WEBVTT 00:00:00.060 --> 00:00:01.780 The following content is provided 00:00:01.780 --> 00:00:04.019 under a Creative Commons license. 00:00:04.019 --> 00:00:06.870 Your support will help MIT OpenCourseWare continue 00:00:06.870 --> 00:00:10.730 to offer high quality educational resources for free. 00:00:10.730 --> 00:00:13.340 To make a donation or view additional materials 00:00:13.340 --> 00:00:17.236 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.236 --> 00:00:17.861 at ocw.mit.edu. 00:00:26.450 --> 00:00:28.080 PROFESSOR: So as you recall last time 00:00:28.080 --> 00:00:30.780 we talked about chromatin structure and chromatin 00:00:30.780 --> 00:00:32.000 regulation. 00:00:32.000 --> 00:00:35.390 And now we're going to move on to genetic analysis. 00:00:35.390 --> 00:00:38.160 But before we did that, I want us to touch on two points 00:00:38.160 --> 00:00:41.440 that we talked about briefly last time. 00:00:41.440 --> 00:00:44.880 One was 5C analysis. 00:00:44.880 --> 00:00:48.420 Who was it that brought up-- who was the 5C expert here? 00:00:48.420 --> 00:00:50.010 Anybody? 00:00:50.010 --> 00:00:51.790 No? 00:00:51.790 --> 00:00:52.920 Nobody wants to own 5C. 00:00:52.920 --> 00:00:53.500 OK. 00:00:53.500 --> 00:00:56.100 But as you recall, we talked about ChIA-PET 00:00:56.100 --> 00:01:00.090 as one way of analyzing any to any interactions in the way 00:01:00.090 --> 00:01:04.370 that the genome folds up and enhancers talk to promoters. 00:01:04.370 --> 00:01:06.114 And 5C is a very similar technique. 00:01:06.114 --> 00:01:07.530 I just wanted to show you the flow 00:01:07.530 --> 00:01:10.260 chart for how the protocol goes. 00:01:10.260 --> 00:01:12.950 There is a cross linking. 00:01:12.950 --> 00:01:14.720 A digestion with a restriction enzyme 00:01:14.720 --> 00:01:18.040 step, followed by a proximity ligation step, 00:01:18.040 --> 00:01:21.900 which gives you molecules that had been brought together 00:01:21.900 --> 00:01:25.320 by an enhancer, promoter complex, or any other kind 00:01:25.320 --> 00:01:29.030 of distal protein-protein interaction. 00:01:29.030 --> 00:01:35.660 And then, what happens is that you design specific timers 00:01:35.660 --> 00:01:38.600 to detect those ligation events. 00:01:38.600 --> 00:01:41.150 And you sequence the result of what 00:01:41.150 --> 00:01:44.390 is known as ligation mediated amplification. 00:01:44.390 --> 00:01:46.730 So those primers are only going to ligate 00:01:46.730 --> 00:01:49.910 if they're brought together at a particular junction, which 00:01:49.910 --> 00:01:53.230 is defined by the restriction sites lining up. 00:01:53.230 --> 00:01:58.500 So, 5C is a method of looking at which regions of the genome 00:01:58.500 --> 00:02:04.170 interact and can produce these sorts of results, 00:02:04.170 --> 00:02:05.680 showing which parts of the genome 00:02:05.680 --> 00:02:07.190 interact with one another. 00:02:07.190 --> 00:02:12.630 The key difference, I think, between chIA-PET and 5C 00:02:12.630 --> 00:02:15.660 is that you actually have to have these primers designed 00:02:15.660 --> 00:02:19.050 and pick the particular locations you want to query. 00:02:19.050 --> 00:02:23.110 So the primers that you design represent query locations 00:02:23.110 --> 00:02:26.840 and you can then either apply the results to a microarray, 00:02:26.840 --> 00:02:31.710 or to high throughput sequencing to detect these interactions. 00:02:31.710 --> 00:02:33.900 But the essential idea is the same. 00:02:33.900 --> 00:02:36.540 Where you do proximity based ligation 00:02:36.540 --> 00:02:40.440 to form molecules that contain components 00:02:40.440 --> 00:02:42.230 of two different pieces of the genome 00:02:42.230 --> 00:02:47.270 that have been brought together for some functional reason. 00:02:47.270 --> 00:02:50.580 The next thing I want to touch upon 00:02:50.580 --> 00:02:55.500 was this idea of the CpG dinucleotides 00:02:55.500 --> 00:02:59.930 that are connected by a phosphate bond. 00:02:59.930 --> 00:03:01.880 And you recall that I talked about the idea 00:03:01.880 --> 00:03:03.310 that they were symmetric. 00:03:03.310 --> 00:03:07.430 So you could have methyl groups on the cytosines in such a way 00:03:07.430 --> 00:03:10.810 that, because they could mirror one another, 00:03:10.810 --> 00:03:14.770 they could be transferred from one strand of DNA 00:03:14.770 --> 00:03:18.890 to the other strand of DNA, during cell replication 00:03:18.890 --> 00:03:21.530 by DNA methyltransferase. 00:03:21.530 --> 00:03:25.750 So it forms a more stable kind of mark and as you recall, 00:03:25.750 --> 00:03:27.750 DNA methylation where something occurred 00:03:27.750 --> 00:03:32.210 in lowly expressed genes and typically in regions 00:03:32.210 --> 00:03:34.850 of the genome that are methylated. 00:03:34.850 --> 00:03:36.430 Other histone marks are not present 00:03:36.430 --> 00:03:39.050 and the genes are turned off. 00:03:39.050 --> 00:03:39.680 OK. 00:03:39.680 --> 00:03:41.055 So those were the points I wanted 00:03:41.055 --> 00:03:44.380 to touch upon from last lecture. 00:03:44.380 --> 00:03:48.090 Now we're going to embark upon an adventure, 00:03:48.090 --> 00:03:54.670 looking for the answer to, wear is missing heritability found? 00:03:54.670 --> 00:03:57.560 So it's a big open question now in genetics. 00:03:57.560 --> 00:04:00.240 In human genetics, which is that we really 00:04:00.240 --> 00:04:03.830 can't find all the heritability. 00:04:03.830 --> 00:04:06.990 And as a point of introduction, the narrative 00:04:06.990 --> 00:04:10.760 arc for today's lecture is that, generally speaking, 00:04:10.760 --> 00:04:13.160 you're more like your relatives than random people 00:04:13.160 --> 00:04:14.480 on the planet. 00:04:14.480 --> 00:04:15.770 And why is this? 00:04:15.770 --> 00:04:20.529 Well obviously you contain components of your mom 00:04:20.529 --> 00:04:22.089 and dad's genomes. 00:04:22.089 --> 00:04:27.800 And they are providing you with components of your traits. 00:04:27.800 --> 00:04:30.580 And the heritability of a trait is 00:04:30.580 --> 00:04:34.310 defined by the fraction of phenotypic variance 00:04:34.310 --> 00:04:37.830 that can be explained by genetics. 00:04:37.830 --> 00:04:41.600 And we're going to talk today about computational models that 00:04:41.600 --> 00:04:44.250 can predict phenotype from genotype. 00:04:44.250 --> 00:04:46.480 And this is very important, obviously, 00:04:46.480 --> 00:04:51.380 for understanding the sources of various traits and phenotypes. 00:04:51.380 --> 00:04:54.760 As well as fields such as pharmacogenomics 00:04:54.760 --> 00:04:59.640 that try and predict the best therapy for a disease 00:04:59.640 --> 00:05:03.440 based upon your genetic makeup. 00:05:03.440 --> 00:05:09.110 So, individual loci in the genome 00:05:09.110 --> 00:05:12.140 that contribute to quantitative traits 00:05:12.140 --> 00:05:17.395 are called quantitative trait locis, or QTLs. 00:05:17.395 --> 00:05:19.520 So we're going to talked about how to discover them 00:05:19.520 --> 00:05:24.150 and how to build models of quantitative traits using QTLs. 00:05:24.150 --> 00:05:27.490 And finally, as I said at the outset, 00:05:27.490 --> 00:05:29.980 our models are insufficient today. 00:05:29.980 --> 00:05:33.150 They really can't find all of the heritability. 00:05:33.150 --> 00:05:35.730 So we're going to go searching for this missing heritability 00:05:35.730 --> 00:05:39.460 and see where it might be found. 00:05:39.460 --> 00:05:44.320 Computationally, we're going to apply a variety of techniques 00:05:44.320 --> 00:05:45.830 to these problems. 00:05:45.830 --> 00:05:48.820 A preview is, we're going to build 00:05:48.820 --> 00:05:52.040 linear models of phenotype and we're 00:05:52.040 --> 00:05:56.124 going to use stepwise regression to learn these models using 00:05:56.124 --> 00:05:57.290 a forward feature selection. 00:05:57.290 --> 00:05:59.210 And I'll talk about what that is when 00:05:59.210 --> 00:06:01.320 we get to that point of the lecture. 00:06:01.320 --> 00:06:04.310 We're going to derive test statistics for discovering 00:06:04.310 --> 00:06:08.530 which QTLs are significant and which QTLs are not, 00:06:08.530 --> 00:06:10.211 to include in our model. 00:06:10.211 --> 00:06:11.960 And finally, we're going to talk about how 00:06:11.960 --> 00:06:15.200 to measure narrow sense heritability and broad sense 00:06:15.200 --> 00:06:17.435 heritability in environmental variance. 00:06:20.010 --> 00:06:21.990 OK. 00:06:21.990 --> 00:06:30.400 So, one great resource for traits that are fairly simple. 00:06:30.400 --> 00:06:35.600 That primarily are the result of a single gene mutation, 00:06:35.600 --> 00:06:40.040 or where a single gene mutation plays a dominant role, 00:06:40.040 --> 00:06:45.130 is something called Online Mendelian Inheritance in Man. 00:06:45.130 --> 00:06:46.770 And it's a resource. 00:06:46.770 --> 00:06:49.690 It has about 21,000 genes in it right now. 00:06:49.690 --> 00:06:55.100 And it's a great way to explore what human genes function 00:06:55.100 --> 00:06:57.170 is in various diseases. 00:06:57.170 --> 00:06:58.500 And you could query by disease. 00:06:58.500 --> 00:07:00.060 You can query by gene. 00:07:00.060 --> 00:07:07.130 And it is a very carefully annotated and maintained 00:07:07.130 --> 00:07:10.190 collection that is worthy of study, 00:07:10.190 --> 00:07:13.460 if you're interested in particular disease genes. 00:07:13.460 --> 00:07:19.132 We're going to be looking at more complex analyses today. 00:07:19.132 --> 00:07:20.590 The analyses we're going to look at 00:07:20.590 --> 00:07:22.275 are where there are many genes that 00:07:22.275 --> 00:07:23.540 influence a particular trait. 00:07:23.540 --> 00:07:25.630 And we would like to come up with general methods 00:07:25.630 --> 00:07:30.902 for discovering how we can de novo from experimental data-- 00:07:30.902 --> 00:07:32.985 discover all the different genes that participate. 00:07:36.680 --> 00:07:39.910 Now just as a quick review of statistics, 00:07:39.910 --> 00:07:43.660 I think that we've talked before about means in class 00:07:43.660 --> 00:07:44.989 and variances. 00:07:44.989 --> 00:07:46.530 We're also going to talk a little bit 00:07:46.530 --> 00:07:48.732 about covariances today. 00:07:48.732 --> 00:07:50.190 But these are terms that you should 00:07:50.190 --> 00:07:54.210 be familiar with as we're looking today 00:07:54.210 --> 00:08:01.930 at some of our metrics for understanding heritability. 00:08:01.930 --> 00:08:05.960 Are there any question about any of the statistical metrics that 00:08:05.960 --> 00:08:06.460 are up here? 00:08:09.348 --> 00:08:09.848 OK. 00:08:12.760 --> 00:08:16.125 So, a broad overview of genotype to phenotype. 00:08:18.996 --> 00:08:20.620 So, we're primarily going to be working 00:08:20.620 --> 00:08:24.170 with complete genome sequences today, 00:08:24.170 --> 00:08:26.490 which will reveal all of the variance that 00:08:26.490 --> 00:08:28.930 are present in the genome. 00:08:28.930 --> 00:08:32.264 And it's also the case that you can subsample a genome 00:08:32.264 --> 00:08:35.070 and only observe certain variance. 00:08:35.070 --> 00:08:37.710 Typically that's done with microarrays 00:08:37.710 --> 00:08:41.010 that have probes that are specific to particular markers. 00:08:41.010 --> 00:08:42.929 The way those arrays are manufactured 00:08:42.929 --> 00:08:47.110 is that whole genome sequencing is done at the outset, and then 00:08:47.110 --> 00:08:50.570 high prevalence variance, at least 00:08:50.570 --> 00:08:52.190 common variance, which typically are 00:08:52.190 --> 00:08:55.410 at a frequency of at least 5% in the population 00:08:55.410 --> 00:08:58.390 are queried by using a microarray. 00:08:58.390 --> 00:09:01.790 But today we'll talk about complete genome sequence. 00:09:01.790 --> 00:09:03.290 An individual's phenotype, we'll say 00:09:03.290 --> 00:09:05.800 is defined by one or more traits. 00:09:05.800 --> 00:09:09.720 And a non-quantitative trait is something perhaps as simple as 00:09:09.720 --> 00:09:12.590 whether or not something is dead or alive. 00:09:12.590 --> 00:09:15.820 Or whether or not it can survive in a particular condition. 00:09:15.820 --> 00:09:19.920 Or its ability to produce a particular substance. 00:09:19.920 --> 00:09:22.370 A quantitative trait, on the other hand, 00:09:22.370 --> 00:09:25.274 is a continuous variable. 00:09:25.274 --> 00:09:26.815 Height, for example, of an individual 00:09:26.815 --> 00:09:28.840 is a quantitative trait. 00:09:28.840 --> 00:09:32.610 As is growth rate, expression of a particular gene, 00:09:32.610 --> 00:09:34.490 and so forth. 00:09:34.490 --> 00:09:39.310 So we'll be focusing today on estimating quantitative traits. 00:09:39.310 --> 00:09:41.970 And as I said, a quantitative trait or loci, 00:09:41.970 --> 00:09:45.240 is a marker that's associated with a quantitative trait 00:09:45.240 --> 00:09:47.160 and could be used to predict it. 00:09:47.160 --> 00:09:49.520 And you can sometimes hear about eQTLs, 00:09:49.520 --> 00:09:52.900 which are expression quantitative trait loci. 00:09:52.900 --> 00:09:55.540 And they're loci that are related to gene expression. 00:09:59.770 --> 00:10:07.469 So, let's begin then, with a very simple genetic model. 00:10:07.469 --> 00:10:09.510 It's going to be haploid, which means, of course, 00:10:09.510 --> 00:10:11.218 there's only one copy of each chromosome. 00:10:11.218 --> 00:10:12.607 Yeast is the model organism we're 00:10:12.607 --> 00:10:13.940 going to be talking about today. 00:10:13.940 --> 00:10:16.190 It's a haploid organism. 00:10:16.190 --> 00:10:18.020 And we have mom and dad up there. 00:10:18.020 --> 00:10:22.310 Mom on the left, dad on the right in two different colors. 00:10:22.310 --> 00:10:24.900 And you can see that mom and dad in this particular example, 00:10:24.900 --> 00:10:26.200 have n different genes. 00:10:26.200 --> 00:10:29.580 They're going to contribute to the F1 generation, to junior. 00:10:32.110 --> 00:10:37.700 And the relative color is white for mom, black for dad, 00:10:37.700 --> 00:10:41.980 are going to be used to describe the alleles, 00:10:41.980 --> 00:10:44.860 or the allelic variance that are inherited 00:10:44.860 --> 00:10:48.436 by the child, the F1 generation. 00:10:48.436 --> 00:10:50.309 And as I said, a specific phenotype 00:10:50.309 --> 00:10:52.350 might be alive or dead in a specific environment. 00:10:55.290 --> 00:11:03.110 And note that I have drawn the chromosomes to be disconnected. 00:11:03.110 --> 00:11:06.230 Which means that each one of those genes 00:11:06.230 --> 00:11:09.940 is going to be independently inherited. 00:11:09.940 --> 00:11:13.160 So the probability in the F1 generation 00:11:13.160 --> 00:11:16.020 that you're going to get one of those from mom or dad 00:11:16.020 --> 00:11:18.420 is going to be a coin flip. 00:11:18.420 --> 00:11:19.970 We're going to assume that they're 00:11:19.970 --> 00:11:23.400 far enough away that the probability of crossing over 00:11:23.400 --> 00:11:26.410 during meiosis is 0.5. 00:11:26.410 --> 00:11:28.530 And so we get a random assortment 00:11:28.530 --> 00:11:32.050 of alleles from mom and dad. 00:11:32.050 --> 00:11:33.130 OK? 00:11:33.130 --> 00:11:37.520 So let us say that you go off and do an experiment. 00:11:37.520 --> 00:11:44.610 And you have 32 individuals that you produce out of a cross. 00:11:44.610 --> 00:11:47.490 And you test them, OK. 00:11:47.490 --> 00:11:57.130 And two of them are resistant to a particular substance. 00:11:57.130 --> 00:12:00.155 How many genes do you think are involved in that resistance? 00:12:03.320 --> 00:12:07.885 Let's assume that mom is resistant and dad is not. 00:12:07.885 --> 00:12:08.385 OK. 00:12:11.560 --> 00:12:14.780 If you had two that were resistant out of 32, 00:12:14.780 --> 00:12:18.350 how many different genes do you think were involved? 00:12:18.350 --> 00:12:19.635 How do you estimate that? 00:12:26.420 --> 00:12:26.970 Any ideas? 00:12:33.667 --> 00:12:34.645 Yes? 00:12:34.645 --> 00:12:39.046 AUDIENCE: If you had 32 individuals 00:12:39.046 --> 00:12:44.930 and say half of them got it? 00:12:44.930 --> 00:12:46.160 PROFESSOR: Two, let's say. 00:12:46.160 --> 00:12:51.760 One out of 16 is resistant. 00:12:51.760 --> 00:12:53.970 And mom is resistant. 00:12:53.970 --> 00:12:56.940 AUDIENCE: Because I was thinking that if it was half of them 00:12:56.940 --> 00:13:00.212 were resistant, then you would maybe guess one gene, 00:13:00.212 --> 00:13:01.170 or something like that. 00:13:01.170 --> 00:13:02.220 PROFESSOR: Very good. 00:13:02.220 --> 00:13:04.970 AUDIENCE: So then if only eight were 00:13:04.970 --> 00:13:09.720 resistant you might guess two genes, or something like that? 00:13:09.720 --> 00:13:11.960 PROFESSOR: Yeah. 00:13:11.960 --> 00:13:15.320 What you say is, that if mom's resistant, then 00:13:15.320 --> 00:13:16.850 we're going to assume that you need 00:13:16.850 --> 00:13:20.030 to get the right number of genes from mom to be resistant. 00:13:20.030 --> 00:13:21.390 Right? 00:13:21.390 --> 00:13:25.369 And so, let's say that you had to get four genes from mom. 00:13:25.369 --> 00:13:27.410 What's the chance of getting four genes from mom? 00:13:30.236 --> 00:13:33.070 AUDIENCE: Half to the power of four. 00:13:33.070 --> 00:13:35.290 PROFESSOR: Yeah, which is one out of 16, right? 00:13:35.290 --> 00:13:39.200 So, if you, for example had two that were resistant out of 32, 00:13:39.200 --> 00:13:41.240 the chances are one in 16. 00:13:41.240 --> 00:13:41.960 Right? 00:13:41.960 --> 00:13:46.230 So you would naively think, and properly so, 00:13:46.230 --> 00:13:51.620 that you had to give four genes from mom to be resistant. 00:13:51.620 --> 00:13:54.440 So the way to think about these sorts 00:13:54.440 --> 00:13:57.450 of non-quantitative traits is that you 00:13:57.450 --> 00:14:00.630 can estimate the number of genes involved. 00:14:00.630 --> 00:14:02.930 The simply is log base 2 over the number 00:14:02.930 --> 00:14:07.570 of F1s tested over the number of the F1s with the phenotype. 00:14:07.570 --> 00:14:09.790 It tells you roughly how many genes 00:14:09.790 --> 00:14:16.160 are involved in providing a particular trait, 00:14:16.160 --> 00:14:18.530 assuming that the genes are unlinked. 00:14:18.530 --> 00:14:21.415 It's a coin flip, whether you get them or not. 00:14:21.415 --> 00:14:22.415 Does everybody see that? 00:14:25.090 --> 00:14:26.300 Yes? 00:14:26.300 --> 00:14:27.760 Any questions at all about that? 00:14:33.025 --> 00:14:33.775 About the details? 00:14:37.390 --> 00:14:38.940 OK. 00:14:38.940 --> 00:14:44.400 Let's talk now about quantitative traits then. 00:14:44.400 --> 00:14:47.905 We'll go back to our model and imagine 00:14:47.905 --> 00:14:50.850 that we have the same set-- actually 00:14:50.850 --> 00:14:53.110 it's going to a different set of n genes. 00:14:53.110 --> 00:14:56.070 We're going to have a coin flip as to 00:14:56.070 --> 00:14:58.890 whether or not you're getting a mom gene or a dad gene. 00:14:58.890 --> 00:15:00.200 OK. 00:15:00.200 --> 00:15:05.826 And each gene in dad has an effect size of 1 over n. 00:15:05.826 --> 00:15:06.326 Yes? 00:15:06.326 --> 00:15:08.618 AUDIENCE: I just wanted to check. 00:15:08.618 --> 00:15:13.438 We're assuming that the parents are homozygous for the trait? 00:15:13.438 --> 00:15:14.402 Is that correct? 00:15:14.402 --> 00:15:16.040 PROFESSOR: Remember these are haploid. 00:15:16.040 --> 00:15:17.540 AUDIENCE: Oh, these are haploid. 00:15:17.540 --> 00:15:18.248 PROFESSOR: Right. 00:15:18.248 --> 00:15:23.300 So they only have one copy of all these genes. 00:15:23.300 --> 00:15:24.760 All right. 00:15:24.760 --> 00:15:25.774 Yes? 00:15:25.774 --> 00:15:30.220 AUDIENCE: [INAUDIBLE] resistant and they're [INAUDIBLE]. 00:15:30.220 --> 00:15:32.030 That could still mean that dad has 00:15:32.030 --> 00:15:35.160 three of the four genes in principle. 00:15:35.160 --> 00:15:36.640 PROFESSOR: The previous slide? 00:15:36.640 --> 00:15:38.588 Is that where what you're talking about? 00:15:38.588 --> 00:15:40.527 AUDIENCE: [INAUDIBLE] knew about it. 00:15:40.527 --> 00:15:42.360 So really what you mean is that dad does not 00:15:42.360 --> 00:15:44.930 have any of the genes that are involved with resistance. 00:15:44.930 --> 00:15:45.888 PROFESSOR: The correct. 00:15:48.602 --> 00:15:50.560 I was saying that dad has to have all of gene-- 00:15:50.560 --> 00:15:52.670 that the child has to have all of the genes that 00:15:52.670 --> 00:15:54.290 are operative to create resistance. 00:15:54.290 --> 00:15:55.750 We're going to assume an AND model. 00:15:55.750 --> 00:15:58.120 He must have all the genes from mom. 00:15:58.120 --> 00:16:01.470 They're involved in the resistance pathway. 00:16:01.470 --> 00:16:04.720 And since only one out of a 16 progeny 00:16:04.720 --> 00:16:08.370 has all those genes from mom, right, it 00:16:08.370 --> 00:16:11.390 appears that given the chance of inheriting something from mom 00:16:11.390 --> 00:16:16.040 is 1/2, that it's four genes you have to inherit from mom. 00:16:16.040 --> 00:16:19.787 Because the chance of inheriting all four is one out of 16. 00:16:19.787 --> 00:16:23.060 AUDIENCE: [INAUDIBLE] in which case-- 00:16:23.060 --> 00:16:27.630 PROFESSOR: No, I'm assuming the dad doesn't have any of those. 00:16:27.630 --> 00:16:29.660 But here we're asking, what is the difference 00:16:29.660 --> 00:16:32.630 in the number of genes between mom and dad? 00:16:32.630 --> 00:16:35.520 So you're right, that the number we're computing 00:16:35.520 --> 00:16:39.360 is the relative number of genes different between mom and dad 00:16:39.360 --> 00:16:40.740 you require. 00:16:40.740 --> 00:16:43.080 And so it might be that dad's a reference 00:16:43.080 --> 00:16:45.790 and we're asking how many additional genes mom brought 00:16:45.790 --> 00:16:47.870 to the table to provide with that resistance. 00:16:47.870 --> 00:16:49.560 But that's a good point. 00:16:49.560 --> 00:16:50.060 OK. 00:16:53.370 --> 00:16:54.410 OK. 00:16:54.410 --> 00:16:59.080 So, now let's look at this quantitative model. 00:16:59.080 --> 00:17:04.440 Let's assume that mom has a bunch of genes that contribute 00:17:04.440 --> 00:17:11.089 zero to an effect size and dad-- each gene 00:17:11.089 --> 00:17:14.640 that dad has produces an effect of 1 over n. 00:17:14.640 --> 00:17:18.560 So the total effect size here for dad is 1. 00:17:18.560 --> 00:17:22.700 So the effect of mom on this particular quantitative trait 00:17:22.700 --> 00:17:23.480 might be zero. 00:17:23.480 --> 00:17:25.920 It might be the amount of ethanol produced 00:17:25.920 --> 00:17:28.190 or some other quantitative value. 00:17:28.190 --> 00:17:31.930 And dad, on the other hand, since he has n genes, 00:17:31.930 --> 00:17:35.890 is going to produce one, because each gene contributes 00:17:35.890 --> 00:17:38.275 a little bit to this quantitative phenotype. 00:17:41.642 --> 00:17:43.050 Is everybody clear on that? 00:17:45.670 --> 00:17:51.550 So, the child is going to inherit genes 00:17:51.550 --> 00:17:56.290 to our coin flip between mom and dad, right. 00:17:56.290 --> 00:17:57.880 So the first fundamental question 00:17:57.880 --> 00:18:01.430 is, how many different levels are there 00:18:01.430 --> 00:18:04.440 in our quantitative phenotype in our trait? 00:18:08.360 --> 00:18:10.020 How many different levels can you have? 00:18:16.274 --> 00:18:16.940 AUDIENCE: N + 1? 00:18:16.940 --> 00:18:20.270 PROFESSOR: N + 1, right, because you can either inherit 00:18:20.270 --> 00:18:24.010 zero, or up to n genes from dad. 00:18:24.010 --> 00:18:27.940 And it gets you n plus 1 different levels. 00:18:27.940 --> 00:18:29.380 OK. 00:18:29.380 --> 00:18:32.410 So, what's the probability then-- well, 00:18:32.410 --> 00:18:33.660 I'll ask a different question. 00:18:33.660 --> 00:18:38.245 What's the expected value of the quantitative phenotype 00:18:38.245 --> 00:18:39.060 of a child? 00:18:43.620 --> 00:18:44.700 Just looking at this. 00:18:48.410 --> 00:18:52.860 If dad's one and mom's zero, and you have a collection of genes 00:18:52.860 --> 00:18:57.507 and you do a coin flip each time, 00:18:57.507 --> 00:18:59.340 you're going to get half your genes from mom 00:18:59.340 --> 00:19:01.410 and half your genes from dad. 00:19:01.410 --> 00:19:02.990 Right. 00:19:02.990 --> 00:19:11.310 And so the expected trait value is 0.5. 00:19:11.310 --> 00:19:13.420 So for these added traits, you're 00:19:13.420 --> 00:19:17.770 going be at the midpoint between mom and dad. 00:19:17.770 --> 00:19:19.880 Right. 00:19:19.880 --> 00:19:28.340 And what is the probability that you 00:19:28.340 --> 00:19:32.055 inherit x copies of dad's genes? 00:19:35.390 --> 00:19:44.260 Well, that's n choose x, times 1 minus .5 n to the minus 00:19:44.260 --> 00:19:47.310 x times 0.5 to the x. 00:19:47.310 --> 00:19:50.080 A simple binomial. 00:19:50.080 --> 00:19:51.700 Right. 00:19:51.700 --> 00:19:54.980 So if you look at this, the probability 00:19:54.980 --> 00:19:58.499 of the distribution for the children 00:19:58.499 --> 00:20:00.040 is going to look something like this, 00:20:00.040 --> 00:20:04.240 where this is the mean, 0.5. 00:20:04.240 --> 00:20:09.670 And the number of distinct values is going to be n plus 1. 00:20:09.670 --> 00:20:12.100 Right. 00:20:12.100 --> 00:20:18.860 So the expected value of x is 0.5 and turns out 00:20:18.860 --> 00:20:26.900 that the expected value, or the variance of x minus 0.5, which 00:20:26.900 --> 00:20:35.012 is the mean squared, is going to be 0.25 over n. 00:20:35.012 --> 00:20:36.720 So I can show you this on the next slide. 00:20:39.550 --> 00:20:43.965 So you can see, this could be ethanol production, 00:20:43.965 --> 00:20:46.700 it could be growth rate, what have you. 00:20:46.700 --> 00:20:49.210 And you can see that the number of genes that you're 00:20:49.210 --> 00:20:54.720 going to get from dad follows this binomial distribution 00:20:54.720 --> 00:20:58.810 and gives you a spread of different phenotypes 00:20:58.810 --> 00:21:00.790 in the child's generation, depending 00:21:00.790 --> 00:21:03.005 upon how many copies of dad's genes that you inherit. 00:21:07.000 --> 00:21:08.840 But does this make sense to everybody? 00:21:08.840 --> 00:21:11.187 Now would be a great time to ask any questions 00:21:11.187 --> 00:21:12.270 about the details of this. 00:21:12.270 --> 00:21:13.152 Yes? 00:21:13.152 --> 00:21:15.462 AUDIENCE: Can you clarify what x is? 00:21:15.462 --> 00:21:17.780 Is x the fraction of genes inherited-- 00:21:17.780 --> 00:21:22.160 PROFESSOR: The number of genes you inherit from dad. 00:21:22.160 --> 00:21:23.790 The number of genes. 00:21:23.790 --> 00:21:27.565 So it would zero, one, two, up to n. 00:21:27.565 --> 00:21:29.990 AUDIENCE: Shouldn't the expectation of n [INAUDIBLE] 00:21:29.990 --> 00:21:32.415 x be n/2? 00:21:32.415 --> 00:21:33.315 PROFESSOR: I'm sorry. 00:21:33.315 --> 00:21:35.810 It is supposed to be n/2. 00:21:35.810 --> 00:21:41.320 But the last two expectations are 00:21:41.320 --> 00:21:44.847 some of the number of genes you've inherited from dad. 00:21:44.847 --> 00:21:46.835 Right, that's correct. 00:21:46.835 --> 00:21:48.326 Yeah, this slide's wrong. 00:21:55.232 --> 00:21:56.065 Any other questions? 00:21:59.540 --> 00:22:00.220 OK. 00:22:00.220 --> 00:22:06.075 So this is a very simple model but it tells us 00:22:06.075 --> 00:22:08.550 a couple of things, right. 00:22:08.550 --> 00:22:13.350 Which is that as n gets to be very large, 00:22:13.350 --> 00:22:16.125 the effect of each gene gets to be quite small. 00:22:18.650 --> 00:22:21.760 So something could be completely heritable, 00:22:21.760 --> 00:22:26.140 but if it's spread over, say 1,000 genes, 00:22:26.140 --> 00:22:28.840 then it will be very difficult to detect, 00:22:28.840 --> 00:22:31.550 because the effect of each gene would be quite small. 00:22:31.550 --> 00:22:37.300 And furthermore, the variance that you see in the offspring 00:22:37.300 --> 00:22:40.870 will be quite small as well, right, 00:22:40.870 --> 00:22:42.450 in terms of the phenotype. 00:22:42.450 --> 00:22:46.170 Because it's going to be 0.25/n in terms of the expected value. 00:22:46.170 --> 00:22:50.090 So as n gets larger, the number genes that 00:22:50.090 --> 00:22:52.820 contribute to that phenotype increase, 00:22:52.820 --> 00:22:54.855 the variance is going to go down linearly. 00:22:58.580 --> 00:22:59.080 OK. 00:22:59.080 --> 00:23:01.390 So we should just keep this in mind 00:23:01.390 --> 00:23:09.010 as we're looking at discovering these sort of traits 00:23:09.010 --> 00:23:15.070 and the underlying QTLs that can be used to predict them. 00:23:15.070 --> 00:23:19.460 And finally, I'd like to point out one other detail which 00:23:19.460 --> 00:23:21.920 is that, if genes are linked, that is, 00:23:21.920 --> 00:23:25.020 if they're in close proximity to one another in the genome 00:23:25.020 --> 00:23:26.620 and it makes it very unlikely there's 00:23:26.620 --> 00:23:29.340 going to be crossing over between them, 00:23:29.340 --> 00:23:31.876 then they're going to act as a unit. 00:23:31.876 --> 00:23:38.450 And if they act as a unit, then we'll get marker correlation. 00:23:38.450 --> 00:23:41.140 And you can also see, effectively, 00:23:41.140 --> 00:23:42.940 that the effect size of those two genes 00:23:42.940 --> 00:23:45.520 is going to be larger. 00:23:45.520 --> 00:23:48.500 And in more complicated models, we obviously 00:23:48.500 --> 00:23:52.930 wouldn't have the same effect size for each gene. 00:23:52.930 --> 00:23:55.250 The effect size might be quite large for some genes, 00:23:55.250 --> 00:23:56.780 might be quite small for some genes. 00:24:00.480 --> 00:24:04.880 And we'll see the effects of marker correlation 00:24:04.880 --> 00:24:08.150 in a little bit. 00:24:08.150 --> 00:24:12.409 So the way we're going to model this is we're going to-- this 00:24:12.409 --> 00:24:14.200 is a definition of the variables that we're 00:24:14.200 --> 00:24:17.160 going to be talking about today. 00:24:17.160 --> 00:24:21.745 And the essential idea is quite simple. 00:24:33.280 --> 00:24:38.140 So the phenotype of an individual-- so p sub 00:24:38.140 --> 00:24:40.620 i is the phenotype of an individual, 00:24:40.620 --> 00:24:45.170 is going to be equal to some function of their genotype 00:24:45.170 --> 00:24:47.285 plus an environmental component. 00:24:49.890 --> 00:24:57.170 This function is the critical thing that we want to discover. 00:24:57.170 --> 00:25:00.470 This function, f, is mapping from the genotype 00:25:00.470 --> 00:25:05.019 of an individual to its phenotype. 00:25:05.019 --> 00:25:06.560 And the environmental component could 00:25:06.560 --> 00:25:14.320 be how well something is fed, how much sunlight it gets, 00:25:14.320 --> 00:25:18.910 things that can greatly influence things like growth 00:25:18.910 --> 00:25:22.550 but they're not described by genetics. 00:25:22.550 --> 00:25:25.630 But this function is going to encapsulate 00:25:25.630 --> 00:25:29.150 what we know about how the genetics 00:25:29.150 --> 00:25:33.145 of a particular individual influences a trait. 00:25:36.600 --> 00:25:46.710 And thus, if we consider a population of individuals, 00:25:46.710 --> 00:25:50.250 the phenotypic variance is going to be 00:25:50.250 --> 00:25:57.220 equal to the genotypic variance plus the environmental variance 00:25:57.220 --> 00:26:05.295 plus two times the covariance between the genotype 00:26:05.295 --> 00:26:06.086 in the environment. 00:26:08.590 --> 00:26:12.280 And we're going to assume, as most studies do, 00:26:12.280 --> 00:26:16.200 that there is no correlation between genotype 00:26:16.200 --> 00:26:17.230 and environment. 00:26:17.230 --> 00:26:19.800 So this term disappears. 00:26:19.800 --> 00:26:23.410 So what we're left with is that the observed phenotypic 00:26:23.410 --> 00:26:25.660 variance is equal to the genotypic variance 00:26:25.660 --> 00:26:27.955 plus the environmental variance. 00:26:31.190 --> 00:26:35.870 And what we would like to do is to come up with a function 00:26:35.870 --> 00:26:41.960 f, that best predicts the genotypic component 00:26:41.960 --> 00:26:44.340 of this equation. 00:26:44.340 --> 00:26:47.041 There's nothing we can do about environmental variance. 00:26:47.041 --> 00:26:47.540 Right. 00:26:50.680 --> 00:26:53.894 But we can measure it. 00:26:53.894 --> 00:26:55.310 Does anybody have any ideas how we 00:26:55.310 --> 00:27:00.361 could measure environmental variance? 00:27:00.361 --> 00:27:00.860 Yes? 00:27:00.860 --> 00:27:02.360 AUDIENCE: Study populations in which 00:27:02.360 --> 00:27:04.588 there's some kind of controlled environment. 00:27:08.110 --> 00:27:11.610 So you study populations that one population 00:27:11.610 --> 00:27:13.610 is one with a homogeneous. 00:27:13.610 --> 00:27:16.332 And another one was a completely different one. 00:27:16.332 --> 00:27:17.040 PROFESSOR: Right. 00:27:17.040 --> 00:27:20.880 So what we could do is we could use controls. 00:27:20.880 --> 00:27:26.290 So typically what we could do is we could study in environments 00:27:26.290 --> 00:27:28.310 where we try and control the environment exactly 00:27:28.310 --> 00:27:33.670 to eliminate this as much as we possibly can, for example. 00:27:33.670 --> 00:27:35.600 As we'll see that we also can do things 00:27:35.600 --> 00:27:37.590 like study clones, where individuals 00:27:37.590 --> 00:27:40.770 have exactly the same genotype. 00:27:40.770 --> 00:27:43.340 And then, all of the variance that we observe-- 00:27:43.340 --> 00:27:47.100 if this term vanishes because the genotypes are identical, 00:27:47.100 --> 00:27:48.370 it is due to the environment. 00:27:50.900 --> 00:27:52.520 So typically, if you're doing things 00:27:52.520 --> 00:27:56.680 like studying humans, since cloning humans isn't really 00:27:56.680 --> 00:28:01.670 a good idea to actually measure environmental variance, 00:28:01.670 --> 00:28:12.110 right, what you could do is you can look at identical twins. 00:28:12.110 --> 00:28:15.080 And identical twins give you a way 00:28:15.080 --> 00:28:17.640 to get at the question of how much environment variance 00:28:17.640 --> 00:28:19.325 there is for a particular phenotype. 00:28:22.110 --> 00:28:28.560 So in sum, this is replicates what I have here 00:28:28.560 --> 00:28:31.230 on the left-hand side of the board. 00:28:31.230 --> 00:28:33.177 And note that today we'll be talking 00:28:33.177 --> 00:28:35.010 about the idea of discovering this function, 00:28:35.010 --> 00:28:38.120 f, and how well we can discover f, 00:28:38.120 --> 00:28:39.620 which is really important, right. 00:28:39.620 --> 00:28:42.530 It's fundamental to be able to predict phenotype 00:28:42.530 --> 00:28:44.860 from genotype. 00:28:44.860 --> 00:28:51.250 It's an extraordinarily central question in genetics. 00:28:51.250 --> 00:28:55.510 And when we do the prediction, there are two kinds of-- oh, 00:28:55.510 --> 00:28:56.480 there's a question? 00:28:56.480 --> 00:28:58.146 AUDIENCE: Could you please explain again 00:28:58.146 --> 00:29:01.540 why the co-variance drops out or it goes away. 00:29:01.540 --> 00:29:03.290 PROFESSOR: Yeah, the co-variance drops out 00:29:03.290 --> 00:29:05.180 because we're going to assume that genotype 00:29:05.180 --> 00:29:06.513 and environment are independent. 00:29:09.030 --> 00:29:12.220 Now if they're not independent, it won't drop out. 00:29:12.220 --> 00:29:16.980 But making that assumption-- and of course, for human studies 00:29:16.980 --> 00:29:19.710 you can't really make that assumption completely, right? 00:29:19.710 --> 00:29:22.020 And one of the problems in doing these sorts of studies 00:29:22.020 --> 00:29:25.830 is that it's very, very easy to get confounded. 00:29:25.830 --> 00:29:28.250 Because when you're trying to decompose 00:29:28.250 --> 00:29:31.694 the observed variance and height, for example. 00:29:31.694 --> 00:29:35.750 You know, there's what mom and dad provided to an individual 00:29:35.750 --> 00:29:37.500 in terms of their height, and there's also 00:29:37.500 --> 00:29:40.060 how much junior ate, right. 00:29:40.060 --> 00:29:42.340 And whether he went to McDonald's a lot, or you know, 00:29:42.340 --> 00:29:44.876 was going to Whole Foods a lot. 00:29:44.876 --> 00:29:46.000 You know, who knows, right? 00:29:46.000 --> 00:29:48.650 But this component and this component, 00:29:48.650 --> 00:29:50.960 it's easy to get confounded between them 00:29:50.960 --> 00:29:55.330 and sometimes you can imagine that genotype 00:29:55.330 --> 00:29:58.670 is related to place of origin in the world. 00:29:58.670 --> 00:30:00.566 And that has a lot to do with environment. 00:30:00.566 --> 00:30:02.565 And so this term wouldn't necessarily disappear. 00:30:07.451 --> 00:30:07.950 OK. 00:30:07.950 --> 00:30:09.533 So there are two kinds of heritability 00:30:09.533 --> 00:30:11.050 I'd like to touch upon today. 00:30:11.050 --> 00:30:14.590 And it's important that you remember there are two kinds 00:30:14.590 --> 00:30:19.810 and one is extraordinarily difficult to recover 00:30:19.810 --> 00:30:24.990 and the other one is in some sense, a more constrained 00:30:24.990 --> 00:30:27.750 problem, because we're much better at building models 00:30:27.750 --> 00:30:30.430 for that kind of heritability estimate. 00:30:30.430 --> 00:30:33.810 The first is broad-sense heritability, 00:30:33.810 --> 00:30:38.560 which describes the upper bound for phenotypic prediction given 00:30:38.560 --> 00:30:39.980 an arbitrary model. 00:30:39.980 --> 00:30:43.430 So it's the total contribution to phenotypic variance 00:30:43.430 --> 00:30:45.740 from genetic causes. 00:30:45.740 --> 00:30:47.660 And we can estimate that, right. 00:30:47.660 --> 00:30:51.420 And we'll see how we can estimate it in a moment. 00:30:51.420 --> 00:30:55.030 And narrow-sense heritability is defined as, 00:30:55.030 --> 00:30:58.710 how much of the heritability can we describe 00:30:58.710 --> 00:31:03.750 when we restrict f to be a linear model. 00:31:03.750 --> 00:31:10.480 So when f is simply linear, as the sum of terms, 00:31:10.480 --> 00:31:15.000 that describes the maximum narrow-sense heritability we 00:31:15.000 --> 00:31:17.950 can recover in terms of the fraction of phenotypic 00:31:17.950 --> 00:31:19.950 variance we can capture in f. 00:31:22.690 --> 00:31:27.820 And it's very useful because it turns out 00:31:27.820 --> 00:31:32.257 that we can compute both broad-sense and narrow-sense 00:31:32.257 --> 00:31:33.840 heritability from first principles-- I 00:31:33.840 --> 00:31:36.590 mean from experiment. 00:31:36.590 --> 00:31:41.860 And the difference between them is part of our quest today. 00:31:41.860 --> 00:31:44.080 Our quest is, to answer the question, 00:31:44.080 --> 00:31:45.990 where is the missing heritability? 00:31:45.990 --> 00:31:52.050 Why can't we build an Oracle f that perfectly 00:31:52.050 --> 00:31:55.390 predicts phenotype from genotype? 00:31:58.270 --> 00:32:03.519 So on that line-- I just want to give you some caveats. 00:32:03.519 --> 00:32:06.060 One is that we're always talking about populations when we're 00:32:06.060 --> 00:32:07.870 talking about heritability because it's 00:32:07.870 --> 00:32:10.030 how we're going to estimate it. 00:32:10.030 --> 00:32:13.580 And when you hear people talk about heritability, 00:32:13.580 --> 00:32:15.550 oftentimes they won't qualify it in terms 00:32:15.550 --> 00:32:18.030 of whether it's broad-sense or narrow-sense. 00:32:18.030 --> 00:32:20.170 And so you should ask them if you're 00:32:20.170 --> 00:32:23.310 engaged in a scientific discussion with them. 00:32:23.310 --> 00:32:26.750 And as we've already discussed, sometimes estimation 00:32:26.750 --> 00:32:30.730 is difficult because of matching environment and eliminating 00:32:30.730 --> 00:32:33.210 this term, the environmental term 00:32:33.210 --> 00:32:37.260 can be a challenge when you're out of the laboratory. 00:32:37.260 --> 00:32:40.330 Like when you're dealing with humans. 00:32:40.330 --> 00:32:43.930 So, let's talk about broad-sense heritability. 00:32:46.660 --> 00:32:52.980 Imagine that we measure environmental variants simply 00:32:52.980 --> 00:32:58.650 by looking at environmental twins or clones, right. 00:32:58.650 --> 00:33:02.470 Because if we, for example, take a bunch of yeast 00:33:02.470 --> 00:33:04.990 that are genotypically identical. 00:33:04.990 --> 00:33:07.660 And we grow them up separately, and we 00:33:07.660 --> 00:33:13.540 measure a trait like how well they respond 00:33:13.540 --> 00:33:17.870 to a particular chemical or their growth rate, 00:33:17.870 --> 00:33:21.760 then the variance we see from each individual to individual 00:33:21.760 --> 00:33:27.850 is simply environmental, because they're genetically identical. 00:33:27.850 --> 00:33:28.440 So 00:33:28.440 --> 00:33:31.510 we can, in that particular case, exactly 00:33:31.510 --> 00:33:33.800 quantify the environmental variance 00:33:33.800 --> 00:33:38.200 given that every individual is genetically identical. 00:33:38.200 --> 00:33:41.070 We simply measure all the growth rates 00:33:41.070 --> 00:33:42.450 and we compute the variance. 00:33:42.450 --> 00:33:45.160 And that's the environmental variance. 00:33:45.160 --> 00:33:47.900 OK? 00:33:47.900 --> 00:33:51.225 As I said for humans, the best we can do is identical twins. 00:33:53.910 --> 00:33:56.680 Monozygotic twins. 00:33:56.680 --> 00:34:01.320 You can go out and for pairs of twins that are identical, 00:34:01.320 --> 00:34:04.630 you can measure height or any other trait that you like 00:34:04.630 --> 00:34:07.370 and compute the variance. 00:34:07.370 --> 00:34:11.239 And then that is an estimate of the environmental component 00:34:11.239 --> 00:34:16.690 of that, because they should be genetically identical. 00:34:19.650 --> 00:34:23.300 And big H squared-- broad-sense is always 00:34:23.300 --> 00:34:25.940 capital H squared and narrow-sense is always 00:34:25.940 --> 00:34:27.420 little h squared. 00:34:27.420 --> 00:34:29.630 Big H squared, which is broad-sense 00:34:29.630 --> 00:34:32.270 heritability is very simple then. 00:34:32.270 --> 00:34:35.290 It's the phenotypic variance, minus the environmental 00:34:35.290 --> 00:34:37.449 variance, over the phenotypic variance. 00:34:37.449 --> 00:34:40.250 So it's the fraction of phenotypic experience 00:34:40.250 --> 00:34:44.587 that can be explained from genetic causes. 00:34:44.587 --> 00:34:46.515 Is that clear to everybody? 00:34:49.420 --> 00:34:52.030 Any questions at all about this? 00:34:55.030 --> 00:34:56.270 OK. 00:34:56.270 --> 00:35:01.030 So, for example, on the right-hand hand side 00:35:01.030 --> 00:35:04.540 here, those three purplish squares 00:35:04.540 --> 00:35:09.310 have three different populations, 00:35:09.310 --> 00:35:12.230 which are genotypically identical. 00:35:12.230 --> 00:35:15.250 They have two genes, a little a, a little a, big A, a little A, 00:35:15.250 --> 00:35:19.280 and big A, big A. And each one is a variance of 1.0. 00:35:19.280 --> 00:35:24.240 out So since there are genetically identical, 00:35:24.240 --> 00:35:29.340 we know that the environmental variance has to be 1.0. 00:35:29.340 --> 00:35:33.640 On the left-hand side, you see the genotypic variance. 00:35:33.640 --> 00:35:37.420 And that reminds us of where we started today. 00:35:37.420 --> 00:35:40.710 It depends on the number of alleles you get of big A, 00:35:40.710 --> 00:35:43.390 as to what the value is. 00:35:43.390 --> 00:35:46.110 And when you put all of that together, 00:35:46.110 --> 00:35:48.920 you get a total variance of 3. 00:35:48.920 --> 00:35:52.840 And so big H squared is simply the genotypic variance, 00:35:52.840 --> 00:35:55.740 which is 2, over the total phenotypic variance, which 00:35:55.740 --> 00:35:56.680 is 3. 00:35:56.680 --> 00:35:58.210 So big H squared is 2/3. 00:36:01.150 --> 00:36:04.274 And so that is a way of computing 00:36:04.274 --> 00:36:05.315 broad-sense heritability. 00:36:09.580 --> 00:36:15.530 Now, if we think about our models, 00:36:15.530 --> 00:36:18.110 we can see that narrow-sense heritability 00:36:18.110 --> 00:36:20.150 has some very nice properties. 00:36:20.150 --> 00:36:21.210 Right. 00:36:21.210 --> 00:36:30.175 That is, if we build and add a model of phenotype, 00:36:30.175 --> 00:36:31.675 to get at narrow-sense heritability. 00:36:31.675 --> 00:36:37.270 So if we were to constraint f here to be linear, 00:36:37.270 --> 00:36:40.880 it's simply going to be a very simple linear model. 00:36:40.880 --> 00:36:46.050 For each particular QTL that we discover, 00:36:46.050 --> 00:36:49.640 we assign an effect size beta to it, 00:36:49.640 --> 00:36:52.900 or a coefficient that describes its deviation 00:36:52.900 --> 00:36:57.330 from the mean for that particular trait. 00:36:57.330 --> 00:37:00.880 And we have an offset, beta zero. 00:37:00.880 --> 00:37:03.550 So our simple linear model is going to take all the discovery 00:37:03.550 --> 00:37:06.270 QTLs that we have-- take each QTL 00:37:06.270 --> 00:37:10.120 and discover which allelic form it's in. 00:37:10.120 --> 00:37:14.620 Typically it's considered either in zero or one form. 00:37:14.620 --> 00:37:23.890 And then add a beta j, where j is the particular QTL 00:37:23.890 --> 00:37:26.220 deviation from mean value. 00:37:26.220 --> 00:37:29.594 Add them all together to compute the phenotype. 00:37:29.594 --> 00:37:30.950 OK. 00:37:30.950 --> 00:37:36.540 So, this is a very simple additive model 00:37:36.540 --> 00:37:39.500 and a consequence of this model is 00:37:39.500 --> 00:37:44.620 that if you think about an F1 or a child of two parents, 00:37:44.620 --> 00:37:50.740 as we said earlier, a child is going to inherit roughly half 00:37:50.740 --> 00:37:55.380 of the alleles from mom and half of the alleles from dad. 00:37:55.380 --> 00:37:58.320 And so for additive models like this, 00:37:58.320 --> 00:38:04.120 the expected value of the child's trait value 00:38:04.120 --> 00:38:08.087 is going to be the midpoint of mom and dad. 00:38:08.087 --> 00:38:10.170 And that can be derived directly from the equation 00:38:10.170 --> 00:38:13.740 above, because you're getting half of the QTLs 00:38:13.740 --> 00:38:15.750 from mom and half of the QTLs from dad. 00:38:18.350 --> 00:38:20.390 So this was observed a long time ago, right, 00:38:20.390 --> 00:38:30.470 because if you did studies and you looked at the deviation 00:38:30.470 --> 00:38:35.040 from the midpoint of parents for human height. 00:38:35.040 --> 00:38:42.320 You can see that the children fall pretty 00:38:42.320 --> 00:38:49.360 close to mid-parent line, where the y-axis here 00:38:49.360 --> 00:38:54.980 is the height in inches and that suggests 00:38:54.980 --> 00:39:04.295 that much of human height can be modeled by a narrow-sense based 00:39:04.295 --> 00:39:05.160 heritability model. 00:39:09.660 --> 00:39:17.970 Now, once again, narrow-sense heritability 00:39:17.970 --> 00:39:20.270 is the fraction of phenotypic variance explained 00:39:20.270 --> 00:39:22.620 by an additive model. 00:39:22.620 --> 00:39:30.690 And we've talked before about the model itself. 00:39:30.690 --> 00:39:32.770 And little h squared is simply going 00:39:32.770 --> 00:39:36.100 to be the amount of variance explained 00:39:36.100 --> 00:39:40.540 by the additive model over the total phenotypic variance. 00:39:40.540 --> 00:39:45.920 And the additive variance is shown on the right-hand side. 00:39:45.920 --> 00:39:50.980 That equation boils down to, you take the phenotypic variance 00:39:50.980 --> 00:39:57.150 and you subtract off the variance that's environmental 00:39:57.150 --> 00:40:01.260 and that cannot be explained by the additive variance, 00:40:01.260 --> 00:40:03.885 and what you're left with is the additive variance. 00:40:09.230 --> 00:40:12.010 And once again, coming back to the question 00:40:12.010 --> 00:40:15.850 of missing heritability, if we observe 00:40:15.850 --> 00:40:19.540 that what we can estimate for little h squared 00:40:19.540 --> 00:40:23.370 is below what we expect, that gap 00:40:23.370 --> 00:40:24.615 has to be explained somehow. 00:40:27.550 --> 00:40:32.150 Some typical values for theoretical h squared. 00:40:32.150 --> 00:40:33.800 So this is not measured h squared 00:40:33.800 --> 00:40:38.020 in terms of building a model and testing it like this. 00:40:38.020 --> 00:40:40.020 But what we can do is we can theoretically 00:40:40.020 --> 00:40:43.510 estimate what h squared should be, 00:40:43.510 --> 00:40:46.585 by looking at the fraction of identity between individuals. 00:40:50.630 --> 00:40:52.930 Morphological traits tend to have 00:40:52.930 --> 00:40:55.810 higher h squared for the fitness traits. 00:40:55.810 --> 00:41:01.320 So human height has a little h square of about 0.8. 00:41:01.320 --> 00:41:05.300 And for those ranchers out there in the audience, 00:41:05.300 --> 00:41:08.120 you'll be happy to know that cattle yearly weight has 00:41:08.120 --> 00:41:10.770 heritability of about 0.35. 00:41:10.770 --> 00:41:14.610 Now, things like life history which are fitness traits 00:41:14.610 --> 00:41:17.980 are less heritable. 00:41:17.980 --> 00:41:21.980 Which would suggest that looking at how long your parents lived 00:41:21.980 --> 00:41:24.470 and trying to estimate how long you're going to live 00:41:24.470 --> 00:41:27.502 is not as productive as looking at how tall you 00:41:27.502 --> 00:41:28.710 are compared to your parents. 00:41:32.677 --> 00:41:34.260 And there's a complete table that I've 00:41:34.260 --> 00:41:37.080 included in the slides for you to look at, 00:41:37.080 --> 00:41:41.050 but it's too small to read on the screen. 00:41:41.050 --> 00:41:45.020 OK, so now we're going to turn to computational models 00:41:45.020 --> 00:41:49.660 and how we can discover a model that figures out 00:41:49.660 --> 00:41:54.870 where the QTLs are, and then assigns that function f to them 00:41:54.870 --> 00:41:56.870 so we can predict phenotype from genotype. 00:41:59.560 --> 00:42:04.190 And we're going to be taking our example from this paper 00:42:04.190 --> 00:42:07.170 by Bloom, et al, which I posted on the Stellar site. 00:42:07.170 --> 00:42:10.300 And it came out last year and it's 00:42:10.300 --> 00:42:15.520 wonderful study in QTL analysis. 00:42:15.520 --> 00:42:20.600 And the setup for this study is quite simple. 00:42:20.600 --> 00:42:23.140 What they did was, is they took two different strains 00:42:23.140 --> 00:42:28.730 of yeast, RM and BY, and they crossed them 00:42:28.730 --> 00:42:35.720 and produced roughly 1,000 F1s. 00:42:35.720 --> 00:42:39.750 And RM and BY are very similar. 00:42:39.750 --> 00:42:44.710 They are about, I think it's about 35,000 snips 00:42:44.710 --> 00:42:46.954 between them. 00:42:46.954 --> 00:42:50.280 Only about 0.5% of their genomes are different. 00:42:50.280 --> 00:42:52.130 So they're really close. 00:42:55.150 --> 00:42:58.670 Just for point of reference, you know, the distance between me 00:42:58.670 --> 00:43:03.622 and you is something like one base for every thousand? 00:43:03.622 --> 00:43:04.455 Something like that. 00:43:07.800 --> 00:43:10.120 And then they assayed all those F1s. 00:43:10.120 --> 00:43:12.340 They genotyped them all. 00:43:12.340 --> 00:43:14.980 So to genotype them, what you do is 00:43:14.980 --> 00:43:16.720 you know what the parental genotypes are 00:43:16.720 --> 00:43:18.980 because they sequence both parents. 00:43:18.980 --> 00:43:23.250 The mom and dad, so to speak, at 50x coverage. 00:43:23.250 --> 00:43:25.750 So they knew the genome sequence is completely 00:43:25.750 --> 00:43:27.780 for both mom and dad. 00:43:27.780 --> 00:43:31.620 And then for each one of the 1,000 F1s 00:43:31.620 --> 00:43:35.170 they put them on a microarray and what 00:43:35.170 --> 00:43:38.030 is shown on the very bottom left is 00:43:38.030 --> 00:43:40.900 a result of genotype in an individual 00:43:40.900 --> 00:43:44.880 where they can see each chromosome 00:43:44.880 --> 00:43:47.331 and whether it came from mom or from dad. 00:43:47.331 --> 00:43:48.830 And you can't see it here, but there 00:43:48.830 --> 00:43:52.540 are 16 different chromosomes and the alternating purple and 00:43:52.540 --> 00:43:56.370 yellow colors show whether that particular part of the genome 00:43:56.370 --> 00:43:59.050 came from mom or from dad. 00:43:59.050 --> 00:44:04.530 So they know for each individual, its source. 00:44:04.530 --> 00:44:07.000 From the left or the right strain. 00:44:07.000 --> 00:44:08.200 OK. 00:44:08.200 --> 00:44:12.150 And they have a thousand different genetic makeups. 00:44:12.150 --> 00:44:17.010 And then they asked, for each one of those individuals, 00:44:17.010 --> 00:44:23.420 how well could they grow in 46 different conditions? 00:44:23.420 --> 00:44:26.610 So they exposed them to different sugars, 00:44:26.610 --> 00:44:32.130 to different unfavorable environments and so forth. 00:44:32.130 --> 00:44:36.212 And they measured growth rate as shown on the right-hand side. 00:44:36.212 --> 00:44:37.920 Or right in the middle, that little thing 00:44:37.920 --> 00:44:40.800 that looks like a bunch of little dots of various sizes. 00:44:40.800 --> 00:44:43.420 By measuring colony size, they could 00:44:43.420 --> 00:44:47.090 measure how well the yeast were growing. 00:44:47.090 --> 00:44:49.680 And so they had two different things, right. 00:44:49.680 --> 00:44:53.800 They had the exact genotype of each individual, 00:44:53.800 --> 00:44:55.520 and they also had how well it was 00:44:55.520 --> 00:44:59.010 growing in a particular condition. 00:44:59.010 --> 00:45:01.250 And so for each condition, they wanted 00:45:01.250 --> 00:45:04.280 to associate the genotype of the individual 00:45:04.280 --> 00:45:05.582 to how well it was growing. 00:45:05.582 --> 00:45:06.290 To its phenotype. 00:45:09.970 --> 00:45:14.740 Now, one fair question is, of these different conditions, 00:45:14.740 --> 00:45:18.260 how many of them were really independent? 00:45:18.260 --> 00:45:20.860 And so to analyze that, they looked 00:45:20.860 --> 00:45:22.710 at the correlation between growth rates 00:45:22.710 --> 00:45:26.350 across conditions to try and figure out whether or not 00:45:26.350 --> 00:45:32.270 they actually had 46 different traits they were measuring. 00:45:32.270 --> 00:45:35.330 So this is a correlation matrix that 00:45:35.330 --> 00:45:38.350 is too small to read on the screen. 00:45:38.350 --> 00:45:41.790 The colors are somewhat visible, where the blue colors 00:45:41.790 --> 00:45:44.310 are perfect correlation and the red colors 00:45:44.310 --> 00:45:46.650 are perfect anti-correlation. 00:45:46.650 --> 00:45:50.839 And you can see that in certain areas of this grid, 00:45:50.839 --> 00:45:52.380 things are more correlated, like what 00:45:52.380 --> 00:45:57.040 sugars the yeast liked to eat. 00:45:57.040 --> 00:46:01.459 But suffice to say, they had a large collection 00:46:01.459 --> 00:46:02.875 of traits they wanted to estimate. 00:46:06.200 --> 00:46:12.720 So, now we want to build a computational model. 00:46:12.720 --> 00:46:15.030 So our next step is figuring out how 00:46:15.030 --> 00:46:17.240 to find those places in the genome that 00:46:17.240 --> 00:46:21.390 allows us to predict, how well, given a trait, 00:46:21.390 --> 00:46:23.390 the yeast would grow. 00:46:23.390 --> 00:46:26.650 The actual growth rate. 00:46:26.650 --> 00:46:44.110 So the key idea is this-- you have genetic markers, which 00:46:44.110 --> 00:46:46.670 are snips down the genome and you're 00:46:46.670 --> 00:46:50.180 going to test a particular marker. 00:46:50.180 --> 00:46:57.360 And if this is a particular trait, 00:46:57.360 --> 00:47:01.320 one possibility is that-- let's say 00:47:01.320 --> 00:47:04.900 that this marker could be either 0 or 1. 00:47:04.900 --> 00:47:08.310 Without loss of generality, it could 00:47:08.310 --> 00:47:10.660 be that here are all the individuals where 00:47:10.660 --> 00:47:12.700 the marker is zero. 00:47:12.700 --> 00:47:19.370 And here are all the markers where the marker is 1. 00:47:19.370 --> 00:47:25.790 And really, fundamentally, whether an individual 00:47:25.790 --> 00:47:28.470 has a 0 or a 1 marker, it doesn't really 00:47:28.470 --> 00:47:33.380 change its growth rate very much. 00:47:33.380 --> 00:47:34.220 OK? 00:47:34.220 --> 00:47:36.900 It's more or less identical. 00:47:36.900 --> 00:47:50.800 It's also possible that this is best 00:47:50.800 --> 00:47:57.120 modeled by two different means for a given trait. 00:47:57.120 --> 00:48:03.780 That when the marker is 1, you're growing-- actually 00:48:03.780 --> 00:48:10.210 this is going to be the growth rate on the x-axis. 00:48:10.210 --> 00:48:11.890 The y-axis is the density. 00:48:11.890 --> 00:48:14.970 That you're growing much better when you have a 1 00:48:14.970 --> 00:48:18.970 in that marker position than a zero. 00:48:18.970 --> 00:48:22.240 And so we need to distinguish between these two cases 00:48:22.240 --> 00:48:25.350 when the marker is predictive of growth rate 00:48:25.350 --> 00:48:28.000 and when the marker is not predictive of growth rate. 00:48:30.630 --> 00:48:32.770 And we've talked about lod likelihood tests before 00:48:32.770 --> 00:48:36.060 and you can see one on the very top. 00:48:36.060 --> 00:48:38.410 And you can see there's an additional degree of freedom 00:48:38.410 --> 00:48:41.117 that we have in the top prediction versus the bottom 00:48:41.117 --> 00:48:42.950 because we're using two different means that 00:48:42.950 --> 00:48:47.530 are conditioned upon the genotypic value 00:48:47.530 --> 00:48:48.738 at a particular marker. 00:48:53.230 --> 00:48:57.650 So we have a lot of different markers indeed. 00:48:57.650 --> 00:49:00.980 So we have-- let's see here, the exact number. 00:49:00.980 --> 00:49:06.770 I think it's about 13,000 markers they had in this study. 00:49:06.770 --> 00:49:07.280 No. 00:49:07.280 --> 00:49:12.620 11,623 different unique markers they found. 00:49:12.620 --> 00:49:15.500 That they could discover, that weren't linked together. 00:49:15.500 --> 00:49:18.210 We talked about linkage earlier on. 00:49:18.210 --> 00:49:23.260 So you've got over 11,000 markers. 00:49:23.260 --> 00:49:26.430 You're going to do a lod likelihood 00:49:26.430 --> 00:49:29.065 test to compute this lod odds score. 00:49:33.750 --> 00:49:36.180 Do we have to worry about multiple hypothesis correction 00:49:36.180 --> 00:49:38.640 here? 00:49:38.640 --> 00:49:41.240 Because you're testing over 11,000 00:49:41.240 --> 00:49:42.810 markers to see whether or not they're 00:49:42.810 --> 00:49:45.360 significant for one trait. 00:49:45.360 --> 00:49:45.860 Right. 00:49:52.920 --> 00:50:01.520 So one thing that we could do is imagine that what we did was 00:50:01.520 --> 00:50:05.970 we scrambled the association between phenotypes 00:50:05.970 --> 00:50:07.620 and individuals. 00:50:07.620 --> 00:50:11.136 So we just randomized it and we did that a thousand times. 00:50:11.136 --> 00:50:15.670 And each time we did it, we computed the distribution 00:50:15.670 --> 00:50:18.330 of these lod scores. 00:50:18.330 --> 00:50:23.400 Because we have broken the association between phenotype 00:50:23.400 --> 00:50:26.410 and genotype, the lod scores which 00:50:26.410 --> 00:50:29.680 we should be seeing if we did this randomization, 00:50:29.680 --> 00:50:33.360 should correspond to essentially noise. 00:50:33.360 --> 00:50:35.360 But we would see it random. 00:50:35.360 --> 00:50:39.750 So it's a null distribution we can look at. 00:50:39.750 --> 00:50:44.875 And so what we'll see is a distribution of lod scores. 00:50:49.410 --> 00:50:51.440 This is the lod. 00:50:51.440 --> 00:51:03.980 This is the probability from a null, a permutation test. 00:51:03.980 --> 00:51:07.970 And since we actually have done the randomization 00:51:07.970 --> 00:51:15.725 over all 11,000 markers, we can directly draw a line 00:51:15.725 --> 00:51:19.960 and ask what are the chances that a lod score would 00:51:19.960 --> 00:51:25.500 be greater than or equal to a particular value at random? 00:51:25.500 --> 00:51:27.730 And we can pick an area inside this tail, 00:51:27.730 --> 00:51:29.660 let's say 0.05, because that's what 00:51:29.660 --> 00:51:32.590 the authors of this particular paper used 00:51:32.590 --> 00:51:37.780 and ask what value of a lod score 00:51:37.780 --> 00:51:42.500 would be very unlikely to have by chance? 00:51:42.500 --> 00:51:48.330 It turns out in their first iteration, it was 2.63. 00:51:48.330 --> 00:51:53.500 That a lod score over 2.63 had a 0.05 chance 00:51:53.500 --> 00:51:59.430 or less of occurring in randomly permuted data. 00:51:59.430 --> 00:52:03.640 And since a permuted data contained all of the markers, 00:52:03.640 --> 00:52:07.700 we don't have to do any multiple hypothesis correction. 00:52:07.700 --> 00:52:10.410 So you can directly compare the statistic 00:52:10.410 --> 00:52:15.520 that you compute against a threshold 00:52:15.520 --> 00:52:21.330 and accept any marker or QTL that has a lod score greater, 00:52:21.330 --> 00:52:26.720 in this case then 2.63 and put it in your model. 00:52:26.720 --> 00:52:30.200 And everything else you can reject. 00:52:30.200 --> 00:52:32.520 And so you start by building a model out 00:52:32.520 --> 00:52:34.870 of all of the markers that are significant 00:52:34.870 --> 00:52:36.670 at this particular level. 00:52:39.750 --> 00:52:44.080 You then assemble the model and you can now 00:52:44.080 --> 00:52:47.860 predict phenotype from genotype. 00:52:47.860 --> 00:52:50.710 But of course, you're going to make errors, right. 00:52:50.710 --> 00:52:53.490 For each individual, there's going to be an error. 00:52:53.490 --> 00:53:05.370 You're going to have a residual for each individual that 00:53:05.370 --> 00:53:15.880 is going to be the phenotype minus the genotype 00:53:15.880 --> 00:53:18.390 of the individual. 00:53:18.390 --> 00:53:22.200 So this is the error that you're making. 00:53:22.200 --> 00:53:27.060 So what these folks did was that you first 00:53:27.060 --> 00:53:34.150 look at predicting the phenotype directly, 00:53:34.150 --> 00:53:37.620 and you pick all the QTLs that are significant at that level. 00:53:37.620 --> 00:53:40.097 And then you compute the residuals 00:53:40.097 --> 00:53:41.680 and you try and predict the residuals. 00:53:44.700 --> 00:53:49.370 And you try and find additional QTLs 00:53:49.370 --> 00:53:55.910 that are significant after you have picked the original ones. 00:53:55.910 --> 00:53:57.410 OK. 00:53:57.410 --> 00:54:02.190 So why might this produce more QTLs then the original pass? 00:54:09.040 --> 00:54:11.190 What do you think? 00:54:11.190 --> 00:54:14.930 Why is it that trying to predict the residuals is 00:54:14.930 --> 00:54:17.642 a good idea after you've tried to predict 00:54:17.642 --> 00:54:18.600 the phenotype directly? 00:54:23.530 --> 00:54:25.168 Any ideas about that? 00:54:34.060 --> 00:54:36.550 Well, what this is telling us, is 00:54:36.550 --> 00:54:39.640 that these QTLs we're going to predict now 00:54:39.640 --> 00:54:44.310 were not significant enough in the original pass, 00:54:44.310 --> 00:54:48.210 but when we're looking at what's left over, after we subtract 00:54:48.210 --> 00:54:50.660 off the effect of all the other QTLs, 00:54:50.660 --> 00:54:52.916 other things might pop up. 00:54:52.916 --> 00:54:57.300 But in some sense, we're obscured by the original QTLs. 00:54:57.300 --> 00:55:00.890 Once we subtract off their influence, 00:55:00.890 --> 00:55:04.500 we can see things that we didn't see before. 00:55:04.500 --> 00:55:07.470 And we start gathering up these additional QTLs 00:55:07.470 --> 00:55:10.340 to predict the residual components. 00:55:10.340 --> 00:55:13.290 And so they do this three times. 00:55:13.290 --> 00:55:15.650 So they predict the original set of QTLs 00:55:15.650 --> 00:55:20.390 and then they iterate three time on the residuals 00:55:20.390 --> 00:55:24.150 to find and fit a linear model that predicts a given 00:55:24.150 --> 00:55:28.230 trait from a collection of QTLs that they discover. 00:55:28.230 --> 00:55:29.830 Yes? 00:55:29.830 --> 00:55:30.496 AUDIENCE: Sorry. 00:55:30.496 --> 00:55:32.670 I'm still confused. 00:55:32.670 --> 00:55:40.328 The second round? [INAUDIBLE] done three additional times? 00:55:40.328 --> 00:55:41.810 Is that right? 00:55:41.810 --> 00:55:42.798 So the-- 00:55:42.798 --> 00:55:45.280 PROFESSOR: Yes. 00:55:45.280 --> 00:55:47.588 AUDIENCE: Is it done on the remainder of QTL 00:55:47.588 --> 00:55:50.444 or on the original list of every-- 00:55:50.444 --> 00:55:52.710 PROFESSOR: Each time you expand your model 00:55:52.710 --> 00:55:55.780 to include all the QTLs you've discovered up to that point. 00:55:55.780 --> 00:56:01.111 So initially, you discover a set of QTLs, call that set one. 00:56:01.111 --> 00:56:04.620 You then compute a model using set one 00:56:04.620 --> 00:56:07.555 and you discover the residuals. 00:56:07.555 --> 00:56:08.505 AUDIENCE: [INAUDIBLE]. 00:56:08.505 --> 00:56:09.296 PROFESSOR: Correct. 00:56:09.296 --> 00:56:10.890 Well, residual [INAUDIBLE] so you use 00:56:10.890 --> 00:56:13.425 set one to build a model, a phenotype. 00:56:16.280 --> 00:56:20.480 So set one is used here to compute this, right. 00:56:20.480 --> 00:56:21.740 And so set one is used. 00:56:21.740 --> 00:56:23.350 And then you compute what's left over 00:56:23.350 --> 00:56:26.980 after you've discovered the first set of QTLs. 00:56:26.980 --> 00:56:30.980 Now you say, we still have this left to go. 00:56:30.980 --> 00:56:32.380 Let's discover some more QTLs. 00:56:32.380 --> 00:56:35.950 And now you discover set two of QTLs. 00:56:35.950 --> 00:56:37.260 OK. 00:56:37.260 --> 00:56:41.520 And that set two then is used to build a model that has set one 00:56:41.520 --> 00:56:44.010 and set two in it. 00:56:44.010 --> 00:56:44.510 Right. 00:56:44.510 --> 00:56:46.200 And that residual is used to discover 00:56:46.200 --> 00:56:49.850 set three and so forth. 00:56:49.850 --> 00:56:52.790 So each time you're expanding the set of QTLs 00:56:52.790 --> 00:56:54.860 by what you've discovered in the residuals. 00:56:54.860 --> 00:56:57.140 Sort of in the trash bin so to speak. 00:56:57.140 --> 00:56:57.640 Yes? 00:56:57.640 --> 00:57:00.130 AUDIENCE: Each time you're doing this randomization 00:57:00.130 --> 00:57:01.130 to determine lod cutoff? 00:57:01.130 --> 00:57:02.213 PROFESSOR: That's correct. 00:57:02.213 --> 00:57:04.285 Each time you have to redo the randomization 00:57:04.285 --> 00:57:05.770 and get to the lod cutoff. 00:57:05.770 --> 00:57:07.502 AUDIENCE: But does that method actually 00:57:07.502 --> 00:57:10.581 work the way you expect it on the second pass, given that you 00:57:10.581 --> 00:57:12.205 have some false positives from the pass 00:57:12.205 --> 00:57:17.052 that you've now subtracted from your data? 00:57:17.052 --> 00:57:19.135 PROFESSOR: I'm not sure I understand the question. 00:57:19.135 --> 00:57:21.115 AUDIENCE: So the second time you do this randomization, 00:57:21.115 --> 00:57:22.739 and you again come up with a threshold, 00:57:22.739 --> 00:57:27.287 you say, oh, above here there are 5% false positives. 00:57:27.287 --> 00:57:27.995 PROFESSOR: Right. 00:57:27.995 --> 00:57:31.324 AUDIENCE: But could it be that that estimate is actually 00:57:31.324 --> 00:57:35.680 significantly wrong based the fact that you've subtracted off 00:57:35.680 --> 00:57:39.068 false positives before you do that process? 00:57:41.630 --> 00:57:43.590 PROFESSOR: I mean, in some sense, what's 00:57:43.590 --> 00:57:46.450 your definition of a false positive? 00:57:46.450 --> 00:57:46.950 Right. 00:57:46.950 --> 00:57:50.080 I mean it gets down to that because we've 00:57:50.080 --> 00:57:53.020 discovered there's an association between that QTL 00:57:53.020 --> 00:57:54.750 and predicting phenotype. 00:57:54.750 --> 00:57:59.230 And in this particular world it's useful for doing that. 00:57:59.230 --> 00:58:01.860 So it's hard to call something a false positive in that sense, 00:58:01.860 --> 00:58:03.932 right. 00:58:03.932 --> 00:58:05.390 But you're right, you actually have 00:58:05.390 --> 00:58:09.327 to reset your threshold every time 00:58:09.327 --> 00:58:10.785 that you go through this iteration. 00:58:14.900 --> 00:58:15.650 Good question. 00:58:15.650 --> 00:58:16.316 Other questions? 00:58:19.710 --> 00:58:21.300 OK. 00:58:21.300 --> 00:58:25.160 So, let's see what happens when you do this. 00:58:25.160 --> 00:58:28.910 What happens is that if you look down the genome, 00:58:28.910 --> 00:58:30.670 you discover a collection. 00:58:30.670 --> 00:58:42.040 For example, this is growth in E6 berbamine. 00:58:42.040 --> 00:58:45.130 And you can see the significant locations 00:58:45.130 --> 00:58:48.590 in the genome, the numbers 1 through 16 of the chromosomes 00:58:48.590 --> 00:58:51.960 and the little red asterisks above the peaks 00:58:51.960 --> 00:58:54.010 indicate that that was a significant lod score. 00:58:54.010 --> 00:58:56.729 The y-axis is a lod score. 00:58:56.729 --> 00:58:58.520 And you can see the locations in the genome 00:58:58.520 --> 00:59:05.030 where we have found places that were associated with growth 00:59:05.030 --> 00:59:10.010 rate in that particular chemical. 00:59:10.010 --> 00:59:11.810 OK. 00:59:11.810 --> 00:59:15.890 Now, why is it, do you think, that in many of those places 00:59:15.890 --> 00:59:20.520 you see sort of a rise and fall that is somewhat gentle 00:59:20.520 --> 00:59:23.000 as opposed to having an impulse function 00:59:23.000 --> 00:59:24.400 right at that particular spot? 00:59:30.029 --> 00:59:31.445 AUDIENCE: Nearby snips are linked? 00:59:31.445 --> 00:59:33.153 PROFESSOR: Yeah, nearby snips are linked. 00:59:33.153 --> 00:59:37.930 That as you come up to a place that is causal, 00:59:37.930 --> 00:59:42.000 you get a lot of other things are linked to that. 00:59:42.000 --> 00:59:44.880 And the closer you get, the higher the correlation is. 00:59:48.440 --> 00:59:52.910 So that is for 1,000 segregants in the top. 00:59:52.910 --> 00:59:58.550 And what was discovered for that particular trait, 00:59:58.550 --> 01:00:04.690 was 15 different loci that explained 01:00:04.690 --> 01:00:10.090 78% of the phenotypic variance. 01:00:10.090 --> 01:00:14.650 And in the bottom, the same procedure 01:00:14.650 --> 01:00:20.040 was used, but was only used on 100 segregants. 01:00:20.040 --> 01:00:23.350 And what you can see is that, in this particular case, 01:00:23.350 --> 01:00:27.330 only two loci were discovered that explain 01:00:27.330 --> 01:00:28.715 21% of the variance. 01:00:31.450 --> 01:00:33.730 So the bottom study was grossly under powered. 01:00:36.740 --> 01:00:41.240 Remember we talked about the problem of finding 01:00:41.240 --> 01:00:45.070 QTLs that had small effect sizes. 01:00:45.070 --> 01:00:47.230 And if you don't have enough individuals 01:00:47.230 --> 01:00:49.830 you're going to be under-powered and you can't actually 01:00:49.830 --> 01:00:51.210 identify all of the QTLs. 01:00:54.080 --> 01:00:57.620 So this is a comparison of this. 01:00:57.620 --> 01:01:00.950 And of course, one of the things that you don't know 01:01:00.950 --> 01:01:05.010 is the environmental variance that you're fighting against. 01:01:05.010 --> 01:01:07.160 Because the number of individuals 01:01:07.160 --> 01:01:11.490 you need, depends both on the number of potential loci 01:01:11.490 --> 01:01:12.890 that you have. 01:01:12.890 --> 01:01:17.380 The more loci you have, the more individuals you need to fight 01:01:17.380 --> 01:01:19.210 against the multiple hypotheses problem, 01:01:19.210 --> 01:01:21.465 which is taken care of by this permutation implicitly. 01:01:24.870 --> 01:01:28.220 And the more QTLs that contribute 01:01:28.220 --> 01:01:31.320 to a particular trait, the smaller they might be. 01:01:31.320 --> 01:01:33.080 And there you need more individuals 01:01:33.080 --> 01:01:34.900 to provide adequate power for your test. 01:01:39.810 --> 01:01:43.400 And out of this model, however, if you 01:01:43.400 --> 01:01:48.090 look at for all the different traits, the predictive insight 01:01:48.090 --> 01:01:50.040 versus the observed phenotype, you 01:01:50.040 --> 01:01:52.565 can see that the model does a reasonably good job. 01:01:56.010 --> 01:02:03.990 So the interesting things that came out of the study 01:02:03.990 --> 01:02:06.620 were that, first of all, it was possible to look 01:02:06.620 --> 01:02:11.860 at the effect sizes of each QTL. 01:02:11.860 --> 01:02:16.700 Now, the effect size in terms of fraction of variance explained 01:02:16.700 --> 01:02:21.590 of a particular marker, is the square of its coefficient. 01:02:21.590 --> 01:02:23.990 It's the beta squared. 01:02:23.990 --> 01:02:29.350 So you can see here the histogram of effect sizes, 01:02:29.350 --> 01:02:33.440 and you can see that most QTLs have very small effects 01:02:33.440 --> 01:02:39.700 on phenotype where phenotype is scaled between 0 and 1 01:02:39.700 --> 01:02:40.400 for this study. 01:02:43.680 --> 01:02:49.790 So, most traits as described here 01:02:49.790 --> 01:02:53.690 have between 5 and 29 different QTL loci in the genome. 01:02:53.690 --> 01:02:56.405 They're used to describe them with a median of 12. 01:03:00.240 --> 01:03:04.260 Now, the question the authors asked, 01:03:04.260 --> 01:03:11.280 was if they looked at the theoretical h squared that they 01:03:11.280 --> 01:03:16.560 computed for the F1s, how well did their model do? 01:03:16.560 --> 01:03:18.680 And you can see that their model does very well. 01:03:18.680 --> 01:03:22.630 That, in terms of looking at narrow sense heritability, 01:03:22.630 --> 01:03:25.560 they can recover almost all of it, all the time. 01:03:29.860 --> 01:03:35.526 However, the problem comes here. 01:03:35.526 --> 01:03:37.150 Remember we talked about how to compute 01:03:37.150 --> 01:03:44.430 broad-sense heritability by looking at clones 01:03:44.430 --> 01:03:47.830 and computing environmental variance directly. 01:03:47.830 --> 01:03:51.270 And so they were able to compute broad-sense heritability 01:03:51.270 --> 01:03:55.080 and compare that the narrow-sense heritability 01:03:55.080 --> 01:03:57.684 that they were able to actually achieve in the study. 01:03:57.684 --> 01:03:59.475 And you can see there are substantial gaps. 01:04:02.430 --> 01:04:06.900 So what could be making up those gaps? 01:04:06.900 --> 01:04:12.380 Why is it that this additive model can't explain growth rate 01:04:12.380 --> 01:04:15.770 in a particular condition? 01:04:15.770 --> 01:04:20.440 So, the next thing that we're going to discover 01:04:20.440 --> 01:04:24.680 are some of the sources of this so-called missing heritability. 01:04:24.680 --> 01:04:26.900 But before I give you some of the stock answers 01:04:26.900 --> 01:04:29.830 that people in the field give, since this is part of our quest 01:04:29.830 --> 01:04:33.370 today to actually look into missing heritability, 01:04:33.370 --> 01:04:36.960 I'll put it to you, my panel of experts. 01:04:36.960 --> 01:04:39.450 What could be causing this heritability to go missing? 01:04:39.450 --> 01:04:46.390 Why can't this additive model predict growth rate accurately, 01:04:46.390 --> 01:04:50.190 given it knows the genotype exactly? 01:04:50.190 --> 01:04:51.010 Yes. 01:04:51.010 --> 01:04:54.986 AUDIENCE: [INAUDIBLE] that you wouldn't 01:04:54.986 --> 01:04:56.980 detect from looking at the DNA sequence. 01:04:56.980 --> 01:04:59.080 PROFESSOR: So epidemic factors-- are 01:04:59.080 --> 01:05:00.980 you talking about protein factors or are you 01:05:00.980 --> 01:05:02.355 talking about epigenetic effects? 01:05:02.355 --> 01:05:04.117 AUDIENCE: More of the epigenetic marks. 01:05:04.117 --> 01:05:05.450 PROFESSOR: Epigenetic marks, OK. 01:05:05.450 --> 01:05:09.545 So it might be now, yeast doesn't have DNA methylation. 01:05:12.490 --> 01:05:15.670 It does have chromatin modifications 01:05:15.670 --> 01:05:18.020 in the form of histone marks. 01:05:18.020 --> 01:05:20.900 So it might be that there's some histone marks that 01:05:20.900 --> 01:05:24.750 are copied from generation to generation that are not 01:05:24.750 --> 01:05:26.310 counted for in our model. 01:05:26.310 --> 01:05:28.330 right? 01:05:28.330 --> 01:05:29.900 OK, that's one possibility. 01:05:29.900 --> 01:05:30.440 Great. 01:05:30.440 --> 01:05:30.940 Yes. 01:05:30.940 --> 01:05:33.874 AUDIENCE: There could be more complex effects 01:05:33.874 --> 01:05:37.297 so two separate genes may come out, other than just adding. 01:05:37.297 --> 01:05:38.764 One could turn the other off. 01:05:38.764 --> 01:05:43.170 So it one's on, it could [INAUDIBLE]. 01:05:43.170 --> 01:05:43.910 PROFESSOR: Right. 01:05:43.910 --> 01:05:47.000 So those are called epistatic effects, 01:05:47.000 --> 01:05:48.250 or they're non-linear effects. 01:05:48.250 --> 01:05:51.036 They're gene-gene interaction effects. 01:05:51.036 --> 01:05:52.410 That's actually thought to be one 01:05:52.410 --> 01:05:56.915 of the major issues in missing heritability. 01:06:00.090 --> 01:06:02.570 What else could there be? 01:06:02.570 --> 01:06:03.080 Yes. 01:06:03.080 --> 01:06:03.996 AUDIENCE: [INAUDIBLE]. 01:06:16.872 --> 01:06:17.580 PROFESSOR: Right. 01:06:17.580 --> 01:06:21.390 So you're saying that there could be inherent noise that 01:06:21.390 --> 01:06:24.250 would cause there to be fluctuations in colony size 01:06:24.250 --> 01:06:26.550 that are unrelated to the genotype. 01:06:26.550 --> 01:06:27.967 And, in fact, that's a good point. 01:06:27.967 --> 01:06:29.508 And that's something that we're going 01:06:29.508 --> 01:06:31.530 to take care of with the environmental variance. 01:06:31.530 --> 01:06:34.580 So we're going to measure how well individuals 01:06:34.580 --> 01:06:37.900 grow with exactly the same genotype in a given condition. 01:06:37.900 --> 01:06:40.860 And so that kind of fluctuation would 01:06:40.860 --> 01:06:43.200 appear in that variance term. 01:06:43.200 --> 01:06:46.010 And we're going to get rid of that. 01:06:46.010 --> 01:06:48.900 But that's a good thought and I think it's important and not 01:06:48.900 --> 01:06:53.110 appreciated that there can be random fluctuations 01:06:53.110 --> 01:06:55.710 in that term. 01:06:55.710 --> 01:06:56.545 Any other ideas? 01:07:02.130 --> 01:07:05.240 So we have epistasis. 01:07:05.240 --> 01:07:06.510 We have epigenetics. 01:07:06.510 --> 01:07:09.170 We've got two E's so far. 01:07:09.170 --> 01:07:10.050 Anything else? 01:07:19.430 --> 01:07:27.870 How about if there are a lot of different loci 01:07:27.870 --> 01:07:33.860 that are influencing a particular trait, 01:07:33.860 --> 01:07:37.180 but the effect sizes are very small. 01:07:37.180 --> 01:07:38.940 That we've captured, sort of the cream. 01:07:38.940 --> 01:07:40.140 We've skimmed off the cream. 01:07:40.140 --> 01:07:45.110 So we get 70% of the variance explained, 01:07:45.110 --> 01:07:49.150 but the rest of the QTLs are small, 01:07:49.150 --> 01:07:50.359 right, and we can't see them. 01:07:50.359 --> 01:07:52.816 We can't see them because we don't have enough individuals. 01:07:52.816 --> 01:07:54.030 We're underpowered, right. 01:07:54.030 --> 01:07:58.284 We just-- more individuals more sequencing, right. 01:07:58.284 --> 01:08:00.450 And that would be the only way to break through this 01:08:00.450 --> 01:08:04.745 and be able to see these very small effects. 01:08:07.410 --> 01:08:11.630 Because if the effects are small, in some sense, 01:08:11.630 --> 01:08:13.540 we're hosed. 01:08:13.540 --> 01:08:15.080 Right? 01:08:15.080 --> 01:08:17.859 You just can't see them through the noise. 01:08:17.859 --> 01:08:24.620 All those effects are going to show up down here 01:08:24.620 --> 01:08:26.500 and we're going to reject them. 01:08:30.700 --> 01:08:33.645 Anything else, people can think about? 01:08:36.555 --> 01:08:38.010 Yes? 01:08:38.010 --> 01:08:42.066 AUDIENCE: Could you content maybe the sum of some areas 01:08:42.066 --> 01:08:48.674 that are-- sorry, the addition sum of those guys 01:08:48.674 --> 01:08:50.365 that have low effects. 01:08:50.365 --> 01:08:52.604 Or is that not detectable by any [INAUDIBLE]? 01:08:52.604 --> 01:08:53.979 PROFESSOR: Well, that's certainly 01:08:53.979 --> 01:08:57.524 what we're trying to do with residuals, right? 01:08:57.524 --> 01:08:59.149 This multi-round round thing is that we 01:08:59.149 --> 01:09:01.109 take all the things we can detect 01:09:01.109 --> 01:09:03.510 that have an effect with a conservative cut off 01:09:03.510 --> 01:09:05.356 and we get rid of them. 01:09:05.356 --> 01:09:07.189 And then we say, oh, is there anything left? 01:09:07.189 --> 01:09:10.660 You know, that's hiding, sort of behind that forest, right. 01:09:10.660 --> 01:09:12.569 If we cut through the first line of trees, 01:09:12.569 --> 01:09:16.600 can we get to another collection of informative QTLs? 01:09:21.090 --> 01:09:21.760 Yeah. 01:09:21.760 --> 01:09:23.242 AUDIENCE: I was wondering if this 01:09:23.242 --> 01:09:24.724 could be an overestimate also. 01:09:24.724 --> 01:09:26.926 Like, for example, if, when you throw out 01:09:26.926 --> 01:09:28.676 the variance for environmental conditions, 01:09:28.676 --> 01:09:32.628 the environmental conditions aren't as exact as we thought 01:09:32.628 --> 01:09:36.860 they were between two yeast growing in the same set, setup. 01:09:36.860 --> 01:09:37.568 PROFESSOR: Right. 01:09:37.568 --> 01:09:41.026 AUDIENCE: Then maybe you would inappropriately 01:09:41.026 --> 01:09:43.990 assign a variance to the environmental condition 01:09:43.990 --> 01:09:51.400 whereas some that could be, in fact-- something 01:09:51.400 --> 01:09:52.882 that wouldn't be explained by. 01:09:52.882 --> 01:09:55.030 PROFESSOR: And probably the other way around. 01:09:55.030 --> 01:09:57.000 The other way around would be that you thought 01:09:57.000 --> 01:10:00.522 you had the conditions exactly duplicated, right. 01:10:00.522 --> 01:10:02.230 But when you actually did something else, 01:10:02.230 --> 01:10:06.240 they weren't exactly duplicated so you see bigger variance 01:10:06.240 --> 01:10:07.190 in another experiment. 01:10:07.190 --> 01:10:11.024 And it appears to be heritable in some sense. 01:10:11.024 --> 01:10:13.190 But, in fact, it would just be that you misestimated 01:10:13.190 --> 01:10:14.970 the environmental component. 01:10:14.970 --> 01:10:16.870 So, there are a variety of things 01:10:16.870 --> 01:10:19.000 that we can think about, right. 01:10:19.000 --> 01:10:20.870 Incorrect heritability estimates. 01:10:20.870 --> 01:10:23.605 We can think about rare variance. 01:10:23.605 --> 01:10:25.230 Now in this particular study we're 01:10:25.230 --> 01:10:27.240 looking at everything, right. 01:10:27.240 --> 01:10:28.330 Nothing is hiding. 01:10:28.330 --> 01:10:30.040 We've got 50x sequencing. 01:10:30.040 --> 01:10:32.400 There are no variants hiding behind the bushes. 01:10:32.400 --> 01:10:35.080 They are all there for us to look at. 01:10:35.080 --> 01:10:37.290 Structural variants-- well in this particular case, 01:10:37.290 --> 01:10:39.770 we know structural variants aren't present, 01:10:39.770 --> 01:10:42.290 but as you know, many kinds of mammalian cells 01:10:42.290 --> 01:10:45.470 exhibit structural variance and other kinds 01:10:45.470 --> 01:10:50.480 of bizarre behaviors with their chromosomes. 01:10:50.480 --> 01:10:52.280 Many common variants of low effect. 01:10:52.280 --> 01:10:54.520 We just talked about that. 01:10:54.520 --> 01:10:56.420 And epistasis was brought up. 01:10:56.420 --> 01:10:58.140 And this does not include epigenetics, 01:10:58.140 --> 01:10:59.720 I'll have to add that to the listen. 01:10:59.720 --> 01:11:01.490 It's a good point. 01:11:01.490 --> 01:11:03.050 OK. 01:11:03.050 --> 01:11:04.650 And then we talked about this idea 01:11:04.650 --> 01:11:10.460 that epistasis is the case where we have nonlinear effects. 01:11:10.460 --> 01:11:14.970 So a very simple example of this is 01:11:14.970 --> 01:11:17.570 when you have little a and big B, and big A and big B 01:11:17.570 --> 01:11:19.210 together, they both had an effect. 01:11:19.210 --> 01:11:22.090 But little a, little b, have no effect. 01:11:22.090 --> 01:11:25.110 And big A and big B have no effect by themselves. 01:11:25.110 --> 01:11:26.780 So you have a pairwise interaction 01:11:26.780 --> 01:11:28.750 between these terms. 01:11:28.750 --> 01:11:29.940 Right. 01:11:29.940 --> 01:11:33.670 So this is sort of the exclusive OR of two terms 01:11:33.670 --> 01:11:36.420 and that non-linear effect can never 01:11:36.420 --> 01:11:40.990 be captured when you're looking at terms one at a time. 01:11:40.990 --> 01:11:42.650 OK. 01:11:42.650 --> 01:11:46.200 Because looking one at a time looks 01:11:46.200 --> 01:11:49.310 like it has no effect whatsoever. 01:11:49.310 --> 01:11:52.060 And these effects, of course, could be more than pairwise, 01:11:52.060 --> 01:11:54.075 if you have a complicated network or pathway. 01:11:59.120 --> 01:12:03.780 Now, what the authors did to examine this, 01:12:03.780 --> 01:12:07.610 is they looked at pairwise effects. 01:12:07.610 --> 01:12:10.710 So they considered all pairs of markers 01:12:10.710 --> 01:12:14.170 and asked whether or not, taken two at a time now, 01:12:14.170 --> 01:12:20.930 they could predict a difference in trait need. 01:12:20.930 --> 01:12:22.547 But what's the problem with this? 01:12:22.547 --> 01:12:24.130 How many markers did I say there were? 01:12:28.140 --> 01:12:31.630 13,000, something like that. 01:12:31.630 --> 01:12:35.160 All pairs of markers is a lot of pairs of markers. 01:12:35.160 --> 01:12:36.600 Right. 01:12:36.600 --> 01:12:39.100 And what happens to your statistical power 01:12:39.100 --> 01:12:42.320 when you get to that many markers? 01:12:42.320 --> 01:12:43.590 You have a serious problem. 01:12:43.590 --> 01:12:45.620 It goes right through the floor. 01:12:45.620 --> 01:12:48.450 So you really are very under-powered to detect 01:12:48.450 --> 01:12:50.820 these interactions. 01:12:50.820 --> 01:12:53.250 The other thing they did was to try 01:12:53.250 --> 01:12:55.450 to get things a little bit better as they said, 01:12:55.450 --> 01:12:57.780 how about this. 01:12:57.780 --> 01:13:02.610 If we know that a given QTL is always important for a trait 01:13:02.610 --> 01:13:05.980 because we discovered it in our additive model. 01:13:05.980 --> 01:13:07.690 Well consider its pairwise interaction 01:13:07.690 --> 01:13:10.980 with all the other possible variants. 01:13:10.980 --> 01:13:13.870 So instead of now 13,000 squared, 01:13:13.870 --> 01:13:17.430 it's only going to be like 22 different QTLs for a given 01:13:17.430 --> 01:13:23.540 trait times 13,000 to reduce the space of search. 01:13:23.540 --> 01:13:26.410 Obviously I got this explanation not completely clear. 01:13:26.410 --> 01:13:27.880 So let me try one more time. 01:13:27.880 --> 01:13:30.460 OK. 01:13:30.460 --> 01:13:33.040 The naive way to go at looking at pairwise interactions 01:13:33.040 --> 01:13:35.570 is consider all pairs and ask whether or not 01:13:35.570 --> 01:13:38.860 all pairs have an influence on a particular trait value. 01:13:38.860 --> 01:13:39.390 Right. 01:13:39.390 --> 01:13:40.430 We've got that much? 01:13:40.430 --> 01:13:41.330 OK. 01:13:41.330 --> 01:13:44.100 Now let's suppose we don't want to look at all pairs. 01:13:44.100 --> 01:13:46.570 How could we pick one element of the pair 01:13:46.570 --> 01:13:50.082 to be interesting, but smaller in number? 01:13:50.082 --> 01:13:50.940 Right. 01:13:50.940 --> 01:13:53.370 So what we'll do is, for a given trait, 01:13:53.370 --> 01:13:57.610 we already know which QTLs are important for it 01:13:57.610 --> 01:14:00.406 because we've built our model already. 01:14:00.406 --> 01:14:02.280 So let's just say, for purpose of discussion, 01:14:02.280 --> 01:14:06.150 there are 20 QTLs that are important for this trait. 01:14:06.150 --> 01:14:09.010 We'll take each one of those 20 QTLs 01:14:09.010 --> 01:14:11.870 and we'll examine whether or not it has a pairwise interaction 01:14:11.870 --> 01:14:14.960 with all of the other variance. 01:14:14.960 --> 01:14:18.220 And that will reduce our search base. 01:14:18.220 --> 01:14:19.500 Is that better? 01:14:19.500 --> 01:14:21.000 OK, good. 01:14:21.000 --> 01:14:27.800 So, when they did that, they did find 01:14:27.800 --> 01:14:30.830 some pairwise interactions. 01:14:30.830 --> 01:14:35.940 In 24 of their 46 traits had pairwise interactions 01:14:35.940 --> 01:14:36.935 and here is an example. 01:14:40.200 --> 01:14:48.640 And you can see the dot plot, or the upper right-hand part 01:14:48.640 --> 01:14:52.710 of this slide, how when you BYBY. 01:14:52.710 --> 01:14:55.920 You have a lower phenotypic value then 01:14:55.920 --> 01:15:02.220 when you have just any RM component 01:15:02.220 --> 01:15:04.590 on the right-hand side. 01:15:04.590 --> 01:15:08.680 So those were two different snips 01:15:08.680 --> 01:15:10.690 on chromosome 7 and chromosome 11 01:15:10.690 --> 01:15:12.915 and showing how they interact with one another 01:15:12.915 --> 01:15:16.760 in a non-linear way. 01:15:16.760 --> 01:15:21.060 If they were linear, then as you added either a chromosome at 7 01:15:21.060 --> 01:15:24.560 or a chromosome 11 contribution it would go up a little bit. 01:15:24.560 --> 01:15:33.410 Here, as soon as you add either contribution from RM, 01:15:33.410 --> 01:15:38.710 it goes all way up to have a mean of zero or higher. 01:15:38.710 --> 01:15:44.300 In this particular case, 71% of the gap between broad-sense 01:15:44.300 --> 01:15:50.360 and narrow-sense was explained by this one pair interaction. 01:15:50.360 --> 01:15:54.010 So it is the case that pairwise interactions 01:15:54.010 --> 01:15:56.235 can explain some of the missing heritability. 01:15:59.540 --> 01:16:01.310 Can anybody think of anything else 01:16:01.310 --> 01:16:02.893 they can explain missing heritability? 01:16:08.760 --> 01:16:09.260 OK. 01:16:11.840 --> 01:16:13.967 What's inherited? 01:16:13.967 --> 01:16:15.550 Let's make a list of everything that's 01:16:15.550 --> 01:16:21.660 inherited from the parental line to the F1s. 01:16:21.660 --> 01:16:23.450 OK. 01:16:23.450 --> 01:16:24.266 Yes. 01:16:24.266 --> 01:16:27.172 AUDIENCE: I mean, because there's 01:16:27.172 --> 01:16:29.164 a lot more things inherited. 01:16:29.164 --> 01:16:31.071 The protein levels are inherited. 01:16:31.071 --> 01:16:31.654 PROFESSOR: OK. 01:16:31.654 --> 01:16:33.734 AUDIENCE: [INAUDIBLE] are inherited as well. 01:16:33.734 --> 01:16:34.400 PROFESSOR: Good. 01:16:34.400 --> 01:16:35.909 I like this line of thinking. 01:16:35.909 --> 01:16:36.825 AUDIENCE: [INAUDIBLE]. 01:16:36.825 --> 01:16:38.325 PROFESSOR: There are a lot of things 01:16:38.325 --> 01:16:40.130 that are inherited, right? 01:16:40.130 --> 01:16:43.690 So what's inherited? 01:16:43.690 --> 01:16:47.790 Some proteins are probably inherited, right? 01:16:47.790 --> 01:16:50.760 What is replicable through generation 01:16:50.760 --> 01:16:54.200 to generation as a genetic material that's inherited? 01:16:54.200 --> 01:16:56.835 Let's just talk about that for a moment. 01:16:56.835 --> 01:16:58.710 Proteins are interesting, don't get me wrong. 01:16:58.710 --> 01:17:01.360 I mean, prions and other things are very interesting. 01:17:01.360 --> 01:17:03.410 But what else is inherited? 01:17:08.370 --> 01:17:09.137 OK, yes? 01:17:09.137 --> 01:17:10.053 AUDIENCE: [INAUDIBLE]. 01:17:18.210 --> 01:17:21.230 PROFESSOR: So there are other genetic molecules. 01:17:21.230 --> 01:17:24.730 Let's just take a really simple one-- mitochondria. 01:17:24.730 --> 01:17:26.760 OK. 01:17:26.760 --> 01:17:28.830 Mitochondria are inherited. 01:17:28.830 --> 01:17:30.610 And it turns out that these two strains 01:17:30.610 --> 01:17:35.830 have can have different mitochondria. 01:17:35.830 --> 01:17:37.120 What else can be inherited? 01:17:40.790 --> 01:17:44.140 Well, we were doing these experiments with our colleagues 01:17:44.140 --> 01:17:46.822 over at the Whitehead and for a long time 01:17:46.822 --> 01:17:48.530 we couldn't figure out what was going on. 01:17:48.530 --> 01:17:50.689 Because we would do the experiments on day one 01:17:50.689 --> 01:17:52.730 and they come out a particular way and on day two 01:17:52.730 --> 01:17:54.030 they come out a different way. 01:17:54.030 --> 01:17:55.100 Right. 01:17:55.100 --> 01:17:59.160 And we're doing some very controlled conditions. 01:17:59.160 --> 01:18:02.460 Until we figured out that everybody 01:18:02.460 --> 01:18:06.230 uses S288C which is the genetic nomenclature 01:18:06.230 --> 01:18:10.010 for the lab trained yeast, right. 01:18:10.010 --> 01:18:12.112 It's lab train because it's very well behaved. 01:18:12.112 --> 01:18:13.070 It's a very nice yeast. 01:18:13.070 --> 01:18:14.210 It grows very well. 01:18:14.210 --> 01:18:16.220 It's been selected for that, right. 01:18:16.220 --> 01:18:19.750 And people always do genetic studies by taking S288C, 01:18:19.750 --> 01:18:22.717 which is the lab yeast, which has being completely sequenced 01:18:22.717 --> 01:18:24.800 and so you want to use it because you can download 01:18:24.800 --> 01:18:29.490 the genome with a wild strain. 01:18:29.490 --> 01:18:33.260 And wild strains come from the wild, right. 01:18:33.260 --> 01:18:35.920 And they come either off of people 01:18:35.920 --> 01:18:37.230 who have yeast infections. 01:18:37.230 --> 01:18:40.190 I mean, human beings, or they come off of grape vines 01:18:40.190 --> 01:18:42.120 or God knows where, right. 01:18:42.120 --> 01:18:44.080 But they are not well behaved. 01:18:44.080 --> 01:18:45.760 And why are they not well behaved? 01:18:45.760 --> 01:18:48.830 What makes these yeast particularly rude? 01:18:48.830 --> 01:18:51.380 Well, the thing that makes them particularly rude 01:18:51.380 --> 01:18:54.120 is that they have things like viruses in them. 01:18:54.120 --> 01:18:55.440 Oh, no. 01:18:55.440 --> 01:18:56.170 OK. 01:18:56.170 --> 01:18:58.470 Because what happens is that when 01:18:58.470 --> 01:19:01.080 you take a yeast that has a virus in it, 01:19:01.080 --> 01:19:04.460 and you cross it with a lab yeast, right. 01:19:04.460 --> 01:19:06.120 All of the kids got the virus. 01:19:08.940 --> 01:19:10.220 Yuck. 01:19:10.220 --> 01:19:11.930 OK. 01:19:11.930 --> 01:19:19.150 And it turns out that the so-called killer virus in yeast 01:19:19.150 --> 01:19:23.950 interacts with various chromosomal changes. 01:19:23.950 --> 01:19:25.590 And so now you have interactions-- 01:19:25.590 --> 01:19:29.340 genetic interactions between a viral element 01:19:29.340 --> 01:19:32.090 and the chromosome. 01:19:32.090 --> 01:19:36.760 And so the phenotype you get out of particular deletions 01:19:36.760 --> 01:19:41.860 in the yeast genome has to do with whether or not 01:19:41.860 --> 01:19:44.220 it's infected with a particular virus. 01:19:44.220 --> 01:19:50.500 It also has to do with which mitochondrial content it has. 01:19:50.500 --> 01:19:51.970 And people didn't appreciate this 01:19:51.970 --> 01:19:57.520 until recently because most of the past yeast studies for QTLs 01:19:57.520 --> 01:20:03.010 were busy crossing lab strains with wild strains 01:20:03.010 --> 01:20:06.960 and whether it was ethanol tolerance or growth and heat, 01:20:06.960 --> 01:20:09.620 a lot of the strains came up with a gene 01:20:09.620 --> 01:20:12.800 as a significant QTL, which was MKT1. 01:20:12.800 --> 01:20:17.580 And people couldn't understand why MKT1 was so popular, right. 01:20:17.580 --> 01:20:22.460 MKT1, maintenance of killer toxin one. 01:20:22.460 --> 01:20:23.050 Yeah. 01:20:23.050 --> 01:20:26.210 That's the viral thing that enables-- the chromosomal thing 01:20:26.210 --> 01:20:28.130 that enables a viral competence. 01:20:28.130 --> 01:20:34.170 So, it turns out that if you look 01:20:34.170 --> 01:20:37.440 at this-- in this particular case, 01:20:37.440 --> 01:20:39.730 we're looking at yeast that don't 01:20:39.730 --> 01:20:43.220 have the virus in the bottom little photograph there. 01:20:43.220 --> 01:20:46.595 You can see they're all sort of, you know, 01:20:46.595 --> 01:20:48.930 they're growing similarly. 01:20:48.930 --> 01:20:53.680 And the yeast with the same genotype above-- those 01:20:53.680 --> 01:20:56.164 are all in tetrads. 01:20:56.164 --> 01:20:58.080 Two out of the four are growing, the other two 01:20:58.080 --> 01:21:02.470 are not, because the other two have a particular deletion. 01:21:02.470 --> 01:21:06.595 And if you look at the model-- a deletion only model, 01:21:06.595 --> 01:21:09.940 the deletion only, only looks at the chromosomal compliment 01:21:09.940 --> 01:21:14.660 doesn't predict the variance very well. 01:21:14.660 --> 01:21:18.150 And if you look at the deletion and whether or not 01:21:18.150 --> 01:21:21.250 you have the virus, you do better. 01:21:21.250 --> 01:21:24.190 But you do even better, if you allow 01:21:24.190 --> 01:21:26.930 for there to be a nonlinear interaction 01:21:26.930 --> 01:21:29.040 between the chromosomal modification 01:21:29.040 --> 01:21:31.520 and whether or not you have a virus. 01:21:31.520 --> 01:21:36.120 And then you recover almost all of missing heritability. 01:21:36.120 --> 01:21:37.930 So I'll leave you with this thought, which 01:21:37.930 --> 01:21:45.560 is that genetics is complicated and QTLs are great, but don't 01:21:45.560 --> 01:21:49.400 forget that there are all sorts of genetic elements. 01:21:49.400 --> 01:21:50.980 And on that note, next time we'll 01:21:50.980 --> 01:21:52.490 talk about human genetics. 01:21:52.490 --> 01:21:54.050 Have a great weekend until then. 01:21:54.050 --> 01:21:54.730 We'll see you. 01:21:54.730 --> 01:21:56.440 Take care.