WEBVTT 00:00:00.000 --> 00:00:00.610 align:middle line:90% 00:00:00.610 --> 00:00:02.440 align:middle line:84% The following content is provided 00:00:02.440 --> 00:00:06.370 align:middle line:84% by MIT OpenCourseWare under a Creative Commons license. 00:00:06.370 --> 00:00:10.120 align:middle line:84% Additional information about our license and MIT OpenCourseWare, 00:00:10.120 --> 00:00:12.730 align:middle line:84% in general, is available at ocw.mit.edu. 00:00:12.730 --> 00:00:16.600 align:middle line:90% 00:00:16.600 --> 00:00:19.030 align:middle line:90% GEORGE CHURCH: OK, welcome back. 00:00:19.030 --> 00:00:21.650 align:middle line:84% I'm sure you're all dying to know the answer, 00:00:21.650 --> 00:00:24.040 align:middle line:84% so y'all came back faster than usual. 00:00:24.040 --> 00:00:26.440 align:middle line:90% [LAUGHTER] 00:00:26.440 --> 00:00:29.860 align:middle line:84% So how do we get from the first top motif 00:00:29.860 --> 00:00:31.840 align:middle line:90% score to the second one? 00:00:31.840 --> 00:00:36.400 align:middle line:84% And I'll show you, just to spice this up, 00:00:36.400 --> 00:00:40.000 align:middle line:84% I'll see two different algorithms they actually, 00:00:40.000 --> 00:00:46.480 align:middle line:84% historically, done and the 100-fold improvement in speed 00:00:46.480 --> 00:00:50.320 align:middle line:84% and also in accuracy that comes from the change. 00:00:50.320 --> 00:00:52.900 align:middle line:84% So the first way, and you already 00:00:52.900 --> 00:00:54.680 align:middle line:84% can see negatively predisposed to this, 00:00:54.680 --> 00:01:01.180 align:middle line:84% but if you look at the motif, the winner, if you will, 00:01:01.180 --> 00:01:04.269 align:middle line:84% the first time around, it has certain base positions 00:01:04.269 --> 00:01:08.830 align:middle line:84% which are particularly high-information concept. 00:01:08.830 --> 00:01:10.870 align:middle line:84% That is to say they really dominate, 00:01:10.870 --> 00:01:15.790 align:middle line:84% and they probably are critical to finding a motif. 00:01:15.790 --> 00:01:19.210 align:middle line:84% If you had a way of, say, knocking out one of those 00:01:19.210 --> 00:01:22.240 align:middle line:84% from the sequence, from all the sequences 00:01:22.240 --> 00:01:24.250 align:middle line:84% which contributed to this motif, then 00:01:24.250 --> 00:01:25.830 align:middle line:84% it would greatly reduce your chances 00:01:25.830 --> 00:01:27.530 align:middle line:90% that you would find it again. 00:01:27.530 --> 00:01:31.360 align:middle line:84% And so that's what we are going to do in slide 47 00:01:31.360 --> 00:01:33.640 align:middle line:84% is we're just going to go through and pick 00:01:33.640 --> 00:01:40.180 align:middle line:84% on one of those bases and turn it into an X. 00:01:40.180 --> 00:01:42.820 align:middle line:84% So an X doesn't really match any of the weight matrices. 00:01:42.820 --> 00:01:48.100 align:middle line:84% And so whenever you have an motif that overlaps it, 00:01:48.100 --> 00:01:49.760 align:middle line:90% it won't have a good score. 00:01:49.760 --> 00:01:51.880 align:middle line:90% And so you won't build up-- 00:01:51.880 --> 00:01:53.770 align:middle line:90% you won't have this transition. 00:01:53.770 --> 00:01:56.780 align:middle line:84% The Gibbs sampler won't go in that direction. 00:01:56.780 --> 00:02:02.110 align:middle line:84% Now, this has a couple of disadvantages from a accuracy 00:02:02.110 --> 00:02:04.840 align:middle line:84% standpoint in that there may be some motifs that you really 00:02:04.840 --> 00:02:13.750 align:middle line:84% like that overlap the original motif slightly. 00:02:13.750 --> 00:02:17.170 align:middle line:90% 00:02:17.170 --> 00:02:20.110 align:middle line:84% And you'll miss those during the sampling. 00:02:20.110 --> 00:02:22.820 align:middle line:90% 00:02:22.820 --> 00:02:30.510 align:middle line:84% So an alternative way of looking for these sort of things, 00:02:30.510 --> 00:02:37.740 align:middle line:84% rather than taking the best continuous sampling in this Xed 00:02:37.740 --> 00:02:40.920 align:middle line:84% out version, instead, what you can do 00:02:40.920 --> 00:02:43.450 align:middle line:84% is maintain a list of all the motifs 00:02:43.450 --> 00:02:44.700 align:middle line:90% you've found up to this point. 00:02:44.700 --> 00:02:46.710 align:middle line:90% In this case, we have just one. 00:02:46.710 --> 00:02:49.950 align:middle line:84% And now, because we were using AlignACE to do this 00:02:49.950 --> 00:02:54.120 align:middle line:84% multi-sequence alignment by sampling-- 00:02:54.120 --> 00:02:59.610 align:middle line:84% but now, as you're going along, building up, 00:02:59.610 --> 00:03:06.450 align:middle line:84% initially, a random motif, you compare it to the first winner. 00:03:06.450 --> 00:03:09.660 align:middle line:84% And you say, is this random motif, or this motif 00:03:09.660 --> 00:03:11.880 align:middle line:84% that's emerging out of this random process, 00:03:11.880 --> 00:03:14.820 align:middle line:84% does it look at all like the previous one? 00:03:14.820 --> 00:03:16.260 align:middle line:84% If it starts to look convincingly 00:03:16.260 --> 00:03:19.382 align:middle line:84% like the winner before, you know where it's going to go. 00:03:19.382 --> 00:03:21.340 align:middle line:84% It's just going to get more and more like that. 00:03:21.340 --> 00:03:22.900 align:middle line:90% So you might as well quit early. 00:03:22.900 --> 00:03:24.810 align:middle line:84% And so that's what you do is now you 00:03:24.810 --> 00:03:26.340 align:middle line:84% haven't Xed out any particular base. 00:03:26.340 --> 00:03:27.780 align:middle line:90% All the information is there. 00:03:27.780 --> 00:03:30.630 align:middle line:84% You can take any kind of motif that expands and changes 00:03:30.630 --> 00:03:31.680 align:middle line:90% the columns and so forth. 00:03:31.680 --> 00:03:34.200 align:middle line:90% 00:03:34.200 --> 00:03:36.510 align:middle line:84% And if you're building up towards a motif you've 00:03:36.510 --> 00:03:40.830 align:middle line:90% seen before, you can reject it. 00:03:40.830 --> 00:03:49.550 align:middle line:90% 00:03:49.550 --> 00:03:51.770 align:middle line:84% This process has the dual advantage 00:03:51.770 --> 00:03:56.270 align:middle line:84% of now allowing you to get overlapping motifs that 00:03:56.270 --> 00:03:58.820 align:middle line:84% might have a different enough column structure 00:03:58.820 --> 00:04:02.420 align:middle line:84% or differ enough weight matrix or are slightly 00:04:02.420 --> 00:04:05.210 align:middle line:84% offset so that it really is a different motif. 00:04:05.210 --> 00:04:07.220 align:middle line:90% You can find those. 00:04:07.220 --> 00:04:09.470 align:middle line:84% The algorithm that you're using to compare these we'll 00:04:09.470 --> 00:04:12.620 align:middle line:90% use a couple of times today. 00:04:12.620 --> 00:04:17.180 align:middle line:84% We'll call it CompareACE for comparing these consensus 00:04:17.180 --> 00:04:20.930 align:middle line:84% elements, or these weight matrices. 00:04:20.930 --> 00:04:27.530 align:middle line:84% And so it not only improves your ability 00:04:27.530 --> 00:04:34.700 align:middle line:84% to discriminate related but statistically separable 00:04:34.700 --> 00:04:38.810 align:middle line:84% consensus elements but it also has about 100-fold increase 00:04:38.810 --> 00:04:39.830 align:middle line:90% in speed. 00:04:39.830 --> 00:04:43.740 align:middle line:84% Because you can stop 100 times earlier in this motif sampling, 00:04:43.740 --> 00:04:45.553 align:middle line:84% which goes-- once you lock into a motif, 00:04:45.553 --> 00:04:46.970 align:middle line:84% you go and you go until you really 00:04:46.970 --> 00:04:49.400 align:middle line:90% get the best possible score. 00:04:49.400 --> 00:04:52.500 align:middle line:84% But now you can reject these weaker ones earlier on. 00:04:52.500 --> 00:04:54.598 align:middle line:84% Now, you may have been wondering all along, 00:04:54.598 --> 00:04:57.140 align:middle line:84% you probably have an intuitive feeling for what the MAP score 00:04:57.140 --> 00:04:59.113 align:middle line:90% is-- and I'm going to take-- 00:04:59.113 --> 00:05:00.530 align:middle line:84% and at the end of this, you're not 00:05:00.530 --> 00:05:04.807 align:middle line:84% going to be able to rederive this from first principles 00:05:04.807 --> 00:05:06.890 align:middle line:84% because I'm not going to go into it in that depth. 00:05:06.890 --> 00:05:09.440 align:middle line:84% But I want to expose you to some of the terms that 00:05:09.440 --> 00:05:12.440 align:middle line:84% are involved in this maximum a posteriori score. 00:05:12.440 --> 00:05:14.955 align:middle line:90% 00:05:14.955 --> 00:05:21.680 align:middle line:84% Of course, the hero of any kind of scoring function 00:05:21.680 --> 00:05:25.700 align:middle line:84% is the weight matrix, the actual number of counts of As, 00:05:25.700 --> 00:05:29.000 align:middle line:84% Cs, Gs, and Ts you have at every position 00:05:29.000 --> 00:05:31.010 align:middle line:90% in every column in this matrix. 00:05:31.010 --> 00:05:34.310 align:middle line:84% Now, remember, we've critiqued this already, 00:05:34.310 --> 00:05:38.000 align:middle line:84% that the typical weight matrices, 00:05:38.000 --> 00:05:41.060 align:middle line:84% there is no codependence of columns the way 00:05:41.060 --> 00:05:42.800 align:middle line:84% there was in RNA secondary structural 00:05:42.800 --> 00:05:46.280 align:middle line:84% or in CpG islands or other Markov chains. 00:05:46.280 --> 00:05:47.780 align:middle line:90% These are independent columns. 00:05:47.780 --> 00:05:53.090 align:middle line:84% So the key player, the hero here, is f sub jb. 00:05:53.090 --> 00:05:55.130 align:middle line:90% This is the weight matrix. 00:05:55.130 --> 00:05:58.850 align:middle line:84% And this is not a frequency, but this is the actual number 00:05:58.850 --> 00:06:00.740 align:middle line:90% of occurrences of each base-- 00:06:00.740 --> 00:06:04.220 align:middle line:84% A, C, G, or T, which is B, at position j 00:06:04.220 --> 00:06:06.020 align:middle line:90% in the column matrix. 00:06:06.020 --> 00:06:10.160 align:middle line:84% These can be the active columns, j going-- 00:06:10.160 --> 00:06:12.470 align:middle line:84% and then the number of occurrences 00:06:12.470 --> 00:06:16.910 align:middle line:84% is just the sum of those occurrences. 00:06:16.910 --> 00:06:20.750 align:middle line:84% We've already been talking about how the width of the motif can 00:06:20.750 --> 00:06:23.180 align:middle line:84% include some columns that are basically on and off, 00:06:23.180 --> 00:06:25.620 align:middle line:84% columns that you believe are significant and those that 00:06:25.620 --> 00:06:26.120 align:middle line:90% aren't. 00:06:26.120 --> 00:06:28.730 align:middle line:84% So the number of columns, c, is less than 00:06:28.730 --> 00:06:32.090 align:middle line:90% or equal to the width. 00:06:32.090 --> 00:06:36.820 align:middle line:84% So for example, when we were doing the GCN4 example, 00:06:36.820 --> 00:06:39.700 align:middle line:84% we had a width of 10 or might at one point 00:06:39.700 --> 00:06:43.435 align:middle line:84% expand to the width of 11 with 10 active columns, c equal 10. 00:06:43.435 --> 00:06:46.360 align:middle line:90% 00:06:46.360 --> 00:06:52.480 align:middle line:84% You'll recognize-- here's the star, the f sub jb here. 00:06:52.480 --> 00:06:57.370 align:middle line:84% And you're adding these pseudocounts here, 00:06:57.370 --> 00:07:01.510 align:middle line:84% these betas, which you remember that every time that you have 00:07:01.510 --> 00:07:04.060 align:middle line:84% a danger that you might, because you 00:07:04.060 --> 00:07:06.670 align:middle line:84% have a limited database that you're looking through, 00:07:06.670 --> 00:07:08.710 align:middle line:84% a limited number of actually observed sites, 00:07:08.710 --> 00:07:11.200 align:middle line:84% you could get a number of sites equal to 0. 00:07:11.200 --> 00:07:13.900 align:middle line:84% And you don't want to have zeros in there. 00:07:13.900 --> 00:07:16.090 align:middle line:84% Because you're basically acknowledging, 00:07:16.090 --> 00:07:18.700 align:middle line:84% because I did lambda sampling, it could have been 1. 00:07:18.700 --> 00:07:20.830 align:middle line:84% If I had sampled one more, it could have been 1. 00:07:20.830 --> 00:07:24.460 align:middle line:84% And so an estimate might be that you add another pseudocount. 00:07:24.460 --> 00:07:27.850 align:middle line:84% And this can be represented here. 00:07:27.850 --> 00:07:30.370 align:middle line:84% You don't want to have-- and these gammas you can think of, 00:07:30.370 --> 00:07:34.600 align:middle line:90% they're kind of like factorials. 00:07:34.600 --> 00:07:36.760 align:middle line:90% And you're taking products. 00:07:36.760 --> 00:07:37.900 align:middle line:90% The pi is products. 00:07:37.900 --> 00:07:41.740 align:middle line:90% 00:07:41.740 --> 00:07:45.190 align:middle line:84% And then I may have mentioned that you 00:07:45.190 --> 00:07:47.830 align:middle line:84% might want to take into account the background 00:07:47.830 --> 00:07:49.160 align:middle line:90% levels of the bases. 00:07:49.160 --> 00:07:53.320 align:middle line:84% If you get, say, a motif that's just a string of As 00:07:53.320 --> 00:07:57.370 align:middle line:84% and you're doing it in a genome that's very AT-rich, 00:07:57.370 --> 00:07:59.240 align:middle line:90% then you want to account. 00:07:59.240 --> 00:08:01.570 align:middle line:84% It's less surprising if you find a string of As 00:08:01.570 --> 00:08:04.090 align:middle line:90% in a genome that's GC-rich. 00:08:04.090 --> 00:08:07.510 align:middle line:84% And that's what this g sub b is the background genome 00:08:07.510 --> 00:08:09.520 align:middle line:90% frequency for base b. 00:08:09.520 --> 00:08:14.123 align:middle line:84% Now, in a double-stranded DNA, the frequency of As 00:08:14.123 --> 00:08:15.790 align:middle line:84% is going to be equal to frequency of Ts. 00:08:15.790 --> 00:08:19.180 align:middle line:84% But a single-stranded RNA virus, for example, there's 00:08:19.180 --> 00:08:22.030 align:middle line:84% going to really be a very independent set of backgrounds 00:08:22.030 --> 00:08:26.560 align:middle line:90% for Gs, As, Ts, and Cs, or Us. 00:08:26.560 --> 00:08:29.740 align:middle line:84% So this gives you some flavor of what's in the MAP score. 00:08:29.740 --> 00:08:35.320 align:middle line:84% A greatly oversimplified version of this detailed slide 49 00:08:35.320 --> 00:08:38.049 align:middle line:90% is in slide 50-- 00:08:38.049 --> 00:08:40.870 align:middle line:84% laughably oversimplified-- is it's basically 00:08:40.870 --> 00:08:42.669 align:middle line:84% the overrepresentation of these sites 00:08:42.669 --> 00:08:45.040 align:middle line:90% is what we're talking about. 00:08:45.040 --> 00:08:48.340 align:middle line:84% It means that these sites, you're 00:08:48.340 --> 00:08:51.490 align:middle line:84% giving a higher score if there's an overrepresentation 00:08:51.490 --> 00:08:53.590 align:middle line:90% in that learning set. 00:08:53.590 --> 00:08:55.690 align:middle line:84% It tells you nothing about the rest of the genome. 00:08:55.690 --> 00:08:57.010 align:middle line:84% It could be they're overrepresented 00:08:57.010 --> 00:08:58.302 align:middle line:90% in the rest of the genome, too. 00:08:58.302 --> 00:09:00.490 align:middle line:84% And that's what we're going to go into next. 00:09:00.490 --> 00:09:05.260 align:middle line:84% But you get a bonus for the number of aligned sites 00:09:05.260 --> 00:09:08.380 align:middle line:84% and the overrepresentation of those sites. 00:09:08.380 --> 00:09:11.021 align:middle line:90% That's what the MAP score is. 00:09:11.021 --> 00:09:14.077 align:middle line:84% STUDENT: Does the background [INAUDIBLE]?? 00:09:14.077 --> 00:09:14.869 align:middle line:90% GEORGE CHURCH: Hmm? 00:09:14.869 --> 00:09:17.873 align:middle line:84% STUDENT: Does the background [INAUDIBLE]?? 00:09:17.873 --> 00:09:19.540 align:middle line:84% GEORGE CHURCH: The background is ignored 00:09:19.540 --> 00:09:22.525 align:middle line:84% in this oversimplification, but it's explicit in slide 49. 00:09:22.525 --> 00:09:25.302 align:middle line:90% 00:09:25.302 --> 00:09:30.072 align:middle line:84% You really should ignore this and think more 00:09:30.072 --> 00:09:31.030 align:middle line:90% about the previous one. 00:09:31.030 --> 00:09:32.590 align:middle line:84% But the main point that I'm making 00:09:32.590 --> 00:09:37.760 align:middle line:84% is the overrepresentation is just half of the story. 00:09:37.760 --> 00:09:40.825 align:middle line:84% The other half is the specificity. 00:09:40.825 --> 00:09:42.850 align:middle line:84% In other words, if it's present in your learning 00:09:42.850 --> 00:09:45.713 align:middle line:84% set or your enriched set, you want to next ask, 00:09:45.713 --> 00:09:47.380 align:middle line:84% is it present in the rest of the genome? 00:09:47.380 --> 00:09:48.370 align:middle line:84% Because if it's present-- and maybe 00:09:48.370 --> 00:09:49.810 align:middle line:84% that's what you mean by background-- 00:09:49.810 --> 00:09:51.560 align:middle line:84% if it's present in the rest of the genome, 00:09:51.560 --> 00:09:54.220 align:middle line:90% then that's not great. 00:09:54.220 --> 00:10:03.730 align:middle line:84% And so what we're going to do is this is an example of running 00:10:03.730 --> 00:10:05.878 align:middle line:84% through-- after you get the first motif-- 00:10:05.878 --> 00:10:07.420 align:middle line:84% running through lots of other motifs. 00:10:07.420 --> 00:10:11.788 align:middle line:84% So the best motif of all for a larger set than the ones 00:10:11.788 --> 00:10:12.580 align:middle line:90% we were looking at. 00:10:12.580 --> 00:10:14.122 align:middle line:84% We were looking at seven, but there's 00:10:14.122 --> 00:10:15.289 align:middle line:90% 116 of these in [INAUDIBLE]. 00:10:15.289 --> 00:10:16.830 align:middle line:84% When you run through the whole thing, 00:10:16.830 --> 00:10:19.180 align:middle line:84% the top MAP score, the one that's most overrepresented, 00:10:19.180 --> 00:10:20.620 align:middle line:90% is this A-rich one. 00:10:20.620 --> 00:10:24.070 align:middle line:84% Now you want to ask, is that specific to the amino acid 00:10:24.070 --> 00:10:25.390 align:middle line:90% biosynthetic genes? 00:10:25.390 --> 00:10:26.830 align:middle line:84% Or is it found all over the place? 00:10:26.830 --> 00:10:29.038 align:middle line:84% And we're going to get to that, how you measure that, 00:10:29.038 --> 00:10:30.042 align:middle line:90% in just a moment. 00:10:30.042 --> 00:10:31.750 align:middle line:84% The one we were kind of highlighting here 00:10:31.750 --> 00:10:36.010 align:middle line:84% is in GCN4 is kind of modestly-- this is not a rank order list. 00:10:36.010 --> 00:10:37.360 align:middle line:90% This is kind of in random order. 00:10:37.360 --> 00:10:40.390 align:middle line:84% But we'll show how you can do the rank ordering, as well, how 00:10:40.390 --> 00:10:43.600 align:middle line:90% you can order this. 00:10:43.600 --> 00:10:47.470 align:middle line:84% But you see all kinds of motifs, some that are stretched out, 00:10:47.470 --> 00:10:49.210 align:middle line:90% different compositions. 00:10:49.210 --> 00:10:52.480 align:middle line:84% So to evaluate motif significance, 00:10:52.480 --> 00:10:57.760 align:middle line:84% we have these five examples that we'll go through. 00:10:57.760 --> 00:11:00.440 align:middle line:84% There's the specificity that I've been talking about 00:11:00.440 --> 00:11:02.540 align:middle line:84% and will be the subject of the next slide. 00:11:02.540 --> 00:11:05.170 align:middle line:84% That little arrow means the slide that's due here. 00:11:05.170 --> 00:11:08.680 align:middle line:84% Group specificity-- is this specific to the group 00:11:08.680 --> 00:11:11.415 align:middle line:84% that you found by clustering, or is it all over the place? 00:11:11.415 --> 00:11:12.790 align:middle line:84% Functional enrichment-- we talked 00:11:12.790 --> 00:11:15.100 align:middle line:90% about this a couple of times. 00:11:15.100 --> 00:11:17.530 align:middle line:84% Are the genes that you're finding 00:11:17.530 --> 00:11:20.500 align:middle line:84% in the cluster or the genes that you're 00:11:20.500 --> 00:11:24.970 align:middle line:84% finding this motif in front of, are they enriched by some 00:11:24.970 --> 00:11:26.710 align:middle line:90% fairly objective criteria? 00:11:26.710 --> 00:11:30.550 align:middle line:84% Is the motifs you're finding in a particular position 00:11:30.550 --> 00:11:32.440 align:middle line:90% in the upstream elements? 00:11:32.440 --> 00:11:36.580 align:middle line:84% Because they have a position in the promoters or enhancers. 00:11:36.580 --> 00:11:39.550 align:middle line:84% Does the motif that you found have interesting symmetry 00:11:39.550 --> 00:11:42.550 align:middle line:84% properties, as you might expect from proteins, 00:11:42.550 --> 00:11:43.870 align:middle line:90% which bind as multimers? 00:11:43.870 --> 00:11:51.780 align:middle line:84% They might have inverted or tandem repeats, 00:11:51.780 --> 00:11:54.390 align:middle line:84% where the elements either point towards each other 00:11:54.390 --> 00:11:56.910 align:middle line:90% or in tandem. 00:11:56.910 --> 00:11:59.130 align:middle line:84% Is the motifs that you're finding, are they related 00:11:59.130 --> 00:12:01.230 align:middle line:84% in any way to motifs that were known 00:12:01.230 --> 00:12:05.653 align:middle line:84% before by more complicated biochemical and genetic assays? 00:12:05.653 --> 00:12:07.320 align:middle line:84% So the first one, the group specificity, 00:12:07.320 --> 00:12:09.840 align:middle line:84% in order to ask whether the motif you found 00:12:09.840 --> 00:12:11.418 align:middle line:84% in the small subset of the genome 00:12:11.418 --> 00:12:12.960 align:middle line:84% is present in the rest of the genome, 00:12:12.960 --> 00:12:14.530 align:middle line:90% we need a way of scanning. 00:12:14.530 --> 00:12:17.670 align:middle line:84% Now, when we introduce weight matrices 00:12:17.670 --> 00:12:19.860 align:middle line:84% in the multi-sequence alignment lecture 00:12:19.860 --> 00:12:23.070 align:middle line:84% and we say we would put off the motif Gibbs sampling 00:12:23.070 --> 00:12:25.080 align:middle line:84% until today, we already introduced 00:12:25.080 --> 00:12:27.210 align:middle line:84% one really trivial way of scanning the genome, 00:12:27.210 --> 00:12:29.940 align:middle line:84% where you basically take the weight matrix, 00:12:29.940 --> 00:12:32.070 align:middle line:84% move it in each position, and you do a simple sum. 00:12:32.070 --> 00:12:34.830 align:middle line:84% That's basically what this is is a simple sum. 00:12:34.830 --> 00:12:39.930 align:middle line:84% But we're taking log ratios of these counts. 00:12:39.930 --> 00:12:43.180 align:middle line:84% Again, the hero, the counts, just like the f-- 00:12:43.180 --> 00:12:46.530 align:middle line:84% so bj before, now it's n sub l b, 00:12:46.530 --> 00:12:49.710 align:middle line:84% slightly different nomenclature taken from different articles, 00:12:49.710 --> 00:12:50.890 align:middle line:90% but it's the same idea. 00:12:50.890 --> 00:12:55.410 align:middle line:84% This is a number of occurrences of base b at position l. 00:12:55.410 --> 00:12:59.820 align:middle line:84% This is the weight matrix as counts, not as frequencies. 00:12:59.820 --> 00:13:04.590 align:middle line:84% And in the denominator is the number of occurrences 00:13:04.590 --> 00:13:05.903 align:middle line:90% of the most common base. 00:13:05.903 --> 00:13:08.070 align:middle line:84% Now, this could be b, or it could be some other one. 00:13:08.070 --> 00:13:09.430 align:middle line:90% But this is the most common one. 00:13:09.430 --> 00:13:11.430 align:middle line:84% This is going to tend to be larger 00:13:11.430 --> 00:13:15.540 align:middle line:84% than or equal to the ends of lb, which is the weight matrix. 00:13:15.540 --> 00:13:19.520 align:middle line:84% And you're going to sum over l, over the length of the binding 00:13:19.520 --> 00:13:20.020 align:middle line:90% site. 00:13:20.020 --> 00:13:25.380 align:middle line:90% This was w in the previous one. 00:13:25.380 --> 00:13:28.110 align:middle line:84% And you're going to just scan this along the entire genome, 00:13:28.110 --> 00:13:29.640 align:middle line:84% stepping it over one base at a time 00:13:29.640 --> 00:13:31.480 align:middle line:84% and coming back on the opposite strand. 00:13:31.480 --> 00:13:33.660 align:middle line:90% And that's going to be ScanACE. 00:13:33.660 --> 00:13:36.060 align:middle line:84% So you've got AlignACE compares to ScanACE. 00:13:36.060 --> 00:13:38.700 align:middle line:84% Now we're going to scan it to see for specificity. 00:13:38.700 --> 00:13:40.370 align:middle line:90% Again, you've got these 0.5's. 00:13:40.370 --> 00:13:42.840 align:middle line:84% You can think of these as pseudocounts. 00:13:42.840 --> 00:13:44.130 align:middle line:90% Keep the zeros out. 00:13:44.130 --> 00:13:46.590 align:middle line:84% You don't want to have a logarithm of 0. 00:13:46.590 --> 00:13:52.140 align:middle line:84% Now, let's walk this through a particular biological data set. 00:13:52.140 --> 00:14:03.420 align:middle line:84% This is a cell cycle data set going through two cycles, cell 00:14:03.420 --> 00:14:04.300 align:middle line:90% division cycles. 00:14:04.300 --> 00:14:04.800 align:middle line:90% here. 00:14:04.800 --> 00:14:07.920 align:middle line:84% There are points, 15 significant time points, 00:14:07.920 --> 00:14:10.150 align:middle line:90% along the horizontal axis. 00:14:10.150 --> 00:14:11.835 align:middle line:84% And this is a particular cluster. 00:14:11.835 --> 00:14:15.030 align:middle line:84% Out of 30 different clusters, this particular one 00:14:15.030 --> 00:14:18.000 align:middle line:84% has a peak just before the S phase, the phase and the cell 00:14:18.000 --> 00:14:23.850 align:middle line:84% cycle where you're trying to get the replication of the cell 00:14:23.850 --> 00:14:26.490 align:middle line:84% at the S phase is where you actually synthesize 00:14:26.490 --> 00:14:28.802 align:middle line:90% a new set of DNA molecules. 00:14:28.802 --> 00:14:30.510 align:middle line:84% You duplicate it, just as we talked about 00:14:30.510 --> 00:14:32.890 align:middle line:90% in the first lecture. 00:14:32.890 --> 00:14:36.610 align:middle line:84% And actually, since you've recorded a time series 00:14:36.610 --> 00:14:38.250 align:middle line:84% through two cell division cycles, 00:14:38.250 --> 00:14:40.380 align:middle line:84% you expect there to be periodicity. 00:14:40.380 --> 00:14:43.062 align:middle line:84% Or genes that are acquired in the first S phase, 00:14:43.062 --> 00:14:45.270 align:middle line:84% you expect them to be acquired in the second S phase. 00:14:45.270 --> 00:14:49.560 align:middle line:84% That's the underlying thought behind designing 00:14:49.560 --> 00:14:52.080 align:middle line:84% this experiment is you would synchronize all the cells. 00:14:52.080 --> 00:14:53.952 align:middle line:84% Normally, cells are all over the place. 00:14:53.952 --> 00:14:55.410 align:middle line:84% Some of them are in S. Some of them 00:14:55.410 --> 00:14:59.830 align:middle line:84% are in M, which is where the metaphase chromosomes separate. 00:14:59.830 --> 00:15:02.610 align:middle line:84% But in this, you synchronize them all up by a method 00:15:02.610 --> 00:15:04.480 align:middle line:84% we'll talk about in just a moment. 00:15:04.480 --> 00:15:06.240 align:middle line:84% And then this is that diagram where 00:15:06.240 --> 00:15:08.573 align:middle line:84% we have the number of standard deviations from the mean. 00:15:08.573 --> 00:15:11.910 align:middle line:84% This is a normalized signal of the RNA expression. 00:15:11.910 --> 00:15:15.300 align:middle line:84% On the vertical axis and horizontal axis 00:15:15.300 --> 00:15:19.980 align:middle line:84% is this time series categorically described as G1-- 00:15:19.980 --> 00:15:23.280 align:middle line:84% gap 1-- synthesis, gap 2-- metaphase-- 00:15:23.280 --> 00:15:25.900 align:middle line:90% mitosis, and so on. 00:15:25.900 --> 00:15:28.890 align:middle line:84% Now, what do we learn from this particular cluster? 00:15:28.890 --> 00:15:33.090 align:middle line:84% This cluster has 186 genes in it. 00:15:33.090 --> 00:15:36.000 align:middle line:84% That means the RNAs for those 186 genes 00:15:36.000 --> 00:15:39.000 align:middle line:90% were in a nice envelope. 00:15:39.000 --> 00:15:43.920 align:middle line:84% It doesn't mean that they're strictly couldn't be 185, 187. 00:15:43.920 --> 00:15:46.137 align:middle line:84% There may be some outliers on the edges. 00:15:46.137 --> 00:15:47.970 align:middle line:84% But that's the number that we're going to be 00:15:47.970 --> 00:15:49.380 align:middle line:90% doing these calculations for. 00:15:49.380 --> 00:15:52.878 align:middle line:90% 00:15:52.878 --> 00:15:54.687 align:middle line:84% The ways we're going to evaluate it 00:15:54.687 --> 00:15:56.520 align:middle line:84% is, first, whether the functional categories 00:15:56.520 --> 00:15:57.280 align:middle line:90% make sense. 00:15:57.280 --> 00:15:59.820 align:middle line:84% Is there an enrichment for a particular functional category? 00:15:59.820 --> 00:16:02.520 align:middle line:84% You may have already, those biologists among you, 00:16:02.520 --> 00:16:05.102 align:middle line:84% may have already had a hypothesis of what 00:16:05.102 --> 00:16:06.810 align:middle line:84% functional categories should be enriched. 00:16:06.810 --> 00:16:08.977 align:middle line:84% If it's going to peak, if these are the RNAs that 00:16:08.977 --> 00:16:10.560 align:middle line:84% are going to peak just before S phase, 00:16:10.560 --> 00:16:12.630 align:middle line:84% just before you need them for DNA synthesis, 00:16:12.630 --> 00:16:15.358 align:middle line:84% maybe these can encode genes that are involved-- 00:16:15.358 --> 00:16:17.400 align:middle line:84% genes [? possibly ?] involved-- in DNA synthesis. 00:16:17.400 --> 00:16:22.800 align:middle line:84% Sure enough, that's the most striking observation 00:16:22.800 --> 00:16:26.603 align:middle line:84% is that in this database, this MIPS 00:16:26.603 --> 00:16:28.020 align:middle line:84% database of functional categories, 00:16:28.020 --> 00:16:31.320 align:middle line:84% you have 82 genes that are described as involved in DNA 00:16:31.320 --> 00:16:32.580 align:middle line:90% synthesis. 00:16:32.580 --> 00:16:36.990 align:middle line:84% And of this cluster that are co-expressed at peak, at S, 00:16:36.990 --> 00:16:40.990 align:middle line:84% you have an overlap of 23 with that. 00:16:40.990 --> 00:16:43.530 align:middle line:84% And that may not sound like a huge overlap-- a few-- 00:16:43.530 --> 00:16:45.450 align:middle line:84% but it's very statistically significant. 00:16:45.450 --> 00:16:48.750 align:middle line:84% It's 10 to the -16 is the probability of that occurring 00:16:48.750 --> 00:16:51.600 align:middle line:84% at random, out of the 6,000 or so [INAUDIBLE] genes, 00:16:51.600 --> 00:16:55.450 align:middle line:84% that having this overlap of 23 is very significant. 00:16:55.450 --> 00:16:56.400 align:middle line:90% So that's the first. 00:16:56.400 --> 00:16:58.140 align:middle line:84% And we'll, in just a moment, show 00:16:58.140 --> 00:16:59.760 align:middle line:90% how we did that calculation. 00:16:59.760 --> 00:17:01.320 align:middle line:90% But that's your first test. 00:17:01.320 --> 00:17:03.900 align:middle line:84% There is a functional category enrichment. 00:17:03.900 --> 00:17:05.730 align:middle line:90% Next, you find the motifs. 00:17:05.730 --> 00:17:07.050 align:middle line:90% You use the AlignACE. 00:17:07.050 --> 00:17:07.800 align:middle line:90% You go through. 00:17:07.800 --> 00:17:08.940 align:middle line:90% You find the top motif. 00:17:08.940 --> 00:17:09.930 align:middle line:90% It's MCB. 00:17:09.930 --> 00:17:13.349 align:middle line:84% You go and you find the very close second-highest motif. 00:17:13.349 --> 00:17:14.220 align:middle line:90% It's SCB. 00:17:14.220 --> 00:17:16.710 align:middle line:90% These are not chosen by hand. 00:17:16.710 --> 00:17:18.839 align:middle line:84% This is all done algorithmically. 00:17:18.839 --> 00:17:21.030 align:middle line:84% The only input-- there's no literature input 00:17:21.030 --> 00:17:24.300 align:middle line:84% except for checking these functional categories-- 00:17:24.300 --> 00:17:29.910 align:middle line:84% for finding the motifs, it's just the microarray data 00:17:29.910 --> 00:17:33.090 align:middle line:84% and the sequence upstream from the genes 00:17:33.090 --> 00:17:35.160 align:middle line:90% that come out of this cluster. 00:17:35.160 --> 00:17:36.940 align:middle line:90% That's how these were found. 00:17:36.940 --> 00:17:38.160 align:middle line:90% Now, they have to have names. 00:17:38.160 --> 00:17:40.800 align:middle line:84% MCB and SCB, we could have just called them x and y. 00:17:40.800 --> 00:17:47.400 align:middle line:84% But these names do mean that the CompareACE score to something 00:17:47.400 --> 00:17:49.480 align:middle line:84% that was in the literature is good. 00:17:49.480 --> 00:17:54.900 align:middle line:84% But a very profound accomplishment of this 00:17:54.900 --> 00:17:56.430 align:middle line:90% is that now-- 00:17:56.430 --> 00:17:58.920 align:middle line:84% unlike the literature, where it's rather challenging 00:17:58.920 --> 00:18:02.460 align:middle line:84% to find the connection from a conclusion, 00:18:02.460 --> 00:18:06.150 align:middle line:84% like this motif is likely to regulate 00:18:06.150 --> 00:18:08.100 align:middle line:84% this gene is likely to be enriched 00:18:08.100 --> 00:18:10.860 align:middle line:84% in this class of genes-- here, it's directly traceable. 00:18:10.860 --> 00:18:12.930 align:middle line:84% You can see the logic that connects this motif 00:18:12.930 --> 00:18:16.690 align:middle line:84% MCB to this cluster via Gibbs algorithm. 00:18:16.690 --> 00:18:20.040 align:middle line:84% And this cluster is traceable back to the RNA profiles 00:18:20.040 --> 00:18:21.120 align:middle line:90% on the microarray. 00:18:21.120 --> 00:18:26.010 align:middle line:84% This is all a very simple, comprehensive study. 00:18:26.010 --> 00:18:28.950 align:middle line:84% But now you want to ask, is this motif-- 00:18:28.950 --> 00:18:31.530 align:middle line:84% we know that it's got a high MAP score. 00:18:31.530 --> 00:18:32.430 align:middle line:90% It's highly enriched. 00:18:32.430 --> 00:18:36.330 align:middle line:84% And it's highly unlikely that a motif this strong 00:18:36.330 --> 00:18:41.192 align:middle line:84% would have occurred in this size cluster of genes. 00:18:41.192 --> 00:18:42.900 align:middle line:84% But what you want to ask, is it specific? 00:18:42.900 --> 00:18:45.400 align:middle line:84% This is the thing we've been putting off for a little while. 00:18:45.400 --> 00:18:46.800 align:middle line:90% Is it specific? 00:18:46.800 --> 00:18:49.560 align:middle line:84% And if you look at the 30 clusters 00:18:49.560 --> 00:18:52.080 align:middle line:84% when you cluster this whole set of genes 00:18:52.080 --> 00:18:55.380 align:middle line:84% that vary during the cell cycle into 30 00:18:55.380 --> 00:18:59.190 align:middle line:84% envelopes, this particular one, envelope number 2, cluster 00:18:59.190 --> 00:19:04.320 align:middle line:84% number 2, which is displayed in the upper left, 00:19:04.320 --> 00:19:06.120 align:middle line:84% down in the lower left, you can see 00:19:06.120 --> 00:19:09.030 align:middle line:84% that all the MCB motifs, almost all of them, 00:19:09.030 --> 00:19:11.430 align:middle line:84% are found in cluster 2 when you use ScanACE, 00:19:11.430 --> 00:19:15.240 align:middle line:84% and very few of them are found in the rest of the genome-- 00:19:15.240 --> 00:19:19.950 align:middle line:84% similarly for the second-most impressive motif 00:19:19.950 --> 00:19:22.380 align:middle line:90% by AlignACE MAP scores, SCB. 00:19:22.380 --> 00:19:25.470 align:middle line:84% And it's also specific to cluster 2. 00:19:25.470 --> 00:19:29.460 align:middle line:84% The fact that you're seeing this non-random enrichment 00:19:29.460 --> 00:19:31.920 align:middle line:84% for functional category, this non-random enrichment 00:19:31.920 --> 00:19:37.080 align:middle line:84% for a motif, this non-random specificity of that motif 00:19:37.080 --> 00:19:40.050 align:middle line:84% and a second motif, kind of tells you that everything is 00:19:40.050 --> 00:19:42.870 align:middle line:84% working, that your RNA data collection is working-- 00:19:42.870 --> 00:19:45.730 align:middle line:84% which, you may spend a lot of money to get to this point, 00:19:45.730 --> 00:19:48.060 align:middle line:90% you should be gratified-- 00:19:48.060 --> 00:19:51.210 align:middle line:84% and the clustering is working, and the motif finding 00:19:51.210 --> 00:19:53.070 align:middle line:84% and specificity scores, all this is working. 00:19:53.070 --> 00:19:55.740 align:middle line:84% It doesn't mean that it's absolutely perfectly tuned 00:19:55.740 --> 00:19:57.390 align:middle line:84% and everything, but it's giving you 00:19:57.390 --> 00:20:00.880 align:middle line:84% feedback that you're taking a step in the right direction. 00:20:00.880 --> 00:20:05.070 align:middle line:84% Similarly, the position of this motif in the promoter 00:20:05.070 --> 00:20:06.000 align:middle line:90% is non-random. 00:20:06.000 --> 00:20:09.210 align:middle line:84% You see this little spike that's coming up just before the-- 00:20:09.210 --> 00:20:11.370 align:middle line:84% it could be the transcription or translation start. 00:20:11.370 --> 00:20:14.220 align:middle line:84% In this case, the ATG is the translation start. 00:20:14.220 --> 00:20:15.420 align:middle line:90% And it's non-random. 00:20:15.420 --> 00:20:17.650 align:middle line:84% How do we measure each of these things? 00:20:17.650 --> 00:20:18.840 align:middle line:90% How do we get this? 00:20:18.840 --> 00:20:20.465 align:middle line:84% Well, before we get that, I'll give you 00:20:20.465 --> 00:20:23.670 align:middle line:84% two more examples, same format, just to show you 00:20:23.670 --> 00:20:25.440 align:middle line:84% that you get different motifs when 00:20:25.440 --> 00:20:28.260 align:middle line:84% you go to different clusters-- two more clusters. 00:20:28.260 --> 00:20:31.140 align:middle line:90% The next one is also periodic. 00:20:31.140 --> 00:20:38.340 align:middle line:84% It has a peak now slightly shifted 00:20:38.340 --> 00:20:41.040 align:middle line:84% to the right from the previous periodic function. 00:20:41.040 --> 00:20:44.010 align:middle line:84% And it repeats at exactly the same periodicity 00:20:44.010 --> 00:20:47.700 align:middle line:84% as if they're part of the same periodic function, which 00:20:47.700 --> 00:20:50.280 align:middle line:84% is exactly how the experiment was designed. 00:20:50.280 --> 00:20:53.130 align:middle line:84% The difference between this and the previous one is now, 00:20:53.130 --> 00:20:57.230 align:middle line:84% the two top motifs are not previously known motifs. 00:20:57.230 --> 00:20:59.020 align:middle line:84% It doesn't mean they're any worse. 00:20:59.020 --> 00:21:02.160 align:middle line:90% But they're new ones. 00:21:02.160 --> 00:21:05.198 align:middle line:84% And the way you evaluate whether they're specific 00:21:05.198 --> 00:21:06.990 align:middle line:84% is the same way we got the specificity for. 00:21:06.990 --> 00:21:09.990 align:middle line:84% Now they're in cluster 14, which is this cluster up 00:21:09.990 --> 00:21:11.040 align:middle line:90% in the upper left. 00:21:11.040 --> 00:21:14.130 align:middle line:84% And both of them are about as specific 00:21:14.130 --> 00:21:16.170 align:middle line:84% as the ones in the previous slide. 00:21:16.170 --> 00:21:19.380 align:middle line:84% The functional category is not as impressive. 00:21:19.380 --> 00:21:22.326 align:middle line:84% It's 10 to the minus 6 instead of-- 00:21:22.326 --> 00:21:25.770 align:middle line:84% sorry, 10 to the minus 4, no 10 to the minus 6, 00:21:25.770 --> 00:21:28.660 align:middle line:84% the previous one's 10 to the minus 16. 00:21:28.660 --> 00:21:32.580 align:middle line:84% Now, this is still statistically significant. 00:21:32.580 --> 00:21:35.430 align:middle line:84% But it could mean that this particular way 00:21:35.430 --> 00:21:38.610 align:middle line:84% of functional categorization which the curators use 00:21:38.610 --> 00:21:41.520 align:middle line:84% may not be ideal for this particular regulatory 00:21:41.520 --> 00:21:46.650 align:middle line:90% mechanism, regulatory regulon. 00:21:46.650 --> 00:21:51.110 align:middle line:84% So this may be a discovery both of a new regulatory set 00:21:51.110 --> 00:21:54.050 align:middle line:90% and of two new motifs. 00:21:54.050 --> 00:21:56.330 align:middle line:84% But in order to establish that, you'd 00:21:56.330 --> 00:21:59.210 align:middle line:84% need some experiments to really, say, knock out these motifs 00:21:59.210 --> 00:22:01.520 align:middle line:84% and see what the consequences are. 00:22:01.520 --> 00:22:05.870 align:middle line:84% Now, the third cluster illustrates yet another set 00:22:05.870 --> 00:22:07.010 align:middle line:90% of ideas. 00:22:07.010 --> 00:22:10.670 align:middle line:84% Here, even though the experiment was designed 00:22:10.670 --> 00:22:14.240 align:middle line:84% specifically to enrich for the most abundant-- 00:22:14.240 --> 00:22:18.980 align:middle line:84% or sorry, for the most periodic gene expression, 00:22:18.980 --> 00:22:24.420 align:middle line:84% there were inevitably features of the experimental design 00:22:24.420 --> 00:22:25.790 align:middle line:90% which were not periodic. 00:22:25.790 --> 00:22:28.310 align:middle line:84% In particular, when you synchronize the cells, 00:22:28.310 --> 00:22:31.010 align:middle line:84% you force them all to be in synchrony for the cell division 00:22:31.010 --> 00:22:34.370 align:middle line:84% cycle, you did that by taking a temperature-sensitive mutant 00:22:34.370 --> 00:22:39.260 align:middle line:84% in the cell division cycle, say CDC15 or 28. 00:22:39.260 --> 00:22:41.840 align:middle line:84% And that temperature-sensitive mutant, 00:22:41.840 --> 00:22:44.900 align:middle line:84% that requires that you raise the temperature to shut down 00:22:44.900 --> 00:22:49.320 align:middle line:84% the function of that gene by unfolding the protein. 00:22:49.320 --> 00:22:51.290 align:middle line:84% And so you have a temperature shift 00:22:51.290 --> 00:22:53.165 align:middle line:84% to allow them to go back into the cell cycle. 00:22:53.165 --> 00:22:55.040 align:middle line:84% So you're going from high temperature to low. 00:22:55.040 --> 00:22:55.980 align:middle line:90% That's one thing. 00:22:55.980 --> 00:22:59.210 align:middle line:84% And so that temperature essentially decays rapidly. 00:22:59.210 --> 00:23:04.080 align:middle line:84% And then you have the residual of that going out in time. 00:23:04.080 --> 00:23:06.513 align:middle line:84% In addition, there's all the physiological effects. 00:23:06.513 --> 00:23:08.180 align:middle line:84% You had all these things kind of waiting 00:23:08.180 --> 00:23:09.860 align:middle line:84% in this funny physiological state. 00:23:09.860 --> 00:23:11.340 align:middle line:90% And then that decays with time. 00:23:11.340 --> 00:23:13.190 align:middle line:90% So that's not cyclic. 00:23:13.190 --> 00:23:20.000 align:middle line:84% That perturbation is a linear or decay. 00:23:20.000 --> 00:23:24.200 align:middle line:84% And sure enough, you find examples of clusters 00:23:24.200 --> 00:23:25.520 align:middle line:90% which are not periodic. 00:23:25.520 --> 00:23:28.340 align:middle line:84% This one peaks in the second cell cycle 00:23:28.340 --> 00:23:31.320 align:middle line:84% but not in the corresponding point of the first cell cycle. 00:23:31.320 --> 00:23:34.430 align:middle line:84% And in fact, most of the 30 clusters, 00:23:34.430 --> 00:23:36.770 align:middle line:84% when you divide this up into 30-- 00:23:36.770 --> 00:23:39.020 align:middle line:84% the entire expression space up into 30-- 00:23:39.020 --> 00:23:39.930 align:middle line:90% are like this. 00:23:39.930 --> 00:23:41.630 align:middle line:90% They're not periodic. 00:23:41.630 --> 00:23:42.830 align:middle line:90% But that's OK. 00:23:42.830 --> 00:23:45.140 align:middle line:84% Because what you're looking for is clustering, 00:23:45.140 --> 00:23:47.030 align:middle line:84% as if these were different conditions or different time 00:23:47.030 --> 00:23:47.530 align:middle line:90% points. 00:23:47.530 --> 00:23:49.040 align:middle line:90% It doesn't matter what it is. 00:23:49.040 --> 00:23:52.220 align:middle line:84% Because they are coexpressed, so going up and down together, 00:23:52.220 --> 00:23:55.260 align:middle line:84% possibly during serendipitous factors. 00:23:55.260 --> 00:23:57.500 align:middle line:84% But you can still apply the same criteria 00:23:57.500 --> 00:23:59.970 align:middle line:84% for asking whether you're impressed with this cluster 00:23:59.970 --> 00:24:00.470 align:middle line:90% or not. 00:24:00.470 --> 00:24:04.190 align:middle line:84% Does it have enrichment for a functional category 00:24:04.190 --> 00:24:06.920 align:middle line:84% in the upper left-hand part of 556? 00:24:06.920 --> 00:24:08.540 align:middle line:90% And wow, it really does. 00:24:08.540 --> 00:24:11.570 align:middle line:84% This is the most impressive one of all 30 clusters. 00:24:11.570 --> 00:24:15.050 align:middle line:84% It has a probability of 10 to the minus 54 that you would 00:24:15.050 --> 00:24:18.590 align:middle line:84% find this degree of overlap between the functional 00:24:18.590 --> 00:24:22.100 align:middle line:84% category-- think of this as a Venn diagram of overlapping 00:24:22.100 --> 00:24:23.310 align:middle line:90% circles-- 00:24:23.310 --> 00:24:26.390 align:middle line:84% the overlap between the class of ribosomal proteins 00:24:26.390 --> 00:24:30.530 align:middle line:84% and the class of this particular cluster, which is not periodic, 00:24:30.530 --> 00:24:34.910 align:middle line:90% is amazingly significant. 00:24:34.910 --> 00:24:36.770 align:middle line:84% In addition, you find two motifs. 00:24:36.770 --> 00:24:40.340 align:middle line:84% The top two motifs are highly enriched. 00:24:40.340 --> 00:24:46.250 align:middle line:84% That's what the Snyder information content 00:24:46.250 --> 00:24:47.330 align:middle line:90% logo means-- 00:24:47.330 --> 00:24:48.770 align:middle line:90% and is highly specific. 00:24:48.770 --> 00:24:51.740 align:middle line:84% That's what the bottom line means. 00:24:51.740 --> 00:24:53.480 align:middle line:84% This is-- it's present in cluster 1 00:24:53.480 --> 00:24:58.340 align:middle line:84% and very little in any of the other clusters by ScanACE 00:24:58.340 --> 00:25:00.895 align:middle line:90% using the motif matrix. 00:25:00.895 --> 00:25:03.270 align:middle line:84% So these are three clusters, each with a different story. 00:25:03.270 --> 00:25:05.690 align:middle line:84% The first one was two known motifs. 00:25:05.690 --> 00:25:08.390 align:middle line:84% The second was two unknown motifs and possibly 00:25:08.390 --> 00:25:09.900 align:middle line:90% a new functional category. 00:25:09.900 --> 00:25:13.250 align:middle line:84% The third one is a whopping match to a functional category, 00:25:13.250 --> 00:25:16.430 align:middle line:84% one known, one unknown motif, and the whole thing 00:25:16.430 --> 00:25:18.558 align:middle line:84% non-periodic, even though the experimental design 00:25:18.558 --> 00:25:19.100 align:middle line:90% was periodic. 00:25:19.100 --> 00:25:21.800 align:middle line:90% 00:25:21.800 --> 00:25:25.610 align:middle line:84% So now we've shown that you can quantitate all these things 00:25:25.610 --> 00:25:28.850 align:middle line:84% that are often casually treated in the discussion 00:25:28.850 --> 00:25:30.443 align:middle line:90% section of biological papers. 00:25:30.443 --> 00:25:32.360 align:middle line:84% Here, they've all been treated quantitatively. 00:25:32.360 --> 00:25:33.350 align:middle line:90% But how do we do that? 00:25:33.350 --> 00:25:36.110 align:middle line:84% What is the algorithm behind each of these things? 00:25:36.110 --> 00:25:38.100 align:middle line:84% We won't talk about how we measure periodicity. 00:25:38.100 --> 00:25:42.110 align:middle line:84% But you can imagine you can measure the periodicity. 00:25:42.110 --> 00:25:43.490 align:middle line:90% And we have. 00:25:43.490 --> 00:25:47.570 align:middle line:90% You could ask specificity. 00:25:47.570 --> 00:25:49.370 align:middle line:84% How did we measure the specificity 00:25:49.370 --> 00:25:50.662 align:middle line:90% and the functional assignments? 00:25:50.662 --> 00:25:54.382 align:middle line:84% It turns out that's almost the same statistical function 00:25:54.382 --> 00:25:56.840 align:middle line:84% we use for those two things-- functional assignments, group 00:25:56.840 --> 00:25:57.800 align:middle line:90% specificity. 00:25:57.800 --> 00:25:59.750 align:middle line:84% Positional bias is a different one. 00:25:59.750 --> 00:26:02.300 align:middle line:84% And CompareACE we can use not only 00:26:02.300 --> 00:26:04.970 align:middle line:84% for looking for previous motifs, as we 00:26:04.970 --> 00:26:07.260 align:middle line:84% did in the AlignACE algorithm itself 00:26:07.260 --> 00:26:10.220 align:middle line:84% and as we do as we want to look through databases of motifs, 00:26:10.220 --> 00:26:14.430 align:middle line:84% we can also look as the motif looks symmetry on itself. 00:26:14.430 --> 00:26:17.720 align:middle line:84% So this is how we do each of these. 00:26:17.720 --> 00:26:20.840 align:middle line:90% We have a choice. 00:26:20.840 --> 00:26:24.830 align:middle line:84% When we ask whether the intersection of two subsets 00:26:24.830 --> 00:26:27.050 align:middle line:90% of all of the possible genes-- 00:26:27.050 --> 00:26:29.870 align:middle line:84% let's say our cluster and a functional category 00:26:29.870 --> 00:26:33.710 align:middle line:84% or a cluster and all the best hits with ScanACE-- 00:26:33.710 --> 00:26:36.290 align:middle line:84% if those overlap in a significant way, 00:26:36.290 --> 00:26:39.888 align:middle line:84% we can think of that as sampling from a population. 00:26:39.888 --> 00:26:41.930 align:middle line:84% The question is, are we sampling with replacement 00:26:41.930 --> 00:26:43.400 align:middle line:90% or without replacement? 00:26:43.400 --> 00:26:46.080 align:middle line:84% It's an easy thing to get confused about. 00:26:46.080 --> 00:26:48.500 align:middle line:84% And I urge you to just look back at the definitions 00:26:48.500 --> 00:26:49.880 align:middle line:90% of these offline. 00:26:49.880 --> 00:26:58.002 align:middle line:84% But there actually-- a mistake was made in the literature 00:26:58.002 --> 00:27:00.460 align:middle line:84% by an author who should have known better because he got it 00:27:00.460 --> 00:27:04.120 align:middle line:84% right the first time and wrong the second time. 00:27:04.120 --> 00:27:07.930 align:middle line:84% But the correct use-- and in fact, in widespread use-- 00:27:07.930 --> 00:27:09.520 align:middle line:90% is the hypergeometric. 00:27:09.520 --> 00:27:12.490 align:middle line:84% Because we are actually, here, sampling without replacement. 00:27:12.490 --> 00:27:16.570 align:middle line:84% When you do that, the two sets, the two subsets of the big 00:27:16.570 --> 00:27:20.260 align:middle line:84% set-- the big set is n, and the two subsets are s1 and s2-- 00:27:20.260 --> 00:27:24.320 align:middle line:84% you have these combinatoric, this simple combinatoric, 00:27:24.320 --> 00:27:27.130 align:middle line:84% where you have s1 choose x where x 00:27:27.130 --> 00:27:29.690 align:middle line:84% is the intersection between the two sets. 00:27:29.690 --> 00:27:30.190 align:middle line:90% And 00:27:30.190 --> 00:27:32.500 align:middle line:84% This will be much clearer in the next slide, where 00:27:32.500 --> 00:27:34.480 align:middle line:84% we have a kind of a diagram to go with it. 00:27:34.480 --> 00:27:38.057 align:middle line:84% But this is the chance of getting exactly x. 00:27:38.057 --> 00:27:39.640 align:middle line:84% In the next slide, we're going to show 00:27:39.640 --> 00:27:45.820 align:middle line:84% how we need to consider the possibility that it 00:27:45.820 --> 00:27:48.100 align:middle line:90% could be x or larger. 00:27:48.100 --> 00:27:50.320 align:middle line:90% Now, so this is the diagram. 00:27:50.320 --> 00:27:53.740 align:middle line:84% n is the total number of genes in [? yeast, ?] somewhere 00:27:53.740 --> 00:27:55.330 align:middle line:90% upwards of 6,000. 00:27:55.330 --> 00:27:57.413 align:middle line:84% And then the subset 1 might be the number 00:27:57.413 --> 00:27:59.080 align:middle line:84% of genes in the cluster that you got out 00:27:59.080 --> 00:28:00.330 align:middle line:90% of your microarray experiment. 00:28:00.330 --> 00:28:01.810 align:middle line:84% And s2 is the number of genes found 00:28:01.810 --> 00:28:03.160 align:middle line:90% in the functional category. 00:28:03.160 --> 00:28:04.510 align:middle line:90% This is the MIPS database. 00:28:04.510 --> 00:28:06.520 align:middle line:84% How surprised are we that we found 00:28:06.520 --> 00:28:09.070 align:middle line:84% x as the intersection between those two sets? 00:28:09.070 --> 00:28:12.980 align:middle line:84% Well, let's say x were 1, and the two sets were about 100 00:28:12.980 --> 00:28:13.480 align:middle line:90% each. 00:28:13.480 --> 00:28:15.880 align:middle line:84% That's not too surprising, right? 00:28:15.880 --> 00:28:18.940 align:middle line:84% But that hypergeometric formula, if you plug in 1, 00:28:18.940 --> 00:28:21.580 align:middle line:84% it's very surprising that you got exactly one. 00:28:21.580 --> 00:28:27.310 align:middle line:84% But the reason is because it could have been bigger than-- 00:28:27.310 --> 00:28:28.900 align:middle line:84% we're saying that it's significant 00:28:28.900 --> 00:28:31.060 align:middle line:90% that they overlap that much. 00:28:31.060 --> 00:28:33.970 align:middle line:84% Well, if it's 1, we have to consider 1 or greater. 00:28:33.970 --> 00:28:37.730 align:middle line:84% Because we're basically saying it could be 1 or greater. 00:28:37.730 --> 00:28:42.100 align:middle line:84% And so what you have to do is do a sum from 1 up. 00:28:42.100 --> 00:28:47.500 align:middle line:84% And what you'll find is that that's 00:28:47.500 --> 00:28:51.640 align:middle line:90% very likely, not surprising. 00:28:51.640 --> 00:28:58.390 align:middle line:84% On the other hand, if we had a very significant overlap 00:28:58.390 --> 00:29:02.860 align:middle line:84% with these two, then the hypothesis that these two 00:29:02.860 --> 00:29:03.793 align:middle line:90% are very related-- 00:29:03.793 --> 00:29:05.710 align:middle line:84% in other words, that you've got an enrichment, 00:29:05.710 --> 00:29:08.620 align:middle line:84% that your cluster is enriched for this functional category 00:29:08.620 --> 00:29:12.460 align:middle line:84% because you've got, say, 100 in s1 and 100 00:29:12.460 --> 00:29:15.100 align:middle line:84% in S2 and the overlap is 99, then 00:29:15.100 --> 00:29:16.600 align:middle line:84% you would have been surprised by 99, 00:29:16.600 --> 00:29:18.460 align:middle line:84% and you would have been surprised by 100. 00:29:18.460 --> 00:29:23.840 align:middle line:84% But both 99 and 100 together are still very rare. 00:29:23.840 --> 00:29:26.110 align:middle line:90% And so you're surprised. 00:29:26.110 --> 00:29:30.630 align:middle line:84% And so the sum has to go from whatever you've got on up. 00:29:30.630 --> 00:29:31.630 align:middle line:90% And that's what this is. 00:29:31.630 --> 00:29:33.370 align:middle line:90% And that's easy to forget, too. 00:29:33.370 --> 00:29:36.160 align:middle line:84% People might just say, oh, this particular intersection 00:29:36.160 --> 00:29:37.172 align:middle line:90% is surprising. 00:29:37.172 --> 00:29:38.380 align:middle line:90% So you have to have that sum. 00:29:38.380 --> 00:29:41.110 align:middle line:90% 00:29:41.110 --> 00:29:43.720 align:middle line:84% Now, I'm going to go from slide 59 to 60. 00:29:43.720 --> 00:29:46.930 align:middle line:84% And there's going to be relatively, graphically, very 00:29:46.930 --> 00:29:47.840 align:middle line:90% little difference. 00:29:47.840 --> 00:29:51.490 align:middle line:84% But it's a radically different thing that we're doing. 00:29:51.490 --> 00:29:53.960 align:middle line:84% Now we're doing group specificity score. 00:29:53.960 --> 00:30:01.990 align:middle line:84% This is the motif you found in the cluster s1. 00:30:01.990 --> 00:30:03.340 align:middle line:90% You looked through s1. 00:30:03.340 --> 00:30:04.905 align:middle line:90% AlignACE found your motif. 00:30:04.905 --> 00:30:07.030 align:middle line:84% Now you want to ask whether that's specific or not. 00:30:07.030 --> 00:30:08.870 align:middle line:84% So you search through the entire genome, 00:30:08.870 --> 00:30:11.260 align:middle line:90% and you pick top 100 matches. 00:30:11.260 --> 00:30:16.960 align:middle line:84% And those are upstream of the genes in s2, subset 2. 00:30:16.960 --> 00:30:20.170 align:middle line:84% If there's a huge overlap of s1 and s2 00:30:20.170 --> 00:30:23.530 align:middle line:84% we'll call x, then you're going to be surprised. 00:30:23.530 --> 00:30:27.130 align:middle line:84% And so again, you take the sum over this hypergeometric 00:30:27.130 --> 00:30:28.220 align:middle line:90% distribution. 00:30:28.220 --> 00:30:30.910 align:middle line:84% And if that's a small number, a small probability, 00:30:30.910 --> 00:30:34.720 align:middle line:84% then that's a measure of how surprised you are. 00:30:34.720 --> 00:30:41.360 align:middle line:84% So if that's 10 to the minus 6, then you're very surprised. 00:30:41.360 --> 00:30:43.090 align:middle line:90% Now, those were hypergeometric. 00:30:43.090 --> 00:30:47.185 align:middle line:84% But positional bias now, it is binomial. 00:30:47.185 --> 00:30:49.780 align:middle line:90% 00:30:49.780 --> 00:30:52.630 align:middle line:84% And you should be able to remember 00:30:52.630 --> 00:30:57.670 align:middle line:84% the binomial is this combinatoric term where 00:30:57.670 --> 00:31:01.720 align:middle line:84% t is the total number of sites, and i 00:31:01.720 --> 00:31:05.080 align:middle line:90% is the amount you're surprised. 00:31:05.080 --> 00:31:09.790 align:middle line:84% So m is the number of sites that are 00:31:09.790 --> 00:31:12.160 align:middle line:90% in the most enriched window. 00:31:12.160 --> 00:31:14.290 align:middle line:84% Now, you can take a window any size you want. 00:31:14.290 --> 00:31:16.660 align:middle line:84% If you make it too small, you're going 00:31:16.660 --> 00:31:18.640 align:middle line:90% to get sampling statistics. 00:31:18.640 --> 00:31:21.640 align:middle line:84% If you make it too big, it'll include the entire 600 base 00:31:21.640 --> 00:31:23.573 align:middle line:90% pair non-coding region. 00:31:23.573 --> 00:31:25.990 align:middle line:84% So you can try a bunch of-- you can try different windows. 00:31:25.990 --> 00:31:28.540 align:middle line:84% But basically, what you're looking 00:31:28.540 --> 00:31:35.200 align:middle line:84% for is how surprised you are that you have 00:31:35.200 --> 00:31:38.560 align:middle line:90% m or more sites in that window. 00:31:38.560 --> 00:31:41.560 align:middle line:84% If you're surprised by 10 sites, then you'd 00:31:41.560 --> 00:31:43.643 align:middle line:84% be even more surprised by more than 10. 00:31:43.643 --> 00:31:44.810 align:middle line:90% So you have to take the sum. 00:31:44.810 --> 00:31:47.350 align:middle line:84% So it's a sum just like the previous hypergeometric ones. 00:31:47.350 --> 00:31:48.850 align:middle line:90% But now it's over a binomial. 00:31:48.850 --> 00:31:51.190 align:middle line:84% And remember, the binomial is this combinatorial term, 00:31:51.190 --> 00:31:54.790 align:middle line:84% a probability to the i power and 1 minus that probability 00:31:54.790 --> 00:31:56.540 align:middle line:90% to the total minus i power. 00:31:56.540 --> 00:32:00.423 align:middle line:84% So this should be very recognizable. 00:32:00.423 --> 00:32:03.090 align:middle line:84% This is the chance that you have enrichment in a particular part 00:32:03.090 --> 00:32:04.510 align:middle line:90% of the promoter. 00:32:04.510 --> 00:32:07.110 align:middle line:90% Now, if we can compare motifs-- 00:32:07.110 --> 00:32:08.742 align:middle line:90% we've mentioned this already-- 00:32:08.742 --> 00:32:10.200 align:middle line:84% we use it in the AlignACE algorithm 00:32:10.200 --> 00:32:14.940 align:middle line:84% itself to cut our losses when we start 00:32:14.940 --> 00:32:19.050 align:middle line:90% refinding the same motif again. 00:32:19.050 --> 00:32:22.830 align:middle line:84% We use it to find whether there were similar motifs. 00:32:22.830 --> 00:32:26.310 align:middle line:84% And through experience and training sets-- 00:32:26.310 --> 00:32:29.130 align:middle line:84% and you can find that, just kind of like a correlation 00:32:29.130 --> 00:32:35.100 align:middle line:84% coefficient, the CompareACE score, as it gets closer to 1, 00:32:35.100 --> 00:32:36.330 align:middle line:90% is more and more believable. 00:32:36.330 --> 00:32:39.690 align:middle line:84% And about 0.7 is where you get statistically 00:32:39.690 --> 00:32:44.340 align:middle line:84% significant matches to other motifs. 00:32:44.340 --> 00:32:46.380 align:middle line:84% And here's an example where you can actually 00:32:46.380 --> 00:32:48.810 align:middle line:84% treat the distances to other motifs, 00:32:48.810 --> 00:32:52.020 align:middle line:84% so similar to other motifs, where 1 is perfectly similar. 00:32:52.020 --> 00:32:57.090 align:middle line:84% As you get along the diagonal, any motif is similar to itself, 00:32:57.090 --> 00:32:58.350 align:middle line:90% by definition. 00:32:58.350 --> 00:33:00.720 align:middle line:84% And you can build up a little matrix 00:33:00.720 --> 00:33:03.190 align:middle line:90% of similarities of motifs. 00:33:03.190 --> 00:33:05.490 align:middle line:84% And then you can do hierarchical clustering of motifs. 00:33:05.490 --> 00:33:08.590 align:middle line:84% And you can, if a and b are sufficiently close together, 00:33:08.590 --> 00:33:12.420 align:middle line:84% then you might consider that they're the same motif 00:33:12.420 --> 00:33:16.110 align:middle line:84% or they're transcription factors where the transcription 00:33:16.110 --> 00:33:18.330 align:middle line:84% factor that binds to that DNA motif 00:33:18.330 --> 00:33:21.270 align:middle line:84% may be related to the protein sequence level. 00:33:21.270 --> 00:33:22.770 align:middle line:84% These are predictions that you might 00:33:22.770 --> 00:33:25.200 align:middle line:84% make from this kind of clustering based 00:33:25.200 --> 00:33:28.380 align:middle line:90% on comparing weight matrices. 00:33:28.380 --> 00:33:33.090 align:middle line:84% Now, if you compare a motif to itself, what does that mean? 00:33:33.090 --> 00:33:36.330 align:middle line:84% If you just compare it to itself over its entirety 00:33:36.330 --> 00:33:39.720 align:middle line:84% in the same orientation-- that's what the previous one-- you'll 00:33:39.720 --> 00:33:41.730 align:middle line:90% get a comparative score of 1. 00:33:41.730 --> 00:33:43.560 align:middle line:84% However, if you flip it-- remember, 00:33:43.560 --> 00:33:46.110 align:middle line:84% DNA being double-stranded, unlike proteins-- when 00:33:46.110 --> 00:33:48.840 align:middle line:84% you flip it and compare the weight matrices, 00:33:48.840 --> 00:33:51.600 align:middle line:84% now you're asking whether it has twofold symmetry. 00:33:51.600 --> 00:33:54.180 align:middle line:84% And this is another very profound connection, I think, 00:33:54.180 --> 00:33:57.180 align:middle line:84% between the weight matrices, which 00:33:57.180 --> 00:34:03.030 align:middle line:84% are kind of a summary of an alignment of many sequences 00:34:03.030 --> 00:34:06.530 align:middle line:84% of evolutionary significance or, in this case, 00:34:06.530 --> 00:34:07.860 align:middle line:90% regulatory significance. 00:34:07.860 --> 00:34:10.170 align:middle line:84% But it's a weight matrix of aligned sequence. 00:34:10.170 --> 00:34:14.880 align:middle line:84% That is actually directly related, conceptually related, 00:34:14.880 --> 00:34:18.510 align:middle line:84% to a very different thought, which 00:34:18.510 --> 00:34:20.639 align:middle line:84% is that the three-dimensional structure 00:34:20.639 --> 00:34:22.710 align:middle line:84% of the protein-nucleic acid interaction 00:34:22.710 --> 00:34:26.010 align:middle line:90% has some symmetry in it. 00:34:26.010 --> 00:34:29.550 align:middle line:84% If you have a protein dimer or a protein domain that's 00:34:29.550 --> 00:34:33.210 align:middle line:84% duplicated, if you have a cell symmetry 00:34:33.210 --> 00:34:36.030 align:middle line:84% to a reverse complement of a motif, that means, 00:34:36.030 --> 00:34:40.679 align:middle line:84% in three-dimensional structure, the two protein motifs 00:34:40.679 --> 00:34:44.580 align:middle line:90% are related by a dyad symmetry. 00:34:44.580 --> 00:34:48.360 align:middle line:84% That means a twofold axis where you rotate 180 degrees in three 00:34:48.360 --> 00:34:49.620 align:middle line:90% dimensions. 00:34:49.620 --> 00:34:52.500 align:middle line:84% On the other hand, if the element, 00:34:52.500 --> 00:34:55.199 align:middle line:84% if the halves of the element or thirds of the element 00:34:55.199 --> 00:35:00.030 align:middle line:84% are related by a direct translation in the motif space, 00:35:00.030 --> 00:35:04.170 align:middle line:84% in the multisequence alignment, then that 00:35:04.170 --> 00:35:06.330 align:middle line:84% means that you have a direct repeat 00:35:06.330 --> 00:35:11.940 align:middle line:84% of DNA-protein interactions where the helical translation 00:35:11.940 --> 00:35:15.410 align:middle line:84% and rotation of the axis is reflected in the protein DNA. 00:35:15.410 --> 00:35:17.970 align:middle line:84% So anyway, there's a connection between motif matrices 00:35:17.970 --> 00:35:20.370 align:middle line:84% and three-dimensional structures. 00:35:20.370 --> 00:35:23.370 align:middle line:84% And here's how it plays out when you do a CompareACE where 00:35:23.370 --> 00:35:26.460 align:middle line:84% you actually go and you compare, column 00:35:26.460 --> 00:35:29.340 align:middle line:84% by column, the weight matrices of motif 1 00:35:29.340 --> 00:35:31.410 align:middle line:84% with itself in reverse complement. 00:35:31.410 --> 00:35:36.690 align:middle line:84% And you can see these three PRRs are in [INAUDIBLE] taken 00:35:36.690 --> 00:35:42.480 align:middle line:84% from bacterial genomes are very significant when you compare it 00:35:42.480 --> 00:35:43.740 align:middle line:90% to its reverse complement. 00:35:43.740 --> 00:35:45.660 align:middle line:84% That means that, very likely, there's 00:35:45.660 --> 00:35:50.490 align:middle line:84% a protein dimer or maybe a closely sequenced 00:35:50.490 --> 00:35:55.650 align:middle line:84% related heterodimer which binds 180 degrees symmetry. 00:35:55.650 --> 00:36:00.930 align:middle line:84% On the other hand, here, when you compare CPXR to itself 00:36:00.930 --> 00:36:03.870 align:middle line:84% reverse complemented, a very poor AlignACE score. 00:36:03.870 --> 00:36:07.380 align:middle line:84% It means it doesn't have this dyad symmetry. 00:36:07.380 --> 00:36:10.290 align:middle line:84% However, if you took the two halves and compared them-- 00:36:10.290 --> 00:36:11.790 align:middle line:84% I don't show it-- but no doubt you 00:36:11.790 --> 00:36:14.360 align:middle line:84% would get a very strong AlignACE-- 00:36:14.360 --> 00:36:16.740 align:middle line:84% a CompareACE score between the two halves, 00:36:16.740 --> 00:36:20.190 align:middle line:84% indicating a direct repeat in sequence space 00:36:20.190 --> 00:36:23.100 align:middle line:84% and sort of a helical repeat in three-dimensional structure 00:36:23.100 --> 00:36:24.330 align:middle line:90% space. 00:36:24.330 --> 00:36:27.330 align:middle line:84% I think this is a very powerful connection between these two. 00:36:27.330 --> 00:36:30.450 align:middle line:84% And that, of course, can be quantitated. 00:36:30.450 --> 00:36:33.210 align:middle line:84% Now we want to say, behind the scenes, 00:36:33.210 --> 00:36:37.620 align:middle line:84% all along, you've had to have some confidence in what 00:36:37.620 --> 00:36:40.890 align:middle line:90% the AlignACE scores meant. 00:36:40.890 --> 00:36:43.140 align:middle line:84% And you do this by doing a test set. 00:36:43.140 --> 00:36:46.230 align:middle line:84% A test that has to be composed of negative controls 00:36:46.230 --> 00:36:48.840 align:middle line:84% and positive controls and very large set 00:36:48.840 --> 00:36:51.750 align:middle line:84% of functional categories from which 00:36:51.750 --> 00:36:54.303 align:middle line:84% we've shown a few examples in the context 00:36:54.303 --> 00:36:55.970 align:middle line:84% of negative controls, positive controls. 00:36:55.970 --> 00:36:59.760 align:middle line:84% So negative controls can be randomly selected genes. 00:36:59.760 --> 00:37:03.000 align:middle line:84% And you want to try different cluster sizes 00:37:03.000 --> 00:37:05.910 align:middle line:84% to see the effect of cluster size on the whole algorithm. 00:37:05.910 --> 00:37:08.670 align:middle line:84% You might be able to predict this completely theoretically. 00:37:08.670 --> 00:37:11.220 align:middle line:84% But it's very gratifying, whether you 00:37:11.220 --> 00:37:14.470 align:middle line:84% can or can't, to run it through exactly the same algorithm, 00:37:14.470 --> 00:37:17.433 align:middle line:84% the same software, with randomly selected sets. 00:37:17.433 --> 00:37:18.600 align:middle line:90% Now, this is very expensive. 00:37:18.600 --> 00:37:20.720 align:middle line:84% Because you can generate-- you need 00:37:20.720 --> 00:37:22.470 align:middle line:84% to generate-- a lot more randomly selected 00:37:22.470 --> 00:37:26.718 align:middle line:90% sets than the actual test sets. 00:37:26.718 --> 00:37:28.260 align:middle line:84% And then for positive controls, there 00:37:28.260 --> 00:37:29.820 align:middle line:84% are actually relatively few of these. 00:37:29.820 --> 00:37:31.620 align:middle line:84% These are cases where you have really 00:37:31.620 --> 00:37:34.260 align:middle line:84% well-defined transcription factors, which 00:37:34.260 --> 00:37:36.930 align:middle line:84% have to have the additional fact that they 00:37:36.930 --> 00:37:38.430 align:middle line:90% have five or more known sites. 00:37:38.430 --> 00:37:41.370 align:middle line:84% Because you need to have five or more sites in order 00:37:41.370 --> 00:37:44.760 align:middle line:84% for AlignACE to get a grip on the problem 00:37:44.760 --> 00:37:47.560 align:middle line:84% and produce a nice multisequence alignment. 00:37:47.560 --> 00:37:49.770 align:middle line:84% OK, so let's go through, first, the results 00:37:49.770 --> 00:37:51.210 align:middle line:90% of the functional categories-- 00:37:51.210 --> 00:37:54.810 align:middle line:84% 248 functional categories-- from these different databases 00:37:54.810 --> 00:37:57.120 align:middle line:84% and then go through the negative and positive controls. 00:37:57.120 --> 00:38:00.300 align:middle line:84% So here are some of the friends that we happen to find-- now, 00:38:00.300 --> 00:38:02.160 align:middle line:84% this is all done from functional categories. 00:38:02.160 --> 00:38:03.662 align:middle line:84% This was not done from microarrays. 00:38:03.662 --> 00:38:06.120 align:middle line:84% But here are some of the friends that we found in this cell 00:38:06.120 --> 00:38:07.380 align:middle line:90% cycle microarray data. 00:38:07.380 --> 00:38:09.660 align:middle line:90% RAF1 was the ribosomal one. 00:38:09.660 --> 00:38:13.020 align:middle line:90% GCN4 we've seen before. 00:38:13.020 --> 00:38:17.910 align:middle line:84% And MCB was the one that was in the S phase. 00:38:17.910 --> 00:38:21.840 align:middle line:90% 00:38:21.840 --> 00:38:23.700 align:middle line:84% And you can see these have been ranked. 00:38:23.700 --> 00:38:24.690 align:middle line:84% And remember, so you could rank them 00:38:24.690 --> 00:38:26.857 align:middle line:84% by three different methods-- by the MAP score, which 00:38:26.857 --> 00:38:32.250 align:middle line:84% is the unlikeliness of finding this good an information 00:38:32.250 --> 00:38:34.590 align:middle line:84% content motif in the learning set. 00:38:34.590 --> 00:38:36.360 align:middle line:84% It doesn't tell you about specificity. 00:38:36.360 --> 00:38:39.300 align:middle line:84% That's the next column to the right. 00:38:39.300 --> 00:38:41.650 align:middle line:84% There's MAP, the specificity score, 00:38:41.650 --> 00:38:44.160 align:middle line:84% which means that it's present in that functional 00:38:44.160 --> 00:38:47.640 align:middle line:84% category and not in lots of other parts of the genome, 00:38:47.640 --> 00:38:48.870 align:middle line:90% and then position the bot. 00:38:48.870 --> 00:38:52.410 align:middle line:84% And remember, that was done by the intersecting Venn diagram 00:38:52.410 --> 00:38:53.400 align:middle line:90% hypergeometric. 00:38:53.400 --> 00:38:56.370 align:middle line:84% And then the positional bias-- that was the binomial-- 00:38:56.370 --> 00:39:02.700 align:middle line:84% is how non-randomly positioned is it in the promoters? 00:39:02.700 --> 00:39:05.070 align:middle line:84% And so this is ranked by the specificity. 00:39:05.070 --> 00:39:09.420 align:middle line:84% And you can see RAF1 is very specific to that 00:39:09.420 --> 00:39:11.850 align:middle line:90% particular functional category. 00:39:11.850 --> 00:39:14.190 align:middle line:84% Now let's rank them by positional bias. 00:39:14.190 --> 00:39:16.018 align:middle line:84% And you get a very different story. 00:39:16.018 --> 00:39:18.060 align:middle line:84% The ones that were on the top of the previous one 00:39:18.060 --> 00:39:19.110 align:middle line:90% are off the chart here. 00:39:19.110 --> 00:39:21.720 align:middle line:84% MCB just barely makes it as number 14. 00:39:21.720 --> 00:39:24.750 align:middle line:84% And this A-rich sequence logo, which you might think 00:39:24.750 --> 00:39:29.400 align:middle line:84% is something that is all over the place, and in fact, it is. 00:39:29.400 --> 00:39:31.620 align:middle line:84% It has a pretty poor specificity score. 00:39:31.620 --> 00:39:33.060 align:middle line:90% It has a high MAP score. 00:39:33.060 --> 00:39:35.410 align:middle line:84% Its positional bias is astronomical. 00:39:35.410 --> 00:39:39.720 align:middle line:84% It is found in a particular place in many promoters 00:39:39.720 --> 00:39:41.640 align:middle line:90% throughout the genome. 00:39:41.640 --> 00:39:45.060 align:middle line:84% So this is a way that you quantitate each of these three 00:39:45.060 --> 00:39:50.010 align:middle line:84% things, the non-randomness in a learning set, 00:39:50.010 --> 00:39:53.250 align:middle line:84% the specificity for that set, and the positional bias 00:39:53.250 --> 00:39:56.620 align:middle line:90% within promoters, in general. 00:39:56.620 --> 00:39:58.245 align:middle line:84% So what are the negative controls here? 00:39:58.245 --> 00:40:01.500 align:middle line:90% 00:40:01.500 --> 00:40:06.180 align:middle line:84% Clusters of size 20, 40, 60, 80, 100 open reading frames, 00:40:06.180 --> 00:40:09.330 align:middle line:84% meaning genes for which you might 00:40:09.330 --> 00:40:12.720 align:middle line:90% have functional categories. 00:40:12.720 --> 00:40:17.730 align:middle line:84% And this allows you to calibrate the false positive rates. 00:40:17.730 --> 00:40:20.040 align:middle line:84% And what you do is you're looking for-- 00:40:20.040 --> 00:40:22.380 align:middle line:90% we could use any criteria here. 00:40:22.380 --> 00:40:25.170 align:middle line:84% We said that a MAP score might, on average, be 0 00:40:25.170 --> 00:40:26.110 align:middle line:90% if it's random. 00:40:26.110 --> 00:40:29.520 align:middle line:84% But if we go up above 10, we'll get 00:40:29.520 --> 00:40:33.090 align:middle line:84% a higher enrichment specificity score of 10 00:40:33.090 --> 00:40:37.170 align:middle line:84% to the minus 5 or lower, meaning-- 00:40:37.170 --> 00:40:39.720 align:middle line:84% and then we apply these two criteria 00:40:39.720 --> 00:40:42.450 align:middle line:84% to the functional categories and to the random controls. 00:40:42.450 --> 00:40:45.630 align:middle line:84% And the functional categories is gratifyingly higher 00:40:45.630 --> 00:40:46.890 align:middle line:90% than the random controls. 00:40:46.890 --> 00:40:48.900 align:middle line:84% And so we can say that about half 00:40:48.900 --> 00:40:53.970 align:middle line:84% of the functional category runs are likely to be real motifs. 00:40:53.970 --> 00:40:57.070 align:middle line:84% Of these, about half of those are known. 00:40:57.070 --> 00:41:02.850 align:middle line:84% And so the rest are probably new discovered 00:41:02.850 --> 00:41:08.220 align:middle line:84% motifs and new discovered regulatons-- regulatory 00:41:08.220 --> 00:41:10.170 align:middle line:90% connected genes. 00:41:10.170 --> 00:41:13.170 align:middle line:84% Now, the positive controls, it's said, are harder to come by. 00:41:13.170 --> 00:41:15.340 align:middle line:84% There are 29 transcription factors. 00:41:15.340 --> 00:41:17.820 align:middle line:90% These are incompletely curated. 00:41:17.820 --> 00:41:21.720 align:middle line:84% One of the boons that will come from this systematic analysis 00:41:21.720 --> 00:41:24.390 align:middle line:84% of microarray data and functional categories 00:41:24.390 --> 00:41:27.570 align:middle line:84% will be a lot of new positive controls. 00:41:27.570 --> 00:41:30.180 align:middle line:84% But until we get them, we can't use them. 00:41:30.180 --> 00:41:33.480 align:middle line:84% So this is what one can use right now. 00:41:33.480 --> 00:41:37.920 align:middle line:84% And in 21 out of 29 cases, an appropriate motif-- meaning you 00:41:37.920 --> 00:41:40.887 align:middle line:84% have to basically rerun AlignACE because you can't really 00:41:40.887 --> 00:41:42.720 align:middle line:84% use the weight matrices from the literature. 00:41:42.720 --> 00:41:44.720 align:middle line:84% They were derived by slightly different methods. 00:41:44.720 --> 00:41:46.480 align:middle line:84% But you can use those to prime AlignACE. 00:41:46.480 --> 00:41:48.420 align:middle line:84% It's a trivial thing for AlignACE 00:41:48.420 --> 00:41:51.360 align:middle line:90% to now derive a weight matrix. 00:41:51.360 --> 00:41:53.280 align:middle line:84% And then you compare it to weight matrices 00:41:53.280 --> 00:41:57.960 align:middle line:90% that come out of the tests. 00:41:57.960 --> 00:42:00.360 align:middle line:90% And 21 and 29 work. 00:42:00.360 --> 00:42:03.825 align:middle line:90% And of the eight-- 00:42:03.825 --> 00:42:06.450 align:middle line:84% the difference between these two is eight-- and of those eight, 00:42:06.450 --> 00:42:08.610 align:middle line:84% five were actually an appropriate functional 00:42:08.610 --> 00:42:09.420 align:middle line:90% category. 00:42:09.420 --> 00:42:12.510 align:middle line:84% So depending on how you interpret these two facts, 00:42:12.510 --> 00:42:15.960 align:middle line:84% you can say the false negative rate is 10% to 30%-- 00:42:15.960 --> 00:42:19.140 align:middle line:84% not great, but neither the positive control set 00:42:19.140 --> 00:42:22.710 align:middle line:84% nor the algorithm are perfect here. 00:42:22.710 --> 00:42:24.030 align:middle line:90% Now, where do we go from here? 00:42:24.030 --> 00:42:27.774 align:middle line:90% 00:42:27.774 --> 00:42:32.250 align:middle line:84% We need to both generalize and to reduce the assumptions 00:42:32.250 --> 00:42:35.950 align:middle line:84% so that we can discover new things. 00:42:35.950 --> 00:42:38.340 align:middle line:84% So for example, one of the assumptions we've been making 00:42:38.340 --> 00:42:40.440 align:middle line:90% is that motifs act in isolation. 00:42:40.440 --> 00:42:42.950 align:middle line:84% We've been discovering motifs one at a time. 00:42:42.950 --> 00:42:43.950 align:middle line:90% We'll find the best one. 00:42:43.950 --> 00:42:46.680 align:middle line:84% We'll cross it off our list, or we'll 00:42:46.680 --> 00:42:48.150 align:middle line:90% filter out subsequence ones. 00:42:48.150 --> 00:42:49.300 align:middle line:90% We'll find all the rest. 00:42:49.300 --> 00:42:51.940 align:middle line:84% But what may really be statistically significant, 00:42:51.940 --> 00:42:54.270 align:middle line:84% and we may be missing by looking at it one at a time, 00:42:54.270 --> 00:42:56.040 align:middle line:90% is motif interactions. 00:42:56.040 --> 00:42:59.700 align:middle line:84% And [INAUDIBLE] and coworkers have 00:42:59.700 --> 00:43:02.070 align:middle line:90% pursued this with a vengeance. 00:43:02.070 --> 00:43:04.870 align:middle line:84% And I think this is a very exciting direction 00:43:04.870 --> 00:43:10.260 align:middle line:90% this can go is what proteins-- 00:43:10.260 --> 00:43:13.860 align:middle line:84% how two or three or more motifs can interact 00:43:13.860 --> 00:43:17.520 align:middle line:90% to produce coregulation. 00:43:17.520 --> 00:43:21.030 align:middle line:84% Then we have these DNA motifs that come out 00:43:21.030 --> 00:43:22.420 align:middle line:90% of this microarray data. 00:43:22.420 --> 00:43:25.050 align:middle line:90% But what's binding to it? 00:43:25.050 --> 00:43:26.370 align:middle line:90% How do we find that connection? 00:43:26.370 --> 00:43:29.310 align:middle line:84% Well, one way of many is in vivo crosslinking. 00:43:29.310 --> 00:43:32.070 align:middle line:84% There are also so-called one-hybrid acids and so forth. 00:43:32.070 --> 00:43:33.570 align:middle line:84% But just think of this conceptually. 00:43:33.570 --> 00:43:35.820 align:middle line:84% As you're catching it in the act, you grab it. 00:43:35.820 --> 00:43:38.370 align:middle line:84% And then you do proteomics to find 00:43:38.370 --> 00:43:42.570 align:middle line:84% which proteins are connected to which nucleic acids. 00:43:42.570 --> 00:43:45.570 align:middle line:84% And the final direction this might be going 00:43:45.570 --> 00:43:49.380 align:middle line:84% is we've said that the different columns in the weight matrices 00:43:49.380 --> 00:43:50.350 align:middle line:90% are independent. 00:43:50.350 --> 00:43:53.440 align:middle line:84% And we've already seen multiple examples in the past fact-- 00:43:53.440 --> 00:43:56.760 align:middle line:84% in fact, I emphasize them on purpose-- 00:43:56.760 --> 00:43:59.970 align:middle line:84% where the columns are not independent in RNA 00:43:59.970 --> 00:44:02.970 align:middle line:84% secondary structure, in CpGs and so forth. 00:44:02.970 --> 00:44:05.370 align:middle line:84% And there's some evidence from this paper 00:44:05.370 --> 00:44:09.630 align:middle line:84% that the interdependence between columns 00:44:09.630 --> 00:44:12.730 align:middle line:84% might be something that you can question. 00:44:12.730 --> 00:44:15.360 align:middle line:84% So in summary, we've talked mainly 00:44:15.360 --> 00:44:16.890 align:middle line:84% about clustering and then where you 00:44:16.890 --> 00:44:22.230 align:middle line:84% go to check that your clusters are biologically significant, 00:44:22.230 --> 00:44:24.388 align:middle line:84% whether you've made discoveries and know 00:44:24.388 --> 00:44:25.680 align:middle line:90% the limits of your discoveries. 00:44:25.680 --> 00:44:27.888 align:middle line:84% What are the false positive and false negative rates? 00:44:27.888 --> 00:44:30.420 align:middle line:84% How do you measure the specificity of your motifs? 00:44:30.420 --> 00:44:35.160 align:middle line:84% How do you measure the functional enrichment, 00:44:35.160 --> 00:44:39.060 align:middle line:84% things that are casual in the classic literature? 00:44:39.060 --> 00:44:43.510 align:middle line:84% So I look forward to seeing you next week. 00:44:43.510 --> 00:44:45.170 align:middle line:90% Thank you. 00:44:45.170 --> 00:44:46.155 align:middle line:90%