1 00:00:15,660 --> 00:00:17,910 MICHALE FEE: Today we're going to continue developing 2 00:00:17,910 --> 00:00:22,020 our equivalent circuit model, the Hodgkin-Huxley model 3 00:00:22,020 --> 00:00:23,610 of a neuron. 4 00:00:23,610 --> 00:00:25,830 And we're still focusing on the mechanism 5 00:00:25,830 --> 00:00:27,450 that generates spikes. 6 00:00:27,450 --> 00:00:30,750 As you recall, there are two conductances, 7 00:00:30,750 --> 00:00:36,260 iron conductances, that lead to action potential generation. 8 00:00:36,260 --> 00:00:40,080 There is sodium conductance that is 9 00:00:40,080 --> 00:00:44,400 connected to a sodium battery that has a high equilibrium 10 00:00:44,400 --> 00:00:45,320 potential. 11 00:00:45,320 --> 00:00:47,310 There is a potassium conductance that 12 00:00:47,310 --> 00:00:50,250 is connected to a potassium battery that 13 00:00:50,250 --> 00:00:53,070 has a negative equilibrium potential, 14 00:00:53,070 --> 00:00:54,990 and those two conductances together 15 00:00:54,990 --> 00:00:56,640 have voltage and time dependence that 16 00:00:56,640 --> 00:00:59,850 lead to the generation of a positive going, 17 00:00:59,850 --> 00:01:03,540 followed by a negative going, fluctuation in the voltage that 18 00:01:03,540 --> 00:01:04,950 is the action potential. 19 00:01:04,950 --> 00:01:08,520 And as you recall, the way that happens, 20 00:01:08,520 --> 00:01:10,940 there is a time dependence to these conductances 21 00:01:10,940 --> 00:01:13,650 so that when the sodium conductance turns on, 22 00:01:13,650 --> 00:01:16,170 this resistor gets really small, and basically connects 23 00:01:16,170 --> 00:01:18,870 the inside of the cell to that positive battery. 24 00:01:18,870 --> 00:01:20,600 When the sodium conductance turns off 25 00:01:20,600 --> 00:01:23,400 and the potassium conductance turns on, 26 00:01:23,400 --> 00:01:26,010 we're disconnecting the sodium battery 27 00:01:26,010 --> 00:01:28,060 and connecting the potassium battery, 28 00:01:28,060 --> 00:01:29,550 which has a negative voltage. 29 00:01:29,550 --> 00:01:31,440 And the voltage of the cell, then, 30 00:01:31,440 --> 00:01:35,370 is driven toward the negative potassium equilibrium 31 00:01:35,370 --> 00:01:37,700 potential. 32 00:01:37,700 --> 00:01:42,130 So last time we worked out the voltage and time dependence 33 00:01:42,130 --> 00:01:44,320 of the potassium conductance. 34 00:01:44,320 --> 00:01:49,000 Today, we're going to focus on the, sorry, focus here 35 00:01:49,000 --> 00:01:52,330 on the sodium conductance and explain 36 00:01:52,330 --> 00:01:56,050 various aspects of the voltage and time dependence 37 00:01:56,050 --> 00:01:59,510 of the sodium conductance. 38 00:01:59,510 --> 00:02:01,940 And then once we do that, we're going 39 00:02:01,940 --> 00:02:03,980 to turn in the second half of the lecture 40 00:02:03,980 --> 00:02:10,970 to a really beautiful, simple model of a disease related 41 00:02:10,970 --> 00:02:14,120 to a defect in the sodium channel. 42 00:02:14,120 --> 00:02:18,170 And it's an example of how we can use modeling 43 00:02:18,170 --> 00:02:24,430 to test and elaborate on hypotheses about how defects 44 00:02:24,430 --> 00:02:27,230 in a circuit, or in an ion channel, 45 00:02:27,230 --> 00:02:32,670 can lead to very complex phenotypes in a whole animal. 46 00:02:32,670 --> 00:02:35,300 So as you recall, our Hodgkin-Huxley model 47 00:02:35,300 --> 00:02:39,050 has three conductances and a capacitance 48 00:02:39,050 --> 00:02:41,780 that represents a capacitor that represents the capacitance 49 00:02:41,780 --> 00:02:42,830 of the membrane. 50 00:02:42,830 --> 00:02:45,170 The total membrane ionic current is just 51 00:02:45,170 --> 00:02:48,080 a sum of the sodium current, the potassium current, 52 00:02:48,080 --> 00:02:51,830 and this voltage independent, time independent, 53 00:02:51,830 --> 00:02:55,110 fixed leak current. 54 00:02:55,110 --> 00:02:57,843 So the equation for the membrane potential, 55 00:02:57,843 --> 00:03:00,010 the differential equation for the membrane potential 56 00:03:00,010 --> 00:03:03,970 in the Hodgkin-Huxley model, is just a simple first order 57 00:03:03,970 --> 00:03:05,440 linear differential equation that 58 00:03:05,440 --> 00:03:11,650 relates the membrane current and the membrane potential. 59 00:03:11,650 --> 00:03:15,240 So last time we described a set of experiments 60 00:03:15,240 --> 00:03:17,730 that were done by Hodgkin and Huxley 61 00:03:17,730 --> 00:03:21,120 to study the voltage and time dependence 62 00:03:21,120 --> 00:03:25,300 of these conductances in the squid giant axon. 63 00:03:25,300 --> 00:03:27,900 And as you remember, this axon is very large. 64 00:03:27,900 --> 00:03:30,000 It's 1 millimeter in diameter, which 65 00:03:30,000 --> 00:03:32,550 makes it very easy to put wires into it, 66 00:03:32,550 --> 00:03:35,280 and change the voltage, and measure the currents, and so 67 00:03:35,280 --> 00:03:36,840 on. 68 00:03:36,840 --> 00:03:40,020 So the experiment they did was a voltage clamp experiment, 69 00:03:40,020 --> 00:03:43,740 where you can hyperpolarize and depolarize the cell. 70 00:03:43,740 --> 00:03:45,930 There's a very fast feedback system 71 00:03:45,930 --> 00:03:48,600 that allows you to set a command voltage, 72 00:03:48,600 --> 00:03:52,080 and this operational amplifier injects however much current 73 00:03:52,080 --> 00:03:56,160 is needed to hold the cell at whatever membrane potential you 74 00:03:56,160 --> 00:03:56,820 command. 75 00:03:56,820 --> 00:03:58,710 And the typical experiment that they would do 76 00:03:58,710 --> 00:04:01,260 would be to hyperpolarize or depolarize 77 00:04:01,260 --> 00:04:03,930 the cell to fixed membrane potentials 78 00:04:03,930 --> 00:04:08,310 and measure how much current passes through the membrane 79 00:04:08,310 --> 00:04:13,060 during and after that transient change in the command voltage. 80 00:04:13,060 --> 00:04:16,110 So if you take a squid giant axon, 81 00:04:16,110 --> 00:04:18,390 you start at minus 65 millivolts, 82 00:04:18,390 --> 00:04:21,313 and you hyperpolarize the cell, not much happens. 83 00:04:21,313 --> 00:04:22,980 And that's because all of those currents 84 00:04:22,980 --> 00:04:28,350 are already off when the cell is hyperpolarize at minus 60 85 00:04:28,350 --> 00:04:30,480 or at low voltages. 86 00:04:30,480 --> 00:04:33,180 On the other hand, if you start at minus 65 millivolts 87 00:04:33,180 --> 00:04:37,560 and depolarize the cell up to 0 millivolts, all of a sudden you 88 00:04:37,560 --> 00:04:41,190 see a very large transient current 89 00:04:41,190 --> 00:04:44,040 that first goes negative, which corresponds 90 00:04:44,040 --> 00:04:46,860 to positive charges going into the cell followed 91 00:04:46,860 --> 00:04:50,220 by a positive current that's associated 92 00:04:50,220 --> 00:04:54,440 with positive charges leaving the cell. 93 00:04:54,440 --> 00:04:56,720 And last time we talked about how 94 00:04:56,720 --> 00:04:59,810 we can dissect these two phases of the current, 95 00:04:59,810 --> 00:05:01,820 this negative phase and this positive phase, 96 00:05:01,820 --> 00:05:06,020 into two different ionic conductances. 97 00:05:06,020 --> 00:05:09,740 That they did that experiment by replacing the sodium 98 00:05:09,740 --> 00:05:13,400 in the extracellular solution that the axon was 99 00:05:13,400 --> 00:05:16,940 sitting in with a solution that has no sodium in it. 100 00:05:16,940 --> 00:05:20,090 They replaced that with choline chloride. 101 00:05:20,090 --> 00:05:24,030 So choline is a positive ionic-- 102 00:05:24,030 --> 00:05:26,220 has a positive charge and chloride, of course, 103 00:05:26,220 --> 00:05:27,490 has a negative charge. 104 00:05:27,490 --> 00:05:29,240 And so you can replace the sodium chloride 105 00:05:29,240 --> 00:05:30,157 with choline chloride. 106 00:05:30,157 --> 00:05:32,480 And now, when you depolarize your cell, 107 00:05:32,480 --> 00:05:36,180 you can see that that negative part is gone. 108 00:05:36,180 --> 00:05:39,120 And the only current you see is this positive-- 109 00:05:39,120 --> 00:05:43,170 this kind of slowly ramping up positive current. 110 00:05:43,170 --> 00:05:47,630 And they identified that as being due to potassium ions. 111 00:05:47,630 --> 00:05:49,752 And if you subtract the current curve 112 00:05:49,752 --> 00:05:52,670 without sodium from the current curve with sodium, 113 00:05:52,670 --> 00:05:56,060 the difference is obviously due to sodium. 114 00:05:56,060 --> 00:05:58,490 And so if you plot the difference between those two 115 00:05:58,490 --> 00:06:02,900 curves, you can see that the sodium current turns 116 00:06:02,900 --> 00:06:09,680 on very rapidly and then decays very rapidly, 117 00:06:09,680 --> 00:06:11,930 that that transient sodium current happens 118 00:06:11,930 --> 00:06:15,410 very quickly, almost before the potassium current even 119 00:06:15,410 --> 00:06:17,730 gets started. 120 00:06:17,730 --> 00:06:21,670 And we talked about how that fast sodium current, followed 121 00:06:21,670 --> 00:06:26,530 by a slower potassium current, is exactly the profile, 122 00:06:26,530 --> 00:06:31,980 that we showed here, that generates depolarizing change 123 00:06:31,980 --> 00:06:34,360 in the voltage followed by a hyperpolarize change 124 00:06:34,360 --> 00:06:38,146 in the voltage that looks like an action potential. 125 00:06:40,910 --> 00:06:43,910 So now, let's just review quickly how 126 00:06:43,910 --> 00:06:49,330 we took these current curves, and from those, extracted 127 00:06:49,330 --> 00:06:53,960 the conductance of the sodium and potassium ion channels 128 00:06:53,960 --> 00:06:57,020 as a function of voltage and time. 129 00:06:57,020 --> 00:06:59,720 So what we did was we looked at the case 130 00:06:59,720 --> 00:07:01,460 where we do our voltage clamp experiment 131 00:07:01,460 --> 00:07:02,660 to different voltages. 132 00:07:02,660 --> 00:07:04,310 We start hyperpolarized. 133 00:07:04,310 --> 00:07:08,930 We step up to minus 40 and measure this potassium current. 134 00:07:08,930 --> 00:07:13,040 We step up to 0, and you see this larger potassium current. 135 00:07:13,040 --> 00:07:15,560 If you step from minus 40 to 40, you 136 00:07:15,560 --> 00:07:18,660 see an even larger potassium current. 137 00:07:18,660 --> 00:07:23,360 And you can plot this peak current, or the steady state 138 00:07:23,360 --> 00:07:26,250 current, as a function of voltage. 139 00:07:26,250 --> 00:07:29,028 That gives you an I-V curve, and we'll look at that in a second. 140 00:07:29,028 --> 00:07:31,070 If you do the same thing for the sodium currents, 141 00:07:31,070 --> 00:07:33,620 you see something different that's 142 00:07:33,620 --> 00:07:36,750 initially very confusing. 143 00:07:36,750 --> 00:07:38,940 If you step from minus 80 to minus 40, 144 00:07:38,940 --> 00:07:41,760 you see a small sodium current. 145 00:07:41,760 --> 00:07:44,310 If you make a larger voltage step up to 0, 146 00:07:44,310 --> 00:07:47,970 you see this bigger sodium current. 147 00:07:47,970 --> 00:07:51,030 But then if you step up from minus 80 millivolts 148 00:07:51,030 --> 00:07:52,980 to 40 millivolts, now you see you just have 149 00:07:52,980 --> 00:07:55,230 a tiny little sodium current. 150 00:07:55,230 --> 00:07:57,870 Anybody remember why that would be? 151 00:07:57,870 --> 00:08:00,930 Why is it that you would see only a very tiny sodium 152 00:08:00,930 --> 00:08:04,517 current, if you step up to 40 millivolts? 153 00:08:09,660 --> 00:08:16,024 What is the equilibrium potential for sodium? 154 00:08:16,024 --> 00:08:17,550 AUDIENCE: [INAUDIBLE] 155 00:08:17,550 --> 00:08:18,550 MICHALE FEE: Good, good. 156 00:08:18,550 --> 00:08:21,790 So what would the sodium current be 157 00:08:21,790 --> 00:08:25,810 if I had stepped this voltage up exactly to 50 millivolts? 158 00:08:25,810 --> 00:08:26,592 AUDIENCE: 0. 159 00:08:26,592 --> 00:08:27,550 MICHALE FEE: It'd be 0. 160 00:08:27,550 --> 00:08:29,530 So this is pretty close to 50 millivolts, 161 00:08:29,530 --> 00:08:35,080 which is why the sodium current is actually pretty small. 162 00:08:35,080 --> 00:08:39,940 So now, let's plot the peak current 163 00:08:39,940 --> 00:08:43,360 as a function of voltage for potassium and the peak current 164 00:08:43,360 --> 00:08:46,750 here as a function of voltage for sodium. 165 00:08:46,750 --> 00:08:48,080 That's what that looks like. 166 00:08:48,080 --> 00:08:50,080 So you can see that the potassium 167 00:08:50,080 --> 00:08:54,800 current is 0 for these voltages down here and grows. 168 00:08:54,800 --> 00:08:59,030 It's actually stay 0 for even more negative voltages. 169 00:08:59,030 --> 00:09:00,660 The sodium current, on the other hand, 170 00:09:00,660 --> 00:09:04,400 has this very kind of funny shape. 171 00:09:04,400 --> 00:09:07,310 It's linear up here around high voltages, 172 00:09:07,310 --> 00:09:11,030 around the sodium equilibrium or reversal potential, 173 00:09:11,030 --> 00:09:14,650 and then at drops to 0. 174 00:09:14,650 --> 00:09:19,540 The sodium current stays at 0 for negative voltages. 175 00:09:19,540 --> 00:09:23,200 And you recall that we use this to think about what 176 00:09:23,200 --> 00:09:24,550 the conductance must be. 177 00:09:24,550 --> 00:09:29,450 So let me just walk you through that logic again. 178 00:09:29,450 --> 00:09:32,350 So remember that the current is just a conductance 179 00:09:32,350 --> 00:09:34,570 times the driving potential. 180 00:09:34,570 --> 00:09:37,450 The driving potential is positive 181 00:09:37,450 --> 00:09:39,730 when you're above the equilibrium potential, 182 00:09:39,730 --> 00:09:43,270 and it's negative when you're below. 183 00:09:43,270 --> 00:09:46,090 So this term here is a straight line. 184 00:09:46,090 --> 00:09:49,660 It's linear in voltage, and it goes through 0 185 00:09:49,660 --> 00:09:53,050 when V is equal to EK. 186 00:09:53,050 --> 00:09:56,800 So there is the driving potential for potassium 187 00:09:56,800 --> 00:09:59,770 as a function of voltage. 188 00:09:59,770 --> 00:10:04,360 Now, you can see clearly that the conductance 189 00:10:04,360 --> 00:10:08,740 as a function of voltage has some voltage dependence, 190 00:10:08,740 --> 00:10:10,420 because this doesn't look like this. 191 00:10:10,420 --> 00:10:12,400 So the difference between this and this 192 00:10:12,400 --> 00:10:15,200 is captured by this voltage-dependent conductance. 193 00:10:15,200 --> 00:10:20,620 And does anyone remember what that conductance, that GK 194 00:10:20,620 --> 00:10:22,090 as a function of V, looks like? 195 00:10:28,042 --> 00:10:29,034 AUDIENCE: Sigmoidal. 196 00:10:29,034 --> 00:10:30,410 MICHALE FEE: Yeah, sigmoidal. 197 00:10:30,410 --> 00:10:33,390 And what is it down here? 198 00:10:33,390 --> 00:10:34,380 It's 0. 199 00:10:34,380 --> 00:10:36,690 So the way that you can get a 0 current, 200 00:10:36,690 --> 00:10:38,910 even with a very negative driving potential, 201 00:10:38,910 --> 00:10:41,550 is if the conductance is 0. 202 00:10:41,550 --> 00:10:43,890 You can see that the current is linear up here, 203 00:10:43,890 --> 00:10:45,810 and the driving potential is linear up here. 204 00:10:45,810 --> 00:10:49,720 So the conductance has to be constant. 205 00:10:49,720 --> 00:10:51,250 And so we have a conductance that 206 00:10:51,250 --> 00:10:56,820 has to be 0 down here and a constant non-zero up here. 207 00:10:56,820 --> 00:10:57,630 Yes? 208 00:10:57,630 --> 00:11:00,325 AUDIENCE: So why is the potassium curve 209 00:11:00,325 --> 00:11:04,090 0 when it's more negative than GK? 210 00:11:04,090 --> 00:11:07,890 Why doesn't it go in the other direction? 211 00:11:07,890 --> 00:11:11,375 MICHALE FEE: Why doesn't this curve do something else? 212 00:11:11,375 --> 00:11:12,500 So what is it that you're-- 213 00:11:12,500 --> 00:11:13,560 AUDIENCE: Like why doesn't it-- why doesn't it-- 214 00:11:13,560 --> 00:11:14,700 MICHALE FEE: Why doesn't it keep going? 215 00:11:14,700 --> 00:11:15,325 AUDIENCE: Yeah. 216 00:11:15,325 --> 00:11:17,363 Why is there like a [INAUDIBLE]? 217 00:11:17,363 --> 00:11:18,030 MICHALE FEE: Ah. 218 00:11:18,030 --> 00:11:20,580 Because-- OK. 219 00:11:20,580 --> 00:11:21,580 That's a great question. 220 00:11:21,580 --> 00:11:25,360 So maybe you can answer it. 221 00:11:25,360 --> 00:11:28,700 How would I change the conductance curve 222 00:11:28,700 --> 00:11:34,130 to make this look more like this? 223 00:11:34,130 --> 00:11:38,060 I could do something very simple to the voltage dependence 224 00:11:38,060 --> 00:11:40,190 of the potassium conductance to actually make 225 00:11:40,190 --> 00:11:41,353 it look like that. 226 00:11:41,353 --> 00:11:42,020 What would I do? 227 00:11:49,920 --> 00:11:53,940 The reason this goes to 0 and stays at 0 228 00:11:53,940 --> 00:11:57,910 is because the voltage dependence of the conductance 229 00:11:57,910 --> 00:12:03,110 turns it off before the driving potential can go negative. 230 00:12:03,110 --> 00:12:05,620 So what would I do to the conductance 231 00:12:05,620 --> 00:12:11,380 to make this current dip below 0 before it comes back, 232 00:12:11,380 --> 00:12:14,346 any suggestions? 233 00:12:14,346 --> 00:12:15,372 AUDIENCE: Translate it. 234 00:12:15,372 --> 00:12:16,580 MICHALE FEE: Yeah, which way? 235 00:12:16,580 --> 00:12:17,450 AUDIENCE: This way. 236 00:12:17,450 --> 00:12:18,590 MICHALE FEE: Good, exactly. 237 00:12:18,590 --> 00:12:22,010 So if I took this curve and I shifted it that way, 238 00:12:22,010 --> 00:12:25,100 if I made the potassium conductance turn off 239 00:12:25,100 --> 00:12:29,930 at a more negative potential, then this 240 00:12:29,930 --> 00:12:33,405 would go down before it got turned off by the conductance. 241 00:12:33,405 --> 00:12:34,280 Does that make sense? 242 00:12:34,280 --> 00:12:36,730 Great question. 243 00:12:36,730 --> 00:12:38,830 Any other questions? 244 00:12:38,830 --> 00:12:41,770 So the answer is, the reason this doesn't go negative 245 00:12:41,770 --> 00:12:44,260 is because the voltage dependence of the potassium 246 00:12:44,260 --> 00:12:47,380 conductance turns off the conductance 247 00:12:47,380 --> 00:12:51,760 before or on the positive side of the equilibrium 248 00:12:51,760 --> 00:12:55,262 potential of potassium. 249 00:12:55,262 --> 00:12:55,762 Yes? 250 00:12:55,762 --> 00:12:58,684 AUDIENCE: Can you explain again why the [INAUDIBLE]?? 251 00:13:02,470 --> 00:13:04,510 MICHALE FEE: So if G were constant, 252 00:13:04,510 --> 00:13:08,570 if G had no voltage dependence and it was just a constant, 253 00:13:08,570 --> 00:13:11,140 what would this current look like? 254 00:13:15,710 --> 00:13:17,230 What would it look like? 255 00:13:17,230 --> 00:13:21,760 If this G were just a constant, no dependent on voltage? 256 00:13:21,760 --> 00:13:22,680 AUDIENCE: [INAUDIBLE] 257 00:13:22,680 --> 00:13:23,430 MICHALE FEE: Good. 258 00:13:23,430 --> 00:13:27,870 It would look just like this, right? 259 00:13:27,870 --> 00:13:31,950 So the reason this curve shuts off and goes to 0 260 00:13:31,950 --> 00:13:36,790 is that the conductance goes to 0 down here, 261 00:13:36,790 --> 00:13:39,450 and it's constant up here. 262 00:13:39,450 --> 00:13:41,780 Does that make sense? 263 00:13:41,780 --> 00:13:44,120 And that curve just looks like that. 264 00:13:44,120 --> 00:13:47,000 It's 0 down here and constant up here. 265 00:13:49,640 --> 00:13:51,210 Good question. 266 00:13:51,210 --> 00:13:51,790 Any other? 267 00:13:51,790 --> 00:13:53,350 There was another hand up here. 268 00:13:53,350 --> 00:13:53,480 Yeah? 269 00:13:53,480 --> 00:13:55,188 AUDIENCE: I was wondering about notation. 270 00:13:55,188 --> 00:13:57,643 So it's GK of V. It's not like GK times V, right? 271 00:13:57,643 --> 00:13:58,310 MICHALE FEE: No. 272 00:13:58,310 --> 00:14:03,180 It's GK as a function of V. Yeah, that's-- 273 00:14:03,180 --> 00:14:07,250 the notation is sometimes a little bit confusing. 274 00:14:07,250 --> 00:14:10,275 You kind of have to read it out from the context. 275 00:14:16,410 --> 00:14:18,360 Any other questions? 276 00:14:18,360 --> 00:14:22,720 So now you can see why this curve looks the way it does. 277 00:14:22,720 --> 00:14:29,370 So now, let's plot the driving potential, V minus Ena. 278 00:14:29,370 --> 00:14:31,770 That's this curve right here. 279 00:14:31,770 --> 00:14:36,130 It's Ohm's law, but it has a battery that makes it centered. 280 00:14:36,130 --> 00:14:40,920 It makes it give 0 current when V is equal to Ena, 281 00:14:40,920 --> 00:14:42,810 which is positive. 282 00:14:42,810 --> 00:14:44,790 So that's why that curve looks like that. 283 00:14:44,790 --> 00:14:47,100 And what is it that makes the sodium 284 00:14:47,100 --> 00:14:50,770 current go to 0 down here? 285 00:14:50,770 --> 00:14:56,220 It must be that the what? 286 00:14:56,220 --> 00:14:59,304 What about the conductance? 287 00:14:59,304 --> 00:15:00,190 AUDIENCE: Turns off. 288 00:15:00,190 --> 00:15:00,940 MICHALE FEE: Good. 289 00:15:00,940 --> 00:15:03,130 The conductance, the sodium conductance, 290 00:15:03,130 --> 00:15:05,890 has to turn off down here. 291 00:15:05,890 --> 00:15:07,060 And what about up here? 292 00:15:07,060 --> 00:15:08,600 This is linear. 293 00:15:08,600 --> 00:15:10,600 This is linear, so the sodium conductance 294 00:15:10,600 --> 00:15:11,770 has to be what up here? 295 00:15:14,330 --> 00:15:15,680 Constant, good. 296 00:15:15,680 --> 00:15:18,530 So you can see that the sodium conductance 297 00:15:18,530 --> 00:15:23,650 has exactly the same shape as the potassium conductance. 298 00:15:23,650 --> 00:15:26,275 It's not exactly at the same voltage, but it's close. 299 00:15:29,320 --> 00:15:30,610 Good. 300 00:15:30,610 --> 00:15:32,290 So now you can see where this kind 301 00:15:32,290 --> 00:15:36,070 of weird shape of these sodium and potassium currents 302 00:15:36,070 --> 00:15:36,610 comes from. 303 00:15:36,610 --> 00:15:38,300 It's actually very simple. 304 00:15:38,300 --> 00:15:42,550 It's just a resistor in series with a battery that gives you 305 00:15:42,550 --> 00:15:47,470 this driving potential offset from 0, 306 00:15:47,470 --> 00:15:51,130 and that's multiplied by this voltage-dependent conductance. 307 00:15:56,110 --> 00:15:59,650 Now, the time dependence of the conductance 308 00:15:59,650 --> 00:16:01,420 is entirely due-- sorry. 309 00:16:01,420 --> 00:16:03,220 The time dependence of the current, 310 00:16:03,220 --> 00:16:06,280 that ramping up current that turns on and then stays 311 00:16:06,280 --> 00:16:08,950 constant for the potassium, is entirely 312 00:16:08,950 --> 00:16:13,570 due to the time dependence of the potassium conductance. 313 00:16:13,570 --> 00:16:16,870 So the potassium conductance just turns on. 314 00:16:16,870 --> 00:16:19,360 That process of the conductance turning on 315 00:16:19,360 --> 00:16:22,160 is called activation. 316 00:16:22,160 --> 00:16:23,180 Same for the sodium-- 317 00:16:23,180 --> 00:16:27,380 the sodium conductance turns on quickly. 318 00:16:27,380 --> 00:16:28,730 That's called activation. 319 00:16:28,730 --> 00:16:31,190 The sodium conductance turns on very fast, 320 00:16:31,190 --> 00:16:35,880 and the potassium conductance turns on slowly. 321 00:16:35,880 --> 00:16:40,350 Now, we talked about how the voltage gates 322 00:16:40,350 --> 00:16:45,700 work in our voltage-dependent ion channel. 323 00:16:45,700 --> 00:16:49,380 And the idea is that you have some gating charges that 324 00:16:49,380 --> 00:16:52,590 are literally charged residues, charged amino acids, 325 00:16:52,590 --> 00:16:55,160 in the protein. 326 00:16:55,160 --> 00:16:59,400 When the membrane potential is very negative, 327 00:16:59,400 --> 00:17:01,410 when the cell is at rest, you can 328 00:17:01,410 --> 00:17:03,840 see that there's a large electric field pointing 329 00:17:03,840 --> 00:17:08,040 that way inside the membrane, and that pushes the charges, 330 00:17:08,040 --> 00:17:11,829 pushes those gating charges, toward the inside of the cell, 331 00:17:11,829 --> 00:17:14,490 and that closes the gate. 332 00:17:14,490 --> 00:17:18,180 When you depolarize the cell, this membrane potential 333 00:17:18,180 --> 00:17:22,380 goes closer to 0, the electric field drops, 334 00:17:22,380 --> 00:17:24,000 and those gating charges are no longer 335 00:17:24,000 --> 00:17:26,349 being pushed into the cell. 336 00:17:26,349 --> 00:17:28,250 And they relax back, and the gate opens. 337 00:17:32,820 --> 00:17:36,710 So that is the basic, sort of a cartoon, 338 00:17:36,710 --> 00:17:40,280 picture of the mechanism by which voltage-dependent ion 339 00:17:40,280 --> 00:17:45,280 channels acquire that voltage dependence. 340 00:17:45,280 --> 00:17:48,250 So remember, we talked about how we 341 00:17:48,250 --> 00:17:50,380 can model that time dependence. 342 00:17:50,380 --> 00:17:52,600 We can model that opened and closed 343 00:17:52,600 --> 00:17:57,700 state of the ion channel as two states, an open state 344 00:17:57,700 --> 00:18:00,220 and a closed state, where the probability, n, of being 345 00:18:00,220 --> 00:18:02,603 in the open state, a probability of 1 minus 346 00:18:02,603 --> 00:18:03,770 n being in the closed state. 347 00:18:03,770 --> 00:18:06,010 Remember, this was for one subunit. 348 00:18:06,010 --> 00:18:08,470 For the potassium channel, there are four subunits, 349 00:18:08,470 --> 00:18:12,350 and all of them have to be open. 350 00:18:12,350 --> 00:18:14,330 And we wrote down a differential equation 351 00:18:14,330 --> 00:18:18,560 for that gating variable, n. 352 00:18:18,560 --> 00:18:21,750 There is an n infinity, a steady state, 353 00:18:21,750 --> 00:18:23,040 that's a function of voltage. 354 00:18:23,040 --> 00:18:27,810 And remember, for the potassium, n infinity 355 00:18:27,810 --> 00:18:31,770 is negative down here and increases 356 00:18:31,770 --> 00:18:35,670 as a function of voltage to get close to 1 357 00:18:35,670 --> 00:18:41,970 at voltages above minus 50, or somewhere between minus 50 358 00:18:41,970 --> 00:18:44,700 and 0 millivolts, that gating variable. 359 00:18:44,700 --> 00:18:48,660 And the n infinity of that gating variable, n, 360 00:18:48,660 --> 00:18:50,600 goes from being very small to being large. 361 00:18:54,510 --> 00:18:56,000 Now, so that's potassium. 362 00:18:56,000 --> 00:18:58,710 We went through that last time. 363 00:18:58,710 --> 00:19:01,590 And now let's talk about sodium. 364 00:19:01,590 --> 00:19:04,920 Sodium looks exactly the same. 365 00:19:04,920 --> 00:19:07,200 The sodium conductance can be modeled 366 00:19:07,200 --> 00:19:09,840 as having two states, an open state and a closed state. 367 00:19:09,840 --> 00:19:12,270 Remember, we did a patch recording 368 00:19:12,270 --> 00:19:14,580 on a single sodium channel. 369 00:19:14,580 --> 00:19:17,190 You could see that it flickers back and forth between open 370 00:19:17,190 --> 00:19:18,420 and closed. 371 00:19:18,420 --> 00:19:22,710 So we can model that process in exactly the same way 372 00:19:22,710 --> 00:19:25,380 that we did for the potassium conductance. 373 00:19:25,380 --> 00:19:28,860 We have an open state, a closed state, a probability, m, 374 00:19:28,860 --> 00:19:30,160 of being in the open state. 375 00:19:30,160 --> 00:19:33,390 So m is our gating variable for-- 376 00:19:33,390 --> 00:19:36,750 our activation gating variable for the sodium conductance. 377 00:19:36,750 --> 00:19:40,080 Probability of being in a closed state is 1 minus m. 378 00:19:40,080 --> 00:19:43,380 There is that same kind of differential equation for the m 379 00:19:43,380 --> 00:19:46,080 gating variable, and a m infinity 380 00:19:46,080 --> 00:19:47,910 that has a voltage dependence that 381 00:19:47,910 --> 00:19:52,447 looks very much like the voltage dependence of n infinity. 382 00:19:55,860 --> 00:20:00,640 So so far, the sodium and potassium conductances 383 00:20:00,640 --> 00:20:02,680 look very similar. 384 00:20:02,680 --> 00:20:09,910 They both have the same kind of activation gating variable, 385 00:20:09,910 --> 00:20:13,840 the same simple model for how to turn on and turn off, 386 00:20:13,840 --> 00:20:17,290 same differential equation, same gating 387 00:20:17,290 --> 00:20:20,500 variable that has this sigmoidal dependence on voltage. 388 00:20:23,028 --> 00:20:24,070 Any questions about that? 389 00:20:28,560 --> 00:20:30,270 So you remember the way we thought 390 00:20:30,270 --> 00:20:33,870 about the time dependence of these 391 00:20:33,870 --> 00:20:38,610 is we simply integrate this differential 392 00:20:38,610 --> 00:20:39,600 equation over time. 393 00:20:39,600 --> 00:20:41,760 It's a first order linear differential equation, 394 00:20:41,760 --> 00:20:44,490 and you can think about the n, the gating variable, 395 00:20:44,490 --> 00:20:48,060 as always relaxing exponentially toward whatever 396 00:20:48,060 --> 00:20:50,060 n infinity is at that moment. 397 00:20:50,060 --> 00:20:53,400 And n infinity is a function of voltage, 398 00:20:53,400 --> 00:20:55,980 and any time dependence it gets comes 399 00:20:55,980 --> 00:20:57,240 from changes in the voltage. 400 00:20:57,240 --> 00:21:01,330 So we're going to simplify things and just consider 401 00:21:01,330 --> 00:21:04,417 piecewise constant changes in the voltage. 402 00:21:04,417 --> 00:21:05,750 So let's do a simple experiment. 403 00:21:05,750 --> 00:21:09,210 We're going to hyperpolarize the voltage to minus 80. 404 00:21:09,210 --> 00:21:13,700 What is n infinity going to be, big or small? 405 00:21:21,350 --> 00:21:25,306 Remember what n infinity looks like is a function of voltage? 406 00:21:25,306 --> 00:21:26,170 AUDIENCE: Small. 407 00:21:26,170 --> 00:21:26,950 MICHALE FEE: Good. 408 00:21:26,950 --> 00:21:30,640 So at hyperpolarized voltages, n infinity is going to be small, 409 00:21:30,640 --> 00:21:33,070 and so is m infinity. 410 00:21:33,070 --> 00:21:38,330 Those ion channels are closed at hyperpolarize voltages. 411 00:21:38,330 --> 00:21:42,436 So the gating variables that represent 412 00:21:42,436 --> 00:21:45,970 what the probability is of being open, those gating variables 413 00:21:45,970 --> 00:21:51,310 are small when the voltage is negative, very negative. 414 00:21:51,310 --> 00:21:53,800 So then we're going to step the voltage up. 415 00:21:53,800 --> 00:21:57,400 And what is n infinity going to do? 416 00:21:57,400 --> 00:21:59,177 AUDIENCE: [INAUDIBLE] 417 00:21:59,177 --> 00:22:01,260 MICHALE FEE: Anybody want to just draw for me what 418 00:22:01,260 --> 00:22:02,550 it's going to do in the air? 419 00:22:02,550 --> 00:22:04,680 It starts out small. 420 00:22:04,680 --> 00:22:07,740 So is it going to ramp up slowly? 421 00:22:07,740 --> 00:22:09,682 Is it going to jump up? 422 00:22:09,682 --> 00:22:10,890 Is it going to wiggle around? 423 00:22:10,890 --> 00:22:12,500 What's it going to do? 424 00:22:12,500 --> 00:22:13,720 So why is it-- 425 00:22:13,720 --> 00:22:15,220 so I have several different answers. 426 00:22:15,220 --> 00:22:17,530 I have some people saying that it's going to ramp up. 427 00:22:17,530 --> 00:22:22,350 I'm asking about M infinity now, not n. 428 00:22:22,350 --> 00:22:26,110 So how many people say it's going to jump up suddenly? 429 00:22:26,110 --> 00:22:27,032 OK, good. 430 00:22:27,032 --> 00:22:28,240 That's what it's going to do. 431 00:22:28,240 --> 00:22:30,400 It's going to start out at a small value 432 00:22:30,400 --> 00:22:36,190 and jump up to a larger value when you depolarize the cell. 433 00:22:36,190 --> 00:22:38,286 And then what is n going to do? 434 00:22:38,286 --> 00:22:39,280 AUDIENCE: [INAUDIBLE] 435 00:22:39,280 --> 00:22:44,590 MICHALE FEE: Good. n is going to start at some initial condition 436 00:22:44,590 --> 00:22:48,820 and relax exponentially toward n infinity. 437 00:22:48,820 --> 00:22:51,990 And then when you turn the voltage back down, 438 00:22:51,990 --> 00:22:57,510 N infinity is going to go from this large value 439 00:22:57,510 --> 00:23:03,010 back down to a small value, and n 440 00:23:03,010 --> 00:23:06,100 is going to relax exponentially to that smaller 441 00:23:06,100 --> 00:23:07,630 value of n infinity. 442 00:23:10,220 --> 00:23:11,300 Any questions about that? 443 00:23:11,300 --> 00:23:13,500 We saw that last time. 444 00:23:13,500 --> 00:23:17,470 Now, what is the conductance going to do? 445 00:23:17,470 --> 00:23:20,620 Where does the conductance depend on n, anybody remember, 446 00:23:20,620 --> 00:23:21,460 for potassium? 447 00:23:26,920 --> 00:23:29,875 How many subunits are there in a potassium? 448 00:23:29,875 --> 00:23:30,500 AUDIENCE: Four. 449 00:23:30,500 --> 00:23:31,360 MICHALE FEE: Four. 450 00:23:31,360 --> 00:23:34,840 And so if the probability that each one is open is n, 451 00:23:34,840 --> 00:23:37,780 and there are four independent, what's 452 00:23:37,780 --> 00:23:40,510 the probability that they're all going to be open? 453 00:23:40,510 --> 00:23:41,410 AUDIENCE: [INAUDIBLE] 454 00:23:41,410 --> 00:23:42,310 MICHALE FEE: Good. 455 00:23:42,310 --> 00:23:48,490 And so the conductance is going to turn on as this relaxing 456 00:23:48,490 --> 00:23:49,900 exponential to the fourth. 457 00:23:49,900 --> 00:23:53,650 And it's going to have that kind of gradual ramping up. 458 00:23:59,980 --> 00:24:00,700 Good. 459 00:24:00,700 --> 00:24:04,540 It looks exactly the same for sodium. 460 00:24:04,540 --> 00:24:09,010 So if you start hyperpolarized, you depolarized the cell, 461 00:24:09,010 --> 00:24:10,990 that m infinity is going to start small, 462 00:24:10,990 --> 00:24:14,220 it's going to jump up to a high value. 463 00:24:14,220 --> 00:24:16,140 M is going to start small, and it's 464 00:24:16,140 --> 00:24:18,510 going to relax exponentially toward that higher 465 00:24:18,510 --> 00:24:21,080 value of m infinity. 466 00:24:21,080 --> 00:24:24,270 Now, anybody want to guess at what the sodium 467 00:24:24,270 --> 00:24:26,130 conductance will look like? 468 00:24:30,280 --> 00:24:33,150 It's going to be some function of m, right? 469 00:24:33,150 --> 00:24:35,140 It turns out that it m cubed. 470 00:24:40,920 --> 00:24:43,920 And the reason is that even though there 471 00:24:43,920 --> 00:24:48,360 are four things that have to all be open, 472 00:24:48,360 --> 00:24:50,430 they're not independent of each other. 473 00:24:50,430 --> 00:24:56,610 And so the exponent is not m to the fourth, it's m cubed. 474 00:24:56,610 --> 00:24:58,950 And Hodgkin and Huxley figured that out simply 475 00:24:58,950 --> 00:25:01,500 by plotting these relaxing exponentials 476 00:25:01,500 --> 00:25:04,050 to different powers. 477 00:25:04,050 --> 00:25:07,650 I imagine them saying, oh, the potassium is 4. 478 00:25:07,650 --> 00:25:10,230 Let's take m to the 4. 479 00:25:10,230 --> 00:25:11,370 But it didn't fit. 480 00:25:11,370 --> 00:25:14,720 So they tried some other, and they found that m cubed fits. 481 00:25:19,850 --> 00:25:21,830 So that's it. 482 00:25:21,830 --> 00:25:24,310 Now, the problem with this model is what? 483 00:25:24,310 --> 00:25:25,850 What is the problem with this model? 484 00:25:25,850 --> 00:25:28,070 Is that when you depolarize the cell, 485 00:25:28,070 --> 00:25:29,990 the potassium current turns on. 486 00:25:29,990 --> 00:25:35,090 The potassium conductance turns on, but then what happens? 487 00:25:35,090 --> 00:25:36,230 What is-- sorry. 488 00:25:36,230 --> 00:25:38,220 The sodium turns on. 489 00:25:38,220 --> 00:25:39,830 What happens? 490 00:25:39,830 --> 00:25:40,760 It doesn't do this. 491 00:25:40,760 --> 00:25:43,040 It doesn't turn on and stay on, right? 492 00:25:43,040 --> 00:25:45,110 The potassium, when you depolarize, 493 00:25:45,110 --> 00:25:47,840 turns on and stays on, just like that model. 494 00:25:47,840 --> 00:25:49,580 But the sodium does something else. 495 00:25:49,580 --> 00:25:50,596 What does it do? 496 00:25:50,596 --> 00:25:51,490 AUDIENCE: [INAUDIBLE] 497 00:25:51,490 --> 00:25:51,970 MICHALE FEE: What's that? 498 00:25:51,970 --> 00:25:53,262 AUDIENCE: It's a voltage clamp. 499 00:25:53,262 --> 00:25:55,210 MICHALE FEE: This is voltage clamp, 500 00:25:55,210 --> 00:25:59,680 so it's we're controlling the voltage. 501 00:25:59,680 --> 00:26:03,630 m is already a maximum here, so it can't shoot up anymore, 502 00:26:03,630 --> 00:26:05,670 right? 503 00:26:05,670 --> 00:26:09,276 Anybody remember what sodium does that's really weird? 504 00:26:09,276 --> 00:26:10,270 AUDIENCE: Deactivation. 505 00:26:10,270 --> 00:26:12,000 MICHALE FEE: It inactivates. 506 00:26:12,000 --> 00:26:15,500 So the current turns on, a conductance turns on, 507 00:26:15,500 --> 00:26:16,530 but it doesn't stay on. 508 00:26:16,530 --> 00:26:22,830 It turns off, and that's what we're going to talk about next. 509 00:26:22,830 --> 00:26:27,960 And once we have that, we've got the whole Hodgkin-Huxley model. 510 00:26:27,960 --> 00:26:31,190 And that'll set us up for this really interesting sodium 511 00:26:31,190 --> 00:26:35,360 channel defect that we're going to talk about. 512 00:26:35,360 --> 00:26:40,900 So that process there of shutting off 513 00:26:40,900 --> 00:26:42,370 is called inactivation. 514 00:26:45,250 --> 00:26:50,320 This process of n turning on is called activation. 515 00:26:50,320 --> 00:26:54,960 n turning off is called deactivation. 516 00:26:54,960 --> 00:26:57,600 m turning on is called activation. 517 00:26:57,600 --> 00:27:00,990 m turning off is called deactivation. 518 00:27:00,990 --> 00:27:03,840 But this other thing has a different name. 519 00:27:03,840 --> 00:27:05,280 It's called inactivation. 520 00:27:07,870 --> 00:27:11,630 It's kind of a little tricky terminology. 521 00:27:15,860 --> 00:27:19,880 So the potassium-- the probability of the sodium 522 00:27:19,880 --> 00:27:21,650 current being-- 523 00:27:21,650 --> 00:27:25,290 the sodium channel being open actually 524 00:27:25,290 --> 00:27:30,500 goes like m cubed times some other gating variable that 525 00:27:30,500 --> 00:27:34,430 describes how this turns off. 526 00:27:34,430 --> 00:27:37,040 And so there's another gating variable, called h. 527 00:27:37,040 --> 00:27:42,070 It's called the inactivation gating variable for sodium. 528 00:27:42,070 --> 00:27:46,240 And so now we're going to figure out how to think about h 529 00:27:46,240 --> 00:27:49,190 and how to describe it mathematically. 530 00:27:49,190 --> 00:27:50,940 You probably wouldn't be surprised to hear 531 00:27:50,940 --> 00:27:53,220 that it's just another first order linear differential 532 00:27:53,220 --> 00:27:54,136 equation-- 533 00:27:57,710 --> 00:28:02,260 activation gating variable, m, inactivation gating variable, 534 00:28:02,260 --> 00:28:04,550 h. 535 00:28:04,550 --> 00:28:06,470 So how do we think about inactivation? 536 00:28:06,470 --> 00:28:12,590 Inactivation is literally just a little loop of goo or snot 537 00:28:12,590 --> 00:28:16,670 on the inside of the sodium channel, and it's charged. 538 00:28:16,670 --> 00:28:18,440 And when the sodium channel opens, 539 00:28:18,440 --> 00:28:22,280 it just falls in and plugs up that the pore. 540 00:28:22,280 --> 00:28:24,610 That's it. 541 00:28:24,610 --> 00:28:28,532 So when the membrane potential is very negative, 542 00:28:28,532 --> 00:28:29,990 the inside of the cell is negative, 543 00:28:29,990 --> 00:28:32,590 there's an electric field pointing this way, 544 00:28:32,590 --> 00:28:36,290 and the inactivation particle is slightly positively charged. 545 00:28:36,290 --> 00:28:40,090 And that pushes it, keeps it out of the way. 546 00:28:47,006 --> 00:28:49,360 It turns out that that's a real thing. 547 00:28:49,360 --> 00:28:52,690 It turns out it's just a loop of amino acids on the inside 548 00:28:52,690 --> 00:28:53,752 of the ion channel. 549 00:28:53,752 --> 00:28:55,210 Hodgkin and Huxley, of course, they 550 00:28:55,210 --> 00:28:58,750 didn't have the structure of the sodium channel, 551 00:28:58,750 --> 00:29:02,463 but they actually predicted the existence of this thing 552 00:29:02,463 --> 00:29:04,255 that they called the inactivation particle. 553 00:29:09,490 --> 00:29:12,660 When you depolarize the cell, when 554 00:29:12,660 --> 00:29:16,500 the membrane potential inside the cell goes more positive, 555 00:29:16,500 --> 00:29:18,780 that positive charge is no longer 556 00:29:18,780 --> 00:29:21,330 actively kept out of the pore. 557 00:29:21,330 --> 00:29:25,240 And so it falls in and blocks the pore. 558 00:29:25,240 --> 00:29:27,080 And that prevents ions from flowing 559 00:29:27,080 --> 00:29:28,080 through the ion channel. 560 00:29:33,620 --> 00:29:35,230 So how would you model this? 561 00:29:35,230 --> 00:29:39,640 There's an open state and a closed state 562 00:29:39,640 --> 00:29:42,380 with energy levels. 563 00:29:42,380 --> 00:29:44,075 How would you want to do that? 564 00:29:44,075 --> 00:29:45,290 AUDIENCE: Use the Boltzmann distribution. 565 00:29:45,290 --> 00:29:47,748 MICHALE FEE: Yeah, you could use the Boltzmann distribution 566 00:29:47,748 --> 00:29:49,520 to compute the voltage dependence. 567 00:29:49,520 --> 00:29:53,060 I haven't done that, but I'm sure it would work pretty well. 568 00:29:53,060 --> 00:29:55,263 How would you model the time dependence? 569 00:30:01,680 --> 00:30:02,840 So let me ask you this. 570 00:30:02,840 --> 00:30:05,090 If there is a gating variable-- let's start with this. 571 00:30:05,090 --> 00:30:06,680 If there is a gating variable, h, 572 00:30:06,680 --> 00:30:09,920 that we're going to use to describe this thing getting 573 00:30:09,920 --> 00:30:13,910 open and closed, what is the voltage dependence 574 00:30:13,910 --> 00:30:17,020 of h infinity going to look like? 575 00:30:17,020 --> 00:30:21,090 When the voltage is very negative, what is h doing? 576 00:30:21,090 --> 00:30:22,320 You think it's big or small? 577 00:30:25,260 --> 00:30:27,950 Here's the equation-- m cubed h. 578 00:30:27,950 --> 00:30:34,610 So when the-- yeah, right. h has to start out high and go small 579 00:30:34,610 --> 00:30:39,080 in order to explain this thing turning off. 580 00:30:39,080 --> 00:30:40,930 Does that make sense? 581 00:30:40,930 --> 00:30:43,110 So what we're going to do is we're going to have-- 582 00:30:43,110 --> 00:30:45,900 we're going to model this again with two states, an open state 583 00:30:45,900 --> 00:30:48,060 and a closed state. h is the probability 584 00:30:48,060 --> 00:30:53,072 that this inactivation particle is in the open state. 585 00:30:53,072 --> 00:30:56,690 It turns out that there's only one of these particles, 586 00:30:56,690 --> 00:31:00,160 and so that explains why it's just times h, 587 00:31:00,160 --> 00:31:01,840 not times h to some power. 588 00:31:04,860 --> 00:31:07,290 And we have a differential equation 589 00:31:07,290 --> 00:31:10,500 that describes how h changes as a function of time 590 00:31:10,500 --> 00:31:12,630 in a way that depends on h infinity. 591 00:31:12,630 --> 00:31:17,010 And Aditu, why don't you draw what h infinity probably looks 592 00:31:17,010 --> 00:31:19,200 like as a function of voltage. 593 00:31:19,200 --> 00:31:20,100 AUDIENCE: High. 594 00:31:20,100 --> 00:31:20,850 MICHALE FEE: Yeah. 595 00:31:20,850 --> 00:31:24,240 It just starts high and goes down. 596 00:31:24,240 --> 00:31:25,890 How do we actually measure that? 597 00:31:25,890 --> 00:31:28,480 Let me show you an experiment how you'd measure that. 598 00:31:28,480 --> 00:31:30,600 So first, let me just show you this. 599 00:31:30,600 --> 00:31:34,860 So when you depolarize the cell, h starts out high, 600 00:31:34,860 --> 00:31:37,590 because h infinity is high. 601 00:31:37,590 --> 00:31:42,540 And then when you depolarize the cell, h infinity gets small, 602 00:31:42,540 --> 00:31:47,010 and h just relaxes exponentially toward the new smaller h 603 00:31:47,010 --> 00:31:47,790 infinity. 604 00:31:47,790 --> 00:31:52,860 And what's really cool is that the tail, this inactivation, 605 00:31:52,860 --> 00:31:55,170 the way that conductance or the current turns off, 606 00:31:55,170 --> 00:31:57,255 is just a single exponential. 607 00:31:57,255 --> 00:32:00,495 It just falls like E to the minus some time constant. 608 00:32:04,190 --> 00:32:07,880 It's just given by this first order linear differential 609 00:32:07,880 --> 00:32:08,380 equation. 610 00:32:11,160 --> 00:32:12,890 Good. 611 00:32:12,890 --> 00:32:17,480 This h getting smaller is called inactivation. 612 00:32:17,480 --> 00:32:21,425 Anybody want to take a guess at what this is called? 613 00:32:21,425 --> 00:32:22,700 AUDIENCE: Deinactivation. 614 00:32:22,700 --> 00:32:25,640 MICHALE FEE: Deinactivation, good. 615 00:32:25,640 --> 00:32:29,030 So there's activation and deactivation. 616 00:32:29,030 --> 00:32:32,150 There's inactivation and deinactivation. 617 00:32:32,150 --> 00:32:35,360 Those are different things. 618 00:32:35,360 --> 00:32:38,390 Just remember activation, which is easy, right? 619 00:32:38,390 --> 00:32:39,600 It's just things turning on. 620 00:32:39,600 --> 00:32:41,180 And then there's the same process 621 00:32:41,180 --> 00:32:43,440 that undoes the turning on. 622 00:32:43,440 --> 00:32:45,530 That's deactivation. 623 00:32:45,530 --> 00:32:48,770 And there's inactivation, which is a separate particle. 624 00:32:48,770 --> 00:32:56,390 And it has a process of blocking and unblocking. 625 00:32:56,390 --> 00:33:00,658 So it's inactivation, deinactivation. 626 00:33:00,658 --> 00:33:01,700 Any questions about that? 627 00:33:01,700 --> 00:33:02,280 Yes? 628 00:33:02,280 --> 00:33:03,990 AUDIENCE: If there is any activation, 629 00:33:03,990 --> 00:33:06,160 does that mean it's already charged up? 630 00:33:06,160 --> 00:33:09,130 So what does deactivation mean? 631 00:33:09,130 --> 00:33:09,880 MICHALE FEE: Yeah. 632 00:33:09,880 --> 00:33:12,020 So when-- here. 633 00:33:12,020 --> 00:33:14,140 Let's just go back to this picture here. 634 00:33:14,140 --> 00:33:17,830 When the cell is hyperpolarized, the thing 635 00:33:17,830 --> 00:33:21,850 is hanging out outside not getting in the way. 636 00:33:21,850 --> 00:33:24,940 When you depolarize the cell, that electric field 637 00:33:24,940 --> 00:33:27,970 is not pushing it out anymore, and it falls in. 638 00:33:27,970 --> 00:33:30,790 But when you hyperpolarize the cell again, 639 00:33:30,790 --> 00:33:34,000 that electric field turns back on. 640 00:33:34,000 --> 00:33:37,190 And what is it going to do? 641 00:33:37,190 --> 00:33:41,720 It pushes the particle back out to the other state, 642 00:33:41,720 --> 00:33:42,710 to the open state. 643 00:33:47,590 --> 00:33:48,838 Any other questions? 644 00:33:51,470 --> 00:33:53,330 Pretty simple, right? 645 00:33:53,330 --> 00:33:55,520 Kind of very machine-like. 646 00:34:01,200 --> 00:34:03,850 And then what we're going to talk about soon 647 00:34:03,850 --> 00:34:09,070 is how this thing sometimes doesn't work, this thing. 648 00:34:09,070 --> 00:34:15,460 There are genetic mutations that turn out 649 00:34:15,460 --> 00:34:20,260 to be fairly common actually, where this doesn't reliably 650 00:34:20,260 --> 00:34:21,190 block the pore. 651 00:34:24,940 --> 00:34:28,230 And we're going to see what happens. 652 00:34:28,230 --> 00:34:30,750 First order linear differential equation. 653 00:34:30,750 --> 00:34:35,250 Exponential relaxation toward new h infinity. 654 00:34:35,250 --> 00:34:37,770 We can actually measure this h infinity 655 00:34:37,770 --> 00:34:41,429 as a function of voltage by doing the following experiment. 656 00:34:41,429 --> 00:34:44,909 What we do is we hold the cell hyperpolarize. 657 00:34:44,909 --> 00:34:49,260 We can then step the cell up to different membrane potentials-- 658 00:34:49,260 --> 00:34:51,730 very low or very high. 659 00:34:51,730 --> 00:34:54,690 And then what we do is we jump the membrane potential 660 00:34:54,690 --> 00:34:59,790 up to turn on the activation gating variable. 661 00:34:59,790 --> 00:35:01,430 And now we can see-- 662 00:35:01,430 --> 00:35:03,410 what you see is, that depending on where 663 00:35:03,410 --> 00:35:06,960 you held the voltage before you did this big voltage step, 664 00:35:06,960 --> 00:35:09,440 you get sodium currents of different size. 665 00:35:09,440 --> 00:35:12,470 And you can guess that if you hold the voltage very negative 666 00:35:12,470 --> 00:35:14,930 and then turn it on, that activation gating 667 00:35:14,930 --> 00:35:17,930 variable for all those ion channels is [AUDIO OUT].. 668 00:35:17,930 --> 00:35:19,790 And when you turn on the sodium-- 669 00:35:19,790 --> 00:35:21,350 turn on the gating variable, you're 670 00:35:21,350 --> 00:35:24,470 going to get a big current, right? 671 00:35:24,470 --> 00:35:29,000 If you hold the cell for a while here at a higher voltage, 672 00:35:29,000 --> 00:35:31,520 most of those sodium channels are 673 00:35:31,520 --> 00:35:35,150 going to have that inactivation gate already closed. 674 00:35:35,150 --> 00:35:39,830 And so now when you step the voltage up, turn on m, 675 00:35:39,830 --> 00:35:44,360 you're going to get a much smaller current. 676 00:35:44,360 --> 00:35:46,330 And so if you just plot the current size 677 00:35:46,330 --> 00:35:49,420 as a function of this holding potential, 678 00:35:49,420 --> 00:35:53,320 you can see that h is big for low voltages 679 00:35:53,320 --> 00:35:55,720 and goes to 0 for higher voltages. 680 00:35:55,720 --> 00:36:00,420 And what this means is that when a cell spikes, 681 00:36:00,420 --> 00:36:06,360 that voltage goes up, and h starts falling, and the sodium 682 00:36:06,360 --> 00:36:07,105 channels-- 683 00:36:07,105 --> 00:36:08,730 many of the sodium channels in the cell 684 00:36:08,730 --> 00:36:11,040 becomes inactivated-- become inactivated. 685 00:36:11,040 --> 00:36:11,720 Yes? 686 00:36:11,720 --> 00:36:14,440 AUDIENCE: The membrane potential on the x-axis, 687 00:36:14,440 --> 00:36:18,105 is that the difference in the-- is that [AUDIO OUT] or is that 688 00:36:18,105 --> 00:36:18,990 the [INAUDIBLE]? 689 00:36:18,990 --> 00:36:23,690 MICHALE FEE: That's the absolute voltage during this holding. 690 00:36:23,690 --> 00:36:24,560 That's right. 691 00:36:24,560 --> 00:36:28,580 You can actually see at rest most cells actually 692 00:36:28,580 --> 00:36:31,250 have a substantial fraction of the sodium channels 693 00:36:31,250 --> 00:36:32,947 already inactivated. 694 00:36:44,160 --> 00:36:45,930 So here's the plan. 695 00:36:45,930 --> 00:36:50,250 We now have a full description of the potassium 696 00:36:50,250 --> 00:36:56,340 and the sodium conductances as a function of voltage and time. 697 00:36:56,340 --> 00:36:59,310 So we're to put it all together and make 698 00:36:59,310 --> 00:37:04,460 a full quantitative description of the Hodgkin-Huxley model. 699 00:37:04,460 --> 00:37:08,690 Our probability of the sodium current, sodium channel, 700 00:37:08,690 --> 00:37:11,210 being open is m cubed h. 701 00:37:11,210 --> 00:37:14,630 I just want to mention that this m cubed 702 00:37:14,630 --> 00:37:17,510 h assumes one thing about the gating variable 703 00:37:17,510 --> 00:37:20,350 and the inactivation variable. 704 00:37:20,350 --> 00:37:25,700 The mechanism for activation and the mechanism for inactivation 705 00:37:25,700 --> 00:37:27,010 assumes what about them? 706 00:37:27,010 --> 00:37:28,260 AUDIENCE: They're independent. 707 00:37:28,260 --> 00:37:29,635 MICHALE FEE: They're independent. 708 00:37:29,635 --> 00:37:32,540 And it turns out that that's not quite true. 709 00:37:32,540 --> 00:37:36,020 It's one of the very few things that Hodgkin and Huxley 710 00:37:36,020 --> 00:37:38,540 didn't get spot-on. 711 00:37:38,540 --> 00:37:43,597 So it's not exactly independent, but it's really not bad either. 712 00:37:43,597 --> 00:37:45,680 So it's a pretty-- it's still a pretty good model. 713 00:37:49,040 --> 00:37:50,960 We can write down the sodium conductance 714 00:37:50,960 --> 00:37:53,240 as just the conductance of the sodium channel 715 00:37:53,240 --> 00:37:55,910 when it's all the way open times m cubed h. 716 00:37:55,910 --> 00:37:56,780 Yes? 717 00:37:56,780 --> 00:38:00,320 AUDIENCE: So do we know what the inactivation particle is? 718 00:38:00,320 --> 00:38:01,070 MICHALE FEE: Yeah. 719 00:38:01,070 --> 00:38:02,362 We're going to see in a second. 720 00:38:02,362 --> 00:38:04,520 I'll show you exactly what it looks like 721 00:38:04,520 --> 00:38:08,660 and where these mutations are that have 722 00:38:08,660 --> 00:38:11,700 this effect on inactivation. 723 00:38:11,700 --> 00:38:18,080 So we can write down the conductance, 724 00:38:18,080 --> 00:38:19,497 and we can write down the current. 725 00:38:19,497 --> 00:38:22,600 The current is just the open conductance 726 00:38:22,600 --> 00:38:28,010 times m cubed h times the driving potential. 727 00:38:28,010 --> 00:38:30,700 And that's our sodium current. 728 00:38:30,700 --> 00:38:32,114 Yes? 729 00:38:32,114 --> 00:38:34,350 AUDIENCE: For the [INAUDIBLE],, I'm 730 00:38:34,350 --> 00:38:40,438 not showing there is [INAUDIBLE] like a number, 731 00:38:40,438 --> 00:38:43,048 like sodium channel or something. 732 00:38:43,048 --> 00:38:43,977 It doesn't have it. 733 00:38:43,977 --> 00:38:45,310 MICHALE FEE: Yeah, that's right. 734 00:38:45,310 --> 00:38:52,960 It's one, one single protein, but it has these transmembrane 735 00:38:52,960 --> 00:38:57,210 alpha-helices that act-- 736 00:38:57,210 --> 00:38:59,680 are multiple voltage sensors. 737 00:38:59,680 --> 00:39:03,580 And they act somewhat independently, but still 738 00:39:03,580 --> 00:39:05,200 a little bit cooperatively, and that's 739 00:39:05,200 --> 00:39:07,990 where this m cubed comes from. 740 00:39:07,990 --> 00:39:08,710 But you're right. 741 00:39:08,710 --> 00:39:12,460 The potassium channel actually has four separate subunits 742 00:39:12,460 --> 00:39:14,890 that form a tetramer. 743 00:39:14,890 --> 00:39:19,608 The sodium channel [AUDIO OUT] that it's all one big protein. 744 00:39:19,608 --> 00:39:20,150 That's right. 745 00:39:20,150 --> 00:39:22,810 AUDIENCE: [INAUDIBLE] 746 00:39:22,810 --> 00:39:23,560 MICHALE FEE: Yeah. 747 00:39:23,560 --> 00:39:25,510 You should really think of this-- 748 00:39:25,510 --> 00:39:27,970 I mean the n and the m were both-- 749 00:39:27,970 --> 00:39:30,610 it was empirically discovered that one 750 00:39:30,610 --> 00:39:34,180 goes as n to the fourth, and the other one goes as m cubed. 751 00:39:34,180 --> 00:39:35,680 And it turns out for potassium it 752 00:39:35,680 --> 00:39:38,550 has a really beautiful relation to the structure. 753 00:39:38,550 --> 00:39:40,150 For sodium, it's a little bit messier. 754 00:39:40,150 --> 00:39:43,510 And I'm sure there are people who actually understand more 755 00:39:43,510 --> 00:39:47,170 about why it's exactly m cubed, but I'm not 756 00:39:47,170 --> 00:39:48,036 one of those people. 757 00:39:48,036 --> 00:39:53,560 So I'm going to refer you to the literature. 758 00:39:53,560 --> 00:39:56,280 And I'm happy-- maybe I can find a good reference for that. 759 00:40:00,050 --> 00:40:03,230 So now that we have the sodium conductance and the sodium 760 00:40:03,230 --> 00:40:05,160 current, let's put this all together. 761 00:40:05,160 --> 00:40:07,370 So here's how we're going to now-- 762 00:40:07,370 --> 00:40:09,800 here's the algorithm for generating an action potential. 763 00:40:09,800 --> 00:40:11,750 And we introduced this last time, 764 00:40:11,750 --> 00:40:14,810 but let's just flesh it out for the full story. 765 00:40:14,810 --> 00:40:20,105 So given an initial voltage, compute n infinity, tau n, 766 00:40:20,105 --> 00:40:24,350 m infinity, tau m, and h infinity and tau h, 767 00:40:24,350 --> 00:40:25,820 as a function of that voltage. 768 00:40:25,820 --> 00:40:28,880 Those are just those algebraic expressions 769 00:40:28,880 --> 00:40:30,950 that give you the alpha n and beta 770 00:40:30,950 --> 00:40:35,090 n for each of those things-- one for potassium, 771 00:40:35,090 --> 00:40:39,400 one for sodium, the m, and one for the h for sodium. 772 00:40:39,400 --> 00:40:41,600 So we're going to calculate all of those. 773 00:40:41,600 --> 00:40:44,510 Steady state gating variables as a function of voltage, 774 00:40:44,510 --> 00:40:47,800 we're going to start from our initial condition of n, m, 775 00:40:47,800 --> 00:40:50,840 and h, and integrate that differential equation one time 776 00:40:50,840 --> 00:40:51,860 step using-- 777 00:40:55,550 --> 00:40:57,560 it's going to relax exponentially 778 00:40:57,560 --> 00:41:01,110 toward n infinity. 779 00:41:01,110 --> 00:41:04,590 We're going to plug that n, m, and h into our equations 780 00:41:04,590 --> 00:41:06,900 for the potassium current, sodium 781 00:41:06,900 --> 00:41:10,300 current, and leak, which doesn't have those gating variables. 782 00:41:10,300 --> 00:41:13,620 So the potassium current is Gn to the 4 times the driving 783 00:41:13,620 --> 00:41:14,430 potential. 784 00:41:14,430 --> 00:41:19,253 Sodium current is Gm cubed h [AUDIO OUT] driving potential. 785 00:41:19,253 --> 00:41:20,920 We're going to add all of those currents 786 00:41:20,920 --> 00:41:24,830 together to give the total membrane current. 787 00:41:24,830 --> 00:41:26,990 That membrane current is going to give us 788 00:41:26,990 --> 00:41:31,820 a V infinity for our cell. 789 00:41:31,820 --> 00:41:35,780 Remember, the V infinity is just the current times 790 00:41:35,780 --> 00:41:37,130 the effective resistance. 791 00:41:37,130 --> 00:41:39,110 So we can use that to also calculate 792 00:41:39,110 --> 00:41:43,440 the membrane time constant. 793 00:41:43,440 --> 00:41:47,890 And then we integrate the voltage one time step. 794 00:41:47,890 --> 00:41:55,480 Go back and recompute those n, m, and h infinities. 795 00:41:55,480 --> 00:41:57,500 And then we just keep cycling through this. 796 00:41:57,500 --> 00:42:01,310 When you do that, and you plot the voltage, 797 00:42:01,310 --> 00:42:03,840 you get an action potential. 798 00:42:03,840 --> 00:42:05,690 Now, you can do that in a hundredth 799 00:42:05,690 --> 00:42:07,155 of a second in MATLAB. 800 00:42:07,155 --> 00:42:09,530 Hodgkin and Huxley we're doing this on their slide rules, 801 00:42:09,530 --> 00:42:12,265 and they got 2/3 of the way through an action potential 802 00:42:12,265 --> 00:42:14,270 and said, let's just publish. 803 00:42:14,270 --> 00:42:16,394 [LAUGHTER] 804 00:42:22,660 --> 00:42:24,220 So here's what that looks like. 805 00:42:24,220 --> 00:42:29,110 Here's V as a function of time for when you 806 00:42:29,110 --> 00:42:32,020 implement that loop in MATLAB. 807 00:42:32,020 --> 00:42:33,400 So you can see what you did. 808 00:42:33,400 --> 00:42:35,650 So this is the injected current through the electrode, 809 00:42:35,650 --> 00:42:37,830 and can see it starts to depolarize 810 00:42:37,830 --> 00:42:40,240 the cell a little bit. 811 00:42:40,240 --> 00:42:43,410 And at some point, what happens is-- 812 00:42:43,410 --> 00:42:46,960 this is just a copy over here so you can line things up-- 813 00:42:46,960 --> 00:42:50,380 when you inject current, the cell starts to depolarize. 814 00:42:50,380 --> 00:42:53,150 And you can see that m starts to grow. 815 00:42:53,150 --> 00:42:56,270 The sodium current is starting to turn on. 816 00:42:56,270 --> 00:43:00,680 And at some point, m gets big enough 817 00:43:00,680 --> 00:43:04,520 that it's turning on a substantial amount of sodium 818 00:43:04,520 --> 00:43:06,963 current into the cell. 819 00:43:06,963 --> 00:43:07,880 And what does that do? 820 00:43:07,880 --> 00:43:11,690 It depolarizes to cell more, which causes m to grow faster, 821 00:43:11,690 --> 00:43:15,350 which causes more current, which depolarizes the cell faster. 822 00:43:15,350 --> 00:43:18,050 And it just runs away-- bam-- 823 00:43:18,050 --> 00:43:21,080 until you reach essentially the equilibrium 824 00:43:21,080 --> 00:43:24,272 potential of sodium. 825 00:43:24,272 --> 00:43:25,980 And then what does the sodium current do? 826 00:43:25,980 --> 00:43:31,160 The sodium current actually stops 827 00:43:31,160 --> 00:43:33,460 even though the channel's open. 828 00:43:33,460 --> 00:43:37,390 Then what happens is, during that whole time, n has, 829 00:43:37,390 --> 00:43:40,570 in this hyperpolarized voltage-- 830 00:43:40,570 --> 00:43:48,010 the potassium channel is starting to open and grows, 831 00:43:48,010 --> 00:43:51,280 potassium current conductance turns on, 832 00:43:51,280 --> 00:43:54,910 and that starts hyperpolerizing the cell. 833 00:43:54,910 --> 00:44:01,410 During that whole time, the inactivation gate-- 834 00:44:01,410 --> 00:44:05,270 this cell is very depolarized, very positive. 835 00:44:05,270 --> 00:44:12,650 That little bit of goo falls in, h drops. 836 00:44:12,650 --> 00:44:16,880 That shuts off the sodium conductance. 837 00:44:16,880 --> 00:44:22,860 Potassium conductance finishes bringing the cell back. 838 00:44:22,860 --> 00:44:23,850 Beautiful, right? 839 00:44:30,950 --> 00:44:31,450 Yes? 840 00:44:31,450 --> 00:44:33,840 AUDIENCE: Is h just the voltage-dependent 841 00:44:33,840 --> 00:44:36,880 or it's also time-dependent? 842 00:44:36,880 --> 00:44:41,320 MICHALE FEE: Time-dependent in exactly the same way 843 00:44:41,320 --> 00:44:45,460 that n and m are time-dependent. 844 00:44:45,460 --> 00:44:50,560 There is a-- h infinity changes as a sum-- 845 00:44:50,560 --> 00:44:52,120 as a function of voltage. 846 00:44:52,120 --> 00:44:57,520 And then h relaxes exponentially toward h infinity. 847 00:45:04,720 --> 00:45:05,920 Any questions about that? 848 00:45:05,920 --> 00:45:08,260 So for the problem set, you'll have code for this, 849 00:45:08,260 --> 00:45:10,960 and you can play around with this and try different things. 850 00:45:10,960 --> 00:45:13,600 And then there's a particular problem 851 00:45:13,600 --> 00:45:16,345 that Daniel and I cooked up for you for this. 852 00:45:16,345 --> 00:45:18,220 I'll basically show you what that looks like. 853 00:45:18,220 --> 00:45:21,610 Here's the crux of it. 854 00:45:21,610 --> 00:45:24,340 If you inject a little bit of current 855 00:45:24,340 --> 00:45:26,830 into the Hodgkin-Huxley neuron, you get a spike. 856 00:45:26,830 --> 00:45:28,880 And then if you wait a few milliseconds 857 00:45:28,880 --> 00:45:33,280 and inject another current pulse, what happens? 858 00:45:37,090 --> 00:45:38,050 You don't get a spike. 859 00:45:40,630 --> 00:45:44,645 Can anybody guess why that is? 860 00:45:44,645 --> 00:45:47,120 AUDIENCE: h is still inactivated. 861 00:45:47,120 --> 00:45:47,870 MICHALE FEE: Yeah. 862 00:45:47,870 --> 00:45:50,780 That thing is still stuck in there 863 00:45:50,780 --> 00:45:55,830 and hasn't had time to fall out yet. 864 00:45:55,830 --> 00:45:59,300 And if you plot h, you can see that it hasn't recovered back 865 00:45:59,300 --> 00:46:02,910 to the state it was at the beginning. 866 00:46:02,910 --> 00:46:06,930 So that's called a "refractory period." 867 00:46:06,930 --> 00:46:12,810 So cells don't like to spike two times in a row to close. 868 00:46:12,810 --> 00:46:13,565 Yes? 869 00:46:13,565 --> 00:46:16,475 AUDIENCE: So what things like [INAUDIBLE] h at which 870 00:46:16,475 --> 00:46:17,980 it's a spike? 871 00:46:17,980 --> 00:46:18,730 MICHALE FEE: Yeah. 872 00:46:18,730 --> 00:46:22,430 So you want to just like-- 873 00:46:22,430 --> 00:46:24,080 what would be the intuitive answer? 874 00:46:27,690 --> 00:46:31,670 So there's not a hard cutoff, right? 875 00:46:31,670 --> 00:46:34,390 If h is right here, it will be much harder. 876 00:46:34,390 --> 00:46:37,600 You'd have to inject a lot more current to make it spike. 877 00:46:37,600 --> 00:46:40,390 If h is recovered to here, then it 878 00:46:40,390 --> 00:46:42,970 would take a little bit less current to make it spike. 879 00:46:42,970 --> 00:46:46,427 So basically, there's a gradual decrease 880 00:46:46,427 --> 00:46:48,010 in the amount of current it would take 881 00:46:48,010 --> 00:46:51,040 to make the neuron spike again. 882 00:46:51,040 --> 00:46:52,610 So there's no one answer. 883 00:46:57,800 --> 00:47:02,400 So let's take a look at what happens 884 00:47:02,400 --> 00:47:03,980 when sodium channels go bad. 885 00:47:07,606 --> 00:47:08,273 [VIDEO PLAYBACK] 886 00:47:08,273 --> 00:47:10,190 [MUSIC PLAYING] 887 00:47:10,190 --> 00:47:12,490 - Most of the animals on this petting farm, 888 00:47:12,490 --> 00:47:18,170 on Maui, Hawaii, are sweet, but nothing too unusual. 889 00:47:18,170 --> 00:47:22,370 And then there are the goats-- 890 00:47:22,370 --> 00:47:25,280 Myotonic goats, to be specific-- 891 00:47:25,280 --> 00:47:28,450 more commonly known as stiff-legged goats, 892 00:47:28,450 --> 00:47:34,700 wooden-leg goats, nervous goats, fainting goats. 893 00:47:34,700 --> 00:47:38,340 Fainting goats are indigenous to North America. 894 00:47:38,340 --> 00:47:40,500 But that name is a bit of a misnomer, 895 00:47:40,500 --> 00:47:42,360 because they never lose consciousness 896 00:47:42,360 --> 00:47:44,500 when they keel over. 897 00:47:44,500 --> 00:47:47,970 If they're startled, a genetic condition causes their muscles 898 00:47:47,970 --> 00:47:49,290 to lock up. 899 00:47:49,290 --> 00:47:52,020 But it only lasts a few moments, and then they're 900 00:47:52,020 --> 00:47:53,350 back on their feet. 901 00:47:53,350 --> 00:47:57,060 Now, until the next time they're spooked. 902 00:47:57,060 --> 00:48:00,170 [END PLAYBACK] 903 00:48:00,170 --> 00:48:03,160 MICHALE FEE: So these fainting goats 904 00:48:03,160 --> 00:48:09,640 have a particular mutation in their sodium channel. 905 00:48:09,640 --> 00:48:12,400 Now, it turns out that the sodium channels that 906 00:48:12,400 --> 00:48:14,860 are in your brain that control action potentials 907 00:48:14,860 --> 00:48:18,460 are a different gene than the sodium channels 908 00:48:18,460 --> 00:48:21,630 that are in your muscles that produce muscle contractions. 909 00:48:21,630 --> 00:48:27,040 So you can have a mutation in the skeletal isoform 910 00:48:27,040 --> 00:48:32,110 of the sodium channel that produces these muscular effects 911 00:48:32,110 --> 00:48:35,530 without having any effect on brain function. 912 00:48:35,530 --> 00:48:38,430 But that same mutation in the brain, 913 00:48:38,430 --> 00:48:43,450 isoform of the sodium channel, is lethal. 914 00:48:43,450 --> 00:48:47,110 So this is actually a condition that exists in humans. 915 00:48:47,110 --> 00:48:50,260 It's called-- there are actually a whole set of these, 916 00:48:50,260 --> 00:48:53,830 what are called "sodium channel myotonias." 917 00:48:53,830 --> 00:48:58,420 One of them is called hyperkalemic periodic 918 00:48:58,420 --> 00:49:00,410 paralysis. 919 00:49:00,410 --> 00:49:03,900 And this just shows a different-- 920 00:49:03,900 --> 00:49:07,890 this is a different phenotype of one of these sodium channel 921 00:49:07,890 --> 00:49:09,100 defects. 922 00:49:09,100 --> 00:49:14,020 So the goats became very stiff and fell over. 923 00:49:14,020 --> 00:49:17,076 It turns out there's a different phenotype that looks like this. 924 00:49:23,750 --> 00:49:26,950 So basically, it causes extreme weakness. 925 00:49:26,950 --> 00:49:29,860 The muscles are completely paralyzed. 926 00:49:29,860 --> 00:49:33,370 They can't contract anymore, and it 927 00:49:33,370 --> 00:49:38,020 seems like that would be a completely different effect-- 928 00:49:38,020 --> 00:49:40,540 what would cause muscles to just go 929 00:49:40,540 --> 00:49:45,505 rigid and a very similar thing would cause paralysis-- 930 00:49:45,505 --> 00:49:48,080 and it turns out that actually those two things 931 00:49:48,080 --> 00:49:49,790 have very similar cause. 932 00:49:49,790 --> 00:49:54,770 That hyperkalemic-- kalemic refers to potassium. 933 00:49:54,770 --> 00:49:58,460 And so this condition is very sensitive to potassium levels. 934 00:49:58,460 --> 00:50:00,950 At high potassium levels, it's much worse 935 00:50:00,950 --> 00:50:04,040 than at low potassium levels. 936 00:50:04,040 --> 00:50:07,840 So there can be an attack of weakness or paralysis, 937 00:50:07,840 --> 00:50:11,740 and then just a few minutes later somebody's all better, 938 00:50:11,740 --> 00:50:15,880 and that paralysis goes away. 939 00:50:15,880 --> 00:50:20,010 So to understand what's going on in this condition, 940 00:50:20,010 --> 00:50:24,710 we need to take a look at how muscle fibers actually work. 941 00:50:24,710 --> 00:50:28,340 So let's take a little detour in that. 942 00:50:28,340 --> 00:50:32,060 So basically, let's start here with the action potential 943 00:50:32,060 --> 00:50:34,370 that drives muscle twitches. 944 00:50:34,370 --> 00:50:37,310 So the way this works is that it an action potential 945 00:50:37,310 --> 00:50:40,640 will propagate down an axon toward the neuromuscular 946 00:50:40,640 --> 00:50:41,840 junction. 947 00:50:41,840 --> 00:50:46,640 That action potential will cause the release of neurotransmitter 948 00:50:46,640 --> 00:50:52,570 that then causes current to flow into the muscle fiber. 949 00:50:52,570 --> 00:50:55,030 That current flowing into the muscle fiber 950 00:50:55,030 --> 00:50:58,690 depolarizes it, turns on sodium channels, 951 00:50:58,690 --> 00:51:01,750 and that causes an action potential in the muscle fiber 952 00:51:01,750 --> 00:51:04,360 that looks very much like the action potential 953 00:51:04,360 --> 00:51:09,740 that we just saw for a neuron for the squid giant axon. 954 00:51:09,740 --> 00:51:12,160 Now, there is this famous problem, 955 00:51:12,160 --> 00:51:15,230 called the "excitation contraction coupling problem," 956 00:51:15,230 --> 00:51:18,040 which is, how does an action potential here 957 00:51:18,040 --> 00:51:23,115 on the surface of a muscle fiber get down into the myofibril 958 00:51:23,115 --> 00:51:25,390 and cause a contraction of the muscle? 959 00:51:29,363 --> 00:51:31,280 So we'll get to that question, but let me just 960 00:51:31,280 --> 00:51:32,610 describe what these things are. 961 00:51:32,610 --> 00:51:37,610 So the myofibrils-- the myofibril 962 00:51:37,610 --> 00:51:43,230 is this little element inside of the muscle fiber itself. 963 00:51:43,230 --> 00:51:52,130 And these are bundles of thick fibers and thin fibers that 964 00:51:52,130 --> 00:51:53,910 essentially-- 965 00:51:53,910 --> 00:51:55,460 here, I think it's on the next slide. 966 00:51:59,010 --> 00:52:02,280 So let me just finish the story about how the action 967 00:52:02,280 --> 00:52:03,870 potential gets inside. 968 00:52:03,870 --> 00:52:06,960 So the action potential propagates 969 00:52:06,960 --> 00:52:10,260 through these little structures called transverse tubules. 970 00:52:10,260 --> 00:52:13,830 These are little tubes that go from the surface of the muscle 971 00:52:13,830 --> 00:52:18,150 fiber down into the muscle cell. 972 00:52:18,150 --> 00:52:19,720 They're like axons. 973 00:52:19,720 --> 00:52:22,120 But instead of going out from the cell body, 974 00:52:22,120 --> 00:52:24,840 they go into the cell body. 975 00:52:24,840 --> 00:52:25,860 That's pretty cool. 976 00:52:25,860 --> 00:52:26,980 This thing is huge. 977 00:52:26,980 --> 00:52:32,650 This muscle fiber is about 100 microns across. 978 00:52:32,650 --> 00:52:36,900 So in order for that signal to get into the myofibril 979 00:52:36,900 --> 00:52:38,430 to cause contraction, it actually 980 00:52:38,430 --> 00:52:40,410 has to propagate down an axon that 981 00:52:40,410 --> 00:52:42,540 goes into the muscle fiber. 982 00:52:45,390 --> 00:52:47,700 So that action potential propagates down 983 00:52:47,700 --> 00:52:53,600 into the t-tubules that's a voltage pulse that opens up 984 00:52:53,600 --> 00:52:58,760 voltage-dependent calcium channels that activate 985 00:52:58,760 --> 00:53:00,980 calcium release in something called 986 00:53:00,980 --> 00:53:02,510 the sarcoplasmic reticulum. 987 00:53:02,510 --> 00:53:04,760 So you may remember that in neurons 988 00:53:04,760 --> 00:53:08,840 the endoplasmic reticulum sequesters calcium. 989 00:53:08,840 --> 00:53:11,270 In a muscle fiber, the sarcoplasmic reticulum 990 00:53:11,270 --> 00:53:12,120 does the same thing. 991 00:53:12,120 --> 00:53:13,490 It's sequesters calcium. 992 00:53:13,490 --> 00:53:15,200 But when this voltage pulse comes down 993 00:53:15,200 --> 00:53:17,690 the t-tubule, its voltage-dependent calcium 994 00:53:17,690 --> 00:53:20,220 channels, which cause the release of calcium, 995 00:53:20,220 --> 00:53:23,480 which then activates calcium-dependent calcium 996 00:53:23,480 --> 00:53:25,610 release through another set of channels, 997 00:53:25,610 --> 00:53:31,380 and it basically floods the myofibrils with calcium. 998 00:53:31,380 --> 00:53:33,720 And that triggers the contraction. 999 00:53:33,720 --> 00:53:35,580 And here's how that works. 1000 00:53:35,580 --> 00:53:40,210 Within these myofibrils are bundles of thick filaments, 1001 00:53:40,210 --> 00:53:45,060 which are myosin and thin filaments, which are actin. 1002 00:53:45,060 --> 00:53:52,080 The thick filaments are these structures right here. 1003 00:53:52,080 --> 00:53:54,990 The actin are filaments, thin filaments, 1004 00:53:54,990 --> 00:54:02,010 that intercalate between the myosin thick filaments. 1005 00:54:02,010 --> 00:54:07,410 The myosin thick filaments are covered with these myosin 1006 00:54:07,410 --> 00:54:08,760 molecules that stick out. 1007 00:54:08,760 --> 00:54:13,650 The myosin heads that are like little feet reach out. 1008 00:54:13,650 --> 00:54:17,040 And if they bind to the actin, then 1009 00:54:17,040 --> 00:54:21,120 these things basically grab the actin and start walking along. 1010 00:54:21,120 --> 00:54:23,830 And they pull the actin. 1011 00:54:23,830 --> 00:54:26,220 They pull this actin filament this way. 1012 00:54:26,220 --> 00:54:29,100 The ones over here walk this direction 1013 00:54:29,100 --> 00:54:31,440 and pull this actin filament that way, 1014 00:54:31,440 --> 00:54:36,615 and that causes these two end plates to pull, 1015 00:54:36,615 --> 00:54:39,660 sorry, these two, what are called "z disks," 1016 00:54:39,660 --> 00:54:41,670 to pull together. 1017 00:54:41,670 --> 00:54:42,985 And the thing shortens. 1018 00:54:42,985 --> 00:54:43,860 Does that make sense? 1019 00:54:46,540 --> 00:54:48,780 And then when the contraction stops, 1020 00:54:48,780 --> 00:54:51,870 these little feet stop walking. 1021 00:54:51,870 --> 00:54:55,470 They relax, and those actin filaments now 1022 00:54:55,470 --> 00:54:58,110 can relax and retract. 1023 00:54:58,110 --> 00:54:59,670 Pretty cool, right? 1024 00:54:59,670 --> 00:55:02,090 So how does the calcium connect to that? 1025 00:55:02,090 --> 00:55:05,475 So the calcium goes in, floods this myofibril. 1026 00:55:05,475 --> 00:55:09,240 The calcium goes in and binds to these little molecules, 1027 00:55:09,240 --> 00:55:14,380 called troponin, that are sitting in grooves of the actin 1028 00:55:14,380 --> 00:55:15,340 filaments. 1029 00:55:15,340 --> 00:55:17,710 And when the calcium binds to troponin, 1030 00:55:17,710 --> 00:55:19,930 it moves out of the way and opens up 1031 00:55:19,930 --> 00:55:23,860 the binding site for these myosin heads to grab 1032 00:55:23,860 --> 00:55:25,180 onto the actin filament. 1033 00:55:25,180 --> 00:55:29,050 They grab on and they pull. 1034 00:55:29,050 --> 00:55:32,980 And as soon as they pull, an ATP comes off. 1035 00:55:32,980 --> 00:55:36,160 These things open up, ATP binds, boom. 1036 00:55:36,160 --> 00:55:37,630 They pull again. 1037 00:55:37,630 --> 00:55:42,580 So they just walk along with one ATP per cycle. 1038 00:55:42,580 --> 00:55:43,780 Then when the calcium-- 1039 00:55:43,780 --> 00:55:47,050 what happens is that the calcium starts being sequestered back 1040 00:55:47,050 --> 00:55:51,040 into the sarcoplasmic reticulum that unbinds from the troponin. 1041 00:55:51,040 --> 00:55:53,320 The troponin falls back into the groove, 1042 00:55:53,320 --> 00:55:57,790 and the myosin heads can no longer connect to the actin. 1043 00:55:57,790 --> 00:56:01,330 And that's the end of the muscle twitch. 1044 00:56:01,330 --> 00:56:02,320 Pretty amazing, right? 1045 00:56:06,480 --> 00:56:13,770 So what goes wrong when sodium channels are inactivated? 1046 00:56:13,770 --> 00:56:16,270 And that's what we're going to talk about next-- when sodium 1047 00:56:16,270 --> 00:56:18,610 channels fail to inactivate. 1048 00:56:18,610 --> 00:56:22,490 So here's what the sodium channel looks like. 1049 00:56:22,490 --> 00:56:30,020 There are these clusters of transmembrane alpha-helices. 1050 00:56:30,020 --> 00:56:32,270 These things together, these four things together, 1051 00:56:32,270 --> 00:56:34,680 form the pore. 1052 00:56:34,680 --> 00:56:38,240 And there's a loop between them here 1053 00:56:38,240 --> 00:56:41,810 that produces the inactivation. 1054 00:56:41,810 --> 00:56:44,840 And you can see, if you look at the sights 1055 00:56:44,840 --> 00:56:47,900 of different mutations of the sodium channel 1056 00:56:47,900 --> 00:56:50,750 that produce defective inactivation, 1057 00:56:50,750 --> 00:56:54,590 they tend to be clustered in these cytoplasmic loops 1058 00:56:54,590 --> 00:56:55,640 of the sodium channel. 1059 00:57:00,550 --> 00:57:04,200 So myotonia and the periodic paralysis 1060 00:57:04,200 --> 00:57:06,090 that we just saw in those movies are 1061 00:57:06,090 --> 00:57:12,390 caused by these different sets of mutations on those loops. 1062 00:57:12,390 --> 00:57:17,340 And again, for these myotonias, these mutations 1063 00:57:17,340 --> 00:57:21,680 are in the skeletal isoform of the sodium channel. 1064 00:57:21,680 --> 00:57:26,590 So now, what do those mutations actually do to this? 1065 00:57:26,590 --> 00:57:28,230 So now, let's take a look at-- let's do 1066 00:57:28,230 --> 00:57:30,870 a patch clamp experiment, where we take 1067 00:57:30,870 --> 00:57:35,260 muscle fiber from a wild-type. 1068 00:57:35,260 --> 00:57:37,830 So you can just take a muscle biopsy-- 1069 00:57:37,830 --> 00:57:40,080 extract a little pinch of muscle. 1070 00:57:40,080 --> 00:57:43,050 You can culture it in a dish. 1071 00:57:43,050 --> 00:57:45,970 And you can do that for wild-type, normal human muscle 1072 00:57:45,970 --> 00:57:46,470 fibers. 1073 00:57:46,470 --> 00:57:49,650 And you can do it for muscle fibers 1074 00:57:49,650 --> 00:57:55,860 from a person with this particular mutation 1075 00:57:55,860 --> 00:57:57,210 of this sodium channel. 1076 00:57:57,210 --> 00:57:59,940 And you can see that just like for the neurons, 1077 00:57:59,940 --> 00:58:02,650 just like for the sodium channels in neurons, 1078 00:58:02,650 --> 00:58:08,220 you can see that depolarizing this ion channel 1079 00:58:08,220 --> 00:58:13,240 produces brief openings that are aligned at the time when 1080 00:58:13,240 --> 00:58:16,030 you do the depolarization step. 1081 00:58:16,030 --> 00:58:18,520 And then there are no more openings. 1082 00:58:18,520 --> 00:58:21,280 The sodium channels turn on, and then 1083 00:58:21,280 --> 00:58:26,510 that gating variable, that inactivation gate, 1084 00:58:26,510 --> 00:58:30,650 shuts off the pores, and there are no more openings. 1085 00:58:30,650 --> 00:58:36,750 But in the muscle fiber that has this mutation, 1086 00:58:36,750 --> 00:58:40,820 you can see that you get this burst of openings right 1087 00:58:40,820 --> 00:58:45,480 at the time of depolarization, but you keep getting openings 1088 00:58:45,480 --> 00:58:46,305 at later times. 1089 00:58:49,820 --> 00:58:55,230 And if you plot the average current over many trials, 1090 00:58:55,230 --> 00:58:57,170 you can see in normal fibers there's 1091 00:58:57,170 --> 00:58:59,630 this very brief pulse of opening, 1092 00:58:59,630 --> 00:59:03,520 and in these fibers, muscle fibers, with a mutation, 1093 00:59:03,520 --> 00:59:10,270 there is a constant extended high probability of that sodium 1094 00:59:10,270 --> 00:59:12,930 channel turning on, opening up. 1095 00:59:12,930 --> 00:59:17,450 And that's what causes all the problems right there. 1096 00:59:17,450 --> 00:59:21,400 In these conditions, that only represents about a 2%, 1097 00:59:21,400 --> 00:59:26,520 a 0.02 probability, of turning on 1098 00:59:26,520 --> 00:59:29,761 at a time when a normal muscle fiber would be inactivated. 1099 00:59:35,070 --> 00:59:38,360 So you can actually study these things in more detail. 1100 00:59:38,360 --> 00:59:40,210 So this shows a set of experiments that were 1101 00:59:40,210 --> 00:59:45,490 done in rat fast twitch muscle. 1102 00:59:45,490 --> 00:59:48,790 This shows a control, and this shows a muscle fiber 1103 00:59:48,790 --> 00:59:54,220 that's been treated with a toxin that comes from the sea 1104 00:59:54,220 --> 01:00:00,610 anemone that produces a toxin that uses this toxin 1105 01:00:00,610 --> 01:00:03,315 to actually help catch prey. 1106 01:00:03,315 --> 01:00:04,690 And it turns out, what that toxin 1107 01:00:04,690 --> 01:00:10,420 does is it mimics the effect of this blockage 1108 01:00:10,420 --> 01:00:13,780 of the inactivation of the sodium channel. 1109 01:00:13,780 --> 01:00:16,720 So you can see that applying this toxin 1110 01:00:16,720 --> 01:00:20,770 also produces these extended openings 1111 01:00:20,770 --> 01:00:24,480 or failures to inactivate. 1112 01:00:24,480 --> 01:00:27,490 If you take that toxin and you [AUDIO OUT] to a muscle fiber, 1113 01:00:27,490 --> 01:00:29,520 you see something really interesting. 1114 01:00:29,520 --> 01:00:30,760 You take a muscle fiber. 1115 01:00:30,760 --> 01:00:34,710 You can hook it up to-- 1116 01:00:34,710 --> 01:00:37,560 tie a string to one end, and tie a string to the other end, 1117 01:00:37,560 --> 01:00:39,780 and kind pull it tight a little bit, 1118 01:00:39,780 --> 01:00:43,890 and measure the force that that muscle fiber is exerting. 1119 01:00:43,890 --> 01:00:46,840 So you can measure force as a function of time. 1120 01:00:46,840 --> 01:00:48,690 If you stimulate that muscle fiber 1121 01:00:48,690 --> 01:00:50,880 with a little electrical shock, you 1122 01:00:50,880 --> 01:00:54,330 can elicit what's called a muscle twitch. 1123 01:00:57,020 --> 01:01:00,800 And in the presence of this ATXII toxin, 1124 01:01:00,800 --> 01:01:06,030 you can see that that twitch is very extended in time. 1125 01:01:06,030 --> 01:01:07,260 Is there a question? 1126 01:01:07,260 --> 01:01:08,290 Did I see a hand? 1127 01:01:08,290 --> 01:01:08,790 No. 1128 01:01:11,410 --> 01:01:12,270 So what's going on? 1129 01:01:12,270 --> 01:01:15,850 So you can now record from this muscle fiber 1130 01:01:15,850 --> 01:01:20,650 when it's been treated with this toxin that produces 1131 01:01:20,650 --> 01:01:25,030 what's called a myotonic run. 1132 01:01:25,030 --> 01:01:28,540 And you can see that [AUDIO OUT] muscle fiber produces 1133 01:01:28,540 --> 01:01:34,850 a single or maybe two action potentials when depolarize it. 1134 01:01:34,850 --> 01:01:38,650 That's what a muscle fiber normally does. 1135 01:01:38,650 --> 01:01:43,450 But when you treat it with this ATXII, 1136 01:01:43,450 --> 01:01:46,522 it generates many action potentials. 1137 01:01:46,522 --> 01:01:47,940 Now, why would that be? 1138 01:01:47,940 --> 01:01:50,910 Does that make sense? 1139 01:01:50,910 --> 01:01:55,640 We're going to explore why that is. 1140 01:01:55,640 --> 01:01:58,340 We're going to look at a particular model for 1141 01:01:58,340 --> 01:01:59,870 how the sodium-- 1142 01:01:59,870 --> 01:02:02,090 the failure to inactivate of the sodium channel 1143 01:02:02,090 --> 01:02:04,040 produces these myotonic runs. 1144 01:02:04,040 --> 01:02:06,500 What's really crazy is that after you turn off 1145 01:02:06,500 --> 01:02:11,950 that current injection that activates the muscle fiber, 1146 01:02:11,950 --> 01:02:13,320 the neuron keeps spiking. 1147 01:02:13,320 --> 01:02:14,745 The muscle fiber keeps spiking. 1148 01:02:20,130 --> 01:02:23,280 That continued spiking corresponds 1149 01:02:23,280 --> 01:02:26,590 to continued contraction of the muscle. 1150 01:02:26,590 --> 01:02:30,240 So you can trigger the muscle to generate some action 1151 01:02:30,240 --> 01:02:31,860 potentials in a normal muscle that 1152 01:02:31,860 --> 01:02:34,140 produces a very brief twitch. 1153 01:02:34,140 --> 01:02:38,220 But in these muscles with this mutated sodium channel-- 1154 01:02:38,220 --> 01:02:39,630 in this case it's with the toxin, 1155 01:02:39,630 --> 01:02:43,620 but the same thing happens in the muscle fibers with 1156 01:02:43,620 --> 01:02:45,350 the mutated sodium channel-- 1157 01:02:45,350 --> 01:02:48,660 it produces continued contraction of the muscle. 1158 01:02:48,660 --> 01:02:51,760 And that's what was happening to the goats. 1159 01:02:51,760 --> 01:02:54,680 Their muscles contracted, and then they didn't relax. 1160 01:02:54,680 --> 01:02:57,543 And so they were stiff like this, and then they fall over. 1161 01:03:02,280 --> 01:03:06,510 Now, that's called a myotonic run. 1162 01:03:06,510 --> 01:03:09,300 It's really interesting and was a big clue 1163 01:03:09,300 --> 01:03:15,930 to what the mechanism is that produces this. 1164 01:03:15,930 --> 01:03:18,810 If you take these muscle fibers and you put them 1165 01:03:18,810 --> 01:03:25,890 into a solution that doesn't have the right osmolarity-- 1166 01:03:25,890 --> 01:03:34,130 so too much, two too many ions, too high an osmolarity, 1167 01:03:34,130 --> 01:03:37,970 or too low an osmolarity, just like pure water, for example-- 1168 01:03:37,970 --> 01:03:40,970 produces what's called an osmotic shock. 1169 01:03:40,970 --> 01:03:45,130 And what it does is it breaks all the t-tubules 1170 01:03:45,130 --> 01:03:47,380 from the membrane. 1171 01:03:47,380 --> 01:03:49,720 So it doesn't break the membrane, 1172 01:03:49,720 --> 01:03:54,780 but it disconnects all the t-tubules from the membrane. 1173 01:03:54,780 --> 01:03:58,930 Now, what happens is you see the myotonic run goes away. 1174 01:03:58,930 --> 01:04:03,490 So something about the t-tubules is causing this myotonic run. 1175 01:04:10,390 --> 01:04:23,150 So there's a really beautiful set of papers from David Corey 1176 01:04:23,150 --> 01:04:29,040 and a person named Cannon, who proposed a hypothesis for why 1177 01:04:29,040 --> 01:04:32,550 this actually happens, and I'll walk you through the hypothesis 1178 01:04:32,550 --> 01:04:34,140 right now. 1179 01:04:34,140 --> 01:04:35,860 So here's the idea. 1180 01:04:35,860 --> 01:04:40,870 So when you have an input from a motor neuron 1181 01:04:40,870 --> 01:04:46,740 onto the muscle fiber you get synaptic input, [AUDIO OUT] 1182 01:04:46,740 --> 01:04:47,520 muscle fibers. 1183 01:04:47,520 --> 01:04:49,140 So this is the motor neuron synapse. 1184 01:04:49,140 --> 01:04:51,090 That's the muscle fiber. 1185 01:04:51,090 --> 01:04:55,200 So you should think about this as being a very long cell here, 1186 01:04:55,200 --> 01:04:59,730 and here's a t-tubule that's represented by a channel coming 1187 01:04:59,730 --> 01:05:00,690 in from the surface. 1188 01:05:00,690 --> 01:05:06,160 So this is a cross-section of the muscle fiber. 1189 01:05:06,160 --> 01:05:08,300 So the idea is that that current injection 1190 01:05:08,300 --> 01:05:11,840 causes an action potential, which causes sodium 1191 01:05:11,840 --> 01:05:13,580 to flow into the cell. 1192 01:05:13,580 --> 01:05:18,270 And on the hyperpolarize phase of the action potential, 1193 01:05:18,270 --> 01:05:21,860 potassium goes out of the cell to bring the cell back 1194 01:05:21,860 --> 01:05:25,170 down to a negative voltage. 1195 01:05:25,170 --> 01:05:28,575 Now, that actual potential propagates into the t-tubule, 1196 01:05:28,575 --> 01:05:30,200 which means you're going to have sodium 1197 01:05:30,200 --> 01:05:32,480 flowing into the cell and potassium flowing out 1198 01:05:32,480 --> 01:05:33,380 of the cell. 1199 01:05:33,380 --> 01:05:38,040 But out of the cell means into the t-tubule, right? 1200 01:05:38,040 --> 01:05:40,650 So what normally happens is, after an action potential, 1201 01:05:40,650 --> 01:05:44,640 you're left with an excess of potassium in the t-tubule. 1202 01:05:44,640 --> 01:05:51,139 So what happens-- think is going to happen, anybody? 1203 01:05:56,067 --> 01:05:57,400 Think back to the first lecture. 1204 01:06:01,638 --> 01:06:02,630 Yeah? 1205 01:06:02,630 --> 01:06:04,130 AUDIENCE: [INAUDIBLE] 1206 01:06:04,130 --> 01:06:05,713 MICHALE FEE: Yeah, there's going to be 1207 01:06:05,713 --> 01:06:07,550 some pumping going on here. 1208 01:06:07,550 --> 01:06:09,350 But actually, most of the potassium 1209 01:06:09,350 --> 01:06:13,460 gets out of the t-tubule by a different mechanism. 1210 01:06:13,460 --> 01:06:15,390 It gets out by diffusion. 1211 01:06:15,390 --> 01:06:18,860 So these extra potassium ions diffuse out 1212 01:06:18,860 --> 01:06:24,700 through that t-tubule back into the extracellular space. 1213 01:06:24,700 --> 01:06:27,840 Now, can we estimate how long it takes that to happen? 1214 01:06:30,700 --> 01:06:32,810 Any idea how we would do that? 1215 01:06:36,380 --> 01:06:39,190 Anybody want to take a guess? 1216 01:06:39,190 --> 01:06:41,570 Does anyone remember how long it takes an ion 1217 01:06:41,570 --> 01:06:44,640 to diffuse across, let's say, a cell body, 10 microns? 1218 01:06:50,250 --> 01:06:51,930 Kind of a few tens of milliseconds, 1219 01:06:51,930 --> 01:06:53,560 right, 50 milliseconds? 1220 01:06:53,560 --> 01:06:55,970 This thing is about 25 microns long. 1221 01:06:55,970 --> 01:06:59,140 And so it will be maybe four times that. 1222 01:06:59,140 --> 01:07:01,350 So that timescale we can calculate 1223 01:07:01,350 --> 01:07:06,180 by just using our equation for the relation between time 1224 01:07:06,180 --> 01:07:08,190 and distance for a diffusion, and you 1225 01:07:08,190 --> 01:07:12,540 find that that's about 300 to 400 milliseconds. 1226 01:07:12,540 --> 01:07:15,950 So that's how long it takes those potassium ions 1227 01:07:15,950 --> 01:07:19,340 to diffuse out of the t-tubule. 1228 01:07:19,340 --> 01:07:28,290 Now, what happens when we have a sodium 1229 01:07:28,290 --> 01:07:31,440 ion that isn't inactivating? 1230 01:07:31,440 --> 01:07:34,750 What happens is you're going to get a lot more spikes. 1231 01:07:34,750 --> 01:07:36,850 You're going to get a lot more spikes generated, 1232 01:07:36,850 --> 01:07:39,760 because this sodium current turns on, 1233 01:07:39,760 --> 01:07:42,120 but now it's not properly inactivating. 1234 01:07:42,120 --> 01:07:44,300 And so you're going to get extra spikes. 1235 01:07:44,300 --> 01:07:47,890 And those failure to enact [AUDIO OUT] extra spikes, 1236 01:07:47,890 --> 01:07:49,550 and extra spikes means you're going 1237 01:07:49,550 --> 01:07:53,460 to have a lot more potassium going into the t-tubule. 1238 01:07:59,820 --> 01:08:03,710 So what is all that-- 1239 01:08:03,710 --> 01:08:07,340 and remember, we now have 300 or 400 milliseconds 1240 01:08:07,340 --> 01:08:10,070 before that potassium can get out of the t-tubule 1241 01:08:10,070 --> 01:08:11,960 by diffusion. 1242 01:08:11,960 --> 01:08:13,490 So what's going to happen when you 1243 01:08:13,490 --> 01:08:19,293 have all that extra potassium in the t-tubule? 1244 01:08:19,293 --> 01:08:20,210 What's it going to do? 1245 01:08:23,633 --> 01:08:24,611 Yeah, [INAUDIBLE]? 1246 01:08:24,611 --> 01:08:27,060 AUDIENCE: It corrects the muscle fiber [INAUDIBLE].. 1247 01:08:27,060 --> 01:08:28,210 MICHALE FEE: Yeah. 1248 01:08:28,210 --> 01:08:32,840 So remember, the equilibrium potential, 1249 01:08:32,840 --> 01:08:34,930 the negative equilibrium potential 1250 01:08:34,930 --> 01:08:39,370 of the muscle fiber, which is normally, like any cell, 1251 01:08:39,370 --> 01:08:45,090 is down around minus 80, that negative potential 1252 01:08:45,090 --> 01:08:47,100 is caused because there's so much more 1253 01:08:47,100 --> 01:08:50,580 potassium inside the cell than outside the cell. 1254 01:08:50,580 --> 01:08:52,649 And so the potassium ions are normally 1255 01:08:52,649 --> 01:08:55,080 kind of leaking out of a cell, and that keeps 1256 01:08:55,080 --> 01:08:56,640 the membrane potential low. 1257 01:08:56,640 --> 01:08:57,600 But now, if you-- 1258 01:08:57,600 --> 01:09:00,020 remember, this is outside the cell. 1259 01:09:00,020 --> 01:09:02,430 So you have now, suddenly, a very high concentration 1260 01:09:02,430 --> 01:09:04,560 of potassium ions outside the cell. 1261 01:09:04,560 --> 01:09:05,670 And what do they do? 1262 01:09:05,670 --> 01:09:08,100 They push their way back in. 1263 01:09:08,100 --> 01:09:13,390 They start diffusing back in, which does what to the cell? 1264 01:09:13,390 --> 01:09:15,689 You now have potassium ions going 1265 01:09:15,689 --> 01:09:20,430 the wrong way, which does what? 1266 01:09:20,430 --> 01:09:22,487 I think you already gave the answer. 1267 01:09:22,487 --> 01:09:23,029 Say it again. 1268 01:09:23,029 --> 01:09:23,660 AUDIENCE: Depolarizes it. 1269 01:09:23,660 --> 01:09:25,355 MICHALE FEE: Depolarizes the cell. 1270 01:09:25,355 --> 01:09:30,752 Puts potassium back in, and it depolarizes the cell. 1271 01:09:30,752 --> 01:09:31,960 And what is that going to do? 1272 01:09:37,684 --> 01:09:39,120 AUDIENCE: Cause more spikes. 1273 01:09:39,120 --> 01:09:43,310 MICHALE FEE: Cause more spikes, which is going to do what? 1274 01:09:43,310 --> 01:09:46,212 Push more potassium into the t-tubule. 1275 01:09:46,212 --> 01:09:50,740 It's runaway instability. 1276 01:09:50,740 --> 01:09:55,630 So that's kind of a cool hypothesis, right? 1277 01:09:55,630 --> 01:09:58,030 You could imagine all sorts of experiments to test this. 1278 01:09:58,030 --> 01:10:00,238 Like you could put a little thing in there to measure 1279 01:10:00,238 --> 01:10:02,030 potassium concentration in the t-tubule. 1280 01:10:02,030 --> 01:10:05,070 Well, that's only a few microns across. 1281 01:10:05,070 --> 01:10:07,390 How do you test this hypothesis? 1282 01:10:07,390 --> 01:10:12,770 How would you-- it's a great idea. 1283 01:10:12,770 --> 01:10:15,570 But how do you know if it even makes any sense when you put it 1284 01:10:15,570 --> 01:10:19,130 all together, any suggestions? 1285 01:10:23,080 --> 01:10:23,700 Yeah? 1286 01:10:23,700 --> 01:10:28,412 AUDIENCE: [INAUDIBLE] the potassium. 1287 01:10:28,412 --> 01:10:29,120 MICHALE FEE: Yep. 1288 01:10:29,120 --> 01:10:32,480 So it's already known that at low potassium 1289 01:10:32,480 --> 01:10:34,850 this problem is less severe. 1290 01:10:34,850 --> 01:10:40,610 The disease is even named after that observation-- hyperkalemic 1291 01:10:40,610 --> 01:10:43,260 periodic paralysis. 1292 01:10:43,260 --> 01:10:44,310 Any other suggestions? 1293 01:10:44,310 --> 01:10:45,810 What are we here for? 1294 01:10:45,810 --> 01:10:46,875 What is this class? 1295 01:10:50,790 --> 01:10:54,810 Introduction to neural computation, right? 1296 01:10:54,810 --> 01:10:56,730 So what can we do? 1297 01:10:56,730 --> 01:10:59,390 This is a word model, right? 1298 01:10:59,390 --> 01:11:01,830 When you actually put it all together, 1299 01:11:01,830 --> 01:11:05,820 you could do all this, and when you model it, 1300 01:11:05,820 --> 01:11:07,515 it makes no sense whatsoever. 1301 01:11:07,515 --> 01:11:09,390 There's something wrong with this word model. 1302 01:11:09,390 --> 01:11:11,955 Neuroscience is full of word models. 1303 01:11:15,700 --> 01:11:20,170 The only way to know if a word model makes any sense 1304 01:11:20,170 --> 01:11:23,710 is to actually write down some equations 1305 01:11:23,710 --> 01:11:28,000 and see if it works the way you think it is going to work. 1306 01:11:28,000 --> 01:11:32,070 See if your word model translates into math. 1307 01:11:32,070 --> 01:11:36,360 And so that's what David Corey and Cannon did. 1308 01:11:36,360 --> 01:11:41,440 They took this picture, and they developed a model 1309 01:11:41,440 --> 01:11:42,970 for what that looks like it. 1310 01:11:42,970 --> 01:11:46,300 And it started with just the Hodgkin-Huxley model. 1311 01:11:46,300 --> 01:11:47,380 Here's Hodgkin-Huxley. 1312 01:11:47,380 --> 01:11:49,420 That's what we've been using all along. 1313 01:11:49,420 --> 01:11:51,430 They added another little compartment 1314 01:11:51,430 --> 01:11:55,240 that represents the conductances and the batteries associated 1315 01:11:55,240 --> 01:11:58,460 with the membrane in the t-tubule. 1316 01:11:58,460 --> 01:12:01,090 And notice, there's a EK here. 1317 01:12:01,090 --> 01:12:02,470 What does EK depend on? 1318 01:12:06,961 --> 01:12:07,960 AUDIENCE: [INAUDIBLE] 1319 01:12:07,960 --> 01:12:09,260 MICHALE FEE: Say it again. 1320 01:12:09,260 --> 01:12:12,075 EK depends on-- 1321 01:12:12,075 --> 01:12:12,950 AUDIENCE: [INAUDIBLE] 1322 01:12:12,950 --> 01:12:13,846 MICHALE FEE: Of-- 1323 01:12:13,846 --> 01:12:14,742 AUDIENCE: Potassium. 1324 01:12:14,742 --> 01:12:15,640 AUDIENCE: Potassium. 1325 01:12:15,640 --> 01:12:18,450 MICHALE FEE: Of potassium ions, and potassium 1326 01:12:18,450 --> 01:12:21,150 ions are changing. 1327 01:12:21,150 --> 01:12:25,980 So let's actually-- so this part you already know. 1328 01:12:25,980 --> 01:12:28,595 That's just Hodgkin and Huxley with a few extra resistors 1329 01:12:28,595 --> 01:12:29,720 attached to the side of it. 1330 01:12:32,510 --> 01:12:33,760 What about the potassium part? 1331 01:12:33,760 --> 01:12:36,760 Let's just flesh out that model a little bit more 1332 01:12:36,760 --> 01:12:40,450 to see how spiking activity would lead to changes 1333 01:12:40,450 --> 01:12:42,340 in potassium, how that change in potassium 1334 01:12:42,340 --> 01:12:43,930 would change the battery, and how 1335 01:12:43,930 --> 01:12:47,200 that would feedback and change the spiking activity. 1336 01:12:47,200 --> 01:12:48,800 So let's do that. 1337 01:12:48,800 --> 01:12:52,390 So we're going to imagine that we 1338 01:12:52,390 --> 01:12:55,123 are going to model our potassium conductance in here. 1339 01:12:55,123 --> 01:12:57,040 So we're going to write down a variable that's 1340 01:12:57,040 --> 01:13:00,130 the potassium concentration inside the t-tubule. 1341 01:13:03,150 --> 01:13:08,020 And what is going to affect that potassium concentration? 1342 01:13:08,020 --> 01:13:10,920 What are the sources of potassium? 1343 01:13:10,920 --> 01:13:13,840 What are the sinks of potassium, anybody? 1344 01:13:19,230 --> 01:13:21,630 Well, one is just diffusion. 1345 01:13:21,630 --> 01:13:25,050 So we can model that, and that looks an awful lot, actually, 1346 01:13:25,050 --> 01:13:27,520 like Fick's first law. 1347 01:13:27,520 --> 01:13:29,900 So the change in potassium concentration 1348 01:13:29,900 --> 01:13:32,480 as a function of time has a contribution 1349 01:13:32,480 --> 01:13:36,110 from the difference between the potassium concentration 1350 01:13:36,110 --> 01:13:37,130 inside and outside. 1351 01:13:40,110 --> 01:13:42,810 That rate of change through diffusion 1352 01:13:42,810 --> 01:13:45,960 is proportional to the difference in concentration 1353 01:13:45,960 --> 01:13:48,570 inside and outside divided by that time constant 1354 01:13:48,570 --> 01:13:50,106 that we've just calculated. 1355 01:13:54,210 --> 01:13:57,640 Now, what-- so that's how potassium leaves. 1356 01:13:57,640 --> 01:14:01,330 That's one way that potassium leaves. 1357 01:14:01,330 --> 01:14:06,240 So the potassium gets into the t-tubule 1358 01:14:06,240 --> 01:14:08,550 at a rate that's just proportional to the potassium 1359 01:14:08,550 --> 01:14:09,120 current. 1360 01:14:09,120 --> 01:14:12,600 The rate of change of the potassium concentration 1361 01:14:12,600 --> 01:14:16,610 is proportional to the potassium current. 1362 01:14:16,610 --> 01:14:17,952 And the potassium current-- 1363 01:14:17,952 --> 01:14:19,910 so let's just flesh this out a little bit more. 1364 01:14:19,910 --> 01:14:21,650 This, we already calculated. 1365 01:14:21,650 --> 01:14:23,960 This is the conductance times the driving potential. 1366 01:14:23,960 --> 01:14:27,830 But that current, we have to do a little bit of changes 1367 01:14:27,830 --> 01:14:29,870 of units to get current into the right 1368 01:14:29,870 --> 01:14:33,050 units for a change in potassium concentration 1369 01:14:33,050 --> 01:14:34,380 as a function of time. 1370 01:14:34,380 --> 01:14:38,240 So current is coulombs per second, 1371 01:14:38,240 --> 01:14:45,570 and here we have moles per liter per second. 1372 01:14:45,570 --> 01:14:47,990 So we need to divide by two things. 1373 01:14:47,990 --> 01:14:51,530 We need the volume of the t-tubule, 1374 01:14:51,530 --> 01:14:53,450 and we need Faraday's constant, which 1375 01:14:53,450 --> 01:14:56,360 is just coulombs per mole. 1376 01:14:56,360 --> 01:14:59,410 That's a well-known number that you can just look up. 1377 01:14:59,410 --> 01:15:01,010 Multiply those two things together, 1378 01:15:01,010 --> 01:15:03,550 you get the contribution of the potassium current 1379 01:15:03,550 --> 01:15:08,070 to the rate of change of potassium concentration. 1380 01:15:08,070 --> 01:15:10,890 The potassium current is just conductance times 1381 01:15:10,890 --> 01:15:12,720 driving potential. 1382 01:15:12,720 --> 01:15:16,080 Notice the EK is a function of potassium concentration. 1383 01:15:16,080 --> 01:15:18,030 I haven't written it in here, but that's just 1384 01:15:18,030 --> 01:15:19,837 the Nernst potential. 1385 01:15:19,837 --> 01:15:21,420 And so we have a differential equation 1386 01:15:21,420 --> 01:15:24,750 for the potassium concentration as a function of time. 1387 01:15:24,750 --> 01:15:29,400 It's a function of the potassium concentration voltage 1388 01:15:29,400 --> 01:15:32,630 and equilibrium potential. 1389 01:15:32,630 --> 01:15:37,620 And now, we just take that and add it to the code 1390 01:15:37,620 --> 01:15:40,155 that we already have for Hodgkin and Huxley. 1391 01:15:43,070 --> 01:15:45,040 And here's what you get. 1392 01:15:45,040 --> 01:15:47,200 So here's a normal muscle fiber. 1393 01:15:47,200 --> 01:15:50,690 You get a single action potential. 1394 01:15:50,690 --> 01:15:52,310 What they did was they modeled-- 1395 01:15:52,310 --> 01:15:54,770 they made some fraction of those ion channels 1396 01:15:54,770 --> 01:15:55,700 fail to inactivate. 1397 01:15:55,700 --> 01:15:57,200 And here's what happens to the model 1398 01:15:57,200 --> 01:16:04,010 when you make 2% sodium channels fail to inactivate. 1399 01:16:04,010 --> 01:16:08,600 You see that you get this large number of action potentials, 1400 01:16:08,600 --> 01:16:13,080 because the sodium channels are not inactivating properly. 1401 01:16:13,080 --> 01:16:15,800 And when you turn the current off, 1402 01:16:15,800 --> 01:16:18,740 you get this high potassium concentration 1403 01:16:18,740 --> 01:16:23,820 in the t-tubule that's now causing additional spikes. 1404 01:16:23,820 --> 01:16:30,550 That is continued contraction of the muscle. 1405 01:16:30,550 --> 01:16:34,630 That is this myotonia. 1406 01:16:34,630 --> 01:16:37,370 The model is exhibiting myotonia. 1407 01:16:37,370 --> 01:16:39,280 How do you explain periodic paralysis? 1408 01:16:39,280 --> 01:16:40,840 That's totally different, right? 1409 01:16:40,840 --> 01:16:43,408 Now the muscle just goes completely limp. 1410 01:16:43,408 --> 01:16:44,200 How do you do that? 1411 01:16:44,200 --> 01:16:45,970 Any thoughts about this? 1412 01:16:48,970 --> 01:16:50,470 What do you think would happen if we 1413 01:16:50,470 --> 01:16:54,520 made a slightly larger fraction of the sodium channels 1414 01:16:54,520 --> 01:16:57,604 fail to inactivate? 1415 01:16:57,604 --> 01:17:00,540 Here's what happens. 1416 01:17:00,540 --> 01:17:03,790 You get more and more action potentials. 1417 01:17:03,790 --> 01:17:10,090 And at some point, what happens is the voltage just locks up. 1418 01:17:10,090 --> 01:17:12,250 The sodium channels go into a different state 1419 01:17:12,250 --> 01:17:15,160 where the system is no longer oscillating. 1420 01:17:15,160 --> 01:17:19,030 It's just fixed at a high voltage. 1421 01:17:19,030 --> 01:17:22,920 It's called depolarization block, 1422 01:17:22,920 --> 01:17:29,830 and it's what happens when there's no longer enough-- 1423 01:17:29,830 --> 01:17:32,770 there aren't enough sodium channels 1424 01:17:32,770 --> 01:17:36,100 active to give you spiking, but there 1425 01:17:36,100 --> 01:17:40,090 are enough non-inactivated sodium channels to just hold 1426 01:17:40,090 --> 01:17:41,710 the voltage high. 1427 01:17:41,710 --> 01:17:46,250 And this muscle fiber is no longer able to contract, 1428 01:17:46,250 --> 01:17:48,530 and it's completely flaccid. 1429 01:17:48,530 --> 01:17:50,600 It's completely loose. 1430 01:17:50,600 --> 01:17:56,310 And so this is the hyperkalemic periodic paralysis. 1431 01:17:56,310 --> 01:18:01,280 So you get both of these really interesting phenotypes 1432 01:18:01,280 --> 01:18:05,760 in this disease just depending on one little parameter, which 1433 01:18:05,760 --> 01:18:10,470 is what fraction of these sodium channels 1434 01:18:10,470 --> 01:18:12,530 are failing to inactivate. 1435 01:18:12,530 --> 01:18:17,790 And so you can see, you get this very complex phenotype 1436 01:18:17,790 --> 01:18:22,780 from a simple mutation of an ion channel. 1437 01:18:22,780 --> 01:18:29,100 And in order to understand really how it's behaving, 1438 01:18:29,100 --> 01:18:31,160 you have to do modeling like this. 1439 01:18:31,160 --> 01:18:36,490 It's the way you understand a system and how it works. 1440 01:18:36,490 --> 01:18:42,100 Until you do this, you don't really understand it. 1441 01:18:42,100 --> 01:18:43,730 So I'll leave it there. 1442 01:18:43,730 --> 01:18:45,420 Thank you.