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 --> 00:00:17,236 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,236 --> 00:00:17,861 at ocw.mit.edu. 8 00:00:21,030 --> 00:00:24,710 PROFESSOR: Today, as I mentioned to you in last lecture, 9 00:00:24,710 --> 00:00:27,640 we're going to really be focusing in quite some depth 10 00:00:27,640 --> 00:00:29,370 into this paper by Sunney Xie. 11 00:00:29,370 --> 00:00:33,940 So I would say that it is one of my all time favorite papers. 12 00:00:33,940 --> 00:00:35,490 And in particular from the standpoint 13 00:00:35,490 --> 00:00:37,380 of discussing a paper in class, I 14 00:00:37,380 --> 00:00:40,190 think it is absolutely wonderful. 15 00:00:40,190 --> 00:00:43,140 It is, I think, clearly written. 16 00:00:43,140 --> 00:00:46,270 It explains why that did all these things. 17 00:00:46,270 --> 00:00:49,130 And they checked all sorts of possible sources 18 00:00:49,130 --> 00:00:52,390 of perhaps being lead astray. 19 00:00:52,390 --> 00:00:54,130 And I think it was a huge amount of work, 20 00:00:54,130 --> 00:00:57,410 and it was a technical tour de force when it came out. 21 00:00:57,410 --> 00:01:01,450 So before this, I would say single molecule biophysics, 22 00:01:01,450 --> 00:01:05,540 by which I mean both single molecule fluorescence, 23 00:01:05,540 --> 00:01:08,480 i.e., detection, as well as single molecule manipulation, 24 00:01:08,480 --> 00:01:12,590 were almost exclusively in vitro techniques. 25 00:01:12,590 --> 00:01:15,320 So we took purified components, and then we 26 00:01:15,320 --> 00:01:18,350 studied the fluorescence, or the mechanical properties 27 00:01:18,350 --> 00:01:22,681 and so forth, of these molecules in the equivalent of a test 28 00:01:22,681 --> 00:01:23,180 tube. 29 00:01:23,180 --> 00:01:25,500 But really, in glass slides, where we just 30 00:01:25,500 --> 00:01:28,082 had to purified components, so no know living cells. 31 00:01:28,082 --> 00:01:30,290 And I think we got a lot of insight into the dynamics 32 00:01:30,290 --> 00:01:33,050 of molecular motors, transcription, translation, 33 00:01:33,050 --> 00:01:35,040 and so forth. 34 00:01:35,040 --> 00:01:37,200 And I think that many of us in the field 35 00:01:37,200 --> 00:01:42,700 thought that this paper was essentially not possible. 36 00:01:42,700 --> 00:01:47,030 I did my Ph.D in the single molecule area, 37 00:01:47,030 --> 00:01:50,140 from of 2002 to 2005, I graduated. 38 00:01:50,140 --> 00:01:53,230 And indeed, I did a little bit of work 39 00:01:53,230 --> 00:01:55,830 in this area of single molecule fluorescence, 40 00:01:55,830 --> 00:01:58,070 and I was basically unsuccessful. 41 00:01:58,070 --> 00:02:00,860 Even just doing this kind of an in vitro setting. 42 00:02:00,860 --> 00:02:05,152 My lab is [INAUDIBLE], we did primarily 43 00:02:05,152 --> 00:02:06,360 single molecule manipulation. 44 00:02:06,360 --> 00:02:10,550 We were playing with the single molecule fluorescence . 45 00:02:10,550 --> 00:02:13,510 And eventually, people in the lab got it to work. 46 00:02:13,510 --> 00:02:16,540 But I would say that my foray into it was maybe unsuccessful. 47 00:02:16,540 --> 00:02:19,880 So I had a very healthy respect for the challenges 48 00:02:19,880 --> 00:02:22,520 that are involved in doing single molecule fluorescence. 49 00:02:22,520 --> 00:02:28,142 And the thought of doing this in live cells was very scary. 50 00:02:28,142 --> 00:02:29,600 And I'd say that many of us thought 51 00:02:29,600 --> 00:02:30,900 it was not going to work. 52 00:02:30,900 --> 00:02:33,940 And indeed, this project was one-- 53 00:02:33,940 --> 00:02:36,877 and the general goal of studying a single molecule 54 00:02:36,877 --> 00:02:38,460 dynamics in living cells, is something 55 00:02:38,460 --> 00:02:39,920 that's Sunney's group had been working on, I think, 56 00:02:39,920 --> 00:02:40,930 for many years. 57 00:02:40,930 --> 00:02:43,060 And it indeed was very hard. 58 00:02:43,060 --> 00:02:45,150 But then there were these two papers 59 00:02:45,150 --> 00:02:47,850 they came out, both from Sunnye's lab actually. 60 00:02:47,850 --> 00:02:51,380 And they came out both, i think, in January of 2006, 61 00:02:51,380 --> 00:02:53,740 one in science, one in Nature, demonstrating 62 00:02:53,740 --> 00:02:55,850 not one way of doing this, but rather two 63 00:02:55,850 --> 00:02:59,897 ways of getting single molecule dynamics inside living cells. 64 00:02:59,897 --> 00:03:02,230 So today, obviously, we're going to be primarily talking 65 00:03:02,230 --> 00:03:03,872 about this paper by [INAUDIBLE]. 66 00:03:03,872 --> 00:03:05,580 But if you're interested in these things, 67 00:03:05,580 --> 00:03:07,788 I encourage you to check out [INAUDIBLE] paper, which 68 00:03:07,788 --> 00:03:11,120 also published, [INAUDIBLE], at the same time. 69 00:03:11,120 --> 00:03:14,940 And that was based on a microfluidic assay, where 70 00:03:14,940 --> 00:03:16,440 instead of doing the single molecule 71 00:03:16,440 --> 00:03:19,850 fluorescence within cells, instead by trapping 72 00:03:19,850 --> 00:03:22,170 the cells in small volumes, and then using 73 00:03:22,170 --> 00:03:25,270 more traditional enzymatic assays, such as this beta 74 00:03:25,270 --> 00:03:27,790 [INAUDIBLE] assay, enclosed in a small volume, 75 00:03:27,790 --> 00:03:30,347 it's almost possible to study, once again, these sort 76 00:03:30,347 --> 00:03:32,572 of busting dynamics in E. coli. 77 00:03:32,572 --> 00:03:34,530 And also they did it in yeast, and demonstrated 78 00:03:34,530 --> 00:03:37,970 that it's kind of a generally practical assay. 79 00:03:37,970 --> 00:03:39,680 So if you're interested in those papers, 80 00:03:39,680 --> 00:03:41,770 I encourage you to check it out. 81 00:03:41,770 --> 00:03:44,980 But for me, this was really an eye-opening thing. 82 00:03:44,980 --> 00:03:49,400 So I graduated with my Ph.D. in December of 2005, 83 00:03:49,400 --> 00:03:55,320 and then I went to a conference in Cambridge, England, 84 00:03:55,320 --> 00:03:57,660 where where Sunney presented this work. 85 00:03:57,660 --> 00:04:01,450 And I think that it really blew many of our minds, this idea 86 00:04:01,450 --> 00:04:04,420 that you could start to get this sort of data within live cells. 87 00:04:04,420 --> 00:04:07,766 And indeed, Sunney's group over the next five years 88 00:04:07,766 --> 00:04:09,390 did a whole series of what I'd consider 89 00:04:09,390 --> 00:04:12,380 to be beautiful studies, probing, for example, 90 00:04:12,380 --> 00:04:16,480 the dynamics of this [INAUDIBLE] repressor binding, unbindings 91 00:04:16,480 --> 00:04:20,750 onto this promoter, the search process. 92 00:04:20,750 --> 00:04:21,250 Yeah. 93 00:04:21,250 --> 00:04:23,040 A whole slew of, I think, really beautiful things. 94 00:04:23,040 --> 00:04:24,500 So we're not going to have the chance 95 00:04:24,500 --> 00:04:26,250 to go over all those papers in this class, 96 00:04:26,250 --> 00:04:30,990 but I encourage you to look at them. 97 00:04:30,990 --> 00:04:34,195 Can somebody say what the primary challenge 98 00:04:34,195 --> 00:04:37,320 is with doing single molecule fluorescence 99 00:04:37,320 --> 00:04:39,520 in these live cells? 100 00:04:48,130 --> 00:04:50,230 So why is it that I did not think 101 00:04:50,230 --> 00:04:52,460 that this was going to work? 102 00:04:52,460 --> 00:04:57,360 And now, you're going to have to give an argument that 103 00:04:57,360 --> 00:04:58,583 ends up not being true. 104 00:04:58,583 --> 00:05:04,308 But why is it that this is such a hard thing to do. 105 00:05:04,308 --> 00:05:05,724 Yeah? 106 00:05:05,724 --> 00:05:08,084 AUDIENCE: [INAUDIBLE] laser at the cell 107 00:05:08,084 --> 00:05:09,500 but you can't kill the cell? 108 00:05:09,500 --> 00:05:09,830 PROFESSOR: Right. 109 00:05:09,830 --> 00:05:10,329 OK. 110 00:05:10,329 --> 00:05:18,030 So one is that there's laser, the cell, and then 111 00:05:18,030 --> 00:05:19,240 there's a big question mark. 112 00:05:19,240 --> 00:05:21,910 Is this going to be OK? 113 00:05:21,910 --> 00:05:25,550 And indeed, we certainly know that at one limit, 114 00:05:25,550 --> 00:05:28,200 it's not going to be OK. 115 00:05:28,200 --> 00:05:32,530 If you take the lasers at Los Alamos National Lab, 116 00:05:32,530 --> 00:05:34,144 you can vaporize the cell. 117 00:05:34,144 --> 00:05:36,060 So it's certainly enough power, and the cell's 118 00:05:36,060 --> 00:05:37,960 going to be dead for sure. 119 00:05:37,960 --> 00:05:39,485 And so the question is maybe, oh, 120 00:05:39,485 --> 00:05:42,590 can you dial down the laser power enough to get-- 121 00:05:42,590 --> 00:05:44,840 and indeed, this is something that they talk about, 122 00:05:44,840 --> 00:05:47,630 their strategy in this paper. 123 00:05:47,630 --> 00:05:50,090 Other challenges, problems? 124 00:05:50,090 --> 00:05:51,850 AUDIENCE: Many molecules. 125 00:05:51,850 --> 00:05:54,760 PROFESSOR: Right. so the principle of many molecules. 126 00:05:54,760 --> 00:05:57,650 So we have to figure out some way of separating them, 127 00:05:57,650 --> 00:05:59,350 either temporarily or spatially. 128 00:05:59,350 --> 00:06:02,130 Indeed in this paper, they actually do both. 129 00:06:05,250 --> 00:06:06,580 We say many molecules. 130 00:06:06,580 --> 00:06:07,860 And of course, we have to decide what we mean by this. 131 00:06:07,860 --> 00:06:09,734 Because ultimately, we're interested in doing 132 00:06:09,734 --> 00:06:12,380 single molecule measurements. 133 00:06:12,380 --> 00:06:15,270 But then, of course, of the plural of single is many. 134 00:06:15,270 --> 00:06:19,427 How many is too many for us to study, and so forth? 135 00:06:19,427 --> 00:06:21,760 The question here is maybe like, how to separate, right? 136 00:06:31,330 --> 00:06:34,757 What are other challenges in this? 137 00:06:34,757 --> 00:06:35,590 AUDIENCE: Diffusion. 138 00:06:35,590 --> 00:06:36,298 PROFESSOR: Right. 139 00:06:36,298 --> 00:06:37,240 There's diffusion. 140 00:06:37,240 --> 00:06:40,211 So we're going to talk more about this, for sure. 141 00:06:40,211 --> 00:06:41,710 Well, actually, all of these things, 142 00:06:41,710 --> 00:06:42,793 we're going to talk about. 143 00:06:42,793 --> 00:06:43,400 Diffusion. 144 00:06:43,400 --> 00:06:46,790 And why is this a problem, though? 145 00:06:46,790 --> 00:06:47,290 Right. 146 00:06:47,290 --> 00:06:51,560 So it's diffusion is maybe fast. 147 00:06:51,560 --> 00:06:55,552 And so this is going to end up being relevant for kind 148 00:06:55,552 --> 00:06:59,120 of signal to noise reasons. 149 00:06:59,120 --> 00:07:01,955 So what's the signal and what's the noise? 150 00:07:13,992 --> 00:07:15,470 AUDIENCE: Autofluorescence. 151 00:07:15,470 --> 00:07:15,590 PROFESSOR: Right. 152 00:07:15,590 --> 00:07:16,756 So there's autofluorescence. 153 00:07:16,756 --> 00:07:21,390 So in particular, this noise is autofluorescence from what? 154 00:07:28,264 --> 00:07:29,809 AUDIENCE: From the cell. 155 00:07:29,809 --> 00:07:30,850 PROFESSOR: From the cell. 156 00:07:30,850 --> 00:07:31,349 Right. 157 00:07:38,270 --> 00:07:40,996 And what's the signal, just to be clear here? 158 00:07:40,996 --> 00:07:43,217 AUDIENCE: Photons from [INAUDIBLE]. 159 00:07:43,217 --> 00:07:43,925 PROFESSOR: Right. 160 00:07:43,925 --> 00:07:47,115 So it's photons from, in this case, the GFP-like molecule. 161 00:07:47,115 --> 00:07:48,520 Yeah? 162 00:07:48,520 --> 00:07:51,920 So we want to do single molecule measurements. 163 00:07:51,920 --> 00:07:54,590 We want to be able to measure or detect 164 00:07:54,590 --> 00:07:57,830 the fluorescence coming from this single fluorescent 165 00:07:57,830 --> 00:07:59,240 protein. 166 00:07:59,240 --> 00:08:01,600 Now the question is, if it's a single molecule, 167 00:08:01,600 --> 00:08:03,350 does that mean that it's going to send out 168 00:08:03,350 --> 00:08:04,225 just a single photon? 169 00:08:07,600 --> 00:08:08,167 No. 170 00:08:08,167 --> 00:08:09,750 Maybe they come out as single photons. 171 00:08:09,750 --> 00:08:13,410 But we can detect them. 172 00:08:13,410 --> 00:08:17,090 Now the challenge in, in some ways surprising, 173 00:08:17,090 --> 00:08:21,450 is not that the number of photons is so small. 174 00:08:21,450 --> 00:08:24,310 Does anybody have any rough sense of maybe 175 00:08:24,310 --> 00:08:28,125 how many photons are we collecting from each of these? 176 00:08:28,125 --> 00:08:29,460 AUDIENCE: Many thousands. 177 00:08:29,460 --> 00:08:30,170 PROFESSOR: Yes. 178 00:08:30,170 --> 00:08:31,960 I'd say many thousands. 179 00:08:31,960 --> 00:08:35,090 In particular-- so we'll say many thousands. 180 00:08:39,880 --> 00:08:43,610 It could be even 10 to the 4 per second or so. 181 00:08:43,610 --> 00:08:46,300 It depends on the laser intensity. 182 00:08:46,300 --> 00:08:48,630 Many thousands of photons collected. 183 00:08:53,013 --> 00:08:53,961 Yes? 184 00:08:53,961 --> 00:08:55,460 AUDIENCE: That's before [INAUDIBLE]. 185 00:08:55,460 --> 00:08:56,170 PROFESSOR: Yes. 186 00:08:56,170 --> 00:08:58,280 That's right. 187 00:08:58,280 --> 00:09:01,869 And indeed, the stronger the intensity of the laser 188 00:09:01,869 --> 00:09:03,910 light that you illuminate with, the faster you're 189 00:09:03,910 --> 00:09:05,910 going to collect the photons, but in general, it 190 00:09:05,910 --> 00:09:10,100 won't increase the total number of photons that you collect. 191 00:09:10,100 --> 00:09:13,910 So in these sorts of situations, you 192 00:09:13,910 --> 00:09:18,240 might get, say-- we'll say 10 to the 4, plus or minus 193 00:09:18,240 --> 00:09:21,260 in order of magnitude, photons per second. 194 00:09:21,260 --> 00:09:23,630 And they might last for, depending 195 00:09:23,630 --> 00:09:26,255 on how-- for 30 seconds or so. 196 00:09:26,255 --> 00:09:29,200 And of course, we'll look at the actual numbers in this paper. 197 00:09:29,200 --> 00:09:31,880 But in many of these situations-- 198 00:09:31,880 --> 00:09:33,925 times 10 to 100 seconds. 199 00:09:39,360 --> 00:09:41,760 In this case, it actually bleached faster. 200 00:09:41,760 --> 00:09:42,540 Right. 201 00:09:42,540 --> 00:09:44,519 But we'll see. 202 00:09:44,519 --> 00:09:46,060 Well, you might be able to get also-- 203 00:09:46,060 --> 00:09:50,956 if you use organic dyes and other-- right. 204 00:09:50,956 --> 00:09:52,830 But this gives you some sense of that there's 205 00:09:52,830 --> 00:09:55,079 a fair number of photons that you could, in principle, 206 00:09:55,079 --> 00:09:56,580 collect from a single molecule. 207 00:09:58,599 --> 00:10:00,390 Now, of course, you might be worried, well, 208 00:10:00,390 --> 00:10:03,430 these are the photons that you shine on your camera. 209 00:10:03,430 --> 00:10:06,760 But then your camera won't pick up all of them. 210 00:10:06,760 --> 00:10:08,610 The way that we think about this is 211 00:10:08,610 --> 00:10:11,410 by what's known as the quantum efficiency. 212 00:10:11,410 --> 00:10:14,510 Quantum efficiency tells us basically 213 00:10:14,510 --> 00:10:20,020 this is the fraction of photons detected. 214 00:10:20,020 --> 00:10:24,725 But with modern cameras, actually, this thing 215 00:10:24,725 --> 00:10:25,690 is approximately one. 216 00:10:28,240 --> 00:10:32,350 So it's 0.9 maybe with modern cameras, 217 00:10:32,350 --> 00:10:37,010 which is for our purposes, basically one. 218 00:10:37,010 --> 00:10:39,150 Which means that you can detect, actually, 219 00:10:39,150 --> 00:10:43,540 the majority of the photons that are hitting your camera. 220 00:10:43,540 --> 00:10:46,130 From that standpoint, the number of photons 221 00:10:46,130 --> 00:10:49,270 is not actually the problem. 222 00:10:49,270 --> 00:10:53,970 You can collect many thousands of photons. 223 00:10:53,970 --> 00:10:55,970 So the problem is really detecting that signal 224 00:10:55,970 --> 00:10:57,700 over the background signal. 225 00:10:57,700 --> 00:11:02,140 Over the autofluorescence of the cell. 226 00:11:02,140 --> 00:11:06,910 And indeed, if you look at the figure, figure one, 227 00:11:06,910 --> 00:11:10,900 you can very clearly see the autofluorescence of the cell. 228 00:11:10,900 --> 00:11:13,550 So the fluorescence where there's the cell 229 00:11:13,550 --> 00:11:16,990 is indeed much larger than where there's no cell. 230 00:11:16,990 --> 00:11:21,190 The autofluorescence is, I'd say, the primary challenge 231 00:11:21,190 --> 00:11:22,060 here. 232 00:11:22,060 --> 00:11:23,850 Of course, there are many, many others. 233 00:11:23,850 --> 00:11:24,350 Right. 234 00:11:24,350 --> 00:11:27,300 So this is potentially a big problem. 235 00:11:31,037 --> 00:11:32,620 And in order to get around that, there 236 00:11:32,620 --> 00:11:35,720 are all these other strategies that the author's 237 00:11:35,720 --> 00:11:36,890 going to implement. 238 00:11:36,890 --> 00:11:37,638 Yes? 239 00:11:37,638 --> 00:11:39,054 AUDIENCE: What is the [INAUDIBLE]? 240 00:11:42,794 --> 00:11:43,460 PROFESSOR: Yeah. 241 00:11:43,460 --> 00:11:46,170 So many things are weakly fluorescent, 242 00:11:46,170 --> 00:11:47,750 I think is the short answer. 243 00:11:47,750 --> 00:11:51,285 And this also depends upon, for example, cells 244 00:11:51,285 --> 00:11:53,660 are more autofluorescent if you grow them in a rich media 245 00:11:53,660 --> 00:11:56,540 than in minimal media, for some mysterious reason. 246 00:11:56,540 --> 00:11:57,190 Yeah. 247 00:11:57,190 --> 00:11:58,510 But it's really just that there are many things that 248 00:11:58,510 --> 00:11:59,440 are weakly fluorescent. 249 00:11:59,440 --> 00:12:01,648 And it's just there are a lot of molecules in a cell. 250 00:12:04,384 --> 00:12:06,220 AUDIENCE: [INAUDIBLE]. 251 00:12:06,220 --> 00:12:09,370 PROFESSOR: Yeah, right. 252 00:12:09,370 --> 00:12:11,890 In the case that you put in a fluorescent protein 253 00:12:11,890 --> 00:12:14,780 or a fluorescent dye, then it has 254 00:12:14,780 --> 00:12:18,430 rather well-defined absorption and emission spectra. 255 00:12:18,430 --> 00:12:21,020 And each individual absorber emitter 256 00:12:21,020 --> 00:12:23,722 indeed has a well-defined absorption emission profile. 257 00:12:23,722 --> 00:12:25,930 But then in the cell, there are just many, many, many 258 00:12:25,930 --> 00:12:27,740 of them, which means that there's rather 259 00:12:27,740 --> 00:12:29,970 what you want to call an absorption 260 00:12:29,970 --> 00:12:32,520 of broadband emission. 261 00:12:32,520 --> 00:12:36,150 So indeed, in some wavelengths, it's worse than in others. 262 00:12:36,150 --> 00:12:39,130 But it's not that you get well-defined peaks the way 263 00:12:39,130 --> 00:12:42,130 you do for a single kind of [INAUDIBLE]. 264 00:12:42,130 --> 00:12:44,455 AUDIENCE: I guess I was just wondering [INAUDIBLE]. 265 00:12:47,505 --> 00:12:48,130 PROFESSOR: Yes. 266 00:12:48,130 --> 00:12:51,300 And indeed, in this case, they're exciting with a laser. 267 00:12:51,300 --> 00:12:52,900 So at least on the excitation, it's 268 00:12:52,900 --> 00:12:55,560 as precise as you can hope for. 269 00:12:55,560 --> 00:12:59,970 And indeed, on the emission they will use a filter. 270 00:12:59,970 --> 00:13:01,790 So they're not going to be absorbed. 271 00:13:01,790 --> 00:13:03,750 It's probably a few tens of nanometers 272 00:13:03,750 --> 00:13:05,350 that they're looking at. 273 00:13:05,350 --> 00:13:07,100 So in that sense, they are filtering out, 274 00:13:07,100 --> 00:13:08,800 but still, there is autofluorescence. 275 00:13:17,134 --> 00:13:19,570 All right. 276 00:13:19,570 --> 00:13:26,690 Now getting at this question of the single molecule 277 00:13:26,690 --> 00:13:29,720 fluorescence, the limitations, diffusion, 278 00:13:29,720 --> 00:13:33,630 and so forth, it's always valuable to have 279 00:13:33,630 --> 00:13:37,840 a sense of scale in anything that you're ever doing. 280 00:13:37,840 --> 00:13:40,170 So just let's wake up by reminding ourselves, 281 00:13:40,170 --> 00:13:41,501 how big is a protein? 282 00:13:41,501 --> 00:13:42,000 Right. 283 00:13:42,000 --> 00:13:43,790 So, typical protein. 284 00:13:43,790 --> 00:13:44,590 Typical protein. 285 00:13:47,670 --> 00:13:49,590 And for now, we'll say e.g. 286 00:13:49,590 --> 00:13:51,840 For example, GFP or whatever. 287 00:14:15,650 --> 00:14:16,440 All right. 288 00:14:16,440 --> 00:14:19,110 We're not going to give you very much time to think about this. 289 00:14:19,110 --> 00:14:22,020 But I just want to make sure that we all 290 00:14:22,020 --> 00:14:26,250 keep track of senses of scale in the world. 291 00:14:26,250 --> 00:14:27,010 Ready. 292 00:14:27,010 --> 00:14:30,590 Three, two, one. 293 00:14:30,590 --> 00:14:31,170 All right. 294 00:14:31,170 --> 00:14:34,760 So we've got some B's, C's, D's. 295 00:14:34,760 --> 00:14:37,411 All right. 296 00:14:37,411 --> 00:14:37,910 Wow. 297 00:14:37,910 --> 00:14:44,462 We got a lot of surprisingly wide wide range, actually. 298 00:14:44,462 --> 00:14:45,840 [LAUGHING] OK. 299 00:14:45,840 --> 00:14:49,950 Well, we also have the mirror image problem over here. 300 00:14:49,950 --> 00:14:53,200 OK, right. 301 00:14:53,200 --> 00:14:59,937 So, indeed, I'll say this is a typical protein size. 302 00:15:03,416 --> 00:15:05,500 So, it's a few nanometers. 303 00:15:05,500 --> 00:15:09,270 Depending on, there are some that get longer, 304 00:15:09,270 --> 00:15:11,400 especially if you're thinking about a long-- 305 00:15:11,400 --> 00:15:13,250 there are some structural-- well, you know. 306 00:15:13,250 --> 00:15:17,360 Of course, if you're talking about filaments, they can be-- 307 00:15:17,360 --> 00:15:19,665 but if you're talking about a typical globular protein, 308 00:15:19,665 --> 00:15:21,081 it's a few nanometers in diameter. 309 00:15:27,060 --> 00:15:29,850 The question is, let's say that this is 310 00:15:29,850 --> 00:15:31,720 a fluorescent protein, or GFP. 311 00:15:31,720 --> 00:15:35,210 And now what we do is we look at it. 312 00:15:35,210 --> 00:15:37,650 And we're going to get some fluorescent spot. 313 00:15:45,620 --> 00:15:52,020 So this is plotting the intensity 314 00:15:52,020 --> 00:15:53,970 as a function of position. 315 00:15:53,970 --> 00:15:55,470 Right? 316 00:15:55,470 --> 00:16:04,140 So this is the intensity I is a function of position X. 317 00:16:04,140 --> 00:16:06,790 Now the question is, what is going 318 00:16:06,790 --> 00:16:09,870 to be the size of the spot? 319 00:16:14,220 --> 00:16:19,640 We conveniently have some size scales up on the board. 320 00:16:19,640 --> 00:16:23,070 I'll let us think about this for eight seconds. 321 00:16:32,850 --> 00:16:33,350 All right. 322 00:16:33,350 --> 00:16:34,080 Ready. 323 00:16:34,080 --> 00:16:36,530 Three, two, one. 324 00:16:40,620 --> 00:16:41,170 OK. 325 00:16:41,170 --> 00:16:42,670 We have a majority of the group that 326 00:16:42,670 --> 00:16:44,840 is saying that indeed, it's going to be D. 327 00:16:44,840 --> 00:16:47,530 So this is what's known as a diffraction limited spot. 328 00:16:56,870 --> 00:17:01,960 And this is a fundamental physics limitation, 329 00:17:01,960 --> 00:17:07,790 that if you are imaging something with light that 330 00:17:07,790 --> 00:17:11,210 is of some wavelength, lambda, this 331 00:17:11,210 --> 00:17:14,765 is of order lambda over 2-- it depends on numerical aperture 332 00:17:14,765 --> 00:17:15,890 or projective and so forth. 333 00:17:15,890 --> 00:17:16,940 But you know. 334 00:17:16,940 --> 00:17:17,990 So order of lambda. 335 00:17:17,990 --> 00:17:18,990 A little bit less maybe. 336 00:17:21,900 --> 00:17:25,800 And indeed, the wavelength of the light 337 00:17:25,800 --> 00:17:29,070 that's being used here is-- they're 338 00:17:29,070 --> 00:17:30,780 exciting with 500 something. 339 00:17:30,780 --> 00:17:39,630 And then let me just-- 514. 340 00:17:39,630 --> 00:17:41,050 OK. 341 00:17:41,050 --> 00:17:44,280 So indeed, what happens is that we shine in light. 342 00:17:44,280 --> 00:17:52,340 So this is the lambda incident that is 514. 343 00:17:52,340 --> 00:17:56,890 Now, there's going to be some GFP that looks like this. 344 00:17:56,890 --> 00:18:02,060 And then, we're going to get out lambda emission. 345 00:18:02,060 --> 00:18:02,560 All right. 346 00:18:02,560 --> 00:18:05,300 Question, is the emitted light going to be equal? 347 00:18:05,300 --> 00:18:07,650 Is the wavelength going to be 514 nanometers? 348 00:18:07,650 --> 00:18:08,250 Yes or no? 349 00:18:08,250 --> 00:18:08,810 Ready? 350 00:18:08,810 --> 00:18:11,516 Three, two, one. 351 00:18:11,516 --> 00:18:12,210 AUDIENCE: No. 352 00:18:12,210 --> 00:18:13,410 PROFESSOR: No. 353 00:18:13,410 --> 00:18:14,230 Lambda emission. 354 00:18:14,230 --> 00:18:18,330 Is it going to be greater than or less than lambda incident? 355 00:18:18,330 --> 00:18:19,130 Ready? 356 00:18:19,130 --> 00:18:20,602 Three, two, one. 357 00:18:20,602 --> 00:18:21,560 AUDIENCE: Greater than. 358 00:18:21,560 --> 00:18:22,730 PROFESSOR: Greater than. 359 00:18:22,730 --> 00:18:27,030 So this thing is greater than 514. 360 00:18:27,030 --> 00:18:31,120 Now, if you just have scattering off something-- so let's 361 00:18:31,120 --> 00:18:33,510 say that we had a gold particle, and we 362 00:18:33,510 --> 00:18:36,290 shine-- what's going to be the relationship 363 00:18:36,290 --> 00:18:38,652 between lamba incident and lambda emission? 364 00:18:42,990 --> 00:18:45,610 Is it possible to have the same wavelength come out 365 00:18:45,610 --> 00:18:47,965 as you put in of some object? 366 00:18:52,620 --> 00:18:53,120 Yes. 367 00:18:53,120 --> 00:18:55,800 If you just have something, a mirror, 368 00:18:55,800 --> 00:18:57,960 you can get back-- so it is possible. 369 00:18:57,960 --> 00:19:01,560 But in general, there's going to be some dissipation. 370 00:19:01,560 --> 00:19:03,340 It's a question of how much and so forth. 371 00:19:03,340 --> 00:19:06,600 But certainly for something like fluorescence, 372 00:19:06,600 --> 00:19:09,260 you have a higher energy photon, and you 373 00:19:09,260 --> 00:19:10,790 have a photon that's emitted. 374 00:19:14,160 --> 00:19:16,090 And of course, energy goes as 1 over lambda. 375 00:19:18,620 --> 00:19:23,070 Now, this is useful because you can actually 376 00:19:23,070 --> 00:19:24,590 spectrally separate things. 377 00:19:29,815 --> 00:19:31,190 I just want to highlight, though, 378 00:19:31,190 --> 00:19:34,330 that if this separation is of order 300 379 00:19:34,330 --> 00:19:42,300 nanometers and our protein is-- that [INAUDIBLE] our GFP. 380 00:19:42,300 --> 00:19:43,460 Nicely drawn. 381 00:19:43,460 --> 00:19:44,800 Not even quite to scale. 382 00:19:44,800 --> 00:19:47,340 To scale, it's actually even smaller. 383 00:19:47,340 --> 00:19:49,430 It's a factor of 100 in size. 384 00:19:49,430 --> 00:19:58,480 This thing is only 3 nanometers in size, 300 nanometers wide. 385 00:20:03,570 --> 00:20:07,790 Now, it's important to be clear about what this means, 386 00:20:07,790 --> 00:20:10,580 this diffraction limited spot. 387 00:20:10,580 --> 00:20:13,830 The first thing to note is that what it means 388 00:20:13,830 --> 00:20:16,900 is that if you have two proteins-- so for example, 389 00:20:16,900 --> 00:20:19,560 I add another one over here-- that it's 390 00:20:19,560 --> 00:20:21,940 going to be very hard to tell that we have those two 391 00:20:21,940 --> 00:20:24,180 proteins next to each other. 392 00:20:24,180 --> 00:20:25,680 Because the resulting fluorescence 393 00:20:25,680 --> 00:20:29,670 pattern will look essentially the same. 394 00:20:29,670 --> 00:20:32,320 Will it be exactly the same? 395 00:20:32,320 --> 00:20:33,920 What's going to change? 396 00:20:33,920 --> 00:20:34,710 The intensity. 397 00:20:34,710 --> 00:20:37,670 The intensity, you expect to go up by a factor of two, 398 00:20:37,670 --> 00:20:40,170 absent some interaction between. 399 00:20:40,170 --> 00:20:42,160 You can, in principle, get interactions there. 400 00:20:42,160 --> 00:20:44,500 But let's for now assume that there's no interaction. 401 00:20:44,500 --> 00:20:44,620 Right. 402 00:20:44,620 --> 00:20:47,161 Then the intensity wouldn't need to go up by a factor of two. 403 00:20:47,161 --> 00:20:51,290 But unless you're very careful about all of your optics 404 00:20:51,290 --> 00:20:53,000 and so forth, it's actually a challenge 405 00:20:53,000 --> 00:20:59,610 to use this intensity alone to distinguish these things. 406 00:20:59,610 --> 00:21:02,030 It's only-- so the statement with a diffraction-- 407 00:21:02,030 --> 00:21:06,180 you need these two proteins to be separated by something 408 00:21:06,180 --> 00:21:08,190 like lambda over 2 in order for you 409 00:21:08,190 --> 00:21:10,180 to start to see the separation. 410 00:21:10,180 --> 00:21:10,680 Right. 411 00:21:10,680 --> 00:21:12,870 Because then you have something that looks like this. 412 00:21:12,870 --> 00:21:14,161 Something that looks like this. 413 00:21:14,161 --> 00:21:21,019 And then the sum of those two, indeed-- so you say, 414 00:21:21,019 --> 00:21:23,560 all right, well, it looks like there are two molecules there. 415 00:21:28,570 --> 00:21:33,009 Now, I just want to-- and the notion 416 00:21:33,009 --> 00:21:35,300 of a lot of these so-called super resolution techniques 417 00:21:35,300 --> 00:21:37,120 is figuring out a way to distinguish these things, 418 00:21:37,120 --> 00:21:39,328 and we'll maybe say something about that in a moment. 419 00:21:39,328 --> 00:21:42,030 But I just want to highlight that if we come back 420 00:21:42,030 --> 00:21:46,360 to the situation where we have a single protein there. 421 00:21:46,360 --> 00:21:52,240 Now the question is, how accurately can we 422 00:21:52,240 --> 00:21:54,750 tell where that protein is, if we know that there's 423 00:21:54,750 --> 00:21:55,916 just a single protein there? 424 00:22:19,230 --> 00:22:22,320 Now in particular, this size of the spot 425 00:22:22,320 --> 00:22:30,590 is telling us something, but it might not 426 00:22:30,590 --> 00:22:32,410 be quite as strong of a limitation 427 00:22:32,410 --> 00:22:35,300 as it appears at first glance. 428 00:22:35,300 --> 00:22:38,400 And that's because in this case, well maybe 429 00:22:38,400 --> 00:22:42,990 I'll bring it back, what we see is a big spot. 430 00:22:42,990 --> 00:22:45,300 300 nanometers, kind of wide. 431 00:22:45,300 --> 00:22:48,450 But if we see this and we know it's just a single protein 432 00:22:48,450 --> 00:22:51,440 there, I mean, could the protein be over here? 433 00:22:51,440 --> 00:22:52,040 No. 434 00:22:52,040 --> 00:22:53,914 If the protein where over here, then the spot 435 00:22:53,914 --> 00:22:58,816 would be over there right. 436 00:22:58,816 --> 00:23:02,000 So actually, even though the size of the spot 437 00:23:02,000 --> 00:23:04,332 is 300 nanometers, in principle, if you 438 00:23:04,332 --> 00:23:05,790 want to know where that protein is, 439 00:23:05,790 --> 00:23:08,327 if you know there's just a single protein, 440 00:23:08,327 --> 00:23:10,160 well, in that case what you want to know is, 441 00:23:10,160 --> 00:23:13,860 where's the center of that distribution? 442 00:23:13,860 --> 00:23:17,040 And that problem, well, the width of the distribution 443 00:23:17,040 --> 00:23:19,100 is relevant. 444 00:23:19,100 --> 00:23:21,910 But there's something else that's also very relevant. 445 00:23:25,570 --> 00:23:30,600 And quite generally, if you measure some quantity n times, 446 00:23:30,600 --> 00:23:42,960 and you want to know-- so you're measuring the height of min 447 00:23:42,960 --> 00:23:48,760 entering the army-- if you want to know the mean, what 448 00:23:48,760 --> 00:23:54,561 is it that determines your uncertainty around the mean? 449 00:23:54,561 --> 00:23:55,060 Right. 450 00:23:55,060 --> 00:23:57,840 There's the sample size. 451 00:23:57,840 --> 00:23:59,850 Now, does the width of the distribution enter? 452 00:24:02,341 --> 00:24:02,840 Yeah. 453 00:24:02,840 --> 00:24:11,590 So in general, your uncertainty in the mean 454 00:24:11,590 --> 00:24:16,070 is going to go with the width of the distribution, sigma 455 00:24:16,070 --> 00:24:23,005 of whatever, divided by-- what do I put down here? 456 00:24:23,005 --> 00:24:27,580 Root of N, where N is the number of samples that we take. 457 00:24:33,180 --> 00:24:38,490 What this is saying is that as we sample 458 00:24:38,490 --> 00:24:42,210 this distribution more and more, does 459 00:24:42,210 --> 00:24:47,520 the standard deviation of the distribution, does it go to 0? 460 00:24:47,520 --> 00:24:48,020 No. 461 00:24:50,446 --> 00:24:51,820 These are all trivial statements, 462 00:24:51,820 --> 00:24:53,940 but I can't tell you how many times 463 00:24:53,940 --> 00:24:55,180 I see this getting confused. 464 00:24:55,180 --> 00:24:55,680 OK. 465 00:24:55,680 --> 00:24:57,450 So if you measure many, many, many times, 466 00:24:57,450 --> 00:25:00,260 you get a very beautiful distribution. 467 00:25:00,260 --> 00:25:01,740 Right. 468 00:25:01,740 --> 00:25:03,570 The width of this region of the sigma, 469 00:25:03,570 --> 00:25:05,805 that you get very accurately. 470 00:25:05,805 --> 00:25:08,744 It's true also that your uncertainty in the width, that 471 00:25:08,744 --> 00:25:09,660 actually does go to 0. 472 00:25:09,660 --> 00:25:11,618 But the width of it, the width doesn't go to 0. 473 00:25:11,618 --> 00:25:13,890 The width of the distribution. 474 00:25:13,890 --> 00:25:17,700 But your uncertainty in the mean, that goes down as 1 475 00:25:17,700 --> 00:25:23,100 over root of N. And what is N in the case our detection business 476 00:25:23,100 --> 00:25:25,650 here? 477 00:25:25,650 --> 00:25:26,670 The number of photons. 478 00:25:26,670 --> 00:25:27,170 Right? 479 00:25:27,170 --> 00:25:30,550 Now, of course, in the actual experiment, 480 00:25:30,550 --> 00:25:32,600 we don't get precisely this distribution. 481 00:25:32,600 --> 00:25:35,486 Instead, it's kind of sort of quantized somehow 482 00:25:35,486 --> 00:25:36,860 spatially, because we're actually 483 00:25:36,860 --> 00:25:38,840 detecting it on a CCD chip. 484 00:25:38,840 --> 00:25:39,340 All right. 485 00:25:39,340 --> 00:25:41,760 So you can go and do the math, figure out everything. 486 00:25:41,760 --> 00:25:43,635 But actually, that's not as much a limitation 487 00:25:43,635 --> 00:25:45,220 as you might have expected. 488 00:25:45,220 --> 00:25:47,970 In many cases, the pixel size on the image plane 489 00:25:47,970 --> 00:25:51,060 is actually something like 100 nanometers. 490 00:25:51,060 --> 00:25:53,662 So this distribution that measure, 491 00:25:53,662 --> 00:25:56,120 although in principle it looks like this, what you actually 492 00:25:56,120 --> 00:26:00,410 measure is something that looks like-- well, maybe I 493 00:26:00,410 --> 00:26:09,960 should-- something like that. 494 00:26:09,960 --> 00:26:10,670 Right. 495 00:26:10,670 --> 00:26:16,990 Because you have discrete pixels on the CCD. 496 00:26:16,990 --> 00:26:20,210 And it feels that that should just kind of totally screw you. 497 00:26:20,210 --> 00:26:21,800 But if you go and do the math, you 498 00:26:21,800 --> 00:26:24,430 find it's not as bad as you might expect. 499 00:26:24,430 --> 00:26:26,604 So broadly, you do get essentially something 500 00:26:26,604 --> 00:26:28,020 that goes as 1 over the root of N, 501 00:26:28,020 --> 00:26:29,394 where N is the number of photons. 502 00:26:29,394 --> 00:26:34,275 And if you collect 10 to the 4 photons, that actually, 503 00:26:34,275 --> 00:26:35,940 it's a lot of photons. 504 00:26:35,940 --> 00:26:38,740 So if we want to know the uncertainty 505 00:26:38,740 --> 00:26:42,530 in the center of our distribution, well, this thing, 506 00:26:42,530 --> 00:26:46,910 we might have something that's of order 300 nanometers here. 507 00:26:46,910 --> 00:26:48,610 We take the square root of 10 to the 4. 508 00:26:51,130 --> 00:26:51,630 All right. 509 00:26:51,630 --> 00:26:55,340 So we get to divide by something like 100. 510 00:26:55,340 --> 00:26:57,330 And these are all very rough numbers. 511 00:26:57,330 --> 00:27:01,180 But the point is that we can get down 512 00:27:01,180 --> 00:27:05,340 to nanometer resolution in terms of the uncertainty 513 00:27:05,340 --> 00:27:08,060 that which we know the mean of that distribution. 514 00:27:08,060 --> 00:27:08,614 Yes? 515 00:27:08,614 --> 00:27:09,530 AUDIENCE: [INAUDIBLE]. 516 00:27:13,019 --> 00:27:13,935 PROFESSOR: Yeah, yeah. 517 00:27:13,935 --> 00:27:14,435 Right. 518 00:27:14,435 --> 00:27:15,940 So again, it's surprising. 519 00:27:15,940 --> 00:27:18,905 The thing is that even with just two, 520 00:27:18,905 --> 00:27:20,530 in principle, we can be very sensitive. 521 00:27:20,530 --> 00:27:21,029 Right? 522 00:27:21,029 --> 00:27:25,250 I mean, actually, sometimes people actually 523 00:27:25,250 --> 00:27:27,580 do just put it on like quadrant photo detector, where 524 00:27:27,580 --> 00:27:30,610 you really only get essentially binary information. 525 00:27:30,610 --> 00:27:34,930 But even with just two, if I say OK, well, it looks like this, 526 00:27:34,930 --> 00:27:37,430 or if it looks a little bit like that, 527 00:27:37,430 --> 00:27:39,380 if there's no error in our measurements there, 528 00:27:39,380 --> 00:27:43,120 then you can actually get that location very well. 529 00:27:43,120 --> 00:27:44,950 Yeah. 530 00:27:44,950 --> 00:27:45,840 It's surprising. 531 00:27:45,840 --> 00:27:48,290 I'm not going to like. 532 00:27:48,290 --> 00:27:50,520 Yeah, but even with this quantization 533 00:27:50,520 --> 00:27:52,607 of some sort that's due to the CCD, city 534 00:27:52,607 --> 00:27:54,565 you can still get down to nanometer resolution. 535 00:27:58,697 --> 00:28:01,280 Your resolution is worse than it would be if you knew actually 536 00:28:01,280 --> 00:28:02,863 exactly where each photon was hitting, 537 00:28:02,863 --> 00:28:06,660 but it's not very sensitive, actually. 538 00:28:06,660 --> 00:28:08,400 And indeed, in the presence of-- and 539 00:28:08,400 --> 00:28:09,858 this is a highly technical comment. 540 00:28:09,858 --> 00:28:12,550 But in the presence of read noise and other kinds 541 00:28:12,550 --> 00:28:15,050 of noise in the CCD, actually, in many cases, 542 00:28:15,050 --> 00:28:17,610 it's actually better to have somewhat larger pixels, 543 00:28:17,610 --> 00:28:19,960 again, than you would expect. 544 00:28:19,960 --> 00:28:22,432 So these balancing many different things. 545 00:28:22,432 --> 00:28:24,390 People have thought carefully about this stuff. 546 00:28:24,390 --> 00:28:28,780 But in the end, 100 nanometer pixel is actually fine. 547 00:28:28,780 --> 00:28:33,120 And just to be clear, it's 100 nanometers at the sample plane. 548 00:28:33,120 --> 00:28:35,530 So it's typically of order 10 microns 549 00:28:35,530 --> 00:28:38,470 size on the camera itself. 550 00:28:38,470 --> 00:28:44,230 So the physical size of each of the pixels on the cameras, 10 551 00:28:44,230 --> 00:28:47,030 microns within a factor of 2, between 5 and 20, 552 00:28:47,030 --> 00:28:49,840 but then you get 100x typically magnification 553 00:28:49,840 --> 00:28:52,620 at the sample point. 554 00:28:52,620 --> 00:28:55,510 So to be clear, 10 microns divided by 100 555 00:28:55,510 --> 00:28:58,770 is 100 nanometers. 556 00:28:58,770 --> 00:29:00,280 Is everybody following? 557 00:29:00,280 --> 00:29:03,820 OK I don't want to-- all right. 558 00:29:03,820 --> 00:29:05,710 The key thing-- three, you can ignore. 559 00:29:05,710 --> 00:29:07,940 But the key thing to notice here is 560 00:29:07,940 --> 00:29:10,370 this thing that's here, which is nanometer resolution. 561 00:29:14,980 --> 00:29:19,510 And it's been known for decades that this is, in principle, 562 00:29:19,510 --> 00:29:20,890 possible and so forth. 563 00:29:20,890 --> 00:29:23,790 But I think that within the realm of single molecule 564 00:29:23,790 --> 00:29:30,370 biophysics, it was really popularized in some very nice 565 00:29:30,370 --> 00:29:37,060 papers by Ahmet Yildiz, et al, where they attached 566 00:29:37,060 --> 00:29:41,240 single molecules onto the heads of various motors 567 00:29:41,240 --> 00:29:44,100 as they were walking along tracks, and showing 568 00:29:44,100 --> 00:29:46,190 that these motors were walking kind of like this, 569 00:29:46,190 --> 00:29:47,990 by catching fluorophores here, and then you could really just 570 00:29:47,990 --> 00:29:49,460 see it, see them walking it. 571 00:29:54,490 --> 00:29:56,460 Any questions about why it's in principle 572 00:29:56,460 --> 00:30:00,536 possible to get nanometer resolution in this process? 573 00:30:00,536 --> 00:30:02,464 AUDIENCE: Doesn't this assume that the protein 574 00:30:02,464 --> 00:30:04,874 is 100% static? 575 00:30:04,874 --> 00:30:05,838 PROFESSOR: Yes. 576 00:30:05,838 --> 00:30:06,754 AUDIENCE: [INAUDIBLE]. 577 00:30:11,064 --> 00:30:11,730 PROFESSOR: Yeah. 578 00:30:11,730 --> 00:30:12,480 Yeah, indeed. 579 00:30:12,480 --> 00:30:15,360 Right now, I'm assuming that this thing is constant. 580 00:30:15,360 --> 00:30:19,330 And the question is like, how much movement is a problem? 581 00:30:19,330 --> 00:30:21,626 And so then you have to-- you know. 582 00:30:21,626 --> 00:30:22,542 AUDIENCE: [INAUDIBLE]. 583 00:30:25,360 --> 00:30:26,360 PROFESSOR: That's right. 584 00:30:26,360 --> 00:30:30,210 So indeed, often, you're trading off spatial resolution 585 00:30:30,210 --> 00:30:31,690 for temporal resolution. 586 00:30:31,690 --> 00:30:34,455 And also, the intensity of your laser, and so forth. 587 00:30:34,455 --> 00:30:35,830 But in these sort of experiments, 588 00:30:35,830 --> 00:30:39,120 I think that what they did is they slowed down 589 00:30:39,120 --> 00:30:40,910 the motors quite a lot. 590 00:30:40,910 --> 00:30:42,410 So it was limiting ATP. 591 00:30:42,410 --> 00:30:44,260 So indeed, the motors in those experiments, 592 00:30:44,260 --> 00:30:48,340 I think they were taking steps of order every second 593 00:30:48,340 --> 00:30:48,990 or 10 seconds. 594 00:30:48,990 --> 00:30:52,080 I mean, it was as slow as you can go, and still, yes. 595 00:30:52,080 --> 00:30:53,530 And then at each location, I think 596 00:30:53,530 --> 00:30:56,175 they were collecting 10 to the 4 or a few 10 to the 4 photons. 597 00:30:59,310 --> 00:31:01,080 And incidentally in this case, these 598 00:31:01,080 --> 00:31:02,850 are the photons that are being collected. 599 00:31:02,850 --> 00:31:05,100 And typically, you would only be collecting 600 00:31:05,100 --> 00:31:07,820 10%, 15% of the photons. 601 00:31:07,820 --> 00:31:11,380 Because the photons are actually being emitted everywhere. 602 00:31:11,380 --> 00:31:14,180 But you only collect the ones that go back to your objective. 603 00:31:20,680 --> 00:31:21,750 All right. 604 00:31:21,750 --> 00:31:24,710 I just want to make one comment about the super resolution 605 00:31:24,710 --> 00:31:27,500 techniques that have been spreading. 606 00:31:27,500 --> 00:31:29,000 So the question here is, well, let's 607 00:31:29,000 --> 00:31:31,804 say that you have two proteins next to each other. 608 00:31:31,804 --> 00:31:32,470 What can you do? 609 00:31:35,110 --> 00:31:39,610 Now, the basic idea of all these super resolution techniques 610 00:31:39,610 --> 00:31:45,200 is that if we know that we have a signal for only one protein, 611 00:31:45,200 --> 00:31:47,120 then we can actually figure out where it is. 612 00:31:47,120 --> 00:31:48,619 So what you need to do is figure out 613 00:31:48,619 --> 00:31:51,595 a way so you just have one at a time emitting. 614 00:31:51,595 --> 00:31:53,220 So there are various schemes to make it 615 00:31:53,220 --> 00:31:57,690 so that these proteins can either turn on or off. 616 00:31:57,690 --> 00:32:00,774 Now, what you can do is if just one turns on, 617 00:32:00,774 --> 00:32:02,690 you got some photons, you say OK, this protein 618 00:32:02,690 --> 00:32:04,610 goes over here. 619 00:32:04,610 --> 00:32:08,970 Then if later, this other protein becomes fluorescent, 620 00:32:08,970 --> 00:32:11,090 now you can figure out where that is. 621 00:32:11,090 --> 00:32:14,860 And so you do this basic super resolution localization 622 00:32:14,860 --> 00:32:18,110 multiple times, and then you can identify where things are. 623 00:32:21,740 --> 00:32:22,240 Yeah. 624 00:32:22,240 --> 00:32:25,170 So all the microscopy guys really 625 00:32:25,170 --> 00:32:30,960 like to have fun acronyms. 626 00:32:30,960 --> 00:32:38,735 So these guys, when they did it, they called it FIONA. 627 00:32:41,990 --> 00:32:43,900 So this is-- is it DreamWorks? 628 00:32:43,900 --> 00:32:48,290 Or this is where the green ogre like that and then 629 00:32:48,290 --> 00:32:49,350 the red head? 630 00:32:49,350 --> 00:32:50,190 AUDIENCE: Shrek. 631 00:32:50,190 --> 00:32:50,620 PROFESSOR: Shrek? 632 00:32:50,620 --> 00:32:50,950 All right. 633 00:32:50,950 --> 00:32:51,460 So Shrek. 634 00:32:51,460 --> 00:32:53,710 And so Fiona was the redhead. 635 00:32:53,710 --> 00:32:55,960 And this stands for fluorescent imaging 636 00:32:55,960 --> 00:32:57,410 with 1 nanometer accuracy. 637 00:32:59,930 --> 00:33:04,610 And then indeed, a group at UCSF then 638 00:33:04,610 --> 00:33:08,910 developed SHREK, which is simultaneous high resolution 639 00:33:08,910 --> 00:33:10,610 imaging-- something. 640 00:33:10,610 --> 00:33:11,110 OK. 641 00:33:11,110 --> 00:33:12,360 I can't remember how it ended. 642 00:33:12,360 --> 00:33:14,210 But, yeah. 643 00:33:14,210 --> 00:33:16,170 So the super resolution techniques, 644 00:33:16,170 --> 00:33:21,150 they call them-- so Xiaowei Zhuang at Harvard called 645 00:33:21,150 --> 00:33:26,050 hers STORM, stochastic reconstruction 646 00:33:26,050 --> 00:33:28,270 of something or another. 647 00:33:28,270 --> 00:33:30,860 So this is the Zhuang method. 648 00:33:30,860 --> 00:33:34,150 And then Eric Betzig called his PALM, which 649 00:33:34,150 --> 00:33:36,230 stood still for something else. 650 00:33:36,230 --> 00:33:36,820 I don't know. 651 00:33:36,820 --> 00:33:40,570 But in particular, Betzig-- there's 652 00:33:40,570 --> 00:33:43,840 a long history of the hard core microscopists, 653 00:33:43,840 --> 00:33:48,695 somehow like, developing their techniques in their garages. 654 00:33:48,695 --> 00:33:50,320 I don't know what it is, but there have 655 00:33:50,320 --> 00:33:51,550 been a number of these cases. 656 00:33:51,550 --> 00:33:53,450 And Betzig I think was one of them. 657 00:33:53,450 --> 00:33:56,620 Now he's at Janelia Farm, HHMI, and has 658 00:33:56,620 --> 00:34:00,264 been developing all sorts of advanced microscopy techniques. 659 00:34:00,264 --> 00:34:01,930 So I think that that [INAUDIBLE] did not 660 00:34:01,930 --> 00:34:03,930 develop hers in the garage. 661 00:34:03,930 --> 00:34:04,490 But um-- 662 00:34:04,490 --> 00:34:07,050 AUDIENCE: And they're all based on the same principle-- 663 00:34:07,050 --> 00:34:07,900 PROFESSOR: Yeah. 664 00:34:07,900 --> 00:34:09,870 It's all about temporal. 665 00:34:09,870 --> 00:34:12,780 It's a question of how you're getting 666 00:34:12,780 --> 00:34:16,150 them to turn on and off. 667 00:34:16,150 --> 00:34:18,610 AUDIENCE: It sounds like [INAUDIBLE] acronyms. 668 00:34:18,610 --> 00:34:20,041 PROFESSOR: Oh do they also have? 669 00:34:20,041 --> 00:34:21,250 AUDIENCE: ROSY, COZY, NOSY. 670 00:34:21,250 --> 00:34:22,089 PROFESSOR: Yeah. 671 00:34:22,089 --> 00:34:22,630 Right, right. 672 00:34:22,630 --> 00:34:24,338 For the different sequences or something? 673 00:34:24,338 --> 00:34:25,141 Yeah, yeah. 674 00:34:28,300 --> 00:34:33,639 All of these acronyms, maybe I just never came up 675 00:34:33,639 --> 00:34:36,490 with a good one, so then I-- 676 00:34:36,490 --> 00:34:38,880 AUDIENCE: [INAUDIBLE]. 677 00:34:38,880 --> 00:34:39,820 PROFESSOR: Yes. 678 00:34:39,820 --> 00:34:40,870 Indeed. 679 00:34:40,870 --> 00:34:43,610 I always like when somebody uses acronyms that I don't know, 680 00:34:43,610 --> 00:34:47,761 I always like to say, oh, all these TLAs are tricky, 681 00:34:47,761 --> 00:34:48,260 or whatever. 682 00:34:48,260 --> 00:34:52,002 And then I say, it's three letter acronym. 683 00:34:52,002 --> 00:34:53,480 AUDIENCE: [LAUGHING] 684 00:34:53,480 --> 00:34:55,830 PROFESSOR: I very much like self-referential humor. 685 00:34:58,980 --> 00:35:00,420 OK. 686 00:35:00,420 --> 00:35:02,670 So that's the idea of the super resolution techniques. 687 00:35:06,924 --> 00:35:08,340 Any questions about that before we 688 00:35:08,340 --> 00:35:10,140 kind of get back actually to the paper? 689 00:35:13,530 --> 00:35:14,660 OK. 690 00:35:14,660 --> 00:35:17,140 Now in this whole discussion, as was pointed out, 691 00:35:17,140 --> 00:35:20,950 we've been assuming that the protein is not moving around 692 00:35:20,950 --> 00:35:23,430 during our imaging time. 693 00:35:23,430 --> 00:35:26,120 So one of the major challenges of doing this whole business 694 00:35:26,120 --> 00:35:28,410 in live cells is not only is there 695 00:35:28,410 --> 00:35:33,230 a lot of autofluorescence, but in addition, you 696 00:35:33,230 --> 00:35:35,970 can't necessarily wait 10 seconds 697 00:35:35,970 --> 00:35:39,190 to localize where this thing is, because it will have 698 00:35:39,190 --> 00:35:41,180 moved somewhere else right. 699 00:35:41,180 --> 00:35:46,250 And in particular, diffusion is a problem. 700 00:35:46,250 --> 00:35:50,272 Can somebody remind us what the authors 701 00:35:50,272 --> 00:35:52,355 did in order to get around the diffusion problems? 702 00:35:55,700 --> 00:35:56,902 I'm sorry what was it? 703 00:35:56,902 --> 00:35:58,600 AUDIENCE: [INAUDIBLE]. 704 00:35:58,600 --> 00:36:00,640 PROFESSOR: They attached it to the membrane. 705 00:36:00,640 --> 00:36:01,950 And why does that help? 706 00:36:06,207 --> 00:36:08,854 AUDIENCE: [INAUDIBLE]. 707 00:36:08,854 --> 00:36:09,520 PROFESSOR: Yeah. 708 00:36:09,520 --> 00:36:10,920 That's perfect. 709 00:36:10,920 --> 00:36:12,270 Proteins diffuse slower. 710 00:36:12,270 --> 00:36:13,877 And I think depending on the organism, 711 00:36:13,877 --> 00:36:15,960 there's more or less diffusion and so forth right. 712 00:36:15,960 --> 00:36:25,500 But what they did is they anchored to the membrane 713 00:36:25,500 --> 00:36:26,960 to reduce diffusion. 714 00:36:26,960 --> 00:36:28,418 I'll just say it reduces diffusion. 715 00:36:34,330 --> 00:36:36,969 And indeed, just from a back of the envelope calculation, 716 00:36:36,969 --> 00:36:38,760 you can convince yourself that you probably 717 00:36:38,760 --> 00:36:41,770 are going to need to do this. 718 00:36:41,770 --> 00:36:45,160 So in particular, let's ask-- in this paper, 719 00:36:45,160 --> 00:36:50,390 actually, they image the fluorophore for 0.1 seconds, 720 00:36:50,390 --> 00:36:52,610 right? 721 00:36:52,610 --> 00:36:53,790 Does that sound right? 722 00:36:53,790 --> 00:37:05,340 So the image collected, so delta t is equal to 0.1 sets. 723 00:37:05,340 --> 00:37:07,870 So the question is, how far will a protein typically 724 00:37:07,870 --> 00:37:09,590 diffuse in 0.1 seconds? 725 00:37:13,120 --> 00:37:16,620 Well, this is why we have diffusion calculations. 726 00:37:16,620 --> 00:37:18,630 Right. 727 00:37:18,630 --> 00:37:23,020 First of all, the diffusion coefficient, 728 00:37:23,020 --> 00:37:26,210 we're going to talk more about diffusion in a few weeks. 729 00:37:26,210 --> 00:37:30,077 But you should also in principal be 730 00:37:30,077 --> 00:37:31,660 able to calculate how these things go. 731 00:37:31,660 --> 00:37:33,750 So in general, this is going to be 732 00:37:33,750 --> 00:37:39,860 a kT over some gamma, which tells us how hard-- so kT is 733 00:37:39,860 --> 00:37:40,791 thermal energy. 734 00:37:40,791 --> 00:37:41,290 OK. 735 00:37:44,660 --> 00:37:45,940 So, thermal. 736 00:37:45,940 --> 00:37:50,530 And at room temperature kT is around 4.1 737 00:37:50,530 --> 00:37:53,095 piconewton nanometers in some unit. 738 00:37:53,095 --> 00:37:55,435 There are many different ways you can write that. 739 00:37:55,435 --> 00:38:00,730 Whereas gamma tells us just how hard it is to push something. 740 00:38:00,730 --> 00:38:05,370 In particular, if you push them with some force, 741 00:38:05,370 --> 00:38:08,650 it will move with some velocity. 742 00:38:08,650 --> 00:38:13,040 Now is this consistent with freshman mechanics? 743 00:38:17,390 --> 00:38:17,940 No. 744 00:38:17,940 --> 00:38:18,640 It's not. 745 00:38:18,640 --> 00:38:19,140 OK. 746 00:38:21,975 --> 00:38:22,725 Is that a problem? 747 00:38:26,160 --> 00:38:28,080 So why is it that I'm writing this? 748 00:38:30,555 --> 00:38:32,554 AUDIENCE: Solvents exerting a force [INAUDIBLE]? 749 00:38:32,554 --> 00:38:33,262 PROFESSOR: Right. 750 00:38:33,262 --> 00:38:35,630 So solvents exerting a force. 751 00:38:35,630 --> 00:38:36,600 That's true. 752 00:38:36,600 --> 00:38:39,970 But in the case of freshman mechanics, 753 00:38:39,970 --> 00:38:43,100 when we're pushing blocks, it's also true 754 00:38:43,100 --> 00:38:45,050 that the other things are exerting forces. 755 00:38:45,050 --> 00:38:45,780 The tables. 756 00:38:45,780 --> 00:38:49,210 But we still write down F is equal to MA. 757 00:38:49,210 --> 00:38:52,365 So it's not just that other things are exerting forces. 758 00:38:52,365 --> 00:38:53,335 Yeah? 759 00:38:53,335 --> 00:38:57,101 AUDIENCE: They're always in a continuum? 760 00:38:57,101 --> 00:38:58,476 PROFESSOR: Always in a continuum. 761 00:38:58,476 --> 00:39:01,380 AUDIENCE: They're always surrounded by [INAUDIBLE]. 762 00:39:01,380 --> 00:39:02,160 PROFESSOR: OK. 763 00:39:02,160 --> 00:39:03,130 Yeah. 764 00:39:03,130 --> 00:39:06,020 It's always surrounded-- but I'm actually 765 00:39:06,020 --> 00:39:07,290 surrounded by fluid now too. 766 00:39:07,290 --> 00:39:10,364 You know, you can wave your arms and feel it. 767 00:39:10,364 --> 00:39:11,280 AUDIENCE: [INAUDIBLE]. 768 00:39:11,280 --> 00:39:12,155 PROFESSOR: OK, right. 769 00:39:12,155 --> 00:39:13,790 So it comes down to the viscosity. 770 00:39:13,790 --> 00:39:16,890 Indeed, this whole thing about being a low Reynolds number, 771 00:39:16,890 --> 00:39:19,690 we're going to talk about this in much more detail 772 00:39:19,690 --> 00:39:22,880 in a few weeks, when we think about how bacteria swim, 773 00:39:22,880 --> 00:39:23,740 and so forth. 774 00:39:23,740 --> 00:39:25,280 But I just want to mention that this 775 00:39:25,280 --> 00:39:27,780 is because we're at this low Reynolds number, where 776 00:39:27,780 --> 00:39:33,020 the so-called inertial forces, like momentum are negligible. 777 00:39:33,020 --> 00:39:34,370 Inertia forces are negligible. 778 00:39:34,370 --> 00:39:36,470 So then it's really, this is in some ways 779 00:39:36,470 --> 00:39:40,090 more like Aristotelian physics, but it ends up 780 00:39:40,090 --> 00:39:43,800 being true for small objects in viscous liquids. 781 00:39:46,330 --> 00:39:50,100 And indeed, this thing it scales as the radius. 782 00:39:50,100 --> 00:39:56,780 So in principle, we can actually calculate roughly 783 00:39:56,780 --> 00:39:59,054 how the diffusion coefficient is going to behave 784 00:39:59,054 --> 00:39:59,970 as a function of size. 785 00:39:59,970 --> 00:40:00,990 The object and so forth. 786 00:40:00,990 --> 00:40:05,270 But I'll just tell you that for a protein size object 787 00:40:05,270 --> 00:40:07,550 in the cell, you might get something 788 00:40:07,550 --> 00:40:11,920 like 10 micron squared per second. 789 00:40:14,570 --> 00:40:19,590 Now, already just from units, you 790 00:40:19,590 --> 00:40:22,180 can see how the kind of typical diffusion distance 791 00:40:22,180 --> 00:40:24,800 has to scale with time. 792 00:40:24,800 --> 00:40:26,800 And in particular, you're going to get 793 00:40:26,800 --> 00:40:29,700 that the typical kind of distance 794 00:40:29,700 --> 00:40:35,590 that you go in a typical distance-- we'll 795 00:40:35,590 --> 00:40:38,570 say square root, because it's the square root of 2 times D 796 00:40:38,570 --> 00:40:40,450 times time. 797 00:40:40,450 --> 00:40:44,272 So you can see if you multiply the time by the D, 798 00:40:44,272 --> 00:40:45,880 then you end up with a micron squared, 799 00:40:45,880 --> 00:40:48,475 so you have to take a square root to get something that's 800 00:40:48,475 --> 00:40:51,320 a characteristic distance. 801 00:40:51,320 --> 00:40:54,450 And indeed, this is the kind of math that I can do. 802 00:40:54,450 --> 00:40:58,230 So this is an order one micron. 803 00:41:03,160 --> 00:41:06,483 And how big is an E. coli cell? 804 00:41:06,483 --> 00:41:07,780 AUDIENCE: One micron? 805 00:41:07,780 --> 00:41:09,450 PROFESSOR: One micron, roughly, right? 806 00:41:09,450 --> 00:41:11,860 So it might be a couple microns long. 807 00:41:11,860 --> 00:41:13,400 A bit less than a micron in width. 808 00:41:13,400 --> 00:41:15,842 And what this is saying is that 0.1 seconds, which 809 00:41:15,842 --> 00:41:17,300 is our exposure time on our camera, 810 00:41:17,300 --> 00:41:19,660 you would expect something like GFP 811 00:41:19,660 --> 00:41:22,550 to diffuse around roughly the cell volume. 812 00:41:22,550 --> 00:41:24,951 And maybe not the entire one, but a fair fraction of it. 813 00:41:24,951 --> 00:41:26,950 What this is saying is that the diffusion really 814 00:41:26,950 --> 00:41:30,114 would be a problem, even with this relatively short exposure 815 00:41:30,114 --> 00:41:30,614 time. 816 00:41:30,614 --> 00:41:31,916 Yeah? 817 00:41:31,916 --> 00:41:32,833 AUDIENCE: [INAUDIBLE]? 818 00:41:32,833 --> 00:41:33,457 PROFESSOR: Yes. 819 00:41:33,457 --> 00:41:35,424 So this is assuming that the cytoplasm has 820 00:41:35,424 --> 00:41:37,340 a viscosity that's maybe an order of magnitude 821 00:41:37,340 --> 00:41:38,380 larger than water. 822 00:41:38,380 --> 00:41:40,030 And that's just because the inside 823 00:41:40,030 --> 00:41:42,510 is chock full of proteins and so forth. 824 00:41:42,510 --> 00:41:45,050 Now, there's a lot of discussion of what 825 00:41:45,050 --> 00:41:49,170 the mechanism is of diffusion and transport inside cells. 826 00:41:49,170 --> 00:41:50,630 It may depend on the size. 827 00:41:50,630 --> 00:41:52,420 It's a very complicated area. 828 00:41:52,420 --> 00:41:55,171 But for our purposes, this is a reasonable way 829 00:41:55,171 --> 00:41:55,920 to think about it. 830 00:41:55,920 --> 00:41:58,270 But indeed, the viscosity of the cytoplasm, you'd 831 00:41:58,270 --> 00:42:00,900 expect to be significantly more than the viscosity of water. 832 00:42:03,760 --> 00:42:04,563 Yeah? 833 00:42:04,563 --> 00:42:08,270 AUDIENCE: [INAUDIBLE] lower the [INAUDIBLE] time? 834 00:42:08,270 --> 00:42:09,475 PROFESSOR: Lower the? 835 00:42:09,475 --> 00:42:10,100 AUDIENCE: Yeah. 836 00:42:10,100 --> 00:42:11,982 Like two orders of magnitude instead of one? 837 00:42:11,982 --> 00:42:12,690 PROFESSOR: Right. 838 00:42:12,690 --> 00:42:15,390 So in principle, we could. 839 00:42:15,390 --> 00:42:17,610 There are technical issues on various sides. 840 00:42:17,610 --> 00:42:20,340 So of course, you have to say, oh well, a typical camera, just 841 00:42:20,340 --> 00:42:22,280 the shutter of opening, shutting, 842 00:42:22,280 --> 00:42:23,670 that actually has some limit. 843 00:42:23,670 --> 00:42:26,640 But you can get around that using kind of strob-- you know, 844 00:42:26,640 --> 00:42:28,930 there are fancy things you can do. 845 00:42:28,930 --> 00:42:31,460 But there's just a more fundamental thing here, 846 00:42:31,460 --> 00:42:35,380 which is-- so this is already 100 milliseconds. 847 00:42:35,380 --> 00:42:37,660 If you go down to like say, 1 millisecond, 848 00:42:37,660 --> 00:42:39,220 then it's true that the protein won't 849 00:42:39,220 --> 00:42:41,344 be able to diffuse very far, but then you also just 850 00:42:41,344 --> 00:42:42,704 don't collect any photons. 851 00:42:42,704 --> 00:42:44,370 The number of photons you collect scales 852 00:42:44,370 --> 00:42:45,670 linearly with the time, right? 853 00:42:45,670 --> 00:42:47,461 So at some point, it's just that you really 854 00:42:47,461 --> 00:42:48,730 don't get very many photons. 855 00:42:48,730 --> 00:42:51,300 And then again, you have this extra problem 856 00:42:51,300 --> 00:42:55,630 of distinguishing the fluorescence 857 00:42:55,630 --> 00:42:57,270 from the autofluorescence. 858 00:42:57,270 --> 00:42:59,630 And I just want to maybe mention one more thing. 859 00:42:59,630 --> 00:43:01,720 In Figure 1, you can actually see 860 00:43:01,720 --> 00:43:06,300 how big the fluorescence intensity of this Venus protein 861 00:43:06,300 --> 00:43:08,310 is, as compared to the autofluorescence. 862 00:43:08,310 --> 00:43:12,030 And you see that if you decrease that exposure time by even one 863 00:43:12,030 --> 00:43:14,360 order of magnitude, you wouldn't be able to see them 864 00:43:14,360 --> 00:43:15,480 over the background. 865 00:43:15,480 --> 00:43:16,040 Right? 866 00:43:16,040 --> 00:43:17,360 And that's true, even though they won't 867 00:43:17,360 --> 00:43:18,250 have had a chance to diffuse. 868 00:43:18,250 --> 00:43:20,368 It's just that you don't have enough signal. 869 00:43:20,368 --> 00:43:21,284 AUDIENCE: [INAUDIBLE]. 870 00:43:24,040 --> 00:43:25,110 PROFESSOR: Oh. 871 00:43:25,110 --> 00:43:25,610 Right. 872 00:43:25,610 --> 00:43:28,340 So you can also increase the intensity. 873 00:43:28,340 --> 00:43:29,880 Yeah, that's right. 874 00:43:29,880 --> 00:43:33,090 And there is some limit to how much 875 00:43:33,090 --> 00:43:35,310 you can increase the intensity of the laser, 876 00:43:35,310 --> 00:43:37,390 just because there is some cycling 877 00:43:37,390 --> 00:43:41,940 time of the protein in terms of, you excite it, 878 00:43:41,940 --> 00:43:44,190 and then it takes some time before it's going to emit. 879 00:43:44,190 --> 00:43:47,270 So that actually sets a fundamental limit. 880 00:43:47,270 --> 00:43:50,700 Yeah, I don't know enough about the details of this 881 00:43:50,700 --> 00:43:53,460 in the sense of whether maybe it would've been possible for them 882 00:43:53,460 --> 00:43:56,250 to try to adjust these various parameters 883 00:43:56,250 --> 00:43:58,350 to do it in some other way. 884 00:43:58,350 --> 00:44:02,050 But these are all the things you have to consider. 885 00:44:02,050 --> 00:44:02,550 Question? 886 00:44:11,410 --> 00:44:12,770 OK. 887 00:44:12,770 --> 00:44:16,280 So what we have now is some sense-- OK, 888 00:44:16,280 --> 00:44:18,000 we need to maybe anchor into the membrane 889 00:44:18,000 --> 00:44:19,160 to reduce the diffusion. 890 00:44:19,160 --> 00:44:19,660 All right. 891 00:44:19,660 --> 00:44:21,290 So they did that. 892 00:44:21,290 --> 00:44:24,487 And we'll maybe say something more about this anchoring 893 00:44:24,487 --> 00:44:25,320 process in a moment. 894 00:44:25,320 --> 00:44:27,620 But first, I want to make sure that we're 895 00:44:27,620 --> 00:44:29,987 all on the same page in understanding 896 00:44:29,987 --> 00:44:32,570 their arguments for why this is a single molecule that they're 897 00:44:32,570 --> 00:44:33,990 looking at. 898 00:44:33,990 --> 00:44:38,319 Can somebody remind us their primary evidence 899 00:44:38,319 --> 00:44:39,610 that this is a single molecule? 900 00:44:52,090 --> 00:44:57,520 So question is, a molecule , we'll say single fluorophore, 901 00:44:57,520 --> 00:45:05,140 just to-- question mark. 902 00:45:05,140 --> 00:45:06,139 How do we know? 903 00:45:06,139 --> 00:45:07,555 AUDIENCE: The intensity drops off. 904 00:45:07,555 --> 00:45:08,263 PROFESSOR: Right. 905 00:45:08,263 --> 00:45:11,850 The intensity drops off suddenly. 906 00:45:11,850 --> 00:45:14,960 So if you look at the intensity as a function of time, 907 00:45:14,960 --> 00:45:20,990 what you see is that it looks like, and then. 908 00:45:20,990 --> 00:45:27,199 So it's actually more noise, but this is just to-- now 909 00:45:27,199 --> 00:45:29,240 this is what it looks like for a single molecule, 910 00:45:29,240 --> 00:45:32,080 but we should also be clear of what it would look 911 00:45:32,080 --> 00:45:34,540 like if it were many molecules. 912 00:45:34,540 --> 00:45:37,610 So this is if it's a single molecule. 913 00:45:37,610 --> 00:45:41,770 And this is what we call a bleach event. 914 00:45:41,770 --> 00:45:44,480 And so the molecule dies for one reason or another. 915 00:45:44,480 --> 00:45:49,460 So it goes, some oxygen reaction, something. 916 00:45:49,460 --> 00:45:51,650 Now the question is, what happens if it 917 00:45:51,650 --> 00:45:53,370 said there are many molecules? 918 00:46:02,290 --> 00:46:03,797 AUDIENCE: [INAUDIBLE]. 919 00:46:03,797 --> 00:46:04,380 PROFESSOR: OK. 920 00:46:04,380 --> 00:46:06,120 Now, what we want to do is imaginn-- 921 00:46:06,120 --> 00:46:09,150 let's say that we shined light on a bead 922 00:46:09,150 --> 00:46:11,429 containing fluorescence, containing 923 00:46:11,429 --> 00:46:12,345 fluorescent molecules. 924 00:46:14,960 --> 00:46:16,515 So I'm going to give us some options. 925 00:46:19,680 --> 00:46:22,400 It could be many molecules. 926 00:46:22,400 --> 00:46:22,900 OK. 927 00:46:22,900 --> 00:46:23,581 We could. 928 00:46:43,712 --> 00:46:44,240 All right. 929 00:46:44,240 --> 00:46:47,086 I'll give you a choice those three. 930 00:46:47,086 --> 00:46:48,960 AUDIENCE: So we're talking about [INAUDIBLE]? 931 00:46:48,960 --> 00:46:49,585 PROFESSOR: Yes. 932 00:46:49,585 --> 00:46:53,440 I'm asking if instead-- what happens in the microscope 933 00:46:53,440 --> 00:46:55,720 is you see a spot. 934 00:46:55,720 --> 00:46:57,711 And the spot is always huge. 935 00:46:57,711 --> 00:46:58,210 Right? 936 00:46:58,210 --> 00:46:59,850 300 nanometers. 937 00:46:59,850 --> 00:47:03,710 So there could be one molecule there, or there could be 100. 938 00:47:03,710 --> 00:47:04,940 You could fit 1,000 in there. 939 00:47:04,940 --> 00:47:05,490 No problem. 940 00:47:05,490 --> 00:47:05,990 Right? 941 00:47:05,990 --> 00:47:07,185 10 by 10 by 10 molecules? 942 00:47:07,185 --> 00:47:08,560 That still is only 30 nanometers. 943 00:47:08,560 --> 00:47:10,880 That's still much smaller than defraction limited spot. 944 00:47:10,880 --> 00:47:13,710 So of course, if you see something, 945 00:47:13,710 --> 00:47:18,780 and the spot is 10 microns in width, 946 00:47:18,780 --> 00:47:21,630 you'd be pretty confident that either your optics suck, 947 00:47:21,630 --> 00:47:24,504 or you're looking at many molecules. 948 00:47:24,504 --> 00:47:26,170 But if you see diffraction limited spot, 949 00:47:26,170 --> 00:47:27,040 then it's not so obvious. 950 00:47:27,040 --> 00:47:28,430 And so the question is, if you plot 951 00:47:28,430 --> 00:47:30,221 the intensity of a diffraction limited spot 952 00:47:30,221 --> 00:47:32,134 as a function of time, how do you know 953 00:47:32,134 --> 00:47:33,300 that it's a single molecule? 954 00:47:33,300 --> 00:47:35,210 They claim, oh well, it's because of this. 955 00:47:35,210 --> 00:47:36,880 But it's always good to be clear. 956 00:47:36,880 --> 00:47:39,465 What would it look like if it were not a single molecule, 957 00:47:39,465 --> 00:47:44,240 but instead it were a collection of molecules> Let's go ahead 958 00:47:44,240 --> 00:47:44,870 and vote. 959 00:47:44,870 --> 00:47:45,750 Ready? 960 00:47:45,750 --> 00:47:47,745 Three, two, one. 961 00:47:50,320 --> 00:47:55,340 So we have a fair number of different responses. 962 00:47:55,340 --> 00:47:59,209 It seems to be a split across the room is the only problem. 963 00:47:59,209 --> 00:48:00,750 So I'm not going to have you discuss, 964 00:48:00,750 --> 00:48:03,550 because I think your neighbors typically agree with you. 965 00:48:03,550 --> 00:48:05,180 But in this case, it's going to be 966 00:48:05,180 --> 00:48:08,251 C. And this, it was an attempt of mine of drawing-- 967 00:48:08,251 --> 00:48:08,750 what is it? 968 00:48:08,750 --> 00:48:10,395 Exponential distribution. 969 00:48:10,395 --> 00:48:14,040 So you'll see exponential decay. 970 00:48:14,040 --> 00:48:16,490 So this is typical of processes where 971 00:48:16,490 --> 00:48:20,230 something is happening at a constant rate over time, 972 00:48:20,230 --> 00:48:22,110 and then you're seeing this thing go away. 973 00:48:22,110 --> 00:48:26,060 So this could be, for example, radioactivity 974 00:48:26,060 --> 00:48:27,831 is the classic thing we always talk. 975 00:48:27,831 --> 00:48:28,830 These are random events. 976 00:48:28,830 --> 00:48:31,289 We thought the radiation coming off of some source 977 00:48:31,289 --> 00:48:33,705 is a function of time that's going to decay exponentially. 978 00:48:36,300 --> 00:48:42,350 Similarly here, now this is-- again, 979 00:48:42,350 --> 00:48:44,130 intensity is a function of time. 980 00:48:44,130 --> 00:48:45,790 In the case of many molecules, we 981 00:48:45,790 --> 00:48:48,960 get this thing that look like C. Now, there's 982 00:48:48,960 --> 00:48:54,140 going to be some time scale here which is telling us 983 00:48:54,140 --> 00:49:00,250 about the typical time for this bleach event, which we're told 984 00:49:00,250 --> 00:49:00,750 is what? 985 00:49:03,637 --> 00:49:04,345 250 milliseconds. 986 00:49:08,102 --> 00:49:09,810 And indeed, this is telling us, actually, 987 00:49:09,810 --> 00:49:13,660 that they're already illuminating these guys 988 00:49:13,660 --> 00:49:15,420 at pretty high intensity. 989 00:49:15,420 --> 00:49:19,380 Because 250 milliseconds is not that long. 990 00:49:26,400 --> 00:49:27,311 Yes? 991 00:49:27,311 --> 00:49:28,227 AUDIENCE: [INAUDIBLE]? 992 00:49:32,085 --> 00:49:32,710 PROFESSOR: Yes. 993 00:49:32,710 --> 00:49:33,970 AUDIENCE: Is it really a function 994 00:49:33,970 --> 00:49:35,095 common photons [INAUDIBLE]? 995 00:49:38,180 --> 00:49:40,152 PROFESSOR: It's not really a function of the-- 996 00:49:40,152 --> 00:49:42,527 it ends up being a function of the number of photons that 997 00:49:42,527 --> 00:49:44,310 are emitted, but that's basically because you're 998 00:49:44,310 --> 00:49:45,518 in kind of some ground state. 999 00:49:45,518 --> 00:49:47,900 You excite up to this other state. 1000 00:49:47,900 --> 00:49:51,430 And then, you get this relaxation to a lower state. 1001 00:49:51,430 --> 00:49:55,440 So this is the energy of the absorbed photon. 1002 00:49:55,440 --> 00:49:57,710 This is the energy of the emitted photon. 1003 00:49:57,710 --> 00:50:01,570 The idea is that each time you go around this cycle, that's 1004 00:50:01,570 --> 00:50:03,810 one emission cycle, there's some probability 1005 00:50:03,810 --> 00:50:09,030 that's small-- 1 in 10 to the 5, or something like that-- 1006 00:50:09,030 --> 00:50:10,950 that it reacts with oxygen, or something that 1007 00:50:10,950 --> 00:50:12,520 causes it to go to the start. 1008 00:50:12,520 --> 00:50:14,854 And it's in principle, irreversible state. 1009 00:50:14,854 --> 00:50:17,520 Of course, the dynamics of these things can be more complicated, 1010 00:50:17,520 --> 00:50:20,700 but that's the [INAUDIBLE] way of thinking about it. 1011 00:50:20,700 --> 00:50:24,340 What that means is that that's more or less 1012 00:50:24,340 --> 00:50:29,060 a constant number of photons that you're going to get out. 1013 00:50:29,060 --> 00:50:31,890 There are many cases where this approximation fails. 1014 00:50:37,850 --> 00:50:42,644 This single step bleaching is kind of a classic signature 1015 00:50:42,644 --> 00:50:44,060 of the fact that you're looking at 1016 00:50:44,060 --> 00:50:47,640 a single fluorescent molecule. 1017 00:50:47,640 --> 00:50:52,360 Now, there are secondary arguments 1018 00:50:52,360 --> 00:50:55,804 for why this is a single [INAUDIBLE] Venus 1019 00:50:55,804 --> 00:50:56,970 they're looking at was what? 1020 00:51:06,570 --> 00:51:09,110 What was their supporting evidence? 1021 00:51:09,110 --> 00:51:09,710 Yes? 1022 00:51:09,710 --> 00:51:11,020 AUDIENCE: [INAUDIBLE]. 1023 00:51:11,020 --> 00:51:11,686 PROFESSOR: Yeah. 1024 00:51:11,686 --> 00:51:13,186 The intensity matched what? 1025 00:51:13,186 --> 00:51:14,102 AUDIENCE: [INAUDIBLE]. 1026 00:51:16,380 --> 00:51:17,380 PROFESSOR: That's right. 1027 00:51:17,380 --> 00:51:18,963 So what they said is, well, all right. 1028 00:51:18,963 --> 00:51:25,750 This intensity matched what they measured on a slide. 1029 00:51:25,750 --> 00:51:27,800 Just the molecule. 1030 00:51:27,800 --> 00:51:30,640 But I'd say this really is, I would say, supporting evidence, 1031 00:51:30,640 --> 00:51:33,770 because the intensity of the fluorescence 1032 00:51:33,770 --> 00:51:38,010 can just be different in different environments. 1033 00:51:38,010 --> 00:51:42,470 I think that this is kind of thing that it's-- there are 1034 00:51:42,470 --> 00:51:43,750 many ways that this can fail. 1035 00:51:43,750 --> 00:51:45,920 Right, so I think that in general, we consider 1036 00:51:45,920 --> 00:51:47,128 this to be the gold standard. 1037 00:51:53,935 --> 00:51:55,430 All right. 1038 00:51:55,430 --> 00:51:58,890 Now in their experimental setup, there's 1039 00:51:58,890 --> 00:52:00,390 something that's, I think, very nice 1040 00:52:00,390 --> 00:52:10,760 that they do, which is, if you look at the-- now 1041 00:52:10,760 --> 00:52:13,725 this is the we'll say, laser illumination. 1042 00:52:17,331 --> 00:52:19,080 Here, this is kind of on, and this is off. 1043 00:52:21,630 --> 00:52:24,460 What they do is every three minutes, they illuminate. 1044 00:52:31,950 --> 00:52:36,670 And then, this is not to scale. 1045 00:52:42,480 --> 00:52:46,920 This was 1.2 seconds. 1046 00:52:46,920 --> 00:52:50,850 So we might want to even-- there's a separation in there. 1047 00:52:50,850 --> 00:52:52,430 So they illuminate for 1.2 seconds, 1048 00:52:52,430 --> 00:52:58,020 and they collect the light for the first 0.1 seconds. 1049 00:52:58,020 --> 00:53:11,930 This is the period where they collect for 0.1. 1050 00:53:11,930 --> 00:53:16,480 Can somebody tell us why they might possibly want to do this? 1051 00:53:16,480 --> 00:53:21,630 Shine more light on the sample than they need to? 1052 00:53:21,630 --> 00:53:24,530 They're not going to analyze that data. 1053 00:53:27,900 --> 00:53:31,920 So this is an intentional bleaching step. 1054 00:53:31,920 --> 00:53:34,975 So this part here is to bleach. 1055 00:53:37,620 --> 00:53:40,232 And we'll see that this is actually essential for the way 1056 00:53:40,232 --> 00:53:41,690 that they're collecting their data. 1057 00:53:44,890 --> 00:53:46,520 Given everything that we've just said, 1058 00:53:46,520 --> 00:53:51,170 you should be able to tell me what fraction of the molecules 1059 00:53:51,170 --> 00:53:52,500 will not be bleached. 1060 00:54:04,240 --> 00:54:06,780 That survive bleaching. 1061 00:54:06,780 --> 00:54:09,075 Survive the so-called bleaching step. 1062 00:54:17,430 --> 00:54:18,640 You can ignore my writing. 1063 00:54:18,640 --> 00:54:20,681 You should be able to think about it on your own. 1064 00:54:39,640 --> 00:54:43,390 I'll go ahead, and I'll give you 30 seconds to think about this. 1065 00:54:43,390 --> 00:54:44,925 And I think all of the information 1066 00:54:44,925 --> 00:54:48,960 that you need is in principle written up on the board. 1067 00:54:48,960 --> 00:54:49,914 Yes? 1068 00:54:49,914 --> 00:54:50,830 AUDIENCE: [INAUDIBLE]. 1069 00:54:59,330 --> 00:55:00,270 PROFESSOR: Right. 1070 00:55:00,270 --> 00:55:04,120 I'm assuming that they start out being fluorescent. 1071 00:55:04,120 --> 00:55:06,444 Now over time, we're illuminating them 1072 00:55:06,444 --> 00:55:07,360 with this laser light. 1073 00:55:07,360 --> 00:55:12,100 So eventually, they will bleach. 1074 00:55:12,100 --> 00:55:17,320 But perhaps some of them have survived for that entire 1.2 1075 00:55:17,320 --> 00:55:17,820 seconds. 1076 00:55:17,820 --> 00:55:19,750 So if you looked at it after this bleaching step, 1077 00:55:19,750 --> 00:55:21,000 it would still be fluorescent. 1078 00:55:29,000 --> 00:55:30,610 Maybe another 30 seconds, because-- 1079 00:55:55,994 --> 00:55:56,910 Do you need more time? 1080 00:56:03,560 --> 00:56:05,930 Let me see where we are, just so that we 1081 00:56:05,930 --> 00:56:07,330 can get a sense of things. 1082 00:56:07,330 --> 00:56:07,870 Ready? 1083 00:56:07,870 --> 00:56:09,870 Three, two, one. 1084 00:56:12,930 --> 00:56:13,460 All right. 1085 00:56:13,460 --> 00:56:14,000 Great. 1086 00:56:14,000 --> 00:56:17,060 We're roughly uniformly distributed 1087 00:56:17,060 --> 00:56:18,941 between-- all right. 1088 00:56:18,941 --> 00:56:19,440 Perfect. 1089 00:56:19,440 --> 00:56:21,680 So this is an opportunity to turn to your neighbor 1090 00:56:21,680 --> 00:56:23,170 and discuss. 1091 00:56:23,170 --> 00:56:26,450 You should, even with back of the envelope 1092 00:56:26,450 --> 00:56:29,610 calculations in your head, be able to get roughly where this. 1093 00:56:29,610 --> 00:56:32,560 But you're also welcome, if you want, to double check. 1094 00:56:32,560 --> 00:56:33,450 Pull out your iPhone. 1095 00:56:33,450 --> 00:56:35,150 You can use the Google calculator. 1096 00:56:35,150 --> 00:56:37,660 I give you just a minute or two to turn to a neighbor. 1097 00:56:37,660 --> 00:56:39,535 You should certainly be able to find somebody 1098 00:56:39,535 --> 00:56:41,316 that disagrees with you. 1099 00:56:41,316 --> 00:58:07,102 [STUDENT CHATTER] 1100 00:58:07,102 --> 00:58:09,060 PROFESSOR: Why don't we go ahead and reconvene? 1101 00:58:09,060 --> 00:58:12,330 It's OK if you're still kind of confused by this. 1102 00:58:12,330 --> 00:58:13,940 I've partly doing this to encourage 1103 00:58:13,940 --> 00:58:16,360 you to review your probability distributions, 1104 00:58:16,360 --> 00:58:19,320 because we are going to dive into them rather 1105 00:58:19,320 --> 00:58:21,100 strongly over the next week. 1106 00:58:21,100 --> 00:58:23,009 And so it's good-- if you can't quite 1107 00:58:23,009 --> 00:58:24,550 remember how these are going to work, 1108 00:58:24,550 --> 00:58:26,290 it's good to start reviewing now. 1109 00:58:26,290 --> 00:58:26,790 All right. 1110 00:58:26,790 --> 00:58:27,956 Can I just see where we are? 1111 00:58:27,956 --> 00:58:28,480 Ready? 1112 00:58:28,480 --> 00:58:31,290 Three, two, one. 1113 00:58:31,290 --> 00:58:31,790 OK. 1114 00:58:31,790 --> 00:58:35,380 So we have some B's and C's. 1115 00:58:35,380 --> 00:58:36,782 All right. 1116 00:58:36,782 --> 00:58:38,490 I'm pretty confident it's B, although I'm 1117 00:58:38,490 --> 00:58:40,879 a little bit worried now. 1118 00:58:40,879 --> 00:58:42,420 All right, so what's going to happen? 1119 00:58:42,420 --> 00:58:46,230 So basically, the probability that this thing survives 1120 00:58:46,230 --> 00:58:49,610 as a function of time is the same 1121 00:58:49,610 --> 00:58:53,790 as, essentially, the decay and the overall intensity 1122 00:58:53,790 --> 00:58:56,006 fluorescence for many molecules over time. 1123 00:58:56,006 --> 00:58:57,630 Because this plot here is really a plot 1124 00:58:57,630 --> 00:59:00,285 of the fraction of the molecules that 1125 00:59:00,285 --> 00:59:02,380 have survived as a function of time. 1126 00:59:02,380 --> 00:59:03,510 Right. 1127 00:59:03,510 --> 00:59:07,400 So indeed, the probability of survival 1128 00:59:07,400 --> 00:59:10,660 for an exponential process like this is a function of time, t, 1129 00:59:10,660 --> 00:59:15,610 is going to be equal to e to the minus t 1130 00:59:15,610 --> 00:59:17,700 over some constant [INAUDIBLE]. 1131 00:59:20,720 --> 00:59:22,780 And what is t in tau? 1132 00:59:22,780 --> 00:59:27,630 Well, t is this time 1.2 seconds. 1133 00:59:30,660 --> 00:59:34,610 So we have e to the-- we'll write it like an exponent. 1134 00:59:34,610 --> 00:59:35,720 So now we have a minus. 1135 00:59:35,720 --> 00:59:41,060 We have 1.2 seconds divided by the lifetime in this condition, 1136 00:59:41,060 --> 00:59:42,840 we're told is 250 milliseconds. 1137 00:59:42,840 --> 00:59:49,880 So we can write 0.25 seconds. 1138 00:59:49,880 --> 00:59:56,150 So this is approximately e to the minus 5, 1139 00:59:56,150 --> 00:59:59,715 which indeed, is equal to what I thought is 0.8%. 1140 01:00:02,850 --> 01:00:09,240 So it's around 1%, 1141 01:00:09,240 --> 01:00:12,670 Are there any questions about this logic or this calculation? 1142 01:00:12,670 --> 01:00:15,036 Yes? 1143 01:00:15,036 --> 01:00:15,952 AUDIENCE: [INAUDIBLE]. 1144 01:00:20,300 --> 01:00:21,349 PROFESSOR: Oh, no, no. 1145 01:00:21,349 --> 01:00:21,890 Sorry, sorry. 1146 01:00:21,890 --> 01:00:22,640 No, no. 1147 01:00:22,640 --> 01:00:29,200 Bleaching, this is a result of chemical inactivation 1148 01:00:29,200 --> 01:00:32,210 of the fluorescent protein that is kind of induced 1149 01:00:32,210 --> 01:00:35,900 by being in this excited state. 1150 01:00:35,900 --> 01:00:38,460 So the idea is that if you're shining light 1151 01:00:38,460 --> 01:00:40,800 on this fluorescent protein, then 1152 01:00:40,800 --> 01:00:48,160 it's going to bleach at a rate that is kind of-- distribution 1153 01:00:48,160 --> 01:00:51,920 of say, lifetime's going to be exponential with a time 1154 01:00:51,920 --> 01:00:53,430 constant of 250 milliseconds. 1155 01:00:53,430 --> 01:00:54,346 AUDIENCE: [INAUDIBLE]. 1156 01:00:57,301 --> 01:00:58,300 PROFESSOR: That's right. 1157 01:00:58,300 --> 01:00:58,890 That's right. 1158 01:00:58,890 --> 01:01:00,890 But it's a one-step process though. 1159 01:01:00,890 --> 01:01:01,890 That's what we see here. 1160 01:01:01,890 --> 01:01:04,160 It's not that that individual protein 1161 01:01:04,160 --> 01:01:06,960 is getting worse and worse as it's being used. 1162 01:01:06,960 --> 01:01:09,890 But it's really just that there's some rate 1163 01:01:09,890 --> 01:01:11,590 that it-- some probability, of course, 1164 01:01:11,590 --> 01:01:15,701 time that it cycles that it is, we'll say for now, irreversibly 1165 01:01:15,701 --> 01:01:16,200 inactivated. 1166 01:01:19,460 --> 01:01:22,620 There are also all these so-called blinking events, 1167 01:01:22,620 --> 01:01:27,360 where fluorescent molecules can kind of temporarily 1168 01:01:27,360 --> 01:01:30,065 go into a non-fluorescent state, and then they return, 1169 01:01:30,065 --> 01:01:33,620 but right now, we're talking about these irreversible steps. 1170 01:01:36,890 --> 01:01:39,830 Are there any other questions about what I mean by bleaching, 1171 01:01:39,830 --> 01:01:41,570 or this calculation? 1172 01:01:47,054 --> 01:01:48,320 AUDIENCE: [INAUDIBLE]. 1173 01:01:48,320 --> 01:01:52,300 PROFESSOR: So my claim is that 0.8% is very 1174 01:01:52,300 --> 01:01:54,264 close, is approximately 1%. 1175 01:01:54,264 --> 01:01:55,180 AUDIENCE: [INAUDIBLE]. 1176 01:01:58,150 --> 01:02:01,240 PROFESSOR: Yes, sorry. 1177 01:02:01,240 --> 01:02:03,025 I did something funny here. 1178 01:02:03,025 --> 01:02:03,525 Yeah, yeah. 1179 01:02:09,950 --> 01:02:12,989 So it's useful to just kind of go through these calculations. 1180 01:02:12,989 --> 01:02:15,030 And actually, I think that in going through them, 1181 01:02:15,030 --> 01:02:16,820 you kind of really get to get a sense of why 1182 01:02:16,820 --> 01:02:18,736 they design their experiments the way they did 1183 01:02:18,736 --> 01:02:20,080 and everything. 1184 01:02:20,080 --> 01:02:25,000 So the idea is that what they're doing here every three minutes, 1185 01:02:25,000 --> 01:02:27,890 they're looking at the cells, and they're asking, 1186 01:02:27,890 --> 01:02:31,160 is there are a protein, or maybe more than one here? 1187 01:02:31,160 --> 01:02:35,910 And then they try to kill all those fluorescent proteins. 1188 01:02:35,910 --> 01:02:39,170 And then they look again three minutes later. 1189 01:02:39,170 --> 01:02:43,210 Are there any new proteins that were made. 1190 01:02:43,210 --> 01:02:43,860 Yes? 1191 01:02:43,860 --> 01:02:45,979 AUDIENCE: [INAUDIBLE]. 1192 01:02:45,979 --> 01:02:49,230 You can't see it [INAUDIBLE]. 1193 01:02:49,230 --> 01:02:50,230 PROFESSOR: That's right. 1194 01:02:50,230 --> 01:02:50,730 You don't-- 1195 01:02:50,730 --> 01:02:52,944 AUDIENCE: Do you calibrate the intensity [INAUDIBLE]. 1196 01:02:52,944 --> 01:02:55,360 PROFESSOR: So what they're really doing is they're asking, 1197 01:02:55,360 --> 01:02:57,140 how many spots do I see? 1198 01:03:00,600 --> 01:03:02,340 So in that experiment, they don't know 1199 01:03:02,340 --> 01:03:05,330 that it was a single molecule. 1200 01:03:05,330 --> 01:03:06,700 Although I think that in many-- 1201 01:03:06,700 --> 01:03:11,111 AUDIENCE: Then why do they talk about this [INAUDIBLE]? 1202 01:03:11,111 --> 01:03:13,110 PROFESSOR: Well, that's how they checked to make 1203 01:03:13,110 --> 01:03:14,437 sure it was a single molecule. 1204 01:03:14,437 --> 01:03:16,520 Although I think that actually, in principle here, 1205 01:03:16,520 --> 01:03:20,310 I think they actually maybe do continue to look at them. 1206 01:03:20,310 --> 01:03:21,727 That's not part of their analysis. 1207 01:03:21,727 --> 01:03:23,310 So for many of the case, they actually 1208 01:03:23,310 --> 01:03:25,800 do see that this molecule is here, and then it bleaches, 1209 01:03:25,800 --> 01:03:28,590 and a different molecule was here, and it bleached. 1210 01:03:31,120 --> 01:03:34,110 But what they're really asking is at the beginning, 1211 01:03:34,110 --> 01:03:37,654 how many fluorescent proteins did I see? 1212 01:03:37,654 --> 01:03:40,070 And I think the camera actually maybe was collecting still 1213 01:03:40,070 --> 01:03:41,195 during that bleaching step. 1214 01:03:41,195 --> 01:03:43,050 It's just that it wasn't kind of part of it. 1215 01:03:43,050 --> 01:03:46,624 Their analysis is in some ways really just based on this. 1216 01:03:46,624 --> 01:03:48,290 Or in other experiments, you can go look 1217 01:03:48,290 --> 01:03:51,155 to confirm that it bleaches single step here. 1218 01:03:55,610 --> 01:03:56,580 OK. 1219 01:03:56,580 --> 01:03:59,320 So we spent a long time talking like the general idea of how 1220 01:03:59,320 --> 01:04:02,680 to design these experiments and so forth. 1221 01:04:02,680 --> 01:04:04,900 I'm not going to say very much about the design 1222 01:04:04,900 --> 01:04:09,560 of the experiments, except that they did a number things. 1223 01:04:09,560 --> 01:04:11,640 They used this Venus protein that 1224 01:04:11,640 --> 01:04:17,320 has a faster maturation than traditional GFP. 1225 01:04:17,320 --> 01:04:20,610 They also targeted it to the membrane, 1226 01:04:20,610 --> 01:04:23,500 not by putting Venus into the membrane-- that 1227 01:04:23,500 --> 01:04:25,920 would be tricky, I think-- but rather 1228 01:04:25,920 --> 01:04:30,560 by attaching the Venus protein to another protein that 1229 01:04:30,560 --> 01:04:32,080 is put in the membrane. 1230 01:04:32,080 --> 01:04:34,124 And indeed, this TSR membrane protein, 1231 01:04:34,124 --> 01:04:35,540 we're going to be talking about it 1232 01:04:35,540 --> 01:04:37,600 in a couple of weeks when we're discussing 1233 01:04:37,600 --> 01:04:41,660 the chemotaxis network that is in E. coli for how E. coli find 1234 01:04:41,660 --> 01:04:44,030 food and so forth. 1235 01:04:44,030 --> 01:04:46,820 I think that in reading these papers, it's interesting. 1236 01:04:46,820 --> 01:04:49,720 Sometimes, authors make kind of a side comment 1237 01:04:49,720 --> 01:04:52,775 that just illuminates kind of how difficult everything was. 1238 01:04:52,775 --> 01:04:54,650 And I think that they had a nice one in here, 1239 01:04:54,650 --> 01:04:58,560 where they said that they were checking with TSR to make sure 1240 01:04:58,560 --> 01:05:04,130 that the behavior of the TSR Venus and just Venus 1241 01:05:04,130 --> 01:05:06,670 were similar in terms of the amount of fluorescence. 1242 01:05:06,670 --> 01:05:09,120 And then, they say, no notable difference 1243 01:05:09,120 --> 01:05:11,810 was observed, indicating that the introduction of the TSR 1244 01:05:11,810 --> 01:05:15,890 sequence does not change the yield of Venus production, 1245 01:05:15,890 --> 01:05:18,560 which is not the case for many other membrane targeting 1246 01:05:18,560 --> 01:05:20,060 sequences that we tested. 1247 01:05:20,060 --> 01:05:23,020 So this is like, a little add-on onto the sentence 1248 01:05:23,020 --> 01:05:27,480 that is like, I mean, six months of somebody's life 1249 01:05:27,480 --> 01:05:29,870 was dedicated to trying-- you can just 1250 01:05:29,870 --> 01:05:33,190 imagine all the over coffee, their frustration. 1251 01:05:33,190 --> 01:05:34,940 They tried all of these different things, 1252 01:05:34,940 --> 01:05:39,100 and they always got-- and for an awful lot of these things, 1253 01:05:39,100 --> 01:05:42,860 I would have still been very much interested in the study, 1254 01:05:42,860 --> 01:05:48,092 even if the addition of TSR did change the kinetics. 1255 01:05:48,092 --> 01:05:50,050 Because I think that still is very interesting. 1256 01:05:50,050 --> 01:05:52,890 But they really wanted this to be just airtight, 1257 01:05:52,890 --> 01:05:55,030 or maybe the referees need to be-- I don't know. 1258 01:05:55,030 --> 01:05:57,238 But you can tell that they just went to a lot of work 1259 01:05:57,238 --> 01:06:01,550 to try to find the thing where everything would be just right. 1260 01:06:06,560 --> 01:06:10,610 Now, once they kind of described their setup, 1261 01:06:10,610 --> 01:06:15,020 they had this wonderful paragraph, I think. 1262 01:06:15,020 --> 01:06:17,900 They say, oh, these proteins, they're generating bursts, 1263 01:06:17,900 --> 01:06:19,945 and the number in the bursts varies, 1264 01:06:19,945 --> 01:06:21,320 and there's spread, and so forth. 1265 01:06:21,320 --> 01:06:24,740 And they very nicely tell us, with this data, 1266 01:06:24,740 --> 01:06:27,510 we can ask four questions. 1267 01:06:27,510 --> 01:06:29,700 And they say, do these gene expression bursts 1268 01:06:29,700 --> 01:06:31,135 occur randomly in time? 1269 01:06:31,135 --> 01:06:33,030 That's going to be yes. 1270 01:06:33,030 --> 01:06:35,730 How many mRNA new molecules are responsible for each gene 1271 01:06:35,730 --> 01:06:38,620 expression burst under the repressed conditions? 1272 01:06:38,620 --> 01:06:40,050 One. 1273 01:06:40,050 --> 01:06:42,570 What is the distribution of the number of protein molecules 1274 01:06:42,570 --> 01:06:43,620 in each burst? 1275 01:06:43,620 --> 01:06:46,710 It's going to be geometrically distributed. 1276 01:06:46,710 --> 01:06:48,890 And what is the origin of the temporal spread 1277 01:06:48,890 --> 01:06:50,760 of the individual bursts? 1278 01:06:50,760 --> 01:06:52,489 And now, I think that this is nice, 1279 01:06:52,489 --> 01:06:54,030 just to give a reader a kind of like, 1280 01:06:54,030 --> 01:06:57,200 heads up of where we're heading. 1281 01:06:57,200 --> 01:06:59,690 And the origin of the temporal spread 1282 01:06:59,690 --> 01:07:02,960 is actually-- they're arguing is actually the Venus maturation 1283 01:07:02,960 --> 01:07:04,030 time. 1284 01:07:04,030 --> 01:07:06,940 So in that case, the fact that there's 1285 01:07:06,940 --> 01:07:09,000 a finite time for maturation of the Venus 1286 01:07:09,000 --> 01:07:10,810 ends up allowing them to measure the bursts 1287 01:07:10,810 --> 01:07:12,340 in an interesting way. 1288 01:07:12,340 --> 01:07:14,520 Before we get into the details of that, 1289 01:07:14,520 --> 01:07:19,680 though, I want to make sure that we're all clear about what 1290 01:07:19,680 --> 01:07:22,270 they mean by a burst. 1291 01:07:22,270 --> 01:07:25,450 Because this is something that is oddly-- 1292 01:07:25,450 --> 01:07:29,690 it feels like it's the most trivial statement ever. 1293 01:07:29,690 --> 01:07:31,970 But I think what we're going to find is that there's 1294 01:07:31,970 --> 01:07:34,672 a lot of confusion about it. 1295 01:07:34,672 --> 01:07:36,255 This is a question, how is it that you 1296 01:07:36,255 --> 01:07:39,360 go from the data to the quantities that they plot 1297 01:07:39,360 --> 01:07:41,070 and that they're interested in? 1298 01:07:41,070 --> 01:07:44,210 We want to get a sense of how many proteins are made 1299 01:07:44,210 --> 01:07:46,410 in each one of these bursts? 1300 01:07:46,410 --> 01:07:50,150 And so they have in Figure 3B, they 1301 01:07:50,150 --> 01:07:54,100 plot the number of protein molecules produced. 1302 01:07:54,100 --> 01:07:57,150 Number of proteins produced. 1303 01:08:00,160 --> 01:08:01,425 It's a function of time. 1304 01:08:04,280 --> 01:08:05,790 And they have these things. 1305 01:08:05,790 --> 01:08:08,690 And This was a cell division event. 1306 01:08:08,690 --> 01:08:16,010 And here they say, we have 2, 4. 1307 01:08:16,010 --> 01:08:22,439 And here at 25 minutes, we have this thing here, 1308 01:08:22,439 --> 01:08:23,410 and it looks like. 1309 01:08:30,344 --> 01:08:31,510 And then this thing goes on. 1310 01:08:31,510 --> 01:08:41,109 And there's 50, we have another, and so forth. 1311 01:08:41,109 --> 01:08:46,930 This is a zoom in of Figure 3B, the top panel. 1312 01:08:46,930 --> 01:08:51,880 So what I want to know is, what is the size of the first burst? 1313 01:09:24,279 --> 01:09:27,500 So you can either look at my beautifully drawn illustration, 1314 01:09:27,500 --> 01:09:29,950 or you can look at the paper in front of you. 1315 01:09:29,950 --> 01:09:33,170 So this is a paper analyzing the size distribution 1316 01:09:33,170 --> 01:09:37,960 of protein bursts observed in living cells. 1317 01:09:37,960 --> 01:09:38,479 Right? 1318 01:09:38,479 --> 01:09:40,319 That's the point of this paper. 1319 01:09:42,979 --> 01:09:45,950 Now, the question is, from the data they're collecting, 1320 01:09:45,950 --> 01:09:49,598 we want to know what is the size of the protein burst? 1321 01:09:49,598 --> 01:09:50,598 The first protein burst. 1322 01:10:04,710 --> 01:10:08,815 Now, there's no calculation for you to do. 1323 01:10:08,815 --> 01:10:12,050 There's not much of one. 1324 01:10:12,050 --> 01:10:13,820 So I'm not going to give you maybe anymore 1325 01:10:13,820 --> 01:10:15,357 time to figure this out. 1326 01:10:15,357 --> 01:10:16,440 So let's see where we are. 1327 01:10:16,440 --> 01:10:17,300 Ready? 1328 01:10:17,300 --> 01:10:21,450 Three, two, one. 1329 01:10:21,450 --> 01:10:22,010 All right. 1330 01:10:22,010 --> 01:10:25,650 So we got at least a majority of the group 1331 01:10:25,650 --> 01:10:30,050 is saying that it's indeed 3. 1332 01:10:32,700 --> 01:10:38,146 Now, the issue here is that the weight 1333 01:10:38,146 --> 01:10:40,520 of the experimental design is working so that every three 1334 01:10:40,520 --> 01:10:44,540 minutes, what we're asking is, how many Venus 1335 01:10:44,540 --> 01:10:48,840 molecules kind of folded in that previous three minutes? 1336 01:10:48,840 --> 01:10:51,120 And then, any of them that there are, 1337 01:10:51,120 --> 01:10:53,920 we count, and then we kill them. 1338 01:10:53,920 --> 01:10:54,850 And then, the next. 1339 01:10:54,850 --> 01:10:58,110 And indeed, what happened here is that every three minutes, 1340 01:10:58,110 --> 01:10:59,430 they're asking this question. 1341 01:10:59,430 --> 01:11:01,080 No proteins. 1342 01:11:01,080 --> 01:11:03,860 And then here, they see one. 1343 01:11:03,860 --> 01:11:06,700 Now, that's not yet a protein burst. 1344 01:11:06,700 --> 01:11:09,430 That's maybe a protein verse. 1345 01:11:09,430 --> 01:11:12,806 But it could be that we're in the middle of a protein burst. 1346 01:11:12,806 --> 01:11:14,680 And indeed, what we see is that the next time 1347 01:11:14,680 --> 01:11:18,000 point, the next three minutes, we see, oh, actually, 1348 01:11:18,000 --> 01:11:21,370 now there's two new proteins that were produced 1349 01:11:21,370 --> 01:11:23,020 in that next three minutes. 1350 01:11:23,020 --> 01:11:26,330 So indeed, this whole thing is a protein burst. 1351 01:11:33,820 --> 01:11:35,280 So we got 1 plus 2. 1352 01:11:35,280 --> 01:11:38,110 So that was the calculation I was referring to. 1353 01:11:38,110 --> 01:11:42,430 And so what they're plotting is the distribution 1354 01:11:42,430 --> 01:11:45,682 of these different protein burst sizes. 1355 01:11:45,682 --> 01:11:47,140 Now, this is a small protein burst. 1356 01:11:47,140 --> 01:11:51,207 They see some that get up to be 10, 15. 1357 01:11:51,207 --> 01:11:53,040 And that corresponds to some of these cases, 1358 01:11:53,040 --> 01:11:57,510 where they see something that looks, for example, more 1359 01:11:57,510 --> 01:12:04,685 like-- yeah, question? 1360 01:12:04,685 --> 01:12:05,601 AUDIENCE: [INAUDIBLE]. 1361 01:12:08,760 --> 01:12:10,590 PROFESSOR: Yeah, right. 1362 01:12:10,590 --> 01:12:11,910 AUDIENCE: [INAUDIBLE]. 1363 01:12:11,910 --> 01:12:14,700 PROFESSOR: Yes, exactly. 1364 01:12:14,700 --> 01:12:19,110 And ultimately, first of all, the number 1365 01:12:19,110 --> 01:12:21,550 of protein bursts per cell cycle, 1366 01:12:21,550 --> 01:12:27,690 per hour in these conditions, is of order one. 1367 01:12:27,690 --> 01:12:31,120 And then the width, the time, of a protein burst 1368 01:12:31,120 --> 01:12:34,820 is five, seven minutes. 1369 01:12:34,820 --> 01:12:36,560 Something like that typically. 1370 01:12:36,560 --> 01:12:40,850 So this gives you a sense of how frequently they will overlap. 1371 01:12:40,850 --> 01:12:45,280 And indeed, what you expect from this is that 15% of them 1372 01:12:45,280 --> 01:12:48,200 are actually that they see as one burst might actually 1373 01:12:48,200 --> 01:12:50,710 have been two though. 1374 01:12:50,710 --> 01:12:56,170 It's also worth mentioning that-- right. 1375 01:12:56,170 --> 01:12:59,220 So what I just said is in the model, where you know that it's 1376 01:12:59,220 --> 01:13:03,730 always just one mRNA that is produced each time, what they 1377 01:13:03,730 --> 01:13:06,000 say is they think is that the promoter is tightly 1378 01:13:06,000 --> 01:13:09,230 repressed by the Lac repressor. 1379 01:13:09,230 --> 01:13:11,320 Ever now and then, the Lac repressor falls off, 1380 01:13:11,320 --> 01:13:13,580 and it's going to bind again. 1381 01:13:13,580 --> 01:13:18,226 But some fraction of that time, when the repressor unbinds, 1382 01:13:18,226 --> 01:13:19,850 you get the RNA p binding, and then you 1383 01:13:19,850 --> 01:13:21,880 get a transcription event. 1384 01:13:21,880 --> 01:13:23,720 And I think that in general, it is just one 1385 01:13:23,720 --> 01:13:25,230 mRNA that is produced there. 1386 01:13:25,230 --> 01:13:28,510 So just a single RNA polymerase bound, and made an mRNA. 1387 01:13:28,510 --> 01:13:30,890 But I'm sure that some fraction of the time, it 1388 01:13:30,890 --> 01:13:33,290 was actually two that were produced during that time. 1389 01:13:33,290 --> 01:13:37,110 And those would certainly show up as one protein burst. 1390 01:13:37,110 --> 01:13:37,610 Right? 1391 01:13:37,610 --> 01:13:40,620 Because the lifetime of the mRNAs in this situation 1392 01:13:40,620 --> 01:13:41,560 is of order what? 1393 01:13:44,560 --> 01:13:45,060 Yeah. 1394 01:13:45,060 --> 01:13:47,890 It was, I think, one and a half minutes maybe? 1395 01:13:47,890 --> 01:13:48,510 It was short. 1396 01:13:51,270 --> 01:13:51,770 Yeah. 1397 01:13:51,770 --> 01:13:53,729 One and a half minutes. 1398 01:13:53,729 --> 01:13:55,520 What that means is that on this time scale, 1399 01:13:55,520 --> 01:13:56,894 if there were two mRNAs produced, 1400 01:13:56,894 --> 01:13:59,220 they would look like the same mRNA. 1401 01:13:59,220 --> 01:14:01,810 But from this data what they conclude 1402 01:14:01,810 --> 01:14:05,940 is that there's typically only one mRNA produced 1403 01:14:05,940 --> 01:14:09,580 in each protein burst, and there's not that many protein 1404 01:14:09,580 --> 01:14:12,350 bursts per hour of the cell division, 1405 01:14:12,350 --> 01:14:14,500 so they won't overlap too much. 1406 01:14:14,500 --> 01:14:17,436 But it's going to happen at some rate. 1407 01:14:23,900 --> 01:14:24,400 All right. 1408 01:14:28,520 --> 01:14:32,340 What they see is that the distribution of the protein 1409 01:14:32,340 --> 01:14:36,430 bursts-- we said it was roughly one 1410 01:14:36,430 --> 01:14:40,720 per cell division time, which they found was 55 minutes here. 1411 01:14:40,720 --> 01:14:44,280 And they found that the number of protein bursts per cell 1412 01:14:44,280 --> 01:14:49,160 cycle was distributed Poisson 1413 01:14:49,160 --> 01:14:50,880 So let me write this down somewhere. 1414 01:15:04,730 --> 01:15:12,140 The number of protein bursts per cell cycle. 1415 01:15:14,691 --> 01:15:16,190 So this was distributed as a Poisson 1416 01:15:16,190 --> 01:15:21,950 with mean [INAUDIBLE] lambda of around 1. 1417 01:15:21,950 --> 01:15:24,300 1.2. 1418 01:15:24,300 --> 01:15:27,220 They call this n cycle. 1419 01:15:27,220 --> 01:15:28,250 So I'll be consistent. 1420 01:15:28,250 --> 01:15:39,320 So this n cycle to the 1.2. 1421 01:15:39,320 --> 01:15:41,860 Now, you guys-- the Poisson is a distribution 1422 01:15:41,860 --> 01:15:46,810 that we're going to be spending a lot of time thinking about. 1423 01:15:46,810 --> 01:15:48,830 So the normal way that we write it 1424 01:15:48,830 --> 01:15:57,030 is that if it's the probability of observing some number n-- 1425 01:15:57,030 --> 01:16:00,674 and this is a number n bursts per cycle in this case, p of n. 1426 01:16:00,674 --> 01:16:02,090 We normally write it as a function 1427 01:16:02,090 --> 01:16:06,540 of the mean lambda, where it's lambda to the n over n 1428 01:16:06,540 --> 01:16:07,412 factorial. 1429 01:16:07,412 --> 01:16:08,870 And then for normalization, we have 1430 01:16:08,870 --> 01:16:11,630 to write e to the minus lambda here. 1431 01:16:13,839 --> 01:16:15,630 We're going to spend a lot of time thinking 1432 01:16:15,630 --> 01:16:19,390 about the Poisson next class. 1433 01:16:19,390 --> 01:16:21,690 So I would say that if it's been a while since you've 1434 01:16:21,690 --> 01:16:23,564 thought about probability distributions, then 1435 01:16:23,564 --> 01:16:26,990 you should play via textbook, Wikipedia, whatnot, 1436 01:16:26,990 --> 01:16:32,770 with the Poisson, the exponential, the geometric, 1437 01:16:32,770 --> 01:16:34,870 and also the gamma distributions. 1438 01:16:34,870 --> 01:16:37,335 Because we're going to be using those in the next class. 1439 01:16:42,670 --> 01:16:45,310 Now, in this distribution, what it basically 1440 01:16:45,310 --> 01:16:49,080 ends up being is that sometimes, you see zero bursts. 1441 01:16:49,080 --> 01:16:50,897 Sometimes you see one. 1442 01:16:50,897 --> 01:16:52,230 Every now and then, you see two. 1443 01:16:52,230 --> 01:16:53,700 It's kind of what this means. 1444 01:17:02,660 --> 01:17:05,880 There's one other thing that is, I think, a bit tricky often, 1445 01:17:05,880 --> 01:17:09,740 which is how they calculated that it was typically 1446 01:17:09,740 --> 01:17:14,520 one mRNA that led to each of these proteins bursts. 1447 01:17:14,520 --> 01:17:18,174 Can somebody remind us kind of experimentally 1448 01:17:18,174 --> 01:17:20,007 what they had to do in order to get at that? 1449 01:17:26,830 --> 01:17:29,720 The average RNA per cell, right. 1450 01:17:29,720 --> 01:17:32,380 Right, so they did this RT-PCR. 1451 01:17:32,380 --> 01:17:34,940 So what they did, they reverse transcribed. 1452 01:17:34,940 --> 01:17:37,320 They converted the mRNA into DNA, 1453 01:17:37,320 --> 01:17:40,000 and they amplified to get a sense of how much mRNA there 1454 01:17:40,000 --> 01:17:41,860 was. 1455 01:17:41,860 --> 01:17:45,540 And from that, the formula, when you first look at it, 1456 01:17:45,540 --> 01:17:49,070 it feels kind of mysterious, or something like that. 1457 01:17:49,070 --> 01:17:51,350 But it's one of those things that you just 1458 01:17:51,350 --> 01:17:55,360 have to keep track of like, units and so forth. 1459 01:17:55,360 --> 01:18:00,110 So you can basically think about the number of mRNA. 1460 01:18:00,110 --> 01:18:04,320 And this is indeed, this is per cell. 1461 01:18:04,320 --> 01:18:06,490 But cell, this doesn't have units, right? 1462 01:18:06,490 --> 01:18:09,800 But if we wanted the expectation value, 1463 01:18:09,800 --> 01:18:12,217 the number of the mRNA that's going to be per cell, 1464 01:18:12,217 --> 01:18:14,050 well, that's going to be given by the number 1465 01:18:14,050 --> 01:18:27,140 of the mRNA per burst, times the number of bursts per unit time. 1466 01:18:31,720 --> 01:18:37,620 So this is some rate burst, and then also 1467 01:18:37,620 --> 01:18:39,280 times the lifetime of the mRNA. 1468 01:18:46,140 --> 01:18:48,950 Now in this formula, there's also the added factor, 1469 01:18:48,950 --> 01:18:51,650 where they have like, the time of the cell cycle. 1470 01:18:51,650 --> 01:18:53,380 But that's just because this could 1471 01:18:53,380 --> 01:18:56,450 have been bursts per minute, lifetime of mRNA minutes. 1472 01:18:56,450 --> 01:18:59,170 But then, if you want to put in the extra term, 1473 01:18:59,170 --> 01:19:01,650 then you have to say, oh, the cell cycle is 55 minutes. 1474 01:19:01,650 --> 01:19:03,620 So then you have to do that conversion of time 1475 01:19:03,620 --> 01:19:04,843 into the proper units. 1476 01:19:04,843 --> 01:19:06,218 So that's what ends up happening. 1477 01:19:17,450 --> 01:19:19,915 Are there any questions about what happened here? 1478 01:19:25,860 --> 01:19:31,760 Now, what we're going to do next lecture is kind of go 1479 01:19:31,760 --> 01:19:36,520 through a simplified model of gene expression, 1480 01:19:36,520 --> 01:19:40,680 where there's just some rate of mRNA formation, mRNA 1481 01:19:40,680 --> 01:19:44,360 degradation, the mRNA makes protein, proteins get degraded. 1482 01:19:44,360 --> 01:19:47,275 And then in that model, we want to try to understand 1483 01:19:47,275 --> 01:19:48,525 how everything is distributed. 1484 01:19:50,802 --> 01:19:52,260 And we're going to relate that back 1485 01:19:52,260 --> 01:19:54,218 to some of the experimental data in this paper. 1486 01:19:54,218 --> 01:19:56,860 In particular, for example, this geometric distribution 1487 01:19:56,860 --> 01:19:59,060 of protein burst sizes is something 1488 01:19:59,060 --> 01:20:03,560 that you expect from the most basic simple model 1489 01:20:03,560 --> 01:20:05,160 that you would have written down. 1490 01:20:05,160 --> 01:20:07,180 So from that same point, it's not a surprise. 1491 01:20:07,180 --> 01:20:10,300 It is often assumed this thing should be geometrically 1492 01:20:10,300 --> 01:20:11,590 distributed, and it was. 1493 01:20:11,590 --> 01:20:13,370 And that's wonderful. 1494 01:20:13,370 --> 01:20:15,720 From my standpoint, I think that even things that we 1495 01:20:15,720 --> 01:20:17,590 assume to be true, we should still 1496 01:20:17,590 --> 01:20:19,580 check to see if they are true. 1497 01:20:19,580 --> 01:20:23,280 And in other cases, they may not be, and so forth. 1498 01:20:23,280 --> 01:20:27,391 Are there any questions about this paper? 1499 01:20:27,391 --> 01:20:27,890 No? 1500 01:20:31,041 --> 01:20:31,540 OK. 1501 01:20:31,540 --> 01:20:33,893 Then I will see you our next class.