happen 08:21 when we close the switch? We're going to 08:24 make it more negative, because the pole of the battery 08:26 here is oriented such that when the 08:28 switch is closed, the inside of the cell
8:30
08:29 is going to be more negative than it is 08:31 and depending upon the size of the 08:33 battery… Now we have different sized 08:34 batteries right? You have 1.5 volt 08:36 battery. You have a 9-volt battery. You 08:38 have a 12-volt battery. So by different 08:40 sized batteries are going to make the 08:42 inside of the cell, 08:43 you know, progressively more negative. So 08:45 what you’re going to see, in this little 08:46 animation, is that the switch is going to
8:48
08:48 be repeatedly closed and opened and each 08:50 time it happens the battery is going to 08:52 be replaced with a larger battery. 08:54 So here's the animation. <small battery played quiet buzz. Larger battery played louder buzz, and still larger battery played even louder buzz.) 09:00 See the different 09:01 batteries getting bigger? 09:03 So the different sized batteries, you 09:06 close the switch, are making the inside
9:08
09:08 of the cell progressively more negative. 09:11 Now anytime you make the inside of the 09:13 cell more negative, that potential is 09:15 called a hyper-polarization, right? The 09:18 membrane is more polarized than it 09:20 normally is, hyper, right? Membranes 09:22 hyperpolarize. You need to know a little 09:24 bit about this nomenclature in order to 09:27 follow what we're going to be saying 09:30 throughout the rest of the course. By the 09:31 way, as Dr. Waymire indicated, this
9:34
09:34 material is all cumulative, so if you 09:36 don't understand and remember what I'm 09:38 talking about today, you're not going to 09:40 understand virtually anything that's 09:41 talked about next week. So you have to 09:43 stay up on the material. Okay, so this is 09:46 with the negative pole of battery. Now 09:48 let's flip it around. Put a positive pole 09:52 of the battery connected to the switch, 09:53 and let's just start getting larger,
9:55
right? 09:55 Same thing, but we get very different 09:57 results. 09:58 Okay the inside the cell becomes more 10:00 positive, as you expect, but then you get 10:03 to a certain potential where something 10:05 totally different happens. 10:06 You get to that potential, the threshold, 10:09 where you get this all-or-nothing signal, 10:14 and this is the nerve action potential 10:16 or impulse. There's an interesting
10:18
10:18 difference between this stimulus, these, 10:21 the size of these pulses by the way are 10:23 representative of the size of the 10:24 battery. So this stimulus was sufficient 10:27 to reach threshold and fire an action 10:29 potential, and this stimulus, which was a 10:32 greater intensity, also fired an action 10:34 potential but note the fact, that despite 10:38 the fact that the stimulus is larger 10:40 here than it is here, the action 10:42 potential is the same amplitude. So this
10:44
10:44 again just a restatement of this 10:46 all-or-nothing law of the action 10:48 potential. Either you have an action 10:50 potential or you don't. And if you use a 10:52 greater intensity stimulus to get the 10:54 action potential, you still have an 10:56 action potential, right? I like to 11:00 think of an action potential in terms of 11:02 a thermal analogue. An action potential 11:04 is kind of like the ignition of 11:06 gunpowder. So if you have a flame and you
11:10
11:10 put it to a fuse, a gunpowder fuse, you 11:14 need a certain intensity of that flame 11:16 in order to ignite the gunpowder, right? 11:19 If you use a more intense flame, you know, 11:22 instead of using a match using acetylene 11:24 torch, it isn't going to burn any 11:26 faster or brighter than when you light 11:28 it with a match, right? So there's a 11:30 certain threshold for heat necessary to 11:34 ignite gunpowder and there's a certain 11:36 threshold of depolarization necessary
11:39
to 11:40 initiate an action potential. Now there's 11:43 some nomenclature that you need to know 11:45 about. So note, interestingly, that the 11:48 action potential, when you have an action 11:50 potential, the membrane potential changes 11:51 from its resting potential of about 11:54 minus 60 to a new value of about plus 55 11:56 millivolts. That's called the peak, for 11:59 obvious reasons, right? So the membrane 12:01 potential almost totally reverses in
12:04
its 12:04 polarity from being highly negative to 12:06 being positive. Then there's a region of 12:08 the action potential, let's call the 12:11 overshoot. So here's the zero (0) millivolt level. 12:14 So the region of the action potential 12:17 between the zero millivolt level and its 12:19 peak is called the overshoot. That's the 12:21 shaded region. Then we also can 12:24 characterize the up-stroke phase of the
12:26
12:26 action potential and the down-stroke 12:28 phase. So this is the depolarizing phase 12:31 of the action potential also called the 12:33 up-stroke, and this is the repolarizing 12:36 phase of the action potential sometimes 12:39 called the down-stroke, right? So, 12:43 you're going to be hearing this 12:44 terminology, and you just need to know 12:46 what it means. 12:47 Now there's also a very 12:48 interesting phenomenon that occurs with
12:50
12:49 action potentials and that is when the 12:52 stimulus is terminated, when the action 12:54 potential finishes its repolarizing 12:57 phase, 12:58 it just doesn't return back to the 13:00 resting potential. There's a period of 13:03 time where the membrane potential is 13:05 actually more negative than the resting 13:07 potential, and that is called the 13:10 under-shoot, for obvious reasons. And it's 13:13 also called the hyperpolarizing after 13:15 potential. So it's a potential. It's
13:18
13:18 really not AFTER the action potential; 13:20 it's part of the action potential, but 13:21 it's a potential where the membrane 13:23 potential is more negative or, it's 13:25 hyperpolarizing compared to the resting 13:28 potential. 13:29 So here now, the duration of 13:32 the stimulus was relatively brief. The 13:35 stimulus is 5 milliseconds or less. There 13:38 was only time, only enough time 13:41 for a single action potential to be
13:42
13:42 triggered, but as I showed you in the 13:45 previous lecture on Monday, if you use a 13:48 longer duration stimulus, so as shown 13:52 here, I think this is a 1 second stimulus, 13:54 no, I think it's less but it's longer 13:56 than one millisecond. We're going to use 13:58 different batteries here, and what this 14:00 animation is just going to recapitulate 14:01 is the frequency code. So here's a small 14:04 battery. It produces a depolarization
14:07
but 14:07 that depolarization is sub-threshold. 14:09 You use a larger battery and then the 14:11 stimulus produces a depolarization 14:14 physics threshold but only one action 14:16 potential is elicited. So this, this 14:19 stimulus duration here, is what about 5, 14:21 10, 20 milliseconds. A larger battery 14:24 produces a greater depolarization, 14:31 and a greater, greater number of actions 14:35 potentials. So this is a recapitulation 14:37 of the frequency coding business in the
14:40
14:40 nervous system. Action potentials are all 14:43 or nothing. The action potential here is the 14:45 same intensity as the action potential 14:47 here. The action potential here is the 14:49 same amplitude as here, but what differs 14:52 as a function of stimulus intensity is 14:54 the number or frequency of action 14:56 potentials. 14:57 Okay, this is just this little 15:06 summary of what we said so far. I’m not 15:07 sure if this is in a handout but pieces
15:09
15:09 of it are there. Before you record the 15:12 membrane potential, you can inject a cell 15:15 with a current, either depolarizing or 15:18 hyperpolarizing current. The magnitude of 15:21 the hyperpolarization is proportional to 15:23 the stimulus. And for depolarizing 15:27 stimuli, it's proportional to a certain 15:29 range until you reach a threshold when 15:32 you elicit an all-or-none action 15:33 potential. You have the overshoot. You
15:35
15:35 have the hyperpolarizing after potential 15:37 or undershoot. If the stimulus is brief, 15:39 you can get just a single action 15:40 potential. If you use a longer duration 15:42 stimulus, now you get multiple action 15:45 potentials, the frequency of which is 15:46 dependent upon the intensity of the 15:49 stimulus. 15:50 Okay? So now we want to find out 15:56 what accounts for the initiation of 16:01 these action potentials; what accounts 16:02 for the repolarization of the action
16:04
16:04 potential, and what accounts for the 16:06 hyperpolarizing after potential. So in 16:09 order to answer that question, we need to 16:12 know a little bit more about the resting 16:15 potential. So in order to understand the 16:17 ionic mechanisms of the action potential, 16:20 you need to know about the ionic 16:22 mechanisms for the resting potential. 16:250Now 16:26 that has a long history. It goes back to 16:28 more than hundred years ago where the
16:30
16:30 first satisfactory hypothesis for the 16:33 generation of the resting potential was 16:35 put forward by an early physiologist by 16:38 the name of Julius Bernstein, working in 16:40 Germany, and Bernstein knew from chemical 16:43 analyses that the interior of cells, 16:49 nerve cells but all cells, had high 16:52 concentrations of potassium. There was 16:55 unequal distribution of ions between the 16:57 inside and outside, and in particular,
17:00
17:00 there was a high concentration of 17:02 potassium inside the cells compared the 17:04 outside. And he also knew based on 17:08 chemical analyses that cell membranes 17:10 seemed to be highly permeable to 17:12 potassium but not so permeable to other 17:16 ions. And finally he knew of the work of 17:20 the physical chemist, Nernst, and Nernst 17:23 had developed a mathematical equation 17:26 called the Nernst Equilibrium Potential 17:28 Equation that theoretically predicted a
17:32
17:32 potential that would be generated 17:34 across a membrane, if the membrane was 17:36 permeable to a single ion. 17:41 So based on that, what Bernstein 17:44 suggested was that you could predict the 17:51 membrane potential of a cell based on 17:55 the Nernst potential. Let's just say you have 18:03 a membrane, and this is the outside and. 18:06 this is the inside and what Bernstein 18:10 knew was that the membrane had a high 18:13 concentration of potassium inside the
18:19
18:18 cell and there was a relatively low 18:23 concentration of potassium outside the 18:25 cell. So if this membrane is permeable to 18:27 potassium, what is potassium going to do? 18:30 What if you were potassium inside the 18:33 cell, what would you want to do? Want to 18:37 go out. It's crowded; don't like it in 18:39 there. 18:39 You want to get out and go to a place 18:41 where it's not so crowded. So potassium
18:44
18:43 is going to try to, would like to move 18:46 just on the principle diffusion from its 18:48 region of high concentration to a region 18:50 of low concentration. So what will happen 18:53 if potassium diffuses is that there will 18:56 be a distribution of charge established 19:00 on the outside of the membrane. And if 19:02 potassium is the only ion that can move, 19:05 it's going to leave behind negative
19:10
19:10 charge. And so there will be a charge 19:14 distribution that will be established 19:15 across the membrane with the inside 19:18 surface of the membrane being negative, 19:19 and the outside surface being positive. 19:22 So what will that potential be? Well 19:26 here's where you get into the 19:27 equilibrium. They called it the Nernst 19:29 Equilibrium Potential Equation. Where is 19:32 the equilibrium? I don't see any 19:33 equilibrium here. You would think that
19:35
19:35 potassium is just going to go from 19:36 outside in high concentration, here to 19:39 there, and ultimately the concentration 19:41 the outside of the inside would be the 19:42 same, and there'd be no potential, right? 19:46 So where's the equilibrium come from? 19:49 Because of the gradient, the high 19:51 concentration of potassium here is going 19:53 to want to move outside. 19:54 It's going to leave negative charge 19:56 behind but that negative charge is going
19:58
19:58 to try to pull back the positive charge 20:01 it's leaving, right, because unlike 20:03 charges attract each other. So these 20:05 negative guys in here are going to say, 20:07 “Hey, hold it a second potassium. You can't 20:09 leave. I'm attached to you. I'm 20:10 going to pull you back.” So there's going 20:13 to be this force that tends to move the 20:15 potassium out of the cell, because based 20:17 on the concentration gradient, but 20:19 there'll be an equal and opposite force,
20:21
20:21 an electrical force, that tends to pull 20:25 the potassium back. And the equilibrium 20:28 is established when this force is equal 20:31 to this force and Nernst said there's a 20:34 potential that’s going to be generated, and 20:36 for potassium, it's going to be equal to 20:38 60 times the log of the outside 20:42 potassium concentration divided by the 20:45 inside potassium concentration. And this 20:48 gives you an answer in millivolts. So if 20:52 you know what the concentration is
20:54
20:54 outside and you know what the 20:55 concentration is inside, you can get out 20:58 your calculator and calculate exactly 21:01 what that equilibrium potential will be. 21:04 That's pretty neat, huh? 21:06 So what 21:08 Bernstein said was, “Hey, I think because 21:11 we have a high concentration of 21:14 potassium inside, we have a low 21:16 concentration of potassium outside, the 21:18 membrane is permeable to potassium so 21:20 I'm going to say that the membrane 21:22 potential is equal,
21:25
21:26 question mark here, equal to the 21:28 potassium equilibrium potential.” So 21:32 that's the hypothesis of Bernstein, but 21:34 he couldn't test it because he didn't 21:37 have electrode recording techniques. 21:41 So, 21:42 but we have them now so how could you 21:44 test the Bernstein hypothesis? So what 21:48 was done was that the membrane potential 21:52 was recorded, and the potassium 21:56 concentration in the extracellular
21:58
21:57 medium was systematically altered, and 21:59 each one of these dots was an 22:01 experimental measurement. You can do this 22:03 experiment, you can come up to my lab and do 22:04 this experiment this afternoon if you want 22:07 to. We can have nerve cells, and we can 22:09 change the potassium concentration. It's 22:11 really easy, you just make up a whole 22:12 bunch of different concentrations of 22:14 potassium, and then you stick the 22:16 electrode in the cell and you measure
22:19
22:18 the potential. So up here, by the way this 22:22 is a semi-log plot, what's shown here 22:25 also is the equation for the Nernst 22:29 equilibrium potential for potassium: 22:30 sixty times the log of the outside 22:33 concentration divided by the inside 22:35 concentration, which was 140 which we 22:37 assumed in this experiment is stable. All 22:41 right, so what you can do is you can use 22:42 your calculator and make a plot of this 22:44 equation. If you put in different values
22:47
22:47 here, you get this nice green line, right? 22:52 Now here's the data points, and what you 22:56 see is there's a remarkable 22:58 correspondence between how the membrane 23:02 potential changes with changing 23:04 potassium concentration and what you 23:07 predict by the Nernst equation. So this, 23:10 then, gives strong experimental support. 23:12 In fact, the membrane potential is due to 23:15 the fact that there's this unequal 23:17 distribution of potassium ions, the
23:19
membrane’s 23:19 permeable to potassium, and that accounts 23:21 for the resting potential. So, by the way, 23:24 if you put the electrode in the cell and 23:26 you recorded minus 60 millivolts, that's 23:27 necessary but why isn't it sufficient? 23:29 Because it could be that the resting 23:32 potential is due to the equilibrium 23:34 potential to some other ion. Maybe 23:36 hydrogen ions have an equilibrium 23:38 potential of minus 60 millivolts. Maybe 23:41 calcium ions have an equilibrium
23:44
23:43 potential of minus 60, so just because 23:45 you get minus 60 and that's the value 23:47 for the equilibrium potential of 23:49 potassium, it's not sufficient. You need 23:51 to change the potassium concentrations 23:54 to see if it changes as predicted. Okay 24:01 is that the end of the story? 24:06 If it is, we could we could stop and 24:09 finish the lecture. It's not the end of 24:13 the story. what's …what… You're 24:15 shaking your head, you don't like it. I
24:19
24:18 failed to account for sodium. Okay how do 24:22 you know about sodium? Do you see any sodium 24:26 here? There's a syst, he says, there's a 24:34 systematic difference. Well I think this 24:38 looks pretty damn good, don't you? 24:42 Not on the left, yeah. Okay. 24:47 So this looks great, but when the 24:51 potassium concentration starts getting 24:53 lower, you start to see deviations from 24:57 what you predicted that you would get,
25:00
25:00 and actually what you do get. And what 25:04 you see is that the membrane potential 25:07 is more depolarized than you would 25:10 expect to have from a membrane which is 25:12 exclusively permeable to potassium. So 25:15 this tells you that you need more than 25:18 two points, because if you just look at two 25:20 points right here, you would be fooled 25:23 into thinking that this is, you proved it. 25:25 But if you look at these points down
25:28
25:27 here, you start to see there's something 25:29 wrong with this hypothesis. It doesn't 25:31 completely work. So how do we explain the 25:34 deviation between the Nernst equation 25:37 and Bernstein's beautiful hypothesis, and 25:39 the reality well that's because we 25:42 didn't account for sodium. So this is the 25:47 distribution for potassium. What's the 25:49 distribution for sodium like? Opposite, so 25:53 sodium is in high concentration outside
25:58
25:57 the cell and relatively low 26:00 concentration inside the cell. So if you 26:06 were sodium, if you were sodium what 26:09 would you want to do? You’d want to go in. 26:12 Okay, let's assume, so sodium is in high 26:15 concentration here. It's a positively 26:17 charged ion. You want to go in for two 26:19 reasons: you'd want to go in because 26:21 there's a concentration gradient, but you 26:24 also want to go in because the inside of
26:26
26:25 the cell is negative, and you want to 26:26 find a partner who is negative because 26:29 you're positive. Assume that there is 26:32 some small permeability for sodium. As a 26:36 result, because of the concentration 26:37 gradient, sodium ions will tend to go 26:39 inside the cell and make the inside of 26:42 the cell positive with respect to the 26:44 outside. So because if you assume 26:47 some permeability to sodium, not a lot,
26:50
26:50 that will tend to subtract from the 26:52 negative polarity produced by the 26:55 diffusion of potassium. 26:59 Now we have a membrane that's permeable 27:01 to more than one ion, so the Nernst 27:05 equation can no longer be used to 27:08 predict the membrane potential. We have 27:11 to introduce a new equation, called the 27:18 Goldman Hodgkin Katz equation, also 27:22 called the GHK Equation. Actually Goldman
27:25
27:25 was a medical student at Columbia 27:26 University when he developed this 27:29 equation. So the GHK Equation says that a 27:33 potential across a membrane is permeable 27:38 to two ions, in this case we're going to 27:41 talk about sodium and potassium. You can 27:43 extrapolate this to include lots of 27:45 other ions, but we're just going to talk 27:47 about the form that counts for sodium 27:49 and potassium because they are the ones
27:51
27:50 that have the permeability that we're 27:52 interested in. It's got a 60 in it. It's 27:56 got a log in it. It's got outside 28:02 potassium concentration. It's got the 28:05 inside potassium concentration. So it 28:08 looks kind of similar so far, right? Then 28:12 it has this term, alpha. I'll tell what 28:17 alpha is in a moment the outside sodium 28:20 concentration plus alpha times the 28:26 inside sodium concentration, and that
28:29
28:29 gives an answer in millivolts. 28:32 That's the GHK Equation. Alpha is equal 28:38 to the ratio of the sodium permeability 28:41 divided by the potassium permeability. So 28:45 this looks complicated, but it's really 28:47 not and it can be simplified, you know, if 28:50 you take some extreme cases. So take the 28:52 case where the sodium permeability is 28:55 zero (0). That means you have a membrane 28:56 essentially that's only permeable to 28:58 potassium. If the sodium permeability
29:00
is 29:00 zero, what's alpha? And what is the 29:04 Goldman Hodgkin Katz Equation revert to? 29:06 The Nernst equation. And it better, right? 29:09 It better do that. Take the other extreme, 29:11 let's just say 29:12 the sodium permeability is very high 29:13 relative to the potassium permeability. 29:16 What is the Goldman Hodgkin Katz 29:18 Equation revert to? The Nernst 29:23 equilibrium potential for sodium, right? 29:26 So on one extreme of the Goldman Hodgkin
29:29
29:29 Katz Equation is the Nernst equation for 29:32 potassium, and the other extreme is the 29:33 Nernst equation for sodium. And you can see 29:36 that you get any potential in-between 29:38 simply by adjusting the relative 29:41 permeability of these two ions. So we 29:48 need to test this. The next slide just 29:50 simply shows the same experiment with 29:53 now the same data points, but now showing 29:56 a plot of both the Nernst equation and 30:00 the Goldman Hodgkin Katz Equation here.
30:03
30:03 So the outside potassium concentration - 30:06 that's what's varied, and here's the 30:09 equation. Here's the equation for the 30:11 Nernst. And you see now you get a much 30:14 better fit, still not perfect, but with an 30:16 experimental variability, it's pretty 30:18 darn good. And it reflects the general 30:21 consensus that the resting potential is 30:23 due to the combined permeability of 30:26 potassium and sodium with the potassium 30:28 permeability being much, much greater
30:30
30:30 than the sodium permeability. And in fact 30:33 what is the ratio of those two certain 30:35 permeabilities? So what you see here is 30:38 that this fit was obtained by this value 30:41 here 0.01. What is a 0.01? The 0.01 is our 30:48 friend, the ratio of the sodium potassium 30:50 permeability. So if alpha is 0.01, what 30:54 does that tell you about the relative 30:56 contribution of the sodium permeability
30:59
30:58 system and the potassium permeability 31:00 system? Potassium is much, much more. In 31:05 fact, you can say exactly how much more 31:07 it is. It's a hundred times more. So the 31:10 potassium permeability is a hundred 31:11 times greater than the sodium 31:13 permeability. We don't need to know exactly 31:15 what the numbers are, but you need to 31:17 know about the ratios, right? 31:21 Okay, so that's the story of the resting 31:24 potential. Now we know how the resting
31:26
31:26 potential works, we can move on to a 31:29 discussion of the action potential. By 31:31 the way, in your electronic online 31:34 syllabus, there is something called the 31:36 Membrane Potential Laboratory, and what 31:38 this Membrane Potential Laboratory does. 31:40 Let me just do something here. So here is 31:44 a plot of the Nernst equation for 31:46 potassium. So this blue line here is the 31:49 Goldman Hodgkin Katz Equation and what 31:51 this program allows you to do is put in
31:54
31:54 different values of the extracellular 31:56 concentration of potassium and different 31:58 values of alpha and make a plot and see 32:01 how it affects the predicted membrane 32:02 potential. So you can use these 32:04 laboratories to sort of test your 32:06 understanding. Okay so what we're going 32:09 to do then next time we meet is talk 32:11 about the ionic mechanisms of the action 32:14 potential. Okay I’ll see you then.
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