WEBVTT 00:00:00.000 --> 00:00:00.580 align:middle line:90% 00:00:00.580 --> 00:00:02.440 align:middle line:84% The following content is provided 00:00:02.440 --> 00:00:06.340 align:middle line:84% by MIT OpenCourseWare under a Creative Commons license. 00:00:06.340 --> 00:00:08.500 align:middle line:84% Additional information about our license 00:00:08.500 --> 00:00:10.870 align:middle line:84% and MIT OpenCourseWare in general 00:00:10.870 --> 00:00:12.730 align:middle line:90% is available at ocw.mit.edu. 00:00:12.730 --> 00:00:22.810 align:middle line:90% 00:00:22.810 --> 00:00:23.560 align:middle line:90% GEORGE CHURCH: OK. 00:00:23.560 --> 00:00:24.910 align:middle line:90% Welcome back. 00:00:24.910 --> 00:00:31.180 align:middle line:84% We're going to go through a very specific example of association 00:00:31.180 --> 00:00:34.540 align:middle line:84% studying, illustrating this extremely important statistic, 00:00:34.540 --> 00:00:39.160 align:middle line:84% the chi-square statistic in the simplest case. 00:00:39.160 --> 00:00:46.090 align:middle line:84% That simple case will be a single allele combination, 00:00:46.090 --> 00:00:52.390 align:middle line:84% two alleles and two possible phenotypic outcomes, 00:00:52.390 --> 00:00:57.310 align:middle line:84% HIV resistance and HIV non-resistance. 00:00:57.310 --> 00:01:00.280 align:middle line:84% So to set up this association study, which 00:01:00.280 --> 00:01:03.790 align:middle line:84% would be computational, let's talk a little bit 00:01:03.790 --> 00:01:04.989 align:middle line:90% about the biology here. 00:01:04.989 --> 00:01:08.890 align:middle line:90% 00:01:08.890 --> 00:01:12.550 align:middle line:84% All viruses need to get into your cells somehow. 00:01:12.550 --> 00:01:17.440 align:middle line:84% HIV has a number of proteins to which it binds 00:01:17.440 --> 00:01:18.610 align:middle line:90% on the surface of your cell. 00:01:18.610 --> 00:01:22.210 align:middle line:84% These proteins are not-- they're not designed to bind HIV. 00:01:22.210 --> 00:01:23.480 align:middle line:90% They do something else. 00:01:23.480 --> 00:01:25.810 align:middle line:84% This is in a family of chemokine receptors. 00:01:25.810 --> 00:01:28.960 align:middle line:84% This is involved in intracellular signaling, 00:01:28.960 --> 00:01:34.360 align:middle line:84% and so it's a receptor normally for these chemokines. 00:01:34.360 --> 00:01:38.080 align:middle line:84% But it is also a receptor for the virus. 00:01:38.080 --> 00:01:44.510 align:middle line:84% And in the human population, as we alluded to earlier, 00:01:44.510 --> 00:01:47.830 align:middle line:84% there are at least two alleles, two common alleles. 00:01:47.830 --> 00:01:52.720 align:middle line:84% One of them, the top one, capital CCR5, 00:01:52.720 --> 00:01:54.220 align:middle line:84% has this long, open reading frame. 00:01:54.220 --> 00:01:57.190 align:middle line:84% And this you could translate by your pearl strip 00:01:57.190 --> 00:01:59.080 align:middle line:84% that you wrote for the problem set. 00:01:59.080 --> 00:02:02.450 align:middle line:84% And the DNA sequences in the middle here 00:02:02.450 --> 00:02:07.910 align:middle line:84% and the protein sequence derived from it is on the top strand. 00:02:07.910 --> 00:02:09.789 align:middle line:90% And that's the capital CCR5. 00:02:09.789 --> 00:02:13.900 align:middle line:84% And the little delta or deletion Ccr5 is below it. 00:02:13.900 --> 00:02:17.230 align:middle line:84% You've locked out 32 base pairs, which is not 00:02:17.230 --> 00:02:18.700 align:middle line:90% an interval multiple of three. 00:02:18.700 --> 00:02:21.670 align:middle line:84% And as you know from last lecture, 00:02:21.670 --> 00:02:23.980 align:middle line:84% that means it's going to be a different genetic code. 00:02:23.980 --> 00:02:27.190 align:middle line:84% At every point downstream, this is going to be frame-shifted, 00:02:27.190 --> 00:02:29.480 align:middle line:84% and so you get a whole new set of amino acids 00:02:29.480 --> 00:02:34.400 align:middle line:84% for the entirety of the rest of the carboxy terminus. 00:02:34.400 --> 00:02:37.630 align:middle line:84% So this in black here-- so we're showing 00:02:37.630 --> 00:02:42.730 align:middle line:84% here in the single-letter code a somewhat realistic folding 00:02:42.730 --> 00:02:45.910 align:middle line:84% of the-- schematic folding of the protein, showing here 00:02:45.910 --> 00:02:48.340 align:middle line:90% disulfide between two cysteines. 00:02:48.340 --> 00:02:52.000 align:middle line:84% Transmembrane region, we have these hydrophobic alpha 00:02:52.000 --> 00:02:52.840 align:middle line:90% helices. 00:02:52.840 --> 00:02:55.780 align:middle line:84% And finally, in the black amino acids, 00:02:55.780 --> 00:02:58.120 align:middle line:84% the C terminus, the end of the protein 00:02:58.120 --> 00:03:01.570 align:middle line:84% are all substituted in this deletion mutant. 00:03:01.570 --> 00:03:06.880 align:middle line:84% Now that is sufficient to cause resistance to the virus. 00:03:06.880 --> 00:03:09.370 align:middle line:84% It probably has some effect on its ability 00:03:09.370 --> 00:03:13.490 align:middle line:84% to bind chemokines or react to them in some other way. 00:03:13.490 --> 00:03:17.170 align:middle line:90% And presumably, this is not-- 00:03:17.170 --> 00:03:20.140 align:middle line:84% there is some deleterious effect we do not know about. 00:03:20.140 --> 00:03:23.215 align:middle line:84% But in any case, we can assess this. 00:03:23.215 --> 00:03:25.450 align:middle line:84% We can make a genetic assay for this. 00:03:25.450 --> 00:03:30.070 align:middle line:84% And we can look in human populations 00:03:30.070 --> 00:03:34.870 align:middle line:84% for their resistance to HIV and for the presence of either two 00:03:34.870 --> 00:03:41.440 align:middle line:84% alleles of the resistance or two alleles of the susceptible. 00:03:41.440 --> 00:03:43.690 align:middle line:84% Now I'm kind of biasing you here in this. 00:03:43.690 --> 00:03:45.323 align:middle line:84% We haven't done the association study. 00:03:45.323 --> 00:03:47.740 align:middle line:84% I really shouldn't be referring to it as resistant or not, 00:03:47.740 --> 00:03:50.350 align:middle line:84% but I think it helps you visualize it. 00:03:50.350 --> 00:03:52.460 align:middle line:84% We'll be rigorous enough in the next slide. 00:03:52.460 --> 00:03:57.310 align:middle line:84% So here is, if you will, the big allele, right? 00:03:57.310 --> 00:03:58.590 align:middle line:90% It's the original. 00:03:58.590 --> 00:04:00.130 align:middle line:90% It's the non-deleted allele. 00:04:00.130 --> 00:04:02.560 align:middle line:84% So when you do a PCR assay where you're 00:04:02.560 --> 00:04:06.100 align:middle line:84% amplifying with two primers across the region that 00:04:06.100 --> 00:04:08.200 align:middle line:84% could be deleted or not, you'll tend 00:04:08.200 --> 00:04:10.360 align:middle line:84% to get a large amplification product. 00:04:10.360 --> 00:04:14.170 align:middle line:84% You prime synthesis until you get something 00:04:14.170 --> 00:04:16.355 align:middle line:90% which has 403 base pairs. 00:04:16.355 --> 00:04:18.355 align:middle line:84% And there's enough of it that you can display it 00:04:18.355 --> 00:04:21.100 align:middle line:84% on electrophoretic gel, and it migrates slowly 00:04:21.100 --> 00:04:23.320 align:middle line:90% because it's large. 00:04:23.320 --> 00:04:26.110 align:middle line:84% If you have a homozygote for the deletion allele-- 00:04:26.110 --> 00:04:30.400 align:middle line:84% we'll not call it the HIV resistance allele just yet-- 00:04:30.400 --> 00:04:35.200 align:middle line:84% then you'll get a 371-base-pair PCR product. 00:04:35.200 --> 00:04:36.700 align:middle line:84% And if you have the heterozygote, 00:04:36.700 --> 00:04:40.090 align:middle line:84% you'll get both, the large and the small allele represented 00:04:40.090 --> 00:04:41.560 align:middle line:90% on this electrophoretic assay. 00:04:41.560 --> 00:04:45.820 align:middle line:84% A very simple, very robust DNA PCR-based assay. 00:04:45.820 --> 00:04:49.320 align:middle line:90% 00:04:49.320 --> 00:04:55.430 align:middle line:84% So now let's ask whether one allele or the other 00:04:55.430 --> 00:05:00.680 align:middle line:84% is more abundant in people which are observed to be 00:05:00.680 --> 00:05:02.660 align:middle line:90% seropositive or seronegative. 00:05:02.660 --> 00:05:04.700 align:middle line:84% Seropositive means that they have 00:05:04.700 --> 00:05:07.520 align:middle line:84% circulating antibodies in their serum 00:05:07.520 --> 00:05:12.050 align:middle line:84% which react positively to the HIV virus. 00:05:12.050 --> 00:05:17.160 align:middle line:84% And so that's not necessarily, but is commonly 00:05:17.160 --> 00:05:20.420 align:middle line:84% associated with being heavily exposed to the HIV virus, 00:05:20.420 --> 00:05:22.700 align:middle line:84% and therefore basically infected. 00:05:22.700 --> 00:05:27.320 align:middle line:84% Seronegative means that you are-- 00:05:27.320 --> 00:05:29.510 align:middle line:84% it's an indication that you're resistant. 00:05:29.510 --> 00:05:33.635 align:middle line:84% Now we could do this as a two-by-two matrix here 00:05:33.635 --> 00:05:37.190 align:middle line:84% of alleles versus outcomes, or we 00:05:37.190 --> 00:05:39.440 align:middle line:84% could do it as a three-by-two where we 00:05:39.440 --> 00:05:42.380 align:middle line:90% have genotypes versus outcomes. 00:05:42.380 --> 00:05:46.430 align:middle line:84% The three genotypes are big-big, little-little, 00:05:46.430 --> 00:05:48.065 align:middle line:90% and big-little heterozygote. 00:05:48.065 --> 00:05:50.690 align:middle line:84% But let's just do it-- just keep it simple in terms of alleles. 00:05:50.690 --> 00:05:52.880 align:middle line:90% If there is a selective advan-- 00:05:52.880 --> 00:05:57.860 align:middle line:84% or there's a perceivable association 00:05:57.860 --> 00:06:01.790 align:middle line:84% between the seropositive, seronegative, and the allele, 00:06:01.790 --> 00:06:05.355 align:middle line:84% you should be able to see it in both the genotype or just 00:06:05.355 --> 00:06:05.855 align:middle line:90% the allele. 00:06:05.855 --> 00:06:07.010 align:middle line:90% The allele is simpler. 00:06:07.010 --> 00:06:08.540 align:middle line:90% It's a two-by-two matrix. 00:06:08.540 --> 00:06:13.220 align:middle line:84% And so these are the data, just these four boxes here. 00:06:13.220 --> 00:06:20.750 align:middle line:84% The big allele is 1,278 observed negative and 1,368 observed 00:06:20.750 --> 00:06:23.810 align:middle line:90% positive for a total of 2,646. 00:06:23.810 --> 00:06:26.480 align:middle line:84% You can see that there are fewer total 00:06:26.480 --> 00:06:30.057 align:middle line:84% in the population surveyed of the deletion mutant. 00:06:30.057 --> 00:06:32.390 align:middle line:84% This is consistent with the claim that I made all along. 00:06:32.390 --> 00:06:35.240 align:middle line:84% It's about 9% in general human population, 00:06:35.240 --> 00:06:37.235 align:middle line:90% and it's 9% of this population. 00:06:37.235 --> 00:06:39.240 align:middle line:90% That's good. 00:06:39.240 --> 00:06:40.880 align:middle line:84% But now you have to correct for that. 00:06:40.880 --> 00:06:44.120 align:middle line:84% You need to-- you can't just ask, 00:06:44.120 --> 00:06:45.590 align:middle line:90% is it more frequent here or not? 00:06:45.590 --> 00:06:48.110 align:middle line:84% You have to correct for the actual frequencies 00:06:48.110 --> 00:06:48.890 align:middle line:90% in the population. 00:06:48.890 --> 00:06:55.220 align:middle line:84% And the way that's done is you calculate another table, which 00:06:55.220 --> 00:07:01.820 align:middle line:84% is the expected number of each of these combinations of big 00:07:01.820 --> 00:07:03.680 align:middle line:84% with seronegative, big with seropositive, 00:07:03.680 --> 00:07:05.870 align:middle line:84% and so forth, under the assumption 00:07:05.870 --> 00:07:07.835 align:middle line:90% that it's completely random. 00:07:07.835 --> 00:07:10.220 align:middle line:84% You know the allele frequencies in the population, 00:07:10.220 --> 00:07:13.625 align:middle line:84% but say that they just randomly associated with whether it's 00:07:13.625 --> 00:07:15.170 align:middle line:90% seropositive or seronegative. 00:07:15.170 --> 00:07:17.780 align:middle line:84% You use these totals here and the frequencies 00:07:17.780 --> 00:07:21.530 align:middle line:84% in the population to generate this expected end 00:07:21.530 --> 00:07:22.700 align:middle line:90% of the random assumption. 00:07:22.700 --> 00:07:25.790 align:middle line:84% And then you look for deviation of the real ones 00:07:25.790 --> 00:07:27.505 align:middle line:84% of the observed versus the expected. 00:07:27.505 --> 00:07:34.990 align:middle line:90% 00:07:34.990 --> 00:07:39.310 align:middle line:84% So any deviation between the expected and the observed 00:07:39.310 --> 00:07:40.900 align:middle line:84% is going to be significant in this. 00:07:40.900 --> 00:07:43.490 align:middle line:90% 00:07:43.490 --> 00:07:46.720 align:middle line:84% So you want to do is take the difference between the observed 00:07:46.720 --> 00:07:47.430 align:middle line:90% and expected. 00:07:47.430 --> 00:07:49.840 align:middle line:84% So we're working on a statistic here, 00:07:49.840 --> 00:07:52.120 align:middle line:84% a type of measure that will determine, 00:07:52.120 --> 00:07:55.480 align:middle line:84% how far from expectation are the observations 00:07:55.480 --> 00:07:58.750 align:middle line:84% on the left-hand side in this two-by-two? 00:07:58.750 --> 00:08:02.140 align:middle line:84% And so for every square in the two-by-two, 00:08:02.140 --> 00:08:04.780 align:middle line:84% you find a corresponding expected number 00:08:04.780 --> 00:08:05.920 align:middle line:90% and you subtract it. 00:08:05.920 --> 00:08:07.210 align:middle line:90% That's the starting point. 00:08:07.210 --> 00:08:10.870 align:middle line:84% But you don't care whether it's negative or positive. 00:08:10.870 --> 00:08:12.380 align:middle line:90% You want to make it positive. 00:08:12.380 --> 00:08:14.978 align:middle line:84% So the trick we'll often use is to take the square of that. 00:08:14.978 --> 00:08:16.520 align:middle line:84% So you could take the absolute value. 00:08:16.520 --> 00:08:19.630 align:middle line:84% You take the square for the chi-square, oddly enough. 00:08:19.630 --> 00:08:23.470 align:middle line:84% And then you want to put it on some kind of standard scale 00:08:23.470 --> 00:08:27.040 align:middle line:84% so that when you do a chi-square for any kind of phenomenon, 00:08:27.040 --> 00:08:28.240 align:middle line:90% you'll be able to compare. 00:08:28.240 --> 00:08:31.870 align:middle line:84% And the way you do that is you divide by the expected number. 00:08:31.870 --> 00:08:36.400 align:middle line:84% Or as this puts it on, if these numbers were really huge, 00:08:36.400 --> 00:08:39.530 align:middle line:90% this would bring them down. 00:08:39.530 --> 00:08:41.870 align:middle line:84% Very small, it'll bring the same point. 00:08:41.870 --> 00:08:45.320 align:middle line:84% And so you take the sum over all the squares in here, 00:08:45.320 --> 00:08:47.260 align:middle line:90% and that's 15.6. 00:08:47.260 --> 00:08:53.150 align:middle line:84% And that's saying that it deviates from the expectation 00:08:53.150 --> 00:08:58.640 align:middle line:84% by this amount normalized as a fraction of the expected. 00:08:58.640 --> 00:09:03.980 align:middle line:84% Now to determine just a little sidelight on the chi-square, 00:09:03.980 --> 00:09:07.400 align:middle line:84% in order to determine the probability of 15.6 00:09:07.400 --> 00:09:08.810 align:middle line:84% being significant, what does that 00:09:08.810 --> 00:09:10.762 align:middle line:90% mean, looking at this at 15.6? 00:09:10.762 --> 00:09:12.470 align:middle line:84% You want to turn this into a probability, 00:09:12.470 --> 00:09:15.140 align:middle line:84% because probabilities are the common language that we can all 00:09:15.140 --> 00:09:19.430 align:middle line:84% share our surprise at this being different from expected, 00:09:19.430 --> 00:09:22.255 align:middle line:84% the null hypothesis that this is the same as expected. 00:09:22.255 --> 00:09:23.630 align:middle line:84% And so in order to evaluate that, 00:09:23.630 --> 00:09:25.850 align:middle line:84% you have to ask how much freedom there-- 00:09:25.850 --> 00:09:27.030 align:middle line:90% degrees of freedom. 00:09:27.030 --> 00:09:32.290 align:middle line:84% This is jargon for, how many different ways 00:09:32.290 --> 00:09:34.010 align:middle line:90% can these two numbers vary? 00:09:34.010 --> 00:09:36.970 align:middle line:84% Well, since we know the total number, 00:09:36.970 --> 00:09:44.120 align:middle line:84% when we observe the number of CCR5, that fixes in the columns 00:09:44.120 --> 00:09:45.800 align:middle line:90% the number of deletions, right? 00:09:45.800 --> 00:09:49.250 align:middle line:84% Because it's just going to be the number of big alleles taken 00:09:49.250 --> 00:09:50.730 align:middle line:90% from the total. 00:09:50.730 --> 00:09:52.910 align:middle line:84% So in a way, the degrees of freedom is just one. 00:09:52.910 --> 00:09:57.350 align:middle line:84% You fixed this one number, and the other one is now known. 00:09:57.350 --> 00:09:59.430 align:middle line:84% And the same thing's true for rows and columns. 00:09:59.430 --> 00:10:00.620 align:middle line:90% So the rows minus-- 00:10:00.620 --> 00:10:03.110 align:middle line:84% it's just one and the columns is one. 00:10:03.110 --> 00:10:04.940 align:middle line:84% And so the whole degrees of freedom 00:10:04.940 --> 00:10:07.910 align:middle line:84% is the product that rows and columns, which is one. 00:10:07.910 --> 00:10:08.840 align:middle line:90% So you plug this in. 00:10:08.840 --> 00:10:10.760 align:middle line:84% If you look in your standard statistical-- 00:10:10.760 --> 00:10:14.600 align:middle line:84% or your favorite statistical book or software package, Excel 00:10:14.600 --> 00:10:17.420 align:middle line:84% or whatever, you plug in this chi-square value 00:10:17.420 --> 00:10:20.370 align:middle line:84% and this degrees of freedom, and you get this probability, 00:10:20.370 --> 00:10:21.890 align:middle line:90% which is very significant. 00:10:21.890 --> 00:10:27.110 align:middle line:84% Generally better than 5% means that you will only 00:10:27.110 --> 00:10:29.430 align:middle line:90% be wrong 20% of the time. 00:10:29.430 --> 00:10:32.120 align:middle line:90% Some people would prefer to-- 00:10:32.120 --> 00:10:36.330 align:middle line:84% this means you'll be wrong eight times in 10,000 or something 00:10:36.330 --> 00:10:36.830 align:middle line:90% like that. 00:10:36.830 --> 00:10:39.470 align:middle line:90% Very, very infrequently. 00:10:39.470 --> 00:10:40.640 align:middle line:90% OK. 00:10:40.640 --> 00:10:42.480 align:middle line:90% Now this is great. 00:10:42.480 --> 00:10:43.730 align:middle line:90% This is a two-by-two matrix. 00:10:43.730 --> 00:10:45.290 align:middle line:90% We found an association. 00:10:45.290 --> 00:10:48.080 align:middle line:84% We have a plausible molecular mechanism 00:10:48.080 --> 00:10:49.640 align:middle line:90% in the previous slide. 00:10:49.640 --> 00:10:53.330 align:middle line:84% But how was it that we pulled CCR5 out 00:10:53.330 --> 00:10:54.830 align:middle line:90% of-- this rabbit out of the hat? 00:10:54.830 --> 00:10:57.260 align:middle line:90% I mean, why CCR5? 00:10:57.260 --> 00:11:00.350 align:middle line:84% There are 40,000-some genes in the human genome. 00:11:00.350 --> 00:11:00.920 align:middle line:90% Yes? 00:11:00.920 --> 00:11:01.795 align:middle line:90% AUDIENCE: What is it? 00:11:01.795 --> 00:11:05.960 align:middle line:84% I was curious as to, what population is it? 00:11:05.960 --> 00:11:11.232 align:middle line:84% I mean, in which there's slightly more seropositive 00:11:11.232 --> 00:11:12.190 align:middle line:90% or seronegative people. 00:11:12.190 --> 00:11:14.944 align:middle line:90% This must be a particular-- 00:11:14.944 --> 00:11:17.230 align:middle line:90% GEORGE CHURCH: Oh, yeah. 00:11:17.230 --> 00:11:19.120 align:middle line:84% This is a case control study where 00:11:19.120 --> 00:11:22.000 align:middle line:84% you try to get a roughly equal number of negatives 00:11:22.000 --> 00:11:25.450 align:middle line:84% and positives that are matched for socioeconomic group 00:11:25.450 --> 00:11:27.820 align:middle line:84% and race and gender and things like that. 00:11:27.820 --> 00:11:29.330 align:middle line:90% So that's a setup. 00:11:29.330 --> 00:11:35.620 align:middle line:84% But then the-- if there's not a huge risk ratio for the two 00:11:35.620 --> 00:11:38.280 align:middle line:84% alleles, then you'll expect them to be close to the population 00:11:38.280 --> 00:11:40.030 align:middle line:84% frequency, which means that you can't just 00:11:40.030 --> 00:11:42.490 align:middle line:84% look at it on inspection and say, oh, yeah. 00:11:42.490 --> 00:11:45.280 align:middle line:84% All the seropositive are the big allele. 00:11:45.280 --> 00:11:48.160 align:middle line:84% We wouldn't need a chi-square at that point. 00:11:48.160 --> 00:11:51.950 align:middle line:84% But this is pretty close to the population frequency, 00:11:51.950 --> 00:11:55.950 align:middle line:84% and so that's why we had to do a chi-square. 00:11:55.950 --> 00:11:57.450 align:middle line:90% OK. 00:11:57.450 --> 00:12:03.180 align:middle line:84% But the question that we're taking now 00:12:03.180 --> 00:12:04.630 align:middle line:90% is, how did we pick CCR5? 00:12:04.630 --> 00:12:08.190 align:middle line:84% And I introduced this as being a putative receptor 00:12:08.190 --> 00:12:11.032 align:middle line:84% for the virus, but one of the first pieces of evidence 00:12:11.032 --> 00:12:12.990 align:middle line:84% that this was a putative receptor for the virus 00:12:12.990 --> 00:12:15.700 align:middle line:90% was this association study. 00:12:15.700 --> 00:12:19.332 align:middle line:84% So how was it that it hit the chemokine receptor? 00:12:19.332 --> 00:12:21.540 align:middle line:84% Well, you could say, well, because some kind of hunch 00:12:21.540 --> 00:12:24.030 align:middle line:84% about chemokines being involved in immunology, 00:12:24.030 --> 00:12:27.720 align:middle line:84% and immunology being important in fighting viruses, 00:12:27.720 --> 00:12:30.360 align:middle line:84% but that wouldn't suggest that it's an actual receptor. 00:12:30.360 --> 00:12:33.510 align:middle line:90% 00:12:33.510 --> 00:12:35.150 align:middle line:90% I think these are-- 00:12:35.150 --> 00:12:37.080 align:middle line:84% there's all kinds of inspired guesswork. 00:12:37.080 --> 00:12:40.005 align:middle line:84% There's biochemistry happening behind the scene, and so on. 00:12:40.005 --> 00:12:42.175 align:middle line:84% But let's just put that aside for the moment 00:12:42.175 --> 00:12:43.800 align:middle line:84% and take the more general case that you 00:12:43.800 --> 00:12:46.440 align:middle line:84% wanted to test not just this one hypothesis, 00:12:46.440 --> 00:12:49.110 align:middle line:84% that CCR5 is involved, but you've implicitly 00:12:49.110 --> 00:12:52.922 align:middle line:84% then tested or explicitly tested every gene. 00:12:52.922 --> 00:12:54.630 align:middle line:84% You've gone through every gene and you've 00:12:54.630 --> 00:12:57.750 align:middle line:84% taken either the most common alleles or you've 00:12:57.750 --> 00:12:59.340 align:middle line:84% sequenced your own genome and you've 00:12:59.340 --> 00:13:02.615 align:middle line:84% found the alleles that you have, whether they're common or rare. 00:13:02.615 --> 00:13:03.240 align:middle line:90% You don't care. 00:13:03.240 --> 00:13:06.060 align:middle line:84% And you want to ask, what's the association? 00:13:06.060 --> 00:13:10.850 align:middle line:90% 00:13:10.850 --> 00:13:15.200 align:middle line:84% Let's consider the upper right-hand panel here 00:13:15.200 --> 00:13:20.660 align:middle line:84% where we have some risk ratio, a fairly subtle one, 1.5. 00:13:20.660 --> 00:13:23.300 align:middle line:84% Remember, we were talking about risk ratios of 75 00:13:23.300 --> 00:13:24.350 align:middle line:90% in the case of autism. 00:13:24.350 --> 00:13:25.370 align:middle line:90% This is just 1.5. 00:13:25.370 --> 00:13:29.390 align:middle line:84% Very subtle risk ratio, just like I think in the last one 00:13:29.390 --> 00:13:31.250 align:middle line:84% could have been a subtle risk ratio. 00:13:31.250 --> 00:13:33.930 align:middle line:90% 00:13:33.930 --> 00:13:38.465 align:middle line:84% And the x-axis is going to be the number of alleles 00:13:38.465 --> 00:13:40.580 align:middle line:84% that you're hypothetically testing. 00:13:40.580 --> 00:13:42.500 align:middle line:84% This could be related to the number of genes 00:13:42.500 --> 00:13:44.480 align:middle line:84% that you're testing, or it could be 00:13:44.480 --> 00:13:46.040 align:middle line:84% more than the number of genes that you're testing, 00:13:46.040 --> 00:13:48.080 align:middle line:84% because you can have more than one allele per gene 00:13:48.080 --> 00:13:49.247 align:middle line:90% that you might want to test. 00:13:49.247 --> 00:13:52.400 align:middle line:84% Is this allele of this gene important in this disease, 00:13:52.400 --> 00:13:53.645 align:middle line:90% or is this other one? 00:13:53.645 --> 00:13:55.730 align:middle line:84% For example, sickle cell is important, 00:13:55.730 --> 00:13:59.240 align:middle line:84% but various other hemoglobin mutations are not. 00:13:59.240 --> 00:14:01.910 align:middle line:84% This chemokine deletion is important and maybe another one 00:14:01.910 --> 00:14:02.630 align:middle line:90% isn't. 00:14:02.630 --> 00:14:05.740 align:middle line:84% Many chemokine mutations will be neutral. 00:14:05.740 --> 00:14:06.240 align:middle line:90% OK. 00:14:06.240 --> 00:14:10.010 align:middle line:84% So as you increase the number of genes and alleles from-- 00:14:10.010 --> 00:14:12.680 align:middle line:90% here's 10 to the fourth on up-- 00:14:12.680 --> 00:14:15.920 align:middle line:90% then the number of sib pairs-- 00:14:15.920 --> 00:14:20.570 align:middle line:84% so this is a simulation covering all kinds of experiments 00:14:20.570 --> 00:14:23.600 align:middle line:84% that you could do where you can use 00:14:23.600 --> 00:14:25.460 align:middle line:84% computational methods to help guide 00:14:25.460 --> 00:14:27.860 align:middle line:90% the design of experiments. 00:14:27.860 --> 00:14:29.450 align:middle line:84% If you did an expensive experiment 00:14:29.450 --> 00:14:33.320 align:middle line:84% and you just happened to use too few patients and too 00:14:33.320 --> 00:14:36.575 align:middle line:84% many alleles, then you may have misused your resources. 00:14:36.575 --> 00:14:39.110 align:middle line:84% You should have maybe done fewer alleles and more patients 00:14:39.110 --> 00:14:41.790 align:middle line:90% or something like that. 00:14:41.790 --> 00:14:43.610 align:middle line:84% And this provides some guidance here. 00:14:43.610 --> 00:14:45.290 align:middle line:84% But you can see that in order to get 00:14:45.290 --> 00:14:47.270 align:middle line:84% to a very large number of alleles, 00:14:47.270 --> 00:14:48.950 align:middle line:84% you need a fairly modest increase 00:14:48.950 --> 00:14:50.040 align:middle line:90% in the number of patients. 00:14:50.040 --> 00:14:54.470 align:middle line:84% And that's due to the exponential term 00:14:54.470 --> 00:14:59.160 align:middle line:84% that you have in these probability distributions. 00:14:59.160 --> 00:15:01.130 align:middle line:84% So you actually-- but nevertheless, 00:15:01.130 --> 00:15:06.620 align:middle line:84% it's a big deal cost-wise going up from, say, 00:15:06.620 --> 00:15:11.120 align:middle line:90% 400 patients to 1,600. 00:15:11.120 --> 00:15:13.970 align:middle line:84% Nevertheless, it's only linear in patients 00:15:13.970 --> 00:15:18.440 align:middle line:84% while it's exponential in the number of alleles you can test, 00:15:18.440 --> 00:15:20.470 align:middle line:90% so that's the good news. 00:15:20.470 --> 00:15:22.220 align:middle line:84% And you can see some of these other panels 00:15:22.220 --> 00:15:26.570 align:middle line:84% show the effect of varying other parameters. 00:15:26.570 --> 00:15:28.490 align:middle line:84% For example, here on the left you've 00:15:28.490 --> 00:15:32.480 align:middle line:84% got varying the population frequency of the allele. 00:15:32.480 --> 00:15:35.630 align:middle line:84% As you get to very, very rare alleles 00:15:35.630 --> 00:15:39.890 align:middle line:84% on the right hand of the horizontal axis here, then 00:15:39.890 --> 00:15:44.210 align:middle line:90% the number of sib pairs-- 00:15:44.210 --> 00:15:46.010 align:middle line:84% brothers-sisters, brother-brothers 00:15:46.010 --> 00:15:48.200 align:middle line:84% that you need-- starts to go through the roof. 00:15:48.200 --> 00:15:53.060 align:middle line:84% And now it's exponential on both axes, 00:15:53.060 --> 00:15:55.370 align:middle line:84% or that is to say that it's a direct relationship. 00:15:55.370 --> 00:15:55.910 align:middle line:90% Question? 00:15:55.910 --> 00:15:57.628 align:middle line:84% AUDIENCE: What's that z value over there? 00:15:57.628 --> 00:15:58.420 align:middle line:90% GEORGE CHURCH: Hmm? 00:15:58.420 --> 00:16:00.950 align:middle line:84% AUDIENCE: What's that z value of over there? 00:16:00.950 --> 00:16:05.295 align:middle line:84% GEORGE CHURCH: Oh, that's the population frequency that 00:16:05.295 --> 00:16:05.795 align:middle line:90% you're-- 00:16:05.795 --> 00:16:06.994 align:middle line:90% AUDIENCE: On the bottom? 00:16:06.994 --> 00:16:07.940 align:middle line:90% GEORGE CHURCH: Hmm? 00:16:07.940 --> 00:16:12.800 align:middle line:84% Well, on-- on the one we were just talking about on the left, 00:16:12.800 --> 00:16:15.320 align:middle line:84% the population frequency is the horizontal axis, 00:16:15.320 --> 00:16:20.660 align:middle line:84% and it varies from near unity to 10 to the minus nine. 00:16:20.660 --> 00:16:23.960 align:middle line:84% It's a very rare allele frequency. 00:16:23.960 --> 00:16:27.740 align:middle line:84% On the right, the one we started with, the top right, 00:16:27.740 --> 00:16:30.980 align:middle line:84% we just picked 0.5, which would be very-- 00:16:30.980 --> 00:16:35.820 align:middle line:84% be around here on the left-hand end of the left-hand quadrant. 00:16:35.820 --> 00:16:38.480 align:middle line:84% So you pick one of these allele frequencies, a fairly-- 00:16:38.480 --> 00:16:40.430 align:middle line:84% where it's equal frequency of the two 00:16:40.430 --> 00:16:43.050 align:middle line:84% alleles in the population as where you 00:16:43.050 --> 00:16:44.300 align:middle line:90% do the rest of the simulation. 00:16:44.300 --> 00:16:46.730 align:middle line:84% You can think of all these panels 00:16:46.730 --> 00:16:48.470 align:middle line:84% could be some multi-dimensional display, 00:16:48.470 --> 00:16:51.230 align:middle line:84% but I wanted to take them out one at a time. 00:16:51.230 --> 00:16:54.710 align:middle line:84% And actually, I did all these in Excel 00:16:54.710 --> 00:16:58.630 align:middle line:84% using the equations that are present in this reference 00:16:58.630 --> 00:17:01.070 align:middle line:90% that's given in the slides here. 00:17:01.070 --> 00:17:04.530 align:middle line:90% 00:17:04.530 --> 00:17:06.300 align:middle line:84% A good sign of a well-written paper 00:17:06.300 --> 00:17:08.609 align:middle line:84% is for a sort of average individual 00:17:08.609 --> 00:17:11.500 align:middle line:90% to be able to reproduce it. 00:17:11.500 --> 00:17:16.700 align:middle line:84% So we have how many-- so we've been talking 00:17:16.700 --> 00:17:19.040 align:middle line:90% about new polymorphisms. 00:17:19.040 --> 00:17:21.290 align:middle line:84% In fact, the question that came up during the break 00:17:21.290 --> 00:17:28.069 align:middle line:84% was, if selection and drift cause allele frequencies to fix 00:17:28.069 --> 00:17:31.580 align:middle line:84% fairly rapidly, drift in small populations, 00:17:31.580 --> 00:17:33.530 align:middle line:84% normal-sized populations will drift 00:17:33.530 --> 00:17:37.833 align:middle line:84% in fairly short evolutionary times and selection 00:17:37.833 --> 00:17:40.250 align:middle line:84% if you have a high selection coefficient of cost fixation. 00:17:40.250 --> 00:17:42.140 align:middle line:84% Why do we have any allele frequencies at all? 00:17:42.140 --> 00:17:46.640 align:middle line:84% Why isn't everything fixed at 100% for one particular allele? 00:17:46.640 --> 00:17:48.170 align:middle line:90% And the answer is mutation. 00:17:48.170 --> 00:17:50.578 align:middle line:84% And where all these new mutations or polymorphisms 00:17:50.578 --> 00:17:52.370 align:middle line:84% come from-- actually, these should probably 00:17:52.370 --> 00:17:54.470 align:middle line:84% be called mutations, because most of them 00:17:54.470 --> 00:17:56.780 align:middle line:90% have frequencies less than 1%. 00:17:56.780 --> 00:17:59.883 align:middle line:84% Well, here's a specific model which doesn't follow all 00:17:59.883 --> 00:18:02.300 align:middle line:84% the assumptions we had before, but we'll use a different-- 00:18:02.300 --> 00:18:04.633 align:middle line:84% we'll use a back-of-the-envelope calculation to give you 00:18:04.633 --> 00:18:08.150 align:middle line:84% a feeling for what is true for the-- 00:18:08.150 --> 00:18:10.920 align:middle line:84% what is likely to be the case for the human population. 00:18:10.920 --> 00:18:13.310 align:middle line:84% So the human population, there's a little bit 00:18:13.310 --> 00:18:16.300 align:middle line:84% of unknown in some of these parameters, 00:18:16.300 --> 00:18:18.800 align:middle line:84% so you should take these all with a grain of salt. Actually, 00:18:18.800 --> 00:18:20.220 align:middle line:84% everything I say you should take. 00:18:20.220 --> 00:18:24.470 align:middle line:84% But the number of populations that we've 00:18:24.470 --> 00:18:28.220 align:middle line:84% had since a bottleneck in the human population-- 00:18:28.220 --> 00:18:31.340 align:middle line:84% maybe there were as few as 10 to the fourth humans 00:18:31.340 --> 00:18:33.620 align:middle line:90% at some point or another. 00:18:33.620 --> 00:18:35.300 align:middle line:90% Maybe less. 00:18:35.300 --> 00:18:38.210 align:middle line:84% But since that time, there have been about 5,000 generations. 00:18:38.210 --> 00:18:39.890 align:middle line:84% And during that time, our population 00:18:39.890 --> 00:18:42.140 align:middle line:84% has now grown to six billion people. 00:18:42.140 --> 00:18:45.710 align:middle line:90% That's the n prime nn. 00:18:45.710 --> 00:18:51.783 align:middle line:84% And the mutation rate, as mentioned earlier in response 00:18:51.783 --> 00:18:53.450 align:middle line:84% to a question, is around 10 to the minus 00:18:53.450 --> 00:18:59.580 align:middle line:84% eighth per base pair per genome per generation. 00:18:59.580 --> 00:19:02.270 align:middle line:84% And so the genome size is about six billion. 00:19:02.270 --> 00:19:04.430 align:middle line:84% Coincidentally, the same as the population size. 00:19:04.430 --> 00:19:06.380 align:middle line:90% Total coincidence. 00:19:06.380 --> 00:19:09.830 align:middle line:84% Then 10 to the minus eight times that number of base pairs 00:19:09.830 --> 00:19:12.320 align:middle line:84% means you have about 60 mutations 00:19:12.320 --> 00:19:17.310 align:middle line:90% or so occurring in a generation. 00:19:17.310 --> 00:19:20.050 align:middle line:84% So you've got a steady flow of new mutations. 00:19:20.050 --> 00:19:21.620 align:middle line:84% Now if you take that-- just roughly 00:19:21.620 --> 00:19:23.930 align:middle line:84% speaking, if you take that over 5,000 generations, 00:19:23.930 --> 00:19:26.630 align:middle line:90% you've got 60 times 5,000. 00:19:26.630 --> 00:19:28.490 align:middle line:90% You've got a very large number-- 00:19:28.490 --> 00:19:31.700 align:middle line:84% on the order of 10 to the fourth mutations 00:19:31.700 --> 00:19:33.630 align:middle line:84% that have accumulated in our population. 00:19:33.630 --> 00:19:36.890 align:middle line:84% Assuming relatively little drift because 00:19:36.890 --> 00:19:39.560 align:middle line:84% of this exponentially growing population and relatively 00:19:39.560 --> 00:19:42.830 align:middle line:84% little selection, then this is the number 00:19:42.830 --> 00:19:44.240 align:middle line:90% that might have accumulated. 00:19:44.240 --> 00:19:48.920 align:middle line:84% You can do subtle corrections for this exponential growth. 00:19:48.920 --> 00:19:51.993 align:middle line:84% The number of mutations you got at the beginning 00:19:51.993 --> 00:19:54.410 align:middle line:84% will have higher frequency, but there'll be fewer of them, 00:19:54.410 --> 00:19:55.742 align:middle line:90% because population was smaller. 00:19:55.742 --> 00:19:57.200 align:middle line:84% But anyway, you get the picture, is 00:19:57.200 --> 00:19:59.090 align:middle line:84% that the total number of mutations 00:19:59.090 --> 00:20:02.360 align:middle line:84% in any one of this that are new since that new-- 00:20:02.360 --> 00:20:06.390 align:middle line:84% since 5,000 generations ago will be on the order of 10 00:20:06.390 --> 00:20:12.380 align:middle line:84% to the fourth in your body, not all of them doing good for you. 00:20:12.380 --> 00:20:15.097 align:middle line:84% And for each of those rare mutations-- 00:20:15.097 --> 00:20:17.555 align:middle line:84% they might have a frequency of about 10 to the minus five-- 00:20:17.555 --> 00:20:21.670 align:middle line:90% 00:20:21.670 --> 00:20:26.018 align:middle line:84% there will be about 10 to the fourth people on Earth 00:20:26.018 --> 00:20:28.060 align:middle line:84% that will share that very rare mutation with you. 00:20:28.060 --> 00:20:30.842 align:middle line:84% 10 to the minus 5 sounds very rare, 00:20:30.842 --> 00:20:32.800 align:middle line:84% but when you multiply it by six billion people, 00:20:32.800 --> 00:20:35.140 align:middle line:84% there are a lot of people who share that with you. 00:20:35.140 --> 00:20:36.990 align:middle line:90% It's a new mutation. 00:20:36.990 --> 00:20:37.490 align:middle line:90% OK. 00:20:37.490 --> 00:20:38.980 align:middle line:90% So the take-home is-- 00:20:38.980 --> 00:20:42.340 align:middle line:84% and this is from this reference here. 00:20:42.340 --> 00:20:45.700 align:middle line:84% High genomic deleterious mutations 00:20:45.700 --> 00:20:49.180 align:middle line:90% accumulate over these 4,000-- 00:20:49.180 --> 00:20:51.100 align:middle line:84% some large number of generations. 00:20:51.100 --> 00:20:53.800 align:middle line:84% And they would confound linkage methods 00:20:53.800 --> 00:20:55.840 align:middle line:84% and they would confound assumptions 00:20:55.840 --> 00:20:58.120 align:middle line:84% that say that the common alleles-- 00:20:58.120 --> 00:21:02.190 align:middle line:90% common alleles are causative. 00:21:02.190 --> 00:21:02.700 align:middle line:90% OK. 00:21:02.700 --> 00:21:04.950 align:middle line:84% So let's say we've done an association study. 00:21:04.950 --> 00:21:07.200 align:middle line:84% Either we've done it on one gene, picked 00:21:07.200 --> 00:21:09.480 align:middle line:84% one out of the hat like CCR5, or we've 00:21:09.480 --> 00:21:12.060 align:middle line:84% done it on a full genome survey, 40,000 genes, 00:21:12.060 --> 00:21:15.120 align:middle line:90% all the alleles we know of. 00:21:15.120 --> 00:21:18.180 align:middle line:84% In order to do the latter, we had to have a big patient 00:21:18.180 --> 00:21:19.870 align:middle line:90% population. 00:21:19.870 --> 00:21:21.120 align:middle line:90% But let's say we've done that. 00:21:21.120 --> 00:21:25.020 align:middle line:84% Now we want to prove that that association is-- 00:21:25.020 --> 00:21:26.850 align:middle line:84% that great statistic that we got out, 00:21:26.850 --> 00:21:28.740 align:middle line:84% if we have a large enough patient population, 00:21:28.740 --> 00:21:30.990 align:middle line:90% is still just a statistic. 00:21:30.990 --> 00:21:35.040 align:middle line:84% What will constitute proof is after we find the association, 00:21:35.040 --> 00:21:38.550 align:middle line:84% we make a copy of that mutation, isolated away 00:21:38.550 --> 00:21:41.100 align:middle line:84% from the three million other polymorphisms that 00:21:41.100 --> 00:21:43.870 align:middle line:84% are floating around in your body, 00:21:43.870 --> 00:21:45.390 align:middle line:90% and we do some kind of test. 00:21:45.390 --> 00:21:48.510 align:middle line:84% Ideally, we would make an isogenic pair 00:21:48.510 --> 00:21:51.450 align:middle line:84% of humans that only differ by this one mutation. 00:21:51.450 --> 00:21:58.980 align:middle line:84% That is not generally considered medically feasible or ethical. 00:21:58.980 --> 00:22:01.590 align:middle line:84% But somehow or another, you can do it on human cells 00:22:01.590 --> 00:22:07.110 align:middle line:84% or you can do it in a mammalian model system. 00:22:07.110 --> 00:22:08.880 align:middle line:84% But you have to make something that's 00:22:08.880 --> 00:22:11.580 align:middle line:84% close to isogenic, a copy of this mutation, 00:22:11.580 --> 00:22:14.800 align:middle line:84% and show that it has a phenotype that makes sense. 00:22:14.800 --> 00:22:17.070 align:middle line:84% And then, just to make sure you haven't introduced 00:22:17.070 --> 00:22:20.310 align:middle line:84% other mutations, the really careful scientists 00:22:20.310 --> 00:22:23.610 align:middle line:84% will then revert that one polymorphism and show now 00:22:23.610 --> 00:22:26.070 align:middle line:84% you no longer have that phenotype. 00:22:26.070 --> 00:22:27.030 align:middle line:90% OK. 00:22:27.030 --> 00:22:31.480 align:middle line:84% So let's walk through an example. 00:22:31.480 --> 00:22:35.990 align:middle line:84% Here's the third example in this lecture 00:22:35.990 --> 00:22:38.790 align:middle line:84% of a very specific allele where we've 00:22:38.790 --> 00:22:41.010 align:middle line:84% shown the molecular basis of it, and it's 00:22:41.010 --> 00:22:43.158 align:middle line:84% the second example where it's not coding, 00:22:43.158 --> 00:22:45.450 align:middle line:84% and it's the second example where it's going to repeat. 00:22:45.450 --> 00:22:47.160 align:middle line:90% So this is just to-- 00:22:47.160 --> 00:22:48.870 align:middle line:84% I'm not giving you a random sample here. 00:22:48.870 --> 00:22:53.640 align:middle line:84% I'm specifically biasing this towards very interesting genes, 00:22:53.640 --> 00:22:57.240 align:middle line:84% very interesting traits that are associated 00:22:57.240 --> 00:23:00.150 align:middle line:84% with non-coding repetitive alleles. 00:23:00.150 --> 00:23:03.750 align:middle line:84% In this case, the trait that got the attention 00:23:03.750 --> 00:23:06.870 align:middle line:84% of these researchers-- it isn't necessarily proven 00:23:06.870 --> 00:23:09.240 align:middle line:90% that this is the relationship. 00:23:09.240 --> 00:23:10.890 align:middle line:84% But the association that was studied 00:23:10.890 --> 00:23:15.240 align:middle line:84% was between anxiety-related traits, anxiety, 00:23:15.240 --> 00:23:18.840 align:middle line:84% and a polymorphism in the serotonin transporter. 00:23:18.840 --> 00:23:22.140 align:middle line:90% This is a science paper. 00:23:22.140 --> 00:23:24.540 align:middle line:84% Now the next step in this is to-- 00:23:24.540 --> 00:23:26.820 align:middle line:90% OK, that was found associated. 00:23:26.820 --> 00:23:33.330 align:middle line:84% There were lots of other alleles randomly being moved around, 00:23:33.330 --> 00:23:35.070 align:middle line:90% because these are humans. 00:23:35.070 --> 00:23:39.432 align:middle line:84% We have no control over who mates with who, or very little. 00:23:39.432 --> 00:23:42.210 align:middle line:90% 00:23:42.210 --> 00:23:44.190 align:middle line:90% So you get what you're given. 00:23:44.190 --> 00:23:46.020 align:middle line:84% You can do the survey as best you can. 00:23:46.020 --> 00:23:50.610 align:middle line:84% But now in order to move it towards a mechanistic basis 00:23:50.610 --> 00:23:54.300 align:middle line:84% and a proof of introducing just this one point mutation. 00:23:54.300 --> 00:23:58.050 align:middle line:84% Now what is the mutation found in this case of anxiety 00:23:58.050 --> 00:24:00.790 align:middle line:84% relationship in this serotonin transporter? 00:24:00.790 --> 00:24:05.130 align:middle line:84% It's upstream of the first RNA encoding axon one. 00:24:05.130 --> 00:24:09.080 align:middle line:84% It is a 44 base pair deletion in a repetitive region, 00:24:09.080 --> 00:24:13.110 align:middle line:84% in a region which might be responsible for promoting 00:24:13.110 --> 00:24:14.760 align:middle line:90% transcription. 00:24:14.760 --> 00:24:18.690 align:middle line:84% You have the short and the long alleles, just like in the CCR5. 00:24:18.690 --> 00:24:21.450 align:middle line:84% In this case, it's in a putative promoter element. 00:24:21.450 --> 00:24:25.020 align:middle line:84% And when you make this construct and you hook it up 00:24:25.020 --> 00:24:30.970 align:middle line:84% to a luciferase enzymatic activity in vitro, 00:24:30.970 --> 00:24:33.090 align:middle line:84% in cultured cells so you don't actually 00:24:33.090 --> 00:24:36.300 align:middle line:84% have to construct a mutant human, 00:24:36.300 --> 00:24:38.490 align:middle line:84% you can now see the long allele always 00:24:38.490 --> 00:24:41.820 align:middle line:84% produces higher levels of expression 00:24:41.820 --> 00:24:42.870 align:middle line:90% than the short allele. 00:24:42.870 --> 00:24:48.090 align:middle line:84% And these little error bars on top of each of the measures 00:24:48.090 --> 00:24:51.720 align:middle line:84% show your statistical measure of standard deviation, 00:24:51.720 --> 00:24:54.915 align:middle line:90% as we did in the first lecture. 00:24:54.915 --> 00:25:00.150 align:middle line:84% And if the black mean, which is the height of the bar, 00:25:00.150 --> 00:25:03.293 align:middle line:84% is different from the white mean by more than a couple 00:25:03.293 --> 00:25:05.460 align:middle line:84% of these standard deviations, which is the root mean 00:25:05.460 --> 00:25:08.700 align:middle line:84% square of the standard deviations of each 00:25:08.700 --> 00:25:12.790 align:middle line:84% of the measures, then you call it statistically significant. 00:25:12.790 --> 00:25:14.790 align:middle line:84% And that's what these triple stars mean. 00:25:14.790 --> 00:25:17.160 align:middle line:84% It's the statistical shorthand for this 00:25:17.160 --> 00:25:20.220 align:middle line:84% is statistically significant at the cutoff that we're using. 00:25:20.220 --> 00:25:21.900 align:middle line:90% Say, 5%. 00:25:21.900 --> 00:25:23.760 align:middle line:84% Now in this case, it's kind of showing off 00:25:23.760 --> 00:25:25.510 align:middle line:84% because every one of them is statistically 00:25:25.510 --> 00:25:29.550 align:middle line:90% significant by two different-- 00:25:29.550 --> 00:25:31.110 align:middle line:84% completely different assays here. 00:25:31.110 --> 00:25:33.270 align:middle line:84% But the point is this does not prove 00:25:33.270 --> 00:25:39.540 align:middle line:84% that anxiety is meaningfully associated with this. 00:25:39.540 --> 00:25:44.580 align:middle line:84% But it does prove that this repetitive polymorphism 00:25:44.580 --> 00:25:52.830 align:middle line:84% is causally capable of differential transcription 00:25:52.830 --> 00:25:55.650 align:middle line:90% levels for a reporter gene. 00:25:55.650 --> 00:26:03.300 align:middle line:84% So by introducing it into a clean cellular system, 00:26:03.300 --> 00:26:06.420 align:middle line:84% you can test at least part of the mechanism that 00:26:06.420 --> 00:26:08.790 align:middle line:84% might be involved in the association that originally 00:26:08.790 --> 00:26:11.520 align:middle line:90% got your attention. 00:26:11.520 --> 00:26:14.490 align:middle line:84% Now as you can see, we're getting 00:26:14.490 --> 00:26:21.150 align:middle line:84% into a fairly mature and fairly new phase of human genetics. 00:26:21.150 --> 00:26:22.860 align:middle line:84% Some of the concepts that are used here 00:26:22.860 --> 00:26:25.440 align:middle line:84% will be useful in a variety of other systems 00:26:25.440 --> 00:26:28.860 align:middle line:84% where we have relatively little control over the genetics. 00:26:28.860 --> 00:26:33.510 align:middle line:84% But certainly in humans, there's a very large need. 00:26:33.510 --> 00:26:36.240 align:middle line:84% And where this happened historically 00:26:36.240 --> 00:26:39.090 align:middle line:84% is with Mendelian linkage, which would involve 00:26:39.090 --> 00:26:43.950 align:middle line:84% very large families with a complete pedigree, 00:26:43.950 --> 00:26:47.160 align:middle line:84% multi-generation, great-grandfathers and mothers, 00:26:47.160 --> 00:26:50.775 align:middle line:84% all the way down, hundreds of people in a family. 00:26:50.775 --> 00:26:53.400 align:middle line:84% And that's the problem, because there aren't that many diseases 00:26:53.400 --> 00:26:54.775 align:middle line:84% for which you have large families 00:26:54.775 --> 00:26:56.670 align:middle line:84% with simple Mendelian inheritance. 00:26:56.670 --> 00:26:59.010 align:middle line:84% Common diseases tend to be much more complicated, 00:26:59.010 --> 00:27:01.920 align:middle line:84% involving multiple genes simultaneously 00:27:01.920 --> 00:27:05.280 align:middle line:90% and small families. 00:27:05.280 --> 00:27:09.000 align:middle line:84% Then there's linkage disequilibrium, 00:27:09.000 --> 00:27:14.633 align:middle line:84% which depends on these common alleles 00:27:14.633 --> 00:27:16.800 align:middle line:84% where the population has gone through a particularly 00:27:16.800 --> 00:27:20.640 align:middle line:84% small bottleneck and where your common allele is 00:27:20.640 --> 00:27:23.400 align:middle line:84% a pretty good distance away from the causative one. 00:27:23.400 --> 00:27:25.980 align:middle line:84% But it allows you to map it into a ballpark, 00:27:25.980 --> 00:27:31.200 align:middle line:84% and then you hunker down and do the more expensive testing 00:27:31.200 --> 00:27:33.960 align:middle line:84% of hypotheses for all and sequencing and looking 00:27:33.960 --> 00:27:35.688 align:middle line:84% for potentially causative alleles. 00:27:35.688 --> 00:27:37.980 align:middle line:84% Once you find a potentially causative allele, something 00:27:37.980 --> 00:27:40.000 align:middle line:84% that looks suspicious, maybe something 00:27:40.000 --> 00:27:42.330 align:middle line:84% that's in a coding region that it's conserved-- 00:27:42.330 --> 00:27:45.510 align:middle line:84% that's the first priority, despite all the counterexamples 00:27:45.510 --> 00:27:46.780 align:middle line:90% I've given. 00:27:46.780 --> 00:27:48.010 align:middle line:90% And then you go ahead. 00:27:48.010 --> 00:27:49.802 align:middle line:84% But the problem is that you're at the mercy 00:27:49.802 --> 00:27:51.677 align:middle line:84% of the recombination that might have occurred 00:27:51.677 --> 00:27:54.480 align:middle line:84% in that population, but you get to very interesting populations 00:27:54.480 --> 00:27:58.770 align:middle line:84% like people of African American descent 00:27:58.770 --> 00:28:01.650 align:middle line:84% where the population is very old, hasn't 00:28:01.650 --> 00:28:04.350 align:middle line:84% passed through a population bottleneck. 00:28:04.350 --> 00:28:06.870 align:middle line:84% The useful linkage disequilibrium 00:28:06.870 --> 00:28:10.320 align:middle line:84% is on a couple of kilobases rather than hundreds 00:28:10.320 --> 00:28:12.510 align:middle line:84% of kilobases, so it actually is hard to find 00:28:12.510 --> 00:28:13.830 align:middle line:90% things that are linked. 00:28:13.830 --> 00:28:16.410 align:middle line:84% That is to say, insists but not causatives. 00:28:16.410 --> 00:28:19.380 align:middle line:90% Insists to the causative allele. 00:28:19.380 --> 00:28:22.020 align:middle line:84% Instead, you have to look directly for causative alleles. 00:28:22.020 --> 00:28:24.840 align:middle line:84% And that's where-- now you look for common causative alleles. 00:28:24.840 --> 00:28:27.765 align:middle line:90% 00:28:27.765 --> 00:28:29.890 align:middle line:84% This has the problem that we've been talking about, 00:28:29.890 --> 00:28:34.860 align:middle line:84% which is that maybe common alleles aren't often causative. 00:28:34.860 --> 00:28:36.330 align:middle line:90% They've been selected out. 00:28:36.330 --> 00:28:38.400 align:middle line:84% So then you get into the scenario, what if we 00:28:38.400 --> 00:28:39.930 align:middle line:90% wanted to look at all alleles? 00:28:39.930 --> 00:28:43.770 align:middle line:84% Well, theoretically, there's nothing wrong with that. 00:28:43.770 --> 00:28:45.450 align:middle line:90% It'd be great. 00:28:45.450 --> 00:28:47.070 align:middle line:84% We could do the association studies. 00:28:47.070 --> 00:28:50.310 align:middle line:84% We'd have to have fairly large populations. 00:28:50.310 --> 00:28:52.650 align:middle line:84% But you saw it was linear with an exponential increase 00:28:52.650 --> 00:28:55.710 align:middle line:84% in the number of hypotheses, and you could rank those hypotheses 00:28:55.710 --> 00:28:59.280 align:middle line:84% by a priori likelihood and so forth, but it's expensive. 00:28:59.280 --> 00:29:02.820 align:middle line:84% And so the discussion now has to include 00:29:02.820 --> 00:29:07.110 align:middle line:84% a little bit of discussion of the new technologies that 00:29:07.110 --> 00:29:10.470 align:middle line:84% might make this less expensive, and a discussion of how we got 00:29:10.470 --> 00:29:12.900 align:middle line:84% the first genome and how the new technologies might 00:29:12.900 --> 00:29:14.580 align:middle line:90% be a little different. 00:29:14.580 --> 00:29:17.070 align:middle line:84% But we're going to do this in the context of computation 00:29:17.070 --> 00:29:19.810 align:middle line:84% in the sense of, how do we deal with random and systematic 00:29:19.810 --> 00:29:20.310 align:middle line:90% errors? 00:29:20.310 --> 00:29:23.370 align:middle line:84% As we plan our strategy for getting 00:29:23.370 --> 00:29:26.640 align:middle line:84% each of our genomes, personal genomes sequence for $1,000 00:29:26.640 --> 00:29:30.850 align:middle line:84% or so, how do we choose which technology to pursue? 00:29:30.850 --> 00:29:34.050 align:middle line:84% Which ones have the lowest intrinsic, random, 00:29:34.050 --> 00:29:35.350 align:middle line:90% and systematic errors? 00:29:35.350 --> 00:29:37.110 align:middle line:84% So we needed to study the first genome 00:29:37.110 --> 00:29:41.190 align:middle line:84% to see, what would we mean by random and systematic errors? 00:29:41.190 --> 00:29:44.790 align:middle line:84% How many people here know what the difference is already? 00:29:44.790 --> 00:29:47.370 align:middle line:90% 00:29:47.370 --> 00:29:47.890 align:middle line:90% A few. 00:29:47.890 --> 00:29:48.390 align:middle line:90% OK. 00:29:48.390 --> 00:29:51.720 align:middle line:84% But anyway, whether you do or not, it's good for the soul 00:29:51.720 --> 00:29:54.420 align:middle line:84% to go through some real examples of this. 00:29:54.420 --> 00:29:56.160 align:middle line:84% A random mutation is something which 00:29:56.160 --> 00:29:59.040 align:middle line:84% occurs every time you do the experiment. 00:29:59.040 --> 00:30:01.680 align:middle line:90% You get a different error. 00:30:01.680 --> 00:30:06.240 align:middle line:84% And a systematic one is something 00:30:06.240 --> 00:30:08.560 align:middle line:84% where if you do it over and over the same way, 00:30:08.560 --> 00:30:10.920 align:middle line:84% you'll get the same error or a simple class 00:30:10.920 --> 00:30:15.510 align:middle line:84% of errors occurring more than once, over and over. 00:30:15.510 --> 00:30:20.045 align:middle line:84% So for sequencing, the process involves picking something 00:30:20.045 --> 00:30:21.420 align:middle line:84% that you want to sequence-- we'll 00:30:21.420 --> 00:30:22.950 align:middle line:90% call it a clone or a template. 00:30:22.950 --> 00:30:24.810 align:middle line:84% Then actually doing the sequencing 00:30:24.810 --> 00:30:27.900 align:middle line:84% and then assembling this into a meaningful 00:30:27.900 --> 00:30:29.690 align:middle line:90% interpreted sequence. 00:30:29.690 --> 00:30:34.500 align:middle line:84% And this is an example where we might 00:30:34.500 --> 00:30:41.370 align:middle line:90% have chosen these big clones. 00:30:41.370 --> 00:30:43.920 align:middle line:84% In other words, you might fragment the genome up randomly 00:30:43.920 --> 00:30:46.140 align:middle line:84% into large clones of 100 kilobases called 00:30:46.140 --> 00:30:48.690 align:middle line:84% bacterial artificial chromosomes, for example. 00:30:48.690 --> 00:30:51.150 align:middle line:84% And then that's all random, and so there's 00:30:51.150 --> 00:30:52.920 align:middle line:90% a shotgun of that scale. 00:30:52.920 --> 00:30:55.840 align:middle line:84% And then we break it up randomly into smaller pieces, 00:30:55.840 --> 00:30:57.480 align:middle line:84% which provide us with little sequences. 00:30:57.480 --> 00:30:59.940 align:middle line:84% And then in the computer, we assemble these by methods 00:30:59.940 --> 00:31:04.410 align:middle line:84% that we'll discuss in the next lecture, which 00:31:04.410 --> 00:31:07.600 align:middle line:84% can take even fairly different sequences than assemble them. 00:31:07.600 --> 00:31:11.040 align:middle line:84% In this case, we're talking about very similar sequences. 00:31:11.040 --> 00:31:13.823 align:middle line:84% And then you assemble the little sequences into big sequences, 00:31:13.823 --> 00:31:15.240 align:middle line:84% and you assemble the big sequences 00:31:15.240 --> 00:31:17.910 align:middle line:84% into even bigger sequences, and then you have the whole thing. 00:31:17.910 --> 00:31:21.378 align:middle line:84% But you can see there's a lot of opportunity for error here. 00:31:21.378 --> 00:31:22.920 align:middle line:84% We make it look simple in this slide, 00:31:22.920 --> 00:31:25.980 align:middle line:84% but we're going to talk about random and systematic errors 00:31:25.980 --> 00:31:28.020 align:middle line:90% in a moment. 00:31:28.020 --> 00:31:29.610 align:middle line:84% Where did we get those sequences, 00:31:29.610 --> 00:31:32.340 align:middle line:84% those little sequences that we want to assemble? 00:31:32.340 --> 00:31:34.600 align:middle line:84% We're going to go through a few methods in a moment, 00:31:34.600 --> 00:31:37.140 align:middle line:84% but the most common one by far I think 00:31:37.140 --> 00:31:40.380 align:middle line:84% that generates over 90% of the human genome 00:31:40.380 --> 00:31:42.420 align:middle line:84% sequence in the last couple of years 00:31:42.420 --> 00:31:47.130 align:middle line:84% is capillary electrophoresis of fluorescently labeled 00:31:47.130 --> 00:31:49.320 align:middle line:90% polymerase terminated products. 00:31:49.320 --> 00:31:51.390 align:middle line:84% When you electrophoresis things, you're 00:31:51.390 --> 00:31:57.375 align:middle line:84% separating DNA fragments, which are n nucleotides long, 00:31:57.375 --> 00:32:00.630 align:middle line:84% from a DNA fragment which is n plus one nucleotides long. 00:32:00.630 --> 00:32:03.030 align:middle line:84% That's a very subtle difference as n gets big. 00:32:03.030 --> 00:32:05.280 align:middle line:84% As n gets big, it gets harder and harder 00:32:05.280 --> 00:32:07.395 align:middle line:90% to separate n from n plus one. 00:32:07.395 --> 00:32:10.320 align:middle line:84% As it does so, you start getting all kinds of errors. 00:32:10.320 --> 00:32:14.310 align:middle line:84% The total number of errors here in the lower left-hand corner 00:32:14.310 --> 00:32:16.740 align:middle line:84% is the number of insertions plus the number of deletions 00:32:16.740 --> 00:32:20.310 align:middle line:84% plus the number of substitutions plus n, which 00:32:20.310 --> 00:32:23.640 align:middle line:90% is an abbreviation for no call. 00:32:23.640 --> 00:32:27.000 align:middle line:84% It means the software felt that it was so close that it 00:32:27.000 --> 00:32:28.000 align:middle line:90% couldn't call it at all. 00:32:28.000 --> 00:32:28.830 align:middle line:90% It just said it's n. 00:32:28.830 --> 00:32:30.413 align:middle line:84% I don't know whether it's an A, C-- it 00:32:30.413 --> 00:32:34.390 align:middle line:84% doesn't know whether it's an A, C, G, or T. Calls it a no call. 00:32:34.390 --> 00:32:36.660 align:middle line:84% And so if you look through this table, 00:32:36.660 --> 00:32:43.680 align:middle line:84% it shows on the vertical axis for each of these six bar 00:32:43.680 --> 00:32:47.820 align:middle line:84% charts is as you go up on the vertical axis, 00:32:47.820 --> 00:32:50.250 align:middle line:84% you go from very short reads where 00:32:50.250 --> 00:32:52.950 align:middle line:84% it's easy to separate n from n plus one electrophoretically 00:32:52.950 --> 00:32:55.500 align:middle line:84% to very long ones where you start accumulating 00:32:55.500 --> 00:32:58.680 align:middle line:84% insertions deletion errors, insertion deletion 00:32:58.680 --> 00:33:00.240 align:middle line:90% substitution, and n. 00:33:00.240 --> 00:33:02.170 align:middle line:90% They all go up with length. 00:33:02.170 --> 00:33:06.390 align:middle line:84% And so you can think of that as a random error superimposed 00:33:06.390 --> 00:33:10.380 align:middle line:84% on the systematic error of if you always do the experiments, 00:33:10.380 --> 00:33:13.620 align:middle line:84% the same base pair is always at the end of your run, 00:33:13.620 --> 00:33:16.260 align:middle line:84% it's going to always have a higher random error rate. 00:33:16.260 --> 00:33:19.300 align:middle line:84% So this is kind of a combination of random and systematic error. 00:33:19.300 --> 00:33:22.680 align:middle line:84% So let's go through some examples here. 00:33:22.680 --> 00:33:25.770 align:middle line:84% We have just isolating the template 00:33:25.770 --> 00:33:31.350 align:middle line:84% to prepare it for sequencing, there are systematic errors. 00:33:31.350 --> 00:33:33.270 align:middle line:84% If you have certain kinds of repeats, 00:33:33.270 --> 00:33:36.360 align:middle line:84% long, inverted repeats, or certain kinds of restriction 00:33:36.360 --> 00:33:39.150 align:middle line:84% elements that the bacteria doesn't like or likes 00:33:39.150 --> 00:33:42.960 align:middle line:84% to chew up, then you won't get the clone. 00:33:42.960 --> 00:33:45.510 align:middle line:84% And that would plague the early part of the Genome Project, 00:33:45.510 --> 00:33:48.122 align:middle line:84% is you'd keep trying again and again the same way, 00:33:48.122 --> 00:33:49.830 align:middle line:84% and you just wouldn't get certain clones. 00:33:49.830 --> 00:33:51.360 align:middle line:84% It's as if there was a hole there. 00:33:51.360 --> 00:33:52.943 align:middle line:84% You know that there's something there, 00:33:52.943 --> 00:33:55.020 align:middle line:90% but you couldn't clone it. 00:33:55.020 --> 00:33:58.560 align:middle line:84% Sequencing-- hairpins can form in the single strand 00:33:58.560 --> 00:34:00.060 align:middle line:84% of nucleic acids where you're trying 00:34:00.060 --> 00:34:02.100 align:middle line:90% to separate n from n plus one. 00:34:02.100 --> 00:34:06.990 align:middle line:84% And those hairpins then take out the gel electrophoresis 00:34:06.990 --> 00:34:10.800 align:middle line:84% and make it seem like it's much smaller than it actually is. 00:34:10.800 --> 00:34:13.560 align:middle line:84% Tandem repeats cause a problem in all three 00:34:13.560 --> 00:34:16.980 align:middle line:90% of these stages in sequencing. 00:34:16.980 --> 00:34:19.530 align:middle line:84% You get some polymerase stuttering 00:34:19.530 --> 00:34:21.719 align:middle line:90% and you get little artifacts. 00:34:21.719 --> 00:34:24.810 align:middle line:84% In assembly repeats, you're assembling 00:34:24.810 --> 00:34:27.310 align:middle line:90% by sequence alignment. 00:34:27.310 --> 00:34:28.770 align:middle line:84% If you have a repeat, the repeat's 00:34:28.770 --> 00:34:31.110 align:middle line:84% going to align just as well because it's 00:34:31.110 --> 00:34:33.215 align:middle line:84% a repeat within the genome as a repeat 00:34:33.215 --> 00:34:35.340 align:middle line:84% due to experimental repeating, and so the alignment 00:34:35.340 --> 00:34:36.900 align:middle line:90% can be off. 00:34:36.900 --> 00:34:39.150 align:middle line:84% The errors that you got from these earlier steps 00:34:39.150 --> 00:34:40.860 align:middle line:90% make it hard to assemble. 00:34:40.860 --> 00:34:42.570 align:middle line:90% Polymorphisms look like errors. 00:34:42.570 --> 00:34:44.580 align:middle line:84% Chimeric clones means you've got things 00:34:44.580 --> 00:34:52.010 align:middle line:84% that have been misassembled early on here, and so on. 00:34:52.010 --> 00:34:54.670 align:middle line:90% OK. 00:34:54.670 --> 00:34:59.902 align:middle line:84% When we do this random selection of big clones 00:34:59.902 --> 00:35:02.110 align:middle line:84% and random selection of little clones for sequencing, 00:35:02.110 --> 00:35:04.060 align:middle line:90% we want to know when to quit. 00:35:04.060 --> 00:35:05.890 align:middle line:84% Now you could say, well, we're going 00:35:05.890 --> 00:35:07.450 align:middle line:84% to quit once we get it all assembled, 00:35:07.450 --> 00:35:10.120 align:middle line:84% but you need to accumulate a certain amount of data 00:35:10.120 --> 00:35:12.070 align:middle line:84% in advance before you try to assemble it. 00:35:12.070 --> 00:35:15.820 align:middle line:84% And so there are various calculations 00:35:15.820 --> 00:35:17.110 align:middle line:90% as to when to quit. 00:35:17.110 --> 00:35:19.580 align:middle line:84% And this is related to the Poisson distribution, 00:35:19.580 --> 00:35:20.650 align:middle line:90% but it's not exactly. 00:35:20.650 --> 00:35:24.760 align:middle line:84% And in fact, one of the studies done in 1988 00:35:24.760 --> 00:35:28.990 align:middle line:84% made some poor assumptions about-- 00:35:28.990 --> 00:35:32.320 align:middle line:84% remember, we mentioned in the first lecture 00:35:32.320 --> 00:35:36.310 align:middle line:84% the assumptions of the Poisson distribution 00:35:36.310 --> 00:35:38.170 align:middle line:84% that make it an approximation-- when 00:35:38.170 --> 00:35:42.310 align:middle line:84% it becomes an approximation to a more formal distribution 00:35:42.310 --> 00:35:43.180 align:middle line:90% like the binomial. 00:35:43.180 --> 00:35:46.420 align:middle line:84% Anyway, that approximation, you should be getting, 00:35:46.420 --> 00:35:48.130 align:middle line:84% as you get higher and higher coverage, 00:35:48.130 --> 00:35:52.240 align:middle line:84% meaning more and more experimental repeats, 00:35:52.240 --> 00:35:54.460 align:middle line:84% you'll eventually fill all the gaps. 00:35:54.460 --> 00:35:58.630 align:middle line:84% And that means you'll get 100% complete coverage, 00:35:58.630 --> 00:36:00.910 align:middle line:84% and it should asymptotically approach that. 00:36:00.910 --> 00:36:03.850 align:middle line:84% Well, if you use the Poisson incorrectly, 00:36:03.850 --> 00:36:08.080 align:middle line:84% as authors did in 1988, you basically go off to infinity. 00:36:08.080 --> 00:36:12.800 align:middle line:84% You get 200% coverage, which is physically impossible. 00:36:12.800 --> 00:36:15.400 align:middle line:84% But both an earlier study, which they ignored, 00:36:15.400 --> 00:36:17.830 align:middle line:84% and a more recent study got it right. 00:36:17.830 --> 00:36:21.010 align:middle line:84% And these are slightly different measures, 00:36:21.010 --> 00:36:24.250 align:middle line:90% but they both converge on 100%. 00:36:24.250 --> 00:36:26.230 align:middle line:84% And I urge you to look at that if you're 00:36:26.230 --> 00:36:29.560 align:middle line:84% designing an experiment with simple formula. 00:36:29.560 --> 00:36:32.530 align:middle line:84% On the other hand, if you want to design the experiment more 00:36:32.530 --> 00:36:35.080 align:middle line:84% explicit, you eventually get to a point 00:36:35.080 --> 00:36:37.810 align:middle line:84% where a simple analytic formula won't do, 00:36:37.810 --> 00:36:39.160 align:middle line:90% and you have to do Monte Carlo. 00:36:39.160 --> 00:36:41.290 align:middle line:84% We treated this in the first class 00:36:41.290 --> 00:36:44.830 align:middle line:84% of analytic versus numeric differentiable equations 00:36:44.830 --> 00:36:46.340 align:middle line:90% and then many other cases. 00:36:46.340 --> 00:36:49.380 align:middle line:84% The simulation you want to do is beyond-- 00:36:49.380 --> 00:36:52.280 align:middle line:90% is too hard to do analytically. 00:36:52.280 --> 00:36:56.020 align:middle line:84% So Gene Myers set up-- just listed all the things he 00:36:56.020 --> 00:36:57.790 align:middle line:90% thought would be-- 00:36:57.790 --> 00:37:02.470 align:middle line:84% could affect the ability to assemble a genome sequence. 00:37:02.470 --> 00:37:07.990 align:middle line:84% The read length and types of repeats, and all this stuff 00:37:07.990 --> 00:37:09.160 align:middle line:90% was simulated. 00:37:09.160 --> 00:37:13.510 align:middle line:84% And he cranked the simulation on real human genome size projects 00:37:13.510 --> 00:37:16.210 align:middle line:84% and came to the conclusion that you could do a shotgun 00:37:16.210 --> 00:37:18.460 align:middle line:90% assembly of a mammalian genome. 00:37:18.460 --> 00:37:20.320 align:middle line:84% A company called Celera was formed. 00:37:20.320 --> 00:37:24.520 align:middle line:84% Gene Myers was hired as the computer guru. 00:37:24.520 --> 00:37:27.250 align:middle line:84% They put together a large stable of computers 00:37:27.250 --> 00:37:31.060 align:middle line:84% and they started doing this on the human and the mouse genome. 00:37:31.060 --> 00:37:33.640 align:middle line:84% The human genome was in the end not done by this method, 00:37:33.640 --> 00:37:36.550 align:middle line:84% but the mouse genome was, and it was a pretty good assembly. 00:37:36.550 --> 00:37:39.670 align:middle line:84% So the Drosophila genome missing the Drosophila repeats 00:37:39.670 --> 00:37:41.360 align:middle line:90% was also done by this method. 00:37:41.360 --> 00:37:43.870 align:middle line:84% So this is scaled very gracefully 00:37:43.870 --> 00:37:49.480 align:middle line:84% from the first shotgun sequence, which was on a four kV plasmid 00:37:49.480 --> 00:37:52.510 align:middle line:90% to mammalian size genomes. 00:37:52.510 --> 00:37:54.670 align:middle line:84% No mammalian genome is completely sequenced, 00:37:54.670 --> 00:37:56.440 align:middle line:84% so we can't really declare victory. 00:37:56.440 --> 00:37:59.950 align:middle line:84% But the sort of simulation that he did here 00:37:59.950 --> 00:38:01.105 align:middle line:90% has played out very nicely. 00:38:01.105 --> 00:38:03.760 align:middle line:90% 00:38:03.760 --> 00:38:05.980 align:middle line:84% Right here in Boston, there will be-- 00:38:05.980 --> 00:38:07.480 align:middle line:84% when we start thinking of the future 00:38:07.480 --> 00:38:09.160 align:middle line:84% of sequencing technology, we would all 00:38:09.160 --> 00:38:12.040 align:middle line:84% like-- this is almost uncontroversial as 00:38:12.040 --> 00:38:16.090 align:middle line:84% to how much we desire that the genome not cost $3 billion, 00:38:16.090 --> 00:38:17.920 align:middle line:90% but it costs $1,000. 00:38:17.920 --> 00:38:20.110 align:middle line:84% And now there are a number of people 00:38:20.110 --> 00:38:26.980 align:middle line:84% who are taking very definite steps to get us to that point. 00:38:26.980 --> 00:38:30.040 align:middle line:84% To understand systematic and random errors that 00:38:30.040 --> 00:38:32.080 align:middle line:84% can occur in these steps, let's take 00:38:32.080 --> 00:38:35.560 align:middle line:84% this dideoxy gel electrophoresis we've been talking about here. 00:38:35.560 --> 00:38:37.660 align:middle line:84% You have four different colored terminators. 00:38:37.660 --> 00:38:40.750 align:middle line:84% These is where the polymerase can't go any further 00:38:40.750 --> 00:38:43.532 align:middle line:84% because there's a blocking group here, 00:38:43.532 --> 00:38:44.740 align:middle line:90% which is fluorescent labeled. 00:38:44.740 --> 00:38:46.720 align:middle line:84% And if the template on the far left 00:38:46.720 --> 00:38:50.320 align:middle line:84% here is ready to accept an A, you'll get an A. 00:38:50.320 --> 00:38:54.070 align:middle line:84% And this n and n minus one will separate 00:38:54.070 --> 00:38:57.040 align:middle line:84% on this electrophoresis and the four colors will give you 00:38:57.040 --> 00:39:00.700 align:middle line:84% this four-colored pattern where the intensity reflects 00:39:00.700 --> 00:39:03.670 align:middle line:84% good termination at that position, 00:39:03.670 --> 00:39:05.830 align:middle line:84% and you can basically go along reading it. 00:39:05.830 --> 00:39:07.990 align:middle line:90% G, C, G, G, A, T. 00:39:07.990 --> 00:39:09.760 align:middle line:84% Now this is in the well-behaved part. 00:39:09.760 --> 00:39:13.510 align:middle line:84% An example of a systematic error that you get in this extension 00:39:13.510 --> 00:39:17.320 align:middle line:84% occurs here in the upper right-hand corner of slide 40. 00:39:17.320 --> 00:39:19.510 align:middle line:84% Now you've got-- because of one of these hairpins 00:39:19.510 --> 00:39:20.968 align:middle line:84% that I mentioned before, you've got 00:39:20.968 --> 00:39:24.700 align:middle line:84% a pile-up of seven nucleotides all at the same position. 00:39:24.700 --> 00:39:26.242 align:middle line:84% A completely alternative method that 00:39:26.242 --> 00:39:27.700 align:middle line:84% doesn't involve gel electrophoresis 00:39:27.700 --> 00:39:29.920 align:middle line:84% is called pirA sequencing, and this 00:39:29.920 --> 00:39:34.480 align:middle line:84% is an equivalent that can be done with fluorescent addition. 00:39:34.480 --> 00:39:36.760 align:middle line:84% Instead of separating them in time 00:39:36.760 --> 00:39:39.550 align:middle line:84% by their size in electrophoresis, 00:39:39.550 --> 00:39:43.120 align:middle line:84% in time you ask serially, do you want an A here? 00:39:43.120 --> 00:39:45.400 align:middle line:84% If yes, then you get a little green-- 00:39:45.400 --> 00:39:49.070 align:middle line:84% you get a little peek of representing 00:39:49.070 --> 00:39:51.740 align:middle line:84% the release of pyrophosphate or the incorporation 00:39:51.740 --> 00:39:53.055 align:middle line:90% of fluorescent A. 00:39:53.055 --> 00:39:55.130 align:middle line:84% And then you ask, do you want a T, 00:39:55.130 --> 00:39:56.450 align:middle line:90% and so forth, and you go along. 00:39:56.450 --> 00:40:00.230 align:middle line:84% And each signal means yes to the answer 00:40:00.230 --> 00:40:02.550 align:middle line:84% that it's ready for that particular base. 00:40:02.550 --> 00:40:04.490 align:middle line:84% And you can see this doesn't have any problems 00:40:04.490 --> 00:40:06.050 align:middle line:90% with this hairpin region. 00:40:06.050 --> 00:40:08.690 align:middle line:90% 00:40:08.690 --> 00:40:10.190 align:middle line:84% So when you have a systematic error, 00:40:10.190 --> 00:40:11.898 align:middle line:84% you have to change the method that you're 00:40:11.898 --> 00:40:13.670 align:middle line:90% using fairly radically. 00:40:13.670 --> 00:40:17.435 align:middle line:84% The opposite strand or a completely different method. 00:40:17.435 --> 00:40:20.230 align:middle line:90% 00:40:20.230 --> 00:40:24.280 align:middle line:84% If you have-- early on, we had huge differences 00:40:24.280 --> 00:40:27.760 align:middle line:84% in intensity of the fluorophores and new enzymes 00:40:27.760 --> 00:40:31.150 align:middle line:84% and new fluorophores were developed by Tabor and Matthews 00:40:31.150 --> 00:40:32.450 align:middle line:90% and Glaser, and so forth. 00:40:32.450 --> 00:40:36.580 align:middle line:84% And this was a huge advance in making everything uniform 00:40:36.580 --> 00:40:39.320 align:middle line:84% and eliminating systematic errors. 00:40:39.320 --> 00:40:41.950 align:middle line:84% So the sort of things that are on the horizon that hopefully 00:40:41.950 --> 00:40:45.040 align:middle line:84% will be discussed tomorrow in Boston, 00:40:45.040 --> 00:40:51.100 align:middle line:84% we've talked about this short number of base extensions 00:40:51.100 --> 00:40:53.080 align:middle line:84% like power sequencing, the longer 00:40:53.080 --> 00:40:56.980 align:middle line:84% extensions in capillary arrays, which, capillary arrays 00:40:56.980 --> 00:40:58.690 align:middle line:84% are changing from low-end capillaries 00:40:58.690 --> 00:41:01.780 align:middle line:90% into microfabricated chips. 00:41:01.780 --> 00:41:04.015 align:middle line:84% I'll show an example of a mass spec in just a moment. 00:41:04.015 --> 00:41:07.150 align:middle line:90% 00:41:07.150 --> 00:41:08.980 align:middle line:84% Sequencing by hybridization on arrays 00:41:08.980 --> 00:41:13.030 align:middle line:84% will illustrate as a prelude, as an example of Affymetrix 00:41:13.030 --> 00:41:17.860 align:middle line:90% technology in this slide. 00:41:17.860 --> 00:41:18.370 align:middle line:90% OK. 00:41:18.370 --> 00:41:22.750 align:middle line:84% So the idea here, this is mainly for re-sequencing. 00:41:22.750 --> 00:41:25.780 align:middle line:84% Some of the ways of reducing the cost of sequencing 00:41:25.780 --> 00:41:28.480 align:middle line:84% the human genome will not apply to sequencing brand 00:41:28.480 --> 00:41:29.260 align:middle line:90% new genomes. 00:41:29.260 --> 00:41:30.970 align:middle line:84% But still, we need to pursue them, 00:41:30.970 --> 00:41:33.880 align:middle line:84% because this may be the way that we get the $1,000 human genome, 00:41:33.880 --> 00:41:36.260 align:middle line:90% even if we don't get other ones. 00:41:36.260 --> 00:41:39.730 align:middle line:84% And here, you know the sequence, except there's 00:41:39.730 --> 00:41:42.540 align:middle line:84% a possibility that there could be a polymorphism at any base. 00:41:42.540 --> 00:41:45.640 align:middle line:84% Could be any single base substitution at any base. 00:41:45.640 --> 00:41:47.335 align:middle line:84% And so you don't necessarily know 00:41:47.335 --> 00:41:49.690 align:middle line:84% in advance what the common ones are or the rare ones, 00:41:49.690 --> 00:41:52.420 align:middle line:84% but you do know the canonical sequence. 00:41:52.420 --> 00:41:58.750 align:middle line:84% And so at every position, you'll make a 25-mer oligonucleotide 00:41:58.750 --> 00:42:00.520 align:middle line:84% which will bind to a fluorescently labeled 00:42:00.520 --> 00:42:03.910 align:middle line:84% version of your genome, or a piece of your genome. 00:42:03.910 --> 00:42:06.760 align:middle line:84% And this is actually developed for HIV re-sequencing 00:42:06.760 --> 00:42:08.170 align:middle line:90% by Affymetrix. 00:42:08.170 --> 00:42:11.620 align:middle line:84% And at this middle position, you'll 00:42:11.620 --> 00:42:18.785 align:middle line:84% put in all four possible substitutions, T, G, C, or A. 00:42:18.785 --> 00:42:24.870 align:middle line:84% And you'll consider each possible template. 00:42:24.870 --> 00:42:26.750 align:middle line:84% So if you have the template, which is-- let's 00:42:26.750 --> 00:42:28.167 align:middle line:84% say these are the two alleles that 00:42:28.167 --> 00:42:31.820 align:middle line:84% occur in a human population or in your sample. 00:42:31.820 --> 00:42:35.180 align:middle line:84% You can have this sequence and then all the variations on it, 00:42:35.180 --> 00:42:39.453 align:middle line:84% stepping along, changing T, G, C, A for the first base, 00:42:39.453 --> 00:42:41.370 align:middle line:84% the second base, the third base, and so forth, 00:42:41.370 --> 00:42:42.287 align:middle line:90% till you hit this one. 00:42:42.287 --> 00:42:44.540 align:middle line:84% And this is where the real polymorphism occurs. 00:42:44.540 --> 00:42:47.030 align:middle line:84% And you could have either this as the context 00:42:47.030 --> 00:42:49.310 align:middle line:90% or this as the context. 00:42:49.310 --> 00:42:52.310 align:middle line:84% And this is schematic And this is the real data. 00:42:52.310 --> 00:42:54.170 align:middle line:84% These are real data down here where 00:42:54.170 --> 00:42:57.140 align:middle line:84% you have the context of the A allele or the context 00:42:57.140 --> 00:42:58.190 align:middle line:90% of the C allele. 00:42:58.190 --> 00:43:01.640 align:middle line:84% You can have the homozygotes or the heterozygotes. 00:43:01.640 --> 00:43:04.703 align:middle line:84% And in the homozygous A, you can see it lights up 00:43:04.703 --> 00:43:06.620 align:middle line:84% the best, the best hybridization when you have 00:43:06.620 --> 00:43:07.828 align:middle line:90% the A in the middle position. 00:43:07.828 --> 00:43:09.380 align:middle line:84% The middle position is most sensitive 00:43:09.380 --> 00:43:11.250 align:middle line:90% to hybridization changes. 00:43:11.250 --> 00:43:16.280 align:middle line:84% And for the C, you have it in the C row here. 00:43:16.280 --> 00:43:18.410 align:middle line:84% And remember, you're changing all the bases 00:43:18.410 --> 00:43:19.160 align:middle line:90% in every position. 00:43:19.160 --> 00:43:20.077 align:middle line:90% One, two, three, four. 00:43:20.077 --> 00:43:23.150 align:middle line:84% This is the one where the middle base of the middle position 00:43:23.150 --> 00:43:24.780 align:middle line:90% is in the right context. 00:43:24.780 --> 00:43:27.110 align:middle line:84% So this is in the A context and the C context. 00:43:27.110 --> 00:43:30.470 align:middle line:84% And in the heterozygote, you get both the A and the C. 00:43:30.470 --> 00:43:32.720 align:middle line:84% And so this has been done on HIV. 00:43:32.720 --> 00:43:34.730 align:middle line:84% It's been done on BRCA1, on mitochondria. 00:43:34.730 --> 00:43:37.640 align:middle line:84% And now they've applied it with whole wafers 00:43:37.640 --> 00:43:39.630 align:middle line:90% to the entire human genome. 00:43:39.630 --> 00:43:44.630 align:middle line:84% And this probably costs on the order of $3 million or so. 00:43:44.630 --> 00:43:46.400 align:middle line:84% Mass spectrometry is another way that's 00:43:46.400 --> 00:43:48.525 align:middle line:84% used, probably not for sequencing the whole genome, 00:43:48.525 --> 00:43:51.590 align:middle line:84% but it's used for single nucleotide polymorphisms. 00:43:51.590 --> 00:43:56.660 align:middle line:84% This costs on the order of $0.50 per polymorphism. 00:43:56.660 --> 00:44:00.650 align:middle line:84% If there's three million of them in your genome, 00:44:00.650 --> 00:44:03.743 align:middle line:90% that's a lot of $0.50. 00:44:03.743 --> 00:44:07.130 align:middle line:90% [LAUGHTER] 00:44:07.130 --> 00:44:09.680 align:middle line:84% And here's what it looks like when you read it out. 00:44:09.680 --> 00:44:11.690 align:middle line:84% It's really just like electrophoresis. 00:44:11.690 --> 00:44:17.120 align:middle line:84% You can now separate an addition of an A 00:44:17.120 --> 00:44:22.535 align:middle line:84% from an addition of a G. And the difference in mass between an A 00:44:22.535 --> 00:44:23.930 align:middle line:84% and a G, this is even more subtle 00:44:23.930 --> 00:44:25.847 align:middle line:84% than the difference of an n and an n plus one. 00:44:25.847 --> 00:44:27.805 align:middle line:84% This is just a difference between an A and a C. 00:44:27.805 --> 00:44:28.910 align:middle line:90% It's detectable in this. 00:44:28.910 --> 00:44:31.580 align:middle line:84% In fact, it's detectable and quantitative enough 00:44:31.580 --> 00:44:32.912 align:middle line:90% that you can pool samples. 00:44:32.912 --> 00:44:35.120 align:middle line:84% This is a bit of a stunt, but it's an important stunt 00:44:35.120 --> 00:44:40.100 align:middle line:84% to show that this is really a very precise method, albeit 00:44:40.100 --> 00:44:42.530 align:middle line:90% still fairly expensive. 00:44:42.530 --> 00:44:45.320 align:middle line:84% Now just in closing, I want to give you 00:44:45.320 --> 00:44:49.580 align:middle line:84% the simplest possible example of how we 00:44:49.580 --> 00:44:51.020 align:middle line:90% can search through sequences. 00:44:51.020 --> 00:44:53.103 align:middle line:84% Next week, we'll give you a much more rigorous way 00:44:53.103 --> 00:44:54.728 align:middle line:84% that you can look through the sequences 00:44:54.728 --> 00:44:57.090 align:middle line:84% with very extensive differences between the sequences. 00:44:57.090 --> 00:45:00.110 align:middle line:84% But here, the theme of today's talk 00:45:00.110 --> 00:45:02.840 align:middle line:84% is the subtle polymorphism differences 00:45:02.840 --> 00:45:04.370 align:middle line:90% that occur between you and me. 00:45:04.370 --> 00:45:07.160 align:middle line:84% And here, one different-- so generally, you're 00:45:07.160 --> 00:45:08.480 align:middle line:90% looking for exact matches. 00:45:08.480 --> 00:45:11.450 align:middle line:84% And a good way to look for exact matches is-- 00:45:11.450 --> 00:45:14.570 align:middle line:84% good ways are hashing, suffix arrays, and suffix trees 00:45:14.570 --> 00:45:16.500 align:middle line:84% where basically in each of these, 00:45:16.500 --> 00:45:21.110 align:middle line:84% you're looking for using a word, a word either 00:45:21.110 --> 00:45:24.830 align:middle line:84% that's built up and stored from the end, the suffix, 00:45:24.830 --> 00:45:27.530 align:middle line:84% one letter at a time, or it's a chunk 00:45:27.530 --> 00:45:29.150 align:middle line:90% that you might have as a hash. 00:45:29.150 --> 00:45:31.292 align:middle line:90% And you make up a lookup table. 00:45:31.292 --> 00:45:32.750 align:middle line:84% And the size of that lookup table-- 00:45:32.750 --> 00:45:34.542 align:middle line:84% it's a trade-off between speed of searching 00:45:34.542 --> 00:45:35.810 align:middle line:90% and the size of the table. 00:45:35.810 --> 00:45:39.378 align:middle line:84% The size is going to be-- if the word is n nucleotides long, 00:45:39.378 --> 00:45:40.670 align:middle line:90% it's going to be four to the n. 00:45:40.670 --> 00:45:42.253 align:middle line:84% It's going to be the storage space you 00:45:42.253 --> 00:45:45.560 align:middle line:84% have to put on disk or RAM, RAM if you 00:45:45.560 --> 00:45:46.910 align:middle line:90% want it to be a fast search. 00:45:46.910 --> 00:45:50.390 align:middle line:84% And so 16 is the magic number, sort of in the ballpark 00:45:50.390 --> 00:45:52.490 align:middle line:84% for a human genome, because four to the 16th 00:45:52.490 --> 00:45:55.400 align:middle line:84% is four billion sequences you can represent. 00:45:55.400 --> 00:45:56.670 align:middle line:90% But it's a huge table. 00:45:56.670 --> 00:45:59.330 align:middle line:84% You have to have a table of four billion times however 00:45:59.330 --> 00:46:04.130 align:middle line:84% many bytes you need to store the positions. 00:46:04.130 --> 00:46:06.470 align:middle line:84% Typically, about four bytes of storage. 00:46:06.470 --> 00:46:08.060 align:middle line:84% If you cut back on this a little bit, 00:46:08.060 --> 00:46:09.518 align:middle line:84% you'll end up with collisions where 00:46:09.518 --> 00:46:13.310 align:middle line:84% you'll have two things that have the same hash or suffix. 00:46:13.310 --> 00:46:14.930 align:middle line:90% If you make it-- 00:46:14.930 --> 00:46:16.353 align:middle line:84% and that's if you make it smaller. 00:46:16.353 --> 00:46:17.270 align:middle line:90% It'll take less space. 00:46:17.270 --> 00:46:18.680 align:middle line:84% If you make it bigger, it'll take 00:46:18.680 --> 00:46:21.020 align:middle line:90% a ridiculous amount of RAM. 00:46:21.020 --> 00:46:25.070 align:middle line:84% And then here's a kind of whimsical-- 00:46:25.070 --> 00:46:27.500 align:middle line:84% another example of pearl where you not only want 00:46:27.500 --> 00:46:30.110 align:middle line:84% to find all the mutations here at a very high density-- 00:46:30.110 --> 00:46:33.080 align:middle line:84% a ridiculously high density, not one particular base 00:46:33.080 --> 00:46:34.618 align:middle line:90% for every few base pairs. 00:46:34.618 --> 00:46:37.160 align:middle line:84% You not only want to find them, but you want to correct them. 00:46:37.160 --> 00:46:40.130 align:middle line:84% And here, the pearl does the substitution. 00:46:40.130 --> 00:46:43.765 align:middle line:84% And after gene therapy, everybody walks out happy. 00:46:43.765 --> 00:46:44.265 align:middle line:90% OK. 00:46:44.265 --> 00:46:46.360 align:middle line:90% [LAUGHTER]