1 00:00:15,510 --> 00:00:18,070 MICHALE FEE: OK, good morning. 2 00:00:18,070 --> 00:00:21,280 So far in class, we have been developing 3 00:00:21,280 --> 00:00:24,400 an equivalent circuit model of a neuron, 4 00:00:24,400 --> 00:00:30,190 and we have extended that model to understanding how action 5 00:00:30,190 --> 00:00:31,570 potentials are generated. 6 00:00:31,570 --> 00:00:33,610 And, more recently, we extended the model 7 00:00:33,610 --> 00:00:40,000 to understanding the propagation of signals in dendrites. 8 00:00:40,000 --> 00:00:44,620 So today we are going to consider 9 00:00:44,620 --> 00:00:50,740 how we can record activity, record electrical signals 10 00:00:50,740 --> 00:00:54,010 related to neural activity in the brain, 11 00:00:54,010 --> 00:00:56,250 and we're going to understand a little bit 12 00:00:56,250 --> 00:01:02,040 about how we can, in particular, record extracellular signals. 13 00:01:02,040 --> 00:01:04,830 So that will be the focus of today's lecture. 14 00:01:04,830 --> 00:01:10,720 So, so far in class, we have been 15 00:01:10,720 --> 00:01:15,400 analyzing measurements of electrical signals recorded 16 00:01:15,400 --> 00:01:16,760 inside of neurons. 17 00:01:16,760 --> 00:01:21,220 For example in the voltage clamp experiment, 18 00:01:21,220 --> 00:01:24,760 we imagined that we were placing electrodes inside of cells 19 00:01:24,760 --> 00:01:27,790 so that we could measure the voltage inside of this 20 00:01:27,790 --> 00:01:29,110 of cells. 21 00:01:29,110 --> 00:01:31,720 But it's actually quite difficult, in general, 22 00:01:31,720 --> 00:01:36,490 to record membrane potentials of neurons in behaving animals, 23 00:01:36,490 --> 00:01:38,710 although it's certainly possible. 24 00:01:38,710 --> 00:01:43,270 It's much easier to record electrical signals outside 25 00:01:43,270 --> 00:01:44,380 of neurons. 26 00:01:44,380 --> 00:01:47,650 In this case, we can actually record action potentials. 27 00:01:50,740 --> 00:01:52,900 And so those kinds of recordings are 28 00:01:52,900 --> 00:01:58,540 made by placing metal electrodes that are insulated everywhere 29 00:01:58,540 --> 00:02:02,720 along the shank of the electrode except right near the tip. 30 00:02:02,720 --> 00:02:05,560 And if we place a metal electrode in the brain, 31 00:02:05,560 --> 00:02:10,419 we can record voltage changes in the brain 32 00:02:10,419 --> 00:02:12,640 right near cells of interest. 33 00:02:15,940 --> 00:02:20,710 So in this case, we can record from action potentials 34 00:02:20,710 --> 00:02:23,920 of individual neurons in behaving 35 00:02:23,920 --> 00:02:28,030 animals and various aspects of either sensory stimuli 36 00:02:28,030 --> 00:02:28,555 or behavior. 37 00:02:31,790 --> 00:02:35,480 So this kind of recording is called extracellular recording, 38 00:02:35,480 --> 00:02:38,980 and we're going to go through a very simple analysis of how 39 00:02:38,980 --> 00:02:42,790 to think about extracellular recordings. 40 00:02:42,790 --> 00:02:46,660 So recall, of course, that when we measure voltages 41 00:02:46,660 --> 00:02:49,460 in the brain, we're always measuring voltage differences. 42 00:02:49,460 --> 00:02:56,760 So when we place an electrode in the brain near a cell, we are-- 43 00:02:56,760 --> 00:03:00,960 we connect that electrode to an amplifier. 44 00:03:00,960 --> 00:03:04,830 Usually, we use a differential amplifier that gives us-- 45 00:03:04,830 --> 00:03:06,480 that provides us with a measurement 46 00:03:06,480 --> 00:03:08,850 of the voltage difference between two 47 00:03:08,850 --> 00:03:11,970 terminals, the plus terminal and the minus terminal. 48 00:03:11,970 --> 00:03:16,530 So we place-- we connect the electrode to the plus terminal, 49 00:03:16,530 --> 00:03:19,620 and we connect another electrode, 50 00:03:19,620 --> 00:03:23,320 called the ground electrode, that can be placed in the brain 51 00:03:23,320 --> 00:03:25,260 some distance away from the brain area 52 00:03:25,260 --> 00:03:28,110 that we're recording from, or the surface of the skull. 53 00:03:32,930 --> 00:03:38,820 So we're measuring the voltage that's near a cell 54 00:03:38,820 --> 00:03:42,180 relative to the voltage that's someplace further away. 55 00:03:44,810 --> 00:03:50,420 Now, the voltage that we measure in the brain, voltage changes, 56 00:03:50,420 --> 00:03:54,080 are usually or always associated with current flow 57 00:03:54,080 --> 00:03:56,420 through the extracellular space. 58 00:03:56,420 --> 00:03:59,960 So we can analyze this in terms of Ohm's law. 59 00:03:59,960 --> 00:04:04,850 So, basically, the voltage changes that we are measuring 60 00:04:04,850 --> 00:04:10,220 are going to be associated with some current through 61 00:04:10,220 --> 00:04:14,060 extracellular space times some effective resistance 62 00:04:14,060 --> 00:04:15,710 in the extracellular space. 63 00:04:15,710 --> 00:04:17,959 And you remember from previous lectures 64 00:04:17,959 --> 00:04:22,130 that the effective resistance of extracellular space 65 00:04:22,130 --> 00:04:25,820 is proportional to the resistivity in extracellular 66 00:04:25,820 --> 00:04:31,280 space times a length scale divided by an area scale. 67 00:04:34,740 --> 00:04:39,090 So how do we think about what kind of voltage changes 68 00:04:39,090 --> 00:04:44,730 we might expect if we placed an electrode near a cell that is 69 00:04:44,730 --> 00:04:46,930 generating an action potential? 70 00:04:46,930 --> 00:04:50,100 So let's start with a spherical neuron, 71 00:04:50,100 --> 00:04:54,390 and let's give this spherical neuron sodium channels 72 00:04:54,390 --> 00:04:57,090 and potassium channels so that it can generate an action 73 00:04:57,090 --> 00:04:58,840 potential. 74 00:04:58,840 --> 00:05:03,750 So during an action potential, we have an influx of sodium, 75 00:05:03,750 --> 00:05:07,600 followed by an outflux of potassium, 76 00:05:07,600 --> 00:05:09,630 And that influx of sodium produces 77 00:05:09,630 --> 00:05:15,040 a large positive-going change in the voltage inside the cell. 78 00:05:15,040 --> 00:05:17,970 So you can see that during the rising phase of the action 79 00:05:17,970 --> 00:05:21,490 potential, we have sodium flowing in. 80 00:05:21,490 --> 00:05:25,750 But at the same time, we have current flowing 81 00:05:25,750 --> 00:05:30,430 outward through the membrane in the form of capacitive current. 82 00:05:30,430 --> 00:05:35,740 Now, these two currents, the sodium ions 83 00:05:35,740 --> 00:05:40,510 flowing through the membrane and the capacitive current flowing 84 00:05:40,510 --> 00:05:45,970 outwards through the membrane, are co-localized 85 00:05:45,970 --> 00:05:49,720 on the same piece of membrane. 86 00:05:49,720 --> 00:05:52,330 And so there's no spatial separation 87 00:05:52,330 --> 00:05:57,190 of the currents flowing through the membrane. 88 00:05:57,190 --> 00:05:59,140 And as a result of that, there's actually 89 00:05:59,140 --> 00:06:02,680 no current flow in extracellular space, 90 00:06:02,680 --> 00:06:07,750 and so there's no extracellular voltage changes. 91 00:06:07,750 --> 00:06:10,840 The first lesson from this is that, if we 92 00:06:10,840 --> 00:06:16,870 were to record an extracellular space from a spherical neuron 93 00:06:16,870 --> 00:06:20,620 with no dendrites and no axon, we would actually not 94 00:06:20,620 --> 00:06:24,460 be able to measure any extracellular voltage change. 95 00:06:24,460 --> 00:06:27,340 Now let's consider what happens if we 96 00:06:27,340 --> 00:06:31,460 have a neuron with a dendrite. 97 00:06:31,460 --> 00:06:35,880 So in this case, when the sodium current flows into the soma, 98 00:06:35,880 --> 00:06:38,850 that current, part of it will flow out 99 00:06:38,850 --> 00:06:42,000 through the capacitive-- 100 00:06:42,000 --> 00:06:44,550 through capacitive current, but part of that current 101 00:06:44,550 --> 00:06:48,240 will flow down the dendrite, then 102 00:06:48,240 --> 00:06:50,820 out through the membrane through capacitive 103 00:06:50,820 --> 00:06:52,690 current back to the soma. 104 00:06:52,690 --> 00:06:55,710 So we have a closed circuit of current, current flowing 105 00:06:55,710 --> 00:06:57,780 into the soma out through the dendrite, 106 00:06:57,780 --> 00:07:01,380 and then back to the soma through extracellular space. 107 00:07:01,380 --> 00:07:04,740 So in this case, if we write down the equivalent circuit 108 00:07:04,740 --> 00:07:07,540 model of what this looks like-- 109 00:07:07,540 --> 00:07:10,320 this is the somatic compartment, this is the dendritic 110 00:07:10,320 --> 00:07:13,700 compartment-- we have-- 111 00:07:13,700 --> 00:07:20,730 in our earlier calculations of current flow through processes, 112 00:07:20,730 --> 00:07:24,330 through dendrites, we were neglecting the extracellular 113 00:07:24,330 --> 00:07:28,620 resistance, but in this case we are going to include that, 114 00:07:28,620 --> 00:07:32,760 because that extracellular resistance is what provides-- 115 00:07:32,760 --> 00:07:36,370 is what produces a voltage drop in extracellular [? space. ?] 116 00:07:36,370 --> 00:07:38,010 But during an action potential, we 117 00:07:38,010 --> 00:07:40,410 have current flowing in through the soma, 118 00:07:40,410 --> 00:07:43,500 out through the inside of the dendrite, 119 00:07:43,500 --> 00:07:47,520 back out through the membrane of the dendrite, 120 00:07:47,520 --> 00:07:52,950 and through extracellular space back to the soma. 121 00:07:52,950 --> 00:07:59,430 The voltage drop across this region of extracellular space 122 00:07:59,430 --> 00:08:03,210 will be proportional to this extracellular current times 123 00:08:03,210 --> 00:08:04,920 changes in extracellular voltage. 124 00:08:08,900 --> 00:08:18,290 So now, we have a simple view that we have current flowing 125 00:08:18,290 --> 00:08:22,280 into the soma in a region-- 126 00:08:22,280 --> 00:08:24,630 from a region around the soma. 127 00:08:24,630 --> 00:08:28,250 So we have effectively what is known as a current sink. 128 00:08:28,250 --> 00:08:31,250 So we have charges flowing into the soma 129 00:08:31,250 --> 00:08:34,159 in the region around the soma. 130 00:08:34,159 --> 00:08:37,760 That current then flows out through the dendrite 131 00:08:37,760 --> 00:08:40,789 and appears in extracellular space 132 00:08:40,789 --> 00:08:42,409 in the region of the dendrite, and we 133 00:08:42,409 --> 00:08:44,760 call that a current source. 134 00:08:44,760 --> 00:08:47,570 So we have a combination of a current sink 135 00:08:47,570 --> 00:08:49,990 and a current source. 136 00:08:49,990 --> 00:08:54,440 And you can see that the current in extracellular space 137 00:08:54,440 --> 00:09:00,490 is flowing from the current source to the current sink. 138 00:09:00,490 --> 00:09:04,690 So in this case, you can see in our simple equivalent circuit 139 00:09:04,690 --> 00:09:09,520 model that the voltages are more positive in regions 140 00:09:09,520 --> 00:09:14,110 corresponding to current sources, 141 00:09:14,110 --> 00:09:17,320 and the voltages are more negative in regions 142 00:09:17,320 --> 00:09:21,700 of extracellular space corresponding to current sink. 143 00:09:21,700 --> 00:09:23,540 Current is flowing from-- 144 00:09:23,540 --> 00:09:26,160 in extracellular space, this current-- 145 00:09:26,160 --> 00:09:28,650 current is flowing from the region of the dendrite 146 00:09:28,650 --> 00:09:30,600 to the region of the soma. 147 00:09:30,600 --> 00:09:32,640 The voltage here is more positive, 148 00:09:32,640 --> 00:09:34,514 the voltage here is more negative. 149 00:09:37,940 --> 00:09:42,970 Now, let's take a look at understanding the relationship 150 00:09:42,970 --> 00:09:46,450 between the extracellular voltage 151 00:09:46,450 --> 00:09:50,000 change and the intracellular voltage change. 152 00:09:50,000 --> 00:09:51,970 So let's just write down the equation 153 00:09:51,970 --> 00:09:57,670 for the voltage drop across this extracellular space. 154 00:09:57,670 --> 00:10:02,260 That voltage drop is just the external current 155 00:10:02,260 --> 00:10:05,530 times some effective external resistance. 156 00:10:05,530 --> 00:10:08,920 The external current is just the sum 157 00:10:08,920 --> 00:10:11,950 of a capacitive current and a resistive current 158 00:10:11,950 --> 00:10:15,710 through the membrane of the dendrite. 159 00:10:15,710 --> 00:10:19,420 So we can write down that voltage drop is now 160 00:10:19,420 --> 00:10:23,380 proportional to an external resistance-- extracellular 161 00:10:23,380 --> 00:10:25,000 resistance, I should say. 162 00:10:25,000 --> 00:10:28,630 So the-- so we can now write down 163 00:10:28,630 --> 00:10:31,000 an expression for these two currents 164 00:10:31,000 --> 00:10:33,380 as a function of membrane potential. 165 00:10:33,380 --> 00:10:36,160 And you recall from earlier lectures 166 00:10:36,160 --> 00:10:41,260 that the capacitive current is just given by C dV dt, 167 00:10:41,260 --> 00:10:43,570 and the membrane ionic current is 168 00:10:43,570 --> 00:10:47,500 given by some conductance, membrane ionic conductance, 169 00:10:47,500 --> 00:10:49,540 times the driving potential. 170 00:10:49,540 --> 00:10:54,020 Now, in an action potential, voltage change is very rapid. 171 00:10:54,020 --> 00:10:56,170 So dv dt is large. 172 00:10:56,170 --> 00:10:58,600 And, in fact, this term generally 173 00:10:58,600 --> 00:11:01,340 dominates over this term in an action potential. 174 00:11:01,340 --> 00:11:06,640 And so what we find is that the voltage change in extracellular 175 00:11:06,640 --> 00:11:10,750 space is proportional to the derivative 176 00:11:10,750 --> 00:11:12,610 of the membrane potential. 177 00:11:12,610 --> 00:11:15,670 And we can see that this is the case. 178 00:11:15,670 --> 00:11:18,790 In earlier experiments from Gyorgy Buzsaki's lab, 179 00:11:18,790 --> 00:11:21,970 they were able to record simultaneously 180 00:11:21,970 --> 00:11:24,850 from a cell intracellularly-- 181 00:11:24,850 --> 00:11:26,770 that's shown in this trace here-- 182 00:11:26,770 --> 00:11:30,520 and the extracellular voltage recorded 183 00:11:30,520 --> 00:11:34,300 from a microwire electrode placed near the soma. 184 00:11:36,840 --> 00:11:39,930 Extracellular recording is shown here, 185 00:11:39,930 --> 00:11:44,250 that the extracellular signal is actually 186 00:11:44,250 --> 00:11:48,242 quite close to the derivative of the intracellular signal. 187 00:11:48,242 --> 00:11:53,870 Now, why is this voltage negative? 188 00:11:53,870 --> 00:11:59,450 Because the membrane potential near the soma here, 189 00:11:59,450 --> 00:12:03,620 the voltage here goes negative because during the rising phase 190 00:12:03,620 --> 00:12:06,650 of the action potential, we have sodium ions 191 00:12:06,650 --> 00:12:10,700 flowing into the soma from extracellular space. 192 00:12:10,700 --> 00:12:15,560 A current is flowing out of the dendrite out here 193 00:12:15,560 --> 00:12:18,080 and traveling back through extracellular space 194 00:12:18,080 --> 00:12:19,910 to the soma. 195 00:12:19,910 --> 00:12:25,730 So, again, the soma is acting like a voltage sink, 196 00:12:25,730 --> 00:12:30,360 and so the voltage is going negative near the soma. 197 00:12:30,360 --> 00:12:34,150 So now let's take a look at what happens when we have 198 00:12:34,150 --> 00:12:36,260 synaptic input onto a neuron. 199 00:12:36,260 --> 00:12:40,570 So it turns out you can also observe extracellular signals 200 00:12:40,570 --> 00:12:42,820 that result not from action potentials 201 00:12:42,820 --> 00:12:44,990 but from synaptic inputs. 202 00:12:44,990 --> 00:12:51,096 So let's take our example neuron and attach 203 00:12:51,096 --> 00:12:55,770 an excitatory synapse to the dendrite. 204 00:12:55,770 --> 00:12:59,310 In this case, when the synapse is activated, 205 00:12:59,310 --> 00:13:04,560 if the cell is hyperpolarized, when a neurotransmitter is 206 00:13:04,560 --> 00:13:08,980 released onto the postsynaptic compartment of the synapse, 207 00:13:08,980 --> 00:13:12,600 it turns on conductances which allow current to flow 208 00:13:12,600 --> 00:13:14,550 into the dendrite. 209 00:13:14,550 --> 00:13:18,480 That current flows down the dendrite to the soma, 210 00:13:18,480 --> 00:13:21,270 flows back capacitively out through the soma 211 00:13:21,270 --> 00:13:26,640 and back to the synapse through extracellular space. 212 00:13:26,640 --> 00:13:29,130 So you can see that in this case, 213 00:13:29,130 --> 00:13:32,760 the region near the synapse looks like a current sink 214 00:13:32,760 --> 00:13:35,340 as charges are flowing into the cell. 215 00:13:35,340 --> 00:13:39,540 The region near the soma looks like a current source 216 00:13:39,540 --> 00:13:43,540 as current flows out of the soma and back to the current sink. 217 00:13:43,540 --> 00:13:46,950 And see that, in this case, you have charges flowing 218 00:13:46,950 --> 00:13:49,680 into the cell, and that should correspond 219 00:13:49,680 --> 00:13:54,530 to a decrease in the extracellular voltage. 220 00:13:54,530 --> 00:13:56,820 For the soma, you have positive charges 221 00:13:56,820 --> 00:14:02,680 flowing into extracellular space from the inside of the cell, 222 00:14:02,680 --> 00:14:05,600 and that corresponds to an increase. 223 00:14:05,600 --> 00:14:11,640 OK, things look different when you have an inhibitory synapse. 224 00:14:11,640 --> 00:14:14,430 In the case of an inhibitory synapse, 225 00:14:14,430 --> 00:14:19,450 for example if GABA is released onto this GABAergic synapse, 226 00:14:19,450 --> 00:14:21,480 it opens chloride channels. 227 00:14:21,480 --> 00:14:24,100 Chloride is a negative iron that flows into the cell, 228 00:14:24,100 --> 00:14:27,900 but that corresponds to an outward-going current. 229 00:14:27,900 --> 00:14:33,750 So now we have the region around the inhibitory synapse looking 230 00:14:33,750 --> 00:14:35,910 like a current source. 231 00:14:35,910 --> 00:14:38,130 Current flows through extracellular space 232 00:14:38,130 --> 00:14:43,290 to the soma, where the soma now looks like a current sink. 233 00:14:43,290 --> 00:14:47,250 And so in the presence of activation 234 00:14:47,250 --> 00:14:51,570 of inhibitory inputs in the-- near the dendrites, 235 00:14:51,570 --> 00:14:58,150 you actually have an increase in voltage of extracellular space. 236 00:14:58,150 --> 00:15:02,230 While near the soma, you have a decrease in the voltage. 237 00:15:02,230 --> 00:15:05,530 One of the important things to consider 238 00:15:05,530 --> 00:15:07,480 is that, in the discussion we've just had, 239 00:15:07,480 --> 00:15:10,660 we've been thinking about an individual neuron, how 240 00:15:10,660 --> 00:15:13,000 current sources and current sinks 241 00:15:13,000 --> 00:15:18,040 appear as a result of synaptic activity and action potentials 242 00:15:18,040 --> 00:15:20,800 around a single neuron. 243 00:15:20,800 --> 00:15:24,710 But in the brain, neurons are not isolated 244 00:15:24,710 --> 00:15:31,170 but are in the tissue next to many other neurons, that 245 00:15:31,170 --> 00:15:35,170 are also receiving inputs and spiking. 246 00:15:35,170 --> 00:15:40,120 So it turns out that the types of electrical extracellular 247 00:15:40,120 --> 00:15:42,550 signals that you see in the tissue depends 248 00:15:42,550 --> 00:15:47,300 very much on how different cells are organized spatially. 249 00:15:47,300 --> 00:15:52,240 So in some types of tissue, for example in the hippocampus 250 00:15:52,240 --> 00:15:59,440 or in the cortex, cell bodies are lumped together in a layer, 251 00:15:59,440 --> 00:16:04,660 and the dendrites are collinear and are 252 00:16:04,660 --> 00:16:06,380 organized in a different layer. 253 00:16:06,380 --> 00:16:09,250 So this is called a laminar morphology. 254 00:16:09,250 --> 00:16:11,740 In this case, many of the synaptic inputs 255 00:16:11,740 --> 00:16:15,660 arrive onto the dendrites, and currents then 256 00:16:15,660 --> 00:16:18,330 flow into the somata. 257 00:16:18,330 --> 00:16:22,830 And in this case, these extracellular currents 258 00:16:22,830 --> 00:16:25,110 are reinforced. 259 00:16:25,110 --> 00:16:29,550 They reinforce each other, and they sum together 260 00:16:29,550 --> 00:16:35,490 to produce very large extracellular voltage changes. 261 00:16:35,490 --> 00:16:37,020 So now let's turn to the question 262 00:16:37,020 --> 00:16:40,960 of how one actually records neural activity in the brain. 263 00:16:40,960 --> 00:16:43,230 So let's go back to our experimental setup 264 00:16:43,230 --> 00:16:47,190 now where we have an electrode placed 265 00:16:47,190 --> 00:16:49,860 near the soma of a neuron. 266 00:16:49,860 --> 00:16:52,860 And that electrode is connected to a differential amplifier 267 00:16:52,860 --> 00:16:56,400 or an instrumentation amplifier, giving us 268 00:16:56,400 --> 00:17:00,390 the voltage difference between the extracellular 269 00:17:00,390 --> 00:17:03,580 space near the soma and the extracellular space 270 00:17:03,580 --> 00:17:05,210 somewhere far away. 271 00:17:05,210 --> 00:17:10,010 So we-- so this amplifier then measures 272 00:17:10,010 --> 00:17:11,930 that voltage difference and multiplies it 273 00:17:11,930 --> 00:17:14,869 by a gain of typically, let's say, 274 00:17:14,869 --> 00:17:18,079 a couple hundred, or 1,000, or even 10,000. 275 00:17:18,079 --> 00:17:20,119 We then take the output of that amplifier 276 00:17:20,119 --> 00:17:26,119 and put it into an analog to digital converter, that 277 00:17:26,119 --> 00:17:32,030 then measures the voltage at regularly spaced samples 278 00:17:32,030 --> 00:17:39,840 and stores those voltage digitally in computer memory. 279 00:17:39,840 --> 00:17:43,030 So in analog to digital converters, 280 00:17:43,030 --> 00:17:47,940 the voltage is sampled at regular intervals, delta t, 281 00:17:47,940 --> 00:17:51,550 corresponding to some sampling rate, 282 00:17:51,550 --> 00:17:57,910 which is a frequency or a rate that's given by 1 over delta t. 283 00:17:57,910 --> 00:18:01,590 So the rate at which the samples are acquired 284 00:18:01,590 --> 00:18:06,660 is referred to as the sampling rate or sampling frequency. 285 00:18:06,660 --> 00:18:11,310 So if we were to record the extracellular voltage 286 00:18:11,310 --> 00:18:13,860 in a region of the hippocampus, we 287 00:18:13,860 --> 00:18:18,170 might see a signal that looks very much like this. 288 00:18:18,170 --> 00:18:21,530 These are data from Matt Wilson's lab. 289 00:18:21,530 --> 00:18:24,080 The signal has a number of features. 290 00:18:24,080 --> 00:18:27,440 So you can see that there is a slow modulation 291 00:18:27,440 --> 00:18:29,450 of the signal that actually corresponds 292 00:18:29,450 --> 00:18:35,480 to the theta rhythm in a rat. 293 00:18:35,480 --> 00:18:38,300 That slow modulation of the voltage 294 00:18:38,300 --> 00:18:41,270 is actually caused by synaptic currents 295 00:18:41,270 --> 00:18:44,330 in the hippocampus you can also see 296 00:18:44,330 --> 00:18:46,220 that there are very fast deflections 297 00:18:46,220 --> 00:18:49,800 of the voltage corresponding to action potentials. 298 00:18:49,800 --> 00:18:53,120 So, once again, this is about a second's worth 299 00:18:53,120 --> 00:18:56,120 of data of intracellular-- 300 00:18:56,120 --> 00:19:00,140 sorry-- of extracellular recording from rat hippocampus, 301 00:19:00,140 --> 00:19:03,770 and we can see both slow and very fast 302 00:19:03,770 --> 00:19:05,858 components of this signal. 303 00:19:08,370 --> 00:19:11,970 The extracellular-- the action potentials, you can see, 304 00:19:11,970 --> 00:19:13,950 are very brief. 305 00:19:13,950 --> 00:19:16,830 They typically last about a millisecond. 306 00:19:16,830 --> 00:19:20,070 If we were to look at the amount of power 307 00:19:20,070 --> 00:19:27,810 at different frequencies in this signal using a technique called 308 00:19:27,810 --> 00:19:30,810 measuring the power spectrum, which we will cover in more 309 00:19:30,810 --> 00:19:33,270 detail later in class, you can see 310 00:19:33,270 --> 00:19:36,690 that there is a lot of power at low frequencies 311 00:19:36,690 --> 00:19:38,830 and much less power at high frequencies. 312 00:19:38,830 --> 00:19:42,990 So this is a representation of the amount of power 313 00:19:42,990 --> 00:19:45,570 at different frequencies. 314 00:19:45,570 --> 00:19:49,505 So we can actually extract the fast and slow components 315 00:19:49,505 --> 00:19:54,660 of the signal using a technique called high pass and low pass 316 00:19:54,660 --> 00:19:56,200 filtering. 317 00:19:56,200 --> 00:19:57,930 So what we're going to do is we are 318 00:19:57,930 --> 00:20:01,530 going to develop this technique that 319 00:20:01,530 --> 00:20:04,860 allows us to remove high frequency 320 00:20:04,860 --> 00:20:07,290 components from the original signal 321 00:20:07,290 --> 00:20:11,400 to reveal just low-frequency structure within the signals. 322 00:20:11,400 --> 00:20:13,070 So how do we do that? 323 00:20:13,070 --> 00:20:15,750 Well, basically, what we do is we're 324 00:20:15,750 --> 00:20:21,360 going to start by using a technique of low pass filtering 325 00:20:21,360 --> 00:20:24,750 that works basically by convolving 326 00:20:24,750 --> 00:20:27,720 this signal with a kernel. 327 00:20:27,720 --> 00:20:31,710 What that kernel does is it locally averages the signal 328 00:20:31,710 --> 00:20:35,080 over short periods of time. 329 00:20:35,080 --> 00:20:37,290 So what we do is we take that signal, 330 00:20:37,290 --> 00:20:40,830 and we're going to place this kernel 331 00:20:40,830 --> 00:20:43,410 over the signal at different points 332 00:20:43,410 --> 00:20:47,200 in time, average together. 333 00:20:47,200 --> 00:20:48,880 We're going to multiply the kernel 334 00:20:48,880 --> 00:20:53,560 by this signal at different points of time-- in time, 335 00:20:53,560 --> 00:20:57,160 and plot the result down here. 336 00:20:57,160 --> 00:20:59,690 So let me explain what that looks like. 337 00:20:59,690 --> 00:21:02,050 So let's say this is the original signal. 338 00:21:02,050 --> 00:21:04,720 You can see that it's a little bit noisy. 339 00:21:04,720 --> 00:21:08,410 It's fluctuating between 1 and 3, 1, 3, 1, 3. 340 00:21:08,410 --> 00:21:10,300 And then, at a certain point here, it 341 00:21:10,300 --> 00:21:16,750 jumps to a higher value, 5, 3, 5, 3, 5. 342 00:21:16,750 --> 00:21:20,610 So, intuitively, we would expect low 343 00:21:20,610 --> 00:21:24,840 pass filtered version of this signal to be low here, 344 00:21:24,840 --> 00:21:27,950 and then jump up to a higher value here. 345 00:21:27,950 --> 00:21:31,350 Now, here's our kernel. 346 00:21:31,350 --> 00:21:34,695 This is a representation of a kernel that looks like this. 347 00:21:37,300 --> 00:21:41,307 The kernel is 0, 0.5, 0.5, and 0. 348 00:21:41,307 --> 00:21:42,890 And, basically, what we're going to do 349 00:21:42,890 --> 00:21:47,690 is place the kernel at some point in time over our signal, 350 00:21:47,690 --> 00:21:53,430 multiply the kernel by the signal time 351 00:21:53,430 --> 00:21:55,590 element by time element. 352 00:21:55,590 --> 00:21:59,100 So you can see that the product of the kernel with the signal 353 00:21:59,100 --> 00:22:00,160 is 0 here. 354 00:22:00,160 --> 00:22:07,010 0 times 1 is 0, 0.5 times 3 is 1.5, 0.5 times 1 is 0.5, 355 00:22:07,010 --> 00:22:08,640 and 0 times 3 is 0. 356 00:22:08,640 --> 00:22:10,290 So that's the product of the kernel 357 00:22:10,290 --> 00:22:13,260 and the signal within that time window. 358 00:22:13,260 --> 00:22:16,140 Then sum up that-- 359 00:22:16,140 --> 00:22:18,300 the elements of that product. 360 00:22:18,300 --> 00:22:23,350 0 plus 1.5 plus 0.5 plus 0 is 2. 361 00:22:23,350 --> 00:22:26,520 I'm going to write down that sum at this point 362 00:22:26,520 --> 00:22:29,410 in the filtered output. 363 00:22:29,410 --> 00:22:33,980 Now, what we're going to do is just slide the kernel over 364 00:22:33,980 --> 00:22:39,390 by one element and repeat that. 365 00:22:39,390 --> 00:22:47,490 And I also added the earlier values of the output here. 366 00:22:47,490 --> 00:22:50,540 So now we slide the kernel over by one, we repeat. 367 00:22:50,540 --> 00:22:54,170 We get 0, 0.5, 1.5, and 0. 368 00:22:54,170 --> 00:22:56,300 Sum that up, we get a 2. 369 00:22:56,300 --> 00:23:00,020 And write down that filtered output down here. 370 00:23:00,020 --> 00:23:05,090 So you can see that the low pass filtered result of this signal 371 00:23:05,090 --> 00:23:08,520 is 2 everywhere up to here. 372 00:23:08,520 --> 00:23:12,870 Now, if we slide the kernel over one more and multiply, 373 00:23:12,870 --> 00:23:16,730 you can see we get a 0, a 1.5. 374 00:23:16,730 --> 00:23:18,350 Here's 0.5 times 5. 375 00:23:18,350 --> 00:23:20,360 That's 2.5. 376 00:23:20,360 --> 00:23:22,190 0 times 3 is 0. 377 00:23:22,190 --> 00:23:28,260 And the sum of that, the sum of those four elements is 4. 378 00:23:28,260 --> 00:23:30,640 Write down a 4 here. 379 00:23:30,640 --> 00:23:34,220 And if we keep doing that, all of the rest of those values 380 00:23:34,220 --> 00:23:36,300 is 4, which you can verify. 381 00:23:36,300 --> 00:23:39,960 So you can see that the low pass filtered 382 00:23:39,960 --> 00:23:45,380 version of this signal, filtered by this kernel, 383 00:23:45,380 --> 00:23:48,500 is 2 up to this point, and then it jumps up 384 00:23:48,500 --> 00:23:51,350 to 4, which was consistent with our intuition 385 00:23:51,350 --> 00:23:54,710 about what low pass filtering would do. 386 00:23:54,710 --> 00:23:56,750 So that was low pass filtering. 387 00:23:56,750 --> 00:23:58,760 Now, how would we high pass filter? 388 00:23:58,760 --> 00:24:02,990 How would we extract out these high frequency components 389 00:24:02,990 --> 00:24:07,970 from the data, throw away the low frequency components? 390 00:24:07,970 --> 00:24:12,344 Well, one way to think about this is that we actually-- 391 00:24:12,344 --> 00:24:15,020 we can get rid of the low frequency 392 00:24:15,020 --> 00:24:19,490 elements simply by subtracting off the low pass 393 00:24:19,490 --> 00:24:21,330 signal that we just calculated. 394 00:24:21,330 --> 00:24:24,510 So how do we do that? 395 00:24:24,510 --> 00:24:26,630 So we're going to use this kernel here 396 00:24:26,630 --> 00:24:29,030 to do our high pass filtering. 397 00:24:29,030 --> 00:24:32,070 And notice that this kernel has two components. 398 00:24:32,070 --> 00:24:36,120 It has a square component that's negative, 399 00:24:36,120 --> 00:24:38,700 and it has a delta function at 0. 400 00:24:38,700 --> 00:24:42,120 So you can see that this negative component 401 00:24:42,120 --> 00:24:49,990 of this high pass filter looks a lot like the negative of our-- 402 00:24:52,920 --> 00:24:57,510 looks like the negative of our low pass filter. 403 00:24:57,510 --> 00:25:01,700 So if we were to take this kernel 404 00:25:01,700 --> 00:25:04,190 and instead use a kernel that was 405 00:25:04,190 --> 00:25:07,910 the negative of that kernel, like this, then what 406 00:25:07,910 --> 00:25:10,730 we would get is the negative of this low passed, 407 00:25:10,730 --> 00:25:13,790 of this filtered signal. 408 00:25:13,790 --> 00:25:21,660 So this part right here, this part of the high pass filter, 409 00:25:21,660 --> 00:25:25,450 is producing the negative of our low pass filter. 410 00:25:25,450 --> 00:25:27,810 Now let's take a look at this component here. 411 00:25:27,810 --> 00:25:31,230 This component is a delta function with a value of 1 412 00:25:31,230 --> 00:25:32,310 at the peak. 413 00:25:32,310 --> 00:25:35,280 You can see that if you convolve that kernel 414 00:25:35,280 --> 00:25:37,050 with your original signal, it just 415 00:25:37,050 --> 00:25:40,520 gives you back the same original signal. 416 00:25:40,520 --> 00:25:43,060 So what we've done is this component simply gives us 417 00:25:43,060 --> 00:25:44,890 back the original signal. 418 00:25:44,890 --> 00:25:49,930 This component subtracts off the low pass version of the signal. 419 00:25:49,930 --> 00:25:52,570 What we're left with is the high pass version. 420 00:25:52,570 --> 00:25:55,960 Let's look at what that does to the spectrum of our signal. 421 00:25:55,960 --> 00:25:59,050 You can see that, the high pass, we've 422 00:25:59,050 --> 00:26:04,030 gotten rid of all of these low frequencies, all of the power 423 00:26:04,030 --> 00:26:06,010 at low frequencies, and we're left 424 00:26:06,010 --> 00:26:09,130 with just the high frequency part of our signal. 425 00:26:09,130 --> 00:26:12,250 And if we go back and look at the spectrum of what 426 00:26:12,250 --> 00:26:15,800 the low passed signal looks like, 427 00:26:15,800 --> 00:26:21,070 we can see that the low passed output retains all of the power 428 00:26:21,070 --> 00:26:25,090 at low frequencies and gets rid of these high frequency 429 00:26:25,090 --> 00:26:27,690 components [AUDIO OUT]. 430 00:26:27,690 --> 00:26:33,760 Low passed signal has no power at high frequencies. 431 00:26:33,760 --> 00:26:37,550 So once we have extracted high pass filtered 432 00:26:37,550 --> 00:26:40,850 version of the signal, you can see that what you're left with 433 00:26:40,850 --> 00:26:43,800 are action potentials. 434 00:26:43,800 --> 00:26:45,680 So what we're going to talk about now 435 00:26:45,680 --> 00:26:51,010 is how you actually extract these action potentials 436 00:26:51,010 --> 00:26:54,400 and figure out when action potentials occurred 437 00:26:54,400 --> 00:26:57,850 during this behavior. 438 00:26:57,850 --> 00:27:00,900 Next thing we're going to do is detect-- 439 00:27:00,900 --> 00:27:03,060 we're going to do spike detection. 440 00:27:03,060 --> 00:27:06,240 So, basically, the best way to detect spikes 441 00:27:06,240 --> 00:27:10,870 is to look at the signal, plot the signal, 442 00:27:10,870 --> 00:27:17,020 and figure out what amplitude the spikes are. 443 00:27:17,020 --> 00:27:22,210 So look at the voltage of the peak, the peak of the spikes. 444 00:27:22,210 --> 00:27:27,840 And then set a threshold that consistently 445 00:27:27,840 --> 00:27:32,800 is crossed by that peak in the spike waveform. 446 00:27:32,800 --> 00:27:36,050 So here are the individual samples associated 447 00:27:36,050 --> 00:27:38,450 with one action potential. 448 00:27:38,450 --> 00:27:40,610 You can see that a voltage right about here 449 00:27:40,610 --> 00:27:43,850 will reliably detect these spikes. 450 00:27:43,850 --> 00:27:47,930 And then, basically, you write one line of MATLAB code 451 00:27:47,930 --> 00:27:51,620 that detects where this voltage crossed 452 00:27:51,620 --> 00:27:55,580 from being below your threshold on one sample to being 453 00:27:55,580 --> 00:27:58,070 above your threshold on the next. 454 00:27:58,070 --> 00:28:02,300 Now what we can do is, once we detect 455 00:28:02,300 --> 00:28:07,190 the time at which that threshold crossing occurred, 456 00:28:07,190 --> 00:28:10,220 we can write down that threshold crossing time 457 00:28:10,220 --> 00:28:12,580 for each spike in our wave form. 458 00:28:12,580 --> 00:28:14,590 The spike here, we write down that time. 459 00:28:14,590 --> 00:28:16,430 That's t1. 460 00:28:16,430 --> 00:28:18,380 If you have another threshold crossing here, 461 00:28:18,380 --> 00:28:20,650 you write that time down, t2. 462 00:28:20,650 --> 00:28:25,990 And you collect all of these spike times into an array. 463 00:28:25,990 --> 00:28:30,260 So we can now represent the spike train 464 00:28:30,260 --> 00:28:32,280 as a list of spike times. 465 00:28:32,280 --> 00:28:39,710 So we're going represent this as variable t with an index 466 00:28:39,710 --> 00:28:43,730 i, where i goes from 1 to N. Now, 467 00:28:43,730 --> 00:28:48,310 we can also think of spike trains as a delta function. 468 00:28:48,310 --> 00:28:51,980 So you may remember that a delta function 469 00:28:51,980 --> 00:28:56,990 is 0 everywhere except at the time where the argument is 0. 470 00:28:56,990 --> 00:29:00,830 So this delta function is 0 everywhere except when 471 00:29:00,830 --> 00:29:03,425 t is equal to t signal. 472 00:29:03,425 --> 00:29:07,960 That's when t is equal to the time of the signal. 473 00:29:07,960 --> 00:29:12,830 At that time, the delta function has a non-zero value. 474 00:29:12,830 --> 00:29:15,610 So we can write down this spike train 475 00:29:15,610 --> 00:29:18,320 as a sum of delta functions. 476 00:29:18,320 --> 00:29:20,890 So the spike train is a function of time 477 00:29:20,890 --> 00:29:24,100 is delta of t minus t1, corresponding 478 00:29:24,100 --> 00:29:28,750 to the first spike, plus another delta function at time 479 00:29:28,750 --> 00:29:33,730 t2 corresponding to that spike, and so on. 480 00:29:33,730 --> 00:29:39,390 So we can now write down mathematically our spike train 481 00:29:39,390 --> 00:29:45,210 as a sum of delta functions, one at each spike time. 482 00:29:45,210 --> 00:29:48,360 We can also think of a spike train 483 00:29:48,360 --> 00:29:52,600 as being the derivative of a spike count function. 484 00:29:52,600 --> 00:29:56,040 So a spike count function will reflect the number 485 00:29:56,040 --> 00:30:01,260 of spikes that have occurred at times less than the time 486 00:30:01,260 --> 00:30:02,860 in the argument. 487 00:30:02,860 --> 00:30:08,430 So if this is our spike train, then prior to the first spike, 488 00:30:08,430 --> 00:30:13,800 there will be zero spikes in our spike count function. 489 00:30:13,800 --> 00:30:17,730 After the first spike, then we'll have a spike count of 1. 490 00:30:17,730 --> 00:30:21,840 And you can see that you get this stairstep increasing 491 00:30:21,840 --> 00:30:26,840 to the right for each spike in the spike train. 492 00:30:26,840 --> 00:30:31,640 Since the integral of this spike train has units-- 493 00:30:31,640 --> 00:30:35,060 the integral over time has units of spikes, 494 00:30:35,060 --> 00:30:40,220 you can see that the spike train, this rho of t, 495 00:30:40,220 --> 00:30:42,270 has units of spikes per second. 496 00:30:46,360 --> 00:30:49,840 So now let's turn to the question 497 00:30:49,840 --> 00:30:54,220 of what we can extract from neural activity 498 00:30:54,220 --> 00:30:56,500 by measuring spike trains. 499 00:30:56,500 --> 00:30:58,420 So one of the simplest properties 500 00:30:58,420 --> 00:31:03,430 that we find about cells in the brain 501 00:31:03,430 --> 00:31:08,320 is that they usually have a firing rate that 502 00:31:08,320 --> 00:31:10,210 depends on something, either a motor 503 00:31:10,210 --> 00:31:12,760 behavior or a sensory stimulus. 504 00:31:12,760 --> 00:31:17,230 So, for example, simple cells in primary visual cortex, 505 00:31:17,230 --> 00:31:22,480 of the cat in this case, are responsive to the orientation 506 00:31:22,480 --> 00:31:24,210 of visual-- 507 00:31:24,210 --> 00:31:26,870 of stimuli in the visual field. 508 00:31:26,870 --> 00:31:30,670 So this shows a bar of light, but represents 509 00:31:30,670 --> 00:31:34,400 a bright bar of light on a black background, actually. 510 00:31:34,400 --> 00:31:39,610 And you can see that if you move this bar in space, 511 00:31:39,610 --> 00:31:42,190 at this orientation this neuron doesn't respond. 512 00:31:42,190 --> 00:31:44,560 But if we rotate the-- 513 00:31:44,560 --> 00:31:48,320 if we rotate this bar of light and move it in this direction, 514 00:31:48,320 --> 00:31:51,710 now the cell responds with a high firing rate. 515 00:31:51,710 --> 00:31:53,710 So if we quantify the firing rate 516 00:31:53,710 --> 00:31:58,420 as a function of orientation of this bar of light, 517 00:31:58,420 --> 00:32:02,590 you can see that the neuron has a higher firing 518 00:32:02,590 --> 00:32:06,600 rate for some orientations than for others. 519 00:32:06,600 --> 00:32:12,900 That property of being tuned for particular stimulus features 520 00:32:12,900 --> 00:32:17,790 is called tuning, and the measurement 521 00:32:17,790 --> 00:32:21,600 of that firing rate as a function of some parameter 522 00:32:21,600 --> 00:32:24,444 is called a tuning curve. 523 00:32:24,444 --> 00:32:27,630 So you can see that in primary visual cortex, 524 00:32:27,630 --> 00:32:30,450 neurons are tuned to orientation. 525 00:32:30,450 --> 00:32:35,130 And the tuning curves of neurons in primary visual cortex 526 00:32:35,130 --> 00:32:41,850 often have this characteristic of being highly responsive 527 00:32:41,850 --> 00:32:45,240 at particular orientations, and then smoothly dropping off 528 00:32:45,240 --> 00:32:50,130 to being unresponsive at other orientations. 529 00:32:50,130 --> 00:32:52,566 So in a similar-- 530 00:32:52,566 --> 00:32:55,800 similar to the way that neurons in visual cortex 531 00:32:55,800 --> 00:33:00,840 are tuned to orientation, neurons in auditory cortex 532 00:33:00,840 --> 00:33:03,100 are tuned to different frequencies. 533 00:33:03,100 --> 00:33:07,020 So, for example, in the auditory system, 534 00:33:07,020 --> 00:33:09,690 when sound impinges on the ear, it 535 00:33:09,690 --> 00:33:14,030 transmits vibrations into the cochlea. 536 00:33:14,030 --> 00:33:17,480 Those vibrations enter the cochlea and propagate 537 00:33:17,480 --> 00:33:21,020 along a basilar membrane, where vibrations 538 00:33:21,020 --> 00:33:23,480 of particular frequencies are amplified 539 00:33:23,480 --> 00:33:26,750 at particular locations, and the membrane 540 00:33:26,750 --> 00:33:32,280 is unresponsive to vibrations of other frequencies. 541 00:33:32,280 --> 00:33:34,040 So if you [? learn ?] from neurons 542 00:33:34,040 --> 00:33:36,380 in visual cortex and you-- 543 00:33:36,380 --> 00:33:39,020 sorry-- in auditory cortex and you play a tone, 544 00:33:39,020 --> 00:33:46,610 so this shows a philograph of a auditory stimulus. 545 00:33:46,610 --> 00:33:50,570 At some frequency, you can see that this neuron spiked 546 00:33:50,570 --> 00:33:53,476 robustly in response to that. 547 00:33:53,476 --> 00:34:00,090 So Individual neurons are tuned to respond robustly 548 00:34:00,090 --> 00:34:03,810 at particular frequencies but not other frequencies. 549 00:34:03,810 --> 00:34:09,120 And you can see that different neurons 550 00:34:09,120 --> 00:34:11,080 are selective to different frequencies. 551 00:34:11,080 --> 00:34:16,530 So you can see that this curve representing one neuron, 552 00:34:16,530 --> 00:34:20,429 that neuron is most active for frequencies 553 00:34:20,429 --> 00:34:24,060 around a little bit above 5 kilohertz, 554 00:34:24,060 --> 00:34:27,241 whereas other neurons are most responsive to frequencies 555 00:34:27,241 --> 00:34:28,491 around 6 kilohertz, and so on. 556 00:34:31,280 --> 00:34:35,250 So we saw an example now of how firing rates of neurons 557 00:34:35,250 --> 00:34:40,230 in sensory cortex are sensitive to particular parameters 558 00:34:40,230 --> 00:34:41,469 of the sensory stimulus. 559 00:34:44,429 --> 00:34:47,940 This property of tuning applies not only to sensory neurons 560 00:34:47,940 --> 00:34:50,639 but also to neurons in motor cortex. 561 00:34:50,639 --> 00:34:54,630 This shows the results of a classic experiment 562 00:34:54,630 --> 00:34:59,640 on analyzing the spiking activity of neurons 563 00:34:59,640 --> 00:35:03,390 in motor cortex during the movements, 564 00:35:03,390 --> 00:35:05,560 during our movements in different directions. 565 00:35:05,560 --> 00:35:08,280 So this shows a manipulandum. 566 00:35:08,280 --> 00:35:11,220 This is basically a little arm that the monkey 567 00:35:11,220 --> 00:35:14,910 can grab the handle here and move that arm around. 568 00:35:14,910 --> 00:35:18,450 The monkey's task is to hold that-- 569 00:35:18,450 --> 00:35:23,370 hold this arm at a central location. 570 00:35:23,370 --> 00:35:25,620 And then a light comes on, and the monkey 571 00:35:25,620 --> 00:35:28,320 has to move this manipulandum from the center 572 00:35:28,320 --> 00:35:31,590 out to the location of the light that turned on. 573 00:35:31,590 --> 00:35:35,310 And so the experiment is repeated multiple times 574 00:35:35,310 --> 00:35:38,790 where the monkey has to move to different directions. 575 00:35:38,790 --> 00:35:41,250 You can see here the trajectories 576 00:35:41,250 --> 00:35:43,980 that the monkey went through as it moves from the center 577 00:35:43,980 --> 00:35:48,520 location out to these eight different target locations. 578 00:35:51,680 --> 00:35:54,080 And in this experiment, neurons were 579 00:35:54,080 --> 00:36:00,440 recorded at different regions of motor cortex, and the results-- 580 00:36:00,440 --> 00:36:03,290 the resulting spike trains were plotted. 581 00:36:03,290 --> 00:36:05,975 In this figure, you can see what are 582 00:36:05,975 --> 00:36:08,180 called raster plots, where-- 583 00:36:08,180 --> 00:36:13,760 for example, for movements in this direction, 584 00:36:13,760 --> 00:36:16,260 five trials were collected together. 585 00:36:16,260 --> 00:36:18,770 So each row here corresponds to the spikes 586 00:36:18,770 --> 00:36:22,130 that a neuron generated during movements from the center 587 00:36:22,130 --> 00:36:24,154 to this direction. 588 00:36:24,154 --> 00:36:29,640 You can see that the neuron became active just after 589 00:36:29,640 --> 00:36:33,240 the [INAUDIBLE],, indicating which direction was turned 590 00:36:33,240 --> 00:36:36,550 on, and prior to the onset of the movement, 591 00:36:36,550 --> 00:36:39,234 which is indicated [AUDIO OUT]. 592 00:36:39,234 --> 00:36:42,160 You can see that the neuron responded robustly 593 00:36:42,160 --> 00:36:46,300 on every single trial to movements in this direction. 594 00:36:46,300 --> 00:36:50,230 But the neuron responded quite differently 595 00:36:50,230 --> 00:36:51,730 in some other direction. 596 00:36:51,730 --> 00:36:54,460 So you can see that the response to downward movement 597 00:36:54,460 --> 00:36:55,750 was quite weak. 598 00:36:55,750 --> 00:36:58,750 There was essentially no change in the firing rate. 599 00:36:58,750 --> 00:37:01,100 And you can see the to movements in other directions, 600 00:37:01,100 --> 00:37:03,580 for example to the right, were associated 601 00:37:03,580 --> 00:37:07,330 with an actual suppression of the spiking activity. 602 00:37:07,330 --> 00:37:11,650 So I should just point out briefly that these spikes here 603 00:37:11,650 --> 00:37:16,330 and here, before and after the onset of the trial, 604 00:37:16,330 --> 00:37:20,980 are spontaneous spikes that occurred continuously even when 605 00:37:20,980 --> 00:37:25,070 the monkey wasn't engaged in moving the handle. 606 00:37:25,070 --> 00:37:27,740 So we have a spontaneous firing rate, 607 00:37:27,740 --> 00:37:30,680 the trial initiates an increase in firing rate, 608 00:37:30,680 --> 00:37:36,680 and then a recovery to the baseline position. 609 00:37:36,680 --> 00:37:38,660 So you can see that these motor cortical 610 00:37:38,660 --> 00:37:43,490 neurons exhibit tuning for particular movement directions. 611 00:37:43,490 --> 00:37:47,480 And we can quantify this now by counting the number of spikes 612 00:37:47,480 --> 00:37:50,660 in this movement interval, and plotting that 613 00:37:50,660 --> 00:37:53,760 as a function of the angle of the movement. 614 00:37:53,760 --> 00:37:57,250 And when you that, you can see that movements 615 00:37:57,250 --> 00:38:00,150 in particular directions, in this case 616 00:38:00,150 --> 00:38:05,620 [AUDIO OUT] by degree direction, resulted in high firing rates, 617 00:38:05,620 --> 00:38:07,450 whereas movements in other directions 618 00:38:07,450 --> 00:38:11,090 resulted in lower firing rates. 619 00:38:11,090 --> 00:38:14,080 So in order to do this kind of quantification, 620 00:38:14,080 --> 00:38:16,600 we need to be able to-- 621 00:38:16,600 --> 00:38:19,480 we need to understand a few different methods 622 00:38:19,480 --> 00:38:23,080 for how we can actually quantify firing rates. 623 00:38:23,080 --> 00:38:25,030 The simplest thing that I just described 624 00:38:25,030 --> 00:38:27,910 here is to just count the number of spikes 625 00:38:27,910 --> 00:38:30,880 in some particular interval that you decide 626 00:38:30,880 --> 00:38:32,960 is relevant for your experiment. 627 00:38:32,960 --> 00:38:36,400 So, for example, let's say we have a stimulus that 628 00:38:36,400 --> 00:38:40,510 turns on at a particular time, is-- it stays on, 629 00:38:40,510 --> 00:38:43,420 and then turns off at some later time. 630 00:38:43,420 --> 00:38:46,690 On different trials of that-- or different presentations 631 00:38:46,690 --> 00:38:49,750 of that stimulus, you can see that the spike 632 00:38:49,750 --> 00:38:56,390 train- that the neuron spikes in a somewhat different way. 633 00:38:56,390 --> 00:38:59,960 But you can see that this sample neuron here, 634 00:38:59,960 --> 00:39:04,170 that I just made up, you can see that, in general, there 635 00:39:04,170 --> 00:39:08,840 is a vague increase in the firing rate after the onset 636 00:39:08,840 --> 00:39:10,440 of the stimulus. 637 00:39:10,440 --> 00:39:14,510 So we can quantify that by simply setting a relevant time 638 00:39:14,510 --> 00:39:19,262 window and counting the number of spikes in that time window. 639 00:39:19,262 --> 00:39:20,720 So we're going to set a time window 640 00:39:20,720 --> 00:39:24,740 T from the onset of the stimulus to the offset of the stimulus, 641 00:39:24,740 --> 00:39:29,300 and simply count the number of spikes on each trial. 642 00:39:29,300 --> 00:39:34,030 So N is the number of spikes that occurred on the ith trial. 643 00:39:34,030 --> 00:39:40,450 The brackets here represent the average over that quantity 644 00:39:40,450 --> 00:39:42,630 i, which is trial number. 645 00:39:42,630 --> 00:39:45,510 So we're going to count the number of spikes on the ith 646 00:39:45,510 --> 00:39:49,215 trial and average that over trials. 647 00:39:53,380 --> 00:39:56,350 So then, once we have that average count, 648 00:39:56,350 --> 00:40:01,600 we simply divide by the interval T that we're counting over, 649 00:40:01,600 --> 00:40:03,070 and that gives us a rate. 650 00:40:03,070 --> 00:40:07,570 Now, you can see that the number of spikes, the firing rate 651 00:40:07,570 --> 00:40:08,620 is not constant. 652 00:40:08,620 --> 00:40:10,690 So you can see in this little toy example 653 00:40:10,690 --> 00:40:13,170 here that, the way I've drawn it, 654 00:40:13,170 --> 00:40:18,520 that the spike rate increases at stimulus onset, 655 00:40:18,520 --> 00:40:20,900 and then it decayed away, which is very typical. 656 00:40:20,900 --> 00:40:23,440 So you're throwing away a lot of information. 657 00:40:23,440 --> 00:40:25,960 Now, the way that we just quantified that firing rate, 658 00:40:25,960 --> 00:40:29,540 we just counted spikes over the whole stimulus presentation. 659 00:40:29,540 --> 00:40:32,620 But if we want to get more temporal resolution in how 660 00:40:32,620 --> 00:40:35,140 we quantify the firing rate, we can actually 661 00:40:35,140 --> 00:40:37,420 just break the period of interest 662 00:40:37,420 --> 00:40:41,650 up into smaller pieces, count the number of spikes, 663 00:40:41,650 --> 00:40:47,290 the average number of spikes in each one of these smaller bins, 664 00:40:47,290 --> 00:40:51,040 and divide by the interval of these smaller bins. 665 00:40:51,040 --> 00:40:53,560 So, for example, we can have-- 666 00:40:53,560 --> 00:41:01,810 we can count the number of spikes on trial i and then j. 667 00:41:01,810 --> 00:41:04,600 And we can average the number of spikes 668 00:41:04,600 --> 00:41:07,360 in the jth bin, overall trials. 669 00:41:07,360 --> 00:41:08,800 So that's just the average number 670 00:41:08,800 --> 00:41:11,140 of spikes in this first bin, for example, 671 00:41:11,140 --> 00:41:13,440 and divide by the interval delta T. 672 00:41:13,440 --> 00:41:17,080 And so now you can see that you have a different rate, finer 673 00:41:17,080 --> 00:41:19,270 temporal resolution. 674 00:41:19,270 --> 00:41:22,550 So, for example, if you look at the analysis 675 00:41:22,550 --> 00:41:26,090 that Georgopoulos did in that 1982 paper 676 00:41:26,090 --> 00:41:28,670 for the arm movements of the monkey, 677 00:41:28,670 --> 00:41:38,270 they broke the trials up into small bins of about 10 678 00:41:38,270 --> 00:41:42,460 or 20 milliseconds each, counted the number of spikes 679 00:41:42,460 --> 00:41:45,220 in each one of those bins, divided by that bin width, 680 00:41:45,220 --> 00:41:50,082 and computed the firing rate, spikes per second, 681 00:41:50,082 --> 00:41:51,926 in each one of those bins. 682 00:41:51,926 --> 00:41:55,060 You can see that they did one other thing here. 683 00:41:55,060 --> 00:42:02,160 The average firing rate during each bin 684 00:42:02,160 --> 00:42:06,530 in which we've subtracted off the firing rate 685 00:42:06,530 --> 00:42:10,260 in the pre-stimulus period. 686 00:42:10,260 --> 00:42:12,980 So that is, very typically, what you'll 687 00:42:12,980 --> 00:42:15,860 see in a neuroscience paper describing 688 00:42:15,860 --> 00:42:18,410 the behavior of neurons to a stimulus 689 00:42:18,410 --> 00:42:22,230 or during a motor task. 690 00:42:22,230 --> 00:42:26,100 And so we can use similar tricks to estimate 691 00:42:26,100 --> 00:42:32,520 the firing rate of neurons in just a continuous spike train. 692 00:42:32,520 --> 00:42:35,130 So not all neuroscience experiments 693 00:42:35,130 --> 00:42:39,420 are done in trials like this, where we present a stimulus 694 00:42:39,420 --> 00:42:41,040 and then turn it off. 695 00:42:41,040 --> 00:42:43,800 Some trials-- some experiments are done, for example, 696 00:42:43,800 --> 00:42:45,120 where a movie may-- 697 00:42:45,120 --> 00:42:49,140 a monkey or an animal might be in a movie 698 00:42:49,140 --> 00:42:51,630 where stimuli are presented continuously. 699 00:42:51,630 --> 00:42:54,210 So you don't have this clear trial structure. 700 00:42:54,210 --> 00:42:57,060 So we can also quantify firing rates 701 00:42:57,060 --> 00:42:59,640 in cases where we just have a continuous spike 702 00:42:59,640 --> 00:43:01,770 train without trials. 703 00:43:01,770 --> 00:43:03,810 And we can do that, again, by just taking 704 00:43:03,810 --> 00:43:09,270 that continuous spike train and breaking it up into intervals. 705 00:43:09,270 --> 00:43:14,310 So there will be N sub j spikes in bin j, 706 00:43:14,310 --> 00:43:18,330 and then the bin has some width delta T. Now, 707 00:43:18,330 --> 00:43:20,580 one problem that you can see immediately from this 708 00:43:20,580 --> 00:43:25,320 is that the answer you get will depend on where you place 709 00:43:25,320 --> 00:43:26,530 the boundaries of the bin. 710 00:43:26,530 --> 00:43:30,390 So if you take all these bins and you shift them over by, 711 00:43:30,390 --> 00:43:32,820 let's say, half of-- 712 00:43:32,820 --> 00:43:34,620 shift them over by delta T over 2, 713 00:43:34,620 --> 00:43:37,870 you can see that you can get a completely different set of-- 714 00:43:37,870 --> 00:43:42,690 a different set of firing rates for this same spike train. 715 00:43:42,690 --> 00:43:46,720 So there's not a unique answer. 716 00:43:46,720 --> 00:43:54,060 So another way to do this is to quantify firing rates 717 00:43:54,060 --> 00:43:58,910 in bins that are shifted to all possible times. 718 00:43:58,910 --> 00:44:05,860 So, for example, we can take a window 719 00:44:05,860 --> 00:44:11,540 where we have 0 everywhere except within this window. 720 00:44:11,540 --> 00:44:13,828 We can now multiply the spike train. 721 00:44:13,828 --> 00:44:15,370 Well, one way to do this would simply 722 00:44:15,370 --> 00:44:19,030 be to count the number of spikes within that window, 723 00:44:19,030 --> 00:44:21,940 and then shift the window over and count the number of spikes, 724 00:44:21,940 --> 00:44:24,730 and shift the window over and count the number of spikes. 725 00:44:24,730 --> 00:44:26,860 And now you get a count of number 726 00:44:26,860 --> 00:44:29,670 of spikes in each of those windows 727 00:44:29,670 --> 00:44:31,780 for all the windows that have width delta T, 728 00:44:31,780 --> 00:44:37,330 but we've shifted it in small time steps. 729 00:44:37,330 --> 00:44:40,070 But how can we describe that mathematically? 730 00:44:40,070 --> 00:44:44,630 Well, you may recall that this, in fact, 731 00:44:44,630 --> 00:44:47,030 looks a lot like a convolution. 732 00:44:47,030 --> 00:44:50,450 We're going to take this square kernel, 733 00:44:50,450 --> 00:44:54,530 and we're going to multiply it by the spike train 734 00:44:54,530 --> 00:44:56,900 and count the number of spikes, take 735 00:44:56,900 --> 00:44:59,100 the integral over that product. 736 00:44:59,100 --> 00:45:00,680 And you can see that that's basically 737 00:45:00,680 --> 00:45:03,350 going to give you the number of spikes 738 00:45:03,350 --> 00:45:06,170 within that window from t1 to t2. 739 00:45:06,170 --> 00:45:08,480 So, for example, in this case we're 740 00:45:08,480 --> 00:45:11,020 going to use a square window. 741 00:45:11,020 --> 00:45:12,980 The firing rate is just going to be 742 00:45:12,980 --> 00:45:14,960 given by the number of spikes divided 743 00:45:14,960 --> 00:45:16,670 by the width of the window. 744 00:45:16,670 --> 00:45:19,760 And that's just 1 over delta T times 745 00:45:19,760 --> 00:45:23,870 the integral t minus delta T over 2 to t 746 00:45:23,870 --> 00:45:28,760 plus delta T over 2, sliding that gradually 747 00:45:28,760 --> 00:45:31,480 over the spike train. 748 00:45:31,480 --> 00:45:34,780 So we're effectively convolving our spike train 749 00:45:34,780 --> 00:45:36,310 with this rectangular kernel. 750 00:45:40,440 --> 00:45:42,750 And that's what it looks like mathematically. 751 00:45:42,750 --> 00:45:46,890 The firing rate is the convolution of the spike train 752 00:45:46,890 --> 00:45:50,540 with this smoothing kernel. 753 00:45:50,540 --> 00:45:53,730 So, as I mentioned, that's just a convolution, 754 00:45:53,730 --> 00:45:56,610 and we're convolving our spike train with this square kernel 755 00:45:56,610 --> 00:45:57,270 of this width. 756 00:45:57,270 --> 00:46:00,790 So that is the mathematical expression for a convolution. 757 00:46:00,790 --> 00:46:03,690 the firing rate is just the convolution 758 00:46:03,690 --> 00:46:08,430 of this kernel with the spike train. 759 00:46:08,430 --> 00:46:11,520 And, again, the kernel is 0 everywhere 760 00:46:11,520 --> 00:46:15,660 except within this window, minus delta T over 2 761 00:46:15,660 --> 00:46:20,010 to plus delta T over 2, and it has a height of 1 over delta T 762 00:46:20,010 --> 00:46:24,270 such that we make the area 1. 763 00:46:24,270 --> 00:46:29,760 Notationally, we often write that as a star, rho star K. 764 00:46:29,760 --> 00:46:32,710 Now, in this case we were convolving our spike train 765 00:46:32,710 --> 00:46:36,440 with a square kernel. 766 00:46:36,440 --> 00:46:38,060 The problem with a square kernel is 767 00:46:38,060 --> 00:46:41,960 that it changes abruptly every time a spike 768 00:46:41,960 --> 00:46:44,750 comes into the window or drops out of the window. 769 00:46:44,750 --> 00:46:47,000 A more common way of quantifying firing rates 770 00:46:47,000 --> 00:46:50,360 is to convolve the spike train with a Gaussian kernel. 771 00:46:50,360 --> 00:46:54,620 So instead of using a square kernel here, 772 00:46:54,620 --> 00:46:58,200 we're going to use a Gaussian kernel that looks like this. 773 00:46:58,200 --> 00:47:01,490 The kernel is just defined as this Gaussian function. 774 00:47:01,490 --> 00:47:09,140 And it's normalized by 1 over sigma root 2 pi, 775 00:47:09,140 --> 00:47:12,820 and this normalization gives area under that kernel, 1. 776 00:47:12,820 --> 00:47:17,320 So it's still essentially counting the number 777 00:47:17,320 --> 00:47:20,210 of spikes within that window. 778 00:47:20,210 --> 00:47:22,030 It's again just a weighted average 779 00:47:22,030 --> 00:47:29,010 of the number of spikes divided by the width of the kernel, 780 00:47:29,010 --> 00:47:31,740 but there's less weight at the edges. 781 00:47:31,740 --> 00:47:34,590 It has smoother edges, and that gives you 782 00:47:34,590 --> 00:47:38,340 a less steppy-looking result. So let me show you 783 00:47:38,340 --> 00:47:39,250 what that looks like. 784 00:47:39,250 --> 00:47:40,920 So here's a spike train. 785 00:47:40,920 --> 00:47:45,030 If we take fixed bins and compute the firing rate 786 00:47:45,030 --> 00:47:47,560 as a function of time, it looks like this. 787 00:47:47,560 --> 00:47:51,300 If we take that spike train and we convolve it, 788 00:47:51,300 --> 00:47:53,670 and that estimate of firing it would 789 00:47:53,670 --> 00:47:56,910 depend very much on where exactly the windows are placed. 790 00:47:56,910 --> 00:47:59,910 On the other hand, this shows the firing rate 791 00:47:59,910 --> 00:48:04,580 estimated with a square kernel of the same width. 792 00:48:04,580 --> 00:48:09,390 And you can see that it shows a much smoother estimate, 793 00:48:09,390 --> 00:48:13,218 a smoother representation of the firing rate varying over time. 794 00:48:13,218 --> 00:48:14,760 And if you take that same spike train 795 00:48:14,760 --> 00:48:16,840 and you convolve it with a Gaussian, 796 00:48:16,840 --> 00:48:18,930 then you get a function that looks like this. 797 00:48:18,930 --> 00:48:23,670 And we think of this as perhaps better representing 798 00:48:23,670 --> 00:48:25,980 the underlying process in the brain 799 00:48:25,980 --> 00:48:29,280 that produces this time-varying firing 800 00:48:29,280 --> 00:48:32,070 rate, this time-varying spike train, 801 00:48:32,070 --> 00:48:35,760 than either of these two. 802 00:48:35,760 --> 00:48:39,000 You don't really think that the firing rate of this neuron 803 00:48:39,000 --> 00:48:41,880 is jumping around in rectangular steps. 804 00:48:41,880 --> 00:48:43,740 We think of it as being some kind 805 00:48:43,740 --> 00:48:46,080 of smooth, continuous underlying function 806 00:48:46,080 --> 00:48:48,885 that represents maybe the input to that neuron. 807 00:48:48,885 --> 00:48:52,110 Youll see that in these estimates of firing rate, 808 00:48:52,110 --> 00:48:55,250 we had to actually choose a width for our window. 809 00:48:55,250 --> 00:48:57,042 We had to choose a bin size. 810 00:48:57,042 --> 00:48:59,250 We had to choose the width of our square kernel here, 811 00:48:59,250 --> 00:49:02,700 and we had to choose the width of our Gaussian kernel here. 812 00:49:02,700 --> 00:49:06,690 And you can see that the answer, actually, 813 00:49:06,690 --> 00:49:10,530 that you get for firing rate as a function of time 814 00:49:10,530 --> 00:49:15,240 depends very strongly on the size 815 00:49:15,240 --> 00:49:18,220 or the width of that kernel that you choose to use. 816 00:49:18,220 --> 00:49:21,180 And now we smooth it with a Gaussian kernel 817 00:49:21,180 --> 00:49:23,960 that has a width, a sigma, of 4 milliseconds. 818 00:49:23,960 --> 00:49:26,400 So that's the standard deviation of the Gaussian 819 00:49:26,400 --> 00:49:28,490 that we use to smooth the spike train. 820 00:49:28,490 --> 00:49:32,340 And you can see that what you get 821 00:49:32,340 --> 00:49:36,340 is a very peaky estimate of the firing rate. 822 00:49:36,340 --> 00:49:40,000 So that spike produces this little peak. 823 00:49:40,000 --> 00:49:43,350 But the question is, what's the right answer? 824 00:49:43,350 --> 00:49:46,980 How should you actually choose the size 825 00:49:46,980 --> 00:49:50,070 of the kernel to use to estimate firing 826 00:49:50,070 --> 00:49:52,710 rate for your experiment? 827 00:49:52,710 --> 00:49:56,760 The answer is that it really depends on the experiment. 828 00:49:56,760 --> 00:50:01,650 So neural spike trains have widely different 829 00:50:01,650 --> 00:50:02,800 temporal structure. 830 00:50:02,800 --> 00:50:06,990 So, first of all, neuronal responses aren't constant. 831 00:50:06,990 --> 00:50:09,270 Firing rates are not a constant thing. 832 00:50:09,270 --> 00:50:11,970 Neurons-- neural firing rates are constantly 833 00:50:11,970 --> 00:50:16,062 changing depending on the type of stimulus that you use. 834 00:50:16,062 --> 00:50:17,520 And different types of neurons have 835 00:50:17,520 --> 00:50:20,352 different temporal structure in response to the same stimuli. 836 00:50:20,352 --> 00:50:23,520 So, for example, this shows the response 837 00:50:23,520 --> 00:50:32,370 of four different neurons to stimuli, to-- 838 00:50:32,370 --> 00:50:34,200 four different neurons in rat vibrissa 839 00:50:34,200 --> 00:50:36,910 cortex in response to whisker deflections. 840 00:50:36,910 --> 00:50:41,790 So this shows a raster, a histogram 841 00:50:41,790 --> 00:50:48,240 of firing rate as a function of time for one neuron in response 842 00:50:48,240 --> 00:50:50,970 to a deflection of one of the whiskers right here. 843 00:50:50,970 --> 00:50:54,750 So the whisker is at rest, deflected, and then 844 00:50:54,750 --> 00:50:57,760 relaxed back to its original position. 845 00:50:57,760 --> 00:50:59,730 You can see that this neuron shows 846 00:50:59,730 --> 00:51:03,300 a little burst of activity at the onset of the deflection, 847 00:51:03,300 --> 00:51:06,810 and it's fairly persistent throughout the deflection. 848 00:51:06,810 --> 00:51:10,170 Here's another neuron during a deflection. 849 00:51:10,170 --> 00:51:13,770 Increased activity at the onset of the deflection, 850 00:51:13,770 --> 00:51:18,120 followed by a fairly persistent increased spiking 851 00:51:18,120 --> 00:51:20,080 rate throughout the deflection. 852 00:51:20,080 --> 00:51:26,190 Now, a different neuron was quite a different behavior. 853 00:51:26,190 --> 00:51:33,390 So this neuron shows a brief increase in firing rate 854 00:51:33,390 --> 00:51:37,550 just at the time of the deflection, a little increase 855 00:51:37,550 --> 00:51:40,670 of firing rate when the deflection is removed, 856 00:51:40,670 --> 00:51:43,040 and [INAUDIBLE] no activity that persists 857 00:51:43,040 --> 00:51:46,130 during this constant part of the deflection. 858 00:51:46,130 --> 00:51:48,000 Here's another neuron. 859 00:51:48,000 --> 00:51:53,000 This neuron was primarily active at the onset of the deflection. 860 00:51:53,000 --> 00:51:56,840 Here's another neuron that was silent 861 00:51:56,840 --> 00:52:01,535 at the onset of the deflection, and then gave 862 00:52:01,535 --> 00:52:03,260 a robust response. 863 00:52:03,260 --> 00:52:07,250 Neurons, the changes in firing rate 864 00:52:07,250 --> 00:52:11,360 are not of a particular timescale. 865 00:52:11,360 --> 00:52:13,820 Different neurons have different time scales 866 00:52:13,820 --> 00:52:17,740 on which the changes in their firing rate are important. 867 00:52:17,740 --> 00:52:21,380 But let's come back to our example of our auditory neuron. 868 00:52:21,380 --> 00:52:23,480 Here's the spiking of an auditory neuron 869 00:52:23,480 --> 00:52:26,510 during the presentation of an auditory stimulus [INAUDIBLE] 870 00:52:26,510 --> 00:52:28,280 right here. 871 00:52:28,280 --> 00:52:32,010 This neuron-- in fact, you can't see it here, 872 00:52:32,010 --> 00:52:37,220 but this neuron shows spiking at a particular phase 873 00:52:37,220 --> 00:52:41,390 of the auditory stimulus, much like the auditory 874 00:52:41,390 --> 00:52:44,960 neurons that we discussed for sound localization in the owl. 875 00:52:44,960 --> 00:52:51,370 So if you plot the firing rate of this neuron 876 00:52:51,370 --> 00:52:55,450 as a function of time during the presentation of this stimulus, 877 00:52:55,450 --> 00:52:59,420 you can see that the firing rates are rapidly 878 00:52:59,420 --> 00:53:00,500 modulated in time. 879 00:53:00,500 --> 00:53:03,170 You can see that, at particular phases of this stimulus, 880 00:53:03,170 --> 00:53:05,010 the firing rate is very high. 881 00:53:05,010 --> 00:53:07,070 And then just a millisecond later, 882 00:53:07,070 --> 00:53:10,520 the firing rate is very low. 883 00:53:10,520 --> 00:53:13,880 So in this case, you can see that the spikes 884 00:53:13,880 --> 00:53:17,840 are locked temporally at particular phases 885 00:53:17,840 --> 00:53:20,240 of the stimulus. 886 00:53:20,240 --> 00:53:23,810 That's reflected when you make plots of firing rate 887 00:53:23,810 --> 00:53:24,860 as a function of time. 888 00:53:24,860 --> 00:53:27,650 It's reflected in various modulations. 889 00:53:27,650 --> 00:53:31,700 The neurons are firing at a particular time. 890 00:53:31,700 --> 00:53:34,570 So this corresponds to a case in which 891 00:53:34,570 --> 00:53:39,370 we would say that the spike timing is precisely 892 00:53:39,370 --> 00:53:41,150 controlled by the stimulus. 893 00:53:41,150 --> 00:53:46,390 It's, in many ways, more natural here to think about spike times 894 00:53:46,390 --> 00:53:51,700 as being controlled rather than spike firing rate being 895 00:53:51,700 --> 00:53:52,330 modulated. 896 00:53:55,310 --> 00:54:00,940 So you can see here that sensory neurons, neurons 897 00:54:00,940 --> 00:54:05,200 can spike more in response to some stimuli than others. 898 00:54:05,200 --> 00:54:09,310 Motor neurons spike more during some behaviors more 899 00:54:09,310 --> 00:54:10,460 than others. 900 00:54:10,460 --> 00:54:13,450 We can think about information being carried 901 00:54:13,450 --> 00:54:19,120 in the number of spikes that are generated by a stimulus 902 00:54:19,120 --> 00:54:21,720 or during a motor act. 903 00:54:21,720 --> 00:54:24,780 Now, all neurons exhibit temporal modulation 904 00:54:24,780 --> 00:54:26,160 in their firing rates. 905 00:54:26,160 --> 00:54:30,960 They fire more during a movement or after the presentation 906 00:54:30,960 --> 00:54:32,070 of a stimulus. 907 00:54:32,070 --> 00:54:35,490 Sometimes that information is carried by slow modulations 908 00:54:35,490 --> 00:54:36,300 in the firing rate. 909 00:54:36,300 --> 00:54:42,090 For example, the response to different oriented bars 910 00:54:42,090 --> 00:54:45,780 is carried in the average firing rate of the neuron 911 00:54:45,780 --> 00:54:49,220 during that particular stimulus. 912 00:54:49,220 --> 00:54:51,600 And we can refer to that kind of code 913 00:54:51,600 --> 00:54:55,460 and that kind of representation of information as rate coding. 914 00:54:55,460 --> 00:54:58,280 We can say that information about the stimulus 915 00:54:58,280 --> 00:55:03,200 is carried in the rate, the firing rate of the neurons. 916 00:55:03,200 --> 00:55:05,320 But in other cases, like the auditory neuron 917 00:55:05,320 --> 00:55:07,900 that we just saw, we can see that information 918 00:55:07,900 --> 00:55:12,550 is carried by rapid, by fast modulations, 919 00:55:12,550 --> 00:55:15,490 rapid changes in spike probability. 920 00:55:15,490 --> 00:55:17,710 And in that case, we often say that information 921 00:55:17,710 --> 00:55:20,690 is coded by spike timing. 922 00:55:20,690 --> 00:55:27,000 So a common question that you often hear about neurons 923 00:55:27,000 --> 00:55:31,172 is whether they're coding information 924 00:55:31,172 --> 00:55:34,760 using firing rate or temporal coding, 925 00:55:34,760 --> 00:55:37,670 rate coding versus temporal coding. 926 00:55:37,670 --> 00:55:39,620 Really, this is a false dichotomy. 927 00:55:39,620 --> 00:55:42,650 You shouldn't think about neurons coding information one 928 00:55:42,650 --> 00:55:43,470 way or the other. 929 00:55:43,470 --> 00:55:48,540 These are just-- really just two limits of a continuum. 930 00:55:48,540 --> 00:55:51,350 The brain uses information at fast time scales 931 00:55:51,350 --> 00:55:53,370 as well as slow time scales. 932 00:55:53,370 --> 00:55:56,990 And how do we determine, how do we know 933 00:55:56,990 --> 00:56:00,170 what's important for the brain? 934 00:56:00,170 --> 00:56:01,940 What time scales are important? 935 00:56:01,940 --> 00:56:04,520 And the answer to that question really 936 00:56:04,520 --> 00:56:09,350 comes from understanding the way spike trains are read out 937 00:56:09,350 --> 00:56:12,920 by the neurons that they project to. 938 00:56:12,920 --> 00:56:15,590 What time scale is relevant for the computation 939 00:56:15,590 --> 00:56:19,250 that's being done in the system that you're studying? 940 00:56:19,250 --> 00:56:21,380 What are the biophysical mechanisms 941 00:56:21,380 --> 00:56:24,260 that those spikes act on. 942 00:56:24,260 --> 00:56:28,460 To understand these questions, then that's 943 00:56:28,460 --> 00:56:30,200 the appropriate level of analysis 944 00:56:30,200 --> 00:56:33,470 to think about how spike trains are 945 00:56:33,470 --> 00:56:38,980 important for our sensory coding and for motor behavior.