1 00:00:00,001 --> 00:00:02,500 NARRATOR: 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 00:00:21,950 --> 00:00:24,240 PROFESSOR: So in terms of what we're 9 00:00:24,240 --> 00:00:26,007 going to be discussing today, it's 10 00:00:26,007 --> 00:00:27,590 various aspects of feed-forward loops. 11 00:00:27,590 --> 00:00:30,750 So first of all, we will go over this idea of a network 12 00:00:30,750 --> 00:00:31,644 motif in more detail. 13 00:00:31,644 --> 00:00:33,560 We talked it about a little bit in the context 14 00:00:33,560 --> 00:00:35,150 of auto regulation. 15 00:00:35,150 --> 00:00:38,140 There is a simple argument there that auto regulation 16 00:00:38,140 --> 00:00:39,090 is a network motif. 17 00:00:39,090 --> 00:00:42,340 And in order to understand how to detect network motifs, 18 00:00:42,340 --> 00:00:44,427 in general we have to look at a little more detail 19 00:00:44,427 --> 00:00:46,760 at these subgraphs and the frequency that they'll appear 20 00:00:46,760 --> 00:00:48,590 and so forth. 21 00:00:48,590 --> 00:00:51,260 And then after seeing that the feed-forward loop is a network 22 00:00:51,260 --> 00:00:53,093 motif, then there's this question-- oh, well 23 00:00:53,093 --> 00:00:55,150 what might be the functional significance? 24 00:00:55,150 --> 00:00:57,720 And in the chapter that you just read, 25 00:00:57,720 --> 00:01:00,720 you found this so-called coherent type one 26 00:01:00,720 --> 00:01:03,560 feed-forward loop has a nice attribute-- that it's 27 00:01:03,560 --> 00:01:06,530 sign sensitive delay element. 28 00:01:06,530 --> 00:01:10,180 The incoherent type one has the feature 29 00:01:10,180 --> 00:01:12,850 that it's a pulse generator, and kind of related to that, 30 00:01:12,850 --> 00:01:15,720 it can also speed up the response time. 31 00:01:15,720 --> 00:01:19,370 So it can make the response time for turning on shorter. 32 00:01:19,370 --> 00:01:21,332 So speed up response rate if you'd like. 33 00:01:21,332 --> 00:01:22,707 We'll also maybe say a little bit 34 00:01:22,707 --> 00:01:25,160 that there's been later work demonstrating 35 00:01:25,160 --> 00:01:31,180 that the incoherent type one can also access a fold detector. 36 00:01:31,180 --> 00:01:35,130 So it can sense changes in the fold change 37 00:01:35,130 --> 00:01:36,739 of concentrations of proteins. 38 00:01:36,739 --> 00:01:38,280 And then finally, we'll say something 39 00:01:38,280 --> 00:01:41,730 about how you can extend these ideas of a network motif 40 00:01:41,730 --> 00:01:42,660 to larger structures. 41 00:01:42,660 --> 00:01:45,875 In particular, how you get useful temporal programs. 42 00:01:54,180 --> 00:01:56,940 So we start out with this network 43 00:01:56,940 --> 00:01:59,570 that is kind of-- our base network 44 00:01:59,570 --> 00:02:04,040 is this transcription network characterized in E. coli. 45 00:02:04,040 --> 00:02:06,670 And we've already talked about it some. 46 00:02:06,670 --> 00:02:12,590 So there's going to be some measure the number of nodes 47 00:02:12,590 --> 00:02:14,660 and the number of edges. 48 00:02:14,660 --> 00:02:18,940 So we have N nodes, and we have E edges. 49 00:02:21,660 --> 00:02:25,040 This is from experimental measurements of-- what 50 00:02:25,040 --> 00:02:28,030 is it that regulates what? 51 00:02:28,030 --> 00:02:33,620 Now from this, we'll have some set of directed edges, 52 00:02:33,620 --> 00:02:35,840 because indeed, we know that there's 53 00:02:35,840 --> 00:02:38,500 going to be some transcription factor that will regulates 54 00:02:38,500 --> 00:02:39,440 some other protein. 55 00:02:39,440 --> 00:02:40,981 And what we want to know is are there 56 00:02:40,981 --> 00:02:43,440 patterns that occur more regularly than what 57 00:02:43,440 --> 00:02:46,720 you'd expect based on chance. 58 00:02:46,720 --> 00:02:48,664 Now auto regulation we found indeed 59 00:02:48,664 --> 00:02:50,830 appeared more regularly, or more frequently than you 60 00:02:50,830 --> 00:02:52,340 would expect by chance. 61 00:02:52,340 --> 00:02:54,650 And there are a limited number of other network motifs 62 00:02:54,650 --> 00:02:56,330 that have that property. 63 00:02:56,330 --> 00:02:58,720 And in particular, we'll kind of analyze this idea 64 00:02:58,720 --> 00:03:03,120 of the feed-forward loop. 65 00:03:03,120 --> 00:03:08,360 Now in the network that we kind of talked about a lot, 66 00:03:08,360 --> 00:03:16,720 there were around 400 genes or proteins, and then around 500 67 00:03:16,720 --> 00:03:19,440 observed edges. 68 00:03:19,440 --> 00:03:23,460 And this would be interactions or regulation. 69 00:03:28,670 --> 00:03:30,990 Now there's this idea of sparseness. 70 00:03:34,230 --> 00:03:36,770 Can somebody remind us maybe what this 71 00:03:36,770 --> 00:03:39,280 is supposed to tell us about? 72 00:03:39,280 --> 00:03:40,066 Yes. 73 00:03:40,066 --> 00:03:42,253 AUDIENCE: There should be roughly N 74 00:03:42,253 --> 00:03:44,930 squared in total edges. 75 00:03:44,930 --> 00:03:48,674 PROFESSOR: So there's N squared possible edges. 76 00:03:48,674 --> 00:03:51,804 AUDIENCE: If you just connected everything that you connected, 77 00:03:51,804 --> 00:03:57,384 and so N is about the order of E. So roughly, there's only 1 78 00:03:57,384 --> 00:03:58,694 out of 500-- 79 00:03:58,694 --> 00:04:00,110 PROFESSOR: And we should be clear, 80 00:04:00,110 --> 00:04:02,609 this N squared possible-- we might even want to add directed 81 00:04:02,609 --> 00:04:12,340 edges since we're-- and what we see is that the actual number 82 00:04:12,340 --> 00:04:16,130 of edges that we observe in this real network is actually around 83 00:04:16,130 --> 00:04:22,810 order N. So this sparseness, which is also this probability 84 00:04:22,810 --> 00:04:25,960 P-- if we're going to make a network somehow that has some 85 00:04:25,960 --> 00:04:28,460 similar property to the observed network, 86 00:04:28,460 --> 00:04:32,910 there's some probably P that an actual edge will appear. 87 00:04:32,910 --> 00:04:35,850 And this is given by the observed number 88 00:04:35,850 --> 00:04:39,967 of edges divided by the total possible number of edges, 89 00:04:39,967 --> 00:04:41,050 which is indeed N squared. 90 00:04:44,140 --> 00:04:46,350 And what you see is that, at least in this network, 91 00:04:46,350 --> 00:04:48,230 this P is much less than one. 92 00:04:51,049 --> 00:04:52,465 So this is what we mean by sparse. 93 00:04:56,560 --> 00:04:59,270 Now you can also think about the question 94 00:04:59,270 --> 00:05:06,720 of how many edges does a typical gene have emanating from it? 95 00:05:06,720 --> 00:05:09,360 Well, you can see that it's around one. 96 00:05:09,360 --> 00:05:11,490 Of course, each edge connects two things, 97 00:05:11,490 --> 00:05:13,690 so if you were to say on average, 98 00:05:13,690 --> 00:05:17,860 each gene has of one edge going out, and one edge going in. 99 00:05:17,860 --> 00:05:19,375 Of course, there might be a reason 100 00:05:19,375 --> 00:05:23,720 to believe that these averages are not as-- 101 00:05:23,720 --> 00:05:25,040 well they can be misleading. 102 00:05:25,040 --> 00:05:26,765 And why might the average be misleading? 103 00:05:29,525 --> 00:05:30,025 Yes. 104 00:05:30,025 --> 00:05:32,070 AUDIENCE: The distribution for heavy tails. 105 00:05:32,070 --> 00:05:33,020 PROFESSOR: Right, it's going to be 106 00:05:33,020 --> 00:05:35,561 a distribution with heavy tails, in particular on which side? 107 00:05:41,240 --> 00:05:42,810 So the average is always the average, 108 00:05:42,810 --> 00:05:46,770 but I guess the question is there 109 00:05:46,770 --> 00:05:49,350 are going to be some proteins, or some genes with many 110 00:05:49,350 --> 00:05:52,500 of these outgoing edges. 111 00:05:52,500 --> 00:05:55,530 And more generally, do you expect 112 00:05:55,530 --> 00:06:00,580 that-- there's a natural limitation in all this. 113 00:06:00,580 --> 00:06:02,050 Part of the value of this approach 114 00:06:02,050 --> 00:06:05,170 is that we're abstracting away from a lot of the microscopic 115 00:06:05,170 --> 00:06:06,254 or the biological details. 116 00:06:06,254 --> 00:06:08,753 But every now and then it's good to go in and think about it 117 00:06:08,753 --> 00:06:09,340 a little bit. 118 00:06:09,340 --> 00:06:12,680 So there's a good reason you'd expect many proteins to not 119 00:06:12,680 --> 00:06:15,150 have any outgoing edges, and why would that be? 120 00:06:20,450 --> 00:06:21,150 Yes. 121 00:06:21,150 --> 00:06:23,630 AUDIENCE: For example, a detector protein, 122 00:06:23,630 --> 00:06:26,029 that only evolved one specific function or another. 123 00:06:26,029 --> 00:06:27,570 PROFESSOR: So there are some proteins 124 00:06:27,570 --> 00:06:30,050 that have rather specific functions, you might say. 125 00:06:30,050 --> 00:06:31,130 And I think that's true. 126 00:06:31,130 --> 00:06:31,790 I think that's part of it. 127 00:06:31,790 --> 00:06:33,206 But there's maybe something that's 128 00:06:33,206 --> 00:06:35,630 maybe even a little bit more general that's 129 00:06:35,630 --> 00:06:36,650 worth pointing out here. 130 00:06:36,650 --> 00:06:37,150 Yeah. 131 00:06:37,150 --> 00:06:39,358 AUDIENCE: Anything that's not a transcription factor. 132 00:06:39,358 --> 00:06:42,220 PROFESSOR: Anything that's not a transcription factor, right. 133 00:06:42,220 --> 00:06:44,550 We say transcription factor, we don't ever really quite 134 00:06:44,550 --> 00:06:45,110 specify. 135 00:06:45,110 --> 00:06:46,800 But what it means is that it's something 136 00:06:46,800 --> 00:06:48,530 that can affect the transcription of other things. 137 00:06:48,530 --> 00:06:50,532 So we're talking about the function of it 138 00:06:50,532 --> 00:06:51,906 when we say transcription factor. 139 00:06:51,906 --> 00:06:54,980 And a majority of the proteins in any genome 140 00:06:54,980 --> 00:06:56,670 are not transcription factors. 141 00:06:56,670 --> 00:07:01,240 What that means is that they, to first order, cannot, 142 00:07:01,240 --> 00:07:05,470 at least directly influence the transcription of other genes. 143 00:07:05,470 --> 00:07:09,100 So this is a reflection of this power law distribution 144 00:07:09,100 --> 00:07:10,210 that we observe. 145 00:07:10,210 --> 00:07:12,740 And so you could argue well maybe not a surprise 146 00:07:12,740 --> 00:07:14,882 that this outgoing edge distribution is power law, 147 00:07:14,882 --> 00:07:17,230 because we know that there are some transcription factors that 148 00:07:17,230 --> 00:07:19,229 control many things, and there are many proteins 149 00:07:19,229 --> 00:07:22,299 they don't control the transcription 150 00:07:22,299 --> 00:07:23,590 of any other proteins directly. 151 00:07:26,280 --> 00:07:29,890 But at least it's just useful to know 152 00:07:29,890 --> 00:07:32,060 what the properties of this thing are on average 153 00:07:32,060 --> 00:07:34,810 even though, for the outgoing edges, 154 00:07:34,810 --> 00:07:36,610 the average is a little bit dangerous. 155 00:07:36,610 --> 00:07:39,450 Because it's really that most proteins don't 156 00:07:39,450 --> 00:07:42,010 have any outgoing edges, and then some have many. 157 00:07:46,014 --> 00:07:47,680 All right so this is this probability P. 158 00:07:47,680 --> 00:07:50,790 And this is going to be useful, because this P will 159 00:07:50,790 --> 00:07:52,350 appear when we're trying to construct 160 00:07:52,350 --> 00:07:53,266 these random networks. 161 00:07:55,654 --> 00:07:57,070 So what we're going to do is we're 162 00:07:57,070 --> 00:08:02,670 going to ask how frequently or how many of a given subgraph 163 00:08:02,670 --> 00:08:05,840 you expect to appear in this larger network 164 00:08:05,840 --> 00:08:06,590 that we have here? 165 00:08:09,710 --> 00:08:17,310 And we're going to characterize each of these subgraphs 166 00:08:17,310 --> 00:08:19,425 by two properties. 167 00:08:25,120 --> 00:08:29,720 And in particular, if we're going to analyze some smaller 168 00:08:29,720 --> 00:08:31,310 graph, we just have to keep track 169 00:08:31,310 --> 00:08:37,020 of how many nodes are in the subgraph, 170 00:08:37,020 --> 00:08:40,059 and how many edges are in the subgraph. 171 00:08:52,710 --> 00:08:55,820 So for example, if we have auto regulation, 172 00:08:55,820 --> 00:08:58,670 then we're just talking about little n equal to one, 173 00:08:58,670 --> 00:09:00,490 little g equal to one. 174 00:09:00,490 --> 00:09:04,699 Whereas in the case of this feed-forward loop, 175 00:09:04,699 --> 00:09:06,240 what is little n and what's little g? 176 00:09:19,720 --> 00:09:23,030 Well we can count now. 177 00:09:23,030 --> 00:09:27,311 Here n is equal to three, one, two, three, and g 178 00:09:27,311 --> 00:09:28,319 is also equal to three. 179 00:09:28,319 --> 00:09:29,860 And we're going to find that actually 180 00:09:29,860 --> 00:09:32,390 the fact that these two numbers are equal 181 00:09:32,390 --> 00:09:35,610 is somehow very relevant in thinking 182 00:09:35,610 --> 00:09:37,760 about the dynamics of these networks later. 183 00:09:42,100 --> 00:09:45,950 In this framework, when I just draw an arrow 184 00:09:45,950 --> 00:09:48,710 in the context of a generic subgraph, 185 00:09:48,710 --> 00:09:53,690 am I necessarily trying to say that this is up regulation 186 00:09:53,690 --> 00:09:55,557 of x up regulating y? 187 00:09:55,557 --> 00:09:57,260 No. 188 00:09:57,260 --> 00:10:00,206 So this is a bit confusing because depending 189 00:10:00,206 --> 00:10:02,080 on the context, sometimes the arrows actually 190 00:10:02,080 --> 00:10:04,540 do mean up regulation, sometimes they just mean regulate. 191 00:10:04,540 --> 00:10:06,790 And in this case, where we're talking about subgraphs, 192 00:10:06,790 --> 00:10:09,710 we're just saying that x regulates y 193 00:10:09,710 --> 00:10:11,380 in one way or another. 194 00:10:11,380 --> 00:10:13,880 This is also how we're going to write 195 00:10:13,880 --> 00:10:16,120 the so-called coherent type one feed-forward loop, 196 00:10:16,120 --> 00:10:20,850 but for right now this is just a generic feed-forward loop. 197 00:10:20,850 --> 00:10:21,594 Yes. 198 00:10:21,594 --> 00:10:23,490 AUDIENCE: Regulate means positive regulation? 199 00:10:23,490 --> 00:10:24,115 PROFESSOR: Yes. 200 00:10:26,319 --> 00:10:26,985 We say activate. 201 00:10:33,800 --> 00:10:36,130 So the way that we think about is we ask, 202 00:10:36,130 --> 00:10:43,232 what's the expected number of some subgraph G? 203 00:10:43,232 --> 00:10:45,440 And indeed what we're going to be doing for right now 204 00:10:45,440 --> 00:10:50,670 is assuming this Erdos-Renyi random network. 205 00:10:50,670 --> 00:10:53,300 Now what we're told is that this is going to look something 206 00:10:53,300 --> 00:10:55,000 like the following. 207 00:11:05,490 --> 00:11:10,045 could somebody explain one of these three terms? 208 00:11:16,690 --> 00:11:17,740 Yes. 209 00:11:17,740 --> 00:11:20,680 AUDIENCE: Well you have to select edges, 210 00:11:20,680 --> 00:11:22,150 and you have choose them correctly. 211 00:11:22,150 --> 00:11:25,805 So for each one, there's a chance that [INAUDIBLE]. 212 00:11:25,805 --> 00:11:27,680 PROFESSOR: So for here what we're going to do 213 00:11:27,680 --> 00:11:32,050 is, for example in this context, we'll say, 214 00:11:32,050 --> 00:11:34,090 we're going to choose these three. 215 00:11:34,090 --> 00:11:38,430 And now the question is, we have to put in three edges 216 00:11:38,430 --> 00:11:41,710 as well to connect those nodes, and each one of them 217 00:11:41,710 --> 00:11:47,450 has some probability P of actually somehow appearing. 218 00:11:47,450 --> 00:11:50,050 Because this is what we're keeping 219 00:11:50,050 --> 00:11:53,140 constant from the original network. 220 00:11:53,140 --> 00:11:55,670 So we're assuming that we have this Erdos-Renyi network 221 00:11:55,670 --> 00:11:59,000 with the same number, say roughly 400 nodes, 222 00:11:59,000 --> 00:12:03,140 and then what we're going to do is grab maybe three of them 223 00:12:03,140 --> 00:12:05,760 and ask, all right, what's the probability that we 224 00:12:05,760 --> 00:12:08,044 get these three actual edges? 225 00:12:08,044 --> 00:12:08,960 So you get P to the g. 226 00:12:11,650 --> 00:12:14,260 Now where does this term come from? 227 00:12:22,236 --> 00:12:22,735 Yes. 228 00:12:22,735 --> 00:12:24,610 AUDIENCE: Selecting a node. 229 00:12:24,610 --> 00:12:27,030 PROFESSOR: So we're going to be selecting N nodes. 230 00:12:27,030 --> 00:12:30,080 We're assuming that this N is much larger. 231 00:12:30,080 --> 00:12:32,400 We're assuming that we have a big network, 232 00:12:32,400 --> 00:12:35,374 so it's much larger than the size of the subgraph 233 00:12:35,374 --> 00:12:36,790 we're looking at, so we don't have 234 00:12:36,790 --> 00:12:39,780 to think about n times n minus one, n minus two, and so forth. 235 00:12:42,910 --> 00:12:46,160 And then there's this factor a here as well, 236 00:12:46,160 --> 00:12:50,870 which, depending on how you do your counting-- 237 00:12:50,870 --> 00:12:55,220 this is a little bit tricky, but what was a again? 238 00:12:55,220 --> 00:12:56,154 Yes. 239 00:12:56,154 --> 00:12:59,402 AUDIENCE: It's the number of ways to arrange the edges. 240 00:12:59,402 --> 00:13:00,885 It's a symmetry factor. 241 00:13:00,885 --> 00:13:02,510 PROFESSOR: Yes, it's a symmetry factor, 242 00:13:02,510 --> 00:13:09,050 it's a way of-- there are multiple ways of looking 243 00:13:09,050 --> 00:13:10,160 at this. 244 00:13:10,160 --> 00:13:11,820 You could think about it as the number 245 00:13:11,820 --> 00:13:14,400 of ways of rearranging x, y, and z 246 00:13:14,400 --> 00:13:21,599 and having the same subgraph, the exact same one. 247 00:13:21,599 --> 00:13:23,140 In this case, there's actually no way 248 00:13:23,140 --> 00:13:25,835 to rearrange x, y, and z to have the same one. 249 00:13:25,835 --> 00:13:29,410 Because x occupies a special spot, 250 00:13:29,410 --> 00:13:31,900 y is indeed again a special spot. z is special. 251 00:13:31,900 --> 00:13:34,080 So there's no permutations that you 252 00:13:34,080 --> 00:13:35,740 can do to get the same thing. 253 00:13:35,740 --> 00:13:40,280 Whereas if you have this repressilator-- now here 254 00:13:40,280 --> 00:13:41,875 I'm just drawing this as an arrow, 255 00:13:41,875 --> 00:13:43,250 because again we're just thinking 256 00:13:43,250 --> 00:13:45,460 about the generic version of these things. 257 00:13:45,460 --> 00:13:48,840 So it's just when we have x, y, and z regulating each other. 258 00:13:48,840 --> 00:13:53,600 In this case, you can get the same network by rotating these 259 00:13:53,600 --> 00:13:54,410 x's, y's, and z's. 260 00:13:54,410 --> 00:13:56,160 So in this case, you get a equal to three. 261 00:14:00,570 --> 00:14:02,820 For pretty much all the conclusions 262 00:14:02,820 --> 00:14:06,280 we're going to talk about, these factors of one, two, three 263 00:14:06,280 --> 00:14:07,900 don't actually end up being relevant. 264 00:14:07,900 --> 00:14:10,530 But it's good to know that they indeed exist. 265 00:14:15,080 --> 00:14:25,960 So this is fine, but it's useful to express this in another way. 266 00:14:25,960 --> 00:14:32,070 In particular, we can always define this lambda, 267 00:14:32,070 --> 00:14:37,290 which is E/N, as the mean number of incoming edges 268 00:14:37,290 --> 00:14:40,120 or the mean number of outgoing edges. 269 00:14:40,120 --> 00:14:44,850 And with this, we can express this guy 270 00:14:44,850 --> 00:14:47,510 in a way that is surprisingly informative. 271 00:15:04,360 --> 00:15:07,260 Nothing happened except that we just 272 00:15:07,260 --> 00:15:09,060 plugged this thing in here. 273 00:15:09,060 --> 00:15:11,151 But by doing, we see something that's 274 00:15:11,151 --> 00:15:13,650 kind of interesting, which is that there's reason to believe 275 00:15:13,650 --> 00:15:17,890 that for many of these networks, this lambda, this mean number 276 00:15:17,890 --> 00:15:21,632 of incoming edges, that lambda will be roughly 277 00:15:21,632 --> 00:15:23,840 similar-- whether you're talking about a network that 278 00:15:23,840 --> 00:15:31,870 is 500 nodes large or 5,000 nodes large. 279 00:15:31,870 --> 00:15:33,820 And indeed in this case, it's around one. 280 00:15:33,820 --> 00:15:38,590 It's just over one. 281 00:15:38,590 --> 00:15:44,230 So that means that when we think about the number of subgraphs 282 00:15:44,230 --> 00:15:47,210 that will be in this large network, 283 00:15:47,210 --> 00:15:51,870 it scales with the size of the overall network. 284 00:15:51,870 --> 00:15:54,110 We had this little n minus little g. 285 00:15:56,670 --> 00:16:00,990 And in particular, in cases when you're analyzing a subgraph 286 00:16:00,990 --> 00:16:03,640 with the same number of nodes as edges, 287 00:16:03,640 --> 00:16:05,530 then you just get n to the 0, and it 288 00:16:05,530 --> 00:16:09,200 doesn't scale with a number. 289 00:16:09,200 --> 00:16:11,540 So for those, and indeed basically 290 00:16:11,540 --> 00:16:15,370 for all those subgraphs where little n is equal to little g-- 291 00:16:15,370 --> 00:16:19,770 then you expect of order one of those-- 292 00:16:19,770 --> 00:16:22,280 if lambda is around one, then you 293 00:16:22,280 --> 00:16:25,480 expect of order one of those to appear in the network. 294 00:16:25,480 --> 00:16:30,370 And so from a very simple standpoint, the networks, 295 00:16:30,370 --> 00:16:33,497 like the feed-forward loop that we see that is a network motif, 296 00:16:33,497 --> 00:16:35,330 the expectation is that in a random network, 297 00:16:35,330 --> 00:16:37,500 you would get around one, maybe two. 298 00:16:37,500 --> 00:16:41,310 Whereas if you see many of them, dozens, then it's 299 00:16:41,310 --> 00:16:42,340 indeed a network motif. 300 00:16:47,840 --> 00:16:49,590 Are there any questions about how 301 00:16:49,590 --> 00:16:52,410 that appeared in the chapter or the argument there? 302 00:17:07,260 --> 00:17:13,910 So indeed, we can actually just then say, 303 00:17:13,910 --> 00:17:17,220 for the feed-forward loop, we can just 304 00:17:17,220 --> 00:17:22,440 go ahead and ask how many were observed in E. coli, 305 00:17:22,440 --> 00:17:26,530 this network that was actually observed? 306 00:17:26,530 --> 00:17:31,910 And this was 42 I believe. 307 00:17:31,910 --> 00:17:35,230 Whereas if you do this analysis for the Erdos-Renyi network, 308 00:17:35,230 --> 00:17:39,710 you get 1.7 plus or minus 1.3. 309 00:17:39,710 --> 00:17:41,422 Because these things appear randomly, 310 00:17:41,422 --> 00:17:42,880 they should be Poisson distributed. 311 00:17:46,950 --> 00:17:50,409 So you expect of order one of them 312 00:17:50,409 --> 00:17:52,450 to appear in a random network with this same kind 313 00:17:52,450 --> 00:17:54,200 of sparseness, the same number of edges. 314 00:17:54,200 --> 00:17:56,200 But we actually observe this much larger number. 315 00:17:56,200 --> 00:17:58,610 So then you can say, all right, this 316 00:17:58,610 --> 00:18:03,450 is evidence for the feed-forwad loop being a network motif. 317 00:18:03,450 --> 00:18:06,770 That for some reason, this subgraph 318 00:18:06,770 --> 00:18:08,150 appears more frequently than what 319 00:18:08,150 --> 00:18:09,640 you'd expect based on genes. 320 00:18:12,560 --> 00:18:15,100 Of course, we alluded to this on the end of class 321 00:18:15,100 --> 00:18:17,810 on Tuesday, that maybe this Erdos-Renyi network is not 322 00:18:17,810 --> 00:18:21,200 the proper null model or null network to be using. 323 00:18:21,200 --> 00:18:23,666 And maybe we should use one of these degree-preserving 324 00:18:23,666 --> 00:18:24,166 networks. 325 00:18:28,700 --> 00:18:33,040 So maybe we should try to preserve more the properties 326 00:18:33,040 --> 00:18:34,850 of the original network. 327 00:18:34,850 --> 00:18:42,492 And So can because somebody say a little bit of what 328 00:18:42,492 --> 00:18:43,700 we mean by degree-preserving? 329 00:18:46,950 --> 00:18:49,600 There's an element that our null model here already preserves 330 00:18:49,600 --> 00:18:52,110 something about the degree. 331 00:18:52,110 --> 00:18:54,530 It preserves the means. 332 00:18:54,530 --> 00:18:57,890 So it's not just that we picked up some random null model, 333 00:18:57,890 --> 00:18:59,720 some random ER network. 334 00:18:59,720 --> 00:19:03,140 So what is it that we want to keep 335 00:19:03,140 --> 00:19:07,210 track of in this degree-preserving network? 336 00:19:07,210 --> 00:19:09,195 I saw a hand over there, but I'm not trying 337 00:19:09,195 --> 00:19:10,320 to call on people randomly. 338 00:19:10,320 --> 00:19:12,410 Although I'm going to start in the second half 339 00:19:12,410 --> 00:19:14,569 of the semester, just after drop date. 340 00:19:14,569 --> 00:19:16,066 [LAUGHTER] 341 00:19:21,270 --> 00:19:24,080 So we're going to preserve not only 342 00:19:24,080 --> 00:19:27,450 the mean of the incoming and outgoing edges, 343 00:19:27,450 --> 00:19:30,120 but also the actual degree distribution. 344 00:19:30,120 --> 00:19:32,080 In a very concrete way, we can actually 345 00:19:32,080 --> 00:19:34,610 just say that each node actually does maintain 346 00:19:34,610 --> 00:19:38,300 the exact same number of edges. 347 00:19:38,300 --> 00:19:42,890 So in particular, here we say that all nodes 348 00:19:42,890 --> 00:19:49,556 maintain their degree distribution 349 00:19:49,556 --> 00:19:54,574 or maintain number of incoming and outgoing. 350 00:20:03,260 --> 00:20:05,786 And there was a simple algorithm for doing that. 351 00:20:05,786 --> 00:20:07,160 If you recall, what you can do is 352 00:20:07,160 --> 00:20:11,710 you can just take two edges randomly and just swap 353 00:20:11,710 --> 00:20:13,080 the locations. 354 00:20:13,080 --> 00:20:14,940 And you do that many, many times, 355 00:20:14,940 --> 00:20:19,290 and you end up maintaining both the incoming and the outgoing 356 00:20:19,290 --> 00:20:20,410 number of edges. 357 00:20:23,350 --> 00:20:26,440 And if you do this analysis on a degree-preserving random 358 00:20:26,440 --> 00:20:31,060 network, you get a seven plus or minus five. 359 00:20:31,060 --> 00:20:35,030 So this makes a big difference. 360 00:20:35,030 --> 00:20:38,590 So if, for example, the experimentally-observed network 361 00:20:38,590 --> 00:20:41,370 had one of these feed-forward loops, then what you'd see 362 00:20:41,370 --> 00:20:44,036 is that actually, comparing to the Erdos-Renyi, 363 00:20:44,036 --> 00:20:46,410 you would have said, oh well that that's a network motif. 364 00:20:46,410 --> 00:20:48,243 Whereas comparing to this degree-preserving, 365 00:20:48,243 --> 00:20:50,680 you would have said it's not. 366 00:20:50,680 --> 00:20:51,929 Yes. 367 00:20:51,929 --> 00:20:54,220 AUDIENCE: I don't know why I haven't asked this before, 368 00:20:54,220 --> 00:20:58,475 but is it also true that this degree-preserving thing is 369 00:20:58,475 --> 00:21:00,016 roughly Poisson in terms of-- I mean, 370 00:21:00,016 --> 00:21:02,560 should we expect deviations always? 371 00:21:02,560 --> 00:21:05,790 PROFESSOR: Yeah, it's close. 372 00:21:05,790 --> 00:21:10,850 But I think it ends up not being quite. 373 00:21:10,850 --> 00:21:13,510 But it is close. 374 00:21:13,510 --> 00:21:15,510 AUDIENCE: So is the entire transcription network 375 00:21:15,510 --> 00:21:18,810 for E. coli? 376 00:21:18,810 --> 00:21:22,870 PROFESSOR: So I think that it is, certainly now-- 377 00:21:22,870 --> 00:21:26,710 well you'll notice that here there are 400 genes. 378 00:21:26,710 --> 00:21:29,935 How many genes does E. coli have, anybody? 379 00:21:33,860 --> 00:21:35,950 A few thousand. 380 00:21:35,950 --> 00:21:39,957 So the network that we analyzed in that original paper 381 00:21:39,957 --> 00:21:42,040 was not the full transcription network of E. coli. 382 00:21:46,351 --> 00:21:48,746 AUDIENCE: How do people-- how do figure out 383 00:21:48,746 --> 00:21:50,183 the whole transcription network? 384 00:21:50,183 --> 00:21:51,810 It actually sounds pretty hard. 385 00:21:51,810 --> 00:21:53,768 PROFESSOR: Well figuring out and any part of it 386 00:21:53,768 --> 00:21:56,940 is actually hard in some ways. 387 00:21:56,940 --> 00:21:58,440 The way that they actually annotated 388 00:21:58,440 --> 00:22:02,380 this particular network, I'm not sure. 389 00:22:02,380 --> 00:22:05,840 I mean what kind of date would you 390 00:22:05,840 --> 00:22:07,620 need in order to get at this? 391 00:22:07,620 --> 00:22:12,160 Does anybody have any-- I mean, if I asked you to do this 392 00:22:12,160 --> 00:22:13,510 in your lab, what would you do? 393 00:22:26,119 --> 00:22:28,160 So you could actually use a computational program 394 00:22:28,160 --> 00:22:32,720 to try to actually estimate binding affinities 395 00:22:32,720 --> 00:22:37,030 of these proteins to the DNA. 396 00:22:37,030 --> 00:22:38,660 And these days actually experimentally 397 00:22:38,660 --> 00:22:42,360 you can actually just measure for the entire proteome 398 00:22:42,360 --> 00:22:46,427 basically, just the affinity of binding to different promoters. 399 00:22:46,427 --> 00:22:48,010 Of course that doesn't prove that it's 400 00:22:48,010 --> 00:22:52,150 going to regulate expression, but that at least points you 401 00:22:52,150 --> 00:22:53,619 in the right direction. 402 00:22:53,619 --> 00:22:55,160 Then you could actually, if you want, 403 00:22:55,160 --> 00:22:58,910 you could just experimentally go and put 404 00:22:58,910 --> 00:23:00,910 this protein on an inducible promoter and just 405 00:23:00,910 --> 00:23:04,300 see if it does regulate expression. 406 00:23:04,300 --> 00:23:07,050 At this stage, for something like E. coli, 407 00:23:07,050 --> 00:23:11,390 we have collections of strains where 408 00:23:11,390 --> 00:23:14,640 every gene has been removed. 409 00:23:14,640 --> 00:23:17,760 We have collections where every gene has been tagged. 410 00:23:17,760 --> 00:23:21,350 And of course, when I say every, this means that it was tried 411 00:23:21,350 --> 00:23:24,030 to make it for every and then of course if it's an essential 412 00:23:24,030 --> 00:23:26,110 gene you can't remove it. 413 00:23:26,110 --> 00:23:26,677 And 414 00:23:26,677 --> 00:23:29,010 In some cases it's hard to attack a fluorescent protein, 415 00:23:29,010 --> 00:23:30,170 and so forth. 416 00:23:30,170 --> 00:23:32,420 But there are collections both E. coli 417 00:23:32,420 --> 00:23:37,014 and for budding yeast where this has been done. 418 00:23:40,950 --> 00:23:42,010 Any other questions? 419 00:23:47,550 --> 00:23:50,910 Can somebody say why it might be-- 420 00:23:50,910 --> 00:23:52,540 is this a surprise that this number is 421 00:23:52,540 --> 00:23:53,540 larger than this number? 422 00:23:58,010 --> 00:24:00,760 And in particular, would the degree-preserving random 423 00:24:00,760 --> 00:24:04,600 network have a larger expectation for every subgraph? 424 00:24:07,730 --> 00:24:08,955 No. 425 00:24:08,955 --> 00:24:10,830 But in particular, for the feed-forward loop, 426 00:24:10,830 --> 00:24:15,160 can hear somebody say why we should have expected 427 00:24:15,160 --> 00:24:17,240 that the degree-preserving would have a larger 428 00:24:17,240 --> 00:24:19,045 number than the-- yeah. 429 00:24:19,045 --> 00:24:22,510 AUDIENCE: All the measures have one outgoing edge, 430 00:24:22,510 --> 00:24:26,470 and so [INAUDIBLE] distribution towards lower numbers 431 00:24:26,470 --> 00:24:27,955 of outgoing edges. 432 00:24:27,955 --> 00:24:33,160 And so you would expect more from forward loops. 433 00:24:36,320 --> 00:24:39,042 PROFESSOR: I think that the explanation had 434 00:24:39,042 --> 00:24:40,500 the right flavor, but I think there 435 00:24:40,500 --> 00:24:45,450 were two inversions in there that-- like a not and a not 436 00:24:45,450 --> 00:24:50,880 turned into a-- Incidentally, this is a non-sequitur, 437 00:24:50,880 --> 00:24:52,370 but this happened to me once. 438 00:24:52,370 --> 00:24:55,790 The airport in San Francisco-- I was going to the airport, 439 00:24:55,790 --> 00:24:57,984 I got the wrong airline in my head. 440 00:24:57,984 --> 00:24:59,650 So I thought I was on the wrong airline, 441 00:24:59,650 --> 00:25:03,920 so I went to the wrong terminal, but then it turned out 442 00:25:03,920 --> 00:25:06,590 that I also was wrong about which airline was in which 443 00:25:06,590 --> 00:25:09,110 terminal, so then I was actually the right terminal even 444 00:25:09,110 --> 00:25:10,902 though I had just made two mistakes. 445 00:25:10,902 --> 00:25:13,110 But you can't account on this happening all the time. 446 00:25:16,350 --> 00:25:18,680 But I think there were two things that were mixed up 447 00:25:18,680 --> 00:25:21,460 in that explanation. 448 00:25:21,460 --> 00:25:22,202 Yeah. 449 00:25:22,202 --> 00:25:23,743 AUDIENCE: For a transcription factor, 450 00:25:23,743 --> 00:25:27,986 it has many outgoing-- outcoming edges. 451 00:25:27,986 --> 00:25:30,110 And you just have to-- 452 00:25:30,110 --> 00:25:32,440 PROFESSOR: So in the actual network, 453 00:25:32,440 --> 00:25:37,230 There are some nodes with many outgoing edges. 454 00:25:37,230 --> 00:25:38,595 And then-- 455 00:25:38,595 --> 00:25:40,860 AUDIENCE: You just need to have another line between. 456 00:25:40,860 --> 00:25:41,860 PROFESSOR: That's right. 457 00:25:41,860 --> 00:25:43,800 You somehow just have to add one more edge. 458 00:25:43,800 --> 00:25:45,780 Because x actually has two outgoing edges. 459 00:25:48,529 --> 00:25:50,320 So there's a sense of the feed-forward loop 460 00:25:50,320 --> 00:25:53,030 here-- you can think about x being some transcription 461 00:25:53,030 --> 00:25:53,840 factor. 462 00:25:53,840 --> 00:25:58,260 And then what you need is just to get-- x might 463 00:25:58,260 --> 00:26:00,100 have many, many outgoing edges. 464 00:26:00,100 --> 00:26:02,100 And so to get a feed-forward loop, what you need 465 00:26:02,100 --> 00:26:06,424 is you need for one of those genes that 466 00:26:06,424 --> 00:26:08,340 are targeted to just target another one that's 467 00:26:08,340 --> 00:26:09,790 in that network. 468 00:26:09,790 --> 00:26:12,830 So if you have x that's regulating one00, 469 00:26:12,830 --> 00:26:17,570 then that actually that presents many opportunities 470 00:26:17,570 --> 00:26:19,217 to generate feed-forward loops. 471 00:26:19,217 --> 00:26:20,678 Yes. 472 00:26:20,678 --> 00:26:23,600 AUDIENCE: At the same time z, it's just going in. 473 00:26:23,600 --> 00:26:28,957 So wouldn't that make the [INAUDIBLE]? 474 00:26:28,957 --> 00:26:31,890 Is that why there's more ingoing edges than outgoing edges? 475 00:26:31,890 --> 00:26:34,223 PROFESSOR: Now this is a problem with verbal arguments-- 476 00:26:34,223 --> 00:26:35,400 you can construct anything. 477 00:26:35,400 --> 00:26:38,880 And indeed, I would say that this is an example. 478 00:26:38,880 --> 00:26:41,450 What we said is that the distribution of incoming edges 479 00:26:41,450 --> 00:26:44,510 is roughly kind of similar to an ER network in the sense 480 00:26:44,510 --> 00:26:47,210 that if the mean is one, then sometimes you 481 00:26:47,210 --> 00:26:48,760 get 0, sometimes one, sometimes two. 482 00:26:48,760 --> 00:26:50,680 And they're all kind of reasonable. 483 00:26:50,680 --> 00:26:54,470 So in that sense, I'd say this z node is not 484 00:26:54,470 --> 00:26:57,980 so unusual from the standpoint of degree-preserving network. 485 00:26:57,980 --> 00:27:02,102 If z had one00 incoming edges, then it's 486 00:27:02,102 --> 00:27:03,560 certainly true what you're saying-- 487 00:27:03,560 --> 00:27:06,110 that the degree-preserving would then have fewer. 488 00:27:14,900 --> 00:27:15,810 All right. 489 00:27:15,810 --> 00:27:18,077 So this is the basic argument for why 490 00:27:18,077 --> 00:27:19,827 you might go and look at what the function 491 00:27:19,827 --> 00:27:21,243 of the feed-forward loop might be. 492 00:27:21,243 --> 00:27:25,240 I just want to say a few things about this original paper 493 00:27:25,240 --> 00:27:26,960 that Uri published. 494 00:27:26,960 --> 00:27:31,960 So it's in Science in 2002. 495 00:27:31,960 --> 00:27:36,130 "Network motifs: Simple Building Blocks of Complex Networks." 496 00:27:36,130 --> 00:27:37,130 All right. 497 00:27:37,130 --> 00:27:39,102 So the authors did indeed analyze both the E. 498 00:27:39,102 --> 00:27:41,060 coli and the yeast transcription network. 499 00:27:41,060 --> 00:27:43,256 But they also analyzed a number of other networks 500 00:27:43,256 --> 00:27:44,630 to look at these networks motifs. 501 00:27:44,630 --> 00:27:49,490 So they also analyzed neurons from C. elegans, the worm, 502 00:27:49,490 --> 00:27:52,111 where the connectome has been known for several decades now. 503 00:27:52,111 --> 00:27:54,360 And again, they found that feed-forward loops appeared 504 00:27:54,360 --> 00:27:56,480 more frequently than what would be expected, 505 00:27:56,480 --> 00:28:00,660 based on the known model of degree preserving. 506 00:28:00,660 --> 00:28:02,590 And that's encouraging is that saying, oh 507 00:28:02,590 --> 00:28:05,160 maybe feed-forward loops really are somehow 508 00:28:05,160 --> 00:28:07,460 preserving some-- they're performing 509 00:28:07,460 --> 00:28:12,090 some useful information-processing task. 510 00:28:12,090 --> 00:28:14,320 Of course, you always have to worry-- there's also 511 00:28:14,320 --> 00:28:15,790 the spatial arrangement. 512 00:28:15,790 --> 00:28:17,290 You can worry about a lot of things. 513 00:28:17,290 --> 00:28:18,950 But that's encouraging. 514 00:28:18,950 --> 00:28:21,830 He also analyzed food webs, where in that case 515 00:28:21,830 --> 00:28:24,620 feed-forward loops were not a network motif, 516 00:28:24,620 --> 00:28:27,890 but other things were, So that's interesting. 517 00:28:27,890 --> 00:28:31,870 He analyzed the design of electronic circuits, 518 00:28:31,870 --> 00:28:34,160 a forward logic chip. 519 00:28:34,160 --> 00:28:35,270 I don't know that is. 520 00:28:35,270 --> 00:28:37,030 But then also the worldwide web, it's 521 00:28:37,030 --> 00:28:38,830 another network people love to analyze. 522 00:28:38,830 --> 00:28:41,250 And indeed, he saw some other patterns. 523 00:28:41,250 --> 00:28:43,540 And the idea is that in each of these contexts, 524 00:28:43,540 --> 00:28:45,200 the network motifs are different, 525 00:28:45,200 --> 00:28:48,390 depending upon the microscopic structure that's leading to it, 526 00:28:48,390 --> 00:28:52,960 or the function that it's maybe evolving towards, or whatnot. 527 00:28:52,960 --> 00:28:55,420 So it's a way of getting insight into the properties 528 00:28:55,420 --> 00:28:56,852 of these complex networks. 529 00:29:05,540 --> 00:29:08,644 Are there any questions about these network-- 530 00:29:08,644 --> 00:29:10,310 the global network structures, before we 531 00:29:10,310 --> 00:29:12,185 get into the feed-forward loop in particular? 532 00:29:17,530 --> 00:29:20,010 So first I want to just go ahead and do 533 00:29:20,010 --> 00:29:21,940 a few of our little concept questions. 534 00:29:21,940 --> 00:29:25,754 Just because you have the cards, and I 535 00:29:25,754 --> 00:29:27,170 think that the chapter is actually 536 00:29:27,170 --> 00:29:29,940 pretty nice in the sense of you can 537 00:29:29,940 --> 00:29:34,240 read it, and get a clear sense of what's going on. 538 00:29:34,240 --> 00:29:36,590 But let's start by just considering 539 00:29:36,590 --> 00:29:40,230 this feed-forward loop, which is this coherent type 1. 540 00:29:40,230 --> 00:29:43,050 So now the arrows actually mean activating. 541 00:29:43,050 --> 00:29:47,890 So we have X going to Y. Now it's going to be going to a Z. 542 00:29:47,890 --> 00:29:50,640 But we have to remember that now that there are two inputs, 543 00:29:50,640 --> 00:29:52,680 we do have to specify how the inputs are 544 00:29:52,680 --> 00:29:54,944 going to be combined. 545 00:29:54,944 --> 00:29:56,360 And for now what we'll do is we'll 546 00:29:56,360 --> 00:29:57,568 assume that it's an AND gate. 547 00:30:01,930 --> 00:30:13,360 And that goes to Z. As always, we're going to have to think. 548 00:30:13,360 --> 00:30:17,060 There's some signal x and signal y that come in here. 549 00:30:17,060 --> 00:30:19,850 In many, many cases, these transcription factors 550 00:30:19,850 --> 00:30:22,130 in addition to being regulated by another, 551 00:30:22,130 --> 00:30:24,010 say transcription factor, may also 552 00:30:24,010 --> 00:30:27,760 be responsive to some signal. 553 00:30:27,760 --> 00:30:32,880 And there was a nice example of this in Uri's book 554 00:30:32,880 --> 00:30:37,900 which was how E. Coli decide whether to make 555 00:30:37,900 --> 00:30:39,800 the suite of proteins that are required 556 00:30:39,800 --> 00:30:45,350 to digest the carbon source arabinose, the sugar arabinose. 557 00:30:45,350 --> 00:30:48,050 But for now, let's just think about this. 558 00:30:48,050 --> 00:30:52,120 And we want to just make sure that we remember. 559 00:30:52,120 --> 00:30:54,494 And once again, it's not that you should necessarily 560 00:30:54,494 --> 00:30:55,410 memorize these things. 561 00:30:55,410 --> 00:30:57,860 But after having seen the argument once or twice, 562 00:30:57,860 --> 00:31:00,020 you should be able to reconstruct 563 00:31:00,020 --> 00:31:02,320 all of these things. 564 00:31:02,320 --> 00:31:05,160 So I claimed that somewhere in here there's 565 00:31:05,160 --> 00:31:06,410 a sign sensitive delay. 566 00:31:16,960 --> 00:31:20,570 Now the question is, in which direction is there a delay. 567 00:31:27,274 --> 00:31:28,940 And so it's going to be some combination 568 00:31:28,940 --> 00:31:30,120 of on and off perhaps. 569 00:31:42,900 --> 00:31:46,230 And check means that it's a delay in that direction. 570 00:31:46,230 --> 00:31:53,630 Well actually we should just from nothing there-- 571 00:31:53,630 --> 00:31:55,910 and D is don't know. 572 00:31:55,910 --> 00:31:57,750 AUDIENCE: In that direction you mean? 573 00:31:57,750 --> 00:32:02,569 PROFESSOR: That there's a-- this means that there's a sign. 574 00:32:02,569 --> 00:32:03,110 That's right. 575 00:32:03,110 --> 00:32:07,010 So this would be going from off to on, so turning on. 576 00:32:07,010 --> 00:32:11,310 So this is turning on, as compared to turning off. 577 00:32:11,310 --> 00:32:15,810 And we're looking at this is delay. 578 00:32:15,810 --> 00:32:20,010 We're talking about, this is in response to Sx 579 00:32:20,010 --> 00:32:28,710 changing concentration of Z. 580 00:32:28,710 --> 00:32:31,706 Any questions about what I'm referring to in this? 581 00:32:31,706 --> 00:32:33,615 AUDIENCE: Is there any Sy? 582 00:32:33,615 --> 00:32:34,240 PROFESSOR: Yes. 583 00:32:34,240 --> 00:32:37,860 Good question I like that right Sy is present. 584 00:32:46,140 --> 00:32:47,056 AUDIENCE: [INAUDIBLE]? 585 00:32:49,082 --> 00:32:49,790 PROFESSOR: Right. 586 00:32:49,790 --> 00:32:53,820 So this is compared to simple regulation, or i.e. 587 00:32:53,820 --> 00:32:56,570 does the concentration of Z immediately 588 00:32:56,570 --> 00:32:59,855 start to change after this Sx changes? 589 00:32:59,855 --> 00:33:05,330 It goes from either 0 to 1, or 1 to 0. 590 00:33:05,330 --> 00:33:07,574 AUDIENCE: So simple regulation in this case 591 00:33:07,574 --> 00:33:09,930 would be erase that line between X and Y? 592 00:33:09,930 --> 00:33:12,520 PROFESSOR: Yes. 593 00:33:12,520 --> 00:33:15,197 And make the AND gate a-- 594 00:33:15,197 --> 00:33:16,280 AUDIENCE: Not an AND gate? 595 00:33:16,280 --> 00:33:19,870 PROFESSOR: Not an AND gate, exactly, yeah. 596 00:33:19,870 --> 00:33:22,280 We're comparing to just if X is just directly regulating 597 00:33:22,280 --> 00:33:26,090 Z. Because what we want to know is, 598 00:33:26,090 --> 00:33:31,750 I mean what might a function of the feed-forward loop be. 599 00:33:31,750 --> 00:33:35,129 So I'll give you 15 seconds to think through this. 600 00:33:35,129 --> 00:33:37,420 Once again, it's not that you should have memorized it. 601 00:33:44,480 --> 00:33:46,230 I don't want anybody saying that they just 602 00:33:46,230 --> 00:33:47,438 couldn't read my handwriting. 603 00:33:52,190 --> 00:33:55,520 AUDIENCE: So this is for the second case we're asking? 604 00:33:55,520 --> 00:33:57,160 PROFESSOR: I'm sorry. 605 00:33:57,160 --> 00:34:02,380 So this is-- I'm asking about for this feed-forward loop, 606 00:34:02,380 --> 00:34:04,290 the coherent type 1 with an AND gate. 607 00:34:04,290 --> 00:34:07,530 And I'm comparing, I'm asking is there 608 00:34:07,530 --> 00:34:13,230 a delay in either turning on or turning off, 609 00:34:13,230 --> 00:34:18,590 as compared to the simple regulation of X regulating Z. 610 00:34:18,590 --> 00:34:20,830 And of course, this is my [INAUDIBLE] Sx. 611 00:34:24,630 --> 00:34:26,425 And we assume that X is already present. 612 00:34:32,840 --> 00:34:35,139 Do you need more time? 613 00:34:35,139 --> 00:34:35,889 All right, ready? 614 00:34:35,889 --> 00:34:39,580 Three, two, one. 615 00:34:39,580 --> 00:34:40,080 OK. 616 00:34:40,080 --> 00:34:45,730 We got a clear majority of the group actually is saying C. 617 00:34:45,730 --> 00:34:53,016 And so we can get at this kind of visually, graphically. 618 00:34:53,016 --> 00:34:55,010 I really like graphs. 619 00:34:55,010 --> 00:34:57,970 I think they're much nicer than equations. 620 00:34:57,970 --> 00:35:00,600 Different people can agree or disagree. 621 00:35:00,600 --> 00:35:01,570 but that's my-- 622 00:35:05,049 --> 00:35:08,080 The idea is that we have Sx. 623 00:35:08,080 --> 00:35:10,370 It starts out off and say turns on. 624 00:35:13,060 --> 00:35:16,930 So if we think about the X star, X was always around. 625 00:35:16,930 --> 00:35:20,250 So means that X star immediately-- 626 00:35:20,250 --> 00:35:23,450 so the signal immediately changes X into X 627 00:35:23,450 --> 00:35:26,690 star, the active version. 628 00:35:26,690 --> 00:35:30,000 Now Y, and this is why we can even 629 00:35:30,000 --> 00:35:33,080 say Y star, because the signal Y is always there. 630 00:35:33,080 --> 00:35:34,450 It starts our here. 631 00:35:34,450 --> 00:35:35,750 It immediately gets the signal. 632 00:35:35,750 --> 00:35:38,370 So it starts coming up. 633 00:35:41,410 --> 00:35:44,525 But of course, this is an AND gate. 634 00:35:44,525 --> 00:35:45,900 Which means that you need to have 635 00:35:45,900 --> 00:35:47,950 both active Y and active X in order 636 00:35:47,950 --> 00:35:50,700 to start getting expression of Z. 637 00:35:50,700 --> 00:35:58,480 So we have if we look at Z, there's 638 00:35:58,480 --> 00:36:03,700 something threshold at which is Y starts allowing 639 00:36:03,700 --> 00:36:06,170 for expression of Z. So just because we have active X, 640 00:36:06,170 --> 00:36:08,545 doesn't mean that we immediately start getting expression 641 00:36:08,545 --> 00:36:10,530 of Z. We need Y as well. 642 00:36:10,530 --> 00:36:11,490 So this comes up. 643 00:36:16,560 --> 00:36:19,400 However, when the signal here goes away, 644 00:36:19,400 --> 00:36:20,830 X star immediately goes away. 645 00:36:20,830 --> 00:36:23,970 This is the separation of timescale idea. 646 00:36:23,970 --> 00:36:26,930 This is just a binding of a small molecule or so. 647 00:36:26,930 --> 00:36:32,050 What that means is that Y star-- is there a delay on Y star? 648 00:36:36,730 --> 00:36:38,100 We're going to do a verbal. 649 00:36:38,100 --> 00:36:41,567 Is there a delay before Y star just starts coming down? 650 00:36:41,567 --> 00:36:43,650 So the question, it's going to decay exponentially 651 00:36:43,650 --> 00:36:44,370 once it starts going. 652 00:36:44,370 --> 00:36:45,786 Does it a start going immediately, 653 00:36:45,786 --> 00:36:47,940 or is there a delay? 654 00:36:47,940 --> 00:36:50,750 So the question is, is there a delay before the exponential 655 00:36:50,750 --> 00:36:52,430 fall off of Y star. 656 00:36:52,430 --> 00:36:55,630 You're going to say yes or no, ready, three, two, one. 657 00:36:55,630 --> 00:36:56,877 AUDIENCE: No. 658 00:36:56,877 --> 00:36:57,710 PROFESSOR: No delay. 659 00:36:57,710 --> 00:36:58,210 Great. 660 00:37:01,550 --> 00:37:06,470 And indeed over here it's the same thing, no delay 661 00:37:06,470 --> 00:37:09,420 because of the AND gate. 662 00:37:09,420 --> 00:37:13,370 Expression of Z requires both X star and Y star. 663 00:37:13,370 --> 00:37:18,670 So although Y star still there, since it's an AND gate, 664 00:37:18,670 --> 00:37:19,470 Z goes down. 665 00:37:24,350 --> 00:37:28,740 That means that in this case we have a sign sensitive delay 666 00:37:28,740 --> 00:37:36,164 for turning on Z, but not for turning off Z. 667 00:37:36,164 --> 00:37:37,580 And of course, this can be useful, 668 00:37:37,580 --> 00:37:39,560 depending upon the costs and benefits 669 00:37:39,560 --> 00:37:42,930 of having false positives and false negatives in the signal. 670 00:37:46,744 --> 00:37:51,020 If this AND gate were switched to an OR gate, 671 00:37:51,020 --> 00:37:53,690 how does this thing change? 672 00:37:53,690 --> 00:37:56,460 I'm going to give you 10 seconds. 673 00:37:56,460 --> 00:37:57,160 All right. 674 00:37:57,160 --> 00:38:00,090 So, question is, if I convert this to an OR gate, 675 00:38:00,090 --> 00:38:01,470 does it change anything or not. 676 00:38:15,810 --> 00:38:18,760 Do you need more time? 677 00:38:18,760 --> 00:38:23,030 Ready, three two one. 678 00:38:23,030 --> 00:38:25,210 Now we got a lot of B's. 679 00:38:25,210 --> 00:38:26,250 Great. 680 00:38:26,250 --> 00:38:29,570 So in this case it's coherent type 1, feed-forward loop 681 00:38:29,570 --> 00:38:31,490 with an OR gate. 682 00:38:31,490 --> 00:38:33,010 I'm not going to go over the logic. 683 00:38:33,010 --> 00:38:36,300 But I encourage you, if you're confused by this, 684 00:38:36,300 --> 00:38:39,560 just make sure that you can reconstruct the argument. 685 00:38:39,560 --> 00:38:42,147 From my standpoint, these equations I mean, 686 00:38:42,147 --> 00:38:43,230 it's good to do equations. 687 00:38:43,230 --> 00:38:46,030 But it's more important to be able to understand 688 00:38:46,030 --> 00:38:46,925 the logic here. 689 00:38:46,925 --> 00:38:48,219 Did you have a question? 690 00:38:48,219 --> 00:38:48,802 AUDIENCE: Yes. 691 00:38:48,802 --> 00:38:51,257 So how is it easy to prove experimentally 692 00:38:51,257 --> 00:38:53,660 what kind of gate there is? 693 00:38:53,660 --> 00:38:54,750 PROFESSOR: Yes. 694 00:38:54,750 --> 00:38:56,820 So the idea is that in many cases 695 00:38:56,820 --> 00:39:00,240 you can put X on an inducible promoter. 696 00:39:00,240 --> 00:39:02,040 You could put Y on an inducible promoter. 697 00:39:02,040 --> 00:39:03,790 So you can-- just some small molecule will 698 00:39:03,790 --> 00:39:06,720 allow you to control these. 699 00:39:06,720 --> 00:39:10,660 And then you can measure, say fluorescence, on Z. 700 00:39:10,660 --> 00:39:12,077 And that's the most direct things. 701 00:39:12,077 --> 00:39:13,659 It's experimentally doing it yourself. 702 00:39:13,659 --> 00:39:15,840 Of course, much of the data that you see the chapter 703 00:39:15,840 --> 00:39:18,680 is kind of just looking at the fluorescent Z as a function 704 00:39:18,680 --> 00:39:21,560 of the signals that you put in. 705 00:39:21,560 --> 00:39:23,910 And that's certainly an argument for it. 706 00:39:23,910 --> 00:39:25,880 And then ultimately what you'd like 707 00:39:25,880 --> 00:39:27,990 is to measure things in multiple different ways, 708 00:39:27,990 --> 00:39:29,420 confirm that it's all consistent. 709 00:39:34,110 --> 00:39:35,610 Any other questions about this idea 710 00:39:35,610 --> 00:39:37,070 of sign sensitive delay element? 711 00:39:41,043 --> 00:39:41,543 Yeah? 712 00:39:41,543 --> 00:39:42,209 AUDIENCE: Sorry. 713 00:39:42,209 --> 00:39:47,010 So among these 42-- these that are this type, 714 00:39:47,010 --> 00:39:50,489 is it possible to look at the actual genes, 715 00:39:50,489 --> 00:39:52,477 and see if that interrelationship actually 716 00:39:52,477 --> 00:39:54,000 makes sense? 717 00:39:54,000 --> 00:39:55,900 PROFESSOR: That's a good question. 718 00:39:55,900 --> 00:39:58,925 So if you look at across both E. coli and yeast, what 719 00:39:58,925 --> 00:40:02,750 you see is that of the feed-forward loops, about half 720 00:40:02,750 --> 00:40:06,940 of them are coherent type 1, which 721 00:40:06,940 --> 00:40:10,549 is one of the eight possible kinds of feed-forward loops. 722 00:40:10,549 --> 00:40:12,340 And so what you're asking is, in this case, 723 00:40:12,340 --> 00:40:14,200 so let's say there are 20 coherent type 1, 724 00:40:14,200 --> 00:40:16,060 how many of them, what fraction of them 725 00:40:16,060 --> 00:40:17,820 does this all makes sense? 726 00:40:17,820 --> 00:40:19,630 And it's a good question. 727 00:40:19,630 --> 00:40:21,940 I don't know. 728 00:40:21,940 --> 00:40:23,192 I haven't looked at it. 729 00:40:23,192 --> 00:40:24,900 Because it's always dangerous, of course, 730 00:40:24,900 --> 00:40:30,150 that we find one example of the 20 where it kind of makes 731 00:40:30,150 --> 00:40:31,070 sense conceptually. 732 00:40:31,070 --> 00:40:32,945 And then we go and we test it experimentally, 733 00:40:32,945 --> 00:40:35,030 and see that it all works. 734 00:40:35,030 --> 00:40:36,690 And then we're convinced. 735 00:40:36,690 --> 00:40:38,530 But you're pointing out that maybe we 736 00:40:38,530 --> 00:40:40,305 shouldn't be convinced yet. 737 00:40:40,305 --> 00:40:41,700 AUDIENCE: But I'm just curious. 738 00:40:41,700 --> 00:40:44,955 If you're proposing a functional kind of explanation, and if 739 00:40:44,955 --> 00:40:45,970 know what the genes are. 740 00:40:45,970 --> 00:40:46,970 PROFESSOR: That's right. 741 00:40:46,970 --> 00:40:50,460 You should be able to go and see whether it somehow make sense. 742 00:40:50,460 --> 00:40:56,010 And of course makes sense is always a slippery concept. 743 00:40:56,010 --> 00:40:59,300 Because we can always-- it's not that this radically 744 00:40:59,300 --> 00:41:01,710 changes the logic. 745 00:41:01,710 --> 00:41:03,430 And then in any given circumstance 746 00:41:03,430 --> 00:41:06,150 you may be say, oh well. 747 00:41:06,150 --> 00:41:09,689 You can kind of wave your arms and make up 748 00:41:09,689 --> 00:41:11,230 a story where it kind of makes sense. 749 00:41:11,230 --> 00:41:14,324 But then the only way to really feel comfortable 750 00:41:14,324 --> 00:41:16,740 with it or not, is for you yourself to go on look at them, 751 00:41:16,740 --> 00:41:19,690 and see how comfortable you are with each of those arguments. 752 00:41:19,690 --> 00:41:21,588 And I haven't actually done that. 753 00:41:27,030 --> 00:41:28,970 So one more question in this regard. 754 00:41:28,970 --> 00:41:29,470 All right. 755 00:41:29,470 --> 00:41:34,870 So let's imagine that instead of thinking about changes in Sx, 756 00:41:34,870 --> 00:41:36,540 with Sy present, let's now flip things. 757 00:41:36,540 --> 00:41:39,560 Let's assume that Sx is present and ask 758 00:41:39,560 --> 00:41:42,040 about Sy turning on and off. 759 00:41:47,020 --> 00:41:51,710 Again with the AND gate, I want to know 760 00:41:51,710 --> 00:41:55,160 in which direction is there a delay when 761 00:41:55,160 --> 00:41:56,690 turning either on or off. 762 00:41:56,690 --> 00:41:59,060 Now we're talking about with Sy turning on or off. 763 00:42:01,975 --> 00:42:03,600 Does everybody understand the question? 764 00:42:06,810 --> 00:42:08,565 I'll give you 10 seconds to make sure. 765 00:42:38,880 --> 00:42:40,910 Do need more time? 766 00:42:40,910 --> 00:42:42,050 Let's go ahead and vote. 767 00:42:42,050 --> 00:42:46,671 Ready, three, two, one. 768 00:42:46,671 --> 00:42:47,800 All right. 769 00:42:47,800 --> 00:42:50,605 OK, so I'd say now it's pretty overwhelming 770 00:42:50,605 --> 00:42:54,140 that the group again agrees that now it'll be A. 771 00:42:54,140 --> 00:43:00,480 So if we have Sx equal to 1, and Sy is changing, then 772 00:43:00,480 --> 00:43:05,030 in this case we don't get any of these delays. 773 00:43:05,030 --> 00:43:09,500 So there's sort of immediate changes in Z as Sy changes. 774 00:43:09,500 --> 00:43:12,015 And that's because this is an AND gate. 775 00:43:12,015 --> 00:43:14,140 If X is already there that means that we've already 776 00:43:14,140 --> 00:43:16,060 satisfied this half of it. 777 00:43:16,060 --> 00:43:18,550 So then we're just reduced to simple regulation. 778 00:43:18,550 --> 00:43:20,907 This is just equivalent to Y regulating Z. 779 00:43:20,907 --> 00:43:23,240 So there are no delays either turning on or turning off. 780 00:43:38,200 --> 00:43:40,020 So what you read about from Uri's book 781 00:43:40,020 --> 00:43:44,037 is what is that the coherent type 1 is perhaps 782 00:43:44,037 --> 00:43:46,120 the most common of the feed-forward loops observed 783 00:43:46,120 --> 00:43:47,750 in these transportation networks. 784 00:43:47,750 --> 00:43:50,140 The other of the feed-forward loops 785 00:43:50,140 --> 00:43:52,540 that is distinctly overrepresented 786 00:43:52,540 --> 00:43:54,090 is this incoherent type 1. 787 00:43:56,772 --> 00:43:59,580 So it's very similar, with the exception that now what we have 788 00:43:59,580 --> 00:44:08,300 is X activating Y, but now Y is going to be repressing Z. 789 00:44:08,300 --> 00:44:16,172 And we have X again activating Z. 790 00:44:16,172 --> 00:44:17,880 And we're going to use an AND gate again. 791 00:44:26,460 --> 00:44:34,140 Its edge going to Z. For me, I find it sometimes a little bit 792 00:44:34,140 --> 00:44:38,130 confusing to think about a repression and an AND gate. 793 00:44:38,130 --> 00:44:41,540 So it is useful to make sure that we kind of understand 794 00:44:41,540 --> 00:44:43,380 the logic of all these things. 795 00:44:43,380 --> 00:44:47,260 So if we have say X star, Y star, 796 00:44:47,260 --> 00:44:53,890 and we can just make sure this is 797 00:44:53,890 --> 00:44:57,380 absence or presence, digital approximation of each 798 00:44:57,380 --> 00:44:58,470 of these things. 799 00:44:58,470 --> 00:45:07,671 And the question is, if we have expression of Z. 800 00:45:07,671 --> 00:45:09,170 Now the way to just think about this 801 00:45:09,170 --> 00:45:13,170 is that this guy is equivalent to kind of inverting 802 00:45:13,170 --> 00:45:17,812 the sign of Y star. 803 00:45:17,812 --> 00:45:19,020 And then we have an AND gate. 804 00:45:19,020 --> 00:45:20,630 So this is a 0,1. 805 00:45:20,630 --> 00:45:23,500 That's not an AND. 806 00:45:23,500 --> 00:45:26,800 Well 0 is enough to give us a 0. 807 00:45:26,800 --> 00:45:27,940 So here we get activation. 808 00:45:27,940 --> 00:45:29,374 Here we don't. 809 00:45:38,740 --> 00:45:41,740 And so we can do a similar kind of story of what we did here. 810 00:45:41,740 --> 00:45:44,620 Except that now instead of Y being an activator, 811 00:45:44,620 --> 00:45:49,000 it's now a repressor. 812 00:45:49,000 --> 00:45:51,670 And again, we're going to think about what happens 813 00:45:51,670 --> 00:45:53,498 with the signal coming in. 814 00:46:11,200 --> 00:46:13,900 Is any difference up to this point? 815 00:46:18,856 --> 00:46:19,730 Let's think about it. 816 00:46:19,730 --> 00:46:21,104 Everything but this for a second. 817 00:46:21,104 --> 00:46:21,690 All right. 818 00:46:21,690 --> 00:46:23,250 So this is a case where we already 819 00:46:23,250 --> 00:46:28,930 have signal Y that's allowing, say, the Y repressor to bind. 820 00:46:28,930 --> 00:46:30,300 Then we make Sx appear. 821 00:46:35,270 --> 00:46:37,110 I want to know verbally, yes or no. 822 00:46:39,900 --> 00:46:43,680 Do I have to draw something new up to this point here? 823 00:46:43,680 --> 00:46:46,330 Ready, so what do I want to say? 824 00:46:46,330 --> 00:46:49,540 Is there a change from this drawing up to this point? 825 00:46:49,540 --> 00:46:52,485 Ready, three, two, one. 826 00:46:52,485 --> 00:46:53,790 AUDIENCE: Yes. 827 00:46:53,790 --> 00:46:54,570 PROFESSOR: Yes. 828 00:46:54,570 --> 00:46:55,310 All right. 829 00:46:55,310 --> 00:46:58,720 And that's because actually Z starts coming up at this point. 830 00:46:58,720 --> 00:47:01,960 It's very, very nerve-wracking, these quizzes, I know. 831 00:47:06,180 --> 00:47:09,360 The idea is that here Y is now a repressor. 832 00:47:09,360 --> 00:47:11,860 So it's not that you need Y in order to get expression of Z. 833 00:47:11,860 --> 00:47:14,680 Is that once you have Y star, then you 834 00:47:14,680 --> 00:47:23,000 stop getting expression of Z. So it looks like maybe I'll 835 00:47:23,000 --> 00:47:26,860 make a-- so in this case everything's the same here. 836 00:47:26,860 --> 00:47:32,720 Except that in this case you start getting Z coming up. 837 00:47:32,720 --> 00:47:36,400 And then once Y gets up to a sufficiently high level, 838 00:47:36,400 --> 00:47:39,300 it starts repressing. 839 00:47:39,300 --> 00:47:43,750 In that case it might do something like this. 840 00:47:47,120 --> 00:47:50,180 Now, depending upon the strength of that repression, 841 00:47:50,180 --> 00:47:52,680 this curve might look different. 842 00:47:52,680 --> 00:47:54,640 Because it could come all the way down to 0. 843 00:47:54,640 --> 00:47:59,400 Depending on if it's a very effective repressor. 844 00:47:59,400 --> 00:48:02,105 And depending upon whether it's fully repressed or only 845 00:48:02,105 --> 00:48:03,980 partially repressed, you might think about it 846 00:48:03,980 --> 00:48:07,730 as either being a pulse generator, so you get some Z, 847 00:48:07,730 --> 00:48:09,970 and then it goes away. 848 00:48:09,970 --> 00:48:11,500 Or you could think about it as a way 849 00:48:11,500 --> 00:48:14,050 of increasing the rate at which you're 850 00:48:14,050 --> 00:48:15,980 able to turn this gene on. 851 00:48:15,980 --> 00:48:18,582 Because it's sort of like this negative autoregulation 852 00:48:18,582 --> 00:48:20,540 idea that initially you get lots of expression. 853 00:48:20,540 --> 00:48:23,020 And then later you stop getting as much. 854 00:48:23,020 --> 00:48:25,920 Of course, here you would get an overshoot. 855 00:48:25,920 --> 00:48:30,230 But maybe that's not all bad. 856 00:48:30,230 --> 00:48:32,955 So in this what you might say is this is a pulse generator. 857 00:48:38,440 --> 00:48:44,540 And this here is a way of making t on go down. 858 00:48:50,705 --> 00:48:52,330 Are there any questions about the logic 859 00:48:52,330 --> 00:48:57,088 of what happens in this incoherent type 1? 860 00:48:57,088 --> 00:48:57,588 Yes? 861 00:48:57,588 --> 00:48:59,580 AUDIENCE: Can you explain the t on? 862 00:48:59,580 --> 00:49:00,990 PROFESSOR: Sure. 863 00:49:00,990 --> 00:49:04,400 So maybe let's zoom in. 864 00:49:04,400 --> 00:49:09,940 And we can look at Z. So it kind of gets expressed. 865 00:49:09,940 --> 00:49:13,320 And then it represses like this. 866 00:49:13,320 --> 00:49:16,150 And then you always have to ask, well what do you mean by t on? 867 00:49:16,150 --> 00:49:18,110 And then we have is working definition, 868 00:49:18,110 --> 00:49:21,590 which is that we say t on is defined as there's 869 00:49:21,590 --> 00:49:24,960 some equilibrium concentration. 870 00:49:24,960 --> 00:49:28,410 So this is Z equilibrium. 871 00:49:28,410 --> 00:49:31,080 And we often define t on as the time in which you 872 00:49:31,080 --> 00:49:34,380 get half of that concentration. 873 00:49:34,380 --> 00:49:37,900 So what we do is we take half of that. 874 00:49:37,900 --> 00:49:39,915 And we say, where does this cross? 875 00:49:39,915 --> 00:49:41,420 It crosses right here. 876 00:49:41,420 --> 00:49:44,050 I maybe overdid my drawing. 877 00:49:44,050 --> 00:49:46,580 It's too good of a-- So t on, in this case, 878 00:49:46,580 --> 00:49:53,502 would be that time right there. 879 00:49:53,502 --> 00:49:54,960 Now of course you have to say, well 880 00:49:54,960 --> 00:49:57,330 what should we compare that to? 881 00:49:57,330 --> 00:50:00,789 And the comparison should be the t 882 00:50:00,789 --> 00:50:03,080 on that you would have had with just simple regulation. 883 00:50:03,080 --> 00:50:04,705 So that's based on the generation time. 884 00:50:04,705 --> 00:50:07,121 And you can actually see what the generation time is here. 885 00:50:07,121 --> 00:50:09,670 Because this thing in the absence of the repression 886 00:50:09,670 --> 00:50:14,410 would have done something like that. 887 00:50:14,410 --> 00:50:18,170 So this tells us that the simple regulation 888 00:50:18,170 --> 00:50:20,840 would have lead to something that looks like this. 889 00:50:20,840 --> 00:50:29,670 So you see the t on here, this is t on simple, 890 00:50:29,670 --> 00:50:32,140 is much larger than the t on that you actually get here. 891 00:50:39,180 --> 00:50:41,600 So from this argument there are-- 892 00:50:41,600 --> 00:50:45,480 we can now try to recapitulate or recall for ourselves 893 00:50:45,480 --> 00:50:51,305 the various strategies for increasing the rate of response 894 00:50:51,305 --> 00:50:51,805 to signals. 895 00:50:55,200 --> 00:51:02,270 So we have, we can think about, you want to decrease t on, 896 00:51:02,270 --> 00:51:03,710 and you want to decrease t off. 897 00:51:06,740 --> 00:51:10,780 And we want to think about maybe different strategies 898 00:51:10,780 --> 00:51:14,810 that we've encountered over the last few weeks. 899 00:51:14,810 --> 00:51:16,185 What were some of the strategies? 900 00:51:22,428 --> 00:51:22,928 Yes? 901 00:51:22,928 --> 00:51:25,042 AUDIENCE: Just having a higher degradation? 902 00:51:25,042 --> 00:51:26,750 PROFESSOR: All right, higher degradation. 903 00:51:26,750 --> 00:51:28,470 Right. 904 00:51:28,470 --> 00:51:34,385 So increase degradation, well maybe I'll 905 00:51:34,385 --> 00:51:35,510 just say decrease lifetime. 906 00:51:38,040 --> 00:51:39,470 Well it's the same thing. 907 00:51:39,470 --> 00:51:43,470 So decrease the protein lifetime. 908 00:51:43,470 --> 00:51:44,865 And what does that do for us? 909 00:51:49,110 --> 00:51:51,930 Does that decrease t on, or does it decrease t off? 910 00:51:55,594 --> 00:51:56,450 Both. 911 00:51:56,450 --> 00:51:56,950 All right. 912 00:51:56,950 --> 00:52:01,775 So this decreases t on, and it decreases t off. 913 00:52:01,775 --> 00:52:03,400 What were some of the other strategies? 914 00:52:06,641 --> 00:52:07,544 Yes? 915 00:52:07,544 --> 00:52:08,960 AUDIENCE: Negative autoregulation. 916 00:52:08,960 --> 00:52:10,370 PROFESSOR: Negative autoregulation. 917 00:52:10,370 --> 00:52:10,730 Great. 918 00:52:10,730 --> 00:52:11,938 And what does that do for us? 919 00:52:19,500 --> 00:52:25,925 AUDIENCE: I think it decreases t off and on also. 920 00:52:25,925 --> 00:52:26,800 PROFESSOR: All right. 921 00:52:26,800 --> 00:52:29,760 So let's do a vote. 922 00:52:29,760 --> 00:52:31,170 This is a good opportunity. 923 00:52:31,170 --> 00:52:33,911 This is like review for exams for you guys right now. 924 00:52:33,911 --> 00:52:34,410 All right. 925 00:52:34,410 --> 00:52:38,260 So negative autoregulation, does it decrease t on, 926 00:52:38,260 --> 00:52:41,700 t off, both, neither, or something or another? 927 00:52:41,700 --> 00:52:42,745 All right, eight seconds. 928 00:52:50,670 --> 00:52:53,505 Ready, three, two, one. 929 00:52:56,180 --> 00:52:56,680 All right. 930 00:52:56,680 --> 00:53:01,600 So we got many C's, but many other things as well. 931 00:53:01,600 --> 00:53:02,100 Right. 932 00:53:02,100 --> 00:53:06,249 But indeed it's only going to decrease t on, actually. 933 00:53:06,249 --> 00:53:08,790 And that's because remember, the negative autoregulation what 934 00:53:08,790 --> 00:53:12,860 it does, is initially, it makes a lot of this protein. 935 00:53:12,860 --> 00:53:15,540 And then once you hit the repression threshold, 936 00:53:15,540 --> 00:53:17,680 then it sort of represses itself. 937 00:53:17,680 --> 00:53:20,690 And so you are able to kind of rapidly get up to that level, 938 00:53:20,690 --> 00:53:22,530 and then you clamp it there. 939 00:53:22,530 --> 00:53:25,150 Whereas turning off that just means that you just 940 00:53:25,150 --> 00:53:26,600 tell to stop making it. 941 00:53:26,600 --> 00:53:29,650 So it's always going to then decay at the rate that 942 00:53:29,650 --> 00:53:32,630 is dictated by its effective lifetime, which 943 00:53:32,630 --> 00:53:34,770 is kind of either from the protein 944 00:53:34,770 --> 00:53:39,310 or from the actual degradation, or from the growth of cell. 945 00:53:39,310 --> 00:53:42,137 So this only decreases t on. 946 00:53:42,137 --> 00:53:44,220 And then indeed, we just learned about another one 947 00:53:44,220 --> 00:53:47,700 here, which was the incoherent, incoherent type 1 948 00:53:47,700 --> 00:53:51,320 feed-forward loop, with kind of modest amounts 949 00:53:51,320 --> 00:53:55,635 of repression, incomplete repression or so. 950 00:53:55,635 --> 00:53:56,760 And what does that do here? 951 00:54:00,770 --> 00:54:02,890 Did we actually even figure out what it did here? 952 00:54:09,930 --> 00:54:12,000 Oh, we maybe didn't say. 953 00:54:12,000 --> 00:54:16,630 Five seconds, again over here. 954 00:54:16,630 --> 00:54:20,590 What does it-- we've-- well I told you one half of it 955 00:54:20,590 --> 00:54:21,090 already. 956 00:54:21,090 --> 00:54:22,340 But what about the other half? 957 00:54:24,141 --> 00:54:24,640 All right. 958 00:54:37,190 --> 00:54:39,430 All right, ready? 959 00:54:39,430 --> 00:54:41,780 Incoherent type 1 feed-forward loop, what does it do? 960 00:54:41,780 --> 00:54:45,250 Ready, three, two, one. 961 00:54:45,250 --> 00:54:45,750 OK. 962 00:54:45,750 --> 00:54:49,440 We've got again, a bunch of C's. 963 00:54:49,440 --> 00:54:53,390 Indeed this is-- and of course, I'm 964 00:54:53,390 --> 00:54:55,520 using the same chart for the sign sensitive delay, 965 00:54:55,520 --> 00:54:58,820 and for the time to turn on turn off. 966 00:54:58,820 --> 00:55:00,790 So I hope that that doesn't confuse you. 967 00:55:00,790 --> 00:55:01,840 If it does, I'm sorry. 968 00:55:01,840 --> 00:55:02,340 All right. 969 00:55:02,340 --> 00:55:06,340 So this is, it decreases t on, but not t off. 970 00:55:06,340 --> 00:55:07,640 This is an AND gate. 971 00:55:07,640 --> 00:55:10,950 So you need both active X star and Y star. 972 00:55:10,950 --> 00:55:16,390 So the moment that you make Sx go away, 973 00:55:16,390 --> 00:55:19,229 then it's going to start-- oh wait. 974 00:55:19,229 --> 00:55:20,520 I'm explaining a different one. 975 00:55:20,520 --> 00:55:20,720 OK. 976 00:55:20,720 --> 00:55:21,220 Sorry. 977 00:55:21,220 --> 00:55:23,210 This is the time. 978 00:55:23,210 --> 00:55:28,440 So we're at Z. But yeah, it immediately starts going down. 979 00:55:28,440 --> 00:55:31,830 But at the same normal rate of effective lifetime. 980 00:55:35,710 --> 00:55:39,870 Many more ways to make a protein quickly, than to get rid of it 981 00:55:39,870 --> 00:55:40,370 quickly. 982 00:55:43,785 --> 00:55:45,910 Are there any questions about what we've said here? 983 00:55:55,460 --> 00:55:58,900 So while we're on the topic of kind of response times 984 00:55:58,900 --> 00:56:01,720 and so forth, it's important to remember 985 00:56:01,720 --> 00:56:04,650 that the characteristic time for all these things 986 00:56:04,650 --> 00:56:07,720 is kind of the generation time, or the protein lifetime. 987 00:56:07,720 --> 00:56:11,940 So these are ways of processing information over time scales 988 00:56:11,940 --> 00:56:14,820 that are kind of like minutes, maybe even 989 00:56:14,820 --> 00:56:16,650 tens of minutes, maybe hours. 990 00:56:16,650 --> 00:56:19,600 So it's rather slow. 991 00:56:19,600 --> 00:56:21,060 Now is that, in general. 992 00:56:21,060 --> 00:56:22,651 Going to be good enough for everything 993 00:56:22,651 --> 00:56:23,650 that a cell needs to do? 994 00:56:26,210 --> 00:56:27,390 No. 995 00:56:27,390 --> 00:56:31,210 So it's important to highlight that transcription is slow. 996 00:56:36,280 --> 00:56:39,601 So that means that transcription networks are going to be slow. 997 00:56:39,601 --> 00:56:41,100 And that's both because you actually 998 00:56:41,100 --> 00:56:43,220 have to do transcription and translation, and so forth. 999 00:56:43,220 --> 00:56:45,886 But also you just have to change the concentrations of proteins. 1000 00:56:48,520 --> 00:56:52,060 So if you need to kind of respond to things more rapidly, 1001 00:56:52,060 --> 00:56:53,570 what is it then you need to do? 1002 00:56:57,049 --> 00:56:58,409 AUDIENCE: Phosphorylate. 1003 00:56:58,409 --> 00:56:59,700 PROFESSOR: Phosphorylate, yeah. 1004 00:56:59,700 --> 00:57:03,180 It's all about phosphorylation, yes. 1005 00:57:03,180 --> 00:57:08,380 Indeed, phosphorylate-- so you need, if you want to be fast, 1006 00:57:08,380 --> 00:57:10,690 you can't be changing overall protein concentrations. 1007 00:57:10,690 --> 00:57:13,010 You have to change protein state. 1008 00:57:13,010 --> 00:57:16,120 Right, and phosphorylation is kind of the classic way 1009 00:57:16,120 --> 00:57:17,660 of doing that. 1010 00:57:17,660 --> 00:57:28,170 so I just want to highlight that for speed you need just 1011 00:57:28,170 --> 00:57:30,310 to do kind of protein networks. 1012 00:57:33,196 --> 00:57:34,570 So we're not actually going to be 1013 00:57:34,570 --> 00:57:39,520 reading the chapter analyzing these map kinase cascades, 1014 00:57:39,520 --> 00:57:41,394 and so forth. 1015 00:57:41,394 --> 00:57:43,060 But if you're interested in such things, 1016 00:57:43,060 --> 00:57:44,590 I very much encourage you do so. 1017 00:57:44,590 --> 00:57:48,640 It's also nice chapters, maybe not 1018 00:57:48,640 --> 00:57:51,100 as nice as the first four, which is part 1019 00:57:51,100 --> 00:57:52,600 of why we're not reading them. 1020 00:57:52,600 --> 00:57:54,774 But it's a very important insight, in the sense 1021 00:57:54,774 --> 00:57:57,190 that we've spent a lot of time talking about transcription 1022 00:57:57,190 --> 00:58:00,110 networks, just because there's a lot of, I think, 1023 00:58:00,110 --> 00:58:03,070 simple, beautiful things that you can say about them. 1024 00:58:03,070 --> 00:58:07,170 Whereas they are intrinsically limited in terms of speed. 1025 00:58:07,170 --> 00:58:10,110 So for much of what a cell needs to do, 1026 00:58:10,110 --> 00:58:13,330 it has to already have the proteins there. 1027 00:58:13,330 --> 00:58:17,190 And then you can take advantage of these rapid processes. 1028 00:58:17,190 --> 00:58:19,810 So we talked about Sx rapidly binding, 1029 00:58:19,810 --> 00:58:23,230 changing the state of X. From the standpoint of transcription 1030 00:58:23,230 --> 00:58:26,540 networks, we just draw this as a straight line. 1031 00:58:26,540 --> 00:58:27,420 It's rapid. 1032 00:58:27,420 --> 00:58:30,660 But what that's saying is that if you just 1033 00:58:30,660 --> 00:58:33,190 change states of proteins, then you 1034 00:58:33,190 --> 00:58:36,180 can do a lot of information processing rather rapidly. 1035 00:58:36,180 --> 00:58:39,520 And you don't have to do just a simple thing of Sx binding 1036 00:58:39,520 --> 00:58:42,780 X. You can also have proteins regulating each other, 1037 00:58:42,780 --> 00:58:46,400 and performing logic functions at the protein-only level. 1038 00:58:53,520 --> 00:58:55,430 What I want to do for the last 20 minutes 1039 00:58:55,430 --> 00:58:58,540 is say something about temporal programs 1040 00:58:58,540 --> 00:59:01,237 that can be implemented with sort of larger network motifs. 1041 00:59:01,237 --> 00:59:03,070 And in particular this is material basically 1042 00:59:03,070 --> 00:59:06,710 from chapter five of the book, which again we're 1043 00:59:06,710 --> 00:59:08,155 not to be reading. 1044 00:59:08,155 --> 00:59:09,730 I think it's again, it's beautiful 1045 00:59:09,730 --> 00:59:10,790 but it's really simple. 1046 00:59:10,790 --> 00:59:14,590 So I think that in 20 minutes we can cover it just fine. 1047 00:59:21,160 --> 00:59:26,370 So for many cases, for example, in the context of metabolic 1048 00:59:26,370 --> 00:59:36,210 pathways, it might be the case that you have some protein 1049 00:59:36,210 --> 00:59:37,330 we'll call them Z's. 1050 00:59:37,330 --> 00:59:42,130 So you'll have some protein Z1 that does something. 1051 00:59:42,130 --> 00:59:47,330 So that catalyzes-- so we might have some molecule one that's 1052 00:59:47,330 --> 00:59:50,220 converted into module two, by Z1, converted 1053 00:59:50,220 --> 00:59:53,420 into molecules three by Z2. 1054 00:59:57,764 --> 00:59:59,680 So many metabolic pathways have this structure 1055 00:59:59,680 --> 01:00:01,820 where there are a series of enzymes 1056 01:00:01,820 --> 01:00:06,720 that are doing something to the product of the previous enzyme. 1057 01:00:06,720 --> 01:00:11,000 Now the question is, let's say that this is some carbon source 1058 01:00:11,000 --> 01:00:12,390 and we didn't before. 1059 01:00:12,390 --> 01:00:16,889 But now it's appeared in our environment. 1060 01:00:16,889 --> 01:00:18,680 So what we would like is we'd like to start 1061 01:00:18,680 --> 01:00:24,390 digesting that carbon source. 1062 01:00:24,390 --> 01:00:27,740 Or in the flip side, maybe we have 1063 01:00:27,740 --> 01:00:31,177 to make some complex molecule or an amino acid or so. 1064 01:00:31,177 --> 01:00:33,510 And so then what we're doing is we're building something 1065 01:00:33,510 --> 01:00:36,350 up, coming down. 1066 01:00:36,350 --> 01:00:40,900 Now in either case, if before you weren't making these Z 1067 01:00:40,900 --> 01:00:47,310 proteins, but now you want them, a question is, 1068 01:00:47,310 --> 01:00:49,680 maybe you could just make them all at the same time. 1069 01:00:49,680 --> 01:00:52,650 But maybe it would be better to make some of them first, 1070 01:00:52,650 --> 01:00:53,640 and some of them later. 1071 01:00:56,060 --> 01:00:56,810 What do you think? 1072 01:00:59,764 --> 01:01:01,180 Let's say for the sake of argument 1073 01:01:01,180 --> 01:01:03,471 that you would want to have some first, and some later, 1074 01:01:03,471 --> 01:01:06,757 which ones would you want first? 1075 01:01:06,757 --> 01:01:08,340 AUDIENCE: The ones that you use first? 1076 01:01:08,340 --> 01:01:10,048 PROFESSOR: Yeah, the ones you need first. 1077 01:01:10,048 --> 01:01:14,755 So you'd maybe want to first have Z1, then Z2, et cetera. 1078 01:01:14,755 --> 01:01:17,440 It's a trivial statement, but you might not actually 1079 01:01:17,440 --> 01:01:18,680 think about it. 1080 01:01:18,680 --> 01:01:21,020 And the question is how might we be able to do this. 1081 01:01:25,180 --> 01:01:30,040 Well there's a very simple thing called a single input module. 1082 01:01:30,040 --> 01:01:32,800 The idea here is there's some transcription factor 1083 01:01:32,800 --> 01:01:36,320 X, which actually does this fabulous thing where 1084 01:01:36,320 --> 01:01:40,640 it creates all these guys. 1085 01:01:47,320 --> 01:01:54,930 Interestingly, this also often has autoregulation in order to, 1086 01:01:54,930 --> 01:01:57,300 for example, stabilize the concentration of it. 1087 01:01:57,300 --> 01:02:01,130 But the reason it's called a single input module is 1088 01:02:01,130 --> 01:02:06,890 because the network motif is saying not just that X makes 1089 01:02:06,890 --> 01:02:08,620 many Z's. 1090 01:02:08,620 --> 01:02:11,020 That actually you can't actually argue 1091 01:02:11,020 --> 01:02:14,470 that that's a network motif, from the standpoint 1092 01:02:14,470 --> 01:02:15,920 of a degree preserving network. 1093 01:02:15,920 --> 01:02:18,320 Because of course, this is just saying well 1094 01:02:18,320 --> 01:02:21,930 some nodes activate many other nodes. 1095 01:02:21,930 --> 01:02:24,210 And in a degree preserving network that's always 1096 01:02:24,210 --> 01:02:25,460 still going to be true, right? 1097 01:02:25,460 --> 01:02:28,680 But you can say that such a thing is a network motif, when 1098 01:02:28,680 --> 01:02:33,370 you say that these Z's are only regulated by X. 1099 01:02:33,370 --> 01:02:35,536 So that happens somehow more frequently 1100 01:02:35,536 --> 01:02:36,660 than what you would expect. 1101 01:02:45,304 --> 01:02:47,470 Although now that I just said that, I'm a little bit 1102 01:02:47,470 --> 01:02:51,890 worried that even the degree preserving would-- 1103 01:02:51,890 --> 01:02:54,300 I think you have to be a little more subtle in defining 1104 01:02:54,300 --> 01:02:55,650 your null model in that case. 1105 01:02:55,650 --> 01:02:58,530 But I'll just say that this happens 1106 01:02:58,530 --> 01:03:00,460 more frequently than you might expect, 1107 01:03:00,460 --> 01:03:03,830 which is that you have one transcription factor, 1108 01:03:03,830 --> 01:03:06,610 say activating many, many different proteins. 1109 01:03:06,610 --> 01:03:07,950 And this makes sense. 1110 01:03:07,950 --> 01:03:10,030 Because if all these Z's are involved 1111 01:03:10,030 --> 01:03:13,620 in the same metabolic program, then when you want Z1, 1112 01:03:13,620 --> 01:03:15,800 you also want Z2, and you also want Z3. 1113 01:03:15,800 --> 01:03:18,060 So this makes a lot of sense. 1114 01:03:18,060 --> 01:03:21,000 But what is a little bit less obvious perhaps, 1115 01:03:21,000 --> 01:03:27,400 is that it's possible to do this such that you first make one, 1116 01:03:27,400 --> 01:03:28,997 and then you make the other. 1117 01:03:28,997 --> 01:03:30,830 And the way that you can do this is just by, 1118 01:03:30,830 --> 01:03:35,580 you have different activation thresholds, K1, K2, et cetera, 1119 01:03:35,580 --> 01:03:39,000 up to Kn for each of these. 1120 01:03:39,000 --> 01:03:43,470 So then if X is turned on, so let's 1121 01:03:43,470 --> 01:03:46,020 say that you first see something. 1122 01:03:46,020 --> 01:03:48,980 So this you actually have to have X start at 0, 1123 01:03:48,980 --> 01:03:50,800 and then grow over time. 1124 01:03:50,800 --> 01:03:56,410 But then if you just have different thresholds, 1125 01:03:56,410 --> 01:03:59,060 the question is where should I draw K1, 1126 01:03:59,060 --> 01:04:02,760 and where should I draw-- Do I draw K1 1127 01:04:02,760 --> 01:04:07,110 the low position or the high position? 1128 01:04:07,110 --> 01:04:07,791 Low. 1129 01:04:07,791 --> 01:04:08,290 Perfect. 1130 01:04:08,290 --> 01:04:08,789 All right. 1131 01:04:08,789 --> 01:04:09,910 So we say K1. 1132 01:04:09,910 --> 01:04:11,250 Here's K2. 1133 01:04:11,250 --> 01:04:13,290 Here is Kn. 1134 01:04:13,290 --> 01:04:15,520 And then there might be some others in between. 1135 01:04:15,520 --> 01:04:19,830 So the idea is that X grows over time. 1136 01:04:19,830 --> 01:04:24,337 Then you first activate expression of gene one, 1137 01:04:24,337 --> 01:04:25,670 and then gene two, and so forth. 1138 01:04:25,670 --> 01:04:27,170 And then the proteins will naturally 1139 01:04:27,170 --> 01:04:28,580 appear in the proper order. 1140 01:04:28,580 --> 01:04:30,038 And there's actually beautiful data 1141 01:04:30,038 --> 01:04:33,714 in chapter five illustrating this in the context of our gene 1142 01:04:33,714 --> 01:04:34,255 biosynthesis. 1143 01:04:37,790 --> 01:04:42,600 So it's quite neat to see that it's not just-- of course, 1144 01:04:42,600 --> 01:04:44,240 it's easy to think up this idea. 1145 01:04:44,240 --> 01:04:45,000 And say, oh yeah. 1146 01:04:45,000 --> 01:04:46,220 Maybe the cell might want to do this. 1147 01:04:46,220 --> 01:04:47,595 But then it's quite cool when you 1148 01:04:47,595 --> 01:04:49,678 see that actually in some cases, the cell actually 1149 01:04:49,678 --> 01:04:50,534 really does do this. 1150 01:04:50,534 --> 01:04:53,075 And you can actually see that they're expressed sequentially, 1151 01:04:53,075 --> 01:04:56,810 in the same order as they appear in the biosynthetic pathway. 1152 01:05:02,750 --> 01:05:07,436 So this kind of gives you a warm, fuzzy feeling inside. 1153 01:05:07,436 --> 01:05:09,310 I'm not going to make you vote on whether you 1154 01:05:09,310 --> 01:05:10,393 have a warm fuzzy feeling. 1155 01:05:10,393 --> 01:05:11,560 But, yeah? 1156 01:05:11,560 --> 01:05:15,710 AUDIENCE: Could you also have just some sort of Z1 1157 01:05:15,710 --> 01:05:17,262 required for transcription? 1158 01:05:17,262 --> 01:05:18,090 PROFESSOR: Ah, yes. 1159 01:05:18,090 --> 01:05:21,694 So you could have a cascade in that way. 1160 01:05:21,694 --> 01:05:23,110 And that's a really good question. 1161 01:05:23,110 --> 01:05:24,630 That would work. 1162 01:05:24,630 --> 01:05:28,690 But there's a problem, which is that it's super slow. 1163 01:05:28,690 --> 01:05:30,489 Because there's a characteristic timescale 1164 01:05:30,489 --> 01:05:33,030 for each of these things, which is this cell generation time. 1165 01:05:33,030 --> 01:05:37,890 And here when I say you want it after the other, what 1166 01:05:37,890 --> 01:05:42,450 I'm saying is you might want it a few minutes after the other. 1167 01:05:42,450 --> 01:05:44,736 So in the context of development, in some cases 1168 01:05:44,736 --> 01:05:46,110 some things really are very slow. 1169 01:05:46,110 --> 01:05:48,090 Then that is actually what happens. 1170 01:05:48,090 --> 01:05:51,570 There's a long cascade of one activating two, activiating-- 1171 01:05:51,570 --> 01:05:54,127 But in the context of this, you really 1172 01:05:54,127 --> 01:05:56,460 want something that's just delayed by five minutes each, 1173 01:05:56,460 --> 01:05:58,920 or maybe even just a couple minutes each. 1174 01:05:58,920 --> 01:06:02,370 And in that case, because really the range over which you 1175 01:06:02,370 --> 01:06:06,365 can have this sort of delay like this, from the beginning 1176 01:06:06,365 --> 01:06:11,220 to the end, I mean this is still-- it might be one to two, 1177 01:06:11,220 --> 01:06:14,700 say cell generations/lifetimes. 1178 01:06:14,700 --> 01:06:17,124 So you just can't get much more of a dynamic range. 1179 01:06:17,124 --> 01:06:18,790 Otherwise you're going to be in trouble. 1180 01:06:18,790 --> 01:06:20,960 Because you can't have this be too close to the top. 1181 01:06:20,960 --> 01:06:23,190 Otherwise if you're a little bit off, you're off. 1182 01:06:23,190 --> 01:06:26,560 So we really maybe we should just even say one generation. 1183 01:06:26,560 --> 01:06:28,690 So that's kind of how much of a delay 1184 01:06:28,690 --> 01:06:31,150 you might reasonably be able to get from this mechanism. 1185 01:06:31,150 --> 01:06:32,586 And indeed, and that's as much as 1186 01:06:32,586 --> 01:06:34,210 you would want for something like this. 1187 01:06:38,650 --> 01:06:41,185 So this is great. 1188 01:06:41,185 --> 01:06:42,810 When I first read this, I was like, oh. 1189 01:06:42,810 --> 01:06:44,270 I was feeling it. 1190 01:06:44,270 --> 01:06:48,960 Now the question is, after this carbon source, or the need 1191 01:06:48,960 --> 01:06:52,250 to make our gene or whatnot, after it goes away, 1192 01:06:52,250 --> 01:06:55,920 then we'll stop making these proteins. 1193 01:06:55,920 --> 01:06:59,750 And the question is, is this what we call 1194 01:06:59,750 --> 01:07:07,880 a FIFO queue, or a LIFO queue? 1195 01:07:07,880 --> 01:07:09,540 LIFO, LIFO? 1196 01:07:09,540 --> 01:07:10,840 It's been a long time. 1197 01:07:10,840 --> 01:07:14,350 I have a lot of faces that are like, what are talking about? 1198 01:07:14,350 --> 01:07:23,160 So this is a First in, first out. 1199 01:07:23,160 --> 01:07:24,990 Have you guys really not-- you never 1200 01:07:24,990 --> 01:07:26,110 took any of these computer science classes 1201 01:07:26,110 --> 01:07:27,318 where they talked about this? 1202 01:07:27,318 --> 01:07:29,370 And this is a Last in, first out. 1203 01:07:32,640 --> 01:07:39,090 So just to be clear, what this means at the grocery store 1204 01:07:39,090 --> 01:07:42,740 is that a first in, first out, or a last in, in first out. 1205 01:07:42,740 --> 01:07:43,990 AUDIENCE: First in, first out. 1206 01:07:43,990 --> 01:07:44,880 PROFESSOR: It's a first in, first out. 1207 01:07:44,880 --> 01:07:45,380 Right? 1208 01:07:45,380 --> 01:07:48,536 If you get in line first, you get out first, hopefully. 1209 01:07:48,536 --> 01:07:49,910 And when that doesn't happen, you 1210 01:07:49,910 --> 01:07:51,650 get very annoyed, and so forth. 1211 01:07:51,650 --> 01:07:54,430 But last in, first out, this is for example 1212 01:07:54,430 --> 01:07:57,780 what happens in your inbox. 1213 01:07:57,780 --> 01:07:59,182 So you have a stack of paper. 1214 01:07:59,182 --> 01:08:00,640 People are giving you things you're 1215 01:08:00,640 --> 01:08:02,970 supposed to sign or fill out. 1216 01:08:02,970 --> 01:08:05,990 And the pile kind of comes up, and then you handle things 1217 01:08:05,990 --> 01:08:07,390 on top of the pile first. 1218 01:08:07,390 --> 01:08:09,170 So the things that get stuck at the bottom 1219 01:08:09,170 --> 01:08:10,420 you never get to them. 1220 01:08:10,420 --> 01:08:15,620 And that's because that's a last in, first out queue. 1221 01:08:15,620 --> 01:08:18,764 And so different, depending on-- well and in computer science, 1222 01:08:18,764 --> 01:08:20,180 then they can choose these things. 1223 01:08:20,180 --> 01:08:21,859 And it's relevant and so forth. 1224 01:08:21,859 --> 01:08:25,240 But there are many situations where this sort of idea 1225 01:08:25,240 --> 01:08:26,220 appears. 1226 01:08:26,220 --> 01:08:29,550 And so the question is, in the single input module, 1227 01:08:29,550 --> 01:08:33,130 do we have a first in, first out, or a last in, first 1228 01:08:33,130 --> 01:08:34,090 out queue? 1229 01:08:34,090 --> 01:08:37,020 I'll give you 15 seconds to think about this. 1230 01:08:37,020 --> 01:08:37,720 Yeah, question? 1231 01:08:37,720 --> 01:08:39,428 AUDIENCE: What do you mean by in and out? 1232 01:08:39,428 --> 01:08:41,149 PROFESSOR: So in and out, what I mean 1233 01:08:41,149 --> 01:08:46,779 is that the concentration of each of these Z's, 1234 01:08:46,779 --> 01:08:51,010 these guys they were produced in some order. 1235 01:08:51,010 --> 01:08:51,510 Right? 1236 01:08:51,510 --> 01:08:55,670 So first we started producing Z1, then Z2's and then so forth 1237 01:08:55,670 --> 01:08:57,279 up to Zn. 1238 01:08:57,279 --> 01:09:01,060 And what I want to know is what order will the concentration 1239 01:09:01,060 --> 01:09:02,530 kind of go away in? 1240 01:09:05,930 --> 01:09:10,340 And you might want to look at this figure. 1241 01:09:10,340 --> 01:09:12,354 Because it's going to be super useful. 1242 01:09:16,380 --> 01:09:19,609 Any other questions about what I-- all right, so in and out 1243 01:09:19,609 --> 01:09:22,615 refers to concentrations going up, and then going down. 1244 01:09:27,871 --> 01:09:28,870 Let's go ahead and vote. 1245 01:09:28,870 --> 01:09:31,390 Ready, three, two, one. 1246 01:09:35,270 --> 01:09:39,500 See, I mean people learned what FIFO and LIFO queues were. 1247 01:09:39,500 --> 01:09:42,390 And now already we can use it. 1248 01:09:42,390 --> 01:09:45,540 So this is a last in, first out queue. 1249 01:09:45,540 --> 01:09:50,319 And in general, which kind of queue do we like? 1250 01:09:50,319 --> 01:09:52,557 We like LIFO queues more. 1251 01:09:52,557 --> 01:09:53,640 Well, OK, you could argue. 1252 01:09:53,640 --> 01:09:59,050 But in this actuation would we like a FIFO or LIFO queue? 1253 01:09:59,050 --> 01:10:01,160 I'll give you 10 seconds. 1254 01:10:01,160 --> 01:10:03,910 In a biosynthetic pathway, would you 1255 01:10:03,910 --> 01:10:05,940 want a LIFO or a FIFO queue? 1256 01:10:13,340 --> 01:10:14,930 Yeah, and if you're totally confused 1257 01:10:14,930 --> 01:10:18,120 by everything I'm saying, you can do the-- flash 1258 01:10:18,120 --> 01:10:21,280 all the letters, numbers, whatever. 1259 01:10:21,280 --> 01:10:21,780 All right. 1260 01:10:21,780 --> 01:10:25,460 Ready, three, two, one. 1261 01:10:25,460 --> 01:10:25,960 All right. 1262 01:10:25,960 --> 01:10:29,560 So there's some disagreement we got. 1263 01:10:29,560 --> 01:10:31,520 But now a majority of people are saying 1264 01:10:31,520 --> 01:10:34,340 that although the single input module gives us 1265 01:10:34,340 --> 01:10:37,050 a LIFO queue, what we might really like is a FIFO queue. 1266 01:10:37,050 --> 01:10:39,450 And can somebody say why that would be? 1267 01:10:39,450 --> 01:10:42,062 AUDIENCE: We don't want that much intermediates. 1268 01:10:42,062 --> 01:10:42,770 PROFESSOR: Right. 1269 01:10:42,770 --> 01:10:45,320 We don't want to pile up those intermediates. 1270 01:10:45,320 --> 01:10:48,490 So just for the same reason that we wanted to start with Z1, 1271 01:10:48,490 --> 01:10:50,166 and then get Z2 and so forth. 1272 01:10:50,166 --> 01:10:51,790 And the reason that was because there's 1273 01:10:51,790 --> 01:10:54,940 no point in having Z2 until after we have Z1. 1274 01:10:54,940 --> 01:10:56,670 Because there's nothing for Z2 to do. 1275 01:10:56,670 --> 01:10:59,090 It would be wasted energy to make it. 1276 01:10:59,090 --> 01:11:01,860 In the same way, when we're getting rid of these proteins, 1277 01:11:01,860 --> 01:11:04,970 we would actually like to get rid of them first this one 1278 01:11:04,970 --> 01:11:06,017 and then later. 1279 01:11:06,017 --> 01:11:06,600 AUDIENCE: Why? 1280 01:11:10,150 --> 01:11:12,805 There's no point in having Z2 if you don't have Z1. 1281 01:11:12,805 --> 01:11:15,787 You technically want to get rid of them in the other way. 1282 01:11:15,787 --> 01:11:18,769 Because then if the carbon source shows up again, 1283 01:11:18,769 --> 01:11:19,520 you want to have-- 1284 01:11:19,520 --> 01:11:21,727 PROFESSOR: Well yeah, carbon source showing up again. 1285 01:11:21,727 --> 01:11:23,360 I think that's a separate argument. 1286 01:11:23,360 --> 01:11:25,360 So the reason that we-- the statement 1287 01:11:25,360 --> 01:11:28,600 is really just that if we first get rid of Zn. 1288 01:11:28,600 --> 01:11:33,906 Then we are just going to pile up molecule n minus 1. 1289 01:11:33,906 --> 01:11:37,411 AUDIENCE: So the metabolism is down. 1290 01:11:37,411 --> 01:11:38,410 PROFESSOR: That's right. 1291 01:11:38,410 --> 01:11:38,790 That's right. 1292 01:11:38,790 --> 01:11:40,350 So you can just think about the flow 1293 01:11:40,350 --> 01:11:43,520 of those of the metabolites and the molecules in there. 1294 01:11:43,520 --> 01:11:46,150 And you kind of want to first get rid of this. 1295 01:11:46,150 --> 01:11:48,230 So then we stop making this. 1296 01:11:48,230 --> 01:11:50,490 And then we kind of travel on down. 1297 01:11:50,490 --> 01:11:53,660 So there are many contexts in which you would perhaps really 1298 01:11:53,660 --> 01:11:57,530 like to have a FIFO queue. 1299 01:11:57,530 --> 01:11:59,240 And indeed, one of the things that 1300 01:11:59,240 --> 01:12:03,190 had been studied previously was the flagellar biosynthesis 1301 01:12:03,190 --> 01:12:03,950 pathway. 1302 01:12:03,950 --> 01:12:06,060 So E. coli and many other bacteria, 1303 01:12:06,060 --> 01:12:08,550 they make these flagella that allows them to swim. 1304 01:12:08,550 --> 01:12:10,758 We're going to talk a lot about that in coming weeks. 1305 01:12:10,758 --> 01:12:13,810 But in this context what had been found actually 1306 01:12:13,810 --> 01:12:16,050 is that it is indeed a FIFO queue. 1307 01:12:16,050 --> 01:12:19,080 So when they first start to make these little flagella, 1308 01:12:19,080 --> 01:12:19,860 they make. 1309 01:12:19,860 --> 01:12:21,500 And it's a big complicated, machine. 1310 01:12:21,500 --> 01:12:22,000 Right? 1311 01:12:22,000 --> 01:12:25,200 But they make it in the order that it's transported and put 1312 01:12:25,200 --> 01:12:26,800 in the membrane. 1313 01:12:26,800 --> 01:12:28,300 But then when it is taken away, when 1314 01:12:28,300 --> 01:12:30,280 you stop making the flagella components, 1315 01:12:30,280 --> 01:12:34,040 then it's again in the same order 1316 01:12:34,040 --> 01:12:37,560 as they were made in, which kind of makes sense. 1317 01:12:37,560 --> 01:12:40,548 Now the question is, how might we be able to do that. 1318 01:12:48,390 --> 01:12:53,340 So let me explain it. 1319 01:12:53,340 --> 01:12:55,720 The basic answer is via an extension 1320 01:12:55,720 --> 01:12:57,490 of these feed-forward loops. 1321 01:13:01,730 --> 01:13:04,510 So it's what we call a multi-output feed-forward loop. 1322 01:13:14,830 --> 01:13:16,780 What we have here is we have some X, 1323 01:13:16,780 --> 01:13:21,420 and it is going to come to Y. And then 1324 01:13:21,420 --> 01:13:26,780 Y again is going to do this thing to Z1 and Z2, 1325 01:13:26,780 --> 01:13:27,730 and all the others. 1326 01:13:32,450 --> 01:13:34,380 But it's a feed-forward loop, because we also 1327 01:13:34,380 --> 01:13:36,890 have X coming in here as so. 1328 01:13:43,259 --> 01:13:45,550 And I think that we do want to have these be AND gates. 1329 01:13:45,550 --> 01:13:51,780 Let me just make sure I'm not-- no here's it's an OR gate. 1330 01:13:58,970 --> 01:14:01,930 So we're going to assume that all of these inputs 1331 01:14:01,930 --> 01:14:05,320 are combined via an OR gate. 1332 01:14:05,320 --> 01:14:12,230 And what we have is we have some K1, K2, et cetera, up to Kn. 1333 01:14:12,230 --> 01:14:14,140 Then we have another set of K's which are 1334 01:14:14,140 --> 01:14:22,090 K1 primes, K2 prime, Kn prime. 1335 01:14:22,090 --> 01:14:24,260 So we have a set of K's corresponding 1336 01:14:24,260 --> 01:14:27,242 to how X interacts with the promoter at the Z. 1337 01:14:27,242 --> 01:14:29,200 We have different set of K primes that tells us 1338 01:14:29,200 --> 01:14:36,300 how Y interacts with the promoter at Z. 1339 01:14:36,300 --> 01:14:39,185 And the question is how can we get a FIFO order. 1340 01:14:51,070 --> 01:14:53,220 I'm going to illustrate some options. 1341 01:14:53,220 --> 01:14:56,518 And you can think about it while I do it. 1342 01:16:03,883 --> 01:16:07,785 AUDIENCE: Are those associations or dissociations? 1343 01:16:07,785 --> 01:16:09,820 PROFESSOR: These are dissociation constants. 1344 01:16:09,820 --> 01:16:14,330 So these are again, this can be thought of as the concentration 1345 01:16:14,330 --> 01:16:18,150 of the active protein which it starts 1346 01:16:18,150 --> 01:16:22,085 being effective in sending a signal to Z. Question? 1347 01:16:22,085 --> 01:16:24,065 AUDIENCE: Would you not like [INAUDIBLE]? 1348 01:16:30,314 --> 01:16:31,230 PROFESSOR: I hope not. 1349 01:16:31,230 --> 01:16:33,105 Because otherwise I'm going to be in trouble. 1350 01:16:35,610 --> 01:16:39,190 Maybe for now let's, assume that I've written the right thing. 1351 01:16:39,190 --> 01:16:43,210 And then we'll find out soon enough. 1352 01:16:51,350 --> 01:16:54,150 Does everyone understand the question here? 1353 01:16:54,150 --> 01:16:56,919 I'll just give you another 15 seconds to think about it. 1354 01:17:25,660 --> 01:17:26,160 All right. 1355 01:17:26,160 --> 01:17:27,226 Do you need more time? 1356 01:17:30,431 --> 01:17:30,930 All right. 1357 01:17:30,930 --> 01:17:32,096 Just a little bit more then. 1358 01:17:43,860 --> 01:17:44,360 All right. 1359 01:17:44,360 --> 01:17:45,693 Let's go ahead and give it a go. 1360 01:17:45,693 --> 01:17:47,245 Ready, three, two, one. 1361 01:17:49,870 --> 01:17:51,280 OK. 1362 01:17:51,280 --> 01:17:54,685 So we got a majority B, but some C's. 1363 01:17:57,680 --> 01:17:58,180 All right. 1364 01:17:58,180 --> 01:17:59,513 So let's try to figure this out. 1365 01:18:01,780 --> 01:18:03,902 So what we assume is that X comes 1366 01:18:03,902 --> 01:18:07,300 and it's going to do this. 1367 01:18:07,300 --> 01:18:09,440 And then it's going to do this. 1368 01:18:09,440 --> 01:18:14,800 And we can just have two values for now, K1 and K2. 1369 01:18:14,800 --> 01:18:19,010 So this is X. Now we're going to have Y. 1370 01:18:19,010 --> 01:18:21,240 And we can talk about-- this is also 1371 01:18:21,240 --> 01:18:24,210 X star Y. We'll assume that we always have these things. 1372 01:18:24,210 --> 01:18:27,000 So Y is also going to come. 1373 01:18:27,000 --> 01:18:33,710 It'll be activated here at some time, 1374 01:18:33,710 --> 01:18:36,960 which we don't-- it's going to be delayed by a little bit, 1375 01:18:36,960 --> 01:18:38,480 right? 1376 01:18:38,480 --> 01:18:38,980 Maybe. 1377 01:18:49,510 --> 01:18:51,180 So that's what Y is going to do. 1378 01:18:51,180 --> 01:18:54,940 Now we want to know about Z1 and Z2, right? 1379 01:18:54,940 --> 01:18:57,440 Well, the idea here is that it's going 1380 01:18:57,440 --> 01:19:03,930 to be the K, the regular K1 and K2 that determine 1381 01:19:03,930 --> 01:19:05,450 the order that it appears. 1382 01:19:05,450 --> 01:19:06,560 We have an OR gate. 1383 01:19:06,560 --> 01:19:08,440 Y is going to be delayed. 1384 01:19:08,440 --> 01:19:13,270 So it's really, the important thing is what the normal K's do 1385 01:19:13,270 --> 01:19:16,795 in terms of turning on Z's. 1386 01:19:16,795 --> 01:19:17,295 Yes? 1387 01:19:20,650 --> 01:19:23,090 And this is especially true because Y is again delayed. 1388 01:19:23,090 --> 01:19:26,404 Because it has its own threshold for turning on. 1389 01:19:26,404 --> 01:19:28,570 So since Y is delayed, it won't really have a chance 1390 01:19:28,570 --> 01:19:33,310 to influence the behavior of the X's. 1391 01:19:33,310 --> 01:19:35,780 And actually I should have drawn this delayed too, as well. 1392 01:19:45,250 --> 01:19:46,640 So it's the order of the K's that 1393 01:19:46,640 --> 01:19:49,910 determine how Z is turned on. 1394 01:19:49,910 --> 01:19:51,780 But it's the order of the K primes 1395 01:19:51,780 --> 01:19:55,490 that tell us how the Z's are turned off. 1396 01:19:55,490 --> 01:20:00,860 And that's again because Y is delayed relative to X. 1397 01:20:00,860 --> 01:20:04,160 And we have an OR gate. 1398 01:20:04,160 --> 01:20:08,792 So indeed, in this case, if we have like this, 1399 01:20:08,792 --> 01:20:11,250 and we want things to be in the opposite order with respect 1400 01:20:11,250 --> 01:20:14,340 to Y. So if we wanted K1 to be less than K2, then 1401 01:20:14,340 --> 01:20:20,380 we actually want say Kn to be-- I'm sorry. 1402 01:20:20,380 --> 01:20:23,360 We want K1 here, and then we want Kn down below. 1403 01:20:27,110 --> 01:20:29,390 And the heart of this is really because of the fact 1404 01:20:29,390 --> 01:20:37,760 that X is also regulating Y with some other constant Ky. 1405 01:20:37,760 --> 01:20:40,220 And this is going to tell us how much Y is delayed relative 1406 01:20:40,220 --> 01:20:46,040 to X. But the heart of this is that since Y is delayed, 1407 01:20:46,040 --> 01:20:48,810 it's really the dynamics of X at the beginning that tell us 1408 01:20:48,810 --> 01:20:50,900 how the Z's are turned on. 1409 01:20:50,900 --> 01:20:56,870 But it's the dynamic of the Y and the K primes, K1 prime, Kn 1410 01:20:56,870 --> 01:21:01,280 prime, that tell us the order at which those Z's 1411 01:21:01,280 --> 01:21:02,860 are going to be turned off. 1412 01:21:02,860 --> 01:21:06,170 So with the proper choice of orderings of K's and K 1413 01:21:06,170 --> 01:21:15,680 primes is you can then get a FIFO queue. 1414 01:21:19,580 --> 01:21:21,220 With that I think we should quit. 1415 01:21:21,220 --> 01:21:23,740 Please read Sunney Xie's paper very carefully, 1416 01:21:23,740 --> 01:21:26,680 because it's going to be focused on a lot over the next lecture. 1417 01:21:26,680 --> 01:21:27,180 All right. 1418 01:21:27,180 --> 01:21:29,330 Have a good weekend.