1 00:00:00,070 --> 00:00:02,500 The following content is provided under a Creative 2 00:00:02,500 --> 00:00:04,019 Commons license. 3 00:00:04,019 --> 00:00:06,360 Your support will help MIT OpenCourseWare 4 00:00:06,360 --> 00:00:10,730 continue to offer high quality educational resources for free. 5 00:00:10,730 --> 00:00:13,340 To make a donation or view additional materials 6 00:00:13,340 --> 00:00:17,217 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,217 --> 00:00:17,842 at ocw.mit.edu. 8 00:00:20,659 --> 00:00:23,200 JEFF GORE: Today, what we want to do is focus more explicitly 9 00:00:23,200 --> 00:00:24,890 on bacterial chemotaxis. 10 00:00:24,890 --> 00:00:26,560 Of course, a discussion that we had 11 00:00:26,560 --> 00:00:29,330 on Thursday about "Life at Low Reynolds Numbers" 12 00:00:29,330 --> 00:00:31,290 is certainly very relevant to this question 13 00:00:31,290 --> 00:00:34,390 of how bacteria are maybe able to find food 14 00:00:34,390 --> 00:00:36,380 or what constraints they're faced in trying 15 00:00:36,380 --> 00:00:37,530 to solve this problem. 16 00:00:37,530 --> 00:00:39,900 Today, we're going to discuss in more depth 17 00:00:39,900 --> 00:00:43,570 this idea of the biased random walk that runs and tumbles 18 00:00:43,570 --> 00:00:46,240 that we talked about on Thursday, that allow bacteria 19 00:00:46,240 --> 00:00:49,680 to swim towards attractants and away from repellents. 20 00:00:49,680 --> 00:00:51,530 But in particular, there's something 21 00:00:51,530 --> 00:00:56,330 that is rather subtle about the particular biased random walk 22 00:00:56,330 --> 00:00:58,310 that bacteria implement. 23 00:00:58,310 --> 00:01:01,170 Now, the way that you might kind of naively 24 00:01:01,170 --> 00:01:03,170 imagine that this thing would work 25 00:01:03,170 --> 00:01:06,100 is that you would just have this tumbling frequency be 26 00:01:06,100 --> 00:01:10,850 a function of the concentration of the attractant, for example. 27 00:01:10,850 --> 00:01:14,210 And that indeed would allow you to swim or to execute 28 00:01:14,210 --> 00:01:16,650 a biased random walk towards, say, food sources, 29 00:01:16,650 --> 00:01:18,910 towards attractants, but it would not 30 00:01:18,910 --> 00:01:22,760 be effective over a very wide range of concentrations. 31 00:01:22,760 --> 00:01:25,697 However, if you experimentally ask, how well can bacteria 32 00:01:25,697 --> 00:01:27,280 swim towards attractants, it turns out 33 00:01:27,280 --> 00:01:29,690 they can respond over five orders of magnitude 34 00:01:29,690 --> 00:01:32,700 of concentration of these attractants, which is really 35 00:01:32,700 --> 00:01:36,760 quite incredible, if you think about the engineering challenge 36 00:01:36,760 --> 00:01:42,950 that these little one-micron cells are able to overcome. 37 00:01:42,950 --> 00:01:45,690 And the basic way that they do this is they 38 00:01:45,690 --> 00:01:48,840 implement what's essentially equivalent to integral feedback 39 00:01:48,840 --> 00:01:51,630 in the context of engineering, where it turns out 40 00:01:51,630 --> 00:01:55,081 that the steady-state tumbling frequency, so the frequency 41 00:01:55,081 --> 00:01:56,580 of which they'd execute one of these 42 00:01:56,580 --> 00:02:00,414 tumbles that randomizes their motion, that displays what's 43 00:02:00,414 --> 00:02:01,580 known as perfect adaptation. 44 00:02:01,580 --> 00:02:08,770 It's not a function of the concentration of-- if you have 45 00:02:08,770 --> 00:02:10,746 a constant concentration of an attractant, 46 00:02:10,746 --> 00:02:12,120 then it's not a function of that. 47 00:02:12,120 --> 00:02:14,720 Of course, changes in concentrations it responds to, 48 00:02:14,720 --> 00:02:18,790 but somehow, E. coli and many other microorganisms 49 00:02:18,790 --> 00:02:21,900 are able to implement this very clever thing where 50 00:02:21,900 --> 00:02:24,540 the steady-state frequency of tumbling, of changing 51 00:02:24,540 --> 00:02:26,040 direction, is somehow not a function 52 00:02:26,040 --> 00:02:29,290 of the overall attractant concentration. 53 00:02:29,290 --> 00:02:33,010 Now, that's already an interesting, I think, 54 00:02:33,010 --> 00:02:34,470 phenomenon. 55 00:02:34,470 --> 00:02:37,040 And in some ways, you can think of it 56 00:02:37,040 --> 00:02:39,550 as some kind of robustness, because there 57 00:02:39,550 --> 00:02:41,990 is some way in which this tumbling frequency is 58 00:02:41,990 --> 00:02:47,372 robust against constant changes in the level of attractants. 59 00:02:47,372 --> 00:02:48,830 And it's that aspect, I think, that 60 00:02:48,830 --> 00:02:51,160 makes this example both rather subtle but also 61 00:02:51,160 --> 00:02:54,610 quite confusing, because it's the phenomenon 62 00:02:54,610 --> 00:02:56,430 of perfect adaptation that already 63 00:02:56,430 --> 00:02:58,630 has some aspects of robustness, but it's 64 00:02:58,630 --> 00:03:00,480 this phenomenon of perfect adaptation 65 00:03:00,480 --> 00:03:03,679 that is robust against changes in concentrations of proteins, 66 00:03:03,679 --> 00:03:05,970 for example, the concentration of the protein [? key ?] 67 00:03:05,970 --> 00:03:08,650 R that we're going to talk about. 68 00:03:08,650 --> 00:03:10,960 So I think that this is in some ways maybe 69 00:03:10,960 --> 00:03:15,120 the prettiest example that we have 70 00:03:15,120 --> 00:03:17,100 of this principle of robustness, but I 71 00:03:17,100 --> 00:03:19,180 think it's also in some ways the most 72 00:03:19,180 --> 00:03:22,840 tricky to wrap your head around, because it's sort of robustness 73 00:03:22,840 --> 00:03:25,340 of a robustness in some ways. 74 00:03:28,665 --> 00:03:30,170 All right. 75 00:03:30,170 --> 00:03:33,640 So our goal for today is going to be to make sure 76 00:03:33,640 --> 00:03:38,120 that we understand the challenge that E. coli are facing 77 00:03:38,120 --> 00:03:41,340 and then to try to understand the genetic circuit 78 00:03:41,340 --> 00:03:45,370 that they use in order to overcome this challenge. 79 00:03:45,370 --> 00:03:48,450 So what I'm going to do for the next hour and 15 minutes 80 00:03:48,450 --> 00:03:51,460 is we're going to leave this network up on the board 81 00:03:51,460 --> 00:03:54,910 so that any time that you're confused about what 82 00:03:54,910 --> 00:03:58,990 is R, B, Z, Y, so forth, you can kind of 83 00:03:58,990 --> 00:04:03,480 look up here and remind yourself what this thing is. 84 00:04:03,480 --> 00:04:05,910 But hopefully, the reading from last night 85 00:04:05,910 --> 00:04:09,290 will help you in following what's going on. 86 00:04:09,290 --> 00:04:12,855 There are a fair number of letters, I will admit it. 87 00:04:17,300 --> 00:04:18,930 So first, I just want to make sure 88 00:04:18,930 --> 00:04:20,410 that we're all kind of remembering 89 00:04:20,410 --> 00:04:24,200 the basic phenomenon that we're trying 90 00:04:24,200 --> 00:04:28,300 to study, which is this idea of consecutive runs and tumbles. 91 00:04:28,300 --> 00:04:33,170 So this random walk is really composed of what you might call 92 00:04:33,170 --> 00:04:36,630 or what we do call runs, where the bacteria goes sort 93 00:04:36,630 --> 00:04:38,430 of straight and then tumbles, which 94 00:04:38,430 --> 00:04:40,240 they randomize their motion. 95 00:04:40,240 --> 00:04:52,020 So this is runs and tumbles, where bacteria, they 96 00:04:52,020 --> 00:05:02,970 go semi-straight for of order a second-- order one second-- 97 00:05:02,970 --> 00:05:05,420 and this is the run. 98 00:05:05,420 --> 00:05:07,620 Then, they have this tumbling that 99 00:05:07,620 --> 00:05:15,460 might last about one second, so a 0.1 second tumble, 100 00:05:15,460 --> 00:05:19,890 over which the motion is sort of random in this axis 101 00:05:19,890 --> 00:05:22,750 of the orientation. 102 00:05:22,750 --> 00:05:25,360 And then, they kind of go in a new direction 103 00:05:25,360 --> 00:05:29,870 and then tumble again and then new direction and so forth. 104 00:05:32,590 --> 00:05:37,920 So it's runs followed by tumbles. 105 00:05:41,680 --> 00:05:44,470 Now, the thing that changes depending 106 00:05:44,470 --> 00:05:46,450 on whether the cells are sensing that they're 107 00:05:46,450 --> 00:05:49,730 moving up or down, say, an attractant gradient 108 00:05:49,730 --> 00:05:53,730 is the frequency of those tumbles, i.e. 109 00:05:53,730 --> 00:05:55,870 how long are the runs? 110 00:05:55,870 --> 00:05:58,090 I said that they're around one second, 111 00:05:58,090 --> 00:06:04,020 but this will vary depending upon whether bacteria 112 00:06:04,020 --> 00:06:05,540 sense that things are getting better 113 00:06:05,540 --> 00:06:06,706 or things are getting worse. 114 00:06:10,140 --> 00:06:14,440 Can somebody remind us how the bacteria actually execute 115 00:06:14,440 --> 00:06:16,525 one of these tumble motions? 116 00:06:20,728 --> 00:06:21,228 Yes? 117 00:06:21,228 --> 00:06:24,180 AUDIENCE: They have this other motors-- they have mini-motors 118 00:06:24,180 --> 00:06:25,902 in their flagella and they usually 119 00:06:25,902 --> 00:06:28,680 all spin one way, which I think is counterclockwise. 120 00:06:28,680 --> 00:06:29,680 JEFF GORE: That's right. 121 00:06:29,680 --> 00:06:32,040 I always have trouble-- so the runs are indeed 122 00:06:32,040 --> 00:06:34,414 when these things are rotating counterclockwise. 123 00:06:34,414 --> 00:06:35,038 AUDIENCE: Yeah. 124 00:06:35,038 --> 00:06:37,585 And one of them can decide to switch 125 00:06:37,585 --> 00:06:39,910 and start turning clockwise. 126 00:06:39,910 --> 00:06:42,015 And what it does, it just sort of-- I don't know. 127 00:06:42,015 --> 00:06:43,890 I just imagine it throws the whole motor off. 128 00:06:43,890 --> 00:06:44,860 JEFF GORE: Exactly. 129 00:06:44,860 --> 00:06:52,920 And the flagella in the context of-- so we have our E. coli. 130 00:06:52,920 --> 00:06:56,530 The velocity is of order, say, 30 microns per second. 131 00:07:00,002 --> 00:07:01,960 Now, they have these flagella that are actually 132 00:07:01,960 --> 00:07:04,650 distributed-- the motors are actually distributed 133 00:07:04,650 --> 00:07:06,010 across the entire cell. 134 00:07:06,010 --> 00:07:07,580 So it's not just on the back. 135 00:07:07,580 --> 00:07:09,690 But then, these individual filaments kind of 136 00:07:09,690 --> 00:07:12,450 come together towards the back and then 137 00:07:12,450 --> 00:07:16,400 they have this corkscrew shape. 138 00:07:16,400 --> 00:07:18,150 When these things are all rotating 139 00:07:18,150 --> 00:07:20,050 in the counterclockwise direction, 140 00:07:20,050 --> 00:07:23,870 that corresponds to a run, when there's directed motion. 141 00:07:23,870 --> 00:07:28,230 But then if one of them goes clockwise, 142 00:07:28,230 --> 00:07:30,207 the bundle falls apart. 143 00:07:30,207 --> 00:07:32,290 And indeed, there are some very nice movies online 144 00:07:32,290 --> 00:07:34,930 where you can see that when they're going clockwise, 145 00:07:34,930 --> 00:07:39,030 you see that the flagella are kind of doing crazy things 146 00:07:39,030 --> 00:07:41,650 and that causes this thing to kind of tumble 147 00:07:41,650 --> 00:07:42,650 in a random orientation. 148 00:07:42,650 --> 00:07:44,350 So it randomizes its direction. 149 00:07:56,910 --> 00:08:00,070 Now, one thing that we did not talk 150 00:08:00,070 --> 00:08:03,920 about in the context of this low Reynolds number motion 151 00:08:03,920 --> 00:08:06,690 was the question of how hard you would 152 00:08:06,690 --> 00:08:10,660 have to pull in order to get a cell 153 00:08:10,660 --> 00:08:12,300 to go 30 microns per second. 154 00:08:16,270 --> 00:08:20,440 Now, remember, we're in the low Reynolds number regime, 155 00:08:20,440 --> 00:08:23,767 where the force you have to apply 156 00:08:23,767 --> 00:08:25,600 is in general proportional to this velocity. 157 00:08:29,050 --> 00:08:33,740 And this thing is very much not a sphere, 158 00:08:33,740 --> 00:08:39,200 but if it were a sphere, for a sphere, the proportionality 159 00:08:39,200 --> 00:08:45,240 constant is this 6 pi eta av, where a here is again 160 00:08:45,240 --> 00:08:45,850 the radius. 161 00:08:50,050 --> 00:08:52,710 Now, regardless of the precise shape, 162 00:08:52,710 --> 00:08:57,080 you'll always get for the low Reynolds regime something that 163 00:08:57,080 --> 00:08:59,620 looks vaguely like this, where this is going to the longest 164 00:08:59,620 --> 00:09:03,560 linear dimension and this here depends on the precise geometry 165 00:09:03,560 --> 00:09:04,250 of the object. 166 00:09:08,940 --> 00:09:11,210 And so just-- it's useful to try to get 167 00:09:11,210 --> 00:09:13,760 a sense of order of magnitude. 168 00:09:13,760 --> 00:09:18,030 How large are these forces that we're talking about? 169 00:09:18,030 --> 00:09:22,040 In particular, how hard would you 170 00:09:22,040 --> 00:09:25,079 have to pull a cell in order to get 171 00:09:25,079 --> 00:09:26,370 it to go 30 microns per second? 172 00:09:29,040 --> 00:09:32,370 Now, of course then, there's a question. 173 00:09:32,370 --> 00:09:35,770 What's roughly the scale that we should be thinking about? 174 00:09:35,770 --> 00:09:39,730 Right now, a newton is the scale that's for macroscopic objects. 175 00:09:39,730 --> 00:09:42,870 So you'd say, OK, probably not going to be up that large. 176 00:09:42,870 --> 00:09:45,110 Then, on the other scale, we can think 177 00:09:45,110 --> 00:09:49,240 about the forces that can be applied or exerted 178 00:09:49,240 --> 00:09:51,330 by individual molecular motors. 179 00:09:55,450 --> 00:09:58,644 Has anybody studied this at all? 180 00:09:58,644 --> 00:10:00,430 AUDIENCE: [INAUDIBLE] 181 00:10:00,430 --> 00:10:03,380 JEFF GORE: Right, order of picanewtons. 182 00:10:03,380 --> 00:10:09,630 So force for a molecular motor is going 183 00:10:09,630 --> 00:10:12,108 to be of order picanewtons. 184 00:10:14,860 --> 00:10:17,780 Now, there's a simple way to kind of 185 00:10:17,780 --> 00:10:22,870 get at why this might actually be, because what is it 186 00:10:22,870 --> 00:10:27,110 that powers many of these molecular motors? 187 00:10:27,110 --> 00:10:28,706 AUDIENCE: [INAUDIBLE] 188 00:10:28,706 --> 00:10:30,330 JEFF GORE: Yeah, so it's often-- you're 189 00:10:30,330 --> 00:10:33,470 thinking of maybe the motors that operate in a membrane. 190 00:10:33,470 --> 00:10:35,200 And then, there might be some difference 191 00:10:35,200 --> 00:10:37,660 in a gradient, so a difference in concentration 192 00:10:37,660 --> 00:10:39,410 across that membrane and that can actually 193 00:10:39,410 --> 00:10:41,609 power, for example, rotation. 194 00:10:41,609 --> 00:10:43,150 We're going to talk a little bit more 195 00:10:43,150 --> 00:10:45,650 about this in the context of the flagella motor, 196 00:10:45,650 --> 00:10:51,370 because this is one of only a few known rotary motors. 197 00:10:51,370 --> 00:10:53,900 I'm just going to write this down so that I don't forget 198 00:10:53,900 --> 00:10:55,133 to say something about it. 199 00:10:58,300 --> 00:10:59,610 But in this case-- 200 00:10:59,610 --> 00:11:00,294 AUDIENCE: ATP? 201 00:11:00,294 --> 00:11:01,210 JEFF GORE: ATP, right? 202 00:11:01,210 --> 00:11:04,190 So in many cases, what happens is that you have, 203 00:11:04,190 --> 00:11:06,280 for example, kinesin or myosin. 204 00:11:06,280 --> 00:11:11,040 These are motors that walk along some track and in many cases, 205 00:11:11,040 --> 00:11:17,390 each step corresponds to a single ATP being hydrolyzed. 206 00:11:17,390 --> 00:11:20,880 And so given that, there's some maximal force 207 00:11:20,880 --> 00:11:23,540 that you can imagine such a motor applying. 208 00:11:23,540 --> 00:11:25,550 So for example-- and what might it depend upon? 209 00:11:32,720 --> 00:11:35,589 AUDIENCE: The energy of ATP hydrolysis [INAUDIBLE] 210 00:11:35,589 --> 00:11:36,630 JEFF GORE: Ah, very good. 211 00:11:36,630 --> 00:11:40,474 So we have delta G for say, ATP. 212 00:11:40,474 --> 00:11:42,390 And there's going to be a length scale, right? 213 00:11:42,390 --> 00:11:44,139 And what's going to be the relevant length 214 00:11:44,139 --> 00:11:46,878 scale in the case of, for example, a motor like kinesin? 215 00:11:46,878 --> 00:11:49,392 AUDIENCE: The flagella, I guess? 216 00:11:49,392 --> 00:11:51,850 JEFF GORE: Well, kinesin is not walking along the flagella, 217 00:11:51,850 --> 00:11:56,060 but in this case, kinesin is walking along microtubules, 218 00:11:56,060 --> 00:11:57,040 for example. 219 00:11:57,040 --> 00:11:59,230 So you're right that we need a length scale, 220 00:11:59,230 --> 00:12:02,560 because this is going to have some units of say, picanewton 221 00:12:02,560 --> 00:12:08,770 nanometers-- oops, that's an Nm-- 222 00:12:08,770 --> 00:12:13,070 and we want to get a picanewton so we're going to need a length 223 00:12:13,070 --> 00:12:14,495 scale to divide by, right? 224 00:12:14,495 --> 00:12:16,480 AUDIENCE: So how long you move each time? 225 00:12:16,480 --> 00:12:17,480 JEFF GORE: That's right. 226 00:12:17,480 --> 00:12:19,896 It's kind of the distance that this thing's moving, right? 227 00:12:19,896 --> 00:12:22,590 So indeed, what happens in the case of kinesin 228 00:12:22,590 --> 00:12:25,480 is that they take steps with what are called "heads" 229 00:12:25,480 --> 00:12:27,700 but we can think of them as "feet" if we want. 230 00:12:27,700 --> 00:12:30,660 So each step is in this case eight nanometers. 231 00:12:30,660 --> 00:12:37,760 For example, delta L for kinesin is equal to eight nanometers. 232 00:12:37,760 --> 00:12:39,510 You don't need to know this, but just it's 233 00:12:39,510 --> 00:12:41,025 useful to have some sense of scale. 234 00:12:43,660 --> 00:12:47,320 Now, of course, delta G of ATP, this 235 00:12:47,320 --> 00:12:52,210 depends upon the concentrations of the reactants, 236 00:12:52,210 --> 00:12:54,420 of the products, and so forth. 237 00:12:54,420 --> 00:12:59,320 But this thing might be of order 100 picanewton nanometers. 238 00:13:04,234 --> 00:13:05,900 Now, depending on conditions, maybe it's 239 00:13:05,900 --> 00:13:08,330 70, but of order here. 240 00:13:08,330 --> 00:13:09,980 And indeed, what this tells us is 241 00:13:09,980 --> 00:13:13,280 that just based on what we've said right now, even 242 00:13:13,280 --> 00:13:16,140 without building any fancy microscopes to measure 243 00:13:16,140 --> 00:13:18,200 how much force these things can apply, 244 00:13:18,200 --> 00:13:21,957 you can see that the maximum force it could possibly apply 245 00:13:21,957 --> 00:13:24,040 would be something on the order of delta G divided 246 00:13:24,040 --> 00:13:26,203 by the length that it's pulling. 247 00:13:28,750 --> 00:13:33,590 Otherwise, you could make a perpetual motion machine. 248 00:13:33,590 --> 00:13:36,430 So this-- well, maybe what we'll do 249 00:13:36,430 --> 00:13:38,149 if we want to make our math simpler, 250 00:13:38,149 --> 00:13:39,440 we could say this is around 80. 251 00:13:39,440 --> 00:13:40,440 It's of order there. 252 00:13:40,440 --> 00:13:43,700 But the point is that this is of order 10 picanewtons, 253 00:13:43,700 --> 00:13:45,100 so it's kind of picanewton scale. 254 00:13:49,471 --> 00:13:50,004 All right. 255 00:13:50,004 --> 00:13:52,420 So given this, it's interesting to ask, how hard would you 256 00:13:52,420 --> 00:13:53,540 have to pull? 257 00:13:53,540 --> 00:13:57,540 So how big is a kinesin model going to be, this protein? 258 00:14:00,715 --> 00:14:02,090 AUDIENCE: About eight nanometers. 259 00:14:02,090 --> 00:14:03,350 JEFF GORE: Yeah, right, about eight nanometers. 260 00:14:03,350 --> 00:14:05,183 Of course, it's kind of long, spindly things 261 00:14:05,183 --> 00:14:07,330 like my skinny legs, right, but let's 262 00:14:07,330 --> 00:14:10,710 indeed going to be around that scale, 263 00:14:10,710 --> 00:14:16,970 whereas the cell is one micron wide, multiple microns long, so 264 00:14:16,970 --> 00:14:18,210 much, much larger. 265 00:14:18,210 --> 00:14:21,655 We'll draw a little-- here's a kinesin in there. 266 00:14:24,650 --> 00:14:26,350 It's even smaller than that. 267 00:14:26,350 --> 00:14:27,704 Kinesin's small. 268 00:14:27,704 --> 00:14:29,620 Now, the question is, how much force would you 269 00:14:29,620 --> 00:14:32,420 have to apply in order to pull an E. coli at 30 microns 270 00:14:32,420 --> 00:14:33,970 a second? 271 00:14:33,970 --> 00:14:39,530 Force to pull E. coli at the speed 272 00:14:39,530 --> 00:14:43,470 that it's actually observed to go-- now, 273 00:14:43,470 --> 00:14:46,260 you're unlikely to be able to do the calculation right here. 274 00:14:46,260 --> 00:14:49,450 It's actually a simple calculation. 275 00:14:49,450 --> 00:14:51,340 We could do it in a moment, but it's 276 00:14:51,340 --> 00:14:54,270 useful to just kind of imagine what scale might it be. 277 00:15:15,110 --> 00:15:18,970 All right, this is a way of-- we can go up as high as we want. 278 00:15:18,970 --> 00:15:22,215 You can continue it on and this is all in units of picanewtons. 279 00:15:26,010 --> 00:15:28,040 Once again, it's useful to make guesses 280 00:15:28,040 --> 00:15:29,540 about your intuition on these things 281 00:15:29,540 --> 00:15:34,591 just so you have some notion of where we might be. 282 00:15:34,591 --> 00:15:37,090 And of course, in this case, nobody wants to guess anything, 283 00:15:37,090 --> 00:15:42,600 because they feel-- all right, I'll 284 00:15:42,600 --> 00:15:45,867 give you 10 seconds just to make your best guess. 285 00:15:45,867 --> 00:15:47,200 Somebody's forcing you to do it. 286 00:15:47,200 --> 00:15:48,435 In this case, it's me. 287 00:15:51,040 --> 00:15:53,820 No reason that you actually should necessarily get this. 288 00:15:57,244 --> 00:15:58,160 Pulling through water. 289 00:16:02,980 --> 00:16:04,160 AUDIENCE: At 30 microns. 290 00:16:04,160 --> 00:16:05,660 JEFF GORE: At 30 microns per second. 291 00:16:11,978 --> 00:16:15,380 AUDIENCE: Could you give us the viscosity 292 00:16:15,380 --> 00:16:16,850 of water in picanewtons? 293 00:16:16,850 --> 00:16:19,340 JEFF GORE: Yeah, it's 10 to the minus nine 294 00:16:19,340 --> 00:16:22,742 in the units of picanewton nanometer second something. 295 00:16:22,742 --> 00:16:24,252 AUDIENCE: Great. 296 00:16:24,252 --> 00:16:24,960 JEFF GORE: Right. 297 00:16:24,960 --> 00:16:25,740 Now, I've given you enough time. 298 00:16:25,740 --> 00:16:26,600 You should have just been able-- now, 299 00:16:26,600 --> 00:16:28,380 I'm going to be disappointed if you don't get it right. 300 00:16:28,380 --> 00:16:28,879 No. 301 00:16:33,494 --> 00:16:34,660 Let's just see where we are. 302 00:16:34,660 --> 00:16:35,290 Ready? 303 00:16:35,290 --> 00:16:38,780 Three, two, one. 304 00:16:38,780 --> 00:16:40,960 OK, so I'd say that we have a bunch of-- I'd say 305 00:16:40,960 --> 00:16:43,730 the mean is kind of a C-D-ish. 306 00:16:43,730 --> 00:16:46,570 We got some A-B's. 307 00:16:46,570 --> 00:16:49,340 All right, so I'd say it's somewhere in the sense of, 308 00:16:49,340 --> 00:16:52,700 yeah, maybe it's 100,000. 309 00:16:52,700 --> 00:16:58,220 So maybe if you had 100 of these kinesins pulling you along, 310 00:16:58,220 --> 00:17:00,676 then you'd be able to go 30 microns a second, although you 311 00:17:00,676 --> 00:17:02,430 have to be careful because kinesin can't actually 312 00:17:02,430 --> 00:17:03,020 go that fast. 313 00:17:03,020 --> 00:17:06,900 But these are details, right? 314 00:17:06,900 --> 00:17:09,260 No, there's a reasonable question. 315 00:17:09,260 --> 00:17:10,740 How hard would you have to pull. 316 00:17:10,740 --> 00:17:13,473 Of course, if we want, we could actually just 317 00:17:13,473 --> 00:17:16,740 do the equations here, right? 318 00:17:16,740 --> 00:17:19,891 The force, it's around 20. 319 00:17:19,891 --> 00:17:21,599 In units of picanewton nanometer seconds, 320 00:17:21,599 --> 00:17:25,339 I told you that the eta is around 10 to the minus 9. 321 00:17:25,339 --> 00:17:25,839 All right. 322 00:17:25,839 --> 00:17:29,130 And the radius, what radius do you want to use? 323 00:17:29,130 --> 00:17:29,950 AUDIENCE: A micron. 324 00:17:29,950 --> 00:17:30,940 JEFF GORE: A micron. 325 00:17:30,940 --> 00:17:32,580 So do we write a 1 here? 326 00:17:32,580 --> 00:17:34,570 Do we write what? 327 00:17:34,570 --> 00:17:36,550 10 to the 3 because I already told you 328 00:17:36,550 --> 00:17:38,890 that this was in units where everything is picanewtons 329 00:17:38,890 --> 00:17:40,180 nanometers seconds. 330 00:17:40,180 --> 00:17:42,580 And velocity, this is again per second. 331 00:17:42,580 --> 00:17:47,740 So this is three times 10 to the 4, because that's how many 332 00:17:47,740 --> 00:17:50,770 nanometers per second. 333 00:17:50,770 --> 00:17:55,489 And this gets us to around-- that's 10 to the seven. 334 00:17:55,489 --> 00:17:57,030 We're going to have to divide by 100, 335 00:17:57,030 --> 00:18:05,627 so this is 60 divided by 100-- so less than a picanewton. 336 00:18:08,490 --> 00:18:12,430 So this is really pretty surprising. 337 00:18:12,430 --> 00:18:17,090 And again, this is a reflection of the wonders of low Reynolds 338 00:18:17,090 --> 00:18:18,300 numbers kind of behavior. 339 00:18:18,300 --> 00:18:21,278 So it's somewhere here. 340 00:18:24,080 --> 00:18:24,580 Yes? 341 00:18:24,580 --> 00:18:26,540 AUDIENCE: So since there are many flagella, 342 00:18:26,540 --> 00:18:29,970 is it telling us-- [INAUDIBLE] is it telling us 343 00:18:29,970 --> 00:18:32,910 that they're very inefficient compared to the [INAUDIBLE] 344 00:18:32,910 --> 00:18:34,785 JEFF GORE: Yeah, it's a good question, right? 345 00:18:34,785 --> 00:18:36,650 So I think there are several ways. 346 00:18:36,650 --> 00:18:41,690 And this is one aspect maybe of what 347 00:18:41,690 --> 00:18:44,610 we read about in the "Life at Low Reynolds Numbers." 348 00:18:44,610 --> 00:18:49,240 The comparison was to a Datsun in Saudi Arabia. 349 00:18:49,240 --> 00:18:52,250 Of course, I think that this was written in the '70s where 350 00:18:52,250 --> 00:18:53,280 that meant something. 351 00:18:53,280 --> 00:18:56,850 But I think that a Datsun, I guess, is a fuel efficient car? 352 00:18:59,430 --> 00:19:02,570 Well, that was my inference from that. 353 00:19:02,570 --> 00:19:05,830 And Saudi Arabia has a lot of oil, still true. 354 00:19:09,320 --> 00:19:12,060 And the saying was that it might only be 1% efficient or so, 355 00:19:12,060 --> 00:19:12,560 right? 356 00:19:12,560 --> 00:19:15,760 But if you don't have to apply very much force there, 357 00:19:15,760 --> 00:19:19,120 then maybe that's not a disaster. 358 00:19:19,120 --> 00:19:20,859 The swimming speed is not actually 359 00:19:20,859 --> 00:19:22,900 a super strong function of the number of flagella 360 00:19:22,900 --> 00:19:24,691 that are there, as far as my understanding. 361 00:19:24,691 --> 00:19:30,200 So I'm actually a little bit-- there are cases 362 00:19:30,200 --> 00:19:34,060 where you do get somewhat higher speed with more flagella, 363 00:19:34,060 --> 00:19:37,050 although I have to confess, just from the geometry 364 00:19:37,050 --> 00:19:40,280 of the multiple flagella I find totally mystifying, because I 365 00:19:40,280 --> 00:19:42,290 would've thought they would get tangled up, 366 00:19:42,290 --> 00:19:45,519 because each of them goes in and they form a corkscrew. 367 00:19:45,519 --> 00:19:46,060 I don't know. 368 00:19:46,060 --> 00:19:47,768 It just doesn't seem that it should work. 369 00:19:50,040 --> 00:19:54,161 But it does, so I'm not going to argue that it doesn't. 370 00:19:54,161 --> 00:19:57,047 AUDIENCE: Probably it has to do with the low Reynolds number. 371 00:19:57,047 --> 00:19:59,940 So you imagine swimming, sort of flying around. 372 00:19:59,940 --> 00:20:01,949 JEFF GORE: Yeah, no, my concern is not even 373 00:20:01,949 --> 00:20:03,740 a matter of the low Reynolds number or not. 374 00:20:03,740 --> 00:20:06,940 It's just a matter of they're each spinning 375 00:20:06,940 --> 00:20:12,810 and then-- this is something really I've never understood, 376 00:20:12,810 --> 00:20:15,240 so I typically avoid talking about it. 377 00:20:19,460 --> 00:20:20,332 I don't know. 378 00:20:20,332 --> 00:20:22,040 I just feel like there's something wrong. 379 00:20:22,040 --> 00:20:27,490 But in any case, you don't need to pull very hard in order 380 00:20:27,490 --> 00:20:32,590 to get even a micron-size object to go rather fast. 381 00:20:34,901 --> 00:20:35,400 Yes? 382 00:20:35,400 --> 00:20:36,275 AUDIENCE: [INAUDIBLE] 383 00:20:39,300 --> 00:20:42,210 JEFF GORE: Oh, I'm not aware of it. 384 00:20:42,210 --> 00:20:44,410 This thing can actually go-- it's 10 microns long, 385 00:20:44,410 --> 00:20:48,020 so this thing is huge, actually. 386 00:20:48,020 --> 00:20:48,580 But I-- 387 00:20:48,580 --> 00:20:50,163 AUDIENCE: It's probably just a repeat. 388 00:20:52,927 --> 00:20:54,859 Or even if it is a repeat, you can 389 00:20:54,859 --> 00:20:56,308 [INAUDIBLE] I'd just be surprised 390 00:20:56,308 --> 00:20:58,740 if it wasn't, since it seems like that. 391 00:20:58,740 --> 00:21:00,120 JEFF GORE: Yeah, so I don't know, 392 00:21:00,120 --> 00:21:03,072 but I'm not even sure if that would necessarily 393 00:21:03,072 --> 00:21:05,030 address my concern, which is it seems like they 394 00:21:05,030 --> 00:21:06,480 have to go through each other. 395 00:21:06,480 --> 00:21:10,530 But it's not true, so I don't want to make the argument too 396 00:21:10,530 --> 00:21:11,350 strongly. 397 00:21:11,350 --> 00:21:13,030 Did you have a question? 398 00:21:13,030 --> 00:21:15,973 AUDIENCE: So I was just thinking about this [INAUDIBLE] 399 00:21:15,973 --> 00:21:20,410 Might it be possible that they, if they are all sync up 400 00:21:20,410 --> 00:21:25,360 their rotations, then it doesn't matter how tangled they are? 401 00:21:25,360 --> 00:21:29,390 JEFF GORE: Yeah, no, even-- even if they're all 402 00:21:29,390 --> 00:21:32,030 spinning at the exact same rate, I still 403 00:21:32,030 --> 00:21:33,690 feel that they should get tangled, 404 00:21:33,690 --> 00:21:35,960 but it's a feeling that is apparently not true. 405 00:21:35,960 --> 00:21:38,514 So I don't want to-- 406 00:21:38,514 --> 00:21:41,570 AUDIENCE: But if they're always tumbling, maybe the time to-- 407 00:21:41,570 --> 00:21:45,370 JEFF GORE: No, no, no, wait-- so it's not-- no, 408 00:21:45,370 --> 00:21:49,076 the tumble is not due to my supposed mechanism. 409 00:21:49,076 --> 00:21:50,950 They're spinning at something like 100 hertz. 410 00:21:50,950 --> 00:21:53,120 The motors are spinning at something like 100 hertz, 411 00:21:53,120 --> 00:21:53,290 right? 412 00:21:53,290 --> 00:21:55,290 So in principle, if they were going to get tangled, 413 00:21:55,290 --> 00:21:56,498 they would've gotten tangled. 414 00:21:56,498 --> 00:21:57,700 AUDIENCE: Seems [INAUDIBLE] 415 00:21:57,700 --> 00:21:59,283 JEFF GORE: That's right, that's right. 416 00:22:04,042 --> 00:22:05,500 I do want to just come back and say 417 00:22:05,500 --> 00:22:08,120 one thing about this question of a rotary motor, 418 00:22:08,120 --> 00:22:11,108 because it's a fascinating question-- oh yes, go ahead. 419 00:22:11,108 --> 00:22:12,983 AUDIENCE: Sorry, I just had a quick question. 420 00:22:12,983 --> 00:22:15,290 What was the units of eta again? 421 00:22:15,290 --> 00:22:20,267 JEFF GORE: Oh, this is the thing. 422 00:22:20,267 --> 00:22:22,100 The units of eta, I always just go back here 423 00:22:22,100 --> 00:22:23,558 and I say, OK, well, it's the units 424 00:22:23,558 --> 00:22:28,890 of a force divided by unit of an area-- or sorry, of a radius, 425 00:22:28,890 --> 00:22:34,890 unit of a velocity, and then I have to plug everything in. 426 00:22:34,890 --> 00:22:37,780 And then, I have to find an equation with a force other 427 00:22:37,780 --> 00:22:39,670 than this equation, because if you put this equation back in, 428 00:22:39,670 --> 00:22:40,836 then you don't get anywhere. 429 00:22:43,332 --> 00:22:44,040 These are useful. 430 00:22:47,420 --> 00:22:50,760 So I always have to actually figure it out fresh each time. 431 00:22:56,100 --> 00:22:58,710 So it turns out that these are indeed rotary motors. 432 00:22:58,710 --> 00:23:04,380 And I think that this was actually the first-- as far 433 00:23:04,380 --> 00:23:08,760 as I'm aware, it's the first example of a rotary motor 434 00:23:08,760 --> 00:23:12,320 in biology that had been demonstrated, 435 00:23:12,320 --> 00:23:18,520 which is a fascinating idea because in human engineering, 436 00:23:18,520 --> 00:23:21,535 rotary motors are everywhere. 437 00:23:24,390 --> 00:23:27,630 Yet somehow, if you look at living things, 438 00:23:27,630 --> 00:23:31,120 they don't seem to have rotary motors. 439 00:23:31,120 --> 00:23:37,840 Now, anybody want to suggest why rotary motors might be rare 440 00:23:37,840 --> 00:23:40,210 in biology, in life? 441 00:23:40,210 --> 00:23:42,210 AUDIENCE: Rotary is just that it rotates, right, 442 00:23:42,210 --> 00:23:46,575 not in terms of a mechanism [INAUDIBLE] because there's 443 00:23:46,575 --> 00:23:49,129 also [INAUDIBLE] 444 00:23:49,129 --> 00:23:51,420 JEFF GORE: Well, I guess I'm thinking of something that 445 00:23:51,420 --> 00:23:53,580 can continuously rotate, right? 446 00:23:53,580 --> 00:23:59,140 It's true that if you look at-- we have ball socket joints 447 00:23:59,140 --> 00:24:02,240 and I can rotate them a little bit, but certainly, 448 00:24:02,240 --> 00:24:05,294 I can't go-- there are limits, right? 449 00:24:05,294 --> 00:24:06,960 And this is a pretty striking difference 450 00:24:06,960 --> 00:24:10,730 between human engineering and biological engineering. 451 00:24:14,094 --> 00:24:14,594 Yeah? 452 00:24:14,594 --> 00:24:17,975 AUDIENCE: If you tried to connect anything across this, 453 00:24:17,975 --> 00:24:19,270 it would be more [INAUDIBLE] 454 00:24:19,270 --> 00:24:20,270 JEFF GORE: That's right. 455 00:24:20,270 --> 00:24:21,220 AUDIENCE: [INAUDIBLE] 456 00:24:21,220 --> 00:24:21,560 JEFF GORE: That's right. 457 00:24:21,560 --> 00:24:22,750 The problem is you just can't have 458 00:24:22,750 --> 00:24:23,958 anything connected across it. 459 00:24:23,958 --> 00:24:27,420 Otherwise, you really do get tangled, right? 460 00:24:27,420 --> 00:24:29,430 Now, the question then is, well, why 461 00:24:29,430 --> 00:24:32,020 is it that it's possible to do that here then? 462 00:24:36,145 --> 00:24:38,020 AUDIENCE: Because we're at such a small scale 463 00:24:38,020 --> 00:24:40,583 that we're not thinking of connecting anything else. 464 00:24:40,583 --> 00:24:43,421 We're individual molecules, anyway. 465 00:24:43,421 --> 00:24:45,214 There's nothing that can go through that. 466 00:24:45,214 --> 00:24:46,630 JEFF GORE: Yeah, it's interesting. 467 00:24:46,630 --> 00:24:48,470 And this is how I think about it that well, 468 00:24:48,470 --> 00:24:50,940 at the molecular scale, you just have some rotary something 469 00:24:50,940 --> 00:24:53,520 and it doesn't have to be attached 470 00:24:53,520 --> 00:24:56,590 via, say, covalent bonds or whatnot. 471 00:24:56,590 --> 00:24:59,960 And you can then force something to rotate. 472 00:24:59,960 --> 00:25:03,540 Of course, it's a little bit funny because this issue 473 00:25:03,540 --> 00:25:07,090 about connecting across this rotation, that 474 00:25:07,090 --> 00:25:09,780 should be a problem for human engineering, as well, 475 00:25:09,780 --> 00:25:12,330 but somehow, we do get around it. 476 00:25:12,330 --> 00:25:14,100 I guess what I would say is I don't have 477 00:25:14,100 --> 00:25:20,140 any comments, except for this was then quite a surprise when 478 00:25:20,140 --> 00:25:23,010 it was discovered that this was a rotor motor, just because we 479 00:25:23,010 --> 00:25:28,130 had not seen any in other macroscopic living things. 480 00:25:28,130 --> 00:25:31,270 So then, it was quite exciting to see it 481 00:25:31,270 --> 00:25:33,470 in the case of the flagellar motor. 482 00:25:33,470 --> 00:25:35,490 And in your book, you'll see that there's 483 00:25:35,490 --> 00:25:39,000 a very nice kind of EM reconstruction of this motor 484 00:25:39,000 --> 00:25:41,610 and you can see how it's hinged and it's 485 00:25:41,610 --> 00:25:44,520 powered by proton gradients that kind of cause this thing 486 00:25:44,520 --> 00:25:45,030 to rotate. 487 00:25:45,030 --> 00:25:46,933 It's really a beautiful, amazing thing. 488 00:25:49,591 --> 00:25:51,930 Does anybody know any other examples of rotary motors? 489 00:25:55,500 --> 00:25:56,310 That's right. 490 00:25:56,310 --> 00:26:00,650 The other really famous one is the F0F1 ATP synthase, 491 00:26:00,650 --> 00:26:04,240 which is, again, something that's across a membrane 492 00:26:04,240 --> 00:26:08,130 and has, once again, a really beautiful structure where 493 00:26:08,130 --> 00:26:11,482 it has this circular thing in the membrane that rotates, 494 00:26:11,482 --> 00:26:13,065 responds to, again, a proton gradient, 495 00:26:13,065 --> 00:26:16,040 and then that drives rotation of this other part 496 00:26:16,040 --> 00:26:17,320 of the protein, F1. 497 00:26:17,320 --> 00:26:19,730 And then, that makes ATP. 498 00:26:19,730 --> 00:26:23,840 And that motor is amazing also because it's reversible, 499 00:26:23,840 --> 00:26:30,550 in that the cell can also burn ATP and drive a proton 500 00:26:30,550 --> 00:26:31,490 gradient. 501 00:26:31,490 --> 00:26:34,085 And indeed, in some single-molecule experiments, 502 00:26:34,085 --> 00:26:35,460 they've even done something where 503 00:26:35,460 --> 00:26:42,040 they attached a little magnetic particle onto this F1 504 00:26:42,040 --> 00:26:44,050 and then rotated themselves. 505 00:26:44,050 --> 00:26:47,530 And they showed that they could actually make ATP. 506 00:26:50,780 --> 00:26:53,720 The efficiency was maybe not great, something like that, 507 00:26:53,720 --> 00:26:55,700 because they're rotating a macroscopic magnet 508 00:26:55,700 --> 00:26:58,670 and then they're making ATPs there. 509 00:26:58,670 --> 00:27:01,390 But it's a pretty remarkable aspect 510 00:27:01,390 --> 00:27:03,620 of these molecular motors. 511 00:27:03,620 --> 00:27:06,820 Now in this class, we're not going 512 00:27:06,820 --> 00:27:08,870 to say anything more about molecular motors, 513 00:27:08,870 --> 00:27:11,520 but I just wanted to mention a few things about them 514 00:27:11,520 --> 00:27:14,590 because they're really fun, beautiful things 515 00:27:14,590 --> 00:27:16,494 and there are other classes that are 516 00:27:16,494 --> 00:27:18,952 at MIT that may give you an opportunity to think about them 517 00:27:18,952 --> 00:27:19,680 some more. 518 00:27:22,520 --> 00:27:25,675 Any question about where we are now? 519 00:27:25,675 --> 00:27:26,550 AUDIENCE: [INAUDIBLE] 520 00:27:30,740 --> 00:27:32,158 JEFF GORE: The common motor? 521 00:27:32,158 --> 00:27:34,070 AUDIENCE: Yeah, [INAUDIBLE] 522 00:27:34,070 --> 00:27:35,320 JEFF GORE: Oh. 523 00:27:35,320 --> 00:27:38,030 Well, I'd say that the other class of motors 524 00:27:38,030 --> 00:27:40,930 that are seen a lot in the context 525 00:27:40,930 --> 00:27:42,850 of these molecular motors are motors that 526 00:27:42,850 --> 00:27:45,140 travel along linear tracks. 527 00:27:45,140 --> 00:27:49,400 So there's kinesin that walks along microtubules. 528 00:27:49,400 --> 00:27:52,780 There are various myosins that walk on actin. 529 00:27:52,780 --> 00:27:55,040 And then, of course, DNA and RNA polymerase, 530 00:27:55,040 --> 00:27:56,748 we don't normally think of them as motors 531 00:27:56,748 --> 00:27:58,820 but indeed, they take an energy fuel 532 00:27:58,820 --> 00:28:02,780 and then they have to walk along the template 533 00:28:02,780 --> 00:28:05,600 as they make either the DNA or the RNA. 534 00:28:05,600 --> 00:28:09,540 So I'd say there are many, many examples of molecular motors 535 00:28:09,540 --> 00:28:13,260 that convert chemical energy into mechanical force 536 00:28:13,260 --> 00:28:16,200 and motion, particularly along one-dimensional tracks. 537 00:28:16,200 --> 00:28:18,780 So those, I think, are the most well-studied examples. 538 00:28:33,250 --> 00:28:36,630 Now, one way to study this run and tumble motion 539 00:28:36,630 --> 00:28:39,560 is, of course, to actually apply a gradient 540 00:28:39,560 --> 00:28:41,620 and then watch the cells as they swim it. 541 00:28:41,620 --> 00:28:44,966 And that has been done. 542 00:28:44,966 --> 00:28:46,840 A lot's been learned from that kind of assay, 543 00:28:46,840 --> 00:28:51,020 but it turns out that there are two other assays that maybe 544 00:28:51,020 --> 00:28:55,610 allowed for more controlled analysis 545 00:28:55,610 --> 00:28:58,580 of this chemotaxis kind of response. 546 00:28:58,580 --> 00:29:01,860 So let's just say-- so studying chemotaxis. 547 00:29:08,550 --> 00:29:13,930 The most obvious thing is to apply a gradient 548 00:29:13,930 --> 00:29:14,660 and then watch. 549 00:29:18,050 --> 00:29:20,310 And indeed, the classic assays where 550 00:29:20,310 --> 00:29:25,550 you add a little pipette with an attractant or a repellent 551 00:29:25,550 --> 00:29:27,840 and watch the bacteria swim toward or away, 552 00:29:27,840 --> 00:29:30,379 that demonstrates there is indeed chemotaxis. 553 00:29:30,379 --> 00:29:32,170 But it's a little bit difficult to quantify 554 00:29:32,170 --> 00:29:34,540 that process in many cases. 555 00:29:34,540 --> 00:29:39,095 What are the assays that maybe you've read about recently? 556 00:29:51,740 --> 00:29:55,200 In [? Yuri's ?] book, how is it that they actually analyzed 557 00:29:55,200 --> 00:29:56,600 this perfect adaptation? 558 00:30:00,710 --> 00:30:01,210 Yes? 559 00:30:01,210 --> 00:30:05,530 AUDIENCE: So you can bind the flagella on the slide and then 560 00:30:05,530 --> 00:30:07,470 [INAUDIBLE] 561 00:30:07,470 --> 00:30:11,570 JEFF GORE: So one thing that you can do is you can-- 562 00:30:11,570 --> 00:30:12,410 I may put it here. 563 00:30:12,410 --> 00:30:12,910 All right. 564 00:30:12,910 --> 00:30:18,695 So you can kind of attach the cell to a slide. 565 00:30:22,900 --> 00:30:25,275 And typically attach it to the slide by what? 566 00:30:30,480 --> 00:30:31,350 This isn't it. 567 00:30:31,350 --> 00:30:34,465 And does it matter where you attach the cell to the slide? 568 00:30:34,465 --> 00:30:35,830 AUDIENCE: By the flagella. 569 00:30:35,830 --> 00:30:36,530 JEFF GORE: Yeah, so you typically 570 00:30:36,530 --> 00:30:38,488 have attach it via this hook that's at the end, 571 00:30:38,488 --> 00:30:41,050 so by some part of the flagella-- to the slide 572 00:30:41,050 --> 00:30:45,190 by the flagella, we'll say. 573 00:30:45,190 --> 00:30:46,010 Flagellum? 574 00:30:46,010 --> 00:30:49,600 Flagella-- whatever. 575 00:30:49,600 --> 00:30:53,430 And the nice thing there is that as the cell is doing its thing 576 00:30:53,430 --> 00:30:56,010 and it's spinning either clockwise or counterclockwise, 577 00:30:56,010 --> 00:30:59,760 you can directly visualize that because the whole cell is 578 00:30:59,760 --> 00:31:02,510 moving. 579 00:31:02,510 --> 00:31:07,710 And the cell is both the thing that is doing the work 580 00:31:07,710 --> 00:31:09,560 and processing the signals and everything, 581 00:31:09,560 --> 00:31:13,270 but it's also your marker for what the state 582 00:31:13,270 --> 00:31:14,910 of this little hook is, right? 583 00:31:14,910 --> 00:31:18,400 This is a wonderfully quantitative assay where you 584 00:31:18,400 --> 00:31:20,480 can get high time resolution. 585 00:31:20,480 --> 00:31:22,560 It's easy to do the image analysis. 586 00:31:22,560 --> 00:31:28,267 And then, how do you typically get this cell to change its, 587 00:31:28,267 --> 00:31:29,600 for example, tumbling frequency? 588 00:31:35,034 --> 00:31:36,516 AUDIENCE: Put an attractant. 589 00:31:36,516 --> 00:31:38,637 JEFF GORE: Right, so you can add an attractant. 590 00:31:38,637 --> 00:31:40,970 And indeed, I just wanted to separate this a little bit, 591 00:31:40,970 --> 00:31:42,997 because you can-- even without doing this-- 592 00:31:42,997 --> 00:31:45,080 this is kind of the next order step-- you can just 593 00:31:45,080 --> 00:31:53,390 add an attractant and mix, because you don't 594 00:31:53,390 --> 00:31:55,440 want the spatial patterns. 595 00:31:55,440 --> 00:31:59,425 But a nice thing here, this is a gradient in space 596 00:31:59,425 --> 00:32:01,900 and then you can watch the bacteria swim. 597 00:32:01,900 --> 00:32:03,920 But you can also have the gradient in time. 598 00:32:03,920 --> 00:32:05,665 And the cells can't tell the difference. 599 00:32:05,665 --> 00:32:07,540 The nice thing here is that you can then just 600 00:32:07,540 --> 00:32:08,810 add the attractant, mix, and then 601 00:32:08,810 --> 00:32:10,730 you just watch all the cells as they're going. 602 00:32:10,730 --> 00:32:13,665 You don't need to try to follow them or whatnot, 603 00:32:13,665 --> 00:32:16,290 but you can just look to see how the tumbling frequency changes 604 00:32:16,290 --> 00:32:16,790 over time. 605 00:32:19,590 --> 00:32:22,340 And of course, you would typically use this trick 606 00:32:22,340 --> 00:32:26,192 together with this in order to study perfect adaptation and so 607 00:32:26,192 --> 00:32:28,330 forth. 608 00:32:28,330 --> 00:32:32,890 If you collect this sort of data and you plot the tumbling 609 00:32:32,890 --> 00:32:43,560 frequency as a function of time, what you might see 610 00:32:43,560 --> 00:32:48,410 is that it starts out at one per second. 611 00:32:52,800 --> 00:33:02,845 Now, if at this time, I add an attractant, 612 00:33:02,845 --> 00:33:06,350 does the tumbling frequency go up or down? 613 00:33:06,350 --> 00:33:07,940 And we're going to do a verbal answer. 614 00:33:07,940 --> 00:33:08,439 Ready? 615 00:33:08,439 --> 00:33:10,286 Three, two, one. 616 00:33:10,286 --> 00:33:10,910 AUDIENCE: Down. 617 00:33:10,910 --> 00:33:11,860 JEFF GORE: Down. 618 00:33:11,860 --> 00:33:13,900 And that makes sense because the cells 619 00:33:13,900 --> 00:33:17,750 think that they're moving up an attractant gradient. 620 00:33:17,750 --> 00:33:23,550 So over a very short time scale, tumbling frequency goes down. 621 00:33:23,550 --> 00:33:31,320 But then, over a time scale of minutes-- 622 00:33:31,320 --> 00:33:36,090 it might be 5, 10 minutes-- that tumbling frequency 623 00:33:36,090 --> 00:33:37,900 goes back to where it started. 624 00:33:37,900 --> 00:33:42,360 I just want to-- this varies, but this 625 00:33:42,360 --> 00:33:44,670 could be order of 10 minutes. 626 00:33:44,670 --> 00:33:46,198 AUDIENCE: Why is it so long? 627 00:33:46,198 --> 00:33:47,590 JEFF GORE: Yeah. 628 00:33:47,590 --> 00:33:49,690 AUDIENCE: 10 minutes is a very long time. 629 00:33:49,690 --> 00:33:52,380 JEFF GORE: Yeah, it's a long time scale. 630 00:33:52,380 --> 00:33:55,880 And here's a question. 631 00:33:55,880 --> 00:33:57,530 Is it because this is the time that it 632 00:33:57,530 --> 00:33:59,500 takes to make new protein? 633 00:34:06,606 --> 00:34:07,980 New protein synthesis, we'll say. 634 00:34:20,277 --> 00:34:22,026 AUDIENCE: You're asking if that's the time 635 00:34:22,026 --> 00:34:24,150 or if that's the reason why is it long? 636 00:34:28,080 --> 00:34:32,760 JEFF GORE: I'm saying is this the explanation for why this 637 00:34:32,760 --> 00:34:35,020 is 10 minutes, because the cell has 638 00:34:35,020 --> 00:34:37,550 to go make new protein in order to do this? 639 00:34:40,695 --> 00:34:43,320 So the cell is presumably going to be making some new proteins, 640 00:34:43,320 --> 00:34:46,489 but is this what you would really 641 00:34:46,489 --> 00:34:49,800 describe as being the causative agent of this thing taking 10, 642 00:34:49,800 --> 00:34:52,540 20 minutes? 643 00:34:52,540 --> 00:34:55,130 Ready? 644 00:34:55,130 --> 00:34:57,790 Three, two, one. 645 00:35:00,631 --> 00:35:01,130 All right. 646 00:35:01,130 --> 00:35:03,260 So I'd say most people are agreeing that actually, 647 00:35:03,260 --> 00:35:04,750 yes, it is. 648 00:35:04,750 --> 00:35:05,700 The answer is no. 649 00:35:05,700 --> 00:35:06,929 This is not. 650 00:35:06,929 --> 00:35:09,220 It may be the case that the cell is making new protein, 651 00:35:09,220 --> 00:35:13,000 but this is not what's setting the time scale there. 652 00:35:16,920 --> 00:35:18,000 Is-- 653 00:35:18,000 --> 00:35:19,824 AUDIENCE: More [INAUDIBLE] 654 00:35:19,824 --> 00:35:22,010 JEFF GORE: Right. 655 00:35:22,010 --> 00:35:25,320 You agreed that that was the answer, but you didn't-- well, 656 00:35:25,320 --> 00:35:28,760 so I would say there are several ways you can think about this, 657 00:35:28,760 --> 00:35:31,400 but we're going to go through the model that is supported 658 00:35:31,400 --> 00:35:33,566 by, I think, a fair amount of experimental evidence. 659 00:35:33,566 --> 00:35:36,440 But the key feature there is that in this model, 660 00:35:36,440 --> 00:35:41,210 it works even if all the protein concentrations are 661 00:35:41,210 --> 00:35:43,780 constant over time. 662 00:35:43,780 --> 00:35:45,790 So everything that's happening in this network 663 00:35:45,790 --> 00:35:48,150 is happening as a result of changes 664 00:35:48,150 --> 00:35:49,370 of the states of the protein. 665 00:35:49,370 --> 00:35:53,350 So proteins are either getting methylated or phosphorylated 666 00:35:53,350 --> 00:35:56,620 and these-- right. 667 00:35:59,350 --> 00:36:01,100 But then, of course, it's the question of, 668 00:36:01,100 --> 00:36:06,980 why is it 10 minutes instead of 10 seconds or a minute? 669 00:36:06,980 --> 00:36:08,960 AUDIENCE: You need a [INAUDIBLE] in there 670 00:36:08,960 --> 00:36:13,167 that's on the order of minutes, like 100 minutes, which 671 00:36:13,167 --> 00:36:14,900 is very slow. 672 00:36:14,900 --> 00:36:16,760 Is there-- 673 00:36:16,760 --> 00:36:23,300 JEFF GORE: Yeah, well, their one question is, this 674 00:36:23,300 --> 00:36:27,850 is what is called the adaptation time. 675 00:36:27,850 --> 00:36:31,890 Now, is this a robust feature in this model 676 00:36:31,890 --> 00:36:33,496 or in the cells, for that matter? 677 00:36:37,600 --> 00:36:39,910 We'll just add verbal, yes or no. 678 00:36:39,910 --> 00:36:40,520 Ready? 679 00:36:40,520 --> 00:36:42,939 Three, two, one, 680 00:36:42,939 --> 00:36:43,480 AUDIENCE: No. 681 00:36:43,480 --> 00:36:44,063 JEFF GORE: No. 682 00:36:46,510 --> 00:36:50,570 Now, and what that means is that indeed, 683 00:36:50,570 --> 00:36:52,860 different kind of versions of this network 684 00:36:52,860 --> 00:36:54,450 will have different times. 685 00:36:54,450 --> 00:36:57,930 And there is data looking at variation in this 686 00:36:57,930 --> 00:36:59,890 between different cells. 687 00:36:59,890 --> 00:37:04,960 And I guess I don't have a clear feeling for what 688 00:37:04,960 --> 00:37:08,880 would be optimal, in the sense of allowing optimal climbing up 689 00:37:08,880 --> 00:37:11,620 of an attractant gradient. 690 00:37:11,620 --> 00:37:14,920 This thing has to be much longer than the typical times 691 00:37:14,920 --> 00:37:18,660 for a tumble. 692 00:37:18,660 --> 00:37:21,980 Otherwise, it's not even-- well, we 693 00:37:21,980 --> 00:37:24,440 wouldn't have been able to measure it, I guess. 694 00:37:24,440 --> 00:37:28,279 But I agree that it could have been one minute 695 00:37:28,279 --> 00:37:29,695 and I wouldn't have batted an eye, 696 00:37:29,695 --> 00:37:31,778 in the sense that I don't have any feeling for why 697 00:37:31,778 --> 00:37:34,720 it had to have been this or something else. 698 00:37:34,720 --> 00:37:36,312 But somebody who actually studies this 699 00:37:36,312 --> 00:37:37,895 might be able to give a better answer. 700 00:37:44,080 --> 00:37:45,231 All right. 701 00:37:45,231 --> 00:37:47,636 AUDIENCE: But I guess-- sorry, just one last thing. 702 00:37:47,636 --> 00:37:49,580 My question is not why it's 10 minutes. 703 00:37:49,580 --> 00:37:51,500 It's not an evolutionary question, 704 00:37:51,500 --> 00:37:53,900 like why is it useful, right? 705 00:37:53,900 --> 00:38:00,020 It's just somehow, [INAUDIBLE] 706 00:38:00,020 --> 00:38:01,959 JEFF GORE: Yeah I think that there 707 00:38:01,959 --> 00:38:03,500 are different ways of looking at this 708 00:38:03,500 --> 00:38:05,208 and then depending on how you look at it, 709 00:38:05,208 --> 00:38:07,050 you either feel surprised or not. 710 00:38:07,050 --> 00:38:15,520 So it's a little-- now on the other hand, 711 00:38:15,520 --> 00:38:16,980 if you had added a repellent, then 712 00:38:16,980 --> 00:38:19,135 the tumbling frequency would actually go up 713 00:38:19,135 --> 00:38:21,340 and then come back down. 714 00:38:21,340 --> 00:38:26,087 But the key, key thing in this system 715 00:38:26,087 --> 00:38:27,670 that we want to focus our attention on 716 00:38:27,670 --> 00:38:32,810 is the fact that it comes back to where it started. 717 00:38:32,810 --> 00:38:35,980 So it's the fact that I can draw this dashed line that 718 00:38:35,980 --> 00:38:37,245 is this perfect adaptation. 719 00:38:52,310 --> 00:38:54,349 And so what we want to do is understand 720 00:38:54,349 --> 00:38:56,140 where this phenomenon of perfect adaptation 721 00:38:56,140 --> 00:39:01,829 comes from and maybe why it is robust to changes 722 00:39:01,829 --> 00:39:03,620 in, for example, the concentrations of some 723 00:39:03,620 --> 00:39:04,369 of these proteins. 724 00:39:08,100 --> 00:39:12,320 Now, let's just make sure that we're 725 00:39:12,320 --> 00:39:15,920 all on the same page in terms of what was known 726 00:39:15,920 --> 00:39:18,280 about this chemotaxis network. 727 00:39:18,280 --> 00:39:23,150 And I think it's worth mentioning, perhaps, here 728 00:39:23,150 --> 00:39:29,070 that the whole series of studies of bacterial chemotaxis 729 00:39:29,070 --> 00:39:31,010 going back to Howard Berg and company 730 00:39:31,010 --> 00:39:34,130 and then later, the studies that in robustness 731 00:39:34,130 --> 00:39:37,370 that Uri Alon and Stan Leibler and Naama Barkai did. 732 00:39:37,370 --> 00:39:41,730 I think they represent really just a wonderfully beautiful 733 00:39:41,730 --> 00:39:44,740 exploration at the interface between physics and biology. 734 00:39:44,740 --> 00:39:47,790 I think you could teach an entire course just 735 00:39:47,790 --> 00:39:50,400 on bacterial chemotaxis and you could hit pretty much 736 00:39:50,400 --> 00:39:54,530 all the major themes in biophysics over the last 40 737 00:39:54,530 --> 00:39:55,300 years. 738 00:39:55,300 --> 00:39:57,876 It's really amazing to me. 739 00:39:57,876 --> 00:39:59,750 I myself have not done any work in the field, 740 00:39:59,750 --> 00:40:03,090 but from afar, I've really just admired the beauty 741 00:40:03,090 --> 00:40:04,860 of all these studies. 742 00:40:04,860 --> 00:40:09,225 And because you go back to Howard Berg and Purcell 743 00:40:09,225 --> 00:40:12,910 and they're thinking about how simple physics can inform 744 00:40:12,910 --> 00:40:15,340 the challenges that bacteria are facing 745 00:40:15,340 --> 00:40:18,790 and how cells are actually able to do a biased random walk 746 00:40:18,790 --> 00:40:23,300 and get anywhere, limits on sensing both concentrations 747 00:40:23,300 --> 00:40:27,250 and gradients-- and then later, the studies 748 00:40:27,250 --> 00:40:29,360 that they're this topic of robustness, 749 00:40:29,360 --> 00:40:31,990 it's really a wonderful example where 750 00:40:31,990 --> 00:40:34,770 Naama Barkai, when she was a postdoc at Stan Leibler, 751 00:40:34,770 --> 00:40:39,097 they had published a Nature paper in maybe '97 basically 752 00:40:39,097 --> 00:40:41,680 saying, this idea of robustness is really important in biology 753 00:40:41,680 --> 00:40:47,260 and in order to have a robust response of perfect adaptation, 754 00:40:47,260 --> 00:40:49,130 a model has to have these features. 755 00:40:49,130 --> 00:40:52,170 So there's no experiments there, but their model 756 00:40:52,170 --> 00:40:53,810 was guided by previous observations 757 00:40:53,810 --> 00:40:56,320 that people had made. 758 00:40:56,320 --> 00:40:58,990 And then, two years later, Uri, when 759 00:40:58,990 --> 00:41:02,290 he was a postdoc in Stan's lab again, 760 00:41:02,290 --> 00:41:04,510 did kind of the experimental confirmation 761 00:41:04,510 --> 00:41:06,431 of the model, where he went in and he 762 00:41:06,431 --> 00:41:07,972 controlled the concentration of chi R 763 00:41:07,972 --> 00:41:11,080 and showed that thee key predictions of the model, i.e. 764 00:41:11,080 --> 00:41:14,140 the perfect adaptation, would be robust to the concentration 765 00:41:14,140 --> 00:41:17,390 but that the tumbling frequency and the adaptation time, they 766 00:41:17,390 --> 00:41:19,224 would not be robust to chi R concentrations. 767 00:41:19,224 --> 00:41:20,640 They would move in a way predicted 768 00:41:20,640 --> 00:41:21,879 by the model and all that. 769 00:41:21,879 --> 00:41:24,170 It's really amazing that it all kind of holds together, 770 00:41:24,170 --> 00:41:29,860 because in many cases, we do the modeling kind of post facto, 771 00:41:29,860 --> 00:41:30,360 right? 772 00:41:30,360 --> 00:41:32,280 And then, it's kind of explaining our results. 773 00:41:32,280 --> 00:41:36,216 But the case where a model is really useful 774 00:41:36,216 --> 00:41:38,090 is when it makes new predictions that get you 775 00:41:38,090 --> 00:41:39,940 to go make new measurements. 776 00:41:39,940 --> 00:41:43,385 And this is a situation where there 777 00:41:43,385 --> 00:41:46,010 are an infinite number of experiments that you could do, 778 00:41:46,010 --> 00:41:48,770 but only some of them will actually provide you 779 00:41:48,770 --> 00:41:50,610 a deep insight into the mechanisms that 780 00:41:50,610 --> 00:41:52,000 are going on in the system. 781 00:41:52,000 --> 00:41:54,650 And I think this was a real case where the models made 782 00:41:54,650 --> 00:41:57,550 some really clear predictions and that allowed, in this case, 783 00:41:57,550 --> 00:42:01,742 Uri to go and make the strains that allowed him to test 784 00:42:01,742 --> 00:42:02,950 the predictions of the model. 785 00:42:02,950 --> 00:42:07,330 And I think it's really amazing that it all kind of works. 786 00:42:07,330 --> 00:42:07,830 All right. 787 00:42:07,830 --> 00:42:11,670 Now, all of the letters that you see up there, 788 00:42:11,670 --> 00:42:14,190 they're not actually-- well, first of all, the letters 789 00:42:14,190 --> 00:42:15,840 are somehow real. 790 00:42:15,840 --> 00:42:19,280 This is the real names of the protein components 791 00:42:19,280 --> 00:42:21,160 in the chemotaxis network in E. coli 792 00:42:21,160 --> 00:42:23,350 and largely in other organisms. 793 00:42:23,350 --> 00:42:29,190 But in each case, there's a chi that comes in front, right? 794 00:42:29,190 --> 00:42:33,690 So R corresponds to chi R, for example. 795 00:42:33,690 --> 00:42:35,940 And then, there's chi B, chi W, chi A. 796 00:42:35,940 --> 00:42:40,640 And these were all identified by genetics, so then 797 00:42:40,640 --> 00:42:43,890 by researchers looking for mutants that 798 00:42:43,890 --> 00:42:47,620 were defective in chemotaxis. 799 00:42:47,620 --> 00:42:51,586 I don't know what happened to C, D, E, F, G, 800 00:42:51,586 --> 00:42:54,210 because it does seem like we got the first part of the alphabet 801 00:42:54,210 --> 00:42:55,626 and the last part of the alphabet. 802 00:42:57,910 --> 00:43:00,024 I don't know. 803 00:43:00,024 --> 00:43:01,010 All right. 804 00:43:01,010 --> 00:43:04,820 Now, the basic idea in the system 805 00:43:04,820 --> 00:43:11,810 is that you have chi W/A that we often here will refer to as X 806 00:43:11,810 --> 00:43:13,290 just for simplicity. 807 00:43:13,290 --> 00:43:17,800 Now, these are proteins in the membrane, 808 00:43:17,800 --> 00:43:20,700 so they have a binding kind of pocket outside 809 00:43:20,700 --> 00:43:24,640 that will allow binding of attractants or repellents. 810 00:43:24,640 --> 00:43:28,390 There might be say, five different kinds 811 00:43:28,390 --> 00:43:31,530 of these receptor complexes that can sense, 812 00:43:31,530 --> 00:43:34,160 that bind at different rates, different kinds of attractants, 813 00:43:34,160 --> 00:43:36,410 repellents, and then the signal is somehow integrated. 814 00:43:39,690 --> 00:43:44,950 Now, this could be either an attractant or a repellant. 815 00:43:44,950 --> 00:43:47,900 The distinction between these two 816 00:43:47,900 --> 00:43:52,440 is that we get different levels of methylation 817 00:43:52,440 --> 00:43:57,008 onto chi W. Now in this lecture, we're 818 00:43:57,008 --> 00:43:59,250 only going to be talking about the methylated state 819 00:43:59,250 --> 00:44:01,070 versus the unmethylated. 820 00:44:01,070 --> 00:44:03,860 But in reality, depending on the receptor complex they have, 821 00:44:03,860 --> 00:44:06,460 they might have four or five different methylation sites. 822 00:44:06,460 --> 00:44:10,290 And this ability to switch between different methylation 823 00:44:10,290 --> 00:44:13,920 states is really at the heart of the phenomenon 824 00:44:13,920 --> 00:44:15,390 of robust perfect adaptation. 825 00:44:18,960 --> 00:44:24,415 The base feature in it, though, is that chi A can phosphorylate 826 00:44:24,415 --> 00:44:30,840 chi Y and chi Y will then go and yield the output, 827 00:44:30,840 --> 00:44:36,084 which is in this case, increased tumbling frequency. 828 00:44:36,084 --> 00:44:38,000 But there are lots of other bells and whistles 829 00:44:38,000 --> 00:44:39,490 that you can see on here, right? 830 00:44:39,490 --> 00:44:42,520 So of course, it's not just that this phosphorylated 831 00:44:42,520 --> 00:44:45,510 chi Y just kind of comes off on its own, 832 00:44:45,510 --> 00:44:49,080 but rather it's actually done by chi Z. 833 00:44:49,080 --> 00:44:50,971 So there's a constant cycling here 834 00:44:50,971 --> 00:44:52,720 and again, there's a constant cycling here 835 00:44:52,720 --> 00:44:57,300 where the methyl groups are taken off and then put back on. 836 00:44:57,300 --> 00:44:58,950 So if you look at this, you really 837 00:44:58,950 --> 00:45:00,720 do feel that it's rather wasteful, 838 00:45:00,720 --> 00:45:03,910 because there's a huge number of these futile cycles going on. 839 00:45:03,910 --> 00:45:06,820 Chi Y is always kind of being phosphorylated and then 840 00:45:06,820 --> 00:45:12,670 dephosphorylated and this is all going to be costly to the cell. 841 00:45:12,670 --> 00:45:14,437 So you can imagine then the only reason 842 00:45:14,437 --> 00:45:16,520 it's there is because it's doing something useful. 843 00:45:20,130 --> 00:45:24,690 Now, there was a comment in the chapter 844 00:45:24,690 --> 00:45:29,520 about what is the rate limiting step in all this. 845 00:45:29,520 --> 00:45:31,300 And can somebody remember what it was? 846 00:45:50,849 --> 00:45:51,349 Yeah? 847 00:45:51,349 --> 00:45:52,515 AUDIENCE: Is it methylation? 848 00:45:54,450 --> 00:45:56,470 JEFF GORE: So methylation, there is a sense 849 00:45:56,470 --> 00:46:00,100 that that is actually the longest time scale, 850 00:46:00,100 --> 00:46:03,610 but I guess because the methylation 851 00:46:03,610 --> 00:46:05,300 is what results in this thing coming 852 00:46:05,300 --> 00:46:07,620 in the perfect adaptation over this 10 minutes. 853 00:46:07,620 --> 00:46:10,610 I guess what I meant-- so yeah, that is the longest time scale. 854 00:46:10,610 --> 00:46:12,860 But I guess what I was thinking about in rate limiting 855 00:46:12,860 --> 00:46:14,870 is the sense of when the cell finds itself 856 00:46:14,870 --> 00:46:18,140 in a new environment, it changes its state 857 00:46:18,140 --> 00:46:20,790 over a much shorter time scale. 858 00:46:20,790 --> 00:46:23,720 So this thing I drew is almost vertical, right? 859 00:46:23,720 --> 00:46:26,640 So this question is, if the cell finds itself 860 00:46:26,640 --> 00:46:29,670 in a new environment suddenly and then it just really 861 00:46:29,670 --> 00:46:33,900 wants to tumble-- so you find yourself in a crappy bar, 862 00:46:33,900 --> 00:46:35,980 how long does it take for you to get out? 863 00:46:35,980 --> 00:46:38,693 Now, what's going to be rate limiting there? 864 00:46:38,693 --> 00:46:39,193 Yeah? 865 00:46:39,193 --> 00:46:41,840 AUDIENCE: Phospho-- phosphorylation. 866 00:46:41,840 --> 00:46:44,000 JEFF GORE: Phosphorylation, yeah, 867 00:46:44,000 --> 00:46:48,530 although it turns out that's not the rate limiting step. 868 00:46:48,530 --> 00:46:50,780 And this actually comes back a little bit to something 869 00:46:50,780 --> 00:46:53,170 that we talked about in the first part of the class 870 00:46:53,170 --> 00:46:55,590 that in these transcription networks, 871 00:46:55,590 --> 00:46:58,907 the characteristic timescale is what? 872 00:46:58,907 --> 00:46:59,406 AUDIENCE: G. 873 00:46:59,406 --> 00:47:01,350 JEFF GORE: Right. 874 00:47:01,350 --> 00:47:04,224 So the characteristic timescale in the case of transcription 875 00:47:04,224 --> 00:47:05,765 networks is the time it takes for you 876 00:47:05,765 --> 00:47:08,330 to change concentrations of proteins, which is kind of cell 877 00:47:08,330 --> 00:47:10,910 generation time or if you have active degradation, 878 00:47:10,910 --> 00:47:14,120 you might be able to make it faster, whereas all of this 879 00:47:14,120 --> 00:47:15,930 is happening rather quickly, say, 880 00:47:15,930 --> 00:47:18,540 maybe 1/10 tenth of a second. 881 00:47:18,540 --> 00:47:22,434 And a lot of these kinds of processes, binding, unbinding, 882 00:47:22,434 --> 00:47:23,850 and actually even the interactions 883 00:47:23,850 --> 00:47:26,350 between the proteins can take place 884 00:47:26,350 --> 00:47:28,000 even maybe faster than that. 885 00:47:28,000 --> 00:47:32,230 So the actual rate limiting step for when the cell finds itself 886 00:47:32,230 --> 00:47:34,357 in a bad environment for it to start tumbling 887 00:47:34,357 --> 00:47:35,565 is actually due to diffusion. 888 00:47:35,565 --> 00:47:36,820 And that's diffusion of what? 889 00:47:40,047 --> 00:47:41,891 AUDIENCE: Y protein. 890 00:47:41,891 --> 00:47:44,790 JEFF GORE: Yeah, diffusion of the phosphorylated Y, right? 891 00:47:44,790 --> 00:47:52,097 And that's because we have the cells here. 892 00:47:52,097 --> 00:47:53,930 They find themselves in the bad environment. 893 00:47:53,930 --> 00:47:58,670 They rapidly bind the repellent or they quickly 894 00:47:58,670 --> 00:48:02,350 phosphorylate chi Y. But then, Y is 895 00:48:02,350 --> 00:48:04,020 going to be formed at one of the poles, 896 00:48:04,020 --> 00:48:05,894 because actually, there's actually clustering 897 00:48:05,894 --> 00:48:08,260 of these receptors at the poles of a cell 898 00:48:08,260 --> 00:48:12,370 and incidentally, we're not going to talk about that here, 899 00:48:12,370 --> 00:48:15,880 but I think there's strong experimental and theoretical 900 00:48:15,880 --> 00:48:18,810 evidence that this actually increases the sensitivity. 901 00:48:18,810 --> 00:48:22,260 And indeed, people have used simple Ising type models 902 00:48:22,260 --> 00:48:24,710 to try to understand how the coupling between the binding 903 00:48:24,710 --> 00:48:28,530 of repellents on what's essentially almost 904 00:48:28,530 --> 00:48:31,410 like a crystalline array of receptors 905 00:48:31,410 --> 00:48:33,592 can allow the array to better than you 906 00:48:33,592 --> 00:48:34,800 build it to as an individual. 907 00:48:34,800 --> 00:48:38,580 We're not going to get into that here, but in any case, 908 00:48:38,580 --> 00:48:41,210 there's receptors at the poles-- I 909 00:48:41,210 --> 00:48:43,000 don't know if it's both poles or one pole, 910 00:48:43,000 --> 00:48:44,630 but one of the poles of the other-- 911 00:48:44,630 --> 00:48:48,120 and that's where chi Y is phosphorylated. 912 00:48:48,120 --> 00:48:50,500 But then, you can see that these flagella are distributed 913 00:48:50,500 --> 00:48:52,400 all around the cell. 914 00:48:52,400 --> 00:48:55,040 So you have to diffuse from say, the pole 915 00:48:55,040 --> 00:49:00,090 to the site of the flagella motor 916 00:49:00,090 --> 00:49:04,870 in order to cause it to go clockwise and then cause 917 00:49:04,870 --> 00:49:06,066 a tumble. 918 00:49:06,066 --> 00:49:06,565 Yeah? 919 00:49:06,565 --> 00:49:08,350 AUDIENCE: So do you need only one motor? 920 00:49:08,350 --> 00:49:09,891 JEFF GORE: Yeah, so you actually only 921 00:49:09,891 --> 00:49:13,298 need one motor to get the tumbling. 922 00:49:13,298 --> 00:49:15,464 And so then, you may not have to diffuse all the way 923 00:49:15,464 --> 00:49:19,600 to the other end, but-- and of course, diffusion is random. 924 00:49:19,600 --> 00:49:24,350 And we all know that 0.1 seconds is around the time 925 00:49:24,350 --> 00:49:26,240 that it takes for a protein-sized object 926 00:49:26,240 --> 00:49:29,580 to diffuse across the volume of a bacterial cell. 927 00:49:29,580 --> 00:49:33,670 We did that calculation a couple weeks ago. 928 00:49:33,670 --> 00:49:36,640 So 0.1 seconds is indeed-- so the rate limiting step 929 00:49:36,640 --> 00:49:39,620 is indeed this step right here, which 930 00:49:39,620 --> 00:49:48,839 is diffusion of chi Y, the phosphorylated version of it. 931 00:49:54,680 --> 00:49:55,180 All right. 932 00:49:55,180 --> 00:49:59,290 Now, we may not get too much into the models 933 00:49:59,290 --> 00:50:01,430 here, because you did read about them. 934 00:50:01,430 --> 00:50:05,460 But I will just kind of sketch out 935 00:50:05,460 --> 00:50:08,510 sort of what you might call the fine-tuned model and then 936 00:50:08,510 --> 00:50:12,890 the key assumption that goes into this robust model. 937 00:50:12,890 --> 00:50:22,100 Now, what both models assume and indeed 938 00:50:22,100 --> 00:50:24,260 what was known from previous work 939 00:50:24,260 --> 00:50:31,420 was that chi R is present at small number. 940 00:50:31,420 --> 00:50:36,800 So chi R, there might be around 100 proteins in the cell. 941 00:50:41,890 --> 00:50:47,170 And what does this mean about the activity of chi R? 942 00:50:49,880 --> 00:50:51,226 What is the other word for it? 943 00:50:51,226 --> 00:50:52,975 It doesn't actually have to quite mean it, 944 00:50:52,975 --> 00:50:56,285 but what is it that-- how-- 945 00:50:56,285 --> 00:50:57,332 AUDIENCE: [INAUDIBLE] 946 00:50:57,332 --> 00:50:58,290 JEFF GORE: What's that? 947 00:50:58,290 --> 00:50:59,797 AUDIENCE: [? High ?] saturation. 948 00:50:59,797 --> 00:51:01,380 JEFF GORE: So yeah, something is high. 949 00:51:01,380 --> 00:51:08,020 And what is typically assumed is that chi R acts at saturation, 950 00:51:08,020 --> 00:51:17,940 chi R. But what do we mean by "saturation" in these models? 951 00:51:21,330 --> 00:51:23,112 AUDIENCE: Maximum. 952 00:51:23,112 --> 00:51:23,820 JEFF GORE: Right. 953 00:51:23,820 --> 00:51:25,980 Does it mean that if we add more chi 954 00:51:25,980 --> 00:51:29,620 R than the rate of methylation, it doesn't increase? 955 00:51:33,269 --> 00:51:35,310 And I should have put a little methyl group here. 956 00:51:46,022 --> 00:51:47,480 There are multiple things you might 957 00:51:47,480 --> 00:51:52,000 mean by "acts at saturation." 958 00:51:52,000 --> 00:51:54,800 And in the models that you read about last night, 959 00:51:54,800 --> 00:51:58,300 is what it means that if we increase the number of chi R 960 00:51:58,300 --> 00:52:01,090 that it doesn't change the rate of methylation? 961 00:52:01,090 --> 00:52:01,630 Yes or no? 962 00:52:01,630 --> 00:52:02,130 Ready? 963 00:52:02,130 --> 00:52:04,329 Three, two, one. 964 00:52:04,329 --> 00:52:04,870 AUDIENCE: No. 965 00:52:04,870 --> 00:52:06,259 JEFF GORE: No. 966 00:52:06,259 --> 00:52:08,550 And what they mean is something rather different, which 967 00:52:08,550 --> 00:52:12,235 is that if we plot or if we calculate the change 968 00:52:12,235 --> 00:52:14,540 in the concentration of the methylated X-- 969 00:52:14,540 --> 00:52:19,980 now, we're calling this whole thing Xm, methylated X, 970 00:52:19,980 --> 00:52:25,760 and this is just X. The assumption is 971 00:52:25,760 --> 00:52:32,950 that we have X is being methylated 972 00:52:32,950 --> 00:52:38,830 at a rate that is-- there's no Michaelis-Menten term. 973 00:52:38,830 --> 00:52:43,215 If we were to write this as it not being saturated, 974 00:52:43,215 --> 00:52:44,090 what is it acting on? 975 00:52:49,348 --> 00:52:51,750 AUDIENCE: [INAUDIBLE] 976 00:52:51,750 --> 00:52:55,370 JEFF GORE: Yeah, it's not the methylated x. 977 00:52:55,370 --> 00:52:58,430 So indeed, if we were to write this, 978 00:52:58,430 --> 00:53:03,220 we're assuming that this is at saturation, as they say. 979 00:53:03,220 --> 00:53:06,105 But any time that you see something like this, 980 00:53:06,105 --> 00:53:07,560 you have to ask, well, what would 981 00:53:07,560 --> 00:53:09,166 be the alternative, right? 982 00:53:09,166 --> 00:53:10,790 And the alternative would be to include 983 00:53:10,790 --> 00:53:16,030 a term that looks kind of like just X over some K plus X, 984 00:53:16,030 --> 00:53:21,940 because R is acting on the unmethylated X. 985 00:53:21,940 --> 00:53:23,200 We're not including that. 986 00:53:23,200 --> 00:53:27,490 What that means is that we're assuming that this thing is 987 00:53:27,490 --> 00:53:32,520 saturated, that the concentration of X to be acted 988 00:53:32,520 --> 00:53:38,077 on is significantly larger than the Michaelis constant there. 989 00:53:38,077 --> 00:53:40,160 And of course, this is related to the amount of R, 990 00:53:40,160 --> 00:53:42,620 because as we get more and more R, 991 00:53:42,620 --> 00:53:48,220 then eventually, we'll remove some of this X 992 00:53:48,220 --> 00:53:51,160 and then we'll get into the non-saturated regime. 993 00:53:51,160 --> 00:53:53,850 So these two statements are related, but not 994 00:53:53,850 --> 00:53:54,620 the same thing. 995 00:53:59,790 --> 00:54:07,420 Now, there's also some rate that the phosphorylated version of B 996 00:54:07,420 --> 00:54:13,456 removes the methyl groups and that's indeed just going 997 00:54:13,456 --> 00:54:14,705 to be this Michaelis constant. 998 00:54:20,820 --> 00:54:24,410 And this is going to be for the fine-tuned model. 999 00:54:28,030 --> 00:54:29,730 The robust model looks very similar, 1000 00:54:29,730 --> 00:54:37,220 but this is the simplest kind of manifestation of this model. 1001 00:54:37,220 --> 00:54:39,380 Now, once we're writing this down, 1002 00:54:39,380 --> 00:54:40,890 it's useful to make sure that we can 1003 00:54:40,890 --> 00:54:42,420 keep track of what's actually happening 1004 00:54:42,420 --> 00:54:44,003 over the course of perfect adaptation. 1005 00:54:46,780 --> 00:54:52,170 So now, let's imagine first that an attractant arrives. 1006 00:54:56,930 --> 00:55:00,490 That's going to change the activity of X. 1007 00:55:00,490 --> 00:55:02,380 And when we say "activity," what we mean 1008 00:55:02,380 --> 00:55:07,124 is the rate that's it's going to phosphorylate both B and Y. 1009 00:55:07,124 --> 00:55:09,290 So let's just make sure that we know this direction. 1010 00:55:09,290 --> 00:55:10,950 So we add an attractant. 1011 00:55:16,220 --> 00:55:19,111 We'll say "add." 1012 00:55:19,111 --> 00:55:19,860 What does this do? 1013 00:55:19,860 --> 00:55:22,575 Does it make activity go up or down? 1014 00:55:29,759 --> 00:55:31,300 I'll give you 15 seconds to make sure 1015 00:55:31,300 --> 00:55:34,635 that you kind of understand the workings of this network. 1016 00:55:39,420 --> 00:55:56,230 This is activity of X, this complex X. All right. 1017 00:55:56,230 --> 00:55:59,075 Do you need more time? 1018 00:55:59,075 --> 00:55:59,574 All right. 1019 00:55:59,574 --> 00:56:00,510 Let's see where we are. 1020 00:56:00,510 --> 00:56:01,010 Ready? 1021 00:56:01,010 --> 00:56:05,251 Three, two, one. 1022 00:56:05,251 --> 00:56:05,750 All right. 1023 00:56:05,750 --> 00:56:06,830 So we got a majority of the group 1024 00:56:06,830 --> 00:56:08,445 is saying that it should go down. 1025 00:56:12,210 --> 00:56:14,420 Well, let's just follow the logic. 1026 00:56:14,420 --> 00:56:17,210 So we imagine an attractant binding. 1027 00:56:17,210 --> 00:56:19,740 If the activity goes down, that means 1028 00:56:19,740 --> 00:56:22,870 that we get less of the phosphorylated chi 1029 00:56:22,870 --> 00:56:28,450 Y. That means we get less propensity to tumbling, 1030 00:56:28,450 --> 00:56:31,536 which means that we keep on going further. 1031 00:56:31,536 --> 00:56:35,140 All right, that sounds reasonable. 1032 00:56:35,140 --> 00:56:37,466 Any questions about that logic? 1033 00:56:37,466 --> 00:56:39,006 Yes? 1034 00:56:39,006 --> 00:56:39,881 AUDIENCE: [INAUDIBLE] 1035 00:56:43,962 --> 00:56:44,670 JEFF GORE: Right. 1036 00:56:44,670 --> 00:56:47,010 So we haven't said anything yet about BM. 1037 00:56:47,010 --> 00:56:48,920 That's what going to happen next. 1038 00:56:48,920 --> 00:56:51,725 And that's actually the slow time scale. 1039 00:56:51,725 --> 00:56:53,100 So what we had in here is that we 1040 00:56:53,100 --> 00:56:54,900 were kind of at this steady-state tumbling 1041 00:56:54,900 --> 00:56:57,100 frequency of one per second. 1042 00:56:57,100 --> 00:56:58,190 We add an attractant. 1043 00:56:58,190 --> 00:57:02,015 The tumbling frequency goes down because of what we just said. 1044 00:57:02,015 --> 00:57:04,140 But now, there's going to be this longer time scale 1045 00:57:04,140 --> 00:57:07,780 process whereby we get recovery, where 1046 00:57:07,780 --> 00:57:09,580 we come back to this steady-state tumbling 1047 00:57:09,580 --> 00:57:10,250 frequency. 1048 00:57:10,250 --> 00:57:17,350 And that's going to involve action on chi B. 1049 00:57:17,350 --> 00:57:17,850 All right. 1050 00:57:17,850 --> 00:57:24,510 So what happens is that the attractant causes less 1051 00:57:24,510 --> 00:57:26,680 of the phosphorylated chi Y. But it's also 1052 00:57:26,680 --> 00:57:36,990 going to cause less of the phosphorylated chi B. Now, that 1053 00:57:36,990 --> 00:57:40,294 means that we're going to-- and remember, 1054 00:57:40,294 --> 00:57:41,710 the phosphorylated chi B is what's 1055 00:57:41,710 --> 00:57:43,010 removing the methyl groups. 1056 00:57:45,670 --> 00:57:50,000 So if we have less flux going to the left, 1057 00:57:50,000 --> 00:57:52,427 but we have the same-- at that moment, 1058 00:57:52,427 --> 00:57:54,760 we don't have any change in the flux going to the right. 1059 00:57:54,760 --> 00:57:59,780 So chi R is still acting on the same unmethylated X's that it 1060 00:57:59,780 --> 00:58:01,670 was operating on before. 1061 00:58:01,670 --> 00:58:05,700 So it's the same flux to the right, less flux to the left. 1062 00:58:05,700 --> 00:58:12,275 So there's a net accumulation of the methylated receptor, which 1063 00:58:12,275 --> 00:58:17,020 we are calling X. So the key thing here is that-- 1064 00:58:17,020 --> 00:58:20,650 and it's this methylated receptor that 1065 00:58:20,650 --> 00:58:23,610 has more activity. 1066 00:58:23,610 --> 00:58:25,697 In this model, this unmethylated version actually 1067 00:58:25,697 --> 00:58:26,780 doesn't have any activity. 1068 00:58:29,860 --> 00:58:33,000 So then, if we get more of the methylated X, then over time, 1069 00:58:33,000 --> 00:58:36,050 we get a buildup of the methylated X 1070 00:58:36,050 --> 00:58:38,267 and that causes the activity to come back up. 1071 00:58:41,224 --> 00:58:42,640 Now, of course, there's a question 1072 00:58:42,640 --> 00:58:44,737 of-- I just said that it comes back up, 1073 00:58:44,737 --> 00:58:46,320 but I didn't say that it comes back up 1074 00:58:46,320 --> 00:58:50,430 exactly to its original tumbling frequency. 1075 00:58:50,430 --> 00:58:54,040 I didn't say that it necessarily displays perfect adaptation. 1076 00:58:54,040 --> 00:58:55,810 And that's because in this model, 1077 00:58:55,810 --> 00:58:57,870 the perfect adaptation arises as a result of what 1078 00:58:57,870 --> 00:58:59,500 we call fine-tuning, because it only 1079 00:58:59,500 --> 00:59:04,200 happens if all of the parameters are just so. 1080 00:59:04,200 --> 00:59:07,740 In Uri's book, he describes a typical condition 1081 00:59:07,740 --> 00:59:09,050 where that would be the case. 1082 00:59:09,050 --> 00:59:10,690 And the problem is that you can always 1083 00:59:10,690 --> 00:59:14,260 fine-tune for some concentrations of everything, 1084 00:59:14,260 --> 00:59:15,720 chi R or chi this, chi that. 1085 00:59:15,720 --> 00:59:17,430 But then if the concentrations change, 1086 00:59:17,430 --> 00:59:20,440 then you're no longer fine-tuned correctly. 1087 00:59:20,440 --> 00:59:22,200 You were fine-tuned for a different world 1088 00:59:22,200 --> 00:59:24,780 and now you're not-- and that's the definition of being 1089 00:59:24,780 --> 00:59:26,280 fine-tuned is that if things change, 1090 00:59:26,280 --> 00:59:27,446 you're no longer fine-tuned. 1091 00:59:27,446 --> 00:59:31,380 You're just finely off-tune, right? 1092 00:59:31,380 --> 00:59:34,950 So this is the problem with the fine-tuned model 1093 00:59:34,950 --> 00:59:37,030 is that you can get it right for a given-- 1094 00:59:37,030 --> 00:59:38,655 for given concentrations of everything, 1095 00:59:38,655 --> 00:59:41,030 you can always find what numbers. 1096 00:59:41,030 --> 00:59:44,010 This is VB and then there's going 1097 00:59:44,010 --> 00:59:49,960 to be-- you can talk about the activities of XM given 1098 00:59:49,960 --> 00:59:52,210 the previous attractant concentration and so on and so 1099 00:59:52,210 --> 00:59:54,030 forth, but it's not going to be fine-tuned 1100 00:59:54,030 --> 00:59:55,440 if you change anything else, like 1101 00:59:55,440 --> 00:59:57,356 if you change concentration of R, for example. 1102 01:00:00,440 --> 01:00:02,520 And I'm happy to go through the math 1103 01:00:02,520 --> 01:00:05,770 and so forth maybe after class if anybody's curious, 1104 01:00:05,770 --> 01:00:09,170 but it's really precisely what Uri did, 1105 01:00:09,170 --> 01:00:11,120 so maybe I won't get into it now. 1106 01:00:14,000 --> 01:00:16,090 But the question then is, well, how 1107 01:00:16,090 --> 01:00:18,980 is it that you might change this model in order 1108 01:00:18,980 --> 01:00:20,475 to make it robust? 1109 01:00:23,190 --> 01:00:29,850 And the change is somehow surprisingly simple, 1110 01:00:29,850 --> 01:00:33,510 which is that what you want is chi B, instead of just 1111 01:00:33,510 --> 01:00:38,260 acting on any old methylated X, you 1112 01:00:38,260 --> 01:00:43,982 want it to act only on the methylated X that 1113 01:00:43,982 --> 01:00:47,620 is in sort of in what we would call this active state, 1114 01:00:47,620 --> 01:00:54,610 where it's actually able to catalyze 1115 01:00:54,610 --> 01:00:57,000 either of those reactions. 1116 01:00:57,000 --> 01:01:00,860 So the notion is that if you have this methylated X, then 1117 01:01:00,860 --> 01:01:02,682 it's kind of over a very fast time scale. 1118 01:01:02,682 --> 01:01:04,890 It's switching between what we call an "active" state 1119 01:01:04,890 --> 01:01:05,820 and some inactive one. 1120 01:01:05,820 --> 01:01:08,720 And it's really only in the active versions 1121 01:01:08,720 --> 01:01:15,640 that chi B is able to act on and remove the methyl group. 1122 01:01:15,640 --> 01:01:20,730 And this is on the one hand a clever thing 1123 01:01:20,730 --> 01:01:23,650 that allows you to implement this integral feedback. 1124 01:01:23,650 --> 01:01:26,406 On the other hand, it's a little bit of like pulling a bunny out 1125 01:01:26,406 --> 01:01:30,970 of a hat, because you feel like, well, these things may 1126 01:01:30,970 --> 01:01:32,820 be happening over microsecond time scales. 1127 01:01:32,820 --> 01:01:38,230 It's hard to know exactly-- how would you actually 1128 01:01:38,230 --> 01:01:41,160 experimentally confirm this is precisely what's going on? 1129 01:01:41,160 --> 01:01:45,960 And I think that here, it's a little bit subtle because you 1130 01:01:45,960 --> 01:01:50,900 could maybe show that indeed the rate of this demethylation 1131 01:01:50,900 --> 01:01:55,730 is proportional to the activity here, 1132 01:01:55,730 --> 01:01:57,591 but you don't necessarily have access 1133 01:01:57,591 --> 01:01:59,840 to all of the molecular dynamics that are taking place 1134 01:01:59,840 --> 01:02:01,920 over microsecond time scales. 1135 01:02:01,920 --> 01:02:08,174 So I think that you can do measurements that give you 1136 01:02:08,174 --> 01:02:10,090 confidence that this is maybe what's going on, 1137 01:02:10,090 --> 01:02:14,550 but you can't quite 100% nail it because 1138 01:02:14,550 --> 01:02:16,875 of the nature of these molecular fluctuations. 1139 01:02:22,650 --> 01:02:33,765 So the idea there is that if we say 1140 01:02:33,765 --> 01:02:35,140 that there's this rapid shuttling 1141 01:02:35,140 --> 01:02:37,510 between the so-called "active" and "inactive" 1142 01:02:37,510 --> 01:02:40,250 methylated guys-- so this is indicating that it's 1143 01:02:40,250 --> 01:02:47,230 what we call "active," able to catalyze this and this-- 1144 01:02:47,230 --> 01:02:49,150 then this ends up being equivalent 1145 01:02:49,150 --> 01:02:53,619 to integral feedback, where you'll always 1146 01:02:53,619 --> 01:02:54,577 get perfect adaptation. 1147 01:03:00,538 --> 01:03:01,038 Yeah? 1148 01:03:01,038 --> 01:03:05,020 AUDIENCE: When you put [INAUDIBLE] 1149 01:03:05,020 --> 01:03:08,340 JEFF GORE: So the idea is that we imagine that we're this 1150 01:03:08,340 --> 01:03:12,640 receptor X. It's chi W, chi A. Now whether it's-- let's say 1151 01:03:12,640 --> 01:03:14,280 it's bound to something. 1152 01:03:14,280 --> 01:03:18,000 It still bound to an attractant, right? 1153 01:03:18,000 --> 01:03:20,697 The way that the attractant influences its activity-- 1154 01:03:20,697 --> 01:03:22,530 and it has to influence its activity if it's 1155 01:03:22,530 --> 01:03:25,040 going to do anything-- what we assume 1156 01:03:25,040 --> 01:03:28,699 is the way that it's doing it is that it's changing 1157 01:03:28,699 --> 01:03:30,240 the sort of fraction of time that I'm 1158 01:03:30,240 --> 01:03:33,020 in some active conformation where I can actually do work, 1159 01:03:33,020 --> 01:03:36,510 versus the inactive conformation where I'm taking a break. 1160 01:03:36,510 --> 01:03:38,260 So when you get the attractant and you 1161 01:03:38,260 --> 01:03:40,385 spend more of your time in this active conformation 1162 01:03:40,385 --> 01:03:43,510 where you're, in this case, phosphorylating proteins, 1163 01:03:43,510 --> 01:03:46,090 and that's sort of the mechanism through which 1164 01:03:46,090 --> 01:03:48,270 an attractant or a repellent or whatnot 1165 01:03:48,270 --> 01:03:50,897 actually transmits its signal. 1166 01:03:50,897 --> 01:03:52,355 And indeed, it has to do something. 1167 01:03:57,910 --> 01:04:00,360 Nothing that we're discussing would work at all 1168 01:04:00,360 --> 01:04:03,700 if we don't allow the signal to be transmitted somehow 1169 01:04:03,700 --> 01:04:04,842 through this receptor. 1170 01:04:04,842 --> 01:04:06,550 So there is this sense that this activity 1171 01:04:06,550 --> 01:04:10,990 has to be a function of the things out there. 1172 01:04:10,990 --> 01:04:15,530 And the assumption that goes into the perfect adaptation 1173 01:04:15,530 --> 01:04:22,220 is really that the rate of demethylation 1174 01:04:22,220 --> 01:04:28,445 is proportional to that kind of active fraction. 1175 01:04:28,445 --> 01:04:30,820 And then, you can argue about how discrete these entities 1176 01:04:30,820 --> 01:04:33,856 have to be in order for the mechanism to work and so forth, 1177 01:04:33,856 --> 01:04:35,480 but certainly, there has to be some way 1178 01:04:35,480 --> 01:04:38,280 that binding to an attractant leads to what we decided 1179 01:04:38,280 --> 01:04:39,050 was less activity. 1180 01:04:42,951 --> 01:04:43,451 Yeah? 1181 01:04:43,451 --> 01:04:44,784 AUDIENCE: Just a quick question. 1182 01:04:44,784 --> 01:04:46,874 So what's the relationship between activity 1183 01:04:46,874 --> 01:04:48,830 and methylation? 1184 01:04:48,830 --> 01:04:49,808 Was it [INAUDIBLE] 1185 01:04:54,210 --> 01:04:56,780 JEFF GORE: So the idea is that we're typically maybe assuming 1186 01:04:56,780 --> 01:04:59,330 that the unmethylated guy has no activity, 1187 01:04:59,330 --> 01:05:03,670 so it doesn't do any of this phosphorylation, 1188 01:05:03,670 --> 01:05:07,290 whereas the methylated guy has some activity. 1189 01:05:07,290 --> 01:05:12,710 And you can characterize it by some rate of activity 1190 01:05:12,710 --> 01:05:14,580 or some fraction of the time that it 1191 01:05:14,580 --> 01:05:17,118 is in this active state that is doing something. 1192 01:05:24,770 --> 01:05:27,240 Now, the question-- and indeed this 1193 01:05:27,240 --> 01:05:34,040 ends up-- well, you can see here that in this model, 1194 01:05:34,040 --> 01:05:38,020 because you're directly acting on the active XM, then 1195 01:05:38,020 --> 01:05:41,870 the steady-state activity you can 1196 01:05:41,870 --> 01:05:47,520 get from just setting this equal to zero and it's some number. 1197 01:05:50,522 --> 01:05:51,980 But then, the question is, how long 1198 01:05:51,980 --> 01:05:55,650 does it take to come back to that steady state? 1199 01:05:55,650 --> 01:05:58,380 And that's where we get differences 1200 01:05:58,380 --> 01:06:03,610 as a function of concentration of chi R, 1201 01:06:03,610 --> 01:06:05,620 because what's happening always is 1202 01:06:05,620 --> 01:06:10,310 that we have some kind of cycle here where 1203 01:06:10,310 --> 01:06:11,930 chi B is removing the methyl groups, 1204 01:06:11,930 --> 01:06:15,020 groups chi R is adding them back. 1205 01:06:15,020 --> 01:06:18,160 So you can imagine that if you have more chi 1206 01:06:18,160 --> 01:06:21,412 R than a steady state, you get more-- when you're moving right 1207 01:06:21,412 --> 01:06:22,870 by a steady state, you have to have 1208 01:06:22,870 --> 01:06:25,078 the same moving to the left, because at steady state, 1209 01:06:25,078 --> 01:06:25,910 it's equal. 1210 01:06:25,910 --> 01:06:28,775 So the more chi R you have, the faster this thing 1211 01:06:28,775 --> 01:06:31,860 is going around. 1212 01:06:31,860 --> 01:06:35,190 And that means that the more chi R that you have, 1213 01:06:35,190 --> 01:06:40,250 the more rapidly that you'll get this perfect adaptation. 1214 01:06:40,250 --> 01:06:44,670 So the experiment that Uri did that I think is very nice 1215 01:06:44,670 --> 01:06:48,630 is he directly modulated the amount of chi R 1216 01:06:48,630 --> 01:06:50,350 and he looked at this adaptation time. 1217 01:06:58,298 --> 01:07:01,440 And he found this kind of came down, 1218 01:07:01,440 --> 01:07:06,860 whereas if you look at the steady-state tumbling 1219 01:07:06,860 --> 01:07:16,560 frequency, this came up, whereas the degree 1220 01:07:16,560 --> 01:07:20,510 of perfect adaptation, say the ratio or the error 1221 01:07:20,510 --> 01:07:22,700 in this thing, perfect adaptation 1222 01:07:22,700 --> 01:07:27,260 was always kind of correct, in the sense it always came back 1223 01:07:27,260 --> 01:07:29,390 to its original value. 1224 01:07:32,330 --> 01:07:33,800 AUDIENCE: Sorry. 1225 01:07:33,800 --> 01:07:40,660 You say the [INAUDIBLE] it only phosphorylates 1226 01:07:40,660 --> 01:07:48,500 chi B when an attractant [INAUDIBLE] 1227 01:07:48,500 --> 01:07:50,907 Y [INAUDIBLE] attractant. 1228 01:07:50,907 --> 01:07:51,490 JEFF GORE: No. 1229 01:07:51,490 --> 01:07:53,190 So the attractant or repellent can 1230 01:07:53,190 --> 01:07:54,690 be combined to either the methylated 1231 01:07:54,690 --> 01:07:55,898 or the non-methylated, right? 1232 01:07:55,898 --> 01:08:00,730 AUDIENCE: But [INAUDIBLE] only [INAUDIBLE] 1233 01:08:00,730 --> 01:08:05,027 phosphorylation of chi B when [INAUDIBLE] 1234 01:08:05,027 --> 01:08:05,610 JEFF GORE: No. 1235 01:08:05,610 --> 01:08:11,170 So you're talking about-- oh, OK. 1236 01:08:11,170 --> 01:08:14,730 So it's really that the methylated state can 1237 01:08:14,730 --> 01:08:16,649 phosphorylate either chi B or chi Y, 1238 01:08:16,649 --> 01:08:20,260 but this is regardless whether an attractant is bound or not. 1239 01:08:20,260 --> 01:08:22,859 The attractant will influence the rate or the activity 1240 01:08:22,859 --> 01:08:23,670 that this happens. 1241 01:08:35,979 --> 01:08:46,130 And given this model, you can see that you have more chi R, 1242 01:08:46,130 --> 01:08:50,910 then at steady state, you're going to have more activity. 1243 01:08:50,910 --> 01:08:54,510 More activity corresponds to more phosphorylated chi 1244 01:08:54,510 --> 01:09:00,261 y and more tumbling, so an increase 1245 01:09:00,261 --> 01:09:01,344 in the tumbling frequency. 1246 01:09:04,487 --> 01:09:04,987 Yes? 1247 01:09:04,987 --> 01:09:06,670 AUDIENCE: I guess it's not clear to me 1248 01:09:06,670 --> 01:09:09,108 where the ligand concentration actually come in. 1249 01:09:09,108 --> 01:09:10,649 JEFF GORE: Where which concentration? 1250 01:09:10,649 --> 01:09:12,107 AUDIENCE: The ligand concentration. 1251 01:09:12,107 --> 01:09:13,300 JEFF GORE: Oh, OK, yeah. 1252 01:09:13,300 --> 01:09:16,441 AUDIENCE: Because that's what [INAUDIBLE] 1253 01:09:16,441 --> 01:09:17,399 JEFF GORE: Yeah, right. 1254 01:09:17,399 --> 01:09:22,279 Yeah, so the idea here is that if we start out 1255 01:09:22,279 --> 01:09:24,890 without any attractant-- so first of all, 1256 01:09:24,890 --> 01:09:27,020 so let's imagine we're at steady state. 1257 01:09:27,020 --> 01:09:29,210 There's no attractant or little attractant 1258 01:09:29,210 --> 01:09:31,859 now, where of course, the fluxes to the left and the right 1259 01:09:31,859 --> 01:09:32,460 are the same. 1260 01:09:32,460 --> 01:09:34,029 So there's some methylated, some not. 1261 01:09:34,029 --> 01:09:37,692 AUDIENCE: No, but I agree the mechanics of just in the actual 1262 01:09:37,692 --> 01:09:39,576 to write an equation for the ligands 1263 01:09:39,576 --> 01:09:40,989 to come in like [INAUDIBLE]. 1264 01:09:43,462 --> 01:09:44,170 JEFF GORE: Right. 1265 01:09:44,170 --> 01:09:48,300 So the idea is that when you bind an attractant, 1266 01:09:48,300 --> 01:09:53,459 that's going to change the activity of the methylated. 1267 01:09:53,459 --> 01:09:55,000 So it's going to change, for example, 1268 01:09:55,000 --> 01:09:57,590 the fraction that are active. 1269 01:09:57,590 --> 01:09:59,510 AUDIENCE: And decreases the activity. 1270 01:09:59,510 --> 01:10:01,510 JEFF GORE: And it decreases the activity, right. 1271 01:10:01,510 --> 01:10:03,250 AUDIENCE: And some sort of signal-- 1272 01:10:03,250 --> 01:10:04,120 JEFF GORE: Yeah, there's some-- right. 1273 01:10:04,120 --> 01:10:06,411 And of course, we haven't specified what that function, 1274 01:10:06,411 --> 01:10:10,140 but the idea is that it leads to a rapid decrease in activity, 1275 01:10:10,140 --> 01:10:13,010 which corresponds to a rapid decrease in this fraction that 1276 01:10:13,010 --> 01:10:14,346 are active XM star. 1277 01:10:19,116 --> 01:10:19,990 Does that make sense? 1278 01:10:26,640 --> 01:10:29,550 So the last thing I wanted to do is say something 1279 01:10:29,550 --> 01:10:32,695 about what this means for individuality. 1280 01:10:37,000 --> 01:10:39,160 In particular, let's imagine that we 1281 01:10:39,160 --> 01:10:46,130 have a clonal population of bacteria. 1282 01:10:46,130 --> 01:10:48,360 And the question is, in what ways 1283 01:10:48,360 --> 01:10:50,284 will they be similar or different? 1284 01:10:57,870 --> 01:10:59,790 So now, we can just imagine an experiment 1285 01:10:59,790 --> 01:11:04,010 where I take a population of cells with exactly 1286 01:11:04,010 --> 01:11:10,740 the same genetic code and I go and I measure, for example, 1287 01:11:10,740 --> 01:11:12,910 the tumbling frequency across this population. 1288 01:11:17,140 --> 01:11:25,160 So we can talk about-- we measure f1, f2, f3, fn-- 1289 01:11:25,160 --> 01:11:27,980 so these are the tumbling frequencies across n cells. 1290 01:11:35,540 --> 01:11:41,360 This is n we'll say genetically identical cells. 1291 01:11:46,040 --> 01:11:51,850 The question is, will we get the same tumbling frequency 1292 01:11:51,850 --> 01:11:55,820 or should these things be the same? 1293 01:11:55,820 --> 01:11:58,880 And if not, why not? 1294 01:11:58,880 --> 01:12:01,440 So let's just do our little votes, all right? 1295 01:12:01,440 --> 01:12:04,230 We have should they be the same or should they be different. 1296 01:12:08,020 --> 01:12:08,790 All right. 1297 01:12:08,790 --> 01:12:10,770 Do you understand the question? 1298 01:12:10,770 --> 01:12:11,270 Let's vote. 1299 01:12:11,270 --> 01:12:11,940 Ready? 1300 01:12:11,940 --> 01:12:15,920 Three, two, one. 1301 01:12:15,920 --> 01:12:16,480 All right. 1302 01:12:16,480 --> 01:12:18,480 Well, OK, so at least the majority of people 1303 01:12:18,480 --> 01:12:19,980 are saying they should be different. 1304 01:12:19,980 --> 01:12:21,313 And why might that be, somebody? 1305 01:12:26,180 --> 01:12:28,552 AUDIENCE: We might have [INAUDIBLE] 1306 01:12:28,552 --> 01:12:29,260 JEFF GORE: Right. 1307 01:12:29,260 --> 01:12:31,710 For example, we might have variation 1308 01:12:31,710 --> 01:12:41,700 in the concentration of chi R. Now, 1309 01:12:41,700 --> 01:12:45,820 this variation is sort of a natural result 1310 01:12:45,820 --> 01:12:48,320 of just fluctuating this or that, right? 1311 01:12:48,320 --> 01:12:50,830 But it's a little bit similar to the experiment Uri did, 1312 01:12:50,830 --> 01:12:52,630 where he actually in this case has actually 1313 01:12:52,630 --> 01:12:56,640 put chi R under the control of an inducible promoter, where 1314 01:12:56,640 --> 01:12:59,240 he could just add IPDG and drive expression 1315 01:12:59,240 --> 01:13:01,354 and then just measure the mean of these things 1316 01:13:01,354 --> 01:13:02,270 across the population. 1317 01:13:02,270 --> 01:13:07,140 But even if you try to have everything be the same, 1318 01:13:07,140 --> 01:13:09,790 you'll have some variation, which 1319 01:13:09,790 --> 01:13:15,050 we found for small numbers of proteins could be large. 1320 01:13:15,050 --> 01:13:19,200 So that variation will transmit itself 1321 01:13:19,200 --> 01:13:22,080 into variations in both the adaptation time 1322 01:13:22,080 --> 01:13:23,282 and the tumbling frequency. 1323 01:13:26,050 --> 01:13:31,800 And this is indeed was observed as early as 1976. 1324 01:13:31,800 --> 01:13:35,930 So there's a paper in Nature in 1976 1325 01:13:35,930 --> 01:13:39,510 by Jim Spudich and Dan Koshland. 1326 01:13:39,510 --> 01:13:41,740 So Spudich went on to study a number 1327 01:13:41,740 --> 01:13:43,330 of these molecular motors. 1328 01:13:43,330 --> 01:13:48,100 In particular, he studied many of these myosins. 1329 01:13:48,100 --> 01:13:53,070 But he wrote this classic paper in '76 called "Non-genetic 1330 01:13:53,070 --> 01:13:56,560 individuality, chance in the single cell." 1331 01:13:56,560 --> 01:14:02,300 What he did is they looked at many different individual cells 1332 01:14:02,300 --> 01:14:05,170 using a few of those techniques that I told you about. 1333 01:14:05,170 --> 01:14:07,600 And what they found is that some of the cells 1334 01:14:07,600 --> 01:14:10,340 seemed to be what they called kind of "twitchy" 1335 01:14:10,340 --> 01:14:12,800 and some of them seemed to be more relaxed. 1336 01:14:12,800 --> 01:14:17,360 So the twitchy cells are the guys that had a larger tumbling 1337 01:14:17,360 --> 01:14:18,180 frequency. 1338 01:14:18,180 --> 01:14:20,570 So they wouldn't swim as far as the others. 1339 01:14:20,570 --> 01:14:22,278 So they'd swim just a little bit and then 1340 01:14:22,278 --> 01:14:25,230 they'd change their mind, swim a little bit, change their mind, 1341 01:14:25,230 --> 01:14:28,867 whereas other cells had much longer kind of runs, 1342 01:14:28,867 --> 01:14:30,700 even though they're all nominally identical. 1343 01:14:33,320 --> 01:14:35,700 Now, can somebody say the time scale 1344 01:14:35,700 --> 01:14:40,900 over which we would expect that personality to persist? 1345 01:14:45,369 --> 01:14:46,660 AUDIENCE: Cell generation time. 1346 01:14:46,660 --> 01:14:47,720 JEFF GORE: Yeah, cell generation time. 1347 01:14:47,720 --> 01:14:48,751 And why is that? 1348 01:14:48,751 --> 01:14:50,712 AUDIENCE: [INAUDIBLE] 1349 01:14:50,712 --> 01:14:51,670 JEFF GORE: Yeah, right. 1350 01:14:51,670 --> 01:14:58,540 So if this is chi R, over time, it's going to do something. 1351 01:14:58,540 --> 01:15:00,710 And so the typical autocorrelation time 1352 01:15:00,710 --> 01:15:04,480 should be kind of the cell generation time. 1353 01:15:04,480 --> 01:15:09,820 So what we call the typical time should be rather generational. 1354 01:15:13,450 --> 01:15:15,080 So indeed, this is the same as humans. 1355 01:15:15,080 --> 01:15:16,510 We have a well-defined personality 1356 01:15:16,510 --> 01:15:19,040 and then we pass on some of our personality to our kids. 1357 01:15:19,040 --> 01:15:21,530 The typical time scale is a generation. 1358 01:15:21,530 --> 01:15:24,150 So I'm teaching you guys super useful things in this class. 1359 01:15:24,150 --> 01:15:26,830 I don't want anybody saying anything else. 1360 01:15:30,780 --> 01:15:34,230 But I think that this is a neat example of how 1361 01:15:34,230 --> 01:15:36,240 different cells can have what you might describe 1362 01:15:36,240 --> 01:15:37,948 as being somehow different personalities, 1363 01:15:37,948 --> 01:15:40,250 but it arises for a very particular reason 1364 01:15:40,250 --> 01:15:42,960 because this information is being transmitted 1365 01:15:42,960 --> 01:15:45,112 through this network. 1366 01:15:45,112 --> 01:15:46,570 Now, despite the fact that they all 1367 01:15:46,570 --> 01:15:48,479 have different chi R concentrations-- 1368 01:15:48,479 --> 01:15:50,520 so they might have different tumbling frequencies 1369 01:15:50,520 --> 01:15:51,650 and so forth, but they should all 1370 01:15:51,650 --> 01:15:53,290 be able to display this phenomenon 1371 01:15:53,290 --> 01:15:56,260 of perfect adaptation. 1372 01:15:56,260 --> 01:15:59,000 So what we then see is that from the experiments 1373 01:15:59,000 --> 01:16:01,170 and from some simple models, you can 1374 01:16:01,170 --> 01:16:04,300 get insight into how it is that this phenomenon 1375 01:16:04,300 --> 01:16:06,589 of perfect adaptation might be robust to changes 1376 01:16:06,589 --> 01:16:08,880 in the concentrations of different things, particularly 1377 01:16:08,880 --> 01:16:10,820 chi R in this case. 1378 01:16:10,820 --> 01:16:12,960 And chi R is the dominant source of error 1379 01:16:12,960 --> 01:16:14,760 because it's present in such small numbers. 1380 01:16:17,430 --> 01:16:18,930 Now, in the last two minutes or so, 1381 01:16:18,930 --> 01:16:22,377 I just want to remind everybody about the other context 1382 01:16:22,377 --> 01:16:24,210 in which we studied robustness, because it's 1383 01:16:24,210 --> 01:16:26,930 a much simpler example and it helps 1384 01:16:26,930 --> 01:16:28,490 to clarify what we mean by it. 1385 01:16:28,490 --> 01:16:30,840 Does anybody remember the other context 1386 01:16:30,840 --> 01:16:32,381 that we have talked about robustness? 1387 01:16:35,608 --> 01:16:36,860 AUDIENCE: [INAUDIBLE] 1388 01:16:36,860 --> 01:16:38,610 JEFF GORE: Negative autoregulation someone 1389 01:16:38,610 --> 01:16:40,587 said, maybe? 1390 01:16:40,587 --> 01:16:41,170 AUDIENCE: Yes. 1391 01:16:41,170 --> 01:16:43,620 JEFF GORE: OK, good, all right. 1392 01:16:43,620 --> 01:16:47,210 So if we have some protein that is negatively 1393 01:16:47,210 --> 01:16:52,460 autoregulating itself, then this adds robustness. 1394 01:16:52,460 --> 01:16:54,860 And this is because we can say, all right, 1395 01:16:54,860 --> 01:16:59,330 this is the degradation term, alpha x, the production term. 1396 01:16:59,330 --> 01:17:03,340 And the limit of being perfect, sharp, negative autoregulation 1397 01:17:03,340 --> 01:17:04,140 looks like this. 1398 01:17:04,140 --> 01:17:05,723 So this is the production/degradation. 1399 01:17:09,020 --> 01:17:11,350 And here, this might be beta. 1400 01:17:11,350 --> 01:17:14,600 This is a k. 1401 01:17:14,600 --> 01:17:18,060 Then, what we can talk about is how 1402 01:17:18,060 --> 01:17:23,000 the steady-state concentration of x here is going to be k. 1403 01:17:23,000 --> 01:17:27,620 And this thing is robust to variations in some things, 1404 01:17:27,620 --> 01:17:29,290 but not other things. 1405 01:17:29,290 --> 01:17:31,870 For example, it's robust to changes in alpha. 1406 01:17:31,870 --> 01:17:32,899 That changes the slope. 1407 01:17:32,899 --> 01:17:34,940 It's robust to changes in beta, because that just 1408 01:17:34,940 --> 01:17:39,030 brings it up and down, but it's not robust to changes in k. 1409 01:17:39,030 --> 01:17:42,360 So I think that any time that if you are confused 1410 01:17:42,360 --> 01:17:46,060 about robustness, in particular thinking about robustness 1411 01:17:46,060 --> 01:17:47,530 in the context of chemotaxis gets 1412 01:17:47,530 --> 01:17:50,150 you confused because of perfect adaptation being confusing, 1413 01:17:50,150 --> 01:17:52,108 I think it's always good to come back and think 1414 01:17:52,108 --> 01:17:55,870 about this because this is the most clear case where you can 1415 01:17:55,870 --> 01:17:57,615 talk about-- this is the robustness 1416 01:17:57,615 --> 01:17:58,990 of the steady-state concentration 1417 01:17:58,990 --> 01:18:03,900 of some protein against variations in alpha and beta, 1418 01:18:03,900 --> 01:18:04,950 but not against k. 1419 01:18:04,950 --> 01:18:09,250 So it reminds you that it's not that this level of x 1420 01:18:09,250 --> 01:18:11,760 is robust against everything, but it's 1421 01:18:11,760 --> 01:18:12,960 robust against some things. 1422 01:18:12,960 --> 01:18:14,668 And you can make sense of which things it 1423 01:18:14,668 --> 01:18:16,950 should be robust against, which things not. 1424 01:18:16,950 --> 01:18:18,700 So with that, I think we're going to quit. 1425 01:18:18,700 --> 01:18:20,960 I just want to remind everybody that none 1426 01:18:20,960 --> 01:18:23,410 of the work that we're talking about here 1427 01:18:23,410 --> 01:18:27,110 in the context of chemotaxis and the genetic network 1428 01:18:27,110 --> 01:18:29,460 will appear on the exam, but we may 1429 01:18:29,460 --> 01:18:32,840 have a problem on low Reynolds number flow, 1430 01:18:32,840 --> 01:18:34,420 maybe something Stokes drag. 1431 01:18:34,420 --> 01:18:37,810 Diffusion might make an appearance. 1432 01:18:37,810 --> 01:18:38,780 Good luck on the exam. 1433 01:18:38,780 --> 01:18:40,673 I'll see you guys on Tuesday.