1 00:00:13,660 --> 00:00:17,480 MICHALE FEE: OK, so let's go ahead and get started. 2 00:00:17,480 --> 00:00:27,410 OK, so in the last lecture, we talked 3 00:00:27,410 --> 00:00:31,340 about how the inputs to neurons actually come into a cell 4 00:00:31,340 --> 00:00:37,820 mostly on the dendrite, which is this extended arborization 5 00:00:37,820 --> 00:00:41,170 of cylinders of cell membrane that 6 00:00:41,170 --> 00:00:43,070 give a very large surface area that 7 00:00:43,070 --> 00:00:47,270 allow many, many synapses to contact onto a neuron, many 8 00:00:47,270 --> 00:00:50,030 more than would be possible if all of those synapses 9 00:00:50,030 --> 00:00:57,860 were trying to connect to this neuron on its soma. 10 00:00:57,860 --> 00:01:03,350 Today, we are going to follow up on that general picture of how 11 00:01:03,350 --> 00:01:04,730 neurons receive inputs. 12 00:01:04,730 --> 00:01:08,240 And today, we're going to focus on the question of how synapses 13 00:01:08,240 --> 00:01:10,800 work. 14 00:01:10,800 --> 00:01:13,070 So we're going to start by looking 15 00:01:13,070 --> 00:01:15,710 at a simple model of synapses. 16 00:01:15,710 --> 00:01:17,900 And we're going to end by understanding 17 00:01:17,900 --> 00:01:20,690 how synapses on different parts of the neuron 18 00:01:20,690 --> 00:01:23,060 can actually do quite different things. 19 00:01:23,060 --> 00:01:26,160 So here's our list of learning objectives for today. 20 00:01:26,160 --> 00:01:29,600 So we're going to learn how to add a synapse to an equivalent 21 00:01:29,600 --> 00:01:31,720 circuit model. 22 00:01:31,720 --> 00:01:35,440 And we're going to describe a simple model 23 00:01:35,440 --> 00:01:40,490 of how that actually generates voltage changes in a neuron 24 00:01:40,490 --> 00:01:43,270 and what those synaptic inputs actually do. 25 00:01:43,270 --> 00:01:47,590 We're going to describe mathematical process called 26 00:01:47,590 --> 00:01:48,700 convolution. 27 00:01:48,700 --> 00:01:52,180 That's going to allow us to extend the idea of how 28 00:01:52,180 --> 00:01:55,030 a neuron responds to a single input 29 00:01:55,030 --> 00:01:59,320 spike from a presynaptic neuron to how a neuron responds 30 00:01:59,320 --> 00:02:04,250 to multiple spikes coming from a presynaptic neuron. 31 00:02:04,250 --> 00:02:07,480 So we're going to introduce this idea of convolution, 32 00:02:07,480 --> 00:02:10,430 which I'm sure many of you have heard of before. 33 00:02:10,430 --> 00:02:13,660 But it's going to play an increasingly important role 34 00:02:13,660 --> 00:02:14,260 in the class. 35 00:02:14,260 --> 00:02:16,210 And so we're going to introduce it here. 36 00:02:16,210 --> 00:02:19,340 We're going to talk about the idea of synaptic saturation, 37 00:02:19,340 --> 00:02:23,710 which is the idea that a single synaptic input can generate 38 00:02:23,710 --> 00:02:25,870 a small response in a neuron. 39 00:02:25,870 --> 00:02:30,370 You would think that as you generate more and more synaptic 40 00:02:30,370 --> 00:02:32,630 inputs to a neuron that the response 41 00:02:32,630 --> 00:02:35,160 of the postsynaptic neuron might just keep increasing. 42 00:02:35,160 --> 00:02:38,200 But, in fact, the response of a neuron to its inputs 43 00:02:38,200 --> 00:02:39,970 saturates at some level. 44 00:02:39,970 --> 00:02:41,920 And that process of saturation actually 45 00:02:41,920 --> 00:02:44,770 has very important consequences for how neurons 46 00:02:44,770 --> 00:02:47,080 respond to their inputs. 47 00:02:47,080 --> 00:02:51,130 And then finally, we're going to end with a fun story 48 00:02:51,130 --> 00:02:55,060 about the different functions of somatic and dendritic 49 00:02:55,060 --> 00:02:55,660 inhibition. 50 00:02:55,660 --> 00:02:57,880 And we're going to tell that story in the context 51 00:02:57,880 --> 00:03:01,930 of a crayfish behavior. 52 00:03:01,930 --> 00:03:05,390 All right, so let's start with chemical synapses. 53 00:03:05,390 --> 00:03:07,340 There are also electrical synapses, which 54 00:03:07,340 --> 00:03:08,590 we're not going to talk about. 55 00:03:08,590 --> 00:03:12,010 And that's basically where two neurons can actually 56 00:03:12,010 --> 00:03:13,390 contact each other. 57 00:03:13,390 --> 00:03:15,887 There are actually proteins that form little holes 58 00:03:15,887 --> 00:03:16,720 between the neurons. 59 00:03:16,720 --> 00:03:19,390 And so they're just directly electrically connected 60 00:03:19,390 --> 00:03:20,260 with each other. 61 00:03:20,260 --> 00:03:22,840 That's called an electrical synapse, or a gap junction. 62 00:03:22,840 --> 00:03:24,548 We're not going to talk about that today. 63 00:03:24,548 --> 00:03:26,690 We're going to focus on chemical synapses. 64 00:03:26,690 --> 00:03:30,220 So this is the structure of a typical excitatory synapse 65 00:03:30,220 --> 00:03:31,700 from a presynaptic neuron. 66 00:03:31,700 --> 00:03:33,910 This is the axon of a presynaptic neuron 67 00:03:33,910 --> 00:03:36,760 onto the dendrites of a postsynaptic neuron. 68 00:03:36,760 --> 00:03:40,600 Postsynaptic dendrites have often these specializations 69 00:03:40,600 --> 00:03:42,880 called spines, which are just little 70 00:03:42,880 --> 00:03:47,560 mushroom like protrusions of the cell membrane of the dendrite 71 00:03:47,560 --> 00:03:50,870 onto which presynaptic neurons can form of synapse. 72 00:03:50,870 --> 00:03:52,930 So this is called the presynaptic component 73 00:03:52,930 --> 00:03:53,650 or terminal. 74 00:03:53,650 --> 00:03:55,630 That's the postsynaptic component 75 00:03:55,630 --> 00:03:58,790 or postsynaptic terminal. 76 00:03:58,790 --> 00:04:01,130 On the presynaptic side, there are 77 00:04:01,130 --> 00:04:04,760 very small synaptic vesicles, about 30 to 40 nanometers 78 00:04:04,760 --> 00:04:07,790 in diameter, that sort of form a cloud 79 00:04:07,790 --> 00:04:10,580 or a cluster on the just on the inside surface 80 00:04:10,580 --> 00:04:12,860 of this synaptic junction. 81 00:04:12,860 --> 00:04:17,910 The synapses are typically about a half a micron across. 82 00:04:17,910 --> 00:04:21,880 And the synaptic cleft is very small. 83 00:04:21,880 --> 00:04:23,400 It's about 20 nanometers. 84 00:04:23,400 --> 00:04:26,530 So this is not quite to scale. 85 00:04:26,530 --> 00:04:29,520 This should be maybe a little bit closer here. 86 00:04:29,520 --> 00:04:33,450 All right, notice that that is very small. 87 00:04:33,450 --> 00:04:35,340 That synapse is really tiny. 88 00:04:35,340 --> 00:04:38,220 It's about the wavelength. 89 00:04:38,220 --> 00:04:42,360 Its size is equal to 1 wavelength of green light. 90 00:04:42,360 --> 00:04:46,120 So it's a tiny structure. 91 00:04:46,120 --> 00:04:48,800 There's a lot going on inside that little thing, though. 92 00:04:48,800 --> 00:04:52,390 And here's we're going to walk through the sequence of events 93 00:04:52,390 --> 00:04:55,450 that just describes how a presynaptic action 94 00:04:55,450 --> 00:04:57,400 potential leads to depolarization 95 00:04:57,400 --> 00:04:59,720 and in a postsynaptic neuron. 96 00:04:59,720 --> 00:05:02,860 So we have an action potential that propagates down. 97 00:05:02,860 --> 00:05:06,070 That's a pulse of depolarizing voltage. 98 00:05:06,070 --> 00:05:08,890 When it reaches the synaptic terminal, 99 00:05:08,890 --> 00:05:11,920 that pulse of depolarizing voltage 100 00:05:11,920 --> 00:05:14,380 is about plus 50 millivolts. 101 00:05:14,380 --> 00:05:19,120 That activates voltage gated calcium channels that turn on, 102 00:05:19,120 --> 00:05:22,540 just the same way that we've described voltage activated 103 00:05:22,540 --> 00:05:26,620 sodium channels and potassium channels. 104 00:05:26,620 --> 00:05:32,020 That allows calcium ions to flow into the presynaptic terminal. 105 00:05:32,020 --> 00:05:37,090 That calcium flows in and binds to presynaptic proteins that 106 00:05:37,090 --> 00:05:42,970 dock these vesicles onto the membrane facing 107 00:05:42,970 --> 00:05:45,380 the synaptic cleft. 108 00:05:45,380 --> 00:05:50,500 That causes those vesicles to fuse with the membrane. 109 00:05:50,500 --> 00:05:52,840 They open up and release their neurotransmitters. 110 00:05:52,840 --> 00:05:56,920 So all of those vesicles are filled with neurotransmitter. 111 00:05:56,920 --> 00:06:00,970 The vesicles are coated with actual pumps that 112 00:06:00,970 --> 00:06:04,930 take neurotransmitter from inside of the cell 113 00:06:04,930 --> 00:06:08,280 and pump it into the vesicles. 114 00:06:08,280 --> 00:06:10,060 So then calcium flows in. 115 00:06:10,060 --> 00:06:12,520 Vesicle fuses, releases neurotransmitter 116 00:06:12,520 --> 00:06:14,050 into the cleft. 117 00:06:14,050 --> 00:06:16,468 Neurotransmitter then diffuses in the cleft. 118 00:06:16,468 --> 00:06:18,010 You could actually calculate how long 119 00:06:18,010 --> 00:06:22,430 it takes to get from one side to the other now, I think. 120 00:06:22,430 --> 00:06:25,460 It's not very long. 121 00:06:25,460 --> 00:06:29,750 Ligand gated ion channels, they're 122 00:06:29,750 --> 00:06:32,270 basically like the kinds of ion channels 123 00:06:32,270 --> 00:06:33,830 we've already been discussing. 124 00:06:33,830 --> 00:06:35,850 But instead of being gated by voltage, 125 00:06:35,850 --> 00:06:39,140 they're gated by the binding of a neurotransmitter to a binding 126 00:06:39,140 --> 00:06:41,180 site on the outside of the protein. 127 00:06:41,180 --> 00:06:42,980 That produces a conformational change 128 00:06:42,980 --> 00:06:47,010 that opens the pour to the flow of ions. 129 00:06:47,010 --> 00:06:54,290 Now, you have neurotransmitter binds to these, opens the pour. 130 00:06:54,290 --> 00:06:58,970 You have now positive ions that flow into the cell, 131 00:06:58,970 --> 00:07:02,720 because the cell is hyperpolarized. 132 00:07:02,720 --> 00:07:04,490 So it has a low voltage. 133 00:07:04,490 --> 00:07:06,410 Positive ions flow into the cell. 134 00:07:06,410 --> 00:07:11,420 That corresponds to an increase in the synaptic conductance. 135 00:07:11,420 --> 00:07:14,660 What is that flow of ions, positive ions, into the cell 136 00:07:14,660 --> 00:07:16,481 do? 137 00:07:16,481 --> 00:07:18,950 It depolarizes the cell. 138 00:07:18,950 --> 00:07:23,230 You have synaptic current flowing in that then-- 139 00:07:23,230 --> 00:07:24,640 I forget to put it on there-- 140 00:07:24,640 --> 00:07:28,240 depolarizes the cell. 141 00:07:28,240 --> 00:07:29,310 Any questions about that? 142 00:07:32,630 --> 00:07:36,520 OK, let's talk a little bit about the sort of some 143 00:07:36,520 --> 00:07:39,550 of the interesting numbers, like how many synapses there are, 144 00:07:39,550 --> 00:07:43,000 how many cells, how many dendrites in a little piece 145 00:07:43,000 --> 00:07:43,980 of neural tissue. 146 00:07:43,980 --> 00:07:47,140 It's pretty staggering actually. 147 00:07:47,140 --> 00:07:49,120 So the synopses are small. 148 00:07:49,120 --> 00:07:53,920 But what's really amazing is that in a cubic millimeter 149 00:07:53,920 --> 00:07:57,900 of cortical tissue, there are a billion synapses. 150 00:07:57,900 --> 00:07:59,690 And if you think about what that means, 151 00:07:59,690 --> 00:08:08,700 there is a synapse on a grid, on a lattice, every 1.1 microns. 152 00:08:08,700 --> 00:08:15,480 So they're sort of some fraction of a micron big. 153 00:08:15,480 --> 00:08:19,020 And there's one of them every micron. 154 00:08:19,020 --> 00:08:20,925 Most of your brain is filled with synapses. 155 00:08:24,050 --> 00:08:33,570 There are 4.1 kilometers of axon in that same cubic millimeter 156 00:08:33,570 --> 00:08:35,640 and 500 meters of dendrite. 157 00:08:41,789 --> 00:08:46,560 A typical cortical cell receives about 10,000 synapses. 158 00:08:46,560 --> 00:08:49,350 Each cell has about 4 millimeters of dendrite 159 00:08:49,350 --> 00:08:52,550 and 4 centimeters of axon. 160 00:08:52,550 --> 00:08:55,850 And there are about 10 to the 5 neurons per cubic millimeter 161 00:08:55,850 --> 00:08:57,850 in the mouse cortex. 162 00:08:57,850 --> 00:09:00,050 And in your entire brain, there are about 10 163 00:09:00,050 --> 00:09:03,050 of the 8 neurons, which is the same roughly as the number 164 00:09:03,050 --> 00:09:04,750 of stars in our galaxy. 165 00:09:10,468 --> 00:09:12,260 And we're going to figure out how it works. 166 00:09:16,910 --> 00:09:18,870 OK, so let's come back to this. 167 00:09:18,870 --> 00:09:21,830 So let's start by adding a synapse to an equivalent 168 00:09:21,830 --> 00:09:24,950 circuit model and understanding how that model works. 169 00:09:27,780 --> 00:09:29,910 So let's start with an ionotropic receptor. 170 00:09:29,910 --> 00:09:35,220 So ionotropic receptors are neurotransmitter receptors 171 00:09:35,220 --> 00:09:39,150 that also form an ion channel. 172 00:09:39,150 --> 00:09:41,640 There are other kinds of neurotransmitter receptors 173 00:09:41,640 --> 00:09:43,500 where a neurotransmitter binds. 174 00:09:43,500 --> 00:09:45,570 And that sends a chemical signal that 175 00:09:45,570 --> 00:09:50,280 opens up a different kind of ion channel. 176 00:09:50,280 --> 00:09:53,700 Those are called metabotropic neurotransmitter receptors. 177 00:09:53,700 --> 00:09:57,670 We're going to focus today on ionotropic receptors. 178 00:09:57,670 --> 00:09:59,340 So a neurotransmitter binds. 179 00:09:59,340 --> 00:10:01,210 That binding opens a gate. 180 00:10:01,210 --> 00:10:04,020 And that allows a current to flow. 181 00:10:04,020 --> 00:10:07,470 So these guys, Magleby and Stevens, 182 00:10:07,470 --> 00:10:12,690 did an experiment to understand how that conductance-- 183 00:10:12,690 --> 00:10:16,440 so when that ion channel opens, it turns on a conductance. 184 00:10:16,440 --> 00:10:19,260 And you can directly measure that conductance 185 00:10:19,260 --> 00:10:22,450 by doing a voltage clamp experiment. 186 00:10:22,450 --> 00:10:24,270 So here's the experiment they did. 187 00:10:24,270 --> 00:10:27,550 They took a muscle fiber from a frog. 188 00:10:27,550 --> 00:10:29,100 They set up a voltage clamp on it, 189 00:10:29,100 --> 00:10:30,960 so an electrode to measure the voltage, 190 00:10:30,960 --> 00:10:33,060 and another electrode to inject current. 191 00:10:33,060 --> 00:10:37,030 You hold the voltage at different levels. 192 00:10:37,030 --> 00:10:40,770 And then what they did was they stimulated electrically 193 00:10:40,770 --> 00:10:45,630 the motor axon, the axon of the motor neuron 194 00:10:45,630 --> 00:10:48,150 that innervates the muscle. 195 00:10:48,150 --> 00:10:51,690 So that then activates this neuromuscular junction 196 00:10:51,690 --> 00:10:54,300 that opens acetylcholine receptors 197 00:10:54,300 --> 00:10:58,850 and produces a current as a function of time 198 00:10:58,850 --> 00:11:01,220 after the synapse is activated. 199 00:11:01,220 --> 00:11:03,000 Any questions about the setup? 200 00:11:03,000 --> 00:11:06,800 We're simply holding the cell at different voltages, 201 00:11:06,800 --> 00:11:09,350 activating the synapse, and measuring how much current 202 00:11:09,350 --> 00:11:11,070 flows through the synapse. 203 00:11:11,070 --> 00:11:11,570 Yes. 204 00:11:11,570 --> 00:11:14,951 AUDIENCE: So with the current flows through the ion 205 00:11:14,951 --> 00:11:16,890 channels in the muscle fibers? 206 00:11:16,890 --> 00:11:20,270 MICHALE FEE: The current is flowing through these ion 207 00:11:20,270 --> 00:11:23,863 channels here in the synapse. 208 00:11:23,863 --> 00:11:25,280 Now, remember, there are all sorts 209 00:11:25,280 --> 00:11:28,400 of sodium channels and potassium channels and all those things. 210 00:11:28,400 --> 00:11:32,305 But do those do anything? 211 00:11:32,305 --> 00:11:34,420 AUDIENCE: Not really. 212 00:11:34,420 --> 00:11:36,810 MICHALE FEE: We're just holding the voltage-- that's 213 00:11:36,810 --> 00:11:39,570 why the voltage is so important, because if you were 214 00:11:39,570 --> 00:11:42,950 to do this experiment without a voltage, you would stimulate 215 00:11:42,950 --> 00:11:44,220 and the muscle would contract. 216 00:11:44,220 --> 00:11:48,110 And it would rip the electrodes out of the muscle fiber. 217 00:11:48,110 --> 00:11:50,520 So when you voltage clamp it, it holds the cell 218 00:11:50,520 --> 00:11:52,950 at a constant potential, so that the cell 219 00:11:52,950 --> 00:11:57,720 can't spike when the current flows in through the synapse. 220 00:11:57,720 --> 00:11:58,944 Yes. 221 00:11:58,944 --> 00:12:03,312 AUDIENCE: On the graph, would the shock [INAUDIBLE] 222 00:12:03,312 --> 00:12:04,520 MICHALE FEE: Yes, the shock-- 223 00:12:04,520 --> 00:12:07,790 AUDIENCE: The difference is like in positive and negative-- 224 00:12:07,790 --> 00:12:09,940 MICHALE FEE: Yeah, I'm going to explain this. 225 00:12:09,940 --> 00:12:11,910 I'm just setting it up right now. 226 00:12:11,910 --> 00:12:15,480 OK, any questions about the setup? 227 00:12:15,480 --> 00:12:16,650 Good questions. 228 00:12:16,650 --> 00:12:18,930 One step ahead of me. 229 00:12:18,930 --> 00:12:21,717 All right, so now, let's look at what actually happens. 230 00:12:21,717 --> 00:12:23,550 So what you can see is that the current that 231 00:12:23,550 --> 00:12:26,940 goes through these ion channels is different 232 00:12:26,940 --> 00:12:30,210 depending on the voltage that you hold the cell at. 233 00:12:30,210 --> 00:12:34,800 So if you hold the cell at a negative potential-- 234 00:12:34,800 --> 00:12:38,620 so here you can see, the voltage it is like minus 120 here. 235 00:12:38,620 --> 00:12:40,800 And what happens is after you shock, 236 00:12:40,800 --> 00:12:44,200 you see this large, inward current. 237 00:12:44,200 --> 00:12:47,800 Remember, inward current, negative current corresponds 238 00:12:47,800 --> 00:12:53,230 to positive ions going into the cell, inward current. 239 00:12:53,230 --> 00:12:59,470 So after you activate the motor axon, 240 00:12:59,470 --> 00:13:01,690 you get a large inward current that 241 00:13:01,690 --> 00:13:04,670 lasts a couple milliseconds. 242 00:13:04,670 --> 00:13:06,950 That corresponds to current going 243 00:13:06,950 --> 00:13:09,620 into the cell that would depolarize the cell 244 00:13:09,620 --> 00:13:12,560 and activate it, right? 245 00:13:12,560 --> 00:13:15,650 But as you raise the voltage, you 246 00:13:15,650 --> 00:13:18,620 can see that the current gets smaller. 247 00:13:18,620 --> 00:13:22,320 And at some point, the current actually goes to zero. 248 00:13:22,320 --> 00:13:26,710 And it goes to zero when you are holding 249 00:13:26,710 --> 00:13:28,450 the membrane potential close to zero. 250 00:13:28,450 --> 00:13:31,420 And as you hold the membrane potential more positive, 251 00:13:31,420 --> 00:13:35,630 you can see that the current actually goes the other way. 252 00:13:35,630 --> 00:13:40,270 So what we can do is we can now plot that peak current 253 00:13:40,270 --> 00:13:44,680 as a function of the holding potential. 254 00:13:44,680 --> 00:13:47,740 So we're measuring current through an ion 255 00:13:47,740 --> 00:13:50,570 channel at different voltages. 256 00:13:50,570 --> 00:13:53,750 So what are we going to plot next? 257 00:13:53,750 --> 00:13:56,660 Just like we did for the sodium channel, 258 00:13:56,660 --> 00:13:59,625 for the potassium channel, we're going to-- what 259 00:13:59,625 --> 00:14:00,500 are we going to plot? 260 00:14:00,500 --> 00:14:01,645 What kind of plot? 261 00:14:01,645 --> 00:14:02,907 AUDIENCE: I-V. 262 00:14:02,907 --> 00:14:03,990 MICHALE FEE: An I-V curve. 263 00:14:03,990 --> 00:14:04,380 Excellent. 264 00:14:04,380 --> 00:14:05,040 Let's do that. 265 00:14:05,040 --> 00:14:09,470 You can see it's actually linear. 266 00:14:09,470 --> 00:14:14,800 So the current is negative when you hold the cell negative. 267 00:14:14,800 --> 00:14:17,860 The current's positive when you hold the cell above zero. 268 00:14:17,860 --> 00:14:19,630 And it crosses at zero. 269 00:14:19,630 --> 00:14:24,070 What do we call that place where it crosses zero? 270 00:14:24,070 --> 00:14:26,820 What does that tell us? 271 00:14:26,820 --> 00:14:29,432 When this ion channel is open-- 272 00:14:29,432 --> 00:14:30,670 AUDIENCE: Reversal potential. 273 00:14:30,670 --> 00:14:32,087 MICHALE FEE: So reversal potential 274 00:14:32,087 --> 00:14:34,180 or the equilibrium potential, that's right. 275 00:14:37,280 --> 00:14:38,480 That's kind of weird, right? 276 00:14:38,480 --> 00:14:40,840 An equilibrium potential that's zero. 277 00:14:40,840 --> 00:14:44,600 What kind of channel has an equilibrium potential at zero? 278 00:14:44,600 --> 00:14:49,130 Remember, sodium was very negative, like minus 80-- 279 00:14:49,130 --> 00:14:52,858 sorry, potassium was very negative. 280 00:14:52,858 --> 00:14:54,850 AUDIENCE: [INAUDIBLE] 281 00:14:54,850 --> 00:14:55,870 MICHALE FEE: Excellent. 282 00:14:55,870 --> 00:14:59,407 It's something that passes both potassium and sodium. 283 00:14:59,407 --> 00:15:00,115 It's like a hole. 284 00:15:02,860 --> 00:15:05,770 So this ion channel is basically like opening 285 00:15:05,770 --> 00:15:10,510 a hole that passes positive ions in both directions. 286 00:15:10,510 --> 00:15:14,140 Potassium goes out, sodium comes in. 287 00:15:14,140 --> 00:15:15,200 Yes. 288 00:15:15,200 --> 00:15:19,955 AUDIENCE: But that is only like [INAUDIBLE] before the-- 289 00:15:19,955 --> 00:15:21,580 MICHALE FEE: Notice that we're plotting 290 00:15:21,580 --> 00:15:24,280 that the current as a function of all 291 00:15:24,280 --> 00:15:28,030 voltages, and it crosses at zero. 292 00:15:28,030 --> 00:15:31,360 There's zero current at zero voltage, which happens when you 293 00:15:31,360 --> 00:15:33,550 have just a non-selective pore. 294 00:15:38,150 --> 00:15:40,070 OK, what does that look like? 295 00:15:40,070 --> 00:15:45,480 An I-V curve that looks like that, what is that? 296 00:15:45,480 --> 00:15:46,920 There's a name for that. 297 00:15:49,550 --> 00:15:54,610 You use it when you build a circuit. 298 00:15:54,610 --> 00:15:58,756 You might have some transistors and some capacitors and some-- 299 00:15:58,756 --> 00:16:00,940 how about some resistors? 300 00:16:00,940 --> 00:16:02,440 It's just a resistor. 301 00:16:02,440 --> 00:16:04,600 That's what the I-V curve of a resistor looks like. 302 00:16:07,890 --> 00:16:09,310 And if we were to put it in series 303 00:16:09,310 --> 00:16:11,685 with a battery, what would the voltage of the battery be? 304 00:16:14,250 --> 00:16:14,750 Zero. 305 00:16:14,750 --> 00:16:16,790 Remember, if we put it in series with a battery, 306 00:16:16,790 --> 00:16:18,200 it produces an offset. 307 00:16:18,200 --> 00:16:22,070 So it's just our same equation-- 308 00:16:22,070 --> 00:16:25,810 the current is just a conductance times a voltage. 309 00:16:25,810 --> 00:16:27,890 It's just Ohm's law. 310 00:16:27,890 --> 00:16:29,840 That's 1 over resistance. 311 00:16:29,840 --> 00:16:31,730 And it's V minus e synaptic. 312 00:16:31,730 --> 00:16:33,950 And e synaptic is just 0. 313 00:16:36,560 --> 00:16:42,080 So that's called the driving potential. 314 00:16:44,592 --> 00:16:45,550 That's the conductance. 315 00:16:45,550 --> 00:16:48,220 Can anyone take a guess at what the conductance looks 316 00:16:48,220 --> 00:16:49,720 like as a function of time? 317 00:16:52,670 --> 00:16:56,920 Somebody just hold your hand up, and-- 318 00:16:56,920 --> 00:17:00,230 I see two answers that are very close. 319 00:17:00,230 --> 00:17:01,895 Lena. 320 00:17:01,895 --> 00:17:03,230 AUDIENCE: Would it be like that? 321 00:17:03,230 --> 00:17:04,079 MICHALE FEE: Start over here. 322 00:17:04,079 --> 00:17:04,940 Like go this way. 323 00:17:10,430 --> 00:17:12,890 What would the conductance do as a function of time 324 00:17:12,890 --> 00:17:14,690 to make the current look like this? 325 00:17:20,140 --> 00:17:21,180 What would it be here? 326 00:17:21,180 --> 00:17:22,740 What would the conductance be here? 327 00:17:22,740 --> 00:17:26,560 Remember, the voltage is being held at some value. 328 00:17:26,560 --> 00:17:27,720 The current is zero. 329 00:17:27,720 --> 00:17:29,525 So the conductance must be? 330 00:17:29,525 --> 00:17:30,150 AUDIENCE: Zero. 331 00:17:30,150 --> 00:17:30,840 MICHALE FEE: Zero. 332 00:17:30,840 --> 00:17:31,680 And how about here? 333 00:17:34,310 --> 00:17:36,448 It should be some big conductance. 334 00:17:36,448 --> 00:17:37,490 And then what about here? 335 00:17:37,490 --> 00:17:38,390 AUDIENCE: Zero. 336 00:17:38,390 --> 00:17:39,140 MICHALE FEE: Zero. 337 00:17:39,140 --> 00:17:42,130 So what is that-- excellent, it just looks like that. 338 00:17:42,130 --> 00:17:46,420 The conductance just turns on and then turns off. 339 00:17:49,980 --> 00:17:53,670 Anybody want to take a guess at why that might be? 340 00:17:53,670 --> 00:17:54,430 Shock. 341 00:17:54,430 --> 00:17:56,800 What happens here? 342 00:17:56,800 --> 00:17:57,760 Why does this turn on? 343 00:18:00,350 --> 00:18:03,110 Because neurotransmitter binds to the receptor, 344 00:18:03,110 --> 00:18:04,340 opens the channel. 345 00:18:04,340 --> 00:18:07,480 And then what happens? 346 00:18:07,480 --> 00:18:10,310 The neurotransmitter falls off. 347 00:18:10,310 --> 00:18:16,950 And the neurotransmitter receptor closes. 348 00:18:16,950 --> 00:18:17,610 That's it. 349 00:18:17,610 --> 00:18:19,980 We're going to do a little bit of mathematical modeling 350 00:18:19,980 --> 00:18:20,480 of that. 351 00:18:20,480 --> 00:18:22,610 But it's going to be pretty simple. 352 00:18:22,610 --> 00:18:23,390 All right? 353 00:18:23,390 --> 00:18:23,910 OK. 354 00:18:23,910 --> 00:18:26,110 So there is our equivalent circuit. 355 00:18:26,110 --> 00:18:31,920 This thing right here equals conductance times 356 00:18:31,920 --> 00:18:37,290 of driving potential electrically is just that. 357 00:18:37,290 --> 00:18:38,370 You remember that, right? 358 00:18:38,370 --> 00:18:43,050 That's the same way we modeled the current of the sodium 359 00:18:43,050 --> 00:18:46,443 channel or the potassium channel. 360 00:18:46,443 --> 00:18:50,488 AUDIENCE: So the graphical [INAUDIBLE] 361 00:18:50,488 --> 00:18:55,150 because it's linear, why would that [INAUDIBLE] 362 00:18:55,150 --> 00:18:56,837 MICHALE FEE: The conductance constant? 363 00:18:56,837 --> 00:18:57,420 AUDIENCE: Yeah 364 00:18:57,420 --> 00:18:58,087 MICHALE FEE: OK. 365 00:18:58,087 --> 00:18:59,620 Because look at the current. 366 00:18:59,620 --> 00:19:01,900 So, remember, these different voltages 367 00:19:01,900 --> 00:19:05,050 here just correspond to these voltages. 368 00:19:05,050 --> 00:19:06,640 Here V minus E sin. 369 00:19:06,640 --> 00:19:08,050 So E sin is what? 370 00:19:08,050 --> 00:19:10,750 The synaptic reversal potential is just zero, right? 371 00:19:10,750 --> 00:19:12,370 So for each one of these experiments, 372 00:19:12,370 --> 00:19:15,160 this driving potential is just constant. 373 00:19:15,160 --> 00:19:20,170 It's just given by this holding potential in the voltage kind 374 00:19:20,170 --> 00:19:21,320 of experiment. 375 00:19:21,320 --> 00:19:22,870 So in order to turn something that 376 00:19:22,870 --> 00:19:27,070 looks like this into something that looks like this, 377 00:19:27,070 --> 00:19:30,680 you have to multiply it by something that looks like that. 378 00:19:30,680 --> 00:19:32,553 Does that makes sense? 379 00:19:32,553 --> 00:19:33,970 For each one of those experiments, 380 00:19:33,970 --> 00:19:38,490 this term is constant. 381 00:19:38,490 --> 00:19:40,870 And so to get a current that looks like this, 382 00:19:40,870 --> 00:19:45,460 the conductance has to look like that. 383 00:19:45,460 --> 00:19:46,590 Does that makes sense? 384 00:19:46,590 --> 00:19:50,630 AUDIENCE: guess she's asking the upper-- 385 00:19:50,630 --> 00:19:53,380 MICHALE FEE: Oh, sorry, did I misunderstand the question? 386 00:19:53,380 --> 00:19:54,153 Ask it again. 387 00:19:54,153 --> 00:19:54,820 AUDIENCE: Sorry. 388 00:19:54,820 --> 00:19:55,910 I was talking about that one. 389 00:19:55,910 --> 00:19:56,120 MICHALE FEE: Oh. 390 00:19:56,120 --> 00:19:58,028 AUDIENCE: But explanation did make sense. 391 00:19:58,028 --> 00:19:59,070 MICHALE FEE: Did it help? 392 00:19:59,070 --> 00:20:00,830 But it was the wrong explanation. 393 00:20:00,830 --> 00:20:02,530 OK, so ask your question again. 394 00:20:02,530 --> 00:20:05,250 AUDIENCE: Yes, so I was trying to relate it 395 00:20:05,250 --> 00:20:07,500 to what we were doing earlier with a [? coefficient ?] 396 00:20:07,500 --> 00:20:08,167 [INAUDIBLE] 397 00:20:08,167 --> 00:20:08,917 MICHALE FEE: Yeah. 398 00:20:08,917 --> 00:20:12,540 AUDIENCE: And it had an I-V curve that looked something 399 00:20:12,540 --> 00:20:14,240 like that curve-- 400 00:20:14,240 --> 00:20:16,580 MICHALE FEE: Oh, it like had some funny shape like this. 401 00:20:16,580 --> 00:20:19,380 AUDIENCE: Yeah, it looked like [INAUDIBLE] at zero. 402 00:20:19,380 --> 00:20:20,870 And then it was like-- 403 00:20:20,870 --> 00:20:24,770 MICHALE FEE: Yeah, so remember, this is as a function of time. 404 00:20:24,770 --> 00:20:27,620 And this is exactly what the sodium conductance looked 405 00:20:27,620 --> 00:20:30,290 like as a function of time. 406 00:20:30,290 --> 00:20:31,310 It turns on. 407 00:20:31,310 --> 00:20:32,700 And then it turns off. 408 00:20:32,700 --> 00:20:35,690 For the sodium conductance, this turning on 409 00:20:35,690 --> 00:20:37,850 happened with a voltage step. 410 00:20:37,850 --> 00:20:40,790 And the turning off happened because of the inactivation 411 00:20:40,790 --> 00:20:42,772 gate. 412 00:20:42,772 --> 00:20:43,980 In this case, it's different. 413 00:20:43,980 --> 00:20:47,820 What's turning this thing on is a neurotransmitter binding 414 00:20:47,820 --> 00:20:49,250 that turns it off. 415 00:20:49,250 --> 00:20:51,347 And what turns it off is not inactivation. 416 00:20:51,347 --> 00:20:53,430 It's the fact that the neurotransmitter falls off. 417 00:20:57,050 --> 00:20:59,350 But it has the same time dependence. 418 00:21:01,940 --> 00:21:03,440 It's just different mechanisms. 419 00:21:03,440 --> 00:21:08,618 And then for this, was there a question still about this? 420 00:21:08,618 --> 00:21:09,160 AUDIENCE: No. 421 00:21:09,160 --> 00:21:11,451 [INAUDIBLE] using that with the-- 422 00:21:11,451 --> 00:21:13,360 MICHALE FEE: Oh, with the tie-- it was, OK-- 423 00:21:13,360 --> 00:21:15,670 and you understand why this doesn't look like this, right? 424 00:21:15,670 --> 00:21:15,880 AUDIENCE: Yeah. 425 00:21:15,880 --> 00:21:17,422 MICHALE FEE: The reason that happened 426 00:21:17,422 --> 00:21:21,280 is because it looked like this for most of it, 427 00:21:21,280 --> 00:21:26,410 but it went back down to 0 here as a function of voltage y. 428 00:21:26,410 --> 00:21:28,240 Because of the voltage dependence 429 00:21:28,240 --> 00:21:30,130 shuts the [AUDIO OUT] off down here, 430 00:21:30,130 --> 00:21:32,357 this doesn't have voltage dependent. 431 00:21:36,260 --> 00:21:39,810 It's cool how all this stuff ties together, right? 432 00:21:39,810 --> 00:21:44,790 It's sort of the same stuff we learned for the Hodgkin Huxley, 433 00:21:44,790 --> 00:21:48,180 just applies to this case here. 434 00:21:48,180 --> 00:21:49,850 All right, so there's the circuit. 435 00:21:49,850 --> 00:21:51,600 Here's the model that we described before. 436 00:21:51,600 --> 00:21:57,600 There's a simple soma with a capacitance and some leak 437 00:21:57,600 --> 00:21:58,560 conductance. 438 00:21:58,560 --> 00:22:02,310 And now that is how we would model 439 00:22:02,310 --> 00:22:08,823 attaching a synapse, any kind of a synapse, onto a soma. 440 00:22:08,823 --> 00:22:10,740 And if we wanted the some to be able to spike, 441 00:22:10,740 --> 00:22:14,130 we would add some potassium, some voltage dependent 442 00:22:14,130 --> 00:22:18,530 potassium and some voltage dependent sodium. 443 00:22:18,530 --> 00:22:19,900 All right, any questions? 444 00:22:19,900 --> 00:22:20,420 Yeah. 445 00:22:20,420 --> 00:22:21,845 AUDIENCE: I probably should have asked this a long time ago 446 00:22:21,845 --> 00:22:23,270 and not [INAUDIBLE] circuit. 447 00:22:23,270 --> 00:22:27,550 Do you know whether to have the big line of the battery-- 448 00:22:27,550 --> 00:22:31,870 MICHALE FEE: Oh, yeah, so that's not a dumb question at all. 449 00:22:31,870 --> 00:22:35,860 The answer is don't worry about it. 450 00:22:35,860 --> 00:22:40,450 Like there's a convention that the big one is the plus side. 451 00:22:40,450 --> 00:22:43,390 And I'm not even 100% sure I've been perfectly consistent 452 00:22:43,390 --> 00:22:44,530 in all my slides. 453 00:22:44,530 --> 00:22:46,660 The long line is supposed to be the positive side 454 00:22:46,660 --> 00:22:47,285 of the battery. 455 00:22:47,285 --> 00:22:48,570 AUDIENCE: [INAUDIBLE] 456 00:22:48,570 --> 00:22:49,820 MICHALE FEE: Just don't worry. 457 00:22:49,820 --> 00:22:51,153 Just make one big and one small. 458 00:22:51,153 --> 00:22:54,160 And don't-- just make it a battery symbol. 459 00:22:54,160 --> 00:22:56,070 And I don't care if it's the right way. 460 00:22:56,070 --> 00:22:56,570 OK. 461 00:23:00,327 --> 00:23:00,827 OK? 462 00:23:05,433 --> 00:23:07,600 You don't want to make it too much like a capacitor, 463 00:23:07,600 --> 00:23:09,267 because if they're the same length, then 464 00:23:09,267 --> 00:23:11,490 it looks like a capacitor. 465 00:23:11,490 --> 00:23:16,690 And if you're worried just draw an arrow and write battery. 466 00:23:16,690 --> 00:23:18,330 OK? 467 00:23:18,330 --> 00:23:20,440 All right, good. 468 00:23:20,440 --> 00:23:25,010 OK, so now, let's step back from our voltage clamp of experiment 469 00:23:25,010 --> 00:23:28,180 and attach this synapse to a real neuron, 470 00:23:28,180 --> 00:23:29,980 like this thing, the one that can't spike. 471 00:23:29,980 --> 00:23:34,780 It's just a leaky soma that's hyperpolarized. 472 00:23:34,780 --> 00:23:37,900 And now, what's the voltage in the cell going to do 473 00:23:37,900 --> 00:23:41,590 when we activate that synapse. 474 00:23:41,590 --> 00:23:43,420 What is the voltage here? 475 00:23:43,420 --> 00:23:45,430 We're turning on this conductance. 476 00:23:45,430 --> 00:23:47,320 What that's means is we're making distance 477 00:23:47,320 --> 00:23:49,720 get really small. 478 00:23:49,720 --> 00:23:54,210 So what is the voltage inside the cell going to do? 479 00:23:54,210 --> 00:23:56,433 It's going to approach something. 480 00:23:56,433 --> 00:23:57,600 What's it going to approach? 481 00:24:03,330 --> 00:24:04,980 We have this circuit. 482 00:24:04,980 --> 00:24:07,410 We have a battery and a resistor. 483 00:24:07,410 --> 00:24:11,500 Let's make that resistor really, really big. 484 00:24:11,500 --> 00:24:14,140 That connects the battery between the outside and inside 485 00:24:14,140 --> 00:24:15,070 of our neuron. 486 00:24:15,070 --> 00:24:19,060 And now we make the resistor really small all of a sudden. 487 00:24:19,060 --> 00:24:22,988 What's going to happen to the voltage in here? 488 00:24:22,988 --> 00:24:25,820 AUDIENCE: What is G I? 489 00:24:25,820 --> 00:24:28,820 MICHALE FEE: Sorry, just some other conductance. 490 00:24:28,820 --> 00:24:32,980 And let's just imagine that it's like potassium conductance 491 00:24:32,980 --> 00:24:35,110 that's kind of holding the cell hyperpolarized. 492 00:24:38,020 --> 00:24:40,020 But I don't want you to focus on this right now. 493 00:24:40,020 --> 00:24:41,670 What I want you to focus on is what 494 00:24:41,670 --> 00:24:44,430 would happen here when I turn on that synapse, when 495 00:24:44,430 --> 00:24:46,530 I make the resistor really small, 496 00:24:46,530 --> 00:24:49,140 when I make the conductance really big. 497 00:24:49,140 --> 00:24:52,175 What's going to happen to the voltage inside the cell? 498 00:24:52,175 --> 00:24:53,550 It's going to approach something. 499 00:24:53,550 --> 00:24:57,730 It's going to be dragged toward something. 500 00:24:57,730 --> 00:25:00,950 It's going to be dragged toward the voltage of that battery. 501 00:25:00,950 --> 00:25:04,536 We're hooking that battery up to the inside of our neuron. 502 00:25:04,536 --> 00:25:06,950 Does that makes sense? 503 00:25:06,950 --> 00:25:09,060 OK, so that's what I'm going to show you now. 504 00:25:09,060 --> 00:25:11,678 So if we have an excitatory synapse-- 505 00:25:11,678 --> 00:25:13,220 so what I'm going to show you is what 506 00:25:13,220 --> 00:25:18,680 happens when we activate a glutamatergic excitatory 507 00:25:18,680 --> 00:25:20,900 synapse on a cell. 508 00:25:20,900 --> 00:25:24,572 We're going to record the voltage in the cell. 509 00:25:24,572 --> 00:25:26,280 And we're going to activate that synapse. 510 00:25:26,280 --> 00:25:30,660 And what you see is that this is what 511 00:25:30,660 --> 00:25:33,060 you would see, for example, for the muscle fiber. 512 00:25:33,060 --> 00:25:34,650 You activate the synapse, and you see 513 00:25:34,650 --> 00:25:37,090 that the voltage of the cell-- 514 00:25:37,090 --> 00:25:39,840 if the cell is hyperpolarized, the voltage of the cell 515 00:25:39,840 --> 00:25:41,580 goes up. 516 00:25:41,580 --> 00:25:45,170 If you hold the cell at a higher voltage, 517 00:25:45,170 --> 00:25:47,860 the voltage also goes up, but a little bit less. 518 00:25:47,860 --> 00:25:50,050 If you hold the cell at zero, you 519 00:25:50,050 --> 00:25:51,550 can see you activate that synapse, 520 00:25:51,550 --> 00:25:55,550 but the cell is already at the potential of the battery. 521 00:25:55,550 --> 00:25:58,540 And so there's no current and no change in the voltage. 522 00:25:58,540 --> 00:26:01,458 If you hold the cell at a positive voltage, 523 00:26:01,458 --> 00:26:03,250 and you activate the synapse, again, you're 524 00:26:03,250 --> 00:26:07,790 connecting the cell to a battery that has 0 volts. 525 00:26:07,790 --> 00:26:10,250 And so the voltage goes down. 526 00:26:10,250 --> 00:26:14,350 So here's what I want to convey here, 527 00:26:14,350 --> 00:26:18,870 that when you activate a synapse, it forces the cell, 528 00:26:18,870 --> 00:26:22,440 forces the voltage in the cell, to approach 529 00:26:22,440 --> 00:26:26,370 the voltage of the reversal potential of the synapse, 530 00:26:26,370 --> 00:26:29,190 the voltage of that battery. 531 00:26:29,190 --> 00:26:30,900 Is that clear? 532 00:26:30,900 --> 00:26:31,679 Yes. 533 00:26:31,679 --> 00:26:35,990 AUDIENCE: So [INAUDIBLE] 534 00:26:35,990 --> 00:26:38,570 MICHALE FEE: It increases the conductance. 535 00:26:38,570 --> 00:26:40,830 Current flows into this cell. 536 00:26:40,830 --> 00:26:43,460 And it flows into the cell in a direction 537 00:26:43,460 --> 00:26:46,610 so that the voltage of approaches the equilibrium 538 00:26:46,610 --> 00:26:47,830 potential. 539 00:26:47,830 --> 00:26:48,952 Yes. 540 00:26:48,952 --> 00:26:51,758 AUDIENCE: [INAUDIBLE] 541 00:26:51,758 --> 00:26:52,800 MICHALE FEE: What's that? 542 00:26:52,800 --> 00:26:54,258 AUDIENCE: [INAUDIBLE] 543 00:26:54,258 --> 00:26:56,110 MICHALE FEE: Ah, yes, good. 544 00:26:56,110 --> 00:26:57,990 In fact, that's a great way to phrase it, 545 00:26:57,990 --> 00:26:59,790 because that kind of experiment here 546 00:26:59,790 --> 00:27:02,340 where we're measuring the voltage inside the cell 547 00:27:02,340 --> 00:27:04,740 is called current clamp experiment. 548 00:27:04,740 --> 00:27:07,680 So there's voltage clamp, where you 549 00:27:07,680 --> 00:27:13,250 force the voltage to be constant by varying the current. 550 00:27:13,250 --> 00:27:17,420 Here, we're holding the current constant, clamping the current, 551 00:27:17,420 --> 00:27:19,215 and measuring the voltage. 552 00:27:19,215 --> 00:27:23,540 AUDIENCE: [INAUDIBLE] 553 00:27:23,540 --> 00:27:25,900 MICHALE FEE: Yeah, let's just go back to the setup 554 00:27:25,900 --> 00:27:28,030 here, this experiment here. 555 00:27:28,030 --> 00:27:29,763 You don't you don't set it up like this. 556 00:27:29,763 --> 00:27:31,930 You set it up like we had on the first day of class, 557 00:27:31,930 --> 00:27:34,260 where you just have a current source connected here 558 00:27:34,260 --> 00:27:41,620 and a volt meter attached to this electrode. 559 00:27:41,620 --> 00:27:42,850 I didn't use that word. 560 00:27:42,850 --> 00:27:45,382 But that was the very first experiment we did. 561 00:27:45,382 --> 00:27:47,710 I think on the second day of class, 562 00:27:47,710 --> 00:27:51,010 we had a cell with a electrode to inject current, 563 00:27:51,010 --> 00:27:52,450 electrode to measure voltage. 564 00:27:52,450 --> 00:27:54,010 That was a current clamp experiment, 565 00:27:54,010 --> 00:27:57,360 because we're holding the current at some constant value. 566 00:27:57,360 --> 00:27:59,020 OK? 567 00:27:59,020 --> 00:28:01,420 Here, we're holding the voltage at some constant value 568 00:28:01,420 --> 00:28:04,040 and measuring current. 569 00:28:04,040 --> 00:28:09,640 All right, so the idea is really simple, 570 00:28:09,640 --> 00:28:11,620 when you have a synapse, the synapse 571 00:28:11,620 --> 00:28:13,180 has a reversal potential. 572 00:28:13,180 --> 00:28:15,040 When you activate the synapse, the cell 573 00:28:15,040 --> 00:28:17,740 is dragged toward the reversal potential. 574 00:28:17,740 --> 00:28:19,960 Here, the reversal potential was zero. 575 00:28:19,960 --> 00:28:21,940 So when I activate the synapse, the voltage 576 00:28:21,940 --> 00:28:24,060 goes toward the reversal potential. 577 00:28:24,060 --> 00:28:24,788 Notice-- yes. 578 00:28:24,788 --> 00:28:26,496 AUDIENCE: Oh, just a very basic question. 579 00:28:26,496 --> 00:28:32,809 So is [INAUDIBLE] the top half is like the synaptic face 580 00:28:32,809 --> 00:28:35,345 of the circuit and the bottom half is like-- 581 00:28:35,345 --> 00:28:37,720 MICHALE FEE: Are you talking about like here versus here? 582 00:28:37,720 --> 00:28:40,780 Yeah, so I've put that pink box around the synapse. 583 00:28:40,780 --> 00:28:41,650 AUDIENCE: OK. 584 00:28:41,650 --> 00:28:43,870 MICHALE FEE: That's the circuit that 585 00:28:43,870 --> 00:28:47,480 corresponds to having a synapse attached to the cell. 586 00:28:47,480 --> 00:28:54,698 And this is the circuit that we developed several weeks ago. 587 00:28:54,698 --> 00:28:55,240 AUDIENCE: OK. 588 00:28:55,240 --> 00:28:58,120 But it's acting like the presynaptic-- 589 00:28:58,120 --> 00:29:00,520 like a cell or-- 590 00:29:00,520 --> 00:29:02,590 MICHALE FEE: Oh, no, the presynaptic cell 591 00:29:02,590 --> 00:29:04,240 is not part of this picture. 592 00:29:04,240 --> 00:29:09,010 The presynaptic cell is kind of like spritzing neurotransmitter 593 00:29:09,010 --> 00:29:15,820 onto this thing, which increases the conductance, which 594 00:29:15,820 --> 00:29:19,590 is the same as reducing the size of a resistor. 595 00:29:19,590 --> 00:29:22,490 Does that makes sense? 596 00:29:22,490 --> 00:29:23,455 Yes. 597 00:29:23,455 --> 00:29:25,580 AUDIENCE: So is the reversal potential always going 598 00:29:25,580 --> 00:29:27,890 to be zero or like just like in this specific example? 599 00:29:27,890 --> 00:29:29,060 MICHALE FEE: Great question. 600 00:29:29,060 --> 00:29:32,210 So the reversal potential is different for different kinds 601 00:29:32,210 --> 00:29:33,500 of synapses. 602 00:29:33,500 --> 00:29:37,010 You can see that this synapse, this kind of synapse 603 00:29:37,010 --> 00:29:40,820 here, if I'm hyperpolarized, it pushes the voltage of the cell 604 00:29:40,820 --> 00:29:41,940 up. 605 00:29:41,940 --> 00:29:45,080 What kind of synapse do you think that is? 606 00:29:45,080 --> 00:29:46,410 An excitatory synapse. 607 00:29:46,410 --> 00:29:48,210 But notice something really cool. 608 00:29:48,210 --> 00:29:50,160 An excitatory synapse doesn't always 609 00:29:50,160 --> 00:29:52,590 push the voltage of the cell up. 610 00:29:52,590 --> 00:29:54,330 If the cell is sitting up here, it 611 00:29:54,330 --> 00:29:57,330 can push the voltage of the cell down. 612 00:29:57,330 --> 00:29:58,390 OK? 613 00:29:58,390 --> 00:29:59,140 Yes. 614 00:29:59,140 --> 00:30:02,200 AUDIENCE: Why doesn't it just stay up? 615 00:30:02,200 --> 00:30:03,040 MICHALE FEE: Why? 616 00:30:03,040 --> 00:30:03,550 Great. 617 00:30:03,550 --> 00:30:04,360 So great question. 618 00:30:04,360 --> 00:30:06,130 You can probably answer that already. 619 00:30:10,585 --> 00:30:12,570 AUDIENCE: Well, it's some-- 620 00:30:12,570 --> 00:30:15,080 MICHALE FEE: Yeah. 621 00:30:15,080 --> 00:30:15,760 Yeah. 622 00:30:15,760 --> 00:30:18,420 I'm hearing a bunch of good answers. 623 00:30:18,420 --> 00:30:21,590 So what happens is we're stimulating the synapse here, 624 00:30:21,590 --> 00:30:23,195 releases neurotransmitter. 625 00:30:23,195 --> 00:30:25,100 The conductance goes up. 626 00:30:25,100 --> 00:30:27,630 Current flows in, depolarizes the cell, 627 00:30:27,630 --> 00:30:29,990 neurotransmitter unbinds. 628 00:30:29,990 --> 00:30:31,280 Current stops. 629 00:30:31,280 --> 00:30:34,220 And this thing brings the cell back down 630 00:30:34,220 --> 00:30:39,030 to its starting point, this other thing. 631 00:30:39,030 --> 00:30:41,210 Yeah, this thing is kind of holding the cell 632 00:30:41,210 --> 00:30:43,970 at some hyperpolarized potential. 633 00:30:43,970 --> 00:30:47,230 AUDIENCE: So even though they've lost a current. 634 00:30:47,230 --> 00:30:50,340 MICHALE FEE: The current is turning on and then turning 635 00:30:50,340 --> 00:30:51,620 off. 636 00:30:51,620 --> 00:30:53,660 Remember, the current-- here it is right here-- 637 00:30:53,660 --> 00:30:56,750 the current is turning on as the conductance turns on. 638 00:30:56,750 --> 00:30:58,610 And then when the conductance goes to zero, 639 00:30:58,610 --> 00:31:00,073 the current goes to zero. 640 00:31:00,073 --> 00:31:03,860 AUDIENCE: Oh, I thought it was a big current clamp. 641 00:31:03,860 --> 00:31:05,770 MICHALE FEE: No. 642 00:31:05,770 --> 00:31:09,170 The experiment we're doing is injecting constant current 643 00:31:09,170 --> 00:31:09,920 into the cell. 644 00:31:09,920 --> 00:31:16,260 And that's how we hold the cell at these different sort of kind 645 00:31:16,260 --> 00:31:18,250 of average voltages. 646 00:31:18,250 --> 00:31:21,370 OK, maybe I should say-- yes. 647 00:31:21,370 --> 00:31:31,940 AUDIENCE: So I just [INAUDIBLE] 648 00:31:31,940 --> 00:31:33,500 MICHALE FEE: Makes it do this? 649 00:31:33,500 --> 00:31:36,302 AUDIENCE: Well, I don't understand how that changes. 650 00:31:36,302 --> 00:31:39,630 I just always want positive ions to flow in. 651 00:31:39,630 --> 00:31:40,880 MICHALE FEE: Yeah. 652 00:31:40,880 --> 00:31:43,550 So positive ions flowing into the cell 653 00:31:43,550 --> 00:31:46,880 raise the voltage in this. 654 00:31:46,880 --> 00:31:51,205 AUDIENCE: But I don't understand if the inside 655 00:31:51,205 --> 00:31:55,040 of cell is already positive, why adding more positive-- 656 00:31:55,040 --> 00:31:56,060 MICHALE FEE: Oh. 657 00:31:56,060 --> 00:31:57,210 OK, great question. 658 00:31:57,210 --> 00:31:58,418 You're talking about up here. 659 00:31:58,418 --> 00:32:01,340 OK, so let me just back up and explain one thing that maybe I 660 00:32:01,340 --> 00:32:02,600 didn't explain very well. 661 00:32:02,600 --> 00:32:05,990 In this experiment, we're injecting current 662 00:32:05,990 --> 00:32:08,840 through our current electrode to just hold 663 00:32:08,840 --> 00:32:14,000 the cell at different voltages while we stimulate the synapse. 664 00:32:14,000 --> 00:32:15,500 Does that makes sense? 665 00:32:15,500 --> 00:32:19,090 Down here, let's say, we're not injecting any current. 666 00:32:19,090 --> 00:32:20,840 And then we inject a little bit of current 667 00:32:20,840 --> 00:32:22,700 to kind of hold the cell up here. 668 00:32:22,700 --> 00:32:26,700 And we activate the synapse and measure changes from there. 669 00:32:26,700 --> 00:32:27,871 Does that make sense? 670 00:32:27,871 --> 00:32:29,835 AUDIENCE: So when it's a current clamp, 671 00:32:29,835 --> 00:32:31,310 it just leaves the input the same? 672 00:32:31,310 --> 00:32:32,185 MICHALE FEE: Exactly. 673 00:32:32,185 --> 00:32:33,980 You're just turning a knob and saying 674 00:32:33,980 --> 00:32:35,270 I'm going to put in 1 nanoamp. 675 00:32:35,270 --> 00:32:37,760 And that's just going to kind of hold the cell up here. 676 00:32:37,760 --> 00:32:39,800 And then I activate the synapse and ask 677 00:32:39,800 --> 00:32:42,380 how does the voltage change. 678 00:32:42,380 --> 00:32:43,785 OK? 679 00:32:43,785 --> 00:32:44,285 Oh. 680 00:32:44,285 --> 00:32:45,767 AUDIENCE: That's not my question. 681 00:32:45,767 --> 00:32:46,600 MICHALE FEE: I know. 682 00:32:46,600 --> 00:32:47,150 AUDIENCE: My question-- 683 00:32:47,150 --> 00:32:48,950 MICHALE FEE: But I realized-- your question 684 00:32:48,950 --> 00:32:50,270 is why does this go down? 685 00:32:50,270 --> 00:32:51,645 AUDIENCE: Like I thought that's-- 686 00:32:51,645 --> 00:32:52,490 MICHALE FEE: Yeah. 687 00:32:52,490 --> 00:32:53,600 Exactly. 688 00:32:53,600 --> 00:32:54,290 Exactly. 689 00:32:54,290 --> 00:32:55,880 Isn't that cool? 690 00:32:55,880 --> 00:32:59,210 Excitatory synapses are not always inject-- so 691 00:32:59,210 --> 00:33:00,290 what happens up here? 692 00:33:00,290 --> 00:33:02,150 You're holding the cell up here. 693 00:33:02,150 --> 00:33:03,530 And now you activate the synapse. 694 00:33:03,530 --> 00:33:05,730 And the voltage actually goes down. 695 00:33:05,730 --> 00:33:08,570 And the answer is that if you're holding 696 00:33:08,570 --> 00:33:12,360 this cell up here positive, more positive than here, 697 00:33:12,360 --> 00:33:13,850 when you turn on that conductance, 698 00:33:13,850 --> 00:33:16,663 the current goes the other way. 699 00:33:16,663 --> 00:33:18,330 AUDIENCE: Passed the reversal potential. 700 00:33:18,330 --> 00:33:21,260 MICHALE FEE: So you've passed the reversal potential. 701 00:33:21,260 --> 00:33:24,310 You're holding the cell up here. 702 00:33:24,310 --> 00:33:27,930 And so [AUDIO OUT] turn on the synapse, 703 00:33:27,930 --> 00:33:30,300 the current flows the other direction. 704 00:33:30,300 --> 00:33:31,830 You have a positive current, which 705 00:33:31,830 --> 00:33:36,110 is positive ions flowing out, which 706 00:33:36,110 --> 00:33:38,210 lowers the voltage of the cell. 707 00:33:38,210 --> 00:33:41,090 So the way to think about this is 708 00:33:41,090 --> 00:33:45,755 that when you have a synapse, you turn the synapse on, 709 00:33:45,755 --> 00:33:48,140 it doesn't matter where the voltage is, 710 00:33:48,140 --> 00:33:52,300 it's always driving it toward the reversal potential. 711 00:33:52,300 --> 00:33:54,570 And if you start above the reversal potential, 712 00:33:54,570 --> 00:33:56,180 the voltage will go down. 713 00:33:56,180 --> 00:33:58,230 If you start below the reversal potential, 714 00:33:58,230 --> 00:33:59,490 the voltage will go up. 715 00:34:02,060 --> 00:34:05,854 It's like not what you learned in 901, right? 716 00:34:05,854 --> 00:34:06,830 AUDIENCE: No. 717 00:34:06,830 --> 00:34:07,760 MICHALE FEE: This is-- 718 00:34:07,760 --> 00:34:09,920 yeah. 719 00:34:09,920 --> 00:34:12,100 But this is how it really works. 720 00:34:12,100 --> 00:34:12,600 OK? 721 00:34:15,560 --> 00:34:19,250 Excitatory synapses, the reason you 722 00:34:19,250 --> 00:34:22,628 think of excitatory synapses as always pushing the voltage up 723 00:34:22,628 --> 00:34:24,170 is because most of the time, the cell 724 00:34:24,170 --> 00:34:25,337 is sitting [AUDIO OUT] here. 725 00:34:32,480 --> 00:34:35,449 But this is going to become much more important and obvious when 726 00:34:35,449 --> 00:34:37,340 we're talking about inhibitory synapses. 727 00:34:37,340 --> 00:34:39,290 So let's talk about inhibitory segments. 728 00:34:39,290 --> 00:34:43,820 So here's a model with the synaptic reversal at zero. 729 00:34:43,820 --> 00:34:46,670 All excitatory synapses have their reversal potential 730 00:34:46,670 --> 00:34:48,010 around zero. 731 00:34:48,010 --> 00:34:51,739 The neuromuscular junction, the glutamatergic synapse, 732 00:34:51,739 --> 00:34:54,110 they're all basically non-specific 733 00:34:54,110 --> 00:34:58,080 pores that have a reversal potential of zero. 734 00:34:58,080 --> 00:35:02,160 Inhibitory synapses are different. 735 00:35:02,160 --> 00:35:04,700 So excitatory-- the reason we call it 736 00:35:04,700 --> 00:35:08,390 an excitatory synapse is because that reversal potential 737 00:35:08,390 --> 00:35:12,720 is above the threshold for the neuron to spike. 738 00:35:12,720 --> 00:35:15,090 And so when you activate the synapse, 739 00:35:15,090 --> 00:35:17,310 you're pushing the voltage of the cell 740 00:35:17,310 --> 00:35:21,970 always toward a voltage that's above the spiking threshold. 741 00:35:21,970 --> 00:35:24,290 That's why it's called an excitatory synapse. 742 00:35:27,600 --> 00:35:30,540 And those are called excitatory postsynaptic potentials, 743 00:35:30,540 --> 00:35:32,070 or EPSP. 744 00:35:32,070 --> 00:35:33,930 That little bump is an EPSP. 745 00:35:36,860 --> 00:35:40,200 All right, now, inhibitory synapses look really different. 746 00:35:40,200 --> 00:35:44,120 And now the effect that I'm talking about is important. 747 00:35:44,120 --> 00:35:46,550 With an inhibitory synapse, the reversal potential 748 00:35:46,550 --> 00:35:48,710 is around minus 75. 749 00:35:48,710 --> 00:35:53,600 Remember, most inhibitory synapses are chloride channels. 750 00:35:53,600 --> 00:35:55,910 And chloride, do you remember on the lecture 751 00:35:55,910 --> 00:35:59,370 about the equilibrium potentials? 752 00:35:59,370 --> 00:36:02,730 The reversal potential for chloride channels 753 00:36:02,730 --> 00:36:04,890 is around minus 75. 754 00:36:04,890 --> 00:36:10,890 And that's why the synaptic reversal potential is minus 75. 755 00:36:10,890 --> 00:36:14,100 And now, you can see that if you hold the cell-- 756 00:36:14,100 --> 00:36:16,530 so here's where a cell normally sits. 757 00:36:16,530 --> 00:36:19,230 You activate the synapse. 758 00:36:19,230 --> 00:36:21,580 The voltage goes down. 759 00:36:21,580 --> 00:36:22,080 All right. 760 00:36:22,080 --> 00:36:23,410 And why does it go down? 761 00:36:23,410 --> 00:36:26,710 Because it's pulled toward the equilibrium 762 00:36:26,710 --> 00:36:31,630 potential for the chloride channel, chloride ion. 763 00:36:31,630 --> 00:36:34,940 Now, notice that-- 764 00:36:34,940 --> 00:36:38,680 OK, so as the cell is more and more depolarized, 765 00:36:38,680 --> 00:36:41,020 you can see that it's more strongly 766 00:36:41,020 --> 00:36:44,950 pulled toward [AUDIO OUT] the voltage change is bigger. 767 00:36:44,950 --> 00:36:46,900 If you hold the cell at minus 75, 768 00:36:46,900 --> 00:36:51,460 there's no voltage change at all from activating 769 00:36:51,460 --> 00:36:54,190 an inhibitory synapse. 770 00:36:54,190 --> 00:36:58,940 And if you hyperpolarize the cell even more, 771 00:36:58,940 --> 00:37:00,530 you can see that when you activate 772 00:37:00,530 --> 00:37:03,740 an inhibitory synapse the voltage of the cell 773 00:37:03,740 --> 00:37:07,170 actually goes up. 774 00:37:07,170 --> 00:37:09,660 So inhibitory synapses don't always 775 00:37:09,660 --> 00:37:12,160 make the potential of the cell go down. 776 00:37:12,160 --> 00:37:15,300 In fact, sometimes they can make this cell go up. 777 00:37:15,300 --> 00:37:18,630 In fact, what's really cool is in juvenile animals, 778 00:37:18,630 --> 00:37:21,030 the chloride reversal potential, there's 779 00:37:21,030 --> 00:37:24,900 more chloride inside of a cell than there is in an adult. 780 00:37:24,900 --> 00:37:27,150 And so the reversal potential of the chloride channels 781 00:37:27,150 --> 00:37:29,220 is actually up here. 782 00:37:29,220 --> 00:37:32,160 And chloride inhibitory synapses can actually 783 00:37:32,160 --> 00:37:33,150 make neurons spike. 784 00:37:36,550 --> 00:37:38,065 You can see where this thing sits. 785 00:37:38,065 --> 00:37:42,076 It just depends on the concentration of chloride ions. 786 00:37:42,076 --> 00:37:45,020 Most of the time inhibitory synapses 787 00:37:45,020 --> 00:37:47,450 have a reversal potential that's minus 75. 788 00:37:47,450 --> 00:37:51,200 And we call that inhibitory because the reversal potential 789 00:37:51,200 --> 00:37:56,170 of the synapse is less than the spiking threshold. 790 00:37:56,170 --> 00:38:01,640 AUDIENCE: What [INAUDIBLE] reversal potential? 791 00:38:01,640 --> 00:38:03,000 MICHALE FEE: Just the-- 792 00:38:03,000 --> 00:38:05,010 OK, you know the answer to that question. 793 00:38:05,010 --> 00:38:05,510 You tell me. 794 00:38:11,620 --> 00:38:13,425 So what are the two things-- 795 00:38:13,425 --> 00:38:14,050 yeah, go ahead. 796 00:38:14,050 --> 00:38:15,390 AUDIENCE: The type of ion. 797 00:38:15,390 --> 00:38:16,140 MICHALE FEE: Good. 798 00:38:16,140 --> 00:38:17,580 The type of iron. 799 00:38:17,580 --> 00:38:18,420 And one more thing. 800 00:38:22,440 --> 00:38:25,110 There were two things we need to have a battery in a neuron. 801 00:38:25,110 --> 00:38:26,430 What are they? 802 00:38:26,430 --> 00:38:29,225 Anybody know? 803 00:38:29,225 --> 00:38:30,580 AUDIENCE: [INAUDIBLE] 804 00:38:30,580 --> 00:38:33,375 MICHALE FEE: And? 805 00:38:33,375 --> 00:38:35,750 AUDIENCE: [INAUDIBLE] 806 00:38:35,750 --> 00:38:40,920 MICHALE FEE: Ion selective permeability. 807 00:38:40,920 --> 00:38:43,020 So the reversal potential depends 808 00:38:43,020 --> 00:38:46,950 on what ion that channel is selective for 809 00:38:46,950 --> 00:38:49,980 and the concentrations of that ion 810 00:38:49,980 --> 00:38:51,300 inside and outside the cell. 811 00:38:55,100 --> 00:38:59,810 So for an inhibitory synapse, there are two types. 812 00:38:59,810 --> 00:39:02,170 There are chloride reversal potentials, 813 00:39:02,170 --> 00:39:05,210 the chloride channels that have a reverse potential minus 75. 814 00:39:05,210 --> 00:39:08,740 And there are also potassium channels 815 00:39:08,740 --> 00:39:10,750 that serve an inhibitory function that 816 00:39:10,750 --> 00:39:12,280 can be activated by synapses. 817 00:39:12,280 --> 00:39:15,148 And they have a reversal potential more like minus 80. 818 00:39:15,148 --> 00:39:20,150 AUDIENCE: [INAUDIBLE] develop [INAUDIBLE] it's 819 00:39:20,150 --> 00:39:21,930 not chloride channel is not changing. 820 00:39:21,930 --> 00:39:23,710 So what the ion channel-- 821 00:39:23,710 --> 00:39:25,128 MICHALE FEE: It's the ion concen-- 822 00:39:25,128 --> 00:39:26,170 AUDIENCE: Change so the-- 823 00:39:26,170 --> 00:39:28,396 MICHALE FEE: The concentration that's different. 824 00:39:32,500 --> 00:39:33,890 OK? 825 00:39:33,890 --> 00:39:36,780 Cool. 826 00:39:36,780 --> 00:39:38,550 You see this kind of stuff all the time. 827 00:39:38,550 --> 00:39:41,100 Inhibitory postsynaptic potentials 828 00:39:41,100 --> 00:39:43,260 are often upward going. 829 00:39:47,270 --> 00:39:49,760 Somebody will be super impressed with you 830 00:39:49,760 --> 00:39:52,820 if you look at a trace like this and you say, 831 00:39:52,820 --> 00:39:56,180 is that an EPSP or an IPSP? 832 00:39:56,180 --> 00:39:59,420 Because you don't know it just by looking at it. 833 00:39:59,420 --> 00:40:01,040 Most people would assume it's an EPSP. 834 00:40:04,544 --> 00:40:05,470 Yeah. 835 00:40:05,470 --> 00:40:08,830 AUDIENCE: Was [INAUDIBLE] to cause like a spike? 836 00:40:08,830 --> 00:40:10,570 MICHALE FEE: Well, so what do you think? 837 00:40:16,030 --> 00:40:19,170 It's inhibitory if the reversal potential [INAUDIBLE] 838 00:40:19,170 --> 00:40:20,650 in the threshold. 839 00:40:20,650 --> 00:40:25,120 So no matter how strong that inhibitory synapse is, 840 00:40:25,120 --> 00:40:28,840 can it ever cause a spike if the reversal potential 841 00:40:28,840 --> 00:40:30,413 is less than the threshold? 842 00:40:33,362 --> 00:40:34,320 All right, let's go on. 843 00:40:34,320 --> 00:40:35,410 Any questions about this. 844 00:40:35,410 --> 00:40:36,760 It's so fundamental. 845 00:40:36,760 --> 00:40:37,370 Yeah. 846 00:40:37,370 --> 00:40:45,260 AUDIENCE: [INAUDIBLE] potential [INAUDIBLE] 847 00:40:45,260 --> 00:40:48,460 MICHALE FEE: So it's normally around minus 60 minus 848 00:40:48,460 --> 00:40:52,215 [AUDIO OUT] minus 75. 849 00:40:52,215 --> 00:40:52,715 OK? 850 00:40:55,990 --> 00:40:58,810 OK, let's go on. 851 00:40:58,810 --> 00:41:02,170 All right, let me just talk a little bit more 852 00:41:02,170 --> 00:41:04,760 about this conductance. 853 00:41:04,760 --> 00:41:09,700 So if you do a single channel patch experiment, 854 00:41:09,700 --> 00:41:12,110 you can take an electrode. 855 00:41:12,110 --> 00:41:14,260 Remember, I showed you what it looks 856 00:41:14,260 --> 00:41:16,780 like if you take an electrode and you stick it 857 00:41:16,780 --> 00:41:19,990 on a single sodium channel or a single potassium channel. 858 00:41:19,990 --> 00:41:21,650 Well, you can do the same thing. 859 00:41:21,650 --> 00:41:27,190 You can stick it on a neurotransmitter receptor. 860 00:41:27,190 --> 00:41:30,580 You can flow neurotransmitter over the receptor. 861 00:41:33,620 --> 00:41:36,520 And what you see is that when you put the neurotransmitter 862 00:41:36,520 --> 00:41:40,970 on, just like sodium and potassium channels, 863 00:41:40,970 --> 00:41:46,740 it flickers between an open state and a closed state. 864 00:41:46,740 --> 00:41:48,080 So it has two states-- 865 00:41:48,080 --> 00:41:50,420 open state and closed state. 866 00:41:50,420 --> 00:41:54,320 You can do the same kind of modeling of it 867 00:41:54,320 --> 00:41:58,880 as where the kinetic rate equation with two states. 868 00:41:58,880 --> 00:42:00,607 You can write down the probability 869 00:42:00,607 --> 00:42:02,690 that the channel is in the open and closed states. 870 00:42:02,690 --> 00:42:05,700 That's going to be a function of what? 871 00:42:05,700 --> 00:42:10,790 Like neurotransmitter concentration and time, right? 872 00:42:10,790 --> 00:42:13,580 And you can write down the total synaptic conductance 873 00:42:13,580 --> 00:42:18,020 as the conductance of a single open neurotransmitter 874 00:42:18,020 --> 00:42:20,810 receptor times the number of neurotransmitter 875 00:42:20,810 --> 00:42:24,230 receptors times the probability that any of them is open, 876 00:42:24,230 --> 00:42:27,781 any one of them is open. 877 00:42:27,781 --> 00:42:30,420 And so now, let's think about this probability 878 00:42:30,420 --> 00:42:34,630 as a function of time. 879 00:42:34,630 --> 00:42:36,970 So we can model the neurotransmitter receptors 880 00:42:36,970 --> 00:42:39,920 and write down the probability that it's open. 881 00:42:39,920 --> 00:42:44,000 The probability that's closed, then has to be 1 minus p. 882 00:42:44,000 --> 00:42:47,210 Alpha and beta are rate constants. 883 00:42:47,210 --> 00:42:52,230 1 over time, they have units of 1 over time. 884 00:42:52,230 --> 00:42:54,890 And what controls the rate at which the channels open? 885 00:42:57,750 --> 00:42:58,290 Good. 886 00:42:58,290 --> 00:43:00,480 So alpha will depend on the concentration 887 00:43:00,480 --> 00:43:01,470 of neurotransmitter. 888 00:43:01,470 --> 00:43:05,310 That controls the rate at which closed channels open. 889 00:43:05,310 --> 00:43:10,050 And how about open to closed? 890 00:43:10,050 --> 00:43:13,020 It's not the concentration of the neurotransmitter. 891 00:43:13,020 --> 00:43:14,942 It'll be something else. 892 00:43:14,942 --> 00:43:16,295 AUDIENCE: [INAUDIBLE] 893 00:43:16,295 --> 00:43:17,170 MICHALE FEE: Exactly. 894 00:43:17,170 --> 00:43:19,630 So there will be basically some rate 895 00:43:19,630 --> 00:43:22,600 constant for a neurotransmitter unwinding. 896 00:43:22,600 --> 00:43:23,743 OK? 897 00:43:23,743 --> 00:43:24,910 All right, so let's do that. 898 00:43:24,910 --> 00:43:26,540 So here's that model. 899 00:43:26,540 --> 00:43:30,730 This is a simplified version of the Magleby-Stevens model. 900 00:43:30,730 --> 00:43:31,880 And it looks like this. 901 00:43:31,880 --> 00:43:35,040 There's a close and an open state. 902 00:43:35,040 --> 00:43:40,690 The open state corresponds to the closed neurotransmitter 903 00:43:40,690 --> 00:43:44,140 receptor R binding to a neurotransmitter, 904 00:43:44,140 --> 00:43:46,460 an unbound neurotransmitter molecule, 905 00:43:46,460 --> 00:43:50,030 forming a complex, bound receptor complex. 906 00:43:50,030 --> 00:43:51,850 There's usually another step-- 907 00:43:51,850 --> 00:43:54,670 the way this is usually modeled in the Magleby-Stevens model 908 00:43:54,670 --> 00:43:57,280 is that the bound receptor complex is closed 909 00:43:57,280 --> 00:43:59,523 and then it opens in another transition. 910 00:43:59,523 --> 00:44:01,940 But we're just going to keep it simple and do it this way. 911 00:44:01,940 --> 00:44:05,230 So we have a closed state unbound neurotransmitter 912 00:44:05,230 --> 00:44:09,040 receptor binds to an unbound neurotransmitter's receptor 913 00:44:09,040 --> 00:44:12,670 molecule and forms our bound receptor complex 914 00:44:12,670 --> 00:44:14,050 that is then open. 915 00:44:14,050 --> 00:44:17,550 So that's P. And that's 1 minus P. 916 00:44:17,550 --> 00:44:19,650 And we can just write down the rate equation just 917 00:44:19,650 --> 00:44:22,410 the same way that we did for analyze the time 918 00:44:22,410 --> 00:44:26,070 dependence of the sodium channel or the potassium channel. 919 00:44:26,070 --> 00:44:27,420 Isn't that amazing? 920 00:44:27,420 --> 00:44:29,520 All that stuff we learned for Hodgkin-Huxley, 921 00:44:29,520 --> 00:44:34,635 just you can use all the same machinery here. 922 00:44:34,635 --> 00:44:36,960 OK? 923 00:44:36,960 --> 00:44:40,790 OK, so that's a simple model. 924 00:44:40,790 --> 00:44:43,460 And you can take a simplification of it. 925 00:44:43,460 --> 00:44:46,190 We're going to assume that the binding is very fast, 926 00:44:46,190 --> 00:44:48,980 that the alpha is very fast. 927 00:44:48,980 --> 00:44:53,150 So that when you put a pulse of neurotransmitter concentration 928 00:44:53,150 --> 00:44:56,313 onto the synapse, the probability of being open, 929 00:44:56,313 --> 00:44:58,230 we're going to assume that this is super fast. 930 00:44:58,230 --> 00:45:01,610 So that the rate at which you go from unbound to bound 931 00:45:01,610 --> 00:45:04,620 is very high. 932 00:45:04,620 --> 00:45:07,590 And now, the neurotransmitter goes away. 933 00:45:07,590 --> 00:45:10,650 And you can see zero concentration here. 934 00:45:10,650 --> 00:45:13,650 Let's say you bind, the probability of being open 935 00:45:13,650 --> 00:45:14,580 gets big. 936 00:45:14,580 --> 00:45:16,980 And then the neurotransmitter goes away. 937 00:45:16,980 --> 00:45:18,630 You can see that this first term goes 938 00:45:18,630 --> 00:45:22,020 to 0, because the neurotransmitter 939 00:45:22,020 --> 00:45:25,150 concentration is zero. 940 00:45:25,150 --> 00:45:28,990 You can see that dP/dt is just minus beta P. 941 00:45:28,990 --> 00:45:31,910 And that's just an exponential decay. 942 00:45:31,910 --> 00:45:35,320 So the model is bind neurotransmitter 943 00:45:35,320 --> 00:45:38,350 opens the neurotransmitter receptor. 944 00:45:38,350 --> 00:45:39,680 Neurotransmitter goes away. 945 00:45:39,680 --> 00:45:42,460 And then there's an exponential decay probability 946 00:45:42,460 --> 00:45:43,860 that you're in the open state. 947 00:45:43,860 --> 00:45:44,360 Yes. 948 00:45:44,360 --> 00:45:46,018 AUDIENCE: So like in a real synapse, 949 00:45:46,018 --> 00:45:48,258 the neurotransmitter wouldn't like go away, right? 950 00:45:48,258 --> 00:45:49,300 MICHALE FEE: What's that? 951 00:45:49,300 --> 00:45:51,100 Oh, yeah, the neurotransmitter goes away. 952 00:45:51,100 --> 00:45:52,440 I forgot to say that. 953 00:45:52,440 --> 00:45:55,220 It's a super important point. 954 00:45:55,220 --> 00:45:57,850 There's one more step that I forgot to include. 955 00:45:57,850 --> 00:46:00,040 Habib is nodding at me like, yeah you forgot that. 956 00:46:03,910 --> 00:46:05,410 What happens is the neurotransmitter 957 00:46:05,410 --> 00:46:07,540 goes into the cleft. 958 00:46:07,540 --> 00:46:12,450 And it gets taken up by neurotransmitter-- 959 00:46:12,450 --> 00:46:13,830 what they called again, Habib? 960 00:46:13,830 --> 00:46:14,690 AUDIENCE: Reuptake. 961 00:46:14,690 --> 00:46:15,607 MICHALE FEE: Reuptake. 962 00:46:15,607 --> 00:46:17,820 Thank you. 963 00:46:17,820 --> 00:46:22,870 That neurotransmitter gets bound by receptors 964 00:46:22,870 --> 00:46:25,960 on glia and the presynaptic terminal 965 00:46:25,960 --> 00:46:30,960 and gets pumped out of the synaptic cleft. 966 00:46:30,960 --> 00:46:35,460 So that's what makes this go away, in addition to diffusion. 967 00:46:35,460 --> 00:46:36,130 OK. 968 00:46:36,130 --> 00:46:39,214 AUDIENCE: [INAUDIBLE] like the time dependence 969 00:46:39,214 --> 00:46:40,520 of the concentration-- 970 00:46:40,520 --> 00:46:41,870 MICHALE FEE: So this is-- 971 00:46:41,870 --> 00:46:42,980 in the full model you do. 972 00:46:42,980 --> 00:46:44,480 And, in fact, what this really looks 973 00:46:44,480 --> 00:46:48,290 like is this kind of turns on more slowly and then goes away 974 00:46:48,290 --> 00:46:49,580 with an exponential. 975 00:46:49,580 --> 00:46:53,150 But I'm just kind of walking you through this super simplified 976 00:46:53,150 --> 00:46:54,230 model. 977 00:46:54,230 --> 00:46:57,455 That's my mental model for how synapse works. 978 00:46:57,455 --> 00:46:57,955 OK? 979 00:47:00,630 --> 00:47:02,370 People who actually work on synapses 980 00:47:02,370 --> 00:47:05,040 would probably laugh at me, but that's 981 00:47:05,040 --> 00:47:07,800 kind of how I think of it. 982 00:47:07,800 --> 00:47:08,909 OK? 983 00:47:08,909 --> 00:47:09,409 Lena. 984 00:47:09,409 --> 00:47:10,951 AUDIENCE: Is that N the binding site? 985 00:47:10,951 --> 00:47:13,875 MICHALE FEE: Oh, yeah, the N, the N is really cool. 986 00:47:13,875 --> 00:47:15,000 What do you think it means? 987 00:47:15,000 --> 00:47:16,370 AUDIENCE: Binding sites? 988 00:47:16,370 --> 00:47:18,760 MICHALE FEE: Yes, it's the number of binding sites. 989 00:47:18,760 --> 00:47:24,290 So you can see that if the receptor requires 990 00:47:24,290 --> 00:47:30,440 two neurotransmitter molecules to bind before it opens, then 991 00:47:30,440 --> 00:47:34,220 you have a concentration squared. 992 00:47:34,220 --> 00:47:37,310 And that has really important consequences on the way 993 00:47:37,310 --> 00:47:40,400 it works, because what it does is 994 00:47:40,400 --> 00:47:42,500 it makes the receptor very sensitive 995 00:47:42,500 --> 00:47:47,340 to high concentrations of neurotransmitter. 996 00:47:47,340 --> 00:47:50,900 So they don't respond to the little leakage 997 00:47:50,900 --> 00:47:54,290 of some residual neurotransmitter left around 998 00:47:54,290 --> 00:47:57,980 that the reuptake systems haven't dealt with yet. 999 00:47:57,980 --> 00:48:00,530 But when a vessel releases, then you 1000 00:48:00,530 --> 00:48:04,260 have a neurotransmitter at a very high concentration. 1001 00:48:04,260 --> 00:48:07,490 And this thing makes it only sensitive to the peak 1002 00:48:07,490 --> 00:48:10,506 of the neurotransmitter concentration. 1003 00:48:10,506 --> 00:48:11,200 OK. 1004 00:48:11,200 --> 00:48:11,791 Yes. 1005 00:48:11,791 --> 00:48:15,639 AUDIENCE: With the probably [INAUDIBLE] 1006 00:48:15,639 --> 00:48:20,880 number of [INAUDIBLE] 1007 00:48:20,880 --> 00:48:21,630 MICHALE FEE: Here. 1008 00:48:21,630 --> 00:48:24,670 In this phase, does this N matter? 1009 00:48:24,670 --> 00:48:25,730 Is that your question? 1010 00:48:25,730 --> 00:48:26,030 AUDIENCE: Yeah. 1011 00:48:26,030 --> 00:48:27,988 MICHALE FEE: Yeah, well, so you know the answer 1012 00:48:27,988 --> 00:48:28,970 to that question. 1013 00:48:28,970 --> 00:48:33,730 Here, you're asking if here this N matters? 1014 00:48:33,730 --> 00:48:36,406 What's that concentration here? 1015 00:48:36,406 --> 00:48:37,340 AUDIENCE: Oh, it's 0. 1016 00:48:37,340 --> 00:48:40,005 MICHALE FEE: So what's 0 to the N? 1017 00:48:40,005 --> 00:48:41,805 AUDIENCE: [INAUDIBLE] 1018 00:48:41,805 --> 00:48:42,430 MICHALE FEE: 0. 1019 00:48:47,280 --> 00:48:51,300 OK, next, so we just did all of that. 1020 00:48:51,300 --> 00:48:53,600 I better speed up. 1021 00:48:53,600 --> 00:48:55,140 Let's talk about convolution. 1022 00:48:55,140 --> 00:48:58,610 So this is what happens when a single action 1023 00:48:58,610 --> 00:49:01,450 potential comes down the axon. 1024 00:49:01,450 --> 00:49:04,520 The presynaptic terminal releases neurotransmitter. 1025 00:49:04,520 --> 00:49:10,970 Boom, you get a pulse of probability of the receptor 1026 00:49:10,970 --> 00:49:12,680 being open. 1027 00:49:12,680 --> 00:49:17,000 That, you recall, is just proportional-- 1028 00:49:17,000 --> 00:49:22,950 yikes, where'd it go. 1029 00:49:22,950 --> 00:49:27,540 That probability is you just multiply it by some constants 1030 00:49:27,540 --> 00:49:28,890 to get the conductance. 1031 00:49:31,970 --> 00:49:38,282 So that is what the conductance looks like. 1032 00:49:38,282 --> 00:49:40,060 OK? 1033 00:49:40,060 --> 00:49:45,180 All right, now, so there's our input spike. 1034 00:49:45,180 --> 00:49:47,700 Our input neuron, our presynaptic neuron 1035 00:49:47,700 --> 00:49:48,960 generates a spike. 1036 00:49:48,960 --> 00:49:51,450 And that produces a response, which 1037 00:49:51,450 --> 00:49:55,470 is a conductance that looks like a pulse 1038 00:49:55,470 --> 00:49:57,850 and an exponential decay. 1039 00:49:57,850 --> 00:49:59,660 OK? 1040 00:49:59,660 --> 00:50:01,140 Now, what do you think would happen 1041 00:50:01,140 --> 00:50:03,510 if [AUDIO OUT] a bunch of spikes like this? 1042 00:50:07,600 --> 00:50:08,470 Good. 1043 00:50:08,470 --> 00:50:10,700 Just does it each time. 1044 00:50:10,700 --> 00:50:11,200 OK? 1045 00:50:11,200 --> 00:50:16,450 And we're ignoring fancy effects like paired pulse depression 1046 00:50:16,450 --> 00:50:18,770 or facilitation or things like that. 1047 00:50:18,770 --> 00:50:19,540 OK? 1048 00:50:19,540 --> 00:50:22,090 There are all kinds of interesting things 1049 00:50:22,090 --> 00:50:25,150 that synapses can do where there's one pulse 1050 00:50:25,150 --> 00:50:27,070 and then there's some residual calcium left 1051 00:50:27,070 --> 00:50:28,390 in the presynaptic terminal. 1052 00:50:28,390 --> 00:50:30,550 And that makes the next pulse produce 1053 00:50:30,550 --> 00:50:31,900 an even bigger response. 1054 00:50:31,900 --> 00:50:36,310 Or sometimes one pulse will use up all the vesicles 1055 00:50:36,310 --> 00:50:36,963 that are bound. 1056 00:50:36,963 --> 00:50:38,380 And so the next pulse will come in 1057 00:50:38,380 --> 00:50:39,797 and there won't be enough vesicles 1058 00:50:39,797 --> 00:50:41,110 and this will be smaller. 1059 00:50:41,110 --> 00:50:43,960 We're just going to ignore all of those complications 1060 00:50:43,960 --> 00:50:44,480 right now. 1061 00:50:44,480 --> 00:50:46,240 And we're just going to think about how 1062 00:50:46,240 --> 00:50:50,530 to model a postsynaptic response given a presynaptic input. 1063 00:50:50,530 --> 00:50:54,750 And we're going to use what's called a linear model. 1064 00:50:54,750 --> 00:50:57,180 We're going to use convolution. 1065 00:50:57,180 --> 00:51:01,410 And we're going to call this single event right here, 1066 00:51:01,410 --> 00:51:04,110 we're going to call that the impulse response. 1067 00:51:04,110 --> 00:51:06,480 The input is an impulse. 1068 00:51:06,480 --> 00:51:09,270 And the response is the impulse response. 1069 00:51:12,470 --> 00:51:15,400 And this is also called a linear kernel. 1070 00:51:19,230 --> 00:51:22,000 The response to multiple inputs can 1071 00:51:22,000 --> 00:51:24,430 be modeled as a convolution. 1072 00:51:24,430 --> 00:51:25,690 It looks a little messy. 1073 00:51:25,690 --> 00:51:30,340 But I'm going to explain how to just visualize it very simply. 1074 00:51:30,340 --> 00:51:31,690 All right? 1075 00:51:31,690 --> 00:51:34,670 So here's how you think about it. 1076 00:51:34,670 --> 00:51:39,340 Notice that the response of the system 1077 00:51:39,340 --> 00:51:42,970 is just this operation where we're 1078 00:51:42,970 --> 00:51:46,150 multiplying the kernel times the stimulus 1079 00:51:46,150 --> 00:51:48,430 and integrating over time. 1080 00:51:48,430 --> 00:51:51,150 OK? 1081 00:51:51,150 --> 00:51:52,890 So what we're going to do is-- 1082 00:51:52,890 --> 00:51:56,120 the way to think about this is to take the kernel K, 1083 00:51:56,120 --> 00:51:59,876 flip it [AUDIO OUT] wards and plot it there. 1084 00:51:59,876 --> 00:52:02,191 OK? 1085 00:52:02,191 --> 00:52:04,830 Now notice that what this thing does 1086 00:52:04,830 --> 00:52:09,870 is it says I'm going to integrate 1087 00:52:09,870 --> 00:52:12,780 the product of the kernel and the stimulus-- 1088 00:52:12,780 --> 00:52:15,740 notice I'm integrating over tau. 1089 00:52:15,740 --> 00:52:19,390 But this [AUDIO OUT] tau and that has a minus tau. 1090 00:52:19,390 --> 00:52:24,360 So what I'm doing is I'm multiplying at a particular-- 1091 00:52:24,360 --> 00:52:27,490 and notice that it's shifted by time t. 1092 00:52:27,490 --> 00:52:28,020 OK? 1093 00:52:28,020 --> 00:52:29,520 So what I'm going to do is I'm going 1094 00:52:29,520 --> 00:52:31,980 to put the kernel at time t. 1095 00:52:31,980 --> 00:52:34,380 And I'm going to integrate the product 1096 00:52:34,380 --> 00:52:35,860 of the kernel and the stimulus. 1097 00:52:35,860 --> 00:52:39,863 So what do I get if I multiply this times this? 1098 00:52:39,863 --> 00:52:40,750 AUDIENCE: 0. 1099 00:52:40,750 --> 00:52:41,610 MICHALE FEE: 0. 1100 00:52:41,610 --> 00:52:45,700 And so at that time, I write down a zero. 1101 00:52:45,700 --> 00:52:46,280 OK? 1102 00:52:46,280 --> 00:52:47,750 Now, I'm going to change t. 1103 00:52:47,750 --> 00:52:53,030 And I'm going to shift this over and multiply them together. 1104 00:52:53,030 --> 00:52:55,910 What do I get? 1105 00:52:55,910 --> 00:52:56,660 Good. 1106 00:52:56,660 --> 00:52:57,740 Another 0. 1107 00:52:57,740 --> 00:52:58,910 Now let's shift it again. 1108 00:52:58,910 --> 00:53:00,470 I'm just increasing t here. 1109 00:53:00,470 --> 00:53:01,655 I'm not integrating over t. 1110 00:53:01,655 --> 00:53:03,440 I'm integrating over tau. 1111 00:53:03,440 --> 00:53:05,580 So I just shift this a little bit. 1112 00:53:05,580 --> 00:53:06,080 Good. 1113 00:53:06,080 --> 00:53:09,420 And now when I multiply them together, what do I get? 1114 00:53:09,420 --> 00:53:11,850 AUDIENCE: [INAUDIBLE] 1115 00:53:11,850 --> 00:53:14,180 MICHALE FEE: Like that [AUDIO OUT] good. 1116 00:53:14,180 --> 00:53:20,920 I just get the area under that curve, and integrate. 1117 00:53:20,920 --> 00:53:22,450 And I get a point here. 1118 00:53:25,850 --> 00:53:27,670 Now, let's shift it again. 1119 00:53:27,670 --> 00:53:28,170 Good. 1120 00:53:28,170 --> 00:53:29,690 Now, multiply them together. 1121 00:53:29,690 --> 00:53:32,030 What do I get? 1122 00:53:32,030 --> 00:53:35,880 Slightly smaller integral. 1123 00:53:35,880 --> 00:53:38,774 And I plot that there. 1124 00:53:38,774 --> 00:53:39,740 OK? 1125 00:53:39,740 --> 00:53:41,150 Shift it again. 1126 00:53:41,150 --> 00:53:42,260 Integrate. 1127 00:53:42,260 --> 00:53:43,410 Plot another point. 1128 00:53:43,410 --> 00:53:44,360 Shift it again. 1129 00:53:44,360 --> 00:53:45,350 Integrate. 1130 00:53:45,350 --> 00:53:51,020 And if I keep shifting, the product is 0 1131 00:53:51,020 --> 00:53:53,090 and the integral is 0. 1132 00:53:53,090 --> 00:53:56,980 OK, so you can see that I can take this kernel, 1133 00:53:56,980 --> 00:54:00,440 convolve it with a stimulus that's an impulse. 1134 00:54:00,440 --> 00:54:02,720 And I get the kernel. 1135 00:54:02,720 --> 00:54:05,282 I get the impulse response. 1136 00:54:05,282 --> 00:54:07,220 Does that makes sense? 1137 00:54:07,220 --> 00:54:14,040 So you can see what I'm doing here is from time I'm 1138 00:54:14,040 --> 00:54:18,900 taking the stimulus at time t. 1139 00:54:18,900 --> 00:54:24,350 And as I integrate over tau, I'm going backwards here, 1140 00:54:24,350 --> 00:54:25,720 and I'm going forwards here. 1141 00:54:25,720 --> 00:54:27,855 So starting from here, I'm integrating like this. 1142 00:54:27,855 --> 00:54:31,910 I'm multiplying these like this. 1143 00:54:31,910 --> 00:54:33,120 And then integrating. 1144 00:54:33,120 --> 00:54:33,620 OK? 1145 00:54:33,620 --> 00:54:38,098 And that's why you flip it over. 1146 00:54:38,098 --> 00:54:39,970 OK? 1147 00:54:39,970 --> 00:54:43,420 So it's very easy to picture what it does. 1148 00:54:43,420 --> 00:54:46,580 So when somebody shows you a linear kernel 1149 00:54:46,580 --> 00:54:48,510 and asks you to convolve it with a stimulus, 1150 00:54:48,510 --> 00:54:51,530 the first thing you do is you just mentally flip it backwards 1151 00:54:51,530 --> 00:54:53,210 and slide it over this [AUDIO OUT] 1152 00:54:53,210 --> 00:54:57,818 and integrate the product at each different position. 1153 00:54:57,818 --> 00:55:00,800 OK? 1154 00:55:00,800 --> 00:55:03,710 Now, you can see that when you do that, when you convolve 1155 00:55:03,710 --> 00:55:05,870 that kernel with a pulse, you just 1156 00:55:05,870 --> 00:55:09,060 recover the impulse response. 1157 00:55:09,060 --> 00:55:09,560 OK? 1158 00:55:09,560 --> 00:55:14,570 So now, let's convolve linear [AUDIO OUT] I'm plotting it 1159 00:55:14,570 --> 00:55:15,920 flipped backwards now-- 1160 00:55:15,920 --> 00:55:18,890 with a single pulse. 1161 00:55:18,890 --> 00:55:21,260 So Daniel made these little demos for us. 1162 00:55:24,560 --> 00:55:29,020 And the resulting conductance is here. 1163 00:55:29,020 --> 00:55:30,460 OK? 1164 00:55:30,460 --> 00:55:34,150 Now, that was really obvious and easy, right? 1165 00:55:34,150 --> 00:55:38,560 We didn't need to have a Matlab program simulate that for us, 1166 00:55:38,560 --> 00:55:39,830 right? 1167 00:55:39,830 --> 00:55:41,420 But what about this? 1168 00:55:41,420 --> 00:55:44,800 Here, we have a spike train. 1169 00:55:44,800 --> 00:55:49,430 There's the postsynaptic response from one spike. 1170 00:55:49,430 --> 00:55:51,490 Now, to get the postsynaptic response 1171 00:55:51,490 --> 00:55:54,310 from a bunch of spikes, we can just convolve the kernel 1172 00:55:54,310 --> 00:55:55,285 with this spike train. 1173 00:55:55,285 --> 00:55:56,410 And let's see what happens. 1174 00:56:00,282 --> 00:56:01,250 Boom. 1175 00:56:01,250 --> 00:56:04,070 Response from the first spike. 1176 00:56:04,070 --> 00:56:04,820 Boom. 1177 00:56:04,820 --> 00:56:05,320 Boom. 1178 00:56:08,188 --> 00:56:11,512 Boom, boom, boom. 1179 00:56:11,512 --> 00:56:12,012 OK? 1180 00:56:15,370 --> 00:56:18,400 And that is actually really, really close to 1181 00:56:18,400 --> 00:56:23,270 what it looks like when a train of pulses comes into a neuron. 1182 00:56:23,270 --> 00:56:24,280 OK? 1183 00:56:24,280 --> 00:56:28,270 What happens is the first spike produces 1184 00:56:28,270 --> 00:56:30,560 a conductance response. 1185 00:56:30,560 --> 00:56:33,950 When you have two spikes close together, 1186 00:56:33,950 --> 00:56:35,780 the conductance from the first spike 1187 00:56:35,780 --> 00:56:39,770 has not decayed yet when the second spike hits. 1188 00:56:39,770 --> 00:56:42,320 And so that comes in and adds to it. 1189 00:56:42,320 --> 00:56:44,610 And it adds linearly. 1190 00:56:44,610 --> 00:56:50,530 So if this is halfway down, you add a full impulse response 1191 00:56:50,530 --> 00:56:51,380 on top of it. 1192 00:56:51,380 --> 00:56:53,320 And now the previous one and the current one 1193 00:56:53,320 --> 00:56:54,610 are decaying back to zero. 1194 00:56:54,610 --> 00:56:57,010 And you can add as many of those on top of each other 1195 00:56:57,010 --> 00:56:57,510 as you want. 1196 00:57:07,230 --> 00:57:10,360 And it turns out this is super easy to do in Matlab. 1197 00:57:10,360 --> 00:57:12,500 You're going to learn how to do this. 1198 00:57:12,500 --> 00:57:15,998 This idea is so fundamental. 1199 00:57:15,998 --> 00:57:17,540 This idea of convolution, we're going 1200 00:57:17,540 --> 00:57:19,310 to use to describe receptive fields. 1201 00:57:19,310 --> 00:57:20,840 We're going to use it to describe 1202 00:57:20,840 --> 00:57:23,780 filtering when we start getting to processing data. 1203 00:57:23,780 --> 00:57:26,792 It's incredibly useful and very powerful. 1204 00:57:26,792 --> 00:57:28,070 OK? 1205 00:57:28,070 --> 00:57:28,940 Yes. 1206 00:57:28,940 --> 00:57:35,050 AUDIENCE: [INAUDIBLE] 1207 00:57:35,050 --> 00:57:37,870 MICHALE FEE: This linear kernel reflects 1208 00:57:37,870 --> 00:57:41,230 that response, the conductance response, 1209 00:57:41,230 --> 00:57:47,100 of the postsynaptic neuron to a single spike, 1210 00:57:47,100 --> 00:57:49,502 single presynaptic spike. 1211 00:57:49,502 --> 00:57:53,230 AUDIENCE: [INAUDIBLE] 1212 00:57:53,230 --> 00:57:54,930 MICHALE FEE: Because if you have a bunch 1213 00:57:54,930 --> 00:58:00,780 of single spikes like this, the answer 1214 00:58:00,780 --> 00:58:03,580 is really obvious, right? 1215 00:58:03,580 --> 00:58:07,000 It's just one of those, one of those little exponentials 1216 00:58:07,000 --> 00:58:08,640 for every spike that comes in. 1217 00:58:08,640 --> 00:58:16,880 But it's less obvious when you have a complex spike 1218 00:58:16,880 --> 00:58:18,730 train like this. 1219 00:58:18,730 --> 00:58:22,840 AUDIENCE: [INAUDIBLE] on top of that. 1220 00:58:22,840 --> 00:58:28,922 So it's just [INAUDIBLE] 1221 00:58:28,922 --> 00:58:30,630 MICHALE FEE: Yeah, the linear convolution 1222 00:58:30,630 --> 00:58:32,490 tells you how the postsynaptic neuron 1223 00:58:32,490 --> 00:58:36,180 is going to respond to a train of action potentials 1224 00:58:36,180 --> 00:58:41,340 that are overlapped, where the response has not gone away 1225 00:58:41,340 --> 00:58:44,242 to the first spike by the time the second spike arrives. 1226 00:58:44,242 --> 00:58:49,440 AUDIENCE: So because the kernel can have like different shapes. 1227 00:58:49,440 --> 00:58:51,990 MICHALE FEE: Yeah, the kernel can have different shapes. 1228 00:58:51,990 --> 00:58:54,990 I've just chosen a particularly simple one, 1229 00:58:54,990 --> 00:58:58,470 because actually an exponentially decaying kernel 1230 00:58:58,470 --> 00:59:01,920 turns out to be really important. 1231 00:59:01,920 --> 00:59:04,806 It's actually a low pass filter. 1232 00:59:04,806 --> 00:59:11,202 AUDIENCE: So be it's a linear [INAUDIBLE] 1233 00:59:11,202 --> 00:59:13,670 MICHALE FEE: Yes. 1234 00:59:13,670 --> 00:59:18,000 The convolution, if you use the convolution, the thing you're 1235 00:59:18,000 --> 00:59:22,120 using as the kernel is always a linear kernel, 1236 00:59:22,120 --> 00:59:24,910 because the convolution is a linear function, 1237 00:59:24,910 --> 00:59:30,180 you call the thing that you convolving a linear kernel. 1238 00:59:30,180 --> 00:59:32,628 It's just terminology. 1239 00:59:32,628 --> 00:59:34,200 AUDIENCE: OK. 1240 00:59:34,200 --> 00:59:36,870 MICHALE FEE: Just focus on what it does and how it works, 1241 00:59:36,870 --> 00:59:38,790 rather than the names. 1242 00:59:38,790 --> 00:59:41,950 Just call it impulse response if that's easier. 1243 00:59:41,950 --> 00:59:44,190 OK? 1244 00:59:44,190 --> 00:59:46,755 All right, let's push on. 1245 00:59:46,755 --> 00:59:48,880 I want to introduce an idea of synaptic saturation. 1246 00:59:48,880 --> 00:59:52,780 And I'm getting really worried about the crayfish. 1247 00:59:56,220 --> 01:00:00,490 OK, synaptic saturation. 1248 01:00:00,490 --> 01:00:02,660 OK, so remember, we introduced the idea 1249 01:00:02,660 --> 01:00:05,020 of a two-compartment model. 1250 01:00:05,020 --> 01:00:08,110 So last time we talked about a model in which 1251 01:00:08,110 --> 01:00:11,155 you have a soma and a dendrite. 1252 01:00:11,155 --> 01:00:14,290 And you simplify the dendrites just by writing it down 1253 01:00:14,290 --> 01:00:17,600 as another little piece of membrane 1254 01:00:17,600 --> 01:00:20,620 or another little cellular compartment that's connected 1255 01:00:20,620 --> 01:00:23,330 to the soma through a resistor. 1256 01:00:23,330 --> 01:00:26,290 And now, you can write a model for the dendritic compartment 1257 01:00:26,290 --> 01:00:28,660 that looks just like a capacitor and a conductance 1258 01:00:28,660 --> 01:00:33,510 with a reversal potential. 1259 01:00:33,510 --> 01:00:35,940 And you have the same kind of model-- 1260 01:00:35,940 --> 01:00:40,560 capacitor, conductance, reversal potential, battery-- 1261 01:00:40,560 --> 01:00:41,347 for the soma. 1262 01:00:41,347 --> 01:00:42,930 And, of course, those two compartments 1263 01:00:42,930 --> 01:00:45,180 are connected to each [AUDIO OUT] resistor that 1264 01:00:45,180 --> 01:00:49,860 represents the axial resistance of the piece of dendrite 1265 01:00:49,860 --> 01:00:51,330 that's really connecting. 1266 01:00:51,330 --> 01:00:52,130 OK? 1267 01:00:52,130 --> 01:00:55,215 So that's called a two-compartment model. 1268 01:00:55,215 --> 01:00:56,820 And what we're going to do is just 1269 01:00:56,820 --> 01:01:01,020 think briefly about how to think about what 1270 01:01:01,020 --> 01:01:06,250 this looks like when you add a synapse to the dendrite. 1271 01:01:06,250 --> 01:01:06,890 OK? 1272 01:01:06,890 --> 01:01:09,200 And what we're going to study is how 1273 01:01:09,200 --> 01:01:10,910 the voltage in the dendrite changes 1274 01:01:10,910 --> 01:01:13,130 as a function of the amount of excitatory 1275 01:01:13,130 --> 01:01:14,240 conductance that you add. 1276 01:01:20,250 --> 01:01:23,620 So we're going to start by-- 1277 01:01:23,620 --> 01:01:25,973 we're doing steady state. 1278 01:01:25,973 --> 01:01:27,890 So we don't need to worry about our capacitor. 1279 01:01:27,890 --> 01:01:32,330 So we can actually just unsolder them and take them out 1280 01:01:32,330 --> 01:01:33,710 of our circuit. 1281 01:01:33,710 --> 01:01:36,200 And we're going to study the voltage response 1282 01:01:36,200 --> 01:01:37,430 in the dendrite. 1283 01:01:37,430 --> 01:01:41,540 So we're going to also throw away our soma 1284 01:01:41,540 --> 01:01:44,510 and just ask, how does the dendrite respond 1285 01:01:44,510 --> 01:01:49,400 to this synaptic input as a function of the amount 1286 01:01:49,400 --> 01:01:51,260 of excitatory conductance? 1287 01:01:51,260 --> 01:01:55,250 And what I'm going to show you is just that the voltage change 1288 01:01:55,250 --> 01:01:58,750 in the dendrite with zero inductance, of course, 1289 01:01:58,750 --> 01:02:02,560 it's sitting there at the potassium reversal potential, 1290 01:02:02,560 --> 01:02:04,930 or e leak. 1291 01:02:04,930 --> 01:02:07,780 And as you add conductance, it corresponds 1292 01:02:07,780 --> 01:02:10,780 to making that conductance, bigger 1293 01:02:10,780 --> 01:02:12,790 making that resistor smaller. 1294 01:02:12,790 --> 01:02:17,470 You're basically attaching the battery 1295 01:02:17,470 --> 01:02:18,940 to the inside of the cell. 1296 01:02:18,940 --> 01:02:20,530 And you can see that what happens 1297 01:02:20,530 --> 01:02:23,200 is as you add more and more conductance, 1298 01:02:23,200 --> 01:02:26,020 as you put more and more neurotransmitter 1299 01:02:26,020 --> 01:02:30,220 onto that receptor, or have more and more neurotransmitter 1300 01:02:30,220 --> 01:02:36,460 receptors, the voltage response goes up and then saturates. 1301 01:02:36,460 --> 01:02:39,550 And it's really obvious why that happens, right? 1302 01:02:39,550 --> 01:02:41,800 Once this resistor gets small enough, 1303 01:02:41,800 --> 01:02:45,210 meaning you've added enough conductance, 1304 01:02:45,210 --> 01:02:50,210 the inside of the cell is connected to the battery. 1305 01:02:50,210 --> 01:02:55,085 And the voltage inside the cell just can't go any higher. 1306 01:02:55,085 --> 01:02:58,580 It is forced to E synaptics, the reversal 1307 01:02:58,580 --> 01:02:59,630 potential of the synapse. 1308 01:02:59,630 --> 01:03:00,810 And it can't go any higher. 1309 01:03:00,810 --> 01:03:04,370 And that's why no matter how much excitatory conductance you 1310 01:03:04,370 --> 01:03:08,920 add, the voltage inside the dendrite cannot go above E 1311 01:03:08,920 --> 01:03:10,045 synapse. 1312 01:03:10,045 --> 01:03:12,950 And that's called synaptic saturation. 1313 01:03:12,950 --> 01:03:16,220 And I was going to show you the derivation of this. 1314 01:03:16,220 --> 01:03:18,450 It's just very simple. 1315 01:03:18,450 --> 01:03:20,390 You just write down Kirchhoff's current law, 1316 01:03:20,390 --> 01:03:25,550 substitute the equation for synaptic current, leak current, 1317 01:03:25,550 --> 01:03:30,770 solve for voltage as a function of G synapse. 1318 01:03:30,770 --> 01:03:35,030 And you can write down an approximation for the case of G 1319 01:03:35,030 --> 01:03:37,460 synapse much smaller than G leak. 1320 01:03:37,460 --> 01:03:39,900 And what you find is it's linear. 1321 01:03:39,900 --> 01:03:42,230 And so there's a linear part [AUDIO OUT] 1322 01:03:42,230 --> 01:03:44,840 voltage change at small conductances. 1323 01:03:44,840 --> 01:03:46,720 And you can write down an approximation 1324 01:03:46,720 --> 01:03:48,200 at high synaptic conductance. 1325 01:03:48,200 --> 01:03:50,060 And you show that it approaches-- 1326 01:03:50,060 --> 01:03:52,090 the voltage approaches E synapse. 1327 01:03:52,090 --> 01:03:54,055 OK, so I'm not going to go through the math. 1328 01:03:54,055 --> 01:03:54,680 But it's there. 1329 01:03:54,680 --> 01:03:56,540 You don't have to be able to derive it yourself. 1330 01:03:56,540 --> 01:03:57,920 But what I want you to understand 1331 01:03:57,920 --> 01:04:02,300 is that for small synaptic conductance, 1332 01:04:02,300 --> 01:04:05,390 the voltage responds linearly. 1333 01:04:05,390 --> 01:04:08,900 But for high synaptic conductance, it saturates. 1334 01:04:11,684 --> 01:04:13,540 OK? 1335 01:04:13,540 --> 01:04:16,390 All right, and now, I want to tell you 1336 01:04:16,390 --> 01:04:20,490 a story about inhibition. 1337 01:04:20,490 --> 01:04:26,900 And the basic story is that we can add inhibition to-- 1338 01:04:26,900 --> 01:04:31,190 so in real neurons in the brain, inhibition sometimes 1339 01:04:31,190 --> 01:04:32,840 connects to dendrites. 1340 01:04:32,840 --> 01:04:37,180 And sometimes inhibitory synapses connect to somata. 1341 01:04:37,180 --> 01:04:39,740 And they're actually different kinds of inhibitory neurons 1342 01:04:39,740 --> 01:04:43,730 that preferentially connect onto dendrites and others that 1343 01:04:43,730 --> 01:04:46,440 preferentially connect onto the somata. 1344 01:04:46,440 --> 01:04:49,070 And it turns out there's a really interesting story 1345 01:04:49,070 --> 01:04:54,380 about how that inhibition has a different effect whether it's 1346 01:04:54,380 --> 01:04:58,438 connected to the dendrite or connected to the soma, right? 1347 01:04:58,438 --> 01:04:59,730 So you see what I've done here. 1348 01:04:59,730 --> 01:05:03,650 I've got a dendrite that has an excitatory synapse. 1349 01:05:03,650 --> 01:05:05,090 That's here. 1350 01:05:05,090 --> 01:05:09,090 And it has an inhibitory synapse. 1351 01:05:09,090 --> 01:05:11,160 Or-- so we can analyze this case-- 1352 01:05:11,160 --> 01:05:14,220 or we consider the case where the excitatory synapse is still 1353 01:05:14,220 --> 01:05:17,370 on the dendrite, but the inhibitory synapse 1354 01:05:17,370 --> 01:05:19,710 comes onto the soma. 1355 01:05:19,710 --> 01:05:21,530 And it turns out those two things 1356 01:05:21,530 --> 01:05:24,500 do something very interesting. 1357 01:05:24,500 --> 01:05:29,950 And this was first shown in the crayfish. 1358 01:05:29,950 --> 01:05:32,030 The crayfish is a really cool model system, 1359 01:05:32,030 --> 01:05:36,530 because it has very stereotyped behaviors. 1360 01:05:36,530 --> 01:05:39,200 And one of its interesting stereotyped behaviors 1361 01:05:39,200 --> 01:05:43,100 is its escape reflexes. 1362 01:05:43,100 --> 01:05:45,920 It has three different kinds of escape reflexes 1363 01:05:45,920 --> 01:05:48,920 that involve different what are called command neurons that 1364 01:05:48,920 --> 01:05:53,650 get sensory input and drive motor output. 1365 01:05:53,650 --> 01:05:56,260 And one of these particular neurons 1366 01:05:56,260 --> 01:05:59,440 is where this effect about inhibition was first shown. 1367 01:05:59,440 --> 01:06:00,460 It's called the LG. 1368 01:06:04,600 --> 01:06:07,840 LG neurons, MG neurons that drive two different kinds 1369 01:06:07,840 --> 01:06:08,960 of escape reflexes. 1370 01:06:08,960 --> 01:06:12,820 So here are the two different kinds of escape reflexes. 1371 01:06:12,820 --> 01:06:18,190 The medial giant neuron drives the MG escape, 1372 01:06:18,190 --> 01:06:21,850 which is if you touch the crayfish on its nose, 1373 01:06:21,850 --> 01:06:24,370 it flicks its tail and goes backwards. 1374 01:06:24,370 --> 01:06:30,250 The LG escape is when you touch the crayfish on its tail, 1375 01:06:30,250 --> 01:06:33,750 and it flicks its tail in a way that makes it go forward. 1376 01:06:33,750 --> 01:06:34,350 OK? 1377 01:06:34,350 --> 01:06:40,510 So let's look at what those behaviors look like. 1378 01:06:40,510 --> 01:06:43,360 We're going to post this video. 1379 01:06:43,360 --> 01:06:49,940 This is from a Journal of Visual Experiments. 1380 01:06:49,940 --> 01:06:54,930 And there's a nice-- it's actually really nice-- 1381 01:06:54,930 --> 01:06:57,330 [VIDEO PLAYBACK] 1382 01:06:57,330 --> 01:07:00,730 - The recordings of neural and muscular field potentials, 1383 01:07:00,730 --> 01:07:03,150 electronic recordings from a pair of bath electrodes 1384 01:07:03,150 --> 01:07:06,135 are synchronized with high speed video recordings and display-- 1385 01:07:06,135 --> 01:07:08,010 MICHALE FEE: So this video shows you actually 1386 01:07:08,010 --> 01:07:10,200 how to set up a tank with electrodes 1387 01:07:10,200 --> 01:07:14,040 so you can record the signals from these neurons 1388 01:07:14,040 --> 01:07:16,050 in a crayfish while it's behaving. 1389 01:07:16,050 --> 01:07:17,400 So you should watch the video. 1390 01:07:17,400 --> 01:07:17,983 [END PLAYBACK] 1391 01:07:17,983 --> 01:07:20,130 MICHALE FEE: But I'm going to show you-- 1392 01:07:20,130 --> 01:07:23,910 I'm going to show you what-- 1393 01:07:23,910 --> 01:07:25,830 [VIDEO PLAYBACK] 1394 01:07:25,830 --> 01:07:28,360 - Here is a look at a series of single, high speed video 1395 01:07:28,360 --> 01:07:30,370 frames and corresponding electric field 1396 01:07:30,370 --> 01:07:32,495 recordings for an escape tail flip in response to-- 1397 01:07:32,495 --> 01:07:33,787 MICHALE FEE: Can you hear that? 1398 01:07:33,787 --> 01:07:35,980 - A stimulus delivered to the head or tail 1399 01:07:35,980 --> 01:07:36,940 of a juvenile crayfish. 1400 01:07:43,234 --> 01:07:44,230 [END PLAYBACK] 1401 01:07:44,230 --> 01:07:46,840 MICHALE FEE: So that was the MG response. 1402 01:07:46,840 --> 01:07:49,360 And he puts two electrodes into the tank. 1403 01:07:49,360 --> 01:07:51,460 And you can actually measure signals 1404 01:07:51,460 --> 01:07:53,748 in the tank from that neuron firing. 1405 01:07:53,748 --> 01:07:54,415 [VIDEO PLAYBACK] 1406 01:07:54,415 --> 01:07:57,850 - The giant neuron and the phasic deflection that follows 1407 01:07:57,850 --> 01:08:01,000 enables non-ambiguous identification of the tail flip 1408 01:08:01,000 --> 01:08:03,250 as mediated by giant neuron activity. 1409 01:08:08,190 --> 01:08:11,070 The backward movement shown in the video traces 1410 01:08:11,070 --> 01:08:15,400 determines the identity of the activated neural circuit. 1411 01:08:15,400 --> 01:08:17,420 Here is a tail flip mediated by the-- 1412 01:08:17,420 --> 01:08:19,500 MICHALE FEE: So here, you touch him on the tail-- 1413 01:08:19,500 --> 01:08:22,710 - Tactile stimulus was applied to the tail. 1414 01:08:22,710 --> 01:08:23,890 Upward and forward motion-- 1415 01:08:23,890 --> 01:08:25,260 MICHALE FEE: You can see it a different movement that 1416 01:08:25,260 --> 01:08:26,130 makes him-- 1417 01:08:26,130 --> 01:08:29,399 - Synchronized electronic trace, displaying the giant spike 1418 01:08:29,399 --> 01:08:31,770 and the large phasic initial deflection 1419 01:08:31,770 --> 01:08:34,335 determines the identity of the activated neural circuit. 1420 01:08:42,640 --> 01:08:44,140 This video demonstrates the-- 1421 01:08:44,140 --> 01:08:48,580 MICHALE FEE: Here's a different escape reflex 1422 01:08:48,580 --> 01:08:53,165 that doesn't involve either of those two neurons. 1423 01:08:53,165 --> 01:08:54,540 Here he spends a little more time 1424 01:08:54,540 --> 01:08:57,370 thinking before he figures out what to do. 1425 01:09:01,870 --> 01:09:04,617 - A giant spike and consists of much-- 1426 01:09:04,617 --> 01:09:05,870 [END PLAYBACK] 1427 01:09:05,870 --> 01:09:06,660 MICHALE FEE: OK. 1428 01:09:06,660 --> 01:09:07,890 All right, so let me just-- 1429 01:09:07,890 --> 01:09:11,760 I probably won't get very far in explaining the inhibition part, 1430 01:09:11,760 --> 01:09:17,040 but you can at least understand a little bit more 1431 01:09:17,040 --> 01:09:18,430 about this behavior. 1432 01:09:18,430 --> 01:09:20,460 So what's really cool is that inhibition 1433 01:09:20,460 --> 01:09:24,149 is used to regulate these two behaviors. 1434 01:09:24,149 --> 01:09:25,950 So the idea is that-- 1435 01:09:25,950 --> 01:09:27,930 so first let me just say that kind of that 1436 01:09:27,930 --> 01:09:33,120 LG neuron, that lateral giant neuron, 1437 01:09:33,120 --> 01:09:35,010 is known as a command neuron. 1438 01:09:35,010 --> 01:09:37,979 And that is because if you activate that neuron, if you 1439 01:09:37,979 --> 01:09:41,815 just depolarize that one neuron, it activates that entire escape 1440 01:09:41,815 --> 01:09:42,315 reflex. 1441 01:09:45,350 --> 01:09:48,859 And if you hyperpolarize that neuron, 1442 01:09:48,859 --> 01:09:50,870 inhibit that neuron, you completely 1443 01:09:50,870 --> 01:09:54,800 suppress the escape reflex. 1444 01:09:54,800 --> 01:09:56,660 And now, what's really interesting 1445 01:09:56,660 --> 01:09:59,900 is that that neuron has inhibitory inputs that 1446 01:09:59,900 --> 01:10:04,430 control the probability that the animal will elicit this escape 1447 01:10:04,430 --> 01:10:06,470 reflex. 1448 01:10:06,470 --> 01:10:10,143 And that kind of modulation of that behavior 1449 01:10:10,143 --> 01:10:11,060 is really interesting. 1450 01:10:11,060 --> 01:10:13,860 And it has some interesting subtleties to it. 1451 01:10:13,860 --> 01:10:16,400 So first of all, if the animal is touched 1452 01:10:16,400 --> 01:10:21,560 on the nose and elicits-- 1453 01:10:21,560 --> 01:10:25,130 touched on the nose and elicits an MG response, the tail flips 1454 01:10:25,130 --> 01:10:27,680 and the animal goes backwards, right? 1455 01:10:27,680 --> 01:10:30,890 But now, if it goes backwards and it bumps into something 1456 01:10:30,890 --> 01:10:33,440 on his backside, when it's going backwards, 1457 01:10:33,440 --> 01:10:36,110 you don't want to have that immediately 1458 01:10:36,110 --> 01:10:39,130 trigger an LG escape, and he bumps into something. 1459 01:10:39,130 --> 01:10:40,970 He's like boom, boom, boom, right? 1460 01:10:40,970 --> 01:10:42,270 That would be terrible. 1461 01:10:42,270 --> 01:10:50,000 So what happens is that when the MG neuron fires and initiates 1462 01:10:50,000 --> 01:10:54,110 that backwards movement, it sends a signal that 1463 01:10:54,110 --> 01:10:57,610 inhibits the LG response. 1464 01:10:57,610 --> 01:11:00,370 OK? 1465 01:11:00,370 --> 01:11:03,650 OK, other cool things, when the animal is restrained, 1466 01:11:03,650 --> 01:11:06,230 when you pick the animal up, if he doesn't get away 1467 01:11:06,230 --> 01:11:11,360 from you with his first escape attempt and you hold him, 1468 01:11:11,360 --> 01:11:12,860 you can touch him on the nose and it 1469 01:11:12,860 --> 01:11:15,140 won't elicit an escape reflex. 1470 01:11:15,140 --> 01:11:18,590 So when the animal is held, the response probability 1471 01:11:18,590 --> 01:11:19,460 goes way down. 1472 01:11:19,460 --> 01:11:22,370 Maybe he's like holding off until he 1473 01:11:22,370 --> 01:11:25,940 feels like your grip loosen a little bit and then he'll try. 1474 01:11:25,940 --> 01:11:26,450 OK? 1475 01:11:26,450 --> 01:11:29,090 So there's no point in wasting escape attempts. 1476 01:11:29,090 --> 01:11:31,340 They're very energetically expensive, 1477 01:11:31,340 --> 01:11:36,470 wasting escape attempts when you're being restrained. 1478 01:11:36,470 --> 01:11:38,090 Another interesting modulation is 1479 01:11:38,090 --> 01:11:41,105 that the LG escape response is suppressed 1480 01:11:41,105 --> 01:11:42,230 while the animal is eating. 1481 01:11:42,230 --> 01:11:43,590 This is threshold. 1482 01:11:43,590 --> 01:11:46,280 This is how much you have to poke in the nose 1483 01:11:46,280 --> 01:11:49,220 or in the tail for him to escape when 1484 01:11:49,220 --> 01:11:51,380 he's just wandering around. 1485 01:11:51,380 --> 01:11:54,450 But then while he's eating, he's getting food. 1486 01:11:54,450 --> 01:11:57,530 And so the threshold for eliciting that escape reflex 1487 01:11:57,530 --> 01:11:58,380 goes up. 1488 01:11:58,380 --> 01:12:01,730 He's like, sorry, I'm eating. 1489 01:12:01,730 --> 01:12:03,230 Leave me alone. 1490 01:12:03,230 --> 01:12:05,450 OK? 1491 01:12:05,450 --> 01:12:08,000 It's not just being hungry, right? 1492 01:12:08,000 --> 01:12:11,060 Because if he's hungry and searching for food, 1493 01:12:11,060 --> 01:12:15,020 there's no increased threshold. 1494 01:12:15,020 --> 01:12:16,820 So it's really because he's eating. 1495 01:12:16,820 --> 01:12:18,200 He's found a food source. 1496 01:12:18,200 --> 01:12:19,550 He doesn't want to leave it. 1497 01:12:19,550 --> 01:12:21,140 So there's a higher-- 1498 01:12:21,140 --> 01:12:23,120 he won't leave until there's like more danger. 1499 01:12:27,830 --> 01:12:31,070 So all this different kinds of modulation and inhibition 1500 01:12:31,070 --> 01:12:34,280 of the behavior is controlled by inhibitory [AUDIO OUT] 1501 01:12:34,280 --> 01:12:37,760 projecting onto this LG neuron. 1502 01:12:37,760 --> 01:12:40,970 So there are two kinds of escape modulation. 1503 01:12:40,970 --> 01:12:43,750 One is absolute. 1504 01:12:43,750 --> 01:12:47,440 When the animal is engaged in an escape reflex, 1505 01:12:47,440 --> 01:12:50,710 it is impossible to activate-- when the animal is engaged 1506 01:12:50,710 --> 01:12:54,520 in an MG escape, it's impossible to activate the LG escape. 1507 01:12:54,520 --> 01:12:57,610 No matter how much he gets poked in the tail, 1508 01:12:57,610 --> 01:13:00,160 he will not initiate an LG. 1509 01:13:00,160 --> 01:13:04,250 So this kind of modulation is absolute. 1510 01:13:04,250 --> 01:13:07,330 There's this other kind of modulation, 1511 01:13:07,330 --> 01:13:10,390 where the likelihood of escape is just reduced, 1512 01:13:10,390 --> 01:13:13,360 but the animal is still able to initiate escape 1513 01:13:13,360 --> 01:13:17,440 if the danger is high enough, if the stimulus is high enough. 1514 01:13:17,440 --> 01:13:19,345 And that's really the crux of the difference 1515 01:13:19,345 --> 01:13:23,620 is that some kinds of suppression of a behavior 1516 01:13:23,620 --> 01:13:24,370 are absolute. 1517 01:13:24,370 --> 01:13:26,080 No matter how strong the stimulus is, 1518 01:13:26,080 --> 01:13:28,670 you don't want to allow that neuron to spike. 1519 01:13:28,670 --> 01:13:30,610 In the other case is I'm just going 1520 01:13:30,610 --> 01:13:33,760 to turn down the probability that I generate 1521 01:13:33,760 --> 01:13:35,750 [AUDIO OUT] because I'm eating. 1522 01:13:35,750 --> 01:13:38,860 But if it's looks dangerous enough I'm still going to go. 1523 01:13:38,860 --> 01:13:42,970 But I'm just going to modulate, gently, the probability. 1524 01:13:42,970 --> 01:13:46,390 And it turns out that's the crux of the difference. 1525 01:13:46,390 --> 01:13:49,140 So it turns out the LG neuron has two sites on it where 1526 01:13:49,140 --> 01:13:51,450 you get sources of inhibition. 1527 01:13:51,450 --> 01:13:53,820 There are a bunch of inhibitory inputs 1528 01:13:53,820 --> 01:13:57,750 on the proximal dendrite near the spike initiation 1529 01:13:57,750 --> 01:13:59,550 zone, which is right here. 1530 01:13:59,550 --> 01:14:01,920 And that's recurrent inhibition, because it's coming 1531 01:14:01,920 --> 01:14:05,920 from the other escape neuron. 1532 01:14:05,920 --> 01:14:08,280 So it's recurrent within the motor system. 1533 01:14:08,280 --> 01:14:11,100 And the other inhibitory synapses come out here 1534 01:14:11,100 --> 01:14:13,400 on the dendrite. 1535 01:14:13,400 --> 01:14:16,760 And they're [AUDIO OUT] higher brain areas. 1536 01:14:16,760 --> 01:14:21,960 And it's called tonic inhibition for historical reasons. 1537 01:14:21,960 --> 01:14:24,870 Now, previous hypothesis was that those inputs here 1538 01:14:24,870 --> 01:14:27,420 allowed inhibition to control different branches 1539 01:14:27,420 --> 01:14:28,050 of the input. 1540 01:14:28,050 --> 01:14:30,590 But it turns out the answer is very simple. 1541 01:14:30,590 --> 01:14:32,580 So let me just summarize this. 1542 01:14:32,580 --> 01:14:35,700 So you have one [AUDIO OUT] input, inhibitory input, 1543 01:14:35,700 --> 01:14:39,090 that's coming from the other escape neuron 1544 01:14:39,090 --> 01:14:41,820 that lands right there on the part of this neuron 1545 01:14:41,820 --> 01:14:44,790 the initiates spikes. 1546 01:14:44,790 --> 01:14:50,250 The other input that suppresses the response during feeding 1547 01:14:50,250 --> 01:14:55,320 is coming far out on the dendrite at the same location 1548 01:14:55,320 --> 01:14:58,110 where those excitatory inputs, the sensory inputs, 1549 01:14:58,110 --> 01:15:01,080 are coming in. 1550 01:15:01,080 --> 01:15:03,800 So that's what the circuit looks like. 1551 01:15:03,800 --> 01:15:07,390 So the input that absolutely suppresses 1552 01:15:07,390 --> 01:15:10,510 the response of this neuron is coming right on the soma, 1553 01:15:10,510 --> 01:15:12,400 right where the spike is generated. 1554 01:15:12,400 --> 01:15:14,320 And the ones that tonic [AUDIO OUT] 1555 01:15:14,320 --> 01:15:17,800 sort of adjust the probability of spiking 1556 01:15:17,800 --> 01:15:21,610 are coming out here where the excitatory inputs are. 1557 01:15:21,610 --> 01:15:25,570 And so they developed the simple equivalent circuit model 1558 01:15:25,570 --> 01:15:27,880 where they have a dendrite out here. 1559 01:15:27,880 --> 01:15:32,480 Out here on the dendrite, you have an excitatory input. 1560 01:15:32,480 --> 01:15:35,920 And you can have recurrent input on the soma. 1561 01:15:35,920 --> 01:15:37,500 And there's another model. 1562 01:15:37,500 --> 01:15:39,170 So in one of these models, they're 1563 01:15:39,170 --> 01:15:41,210 modeling the proximal inhibition. 1564 01:15:41,210 --> 01:15:45,020 In the other model, they put the inhibitory synapse out here 1565 01:15:45,020 --> 01:15:46,880 on the dendrite. 1566 01:15:46,880 --> 01:15:50,280 And they ask, how are those two different sources of inhibition 1567 01:15:50,280 --> 01:15:50,780 different? 1568 01:15:50,780 --> 01:15:53,060 What do they do differently to the neuron? 1569 01:15:53,060 --> 01:15:55,010 And they just did this model. 1570 01:15:55,010 --> 01:15:57,048 They analyzed it mathematically, exactly 1571 01:15:57,048 --> 01:15:58,340 like the way I just showed you. 1572 01:15:58,340 --> 01:15:59,930 That very simple calculation works. 1573 01:15:59,930 --> 01:16:01,820 You just use Kirchhoff's current law. 1574 01:16:01,820 --> 01:16:03,950 And you write down the voltage response 1575 01:16:03,950 --> 01:16:06,530 to the excitatory synapse as a function 1576 01:16:06,530 --> 01:16:09,800 of the strength of these two different kinds of inhibition. 1577 01:16:09,800 --> 01:16:11,360 And here's what you find. 1578 01:16:11,360 --> 01:16:16,960 The proximal inhibition suppresses the response 1579 01:16:16,960 --> 01:16:21,500 to the excitatory input by the same fraction 1580 01:16:21,500 --> 01:16:23,800 no matter how strong the excitation is. 1581 01:16:23,800 --> 01:16:25,930 So if you put in strong inhibition, 1582 01:16:25,930 --> 01:16:30,670 you can always cause that excitatory input 1583 01:16:30,670 --> 01:16:33,460 to be suppressed to zero. 1584 01:16:33,460 --> 01:16:38,500 So inhibitory input approximately at the soma 1585 01:16:38,500 --> 01:16:42,220 can suppress the response of a neuron to an excitatory input, 1586 01:16:42,220 --> 01:16:45,730 no matter how strong the excitatory input is. 1587 01:16:45,730 --> 01:16:49,720 On the other hand, inhibition out 1588 01:16:49,720 --> 01:16:53,900 on the dendrite for any given amount of inhibition, 1589 01:16:53,900 --> 01:16:56,470 there's always an excitation that's 1590 01:16:56,470 --> 01:17:01,360 strong enough to allow the response to get through. 1591 01:17:01,360 --> 01:17:03,550 So this shows the amount of suppression 1592 01:17:03,550 --> 01:17:05,630 as a function of excitatory input. 1593 01:17:05,630 --> 01:17:09,670 And you can see that no matter how strong the inhibition, 1594 01:17:09,670 --> 01:17:12,130 there's always an amount of excitation that 1595 01:17:12,130 --> 01:17:14,720 will overcome the inhibition. 1596 01:17:14,720 --> 01:17:16,480 And you can also do that analysis 1597 01:17:16,480 --> 01:17:18,940 in a much more complicated model. 1598 01:17:18,940 --> 01:17:20,980 And you get exactly the same results. 1599 01:17:20,980 --> 01:17:22,900 But what's really cool is that you 1600 01:17:22,900 --> 01:17:25,150 can understand this just from this very 1601 01:17:25,150 --> 01:17:29,300 simple two-compartment model. 1602 01:17:29,300 --> 01:17:31,600 And I wish I had a little bit more time 1603 01:17:31,600 --> 01:17:34,360 to go through those models and explain why that works. 1604 01:17:34,360 --> 01:17:38,350 But basically, proximal inhibition is absolute. 1605 01:17:38,350 --> 01:17:40,600 You can always make the inhibition win. 1606 01:17:40,600 --> 01:17:45,700 Distal inhibition kind of gently varies the effect 1607 01:17:45,700 --> 01:17:48,280 of the excitatory input. 1608 01:17:48,280 --> 01:17:52,540 All right, so that's what we covered-- synapses, a model, 1609 01:17:52,540 --> 01:17:54,940 convolution, synaptic saturation, 1610 01:17:54,940 --> 01:18:00,330 and the different functions of distal and proximal inhibition.