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 --> 00:00:06.340 align:middle line:84% by MIT OpenCourseWare under a Creative Commons license. 00:00:06.340 --> 00:00:08.470 align:middle line:84% Additional information about our license 00:00:08.470 --> 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 --> 00:00:22.167 align:middle line:90% 00:00:22.167 --> 00:00:22.875 align:middle line:90% PROFESSOR: Ready? 00:00:22.875 --> 00:00:26.076 align:middle line:90% 00:00:26.076 --> 00:00:27.050 align:middle line:90% OK. 00:00:27.050 --> 00:00:32.409 align:middle line:84% Well, welcome to the third lecture. 00:00:32.409 --> 00:00:35.060 align:middle line:84% Quick review of what we did last time-- 00:00:35.060 --> 00:00:36.590 align:middle line:90% first slide. 00:00:36.590 --> 00:00:43.040 align:middle line:84% We talked about purification, basically 00:00:43.040 --> 00:00:46.760 align:middle line:84% at every level of the hierarchy in complexity, 00:00:46.760 --> 00:00:50.870 align:middle line:84% from the elements all the way up to organisms, 00:00:50.870 --> 00:00:54.620 align:middle line:84% and in particular, the awesome purification one 00:00:54.620 --> 00:00:59.630 align:middle line:84% can get by serial dilution down to single molecules-- 00:00:59.630 --> 00:01:02.030 align:middle line:84% recombinant DNA molecules, in this case, 00:01:02.030 --> 00:01:04.940 align:middle line:90% embedded in E. coli cells-- 00:01:04.940 --> 00:01:11.600 align:middle line:84% and how this purification led to a revolution, 00:01:11.600 --> 00:01:14.210 align:middle line:84% first in biochemistry, then in recombinant DNA. 00:01:14.210 --> 00:01:17.720 align:middle line:84% Molecular biology then led to the Genome Project and systems 00:01:17.720 --> 00:01:22.820 align:middle line:84% biology, which brings us to models of interconnections. 00:01:22.820 --> 00:01:27.775 align:middle line:84% And to start in with algorithms that 00:01:27.775 --> 00:01:29.150 align:middle line:84% are useful in systems biology, we 00:01:29.150 --> 00:01:31.567 align:middle line:84% start with one of the simplest and most robust ones, which 00:01:31.567 --> 00:01:35.940 align:middle line:84% is this genetic code, shown here in the lower right-hand corner. 00:01:35.940 --> 00:01:40.550 align:middle line:84% But as one looks at the huge diversity in the tree of life, 00:01:40.550 --> 00:01:44.210 align:middle line:84% you find examples of exceptions to almost everything 00:01:44.210 --> 00:01:46.370 align:middle line:84% you can come up with, including the genetic code. 00:01:46.370 --> 00:01:49.310 align:middle line:84% And we talked about how to cherish 00:01:49.310 --> 00:01:51.560 align:middle line:90% the exceptions, as usual, here. 00:01:51.560 --> 00:01:54.680 align:middle line:84% And then, getting back to systems biology, 00:01:54.680 --> 00:01:57.590 align:middle line:84% in terms of how one creates qualitative and quantitative 00:01:57.590 --> 00:02:02.540 align:middle line:84% models from functional genomics data and establishes evidence. 00:02:02.540 --> 00:02:04.700 align:middle line:84% Finally, we ended on mutations and selection, 00:02:04.700 --> 00:02:08.419 align:middle line:84% as we will do in all three lectures here. 00:02:08.419 --> 00:02:10.610 align:middle line:84% This lecture in particular will focus 00:02:10.610 --> 00:02:12.870 align:middle line:90% on mutations and selection. 00:02:12.870 --> 00:02:16.190 align:middle line:90% So what is today's menu? 00:02:16.190 --> 00:02:19.460 align:middle line:84% We'll start with types of mutants 00:02:19.460 --> 00:02:25.880 align:middle line:84% and how they're represented for bioinformatic purposes. 00:02:25.880 --> 00:02:32.450 align:middle line:84% We'll talk about the three main methods by which mutations 00:02:32.450 --> 00:02:35.300 align:middle line:84% occur, drift, and select so that you 00:02:35.300 --> 00:02:40.220 align:middle line:84% can determine the frequency of different alleles 00:02:40.220 --> 00:02:42.140 align:middle line:90% in populations. 00:02:42.140 --> 00:02:45.840 align:middle line:84% In doing that, we'll rely on our friend from the first lecture, 00:02:45.840 --> 00:02:51.260 align:middle line:84% the binomial distribution, in the context of an exponentially 00:02:51.260 --> 00:02:52.970 align:middle line:90% growing population. 00:02:52.970 --> 00:02:56.030 align:middle line:90% 00:02:56.030 --> 00:03:00.920 align:middle line:84% Then, give you some very practical training 00:03:00.920 --> 00:03:04.850 align:middle line:84% here on association studies, where we illustrate it 00:03:04.850 --> 00:03:09.500 align:middle line:84% with a very important example of HIV resistance 00:03:09.500 --> 00:03:12.800 align:middle line:84% and a very useful statistic, easily as 00:03:12.800 --> 00:03:14.900 align:middle line:84% useful as the binomial and the Gaussian-- 00:03:14.900 --> 00:03:16.610 align:middle line:90% the chi-squared statistic. 00:03:16.610 --> 00:03:18.950 align:middle line:84% And then, we'll continue to talk about association 00:03:18.950 --> 00:03:24.020 align:middle line:84% in the context of causative alleles 00:03:24.020 --> 00:03:26.990 align:middle line:84% and importance of getting haplotypes, 00:03:26.990 --> 00:03:29.840 align:middle line:84% and then technologies that are required 00:03:29.840 --> 00:03:34.340 align:middle line:84% that have been used to get the framework first genome 00:03:34.340 --> 00:03:36.500 align:middle line:84% and how one might change strategy 00:03:36.500 --> 00:03:39.170 align:middle line:84% in getting subsequent genomes in order 00:03:39.170 --> 00:03:45.150 align:middle line:84% to make cost-effective these very large association studies. 00:03:45.150 --> 00:03:47.060 align:middle line:84% And finally, in the context of that, 00:03:47.060 --> 00:03:50.120 align:middle line:84% we'll talk about random and systematic errors 00:03:50.120 --> 00:03:52.730 align:middle line:84% in more detail so you get lots of examples and ways 00:03:52.730 --> 00:03:55.430 align:middle line:84% of dealing with it computationally. 00:03:55.430 --> 00:04:00.030 align:middle line:84% So just to go from our brief discussion about our friend, 00:04:00.030 --> 00:04:06.500 align:middle line:84% the 100% DNA sequence identity, or amino acid sequence identity 00:04:06.500 --> 00:04:13.790 align:middle line:84% that you might find in the lens protein and enolase enzyme, 00:04:13.790 --> 00:04:17.930 align:middle line:84% we can see that, even at 100%, you can find differences 00:04:17.930 --> 00:04:18.600 align:middle line:90% in function. 00:04:18.600 --> 00:04:24.410 align:middle line:84% And so functional measures are a good adjunct to DNA 00:04:24.410 --> 00:04:26.870 align:middle line:90% or amino acids' identity. 00:04:26.870 --> 00:04:31.280 align:middle line:84% At 99.9% identity, we're talking about the level 00:04:31.280 --> 00:04:33.650 align:middle line:84% of single-nucleotide polymorphisms 00:04:33.650 --> 00:04:39.140 align:middle line:84% that might exist between any two positions in your mother 00:04:39.140 --> 00:04:41.360 align:middle line:84% and your father's chromosomes in your body, 00:04:41.360 --> 00:04:43.280 align:middle line:84% or the differences between one of your genomes 00:04:43.280 --> 00:04:44.197 align:middle line:90% and one of my genomes. 00:04:44.197 --> 00:04:46.370 align:middle line:84% About once every kilobase, there will be 00:04:46.370 --> 00:04:49.280 align:middle line:90% a polymorphism, a difference. 00:04:49.280 --> 00:04:53.450 align:middle line:84% It's often a single nucleotide, an A for a G. 00:04:53.450 --> 00:04:56.643 align:middle line:84% Then, as we go to 98% differences, 00:04:56.643 --> 00:04:58.310 align:middle line:84% then we're talking about the differences 00:04:58.310 --> 00:05:01.130 align:middle line:84% between one of our genomes and a chimpanzee genome-- 00:05:01.130 --> 00:05:04.140 align:middle line:84% in other words, a completely different genus and species. 00:05:04.140 --> 00:05:07.040 align:middle line:84% However, by the criterion we mentioned in a previous lecture 00:05:07.040 --> 00:05:10.250 align:middle line:84% about bacterial definitions of species, 00:05:10.250 --> 00:05:12.860 align:middle line:84% those would be almost identical, and you'd 00:05:12.860 --> 00:05:19.820 align:middle line:84% have to go to identities less than 70% in order 00:05:19.820 --> 00:05:21.600 align:middle line:84% to call it a new bacterial species. 00:05:21.600 --> 00:05:24.320 align:middle line:84% So you can see that this is a very soft number, very 00:05:24.320 --> 00:05:30.080 align:middle line:84% dependent upon the context and the branch of the tree of life 00:05:30.080 --> 00:05:31.340 align:middle line:90% that you're working with. 00:05:31.340 --> 00:05:37.670 align:middle line:84% Then, we have sequence homology and very 00:05:37.670 --> 00:05:40.852 align:middle line:84% distant homologs which are only detectable, as we'll 00:05:40.852 --> 00:05:42.560 align:middle line:84% see when we get to the proteomics section 00:05:42.560 --> 00:05:47.210 align:middle line:84% of this course, by three-dimensional structures, 00:05:47.210 --> 00:05:48.080 align:middle line:90% not by sequence. 00:05:48.080 --> 00:05:51.650 align:middle line:84% And that switchover-- sequence homology 00:05:51.650 --> 00:05:55.070 align:middle line:84% will be the topic of next lecture, 00:05:55.070 --> 00:05:57.860 align:middle line:84% and the very distant one in 3D structures 00:05:57.860 --> 00:05:59.450 align:middle line:90% will be later, in proteomics. 00:05:59.450 --> 00:06:05.490 align:middle line:84% But that occurs at about 25% to 30%. 00:06:05.490 --> 00:06:10.070 align:middle line:84% This is just a reminder and an introductory slide 00:06:10.070 --> 00:06:11.280 align:middle line:90% to the next slide. 00:06:11.280 --> 00:06:15.290 align:middle line:84% We have different phenotypic effects 00:06:15.290 --> 00:06:17.420 align:middle line:84% due to different types of mutations. 00:06:17.420 --> 00:06:21.570 align:middle line:84% And ignoring the phenotypes that we talked about before, 00:06:21.570 --> 00:06:23.330 align:middle line:90% you have the types of mutations. 00:06:23.330 --> 00:06:28.520 align:middle line:84% Classes are null mutations, dosage, conditional mutations, 00:06:28.520 --> 00:06:31.460 align:middle line:84% gain-of-function, altered ligand specificity. 00:06:31.460 --> 00:06:34.970 align:middle line:84% Now, that's in broad terms, colloquially. 00:06:34.970 --> 00:06:38.390 align:middle line:84% But how is this achieved on a more molecular level, 00:06:38.390 --> 00:06:40.580 align:middle line:84% and how do we represent it compactly 00:06:40.580 --> 00:06:43.650 align:middle line:90% for bioinformatic discussion? 00:06:43.650 --> 00:06:48.050 align:middle line:90% So we have single substitutions. 00:06:48.050 --> 00:06:52.190 align:middle line:84% These can be a single base par, an AT base pair, 00:06:52.190 --> 00:06:55.880 align:middle line:84% to a CG base pair, or a GC base pair to a TA base pair, 00:06:55.880 --> 00:06:58.400 align:middle line:90% and so on. 00:06:58.400 --> 00:07:01.000 align:middle line:84% There can be deletions and duplications. 00:07:01.000 --> 00:07:04.010 align:middle line:90% 00:07:04.010 --> 00:07:05.180 align:middle line:90% These can range. 00:07:05.180 --> 00:07:08.720 align:middle line:84% The deletions and duplications be as large as a chromosome 00:07:08.720 --> 00:07:10.580 align:middle line:84% or as small as a single base pair. 00:07:10.580 --> 00:07:13.730 align:middle line:84% You can delete that A rather than change it into a C, 00:07:13.730 --> 00:07:17.673 align:middle line:90% and that would be one base pair. 00:07:17.673 --> 00:07:19.340 align:middle line:84% So when you delete an entire chromosome, 00:07:19.340 --> 00:07:21.260 align:middle line:90% that's called aneuploidy. 00:07:21.260 --> 00:07:24.950 align:middle line:84% The example in the previous slide was trisomy 21. 00:07:24.950 --> 00:07:27.770 align:middle line:84% If you remove that chromosome 21 instead 00:07:27.770 --> 00:07:31.980 align:middle line:84% of having three copies of it, it would be monosomy. 00:07:31.980 --> 00:07:35.810 align:middle line:84% And these are huge consequences even 00:07:35.810 --> 00:07:38.510 align:middle line:84% though they're fairly subtle changes in dosage. 00:07:38.510 --> 00:07:41.090 align:middle line:84% Now, a special class of deletion and duplication 00:07:41.090 --> 00:07:45.140 align:middle line:84% occurs when you have a tandem repeat of a sequence. 00:07:45.140 --> 00:07:50.360 align:middle line:84% When you have anywhere from a single base repeat, AAAAA, 00:07:50.360 --> 00:07:54.890 align:middle line:84% or dinucleotide, trinucleotide, all the way up, 00:07:54.890 --> 00:07:59.180 align:middle line:84% those have a very high tendency for 00:07:59.180 --> 00:08:04.790 align:middle line:84% both forward and reverse mutation, both deletions 00:08:04.790 --> 00:08:07.580 align:middle line:84% and duplications, because at the very small level, 00:08:07.580 --> 00:08:13.160 align:middle line:84% you have polymerase slippage and other microscopic events. 00:08:13.160 --> 00:08:15.770 align:middle line:84% And then, at the larger level, you 00:08:15.770 --> 00:08:19.400 align:middle line:84% have some kind of recombination, often homologous 00:08:19.400 --> 00:08:21.440 align:middle line:84% recombination, that occurs that cause deletions 00:08:21.440 --> 00:08:23.750 align:middle line:84% and duplications of tandem repeats. 00:08:23.750 --> 00:08:26.720 align:middle line:90% An inversion here. 00:08:26.720 --> 00:08:30.440 align:middle line:84% We're representing a complicated chemical event which 00:08:30.440 --> 00:08:32.270 align:middle line:84% involves double-stranded DNA going 00:08:32.270 --> 00:08:34.787 align:middle line:84% 5 prime to 3 prime on the top strand, from left to right, 00:08:34.787 --> 00:08:36.620 align:middle line:84% and 5 prime to 3 prime on the bottom strand, 00:08:36.620 --> 00:08:38.413 align:middle line:90% going from right to left. 00:08:38.413 --> 00:08:40.080 align:middle line:84% And you're taking a little chunk of that 00:08:40.080 --> 00:08:42.020 align:middle line:84% and flipping it so that you break some bonds 00:08:42.020 --> 00:08:44.090 align:middle line:90% and remake them. 00:08:44.090 --> 00:08:47.870 align:middle line:84% All the 3 prime is conserved, but you've 00:08:47.870 --> 00:08:50.570 align:middle line:84% done a reverse complement of the top strand 00:08:50.570 --> 00:08:52.640 align:middle line:90% and the bottom strand. 00:08:52.640 --> 00:08:56.330 align:middle line:84% In that reverse complement, you basically turn Cs into Gs 00:08:56.330 --> 00:08:57.890 align:middle line:90% and change the order. 00:08:57.890 --> 00:09:04.130 align:middle line:84% This is sometimes abbreviated for simple genetic description. 00:09:04.130 --> 00:09:06.200 align:middle line:90% Let's say we inverted CDE. 00:09:06.200 --> 00:09:10.040 align:middle line:84% You might change the case or add primes to it, color it. 00:09:10.040 --> 00:09:11.540 align:middle line:84% In some way or another, you indicate 00:09:11.540 --> 00:09:13.550 align:middle line:84% that it's now a reverse complement, 00:09:13.550 --> 00:09:16.880 align:middle line:84% and of course, the gene order or the DNA segment order 00:09:16.880 --> 00:09:19.880 align:middle line:84% is reversed to indicate that inversion. 00:09:19.880 --> 00:09:22.400 align:middle line:90% 00:09:22.400 --> 00:09:25.130 align:middle line:84% Translocations, insertions, and recombination 00:09:25.130 --> 00:09:30.560 align:middle line:84% have in common that you will make a break somewhere, 00:09:30.560 --> 00:09:33.860 align:middle line:84% and then you will bring in a new piece of DNA, 00:09:33.860 --> 00:09:37.610 align:middle line:84% just like the inversion, where you inverted in place. 00:09:37.610 --> 00:09:41.420 align:middle line:84% Here, it involves something acting at more of a distance. 00:09:41.420 --> 00:09:44.540 align:middle line:84% You'll break between B and C and X and Y, 00:09:44.540 --> 00:09:51.170 align:middle line:84% and you'll, in this case, do a reciprocal translocation 00:09:51.170 --> 00:09:55.280 align:middle line:84% where you conserve all the DNA, and A and B 00:09:55.280 --> 00:09:59.070 align:middle line:90% is now next to Y and Z. 00:09:59.070 --> 00:10:04.350 align:middle line:84% An insertion is like that, but now the DNA need not 00:10:04.350 --> 00:10:06.460 align:middle line:90% be reciprocal in any sense. 00:10:06.460 --> 00:10:09.360 align:middle line:84% It can come in, more or less, from outer space. 00:10:09.360 --> 00:10:10.555 align:middle line:90% Here, it came from Greece. 00:10:10.555 --> 00:10:14.370 align:middle line:90% 00:10:14.370 --> 00:10:19.500 align:middle line:84% It can be a transposable element that 00:10:19.500 --> 00:10:21.660 align:middle line:84% came in from who knows where and inserted in 00:10:21.660 --> 00:10:23.580 align:middle line:90% between the A and B. 00:10:23.580 --> 00:10:24.510 align:middle line:90% Recombination. 00:10:24.510 --> 00:10:28.140 align:middle line:84% Here, I illustrated this homologous recombination. 00:10:28.140 --> 00:10:30.810 align:middle line:84% And you can have an non-homologous combination, 00:10:30.810 --> 00:10:34.150 align:middle line:84% but this is by far the most common and interesting. 00:10:34.150 --> 00:10:36.000 align:middle line:84% Even some non-homologous recombination 00:10:36.000 --> 00:10:37.920 align:middle line:84% involves short regions of homology 00:10:37.920 --> 00:10:43.380 align:middle line:84% where you basically have either two sister chromosomes 00:10:43.380 --> 00:10:46.680 align:middle line:84% or homologs from mother and father 00:10:46.680 --> 00:10:49.590 align:middle line:84% or paralogs within the genome where you've 00:10:49.590 --> 00:10:51.990 align:middle line:84% got to duplicate a gene that might even 00:10:51.990 --> 00:10:53.910 align:middle line:90% be on the same chromosome arm. 00:10:53.910 --> 00:10:56.790 align:middle line:84% And now, just as with the deletions and duplication, 00:10:56.790 --> 00:10:59.790 align:middle line:84% where you have tandem repeats, if you have repeats anywhere 00:10:59.790 --> 00:11:03.720 align:middle line:84% in the genome, you can take a small difference. 00:11:03.720 --> 00:11:05.430 align:middle line:84% We're emphasizing the similarities here, 00:11:05.430 --> 00:11:06.972 align:middle line:84% but they have a few small differences 00:11:06.972 --> 00:11:08.700 align:middle line:90% that allow you to track them. 00:11:08.700 --> 00:11:10.770 align:middle line:84% Those can be exchanged by single-strand or 00:11:10.770 --> 00:11:16.320 align:middle line:84% double-stranded DNA, various chemistries, 00:11:16.320 --> 00:11:19.950 align:middle line:84% and you can either do a nice reciprocal exchange here, 00:11:19.950 --> 00:11:22.320 align:middle line:84% where you preserve all the DNA and the little C 00:11:22.320 --> 00:11:26.880 align:middle line:84% gets replacing the big C by some kind of crossover between D 00:11:26.880 --> 00:11:29.220 align:middle line:84% and E, somewhere between C and F, 00:11:29.220 --> 00:11:32.370 align:middle line:84% or you can have a nonreciprocal exchange where you pick up 00:11:32.370 --> 00:11:35.530 align:middle line:84% a little bit of C and duplicate it, 00:11:35.530 --> 00:11:38.880 align:middle line:84% and now there's no big C left over and only little C. 00:11:38.880 --> 00:11:41.490 align:middle line:90% Called gene conversion. 00:11:41.490 --> 00:11:42.870 align:middle line:90% But you get the idea. 00:11:42.870 --> 00:11:45.420 align:middle line:84% These are a fairly exhaustive list 00:11:45.420 --> 00:11:48.690 align:middle line:84% of the kinds of simple, elementary mutations 00:11:48.690 --> 00:11:49.290 align:middle line:90% you can have. 00:11:49.290 --> 00:11:51.840 align:middle line:84% Now, you can pile these in various combinations 00:11:51.840 --> 00:11:54.250 align:middle line:84% with each other, and over long periods of time, 00:11:54.250 --> 00:11:58.020 align:middle line:84% you can get completely new sequences. 00:11:58.020 --> 00:12:01.680 align:middle line:84% There's even ways that you can get de novo synthesis of DNA, 00:12:01.680 --> 00:12:04.380 align:middle line:84% such as mechanisms of terminal transferase, which 00:12:04.380 --> 00:12:06.060 align:middle line:90% is used-- yes? 00:12:06.060 --> 00:12:07.650 align:middle line:84% AUDIENCE: What are the [INAUDIBLE]?? 00:12:07.650 --> 00:12:09.900 align:middle line:84% PROFESSOR: Oh, we're going to get to that a little bit 00:12:09.900 --> 00:12:11.525 align:middle line:84% later on, but I can give you a preview. 00:12:11.525 --> 00:12:14.430 align:middle line:90% 00:12:14.430 --> 00:12:18.390 align:middle line:84% In human genome, these point mutations occurred about 10 00:12:18.390 --> 00:12:24.270 align:middle line:84% to the minus 8 per base pair per generation. 00:12:24.270 --> 00:12:26.970 align:middle line:84% Deletions and duplications, especially in tandem regions, 00:12:26.970 --> 00:12:30.630 align:middle line:84% can be as much as six orders of magnitude higher-frequency 00:12:30.630 --> 00:12:33.300 align:middle line:90% than that. 00:12:33.300 --> 00:12:37.650 align:middle line:84% So there's a huge variation from position to position and types 00:12:37.650 --> 00:12:40.260 align:middle line:84% of alleles that will determine the mutation rate, 00:12:40.260 --> 00:12:42.720 align:middle line:84% and you should be quite aware of that 00:12:42.720 --> 00:12:47.790 align:middle line:84% as you go through various computational exercises. 00:12:47.790 --> 00:12:55.650 align:middle line:84% This is just a bit of commonly accepted nomenclature. 00:12:55.650 --> 00:12:58.530 align:middle line:84% Mutations and polymorphisms are basically same thing. 00:12:58.530 --> 00:13:02.520 align:middle line:84% There are differences between you and me. 00:13:02.520 --> 00:13:05.978 align:middle line:84% They become polymorphisms, meaning 00:13:05.978 --> 00:13:08.520 align:middle line:84% when they are common alleles, when their frequency is greater 00:13:08.520 --> 00:13:10.390 align:middle line:90% than 1% in a population. 00:13:10.390 --> 00:13:14.330 align:middle line:84% This is common in the human genome community. 00:13:14.330 --> 00:13:16.440 align:middle line:90% It may differ for other ones. 00:13:16.440 --> 00:13:20.550 align:middle line:84% But this is roughly where a mutation which is rare-- 00:13:20.550 --> 00:13:22.630 align:middle line:84% less than 1%-- becomes a polymorphism, 00:13:22.630 --> 00:13:25.950 align:middle line:84% which is frequent-- more than 1%. 00:13:25.950 --> 00:13:30.390 align:middle line:84% As a counterpoint to that, I would say that there is a good 00:13:30.390 --> 00:13:34.380 align:middle line:84% chance that every possible single-nucleotide polymorphism 00:13:34.380 --> 00:13:39.240 align:middle line:84% that could exist does exist in a population as large as ours 00:13:39.240 --> 00:13:43.140 align:middle line:84% and mutation rates which are modest but still, 00:13:43.140 --> 00:13:46.590 align:middle line:84% over long periods of time, allow the accumulation of mutations 00:13:46.590 --> 00:13:49.650 align:middle line:84% such that, rather than having maybe 3 million common 00:13:49.650 --> 00:13:52.800 align:middle line:84% single-nucleotide polymorphisms, or SNPs, 00:13:52.800 --> 00:13:54.696 align:middle line:90% we might have 12 billion-- 00:13:54.696 --> 00:13:55.980 align:middle line:90% one at every position. 00:13:55.980 --> 00:13:57.930 align:middle line:84% And in a later slide, we'll actually 00:13:57.930 --> 00:14:04.140 align:middle line:84% go through and calculate crudely why the frequency should 00:14:04.140 --> 00:14:06.150 align:middle line:84% be around 10 to the minus 5 and why 00:14:06.150 --> 00:14:09.780 align:middle line:84% there should be about 10,000 of us representing 00:14:09.780 --> 00:14:13.350 align:middle line:84% each of these so-called rare alleles. 00:14:13.350 --> 00:14:16.515 align:middle line:84% They're rare individually, but they're common as a group. 00:14:16.515 --> 00:14:18.962 align:middle line:90% 00:14:18.962 --> 00:14:21.420 align:middle line:84% It will make a difference as to whether we're talking about 00:14:21.420 --> 00:14:25.980 align:middle line:84% whether these polymorphisms are linked to your favorite trait 00:14:25.980 --> 00:14:28.230 align:middle line:84% or whether they actually cause it, 00:14:28.230 --> 00:14:32.214 align:middle line:84% whether they're part of the cause. 00:14:32.214 --> 00:14:36.730 align:middle line:84% No particular one can be said to be 1-to-1 with a cause. 00:14:36.730 --> 00:14:41.130 align:middle line:84% It's all a collection of mutations and environment. 00:14:41.130 --> 00:14:42.180 align:middle line:90% Now, haplotypes. 00:14:42.180 --> 00:14:43.950 align:middle line:90% What do we mean by haplotypes? 00:14:43.950 --> 00:14:45.960 align:middle line:84% We've introduced SNPs, single-nucleotide 00:14:45.960 --> 00:14:46.980 align:middle line:90% polymorphisms. 00:14:46.980 --> 00:14:51.540 align:middle line:84% If you have a SNP that, let's say, 00:14:51.540 --> 00:14:56.130 align:middle line:84% is involved in causing a APOE4 we'll 00:14:56.130 --> 00:14:59.130 align:middle line:84% introduce in just a moment, an allele that 00:14:59.130 --> 00:15:03.840 align:middle line:84% is associated with increased risk of Alzheimer's disease-- 00:15:03.840 --> 00:15:09.090 align:middle line:84% and let's say that protein has a known change in the protein 00:15:09.090 --> 00:15:13.140 align:middle line:84% three-dimensional structure, and you 00:15:13.140 --> 00:15:16.860 align:middle line:84% can call that the bad allele, or the associated allele. 00:15:16.860 --> 00:15:20.730 align:middle line:84% Now if that protein were expressed 00:15:20.730 --> 00:15:23.400 align:middle line:84% at a low level-- for example, if you had a promoter mutation 00:15:23.400 --> 00:15:25.920 align:middle line:84% or enhancer mutation-- then that haplotype, 00:15:25.920 --> 00:15:29.670 align:middle line:84% that combination of promoter mutation and protein mutation, 00:15:29.670 --> 00:15:33.810 align:middle line:84% is a more significant predictor than either one of them 00:15:33.810 --> 00:15:34.480 align:middle line:90% separately. 00:15:34.480 --> 00:15:36.480 align:middle line:84% And the fact that they're on the same chromosome 00:15:36.480 --> 00:15:39.720 align:middle line:84% is important because if the promoter or enhancer that 00:15:39.720 --> 00:15:43.920 align:middle line:84% determines the level of the protein in cis, 00:15:43.920 --> 00:15:47.410 align:middle line:84% meaning on the same DNA, or in trans, makes a huge difference. 00:15:47.410 --> 00:15:49.200 align:middle line:84% So that's what haplotyping is all about. 00:15:49.200 --> 00:15:51.690 align:middle line:84% It's determining what mutations are 00:15:51.690 --> 00:15:57.330 align:middle line:84% in cis on the same DNA in order to make associations 00:15:57.330 --> 00:16:00.390 align:middle line:84% biologically meaningful and, in terms of systems biology, 00:16:00.390 --> 00:16:01.890 align:middle line:84% interpreting them, in terms of what 00:16:01.890 --> 00:16:08.490 align:middle line:84% you know about regulatory elements and protein elements. 00:16:08.490 --> 00:16:14.070 align:middle line:84% These haplotypes can be inferred indirectly from diploid data 00:16:14.070 --> 00:16:21.690 align:middle line:84% from how alleles segregate in small families or in siblings 00:16:21.690 --> 00:16:23.100 align:middle line:90% and so forth. 00:16:23.100 --> 00:16:27.543 align:middle line:84% Or, easier to think about and probably more accurate, 00:16:27.543 --> 00:16:29.460 align:middle line:84% in general, especially with limited data sets, 00:16:29.460 --> 00:16:32.580 align:middle line:90% is direct observation. 00:16:32.580 --> 00:16:34.470 align:middle line:84% The most extreme direct observation 00:16:34.470 --> 00:16:38.740 align:middle line:84% is you pull out a DNA molecule that has, say, your promoter 00:16:38.740 --> 00:16:42.060 align:middle line:84% mutation in your putative protein mutation, 00:16:42.060 --> 00:16:45.945 align:middle line:84% or just a series of linked polymorphisms. 00:16:45.945 --> 00:16:48.240 align:middle line:84% By cloning out or otherwise physically 00:16:48.240 --> 00:16:52.320 align:middle line:84% isolating that DNA molecule, you can sequence it, 00:16:52.320 --> 00:16:53.520 align:middle line:90% and you can determine. 00:16:53.520 --> 00:16:57.233 align:middle line:84% By definition, if they're all in the same sequence, 00:16:57.233 --> 00:16:58.650 align:middle line:84% then they're on the same molecule. 00:16:58.650 --> 00:17:00.900 align:middle line:84% But you have to be careful about the sequencing method 00:17:00.900 --> 00:17:03.270 align:middle line:84% that you're using there and the specific cloning 00:17:03.270 --> 00:17:06.480 align:middle line:84% and/or physical separation method, because there are 00:17:06.480 --> 00:17:09.300 align:middle line:84% certain methods where you can get a chimeric sequence either 00:17:09.300 --> 00:17:13.630 align:middle line:84% due to cloning of two species together or somehow 00:17:13.630 --> 00:17:17.550 align:middle line:84% disassembling them through bioinformatics. 00:17:17.550 --> 00:17:19.770 align:middle line:84% You can also directly observe it when 00:17:19.770 --> 00:17:26.550 align:middle line:84% you go through the genetic processes of mitosis, which 00:17:26.550 --> 00:17:29.520 align:middle line:84% we've talked about before, which is that, as the cells divide, 00:17:29.520 --> 00:17:31.870 align:middle line:84% they split up the chromosomes, or meiosis, 00:17:31.870 --> 00:17:34.050 align:middle line:84% which is the process by which they get prepared 00:17:34.050 --> 00:17:37.110 align:middle line:84% for recombination, which we'll come back to in a little while. 00:17:37.110 --> 00:17:40.020 align:middle line:90% 00:17:40.020 --> 00:17:42.660 align:middle line:84% So when you do want to do it by linkage, 00:17:42.660 --> 00:17:44.700 align:middle line:84% you want to do a direct observation. 00:17:44.700 --> 00:17:52.740 align:middle line:84% And the best way to follow the haplotype 00:17:52.740 --> 00:17:59.940 align:middle line:84% is, if there is a difference at every position in both 00:17:59.940 --> 00:18:04.410 align:middle line:84% the parents and the child inherits those differences, 00:18:04.410 --> 00:18:06.240 align:middle line:90% then it's called informative. 00:18:06.240 --> 00:18:11.340 align:middle line:84% If the parents happen to share a single-nucleotide polymorphism 00:18:11.340 --> 00:18:14.250 align:middle line:84% even though the child is a heterozygote for one of them, 00:18:14.250 --> 00:18:17.580 align:middle line:84% it could be that the parents have additional alleles that 00:18:17.580 --> 00:18:19.470 align:middle line:84% can confuse things, and it's not informative. 00:18:19.470 --> 00:18:22.260 align:middle line:84% But the point is, if you have enough single-nucleotide 00:18:22.260 --> 00:18:25.950 align:middle line:84% polymorphisms, you can do a case-control study where 00:18:25.950 --> 00:18:28.770 align:middle line:84% you have lots of children that are affected for whatever 00:18:28.770 --> 00:18:30.840 align:middle line:84% trait you're interested in and, hopefully, 00:18:30.840 --> 00:18:33.420 align:middle line:84% a close-to-equal number which are in the control group which 00:18:33.420 --> 00:18:34.193 align:middle line:90% do not have it. 00:18:34.193 --> 00:18:36.360 align:middle line:84% An example of that-- and I'm just trying to give you 00:18:36.360 --> 00:18:37.890 align:middle line:84% a flavor for this and where to look, 00:18:37.890 --> 00:18:40.260 align:middle line:84% rather than to completely empower you on this, 00:18:40.260 --> 00:18:42.510 align:middle line:84% because that would be an entire separate course-- 00:18:42.510 --> 00:18:45.300 align:middle line:84% but you can look for association. 00:18:45.300 --> 00:18:47.580 align:middle line:84% And you have to worry about things like structure 00:18:47.580 --> 00:18:50.460 align:middle line:84% and admixture, where you've had populations that have developed 00:18:50.460 --> 00:18:52.380 align:middle line:84% independently in different parts of the world 00:18:52.380 --> 00:18:56.370 align:middle line:84% and have been randomly mixing, which 00:18:56.370 --> 00:18:59.260 align:middle line:84% is part of the model in these separate populations. 00:18:59.260 --> 00:19:02.220 align:middle line:84% But then, you bring them together very recently, 00:19:02.220 --> 00:19:06.630 align:middle line:84% and now it's no longer fair to model it 00:19:06.630 --> 00:19:10.440 align:middle line:84% as if it were a uniformly mixing population. 00:19:10.440 --> 00:19:15.480 align:middle line:84% And we'll refer throughout the course 00:19:15.480 --> 00:19:20.110 align:middle line:84% to the null hypothesis, which is the thing that you're 00:19:20.110 --> 00:19:22.420 align:middle line:84% trying to rule out, and the probability 00:19:22.420 --> 00:19:24.550 align:middle line:84% refers to the probability that you can 00:19:24.550 --> 00:19:26.292 align:middle line:90% reject this null hypothesis. 00:19:26.292 --> 00:19:28.000 align:middle line:84% And in this case, you're trying to reject 00:19:28.000 --> 00:19:30.430 align:middle line:84% that the allele frequencies in the candidate locus, 00:19:30.430 --> 00:19:33.070 align:middle line:84% whatever you picked, do not depend 00:19:33.070 --> 00:19:35.350 align:middle line:84% on the phenotype within the subpopulations. 00:19:35.350 --> 00:19:39.160 align:middle line:84% And that's the way that they deal with these case studies. 00:19:39.160 --> 00:19:44.920 align:middle line:84% Now, what are some of the motivations for studying 00:19:44.920 --> 00:19:47.800 align:middle line:84% either individual polymorphisms or haplotypes-- 00:19:47.800 --> 00:19:50.230 align:middle line:84% combinations of polymorphisms can affect 00:19:50.230 --> 00:19:52.390 align:middle line:90% the activity of a protein? 00:19:52.390 --> 00:19:55.930 align:middle line:84% Now, I could use hundreds of different examples 00:19:55.930 --> 00:19:59.590 align:middle line:84% of well-established and useful examples. 00:19:59.590 --> 00:20:04.930 align:middle line:84% But here's one that, hopefully, will hit a resonating chord 00:20:04.930 --> 00:20:07.630 align:middle line:84% in the sense that these are actually used now 00:20:07.630 --> 00:20:11.170 align:middle line:84% in certain clinical settings, and certainly 00:20:11.170 --> 00:20:16.930 align:middle line:84% in clinical research, to ask whether a patient population, 00:20:16.930 --> 00:20:19.420 align:middle line:84% either in the process of developing a new drug 00:20:19.420 --> 00:20:28.600 align:middle line:84% or using an established drug to keep the patient toxicity down 00:20:28.600 --> 00:20:30.400 align:middle line:90% and the effectiveness up. 00:20:30.400 --> 00:20:34.600 align:middle line:84% And so in the far left-hand column, 00:20:34.600 --> 00:20:36.550 align:middle line:90% is the gene or enzyme affected? 00:20:36.550 --> 00:20:38.230 align:middle line:84% And then, in the middle is our examples 00:20:38.230 --> 00:20:41.120 align:middle line:84% of drugs which interact with this enzyme. 00:20:41.120 --> 00:20:42.520 align:middle line:84% And then, the quantitative effect 00:20:42.520 --> 00:20:46.180 align:middle line:90% is in the far right-hand side. 00:20:46.180 --> 00:20:49.990 align:middle line:84% For example, thiopurine methyltransferase 00:20:49.990 --> 00:20:54.550 align:middle line:84% is something which, if you have a large amount of the activity, 00:20:54.550 --> 00:20:58.510 align:middle line:84% whether you have, say, a very active enzyme 00:20:58.510 --> 00:21:01.750 align:middle line:84% and/or a very active promoter element that 00:21:01.750 --> 00:21:06.160 align:middle line:84% causes high levels of it, then these various chemotherapeutics 00:21:06.160 --> 00:21:07.675 align:middle line:84% that are used for fighting cancers-- 00:21:07.675 --> 00:21:10.455 align:middle line:90% 00:21:10.455 --> 00:21:12.080 align:middle line:84% the amount of them need to be adjusted. 00:21:12.080 --> 00:21:13.900 align:middle line:84% So you have lots of the methyltransferase. 00:21:13.900 --> 00:21:17.860 align:middle line:84% That means you have to give lots of the drug, or else your drug 00:21:17.860 --> 00:21:21.490 align:middle line:84% study will fail, or your patient will succumb to cancer 00:21:21.490 --> 00:21:22.750 align:middle line:90% because it's ineffective. 00:21:22.750 --> 00:21:24.460 align:middle line:90% You haven't added enough. 00:21:24.460 --> 00:21:33.640 align:middle line:84% The thiopurine methyltransferase is overcoming the drug. 00:21:33.640 --> 00:21:37.360 align:middle line:90% 00:21:37.360 --> 00:21:45.820 align:middle line:84% On the other hand, if you have very low levels 00:21:45.820 --> 00:21:48.760 align:middle line:84% of the modifying enzyme, you want to lower the dose, 00:21:48.760 --> 00:21:51.970 align:middle line:90% or else you'll have toxicity. 00:21:51.970 --> 00:21:54.340 align:middle line:84% So that's an example that's actually 00:21:54.340 --> 00:21:56.080 align:middle line:84% being used in clinical situations 00:21:56.080 --> 00:21:59.620 align:middle line:84% where you can use the information 00:21:59.620 --> 00:22:04.000 align:middle line:84% to adjust drug levels or to stratify 00:22:04.000 --> 00:22:07.060 align:middle line:84% your patient population so that you put patients 00:22:07.060 --> 00:22:10.360 align:middle line:84% into different classes or exclude them from the study 00:22:10.360 --> 00:22:12.820 align:middle line:84% altogether because you know that the drug will 00:22:12.820 --> 00:22:14.390 align:middle line:90% have some bad effect. 00:22:14.390 --> 00:22:17.380 align:middle line:84% And this, hopefully, decreases the costs. 00:22:17.380 --> 00:22:19.660 align:middle line:84% On the downside to pharmaceutical development, 00:22:19.660 --> 00:22:21.850 align:middle line:84% if you do stratify your patient population 00:22:21.850 --> 00:22:25.480 align:middle line:84% and you make it through the drug study with that caveat, 00:22:25.480 --> 00:22:29.110 align:middle line:84% then the FDA will require that you put that proviso, 00:22:29.110 --> 00:22:32.050 align:middle line:84% and that makes the size of the population that 00:22:32.050 --> 00:22:36.520 align:middle line:84% will be buying the drug smaller, since the costs of developing 00:22:36.520 --> 00:22:38.950 align:middle line:90% the drug are fairly fixed. 00:22:38.950 --> 00:22:42.190 align:middle line:90% It decreases the profit. 00:22:42.190 --> 00:22:45.880 align:middle line:84% Now, I pointed out that there may 00:22:45.880 --> 00:22:48.580 align:middle line:84% be a very large number of rare single-nucleotide 00:22:48.580 --> 00:22:49.570 align:middle line:90% polymorphisms. 00:22:49.570 --> 00:22:52.450 align:middle line:84% But in terms of common ones, we're 00:22:52.450 --> 00:22:56.010 align:middle line:84% getting pretty close to saturating the common ones. 00:22:56.010 --> 00:22:58.010 align:middle line:84% And there are databases of these just like there 00:22:58.010 --> 00:22:59.440 align:middle line:84% are databases of almost everything you 00:22:59.440 --> 00:23:01.315 align:middle line:84% can imagine, some of them better than others. 00:23:01.315 --> 00:23:05.140 align:middle line:90% 00:23:05.140 --> 00:23:07.750 align:middle line:84% The common ones will, of course, be the ones 00:23:07.750 --> 00:23:10.900 align:middle line:84% that either are neutral, with respect 00:23:10.900 --> 00:23:12.850 align:middle line:90% to their phenotypic effect. 00:23:12.850 --> 00:23:14.410 align:middle line:84% That is to say, it doesn't really 00:23:14.410 --> 00:23:20.650 align:middle line:84% matter whether they're one common allele or the other one. 00:23:20.650 --> 00:23:23.320 align:middle line:84% The one allele might be at 30% and the other one at 70%, 00:23:23.320 --> 00:23:26.570 align:middle line:84% but they're both fairly neutral with respect to function. 00:23:26.570 --> 00:23:31.810 align:middle line:84% Or it could be that they both provide different advantages 00:23:31.810 --> 00:23:32.890 align:middle line:90% in different scenarios. 00:23:32.890 --> 00:23:35.290 align:middle line:84% Or the heterozygote, where you have one over the other, 00:23:35.290 --> 00:23:36.748 align:middle line:84% provides some advantage, and that's 00:23:36.748 --> 00:23:38.590 align:middle line:90% kept it in the population. 00:23:38.590 --> 00:23:40.210 align:middle line:84% But it's unlikely that they're highly 00:23:40.210 --> 00:23:43.060 align:middle line:84% deleterious because the highly deleterious alleles are 00:23:43.060 --> 00:23:43.840 align:middle line:90% going to be rare. 00:23:43.840 --> 00:23:45.382 align:middle line:84% They're going to be selected against. 00:23:45.382 --> 00:23:47.810 align:middle line:84% And we're going to fully model that in just a moment. 00:23:47.810 --> 00:23:54.640 align:middle line:84% Now, let's say that, somehow, anybody who wanted their genome 00:23:54.640 --> 00:23:57.115 align:middle line:84% could have their genome tomorrow. 00:23:57.115 --> 00:23:58.990 align:middle line:84% You could have your complete genome sequence. 00:23:58.990 --> 00:24:03.250 align:middle line:84% How would you, then, as computational biologists, 00:24:03.250 --> 00:24:07.217 align:middle line:84% prioritize the single-nucleotide polymorphisms you find 00:24:07.217 --> 00:24:08.800 align:middle line:84% in there, relative to the whole genome 00:24:08.800 --> 00:24:10.120 align:middle line:90% sequence, which is in GenBank? 00:24:10.120 --> 00:24:12.078 align:middle line:84% Now, this would be an excellent project for you 00:24:12.078 --> 00:24:14.620 align:middle line:90% to do for the term project. 00:24:14.620 --> 00:24:16.405 align:middle line:84% But what you might say, first of all-- 00:24:16.405 --> 00:24:19.950 align:middle line:90% 00:24:19.950 --> 00:24:22.250 align:middle line:84% what single-nucleotide polymorphisms 00:24:22.250 --> 00:24:24.800 align:middle line:84% would you throw out, for example, 00:24:24.800 --> 00:24:26.858 align:middle line:84% or put low on your priority list? 00:24:26.858 --> 00:24:29.150 align:middle line:84% Or which ones would you put high on your priority list? 00:24:29.150 --> 00:24:32.450 align:middle line:90% 00:24:32.450 --> 00:24:32.950 align:middle line:90% Yeah? 00:24:32.950 --> 00:24:34.800 align:middle line:84% AUDIENCE: Introns would be low-priority. 00:24:34.800 --> 00:24:37.198 align:middle line:90% PROFESSOR: OK, introns. 00:24:37.198 --> 00:24:39.490 align:middle line:84% AUDIENCE: Maybe this is a very simplistic thing to say, 00:24:39.490 --> 00:24:43.600 align:middle line:84% but I guess [INAUDIBLE] matter if they're 00:24:43.600 --> 00:24:46.005 align:middle line:90% different from one another. 00:24:46.005 --> 00:24:49.070 align:middle line:90% [INAUDIBLE] 00:24:49.070 --> 00:24:50.590 align:middle line:90% PROFESSOR: That's fine. 00:24:50.590 --> 00:24:53.470 align:middle line:84% Everybody has their own pet part of the genome they don't like. 00:24:53.470 --> 00:24:55.155 align:middle line:84% Introns almost sunk the Genome Project. 00:24:55.155 --> 00:24:56.780 align:middle line:84% They said, why are we going to sequence 00:24:56.780 --> 00:25:00.070 align:middle line:84% the 98% of the genome that doesn't code for proteins? 00:25:00.070 --> 00:25:02.200 align:middle line:84% Fortunately, we went ahead and sequenced it anyway. 00:25:02.200 --> 00:25:05.080 align:middle line:84% Another favorite thing that people mention 00:25:05.080 --> 00:25:06.860 align:middle line:90% is repetitive DNA. 00:25:06.860 --> 00:25:08.360 align:middle line:84% That was another part of the genome. 00:25:08.360 --> 00:25:09.860 align:middle line:84% But they didn't actually sequence it 00:25:09.860 --> 00:25:13.480 align:middle line:84% from Drosophila, the repetitive DNA. 00:25:13.480 --> 00:25:20.702 align:middle line:84% And it's considered also not protein coding. 00:25:20.702 --> 00:25:22.660 align:middle line:84% And I'm going to give you a couple of examples, 00:25:22.660 --> 00:25:24.743 align:middle line:84% as we go through here, to illustrate other points, 00:25:24.743 --> 00:25:27.280 align:middle line:84% but also to illustrate that repetitive regions that are not 00:25:27.280 --> 00:25:29.170 align:middle line:84% in protein-coding regions, whether introns 00:25:29.170 --> 00:25:31.900 align:middle line:84% or other non-coding regions, can be important. 00:25:31.900 --> 00:25:32.958 align:middle line:90% And here's an example. 00:25:32.958 --> 00:25:34.750 align:middle line:84% This is one of the most repetitive elements 00:25:34.750 --> 00:25:35.583 align:middle line:90% in the human genome. 00:25:35.583 --> 00:25:37.420 align:middle line:90% It's called an Alu repeat. 00:25:37.420 --> 00:25:41.380 align:middle line:84% As those of you who have done bioinformatics before realize, 00:25:41.380 --> 00:25:44.710 align:middle line:84% it's the bane of our existence, in terms of assembling 00:25:44.710 --> 00:25:46.040 align:middle line:90% and searching and so forth. 00:25:46.040 --> 00:25:49.930 align:middle line:84% But here's an example of a single base 00:25:49.930 --> 00:25:51.550 align:middle line:90% mutation in this repeat. 00:25:51.550 --> 00:25:54.250 align:middle line:84% There's about 500,000 copies of this in the human genome 00:25:54.250 --> 00:25:55.070 align:middle line:90% scattered about. 00:25:55.070 --> 00:25:57.670 align:middle line:84% It's called an intersperse repeat as a consequence. 00:25:57.670 --> 00:26:00.400 align:middle line:84% And this A-to-G transmission is found 00:26:00.400 --> 00:26:03.260 align:middle line:84% upstream from the myeloperoxidase enzyme-encoding 00:26:03.260 --> 00:26:03.760 align:middle line:90% gene. 00:26:03.760 --> 00:26:07.940 align:middle line:90% 00:26:07.940 --> 00:26:11.480 align:middle line:84% So how do we find out whether this is important in any sense? 00:26:11.480 --> 00:26:13.480 align:middle line:84% First of all, the observation is that it 00:26:13.480 --> 00:26:17.530 align:middle line:84% is associated with several-fold less transcriptional activity. 00:26:17.530 --> 00:26:21.490 align:middle line:90% 00:26:21.490 --> 00:26:26.680 align:middle line:84% That particular position creates or destroys 00:26:26.680 --> 00:26:30.250 align:middle line:84% binding sites for these transcription elements, 00:26:30.250 --> 00:26:32.470 align:middle line:84% and that might be the reason that it has 00:26:32.470 --> 00:26:34.100 align:middle line:90% lower transcriptional activity. 00:26:34.100 --> 00:26:36.850 align:middle line:84% And finally, it is over-represented 00:26:36.850 --> 00:26:40.820 align:middle line:90% in a particular type of cancer. 00:26:40.820 --> 00:26:43.300 align:middle line:84% And we're going to go through the ways 00:26:43.300 --> 00:26:49.840 align:middle line:84% that we take an observation, like a polymorphism, 00:26:49.840 --> 00:26:54.370 align:middle line:84% move to an association, like here, with cancer, then 00:26:54.370 --> 00:26:56.560 align:middle line:84% take it to a mechanism, such as here, 00:26:56.560 --> 00:26:59.380 align:middle line:84% with the transcriptional regulators. 00:26:59.380 --> 00:27:01.160 align:middle line:84% I think that's what this is about. 00:27:01.160 --> 00:27:03.580 align:middle line:84% It's not sufficient to observe the polymorphism. 00:27:03.580 --> 00:27:06.190 align:middle line:84% You can't say, a priori, whether it's 00:27:06.190 --> 00:27:08.908 align:middle line:84% important or not, whether the Alu repeats are not conserved. 00:27:08.908 --> 00:27:10.450 align:middle line:84% That's another thing that people say. 00:27:10.450 --> 00:27:13.600 align:middle line:84% Throw out all the nonconserved single-nucleotide 00:27:13.600 --> 00:27:14.890 align:middle line:90% polymorphisms. 00:27:14.890 --> 00:27:15.700 align:middle line:90% It's not conserved. 00:27:15.700 --> 00:27:19.210 align:middle line:84% It's not present in mouse, for example. 00:27:19.210 --> 00:27:22.210 align:middle line:84% It's non-coding, and it's repetitive. 00:27:22.210 --> 00:27:24.670 align:middle line:84% Now, in addition to the types of mutations, 00:27:24.670 --> 00:27:27.760 align:middle line:84% we have the modes of inheritance-- that is to say, 00:27:27.760 --> 00:27:33.868 align:middle line:84% the different ways in which a change, a polymorphism 00:27:33.868 --> 00:27:34.660 align:middle line:90% can be transmitted. 00:27:34.660 --> 00:27:38.020 align:middle line:84% And I include this to broaden your perspective. 00:27:38.020 --> 00:27:43.030 align:middle line:84% Rather than getting entirely fixated on the 3 million DNA 00:27:43.030 --> 00:27:45.940 align:middle line:84% SNPs, let's broaden the discussion here a little bit. 00:27:45.940 --> 00:27:48.220 align:middle line:84% You can have not only DNA polymorphisms, 00:27:48.220 --> 00:27:50.080 align:middle line:84% but you can have RNA polymorphisms, 00:27:50.080 --> 00:27:51.730 align:middle line:90% which are heritable. 00:27:51.730 --> 00:27:54.970 align:middle line:84% For example-- and I use this an an extreme case-- 00:27:54.970 --> 00:27:57.460 align:middle line:90% RNAi-- 22 nucleotide or so. 00:27:57.460 --> 00:27:59.650 align:middle line:84% Probably a variety of mechanisms. 00:27:59.650 --> 00:28:02.680 align:middle line:90% 00:28:02.680 --> 00:28:07.280 align:middle line:84% Bits of RNA can be induced in various ways. 00:28:07.280 --> 00:28:11.080 align:middle line:84% And once induced, they can replicate, essentially, 00:28:11.080 --> 00:28:13.127 align:middle line:90% within a cell and between cells. 00:28:13.127 --> 00:28:14.710 align:middle line:84% They can spread throughout an organism 00:28:14.710 --> 00:28:18.730 align:middle line:84% and probably be propagated over generations 00:28:18.730 --> 00:28:21.110 align:middle line:84% between different generations of organisms. 00:28:21.110 --> 00:28:23.830 align:middle line:90% So this is heritable. 00:28:23.830 --> 00:28:26.140 align:middle line:84% And you can consider it epigenetic 00:28:26.140 --> 00:28:28.780 align:middle line:84% or genetic polymorphism, depending on the nomenclature 00:28:28.780 --> 00:28:30.700 align:middle line:90% that you adopt. 00:28:30.700 --> 00:28:35.350 align:middle line:84% Even a protein conformation can be considered a polymorphism 00:28:35.350 --> 00:28:37.510 align:middle line:90% that is heritable. 00:28:37.510 --> 00:28:39.310 align:middle line:84% The central dogma tells us this protein 00:28:39.310 --> 00:28:42.340 align:middle line:84% is encoded by a nucleic acid, and there certainly 00:28:42.340 --> 00:28:44.050 align:middle line:90% is still the case-- 00:28:44.050 --> 00:28:47.770 align:middle line:84% even these heritable polymorphisms and proteins. 00:28:47.770 --> 00:28:49.330 align:middle line:84% But it has a different conformation, 00:28:49.330 --> 00:28:53.710 align:middle line:84% and that conformation recruits other conformations 00:28:53.710 --> 00:28:56.530 align:middle line:84% and so is inherited not only within a cell, 00:28:56.530 --> 00:28:58.810 align:middle line:84% but between cells and between organisms 00:28:58.810 --> 00:29:04.660 align:middle line:84% and is the causation of things like mad cow disease and so on. 00:29:04.660 --> 00:29:08.530 align:middle line:84% And finally, modifications of biopolymers, 00:29:08.530 --> 00:29:11.830 align:middle line:90% such as methylation, can occur. 00:29:11.830 --> 00:29:14.500 align:middle line:84% And this is not formally a DNA sequence change, 00:29:14.500 --> 00:29:20.650 align:middle line:84% but it's a heritable change that can 00:29:20.650 --> 00:29:26.080 align:middle line:84% have very significant effects on things like cancer and gene 00:29:26.080 --> 00:29:28.690 align:middle line:90% expression in general. 00:29:28.690 --> 00:29:34.800 align:middle line:84% Now, this is a broadening of the definition of polymorphisms. 00:29:34.800 --> 00:29:40.350 align:middle line:84% And now let's talk thoroughly about the ways 00:29:40.350 --> 00:29:44.340 align:middle line:84% that it can be inherited as horizontal or vertical. 00:29:44.340 --> 00:29:47.910 align:middle line:84% Horizontal typically means between species, 00:29:47.910 --> 00:29:50.117 align:middle line:84% but in a certain sense, it could reflect 00:29:50.117 --> 00:29:52.200 align:middle line:84% some of the things that are going on here with RNA 00:29:52.200 --> 00:29:55.590 align:middle line:84% and protein inheritance in the sense it is being horizontally 00:29:55.590 --> 00:29:58.770 align:middle line:84% transmitted between different cells within the same organism. 00:29:58.770 --> 00:30:01.830 align:middle line:84% But generally, it's a mechanism that 00:30:01.830 --> 00:30:04.770 align:middle line:84% does not involve mitosis or meiosis 00:30:04.770 --> 00:30:12.240 align:middle line:84% of the nuclear or organellar genomes. 00:30:12.240 --> 00:30:15.150 align:middle line:84% And the natural processes are transduction 00:30:15.150 --> 00:30:19.320 align:middle line:84% and transformation, being distinguished by-- transduction 00:30:19.320 --> 00:30:22.050 align:middle line:84% typically involves a viral or protein 00:30:22.050 --> 00:30:24.360 align:middle line:84% coat for the nucleic acid, and transformation 00:30:24.360 --> 00:30:27.180 align:middle line:84% involves something closer to naked nucleic acids. 00:30:27.180 --> 00:30:32.100 align:middle line:84% Transgenic is a completely laboratory-based version 00:30:32.100 --> 00:30:36.147 align:middle line:84% of these two more natural methods. 00:30:36.147 --> 00:30:37.980 align:middle line:84% I think vertical we've already talked about. 00:30:37.980 --> 00:30:41.700 align:middle line:84% This is what we normally think of inheritance. 00:30:41.700 --> 00:30:44.310 align:middle line:84% Horizontal, we saw in the tree of life, 00:30:44.310 --> 00:30:46.320 align:middle line:84% is very common, even in the late branches 00:30:46.320 --> 00:30:47.460 align:middle line:90% and the early branches. 00:30:47.460 --> 00:30:49.080 align:middle line:84% Vertical, though, is what we normally 00:30:49.080 --> 00:30:52.620 align:middle line:84% think about when we're doing crosses in the laboratory. 00:30:52.620 --> 00:30:55.320 align:middle line:84% Some of these are maternally inherited, 00:30:55.320 --> 00:30:58.320 align:middle line:84% like mitochondria and chloroplasts, 00:30:58.320 --> 00:31:00.150 align:middle line:84% but it's still the same kind of process-- 00:31:00.150 --> 00:31:04.602 align:middle line:90% mitosis, segregation of DNA. 00:31:04.602 --> 00:31:06.060 align:middle line:84% So now we've got types of mutations 00:31:06.060 --> 00:31:08.310 align:middle line:84% we want to talk about, mutation drift and selection, 00:31:08.310 --> 00:31:12.900 align:middle line:84% as the main source of the frequencies 00:31:12.900 --> 00:31:15.400 align:middle line:90% that we find in populations. 00:31:15.400 --> 00:31:20.670 align:middle line:84% We want to know, where do allele frequencies come from? 00:31:20.670 --> 00:31:23.970 align:middle line:84% And I will maintain that, generally speaking, 00:31:23.970 --> 00:31:26.010 align:middle line:84% in almost all living systems, whether they're 00:31:26.010 --> 00:31:29.520 align:middle line:84% cells from organisms that are mutating 00:31:29.520 --> 00:31:33.840 align:middle line:84% or whole organisms, whether they do recombination or not, they 00:31:33.840 --> 00:31:36.970 align:middle line:84% will do mutation selection and drift. 00:31:36.970 --> 00:31:40.200 align:middle line:84% Now, to develop a fairly rigorous model here, 00:31:40.200 --> 00:31:43.038 align:middle line:84% yet simple, we have some assumptions. 00:31:43.038 --> 00:31:44.580 align:middle line:84% We always have assumptions in models. 00:31:44.580 --> 00:31:46.413 align:middle line:84% If people tell you there are no assumptions, 00:31:46.413 --> 00:31:49.990 align:middle line:84% then you need to dig a little further. 00:31:49.990 --> 00:31:52.950 align:middle line:84% The assumptions that we'll make here for a little while-- 00:31:52.950 --> 00:31:54.960 align:middle line:84% and then, I'll give you a nice example 00:31:54.960 --> 00:31:58.305 align:middle line:84% to undermine them all-- but it's constant population size n. 00:31:58.305 --> 00:32:00.930 align:middle line:90% 00:32:00.930 --> 00:32:02.068 align:middle line:90% You have random mating. 00:32:02.068 --> 00:32:04.110 align:middle line:84% Remember, we were talking about admixture before. 00:32:04.110 --> 00:32:08.430 align:middle line:84% Every member of the population can randomly mate. 00:32:08.430 --> 00:32:10.780 align:middle line:84% They're non-overlapping generations. 00:32:10.780 --> 00:32:13.510 align:middle line:90% This is a convenience. 00:32:13.510 --> 00:32:14.970 align:middle line:84% We are not making any assumptions 00:32:14.970 --> 00:32:17.550 align:middle line:84% about the population allele frequencies 00:32:17.550 --> 00:32:19.170 align:middle line:90% being at equilibrium. 00:32:19.170 --> 00:32:21.900 align:middle line:84% Those of you have taken biology courses with-- 00:32:21.900 --> 00:32:24.030 align:middle line:84% Hardy-Weinberg makes that assumption. 00:32:24.030 --> 00:32:25.950 align:middle line:84% Here, this is a much more general model. 00:32:25.950 --> 00:32:28.800 align:middle line:84% It includes non-equilibrium, and equilibrium 00:32:28.800 --> 00:32:30.810 align:middle line:90% can be a special case. 00:32:30.810 --> 00:32:35.850 align:middle line:84% So this is relatively minor non-assumption. 00:32:35.850 --> 00:32:37.380 align:middle line:84% But we are assuming that we do not 00:32:37.380 --> 00:32:38.850 align:middle line:84% have an infinite number of alleles, 00:32:38.850 --> 00:32:44.600 align:middle line:84% nor an infinite number of population size. 00:32:44.600 --> 00:32:48.710 align:middle line:84% So now ignore everything on the slide 00:32:48.710 --> 00:32:55.070 align:middle line:84% but the upper left-hand corner of slide 15 here. 00:32:55.070 --> 00:32:56.520 align:middle line:90% This should look familiar. 00:32:56.520 --> 00:33:00.500 align:middle line:84% This should look somewhat like the logistic map 00:33:00.500 --> 00:33:07.430 align:middle line:84% where we had the incremental, slow exponential increase 00:33:07.430 --> 00:33:12.230 align:middle line:84% of one allele in a population over another, 00:33:12.230 --> 00:33:14.600 align:middle line:84% or one organism over another, based 00:33:14.600 --> 00:33:16.370 align:middle line:84% on the different selection coefficients 00:33:16.370 --> 00:33:17.730 align:middle line:90% of those organisms. 00:33:17.730 --> 00:33:19.760 align:middle line:84% And this could be a very small difference. 00:33:19.760 --> 00:33:22.790 align:middle line:84% Say, a 1% increase per generation 00:33:22.790 --> 00:33:26.900 align:middle line:84% will dominate after a thousand generations 00:33:26.900 --> 00:33:29.413 align:middle line:90% or so, quite definitely. 00:33:29.413 --> 00:33:30.830 align:middle line:84% And so that's what you're seeing-- 00:33:30.830 --> 00:33:32.288 align:middle line:84% the exponential curve-- and then it 00:33:32.288 --> 00:33:38.210 align:middle line:84% plateaus as it gets to 100% allele frequency. 00:33:38.210 --> 00:33:40.730 align:middle line:84% That's the full range on the vertical axis, 00:33:40.730 --> 00:33:43.220 align:middle line:90% is 0% to 100% allele frequency. 00:33:43.220 --> 00:33:48.980 align:middle line:84% And generation goes from 0 to 1,400. 00:33:48.980 --> 00:33:51.530 align:middle line:84% Now, what it actually represents in this particular case 00:33:51.530 --> 00:33:54.075 align:middle line:84% is closely related, a little more complicated 00:33:54.075 --> 00:33:55.700 align:middle line:84% than just one allele replacing another, 00:33:55.700 --> 00:33:59.810 align:middle line:84% because here we have diploids-- that is to say, 00:33:59.810 --> 00:34:01.910 align:middle line:84% not a haploid that just has one allele, 00:34:01.910 --> 00:34:05.390 align:middle line:84% like in the bacterial species that we've implicitly 00:34:05.390 --> 00:34:07.280 align:middle line:90% been talking about. 00:34:07.280 --> 00:34:10.139 align:middle line:84% But you can have, here, now, three combinations of alleles. 00:34:10.139 --> 00:34:19.010 align:middle line:84% You can have, say, the reference genotype of capital A, 00:34:19.010 --> 00:34:25.770 align:middle line:84% capital A, which we'd just call 100% fitness. 00:34:25.770 --> 00:34:28.170 align:middle line:84% So we have fitness and selection coefficient, 00:34:28.170 --> 00:34:30.500 align:middle line:84% which are interchangeable terms that 00:34:30.500 --> 00:34:34.469 align:middle line:84% are-- very trivial mathematical relationship between them. 00:34:34.469 --> 00:34:38.030 align:middle line:84% So we'll use w and s in different contexts here. 00:34:38.030 --> 00:34:40.310 align:middle line:84% It just has population [INAUDIBLE].. 00:34:40.310 --> 00:34:43.100 align:middle line:84% Then, you can have big A, big A, little a, little a, and big A, 00:34:43.100 --> 00:34:44.989 align:middle line:90% little a as the heterozygote. 00:34:44.989 --> 00:34:46.940 align:middle line:84% And we're assuming an additive model here, 00:34:46.940 --> 00:34:50.300 align:middle line:84% where you get a little more selection with one 00:34:50.300 --> 00:34:52.950 align:middle line:84% allele of little a, and then two alleles of little 00:34:52.950 --> 00:34:54.230 align:middle line:90% a results in 2s-- 00:34:54.230 --> 00:34:57.020 align:middle line:90% 1 plus 2s. 00:34:57.020 --> 00:35:02.000 align:middle line:84% And this has a very similar curve to the logistic map, 00:35:02.000 --> 00:35:05.590 align:middle line:84% if you had simple allele replacement. 00:35:05.590 --> 00:35:07.820 align:middle line:84% And what you tend to have in this population-- 00:35:07.820 --> 00:35:10.250 align:middle line:84% a thousand generations, in the big scheme of things, 00:35:10.250 --> 00:35:11.570 align:middle line:90% may seem like a lot to you. 00:35:11.570 --> 00:35:14.520 align:middle line:84% But in the big scheme, it's a very short period of time, 00:35:14.520 --> 00:35:21.050 align:middle line:84% and so you tend to have alleles at frequency of 0% and 100%. 00:35:21.050 --> 00:35:23.330 align:middle line:84% On the other hand, if you have overdominant mode, 00:35:23.330 --> 00:35:25.880 align:middle line:84% where the heterozygote has the highest fitness of the three 00:35:25.880 --> 00:35:31.610 align:middle line:84% possibilities, where 1 plus s is larger than 1 or 1 plus t, 00:35:31.610 --> 00:35:33.650 align:middle line:90% then you aim for equilibrium. 00:35:33.650 --> 00:35:37.400 align:middle line:84% Whether you're starting at close to 0% or close to 100% 00:35:37.400 --> 00:35:40.520 align:middle line:84% the allele frequency will converge on some equilibrium 00:35:40.520 --> 00:35:41.900 align:middle line:90% point-- 00:35:41.900 --> 00:35:48.890 align:middle line:84% in this case, somewhere around 0.6 for one 00:35:48.890 --> 00:35:50.198 align:middle line:90% allele and 0.4 for the other. 00:35:50.198 --> 00:35:51.240 align:middle line:90% And it could be anywhere. 00:35:51.240 --> 00:35:53.900 align:middle line:84% It depends on the relative fitnesses, s and t. 00:35:53.900 --> 00:35:56.990 align:middle line:90% 00:35:56.990 --> 00:35:59.180 align:middle line:84% This is just a reminder slide combining two slides 00:35:59.180 --> 00:36:01.550 align:middle line:90% from before. 00:36:01.550 --> 00:36:03.530 align:middle line:84% That slide connects the logistic map 00:36:03.530 --> 00:36:08.180 align:middle line:84% from lecture 1 to the selection coefficients 00:36:08.180 --> 00:36:12.210 align:middle line:84% we've been talking about in lecture 2 to the diploids 00:36:12.210 --> 00:36:14.210 align:middle line:84% that we're mainly talking about in this lecture, 00:36:14.210 --> 00:36:15.650 align:middle line:90% because humans are diploids. 00:36:15.650 --> 00:36:19.700 align:middle line:84% And here, just connect this to the fact 00:36:19.700 --> 00:36:22.010 align:middle line:84% that these selection coefficients, s, 00:36:22.010 --> 00:36:27.680 align:middle line:84% or the fitness, w, is relevant to different environments 00:36:27.680 --> 00:36:29.600 align:middle line:84% and the different times that organisms 00:36:29.600 --> 00:36:31.530 align:middle line:84% spend in those different environments. 00:36:31.530 --> 00:36:34.880 align:middle line:84% And all mutants are tagged by their DNA, and they're pooled, 00:36:34.880 --> 00:36:36.860 align:middle line:84% and they're selected, and you can read them out 00:36:36.860 --> 00:36:39.120 align:middle line:90% in a variety of methods. 00:36:39.120 --> 00:36:41.900 align:middle line:84% So now let's dig down into where the allele frequencies come 00:36:41.900 --> 00:36:50.030 align:middle line:84% from, based on mutation or migration, 00:36:50.030 --> 00:36:53.580 align:middle line:84% which we'll lump together here as M, selection, and drift. 00:36:53.580 --> 00:36:58.340 align:middle line:84% Now, the mutation will have a forward rate constant 00:36:58.340 --> 00:36:59.240 align:middle line:90% and a reverse. 00:36:59.240 --> 00:37:01.490 align:middle line:84% This should remind you of the conversation 00:37:01.490 --> 00:37:05.070 align:middle line:84% we just had about the different kinds of alleles-- 00:37:05.070 --> 00:37:06.680 align:middle line:84% the duplications and deletions-- how 00:37:06.680 --> 00:37:09.890 align:middle line:90% they can have different rates. 00:37:09.890 --> 00:37:11.990 align:middle line:84% If they're tandem duplication, then that 00:37:11.990 --> 00:37:14.480 align:middle line:90% has a great tendency to delete. 00:37:14.480 --> 00:37:18.260 align:middle line:84% If it deletes down to a single repeat, 00:37:18.260 --> 00:37:20.010 align:middle line:84% there's now no longer any repeat, 00:37:20.010 --> 00:37:24.050 align:middle line:84% and so the chance of generating the exact duplicate is low. 00:37:24.050 --> 00:37:29.210 align:middle line:84% So the frequency of forward and reverse mutation 00:37:29.210 --> 00:37:32.760 align:middle line:84% is represented by f and r, respectively. 00:37:32.760 --> 00:37:33.955 align:middle line:90% Now, what we'll see-- 00:37:33.955 --> 00:37:35.330 align:middle line:84% we're going to walk through this. 00:37:35.330 --> 00:37:39.290 align:middle line:84% Starting with a frequency, t sub i, 00:37:39.290 --> 00:37:47.520 align:middle line:84% where i is the number of mutants in a population size n. 00:37:47.520 --> 00:37:52.800 align:middle line:84% So here, down at the bottom, is i mutants in a population 00:37:52.800 --> 00:37:53.460 align:middle line:90% sized n. 00:37:53.460 --> 00:37:56.700 align:middle line:84% And we'll see that applying the mutation, 00:37:56.700 --> 00:37:58.950 align:middle line:84% applying the selection, and applying the drift 00:37:58.950 --> 00:38:02.040 align:middle line:84% are all applications of binomial distributions 00:38:02.040 --> 00:38:04.350 align:middle line:84% when we're talking about this discrete population of n 00:38:04.350 --> 00:38:06.120 align:middle line:90% individuals. 00:38:06.120 --> 00:38:09.180 align:middle line:84% Remember the three bell-shaped curves [INAUDIBLE]?? 00:38:09.180 --> 00:38:12.060 align:middle line:90% Curves that can be bell-shaped. 00:38:12.060 --> 00:38:15.210 align:middle line:84% Here, it's clearly a discrete population 00:38:15.210 --> 00:38:20.310 align:middle line:84% because we have n individuals, taking i mutants at a time. 00:38:20.310 --> 00:38:22.370 align:middle line:84% So the binomials that we'll be using-- 00:38:22.370 --> 00:38:25.500 align:middle line:84% all three processes have the same form, 00:38:25.500 --> 00:38:28.500 align:middle line:84% where you have a combination of some population, n, 00:38:28.500 --> 00:38:30.870 align:middle line:90% and a subpopulation, i. 00:38:30.870 --> 00:38:34.650 align:middle line:84% And of course, the remainder is n minus i. 00:38:34.650 --> 00:38:39.720 align:middle line:84% And the different combinations are times some probability, 00:38:39.720 --> 00:38:45.840 align:middle line:84% because probability is the last parameter in the binomial here. 00:38:45.840 --> 00:38:49.480 align:middle line:84% A binomial is a function of n, i, and p-- 00:38:49.480 --> 00:38:51.840 align:middle line:84% the population size, subpopulation size, 00:38:51.840 --> 00:38:53.130 align:middle line:90% and some frequency. 00:38:53.130 --> 00:38:56.190 align:middle line:84% It can be either a forward or reverse mutation frequency. 00:38:56.190 --> 00:38:59.190 align:middle line:84% It can be a selection probability, 00:38:59.190 --> 00:39:00.600 align:middle line:84% or it can be a drift probability. 00:39:00.600 --> 00:39:02.830 align:middle line:84% And we'll see how each of these work out. 00:39:02.830 --> 00:39:06.780 align:middle line:90% So we start with a frequency. 00:39:06.780 --> 00:39:13.140 align:middle line:84% You can have i ranges from 0 to If i is 0, 00:39:13.140 --> 00:39:15.720 align:middle line:84% then the frequency is 0 over n, or 0. 00:39:15.720 --> 00:39:18.960 align:middle line:84% If i is n, it's n over n, or frequency is 100%. 00:39:18.960 --> 00:39:23.460 align:middle line:84% Just that same vertical axis we had on all previous slides. 00:39:23.460 --> 00:39:26.880 align:middle line:84% The starting frequencies have some distribution, t sub i, 00:39:26.880 --> 00:39:29.190 align:middle line:90% for i going from 0 to n. 00:39:29.190 --> 00:39:35.040 align:middle line:84% And now we want to derive a new vector of frequencies, 00:39:35.040 --> 00:39:36.600 align:middle line:90% which would be m. 00:39:36.600 --> 00:39:39.720 align:middle line:84% And all we do is we apply the binomial distribution 00:39:39.720 --> 00:39:42.750 align:middle line:84% for the forward process or forward mutation. 00:39:42.750 --> 00:39:45.330 align:middle line:84% And then, once we're done with that, 00:39:45.330 --> 00:39:50.700 align:middle line:84% we now use the m's and adjust it. 00:39:50.700 --> 00:39:53.670 align:middle line:84% So now, give it a chance to do the reverse mutation, 00:39:53.670 --> 00:39:56.880 align:middle line:84% because you'll generate this binomial distribution forwards, 00:39:56.880 --> 00:40:00.720 align:middle line:84% and then you'll give them a chance to revert. 00:40:00.720 --> 00:40:02.190 align:middle line:90% Then, you apply selection. 00:40:02.190 --> 00:40:04.740 align:middle line:90% A new binomial. 00:40:04.740 --> 00:40:10.500 align:middle line:84% Now, here, the probability of a transition from your mutants, 00:40:10.500 --> 00:40:12.660 align:middle line:84% starting with t-- then, you go to m. 00:40:12.660 --> 00:40:15.210 align:middle line:84% Now, to get to s, the transition probability's 00:40:15.210 --> 00:40:17.070 align:middle line:90% a function of this fitness. 00:40:17.070 --> 00:40:20.190 align:middle line:84% Remember, w and s, fitness and selection. 00:40:20.190 --> 00:40:25.560 align:middle line:84% Here, the fitness determines the probability 00:40:25.560 --> 00:40:29.760 align:middle line:84% of a transition in a binomial distribution. 00:40:29.760 --> 00:40:32.373 align:middle line:84% And there are two slightly different equations 00:40:32.373 --> 00:40:34.290 align:middle line:84% that you use, depending on whether the fitness 00:40:34.290 --> 00:40:37.650 align:middle line:84% is greater than 1 or less than 1, 00:40:37.650 --> 00:40:40.860 align:middle line:84% whether it has a tendency to increase 00:40:40.860 --> 00:40:44.100 align:middle line:84% with time, due to selection, or to decrease 00:40:44.100 --> 00:40:47.050 align:middle line:84% that allele with time, as a function of selection. 00:40:47.050 --> 00:40:49.690 align:middle line:84% And that's what these two cases are here. 00:40:49.690 --> 00:40:53.040 align:middle line:84% And then, finally, after you've applied forward 00:40:53.040 --> 00:40:54.930 align:middle line:84% and inverse mutation and selection, 00:40:54.930 --> 00:40:59.170 align:middle line:84% whether it's more fit or less fit, then you apply drift. 00:40:59.170 --> 00:41:01.695 align:middle line:90% Now, drift just means that-- 00:41:01.695 --> 00:41:05.260 align:middle line:90% 00:41:05.260 --> 00:41:05.760 align:middle line:90% think of it. 00:41:05.760 --> 00:41:08.700 align:middle line:84% If you have a small population of individuals-- 00:41:08.700 --> 00:41:13.740 align:middle line:84% let's say they're a set of colored balls in a jar in front 00:41:13.740 --> 00:41:14.330 align:middle line:90% of us, here. 00:41:14.330 --> 00:41:16.920 align:middle line:84% It's a small number, and I pull a handful out, 00:41:16.920 --> 00:41:18.750 align:middle line:84% because in each generation, you're 00:41:18.750 --> 00:41:20.400 align:middle line:84% going to duplicate the population. 00:41:20.400 --> 00:41:23.190 align:middle line:84% But we remember the assumption of constant population size. 00:41:23.190 --> 00:41:26.490 align:middle line:84% If I pull out the new generation and forget 00:41:26.490 --> 00:41:27.990 align:middle line:84% about the rest of the duplicated, 00:41:27.990 --> 00:41:29.388 align:middle line:84% they could all be the same color. 00:41:29.388 --> 00:41:31.680 align:middle line:84% And that's the chance that you could drift to fixation, 00:41:31.680 --> 00:41:35.310 align:middle line:84% where one of them now dominates, not because it's superior, 00:41:35.310 --> 00:41:37.500 align:middle line:84% from a selection standpoint, not because it's 00:41:37.500 --> 00:41:41.220 align:middle line:84% been mutated in a directed way to that point, 00:41:41.220 --> 00:41:43.320 align:middle line:84% but just because of random drift that you 00:41:43.320 --> 00:41:46.500 align:middle line:90% have a constant population. 00:41:46.500 --> 00:41:48.180 align:middle line:84% And so you can see how that would depend 00:41:48.180 --> 00:41:50.010 align:middle line:90% on how many are in the jar. 00:41:50.010 --> 00:41:51.960 align:middle line:84% If I take half of them out of the jar, 00:41:51.960 --> 00:41:55.770 align:middle line:84% and the jar only has five in it, then it's a much higher chance 00:41:55.770 --> 00:41:58.710 align:middle line:84% that we'll go to fixation quickly than if the jar has 00:41:58.710 --> 00:41:59.550 align:middle line:90% millions in it. 00:41:59.550 --> 00:42:01.860 align:middle line:84% If I take half a million out, it's 00:42:01.860 --> 00:42:04.620 align:middle line:84% very likely that it will still be more or less the same 00:42:04.620 --> 00:42:05.410 align:middle line:90% ratios. 00:42:05.410 --> 00:42:07.560 align:middle line:84% And this is exactly how it plays out 00:42:07.560 --> 00:42:10.740 align:middle line:84% when you look at random genetic drift. 00:42:10.740 --> 00:42:13.450 align:middle line:84% It's very dependent on population size. 00:42:13.450 --> 00:42:16.120 align:middle line:84% So here are simulations going out to, say, 00:42:16.120 --> 00:42:19.110 align:middle line:84% 150 generations on the horizontal axis and the allele 00:42:19.110 --> 00:42:22.240 align:middle line:84% frequency, as usual, going from 0% to 100%. 00:42:22.240 --> 00:42:25.980 align:middle line:84% And we start with a population with 50/50 ratio 00:42:25.980 --> 00:42:26.715 align:middle line:90% of two alleles. 00:42:26.715 --> 00:42:29.820 align:middle line:90% 00:42:29.820 --> 00:42:32.310 align:middle line:84% And what you see is, if the population, 00:42:32.310 --> 00:42:37.620 align:middle line:84% the number of individuals, is only 25, then you quickly fix. 00:42:37.620 --> 00:42:41.040 align:middle line:90% Maybe 30 generations, you can-- 00:42:41.040 --> 00:42:43.810 align:middle line:90% and this is anecdotal-- 00:42:43.810 --> 00:42:45.580 align:middle line:90% get fixation. 00:42:45.580 --> 00:42:49.240 align:middle line:84% As it goes up to a population size of 2,500, 00:42:49.240 --> 00:42:51.890 align:middle line:84% you can see it, for all intents and purposes, is flat. 00:42:51.890 --> 00:42:53.410 align:middle line:90% It will eventually fix. 00:42:53.410 --> 00:42:56.830 align:middle line:84% I assure you, this simulation-- if you run it long enough, 00:42:56.830 --> 00:42:58.660 align:middle line:84% one of the two alleles will go to zero, 00:42:58.660 --> 00:43:01.168 align:middle line:84% and the other one will go to 100%. 00:43:01.168 --> 00:43:02.710 align:middle line:84% And you do another simulation, and it 00:43:02.710 --> 00:43:05.085 align:middle line:84% might be the other one, because this is random drift, not 00:43:05.085 --> 00:43:05.700 align:middle line:90% selection. 00:43:05.700 --> 00:43:08.240 align:middle line:90% 00:43:08.240 --> 00:43:10.180 align:middle line:84% So you can see the final frequencies are 00:43:10.180 --> 00:43:13.750 align:middle line:84% going to be some complicated function of mutation rates 00:43:13.750 --> 00:43:18.550 align:middle line:84% and selection rates and drift rates, which, in that last one, 00:43:18.550 --> 00:43:21.190 align:middle line:84% is a function of population size. 00:43:21.190 --> 00:43:23.622 align:middle line:84% When the population size is very, very large, 00:43:23.622 --> 00:43:25.580 align:middle line:84% you can see that's going to be constant enough. 00:43:25.580 --> 00:43:28.060 align:middle line:84% That's why you can see very subtle differences 00:43:28.060 --> 00:43:31.515 align:middle line:90% in selection coefficient. 00:43:31.515 --> 00:43:33.890 align:middle line:84% Now, we're going to come back to the mutation, selection, 00:43:33.890 --> 00:43:36.220 align:middle line:84% and drift in the context of human genetics in just 00:43:36.220 --> 00:43:36.740 align:middle line:90% a moment. 00:43:36.740 --> 00:43:41.200 align:middle line:84% But first, I want to tell you the last component 00:43:41.200 --> 00:43:44.600 align:middle line:84% of population genetics that we'll be talking about, 00:43:44.600 --> 00:43:45.760 align:middle line:90% which is recombination. 00:43:45.760 --> 00:43:48.580 align:middle line:84% Now, this doesn't occur in every biological system. 00:43:48.580 --> 00:43:52.280 align:middle line:84% I made the argument before that the mutation, selection, 00:43:52.280 --> 00:43:55.390 align:middle line:84% and drift occurs in every biological system, 00:43:55.390 --> 00:43:59.410 align:middle line:84% from cells to organisms of all types. 00:43:59.410 --> 00:44:01.270 align:middle line:84% In those biological systems where 00:44:01.270 --> 00:44:06.790 align:middle line:84% DNA can be exchanged by transduction, transformation, 00:44:06.790 --> 00:44:13.090 align:middle line:84% meiotic fusion, and so forth, then you can get recombination. 00:44:13.090 --> 00:44:15.880 align:middle line:84% And these two figures illustrate that. 00:44:15.880 --> 00:44:19.570 align:middle line:84% On the left-hand side of slide 19 00:44:19.570 --> 00:44:22.780 align:middle line:84% is the non-recombination scenario, 00:44:22.780 --> 00:44:25.000 align:middle line:84% and on the right-hand side is the 00:44:25.000 --> 00:44:29.800 align:middle line:84% sexual, or recombination-mediated, change 00:44:29.800 --> 00:44:31.070 align:middle line:90% in gene combinations. 00:44:31.070 --> 00:44:32.230 align:middle line:90% So let's look at this. 00:44:32.230 --> 00:44:34.540 align:middle line:90% Time is going horizontally. 00:44:34.540 --> 00:44:38.350 align:middle line:84% And you can see, at the very left-hand side, the beginning 00:44:38.350 --> 00:44:41.860 align:middle line:84% of each of these scenarios, you get a certain rate 00:44:41.860 --> 00:44:43.790 align:middle line:90% of occurrence of mutations. 00:44:43.790 --> 00:44:45.490 align:middle line:84% This is based on the forward mutation 00:44:45.490 --> 00:44:48.520 align:middle line:90% rate in our previous equations. 00:44:48.520 --> 00:44:50.110 align:middle line:90% And they occur very early on. 00:44:50.110 --> 00:44:51.670 align:middle line:90% A, B, and C all occur. 00:44:51.670 --> 00:44:56.560 align:middle line:84% But they tend to die out because of drift. 00:44:56.560 --> 00:45:00.550 align:middle line:84% And the population size is small enough that half of them 00:45:00.550 --> 00:45:03.610 align:middle line:90% die out and one of them fixes. 00:45:03.610 --> 00:45:07.090 align:middle line:84% And A is destined to fix, but it takes some time for it to fix. 00:45:07.090 --> 00:45:10.750 align:middle line:90% 00:45:10.750 --> 00:45:14.080 align:middle line:84% It starts out at a frequency close to 0, and by the time 00:45:14.080 --> 00:45:17.230 align:middle line:84% it's 50% to 100%, it's ready to start picking up 00:45:17.230 --> 00:45:19.103 align:middle line:84% a second mutation at the same frequency they 00:45:19.103 --> 00:45:20.020 align:middle line:90% were occurring before. 00:45:20.020 --> 00:45:23.890 align:middle line:84% And now you can pick up the B mutation while the C dies off. 00:45:23.890 --> 00:45:25.720 align:middle line:90% It comes and goes due to drift. 00:45:25.720 --> 00:45:28.490 align:middle line:84% And then, finally, once AB fixes, 00:45:28.490 --> 00:45:30.580 align:middle line:84% then you can pick up the C, and you get ABC. 00:45:30.580 --> 00:45:33.820 align:middle line:84% That was a long, slow serial process. 00:45:33.820 --> 00:45:35.920 align:middle line:84% On the right-hand side, we see what 00:45:35.920 --> 00:45:38.710 align:middle line:84% can happen in the case of exchange 00:45:38.710 --> 00:45:42.730 align:middle line:84% of genetic material in a really mixing population 00:45:42.730 --> 00:45:46.450 align:middle line:84% now that A, B, and C all occur at the same frequency 00:45:46.450 --> 00:45:47.440 align:middle line:90% as on the left. 00:45:47.440 --> 00:45:49.810 align:middle line:84% But now, because they're exchanging information 00:45:49.810 --> 00:45:54.400 align:middle line:84% very early on, before B has a chance to die off due to drift, 00:45:54.400 --> 00:45:57.580 align:middle line:84% it combines its DNA with A, and you get AB. 00:45:57.580 --> 00:45:59.705 align:middle line:84% And some of the small A population 00:45:59.705 --> 00:46:01.900 align:middle line:84% is just destined to be fixed anyway, 00:46:01.900 --> 00:46:05.470 align:middle line:84% but happens to combine with C. And again, 00:46:05.470 --> 00:46:13.690 align:middle line:84% before drift can wipe them out, the very small selection 00:46:13.690 --> 00:46:15.970 align:middle line:84% that you have that couldn't overcome drift 00:46:15.970 --> 00:46:20.140 align:middle line:84% in the left-hand panel now fixes them 00:46:20.140 --> 00:46:23.980 align:middle line:84% all, the really favorable combination of A, B, and C, 00:46:23.980 --> 00:46:25.370 align:middle line:90% very early on. 00:46:25.370 --> 00:46:29.470 align:middle line:84% And so there's a whole series of arguments and counterarguments 00:46:29.470 --> 00:46:31.210 align:middle line:84% in the population genetics literature 00:46:31.210 --> 00:46:32.900 align:middle line:90% about why is there sex. 00:46:32.900 --> 00:46:36.250 align:middle line:84% Of course, we all know have our own reasons. 00:46:36.250 --> 00:46:39.220 align:middle line:84% But in here, they say there's a huge cost. 00:46:39.220 --> 00:46:42.700 align:middle line:84% The counterargument is there's a huge cost 00:46:42.700 --> 00:46:44.650 align:middle line:90% of having two genders-- 00:46:44.650 --> 00:46:48.940 align:middle line:84% maybe as much as 50%, possibly higher-- 00:46:48.940 --> 00:46:52.240 align:middle line:84% because they have different morphologies and different 00:46:52.240 --> 00:46:55.400 align:middle line:90% capabilities and so on. 00:46:55.400 --> 00:46:57.190 align:middle line:90% But then, there's this benefit. 00:46:57.190 --> 00:46:58.840 align:middle line:84% This is the risk, and the benefit 00:46:58.840 --> 00:47:00.490 align:middle line:90% is the earlier recombination. 00:47:00.490 --> 00:47:02.770 align:middle line:84% But then there's counterarguments and so forth 00:47:02.770 --> 00:47:05.680 align:middle line:90% that we won't go into. 00:47:05.680 --> 00:47:06.610 align:middle line:90% Yeah? 00:47:06.610 --> 00:47:08.050 align:middle line:90% AUDIENCE: Going back to drift. 00:47:08.050 --> 00:47:09.790 align:middle line:90% The drift is actually random. 00:47:09.790 --> 00:47:13.680 align:middle line:84% What is it that causes either allele to fix? 00:47:13.680 --> 00:47:16.840 align:middle line:84% If you have two different alleles [INAUDIBLE] 00:47:16.840 --> 00:47:20.650 align:middle line:84% zero for one allele, why wouldn't it just [INAUDIBLE] 00:47:20.650 --> 00:47:21.340 align:middle line:90% come back? 00:47:21.340 --> 00:47:22.600 align:middle line:90% PROFESSOR: Well, it can. 00:47:22.600 --> 00:47:24.790 align:middle line:84% You can see here that it's starting 00:47:24.790 --> 00:47:29.020 align:middle line:84% to head so that it's fixing on one allele, 00:47:29.020 --> 00:47:31.930 align:middle line:84% and it changes direction, and it fixes the other one. 00:47:31.930 --> 00:47:37.210 align:middle line:84% So it can go all the way down to close to zero 00:47:37.210 --> 00:47:39.130 align:middle line:90% and then bounce back up. 00:47:39.130 --> 00:47:41.925 align:middle line:84% This is just some typical simulations here. 00:47:41.925 --> 00:47:43.300 align:middle line:84% If you do enough of these, you'll 00:47:43.300 --> 00:47:45.577 align:middle line:90% find every possible behavior. 00:47:45.577 --> 00:47:47.910 align:middle line:84% AUDIENCE: So what you're saying-- basically, eventually, 00:47:47.910 --> 00:47:49.810 align:middle line:84% if you just give it enough time, it will fix. 00:47:49.810 --> 00:47:50.768 align:middle line:90% PROFESSOR: It will fix. 00:47:50.768 --> 00:47:54.485 align:middle line:84% You can't necessarily predict which one will it fix on. 00:47:54.485 --> 00:47:56.110 align:middle line:84% If there's no selection, half the time, 00:47:56.110 --> 00:47:57.568 align:middle line:84% it'll fix on one, half on the other 00:47:57.568 --> 00:48:01.950 align:middle line:84% if they start out at the frequency of 50/50. 00:48:01.950 --> 00:48:04.242 align:middle line:84% But you have to think of it in the context of mutation 00:48:04.242 --> 00:48:06.450 align:middle line:84% and selection, too, because they're all acting there. 00:48:06.450 --> 00:48:09.240 align:middle line:84% And when you say that something is selectively neutral, 00:48:09.240 --> 00:48:10.840 align:middle line:90% what you really mean-- 00:48:10.840 --> 00:48:14.160 align:middle line:84% everything has some very, very tiny selective coefficient. 00:48:14.160 --> 00:48:18.360 align:middle line:84% But if it's tiny enough and the population size 00:48:18.360 --> 00:48:20.880 align:middle line:84% is small enough, then drift will blind you, 00:48:20.880 --> 00:48:22.120 align:middle line:90% and you can't see it. 00:48:22.120 --> 00:48:24.027 align:middle line:84% But if you get really big populations, 00:48:24.027 --> 00:48:25.860 align:middle line:84% then you'll get small drift, and then you'll 00:48:25.860 --> 00:48:28.170 align:middle line:90% see more subtle selection. 00:48:28.170 --> 00:48:31.125 align:middle line:90% 00:48:31.125 --> 00:48:34.260 align:middle line:84% The human population is very large. 00:48:34.260 --> 00:48:37.500 align:middle line:84% Some of the oceanic species are truly enormous. 00:48:37.500 --> 00:48:40.810 align:middle line:84% So you need to think about that as a possibility. 00:48:40.810 --> 00:48:44.340 align:middle line:84% So now let's talk about common diseases. 00:48:44.340 --> 00:48:49.470 align:middle line:84% The question is, are common diseases really-- 00:48:49.470 --> 00:48:51.690 align:middle line:84% to what extent are they caused by common variants? 00:48:51.690 --> 00:48:54.120 align:middle line:84% Clearly, some of them are caused by common variants. 00:48:54.120 --> 00:48:56.640 align:middle line:84% And we've said, well, common variants 00:48:56.640 --> 00:49:01.140 align:middle line:84% really shouldn't be deleterious, because they would be wiped out 00:49:01.140 --> 00:49:03.960 align:middle line:90% by selection. 00:49:03.960 --> 00:49:07.050 align:middle line:84% They could be very, very mildly deleterious such that drift 00:49:07.050 --> 00:49:10.680 align:middle line:84% will cause them to get fixated or persist, 00:49:10.680 --> 00:49:14.910 align:middle line:84% but they can't be really noticeably. 00:49:14.910 --> 00:49:17.400 align:middle line:84% Selection coefficients of 10 to the minus 4-- 00:49:17.400 --> 00:49:19.170 align:middle line:90% very, very tiny effects-- 00:49:19.170 --> 00:49:26.620 align:middle line:84% can be wiped out in normal-sized populations. 00:49:26.620 --> 00:49:30.990 align:middle line:84% So here are three examples of common variants 00:49:30.990 --> 00:49:33.300 align:middle line:84% that almost certainly are associated 00:49:33.300 --> 00:49:34.900 align:middle line:90% with common diseases. 00:49:34.900 --> 00:49:37.620 align:middle line:84% So why are these special cases, in my opinion, 00:49:37.620 --> 00:49:38.880 align:middle line:90% rather than the general case? 00:49:38.880 --> 00:49:40.995 align:middle line:84% APOE4 I earlier alluded to is associated 00:49:40.995 --> 00:49:42.210 align:middle line:90% with Alzheimer's dementia. 00:49:42.210 --> 00:49:46.180 align:middle line:84% It's involved in lipid transport and metabolism. 00:49:46.180 --> 00:49:51.450 align:middle line:84% And this particular allele, the E4 allele, 00:49:51.450 --> 00:49:54.270 align:middle line:90% is present at 20% in humans. 00:49:54.270 --> 00:49:58.950 align:middle line:84% About 80% is the other allele, the second most common allele 00:49:58.950 --> 00:50:02.230 align:middle line:90% is the E3 allele. 00:50:02.230 --> 00:50:05.990 align:middle line:84% And so you might say, well, this bad allele, this E4, 00:50:05.990 --> 00:50:11.640 align:middle line:84% is the one that should be present in the common ancestors 00:50:11.640 --> 00:50:14.300 align:middle line:90% of humans. 00:50:14.300 --> 00:50:16.260 align:middle line:84% The E3, the good one, should be present 00:50:16.260 --> 00:50:20.760 align:middle line:84% in the common ancestors, and this E4 is a recent aberration. 00:50:20.760 --> 00:50:23.460 align:middle line:84% It's somehow getting into human population. 00:50:23.460 --> 00:50:27.510 align:middle line:84% But actually, the E4 is the ancestral one, presumably 00:50:27.510 --> 00:50:29.070 align:middle line:84% due to some difference in diet or 00:50:29.070 --> 00:50:33.210 align:middle line:90% some other selective effects. 00:50:33.210 --> 00:50:37.030 align:middle line:84% The E4, which is currently bad for us, we think, 00:50:37.030 --> 00:50:42.130 align:middle line:84% was really good for some of our related species. 00:50:42.130 --> 00:50:45.930 align:middle line:84% And so we need to think very carefully before we do anything 00:50:45.930 --> 00:50:48.420 align:middle line:84% drastic about eliminating this allele from, say, 00:50:48.420 --> 00:50:51.990 align:middle line:90% the human population. 00:50:51.990 --> 00:50:56.880 align:middle line:84% Hemoglobin sickle cell, the sickle cell allele, 00:50:56.880 --> 00:51:00.030 align:middle line:84% is probably the oldest and most famous 00:51:00.030 --> 00:51:04.830 align:middle line:84% of the molecularly characterized alleles. 00:51:04.830 --> 00:51:09.330 align:middle line:84% Zuckerland and Pauling made this famous many decades ago. 00:51:09.330 --> 00:51:13.450 align:middle line:84% And it exists in 17% of the human population, 00:51:13.450 --> 00:51:18.790 align:middle line:84% and this is responsible for oxygen transport in red blood 00:51:18.790 --> 00:51:19.290 align:middle line:90% cells. 00:51:19.290 --> 00:51:21.240 align:middle line:84% And you saw in one of the earlier slides 00:51:21.240 --> 00:51:23.970 align:middle line:84% today those sickle-shaped cells, which 00:51:23.970 --> 00:51:27.510 align:middle line:84% have a huge effect on the hemodynamics of the red blood 00:51:27.510 --> 00:51:28.650 align:middle line:90% cell. 00:51:28.650 --> 00:51:32.250 align:middle line:84% Well, another red blood cell component, an enzyme, G6PD, 00:51:32.250 --> 00:51:36.720 align:middle line:84% which is involved in maintaining the redox function in the cell, 00:51:36.720 --> 00:51:38.740 align:middle line:90% is as high as 40%. 00:51:38.740 --> 00:51:42.780 align:middle line:84% The mutant, whichever one you want-- they're so close to 50%. 00:51:42.780 --> 00:51:47.640 align:middle line:84% They're just two alleles, and one of them 00:51:47.640 --> 00:51:53.250 align:middle line:84% is deleterious, in a certain sense, a biochemical sense. 00:51:53.250 --> 00:51:58.410 align:middle line:84% But both of these have a heterozygote advantage 00:51:58.410 --> 00:52:00.510 align:middle line:90% in being malaria-resistent. 00:52:00.510 --> 00:52:02.010 align:middle line:84% And so probably that's the reason 00:52:02.010 --> 00:52:03.510 align:middle line:84% that it's common in the population. 00:52:03.510 --> 00:52:09.570 align:middle line:84% And this is probably proving to be the rule that these 00:52:09.570 --> 00:52:11.790 align:middle line:84% are examples of that convergence that we 00:52:11.790 --> 00:52:14.400 align:middle line:84% saw in the case of balanced polymorphisms 00:52:14.400 --> 00:52:16.750 align:middle line:84% where the heterozygote has some advantage, 00:52:16.750 --> 00:52:19.980 align:middle line:84% and so you get a balanced point rather than one 00:52:19.980 --> 00:52:23.880 align:middle line:84% or the other dominating through drift or selection. 00:52:23.880 --> 00:52:26.280 align:middle line:84% And the third example, which we will develop 00:52:26.280 --> 00:52:30.300 align:middle line:90% in much more detail, is CCR5. 00:52:30.300 --> 00:52:32.220 align:middle line:84% There's a deletion of 32 base pairs 00:52:32.220 --> 00:52:35.070 align:middle line:84% which confers resistance to one of the greatest 00:52:35.070 --> 00:52:38.970 align:middle line:84% plagues in the history of the human race, which 00:52:38.970 --> 00:52:41.100 align:middle line:90% is the AIDS virus. 00:52:41.100 --> 00:52:44.250 align:middle line:84% And its frequency is 9% in Caucasians. 00:52:44.250 --> 00:52:49.830 align:middle line:84% I think we wish that it were 100% when we worry about HIV, 00:52:49.830 --> 00:52:53.160 align:middle line:84% but we need to wonder why it's not 100%. 00:52:53.160 --> 00:52:57.120 align:middle line:84% There may be some other reason for it 00:52:57.120 --> 00:53:00.750 align:middle line:84% being a nondeleted version in so many humans, 00:53:00.750 --> 00:53:02.170 align:middle line:90% and we need to understand that. 00:53:02.170 --> 00:53:06.270 align:middle line:84% And as far as I know, we don't understand that. 00:53:06.270 --> 00:53:10.110 align:middle line:84% Now, this is the last slide before the break. 00:53:10.110 --> 00:53:12.690 align:middle line:90% 00:53:12.690 --> 00:53:14.790 align:middle line:84% I promised you that we would take 00:53:14.790 --> 00:53:18.960 align:middle line:84% that simple mathematical treatment of mutation selection 00:53:18.960 --> 00:53:22.500 align:middle line:84% and drift and show that it actually has some impact, 00:53:22.500 --> 00:53:25.890 align:middle line:84% that it's actually used in human genetics. 00:53:25.890 --> 00:53:30.960 align:middle line:84% Now, I must warn you that this is not a consensus view. 00:53:30.960 --> 00:53:32.790 align:middle line:84% This is a view that I find appealing, 00:53:32.790 --> 00:53:38.310 align:middle line:84% in slide 21, that Jon Pritchard has authored. 00:53:38.310 --> 00:53:43.470 align:middle line:84% And he titled it in a provocative way-- 00:53:43.470 --> 00:53:47.010 align:middle line:84% Are Rare Variants Responsible for Susceptibility 00:53:47.010 --> 00:53:49.090 align:middle line:90% to Complex Diseases? 00:53:49.090 --> 00:53:51.150 align:middle line:90% And this is a quote. 00:53:51.150 --> 00:53:52.890 align:middle line:84% It's customary in theoretical work 00:53:52.890 --> 00:53:58.470 align:middle line:84% relating to complex diseases that the allele frequencies 00:53:58.470 --> 00:54:00.460 align:middle line:84% are treated as parameters of the model. 00:54:00.460 --> 00:54:03.570 align:middle line:84% And typically in models, you'll have 00:54:03.570 --> 00:54:07.830 align:middle line:84% derived values and parameters, which 00:54:07.830 --> 00:54:11.820 align:middle line:84% are input, the things that the user is expected to provide. 00:54:11.820 --> 00:54:16.140 align:middle line:84% And you don't want to have to be guessing at allele frequencies 00:54:16.140 --> 00:54:17.520 align:middle line:90% and having those parameters. 00:54:17.520 --> 00:54:22.960 align:middle line:84% So what's new here is that, using an evolutionary process, 00:54:22.960 --> 00:54:25.620 align:middle line:84% which includes-- you guessed it-- selection, mutation, 00:54:25.620 --> 00:54:29.460 align:middle line:84% and genetic drift, we can learn or, as I say, 00:54:29.460 --> 00:54:31.620 align:middle line:84% model the underlying allele frequencies. 00:54:31.620 --> 00:54:35.400 align:middle line:84% They can be derived rather than being required as an input. 00:54:35.400 --> 00:54:38.460 align:middle line:90% 00:54:38.460 --> 00:54:45.900 align:middle line:84% And this is illustrated here with a model. 00:54:45.900 --> 00:54:50.340 align:middle line:84% This is entirely theoretical, but the parameters 00:54:50.340 --> 00:54:53.790 align:middle line:84% that are used are based on some genetic studies that have been 00:54:53.790 --> 00:54:55.890 align:middle line:90% done, for example, on autism. 00:54:55.890 --> 00:54:59.460 align:middle line:84% And so let me just define some of the terms here. 00:54:59.460 --> 00:55:03.510 align:middle line:84% This risk ratio is related, in a certain sense, 00:55:03.510 --> 00:55:05.460 align:middle line:84% to the selection and fitness coefficients 00:55:05.460 --> 00:55:06.370 align:middle line:90% we were talking about before. 00:55:06.370 --> 00:55:07.995 align:middle line:84% Now, selection and fitness coefficients 00:55:07.995 --> 00:55:10.110 align:middle line:90% refer to reproductive fitness. 00:55:10.110 --> 00:55:14.310 align:middle line:84% And in human genetics, we have broader interests 00:55:14.310 --> 00:55:17.460 align:middle line:84% into all sorts of things that either don't affect 00:55:17.460 --> 00:55:19.770 align:middle line:84% reproductive fitness, or we don't know 00:55:19.770 --> 00:55:21.030 align:middle line:90% how it affects reproduction. 00:55:21.030 --> 00:55:23.220 align:middle line:84% But it affects some kind of medical 00:55:23.220 --> 00:55:26.250 align:middle line:90% or just some trait of interest. 00:55:26.250 --> 00:55:31.050 align:middle line:84% In this case, the risk ratio replaces the selection 00:55:31.050 --> 00:55:31.660 align:middle line:90% coefficient. 00:55:31.660 --> 00:55:36.330 align:middle line:84% And this is basically saying, my brother or sister has autism-- 00:55:36.330 --> 00:55:38.140 align:middle line:90% if they did-- 00:55:38.140 --> 00:55:41.460 align:middle line:84% then I would have a 75-fold higher chance 00:55:41.460 --> 00:55:45.270 align:middle line:84% of having it than someone selected randomly 00:55:45.270 --> 00:55:48.220 align:middle line:84% from the same population as I come from. 00:55:48.220 --> 00:55:54.120 align:middle line:84% So the 70-fold increase is a very high heritability 00:55:54.120 --> 00:55:57.390 align:middle line:90% for this particular example. 00:55:57.390 --> 00:56:00.090 align:middle line:84% Also in this example, through some genetics 00:56:00.090 --> 00:56:03.180 align:middle line:84% we won't discuss, it seemed reasonable 00:56:03.180 --> 00:56:08.640 align:middle line:84% that the number of loci involved might be a large number, 00:56:08.640 --> 00:56:10.143 align:middle line:90% on the order of 100 or so. 00:56:10.143 --> 00:56:12.060 align:middle line:84% And you can think of a lot of common diseases. 00:56:12.060 --> 00:56:15.160 align:middle line:84% When you start listing the well-characterized ones, 00:56:15.160 --> 00:56:16.680 align:middle line:84% we start listing the number of genes 00:56:16.680 --> 00:56:19.610 align:middle line:84% that either are known or are plausible, like cancer 00:56:19.610 --> 00:56:22.970 align:middle line:84% or walking down the street, or whatever. 00:56:22.970 --> 00:56:26.600 align:middle line:84% These really complicated traits involve a very large number 00:56:26.600 --> 00:56:31.040 align:middle line:84% of cell types, a large number of cell components, 00:56:31.040 --> 00:56:33.330 align:middle line:84% and hence a large number of genes. 00:56:33.330 --> 00:56:36.210 align:middle line:84% So here, they've assumed a model with 100 loci, 00:56:36.210 --> 00:56:38.990 align:middle line:90% 100 different genes. 00:56:38.990 --> 00:56:44.300 align:middle line:84% And they have multiplicative effects of the polymorphisms 00:56:44.300 --> 00:56:47.270 align:middle line:90% in those genes between loci. 00:56:47.270 --> 00:56:51.800 align:middle line:84% That is to say, you need to have gene 1 working and gene 00:56:51.800 --> 00:56:54.290 align:middle line:84% 2 and gene 3, so that's multiplicative. 00:56:54.290 --> 00:56:57.000 align:middle line:84% But then, the polymorphisms you introduced into a gene-- 00:56:57.000 --> 00:56:58.580 align:middle line:84% you could think there are a lot of genes involved, 00:56:58.580 --> 00:57:00.830 align:middle line:84% and there are a lot of different positions within the gene that 00:57:00.830 --> 00:57:02.990 align:middle line:84% could be involved, and each of those is additive. 00:57:02.990 --> 00:57:08.840 align:middle line:84% You have a little reduction in activity due to first mutation, 00:57:08.840 --> 00:57:10.580 align:middle line:84% and then a second mutation, a third. 00:57:10.580 --> 00:57:13.560 align:middle line:84% Each of those is this or this or this or this, 00:57:13.560 --> 00:57:15.240 align:middle line:84% and so that's an additive effect. 00:57:15.240 --> 00:57:18.620 align:middle line:84% And so they have various historical justifications 00:57:18.620 --> 00:57:21.380 align:middle line:84% for having additive penetrance within the gene 00:57:21.380 --> 00:57:25.400 align:middle line:84% and multiplicative across different loci, different genes 00:57:25.400 --> 00:57:27.210 align:middle line:90% in the genome. 00:57:27.210 --> 00:57:33.530 align:middle line:84% Now, for these 100 loci, there will be a top five 00:57:33.530 --> 00:57:36.950 align:middle line:84% that affect the relative risk the most, 00:57:36.950 --> 00:57:41.645 align:middle line:84% and that's what's been plotted here, where we have-- 00:57:41.645 --> 00:57:44.480 align:middle line:90% 00:57:44.480 --> 00:57:48.110 align:middle line:84% the zero curve, you see, is in the absence 00:57:48.110 --> 00:57:51.800 align:middle line:84% of any of these multiplicative effects. 00:57:51.800 --> 00:57:54.680 align:middle line:84% It's as if you had no loci that were affecting the frequency 00:57:54.680 --> 00:57:56.100 align:middle line:90% of susceptibility alleles. 00:57:56.100 --> 00:58:01.640 align:middle line:84% And so, as in most unselective populations, 00:58:01.640 --> 00:58:07.490 align:middle line:84% you'll have most of the alleles being either 00:58:07.490 --> 00:58:10.010 align:middle line:90% at zero frequency or 100%. 00:58:10.010 --> 00:58:12.860 align:middle line:84% Basically, the zero representing the absence 00:58:12.860 --> 00:58:15.290 align:middle line:90% of the other the alternatives. 00:58:15.290 --> 00:58:16.860 align:middle line:90% The 100% is there. 00:58:16.860 --> 00:58:24.230 align:middle line:84% But if you have these top five loci out of 100 00:58:24.230 --> 00:58:26.150 align:middle line:84% that contribute to the risk ratio, 00:58:26.150 --> 00:58:29.810 align:middle line:84% then those are represented by these four curves. 00:58:29.810 --> 00:58:31.610 align:middle line:84% The frequency of susceptibility alleles, 00:58:31.610 --> 00:58:35.180 align:middle line:84% which range along the horizontal axis now, from 0 to 100%, 00:58:35.180 --> 00:58:38.145 align:middle line:84% have what he calls a probability density. 00:58:38.145 --> 00:58:39.770 align:middle line:84% It's clearly not a probability density, 00:58:39.770 --> 00:58:41.720 align:middle line:84% because it's not going to integrate to 1, 00:58:41.720 --> 00:58:50.330 align:middle line:84% but here, it's the probability, the histogram of risk ratios. 00:58:50.330 --> 00:58:58.820 align:middle line:84% So let's take a break, and we'll drill down 00:58:58.820 --> 00:59:01.475 align:middle line:84% on the association study in a very interesting case. 00:59:01.475 --> 00:59:04.580 align:middle line:90% 00:59:04.580 --> 00:59:10.340 align:middle line:84% Any problem sets to hand in can put them here during the break. 00:59:10.340 --> 00:59:20.020 align:middle line:90% 00:59:20.020 --> 00:59:26.490 align:middle line:84% AUDIENCE: So I understand about modeling mutation selection. 00:59:26.490 --> 00:59:31.000 align:middle line:90%