20. Human Genetics, SNPs, and Genome Wide Associate Studies

20. Human Genetics, SNPs, and Genome Wide Associate Studies


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visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: So everybody
ready to rock and roll today? Or at least roll? OK, if not rock. Welcome back to lecture 20. On Thursday, we have a special
guest appearance just for you from Professor Ron Weiss. He’s going to be talking
about synthetic biology. You know, on Richard
Feynman’s blackboard, when he died, was a little
statement I’ve always really enjoyed that was actually
encased in a little chalk line. And it said, “What I cannot
create, I do not understand.” And so synthetic
biology is one way to approach questions in
the biological sciences by seeing what we
can make– you know, whole organisms, new
genomes, rewiring circuitry. So I think you’ll find it to be
a very interesting discussion on Thursday. But first, before we talk
about synthetic biology, we have the very
exciting discussion today on human genetics, which of
course concerns all of us. And so we’re going to
have an exploration today. And you know, as I
prepared today’s lecture, I wanted to give you the latest
and greatest research findings. So we’re going to talk today
from fundamental techniques to things that are very
controversial that have caused fistfights in bars, so
I’m hopeful that you’ll be as engaged as the
people drinking beer are. So we’ll be turning to that
at the end of the lecture, but first I wanted to tell you
about the broad narrative arc once again that we’re going
to be talking about today. And we’re going to
be looking at how to discover human variation. We’re all different, about
1 based in every 1,000. And there are two different
broad approaches historically people have used. Microarrays for
discovering variants, and we’ll talk about
how those were designed. And we’ll talk about
how to actually test for the significance
of human variation with respect to a particular
disease in a case and control study. And then we’ll talk about how
to use whole genome read data to detect variation
between humans and some of the
challenges in that, because it does not
make as many assumptions as the microarray studies,
and therefore is much, much more complicated to process. And so we’re going to
take a view into the best practices of processing
human read data so you can understand what
the state of the art is. And then we’re going to
turn to a study showing how we can bring together
different threads we’ve talked about in this subject. In particular, we’ve
talked about the idea that we can use other genomic
signals such as histone marks to identify things like
regulatory elements. So we’re going to talk about
how we can take that lens and focus it on the
genome to discover particular genomic variants that
have been revealed to be very important in a
particular disease. And finally, we’ll
talk about the idea that what– the beginning
we’re going to talk about today is all about correlation. And as all of you go forward
in your scientific career, I’m hopeful that you’ll always
be careful to not confuse association or correlation
with causation. You’re always respected
when you clearly articulate the difference when
you’re giving a talk saying that this is correlated,
but we don’t necessarily know it’s causative until we do
the right set of experiments. OK, on that note, we’ll turn
to the computational approaches we’re going to talk about. We’ll talk about contingency
tables and various ways of thinking about
them when we discuss how to identify whether or not
a particular SNP is associated with a disease using
various kinds of tests. And then we talk
about read data, and we’ll talk about
likelihood based tests. How to do things like
take a population of individuals and
their read data and estimate the
genotypic frequencies at a particular
locus using that data in toto using EM
based techniques. OK? So let us begin then. Some of the things we’re
not going to talk about include non-random
genotyping failure, methods to correct for
population stratification, and structural variants
and copy number variations. Point three we’ll
just briefly touch on, but fundamentally they’re
just embellishments on the fundamental techniques
we’re talking about, and so I didn’t really want
to confuse today’s discussion. Now a Mendelian
disorder is a disorder defined by a single gene,
and therefore, they’re relatively easy to map. And they also tend to
be in low frequency in the population because
they’re selected against, especially the more severe
Mendelian disorders. And therefore, they correspond
to very rare mutations in the population. By point of contrast, if you
thought about the genetics we discussed last
time, if you think about a trait that
actually perhaps is influenced by 200 genes and
maybe that one of those genes is not necessary or sufficient
for a particular disease. As a consequence, it could
be a fairly common variant and it’s only if you’re unlucky
enough to get all the other 199 variants will you actually
come down with that syndrome. And therefore, you can see
that the effect of variation in the human genome
is inversely related to its frequency– that
fairly rare variants can have very serious effects, whereas
fairly common variants tend to have fewer effects. And in the first phase of
mapping human variation, people thought that
common variants were things that had
an allelic frequency in the population
of 5% or greater. And then to burrow down deeper,
the 1000 Genomes Project surveyed a collection of
different populations. And therefore, if you
thought that a variant was prevalent in the
population at frequency of 0.5%, how many people
would have in the 1000 Genomes Project roughly? Just make sure among you
we’re phase-locked here. 0.5%, 1,000 people– AUDIENCE: 5. PROFESSOR: 5, great. OK. Good. Now of course, these are three
different populations or more, and so it might be that,
in fact, that variant’s only present in one
of the population. So it just might be
one or two people that actually have a
particular variant. So the idea is that the way that
you design SNP chips to detect single nucleotide polymorphisms,
otherwise known as “SNPs,” is that you do these
population-based sequencing studies and you
design the array based upon all of the common
variants that you find, OK? And therefore, the array
gives you a direct readout in terms of the
variation, in terms of all of these common variants. That’s where we’ll start today. And where we’ll end today is
sequencing based approaches, which make no assumptions
whatsoever and just all hell breaks loose. So you’ll see what happens, OK? But I wanted just to
reinforce the idea that there are different
allelic frequencies of variants and that as we get down to
rarer and rarer alleles, right, we have larger effects. But these higher
frequency alleles could also have effects even
though they’re much smaller. OK, so let’s talk about
how these variants arise and what they mean in terms
of a small little cartoon. So long, long ago,
in a world far, far away, a mutation
occurred where a base G got mutated
to a base A, OK? And this was in the context of
a population of individuals– all happy, smiling individuals
because they all actually do not have a disease. And our story goes,
what happens is that we had yet another
generation of people who are all happy, smiling because
they do not have the disease. Right? Yes, I do tell
stories at night, too. And then another
mutation occurred. And that mutation caused
some subset of those people to get the mutation and for
them to get the disease. So the original mutation was
not sufficient for people to get this genetic disease. It required a second
mutation for them to get the genetic disease, OK? So we got at least two
genes involved in it. OK, the other thing
that we know is that, in this particular
case, some of the people have the disease that
don’t have this mutation. And therefore, this
mutation is not necessary. It’s neither necessary
nor sufficient. Still, it is a marker of a
gene that increases risk. And that’s a
fundamental idea, right, that you can increase
risk without being necessary or sufficient to cause
a particular genetic disorder. OK? And so you get this association
then between genotype and phenotype, and
that’s what we’re going to go looking
for right now. We’re on the hunt. We’re going to go looking
for this relationship. So in certain older
individuals– hopefully, not myself in the
future– what happens is that your maculus, which
is the center of your eye, degenerates as shown here. And you get this
unfortunate property where you can’t actually
see in the center of your field of vision. It’s called age-related
macular degeneration. So to look for the
causes of this, which is known to be
genetically related, the authors of the study
collected a collection– a cohort, as it’s called–
of these European-descent individuals, all who are at
least 60 years old, to study the genetic foundations
for this disorder. And so they found
934 controls that were unaffected by age-related
macular degeneration and 1,238 cases, and they genotyped
them all using arrays. Now the question is, are
any of the identified SNPs on the array related
to this particular disorder? So I’ll give you
the answer first and then we’ll
talk about a couple of different ways of
thinking about this data, OK? So here’s the answer. Here’s a particular
SNP, rs1061170. There are the individuals
with AMD and the controls. And what you’re
looking at up here, these numbers are the
allelic counts, all right? So each person has
how many alleles? Two, right? That’s double the
number of individuals. And the question is,
are the C and T alleles associated with the cases
or controls significantly? And so you can compute
a Chi-square metric on this so-called
contingency table. And one of the things
about contingency tables that I think is
important to point out is that you hear about
marginal probabilities, right? And people probably
know that originally derived from the
idea of these margins along the side of a
contingency table, right? If you think about the marginal
probability of somebody having a C allele, regardless
of whether a case or control, it would be 2,192
over 4,344, right? So the formula for computing
the Chi-square statistic is shown here. It’s this sort of
scary-looking polynomial. And the number of
degrees of freedom is 1. It’s the number of rows
minus 1 times the number of columns minus 1. And the P-value we get is
indeed quite small– 10 to the minus 62. Therefore, the
chance this happened at random– even with
multiple hypothesis correction, given that we’re
testing a million SNPs– is indeed very, very low. This looks like a winner. Looks like we’ve got a
SNP that is associated with this particular disease. Now just to remind you about
Chi-square statistics– I’m sure people have seen this
before– the usual formulation is that you compute this
Chi-square polynomial on the right-hand side,
which is the observed number of something minus the
expected number of something squared over the expected
number or something, right? And you sum it up over
all the different cases. And you can see that the
expected number of As is given by the little
formula on the left. Suffice to say, if you expand
that formula and manipulate it, you get the equation we
had on the previous slide. So it’s still that fuzzy,
friendly Chi-square formula you always knew, just
in a different form, OK? Now is there
another way to think about computing the likelihood
of seeing data in a contingency table at random, right? Because we’re always asking,
could this just be random? I mean, could this have
occurred by chance, that we see the data arranged
in this particular form? Well, we’ve another
convenient way of thinking about
this, which is we could do Fisher’s Exact Test,
which is very related to the idea of the
hypergeometric test that we’ve talked
about before, right? What are the chances we would
see exactly this arrangement? Well, we would need to have,
out of a plus b C alleles, we’d have 8 of them be cases,
which is the first term there in that equation. And of the T alleles, we need to
have c of them out of c plus d be there. And then we need to have a
plus b plus c plus d choose a plus c– that’s the
total number of chances of seeing things. So this is the probability
of the arrangement in the table in this
particular form. Now people– I’ll let
you digest that for one second before I go on. So this is the number of ways
on the numerator of arranging things to get the table
the way that we see it over the total number or
ways of arranging the table, keeping the marginal
totals the same. Is that clear? So this is the probability,
the exact probability, of seeing the table
in this configuration. And then what you do is you
take that probability and all of the probabilities for all the
more extreme values, say, of a. And you sum them all
up and that gives you the probability of
a null hypothesis. So this is another
way to approach looking at the chance a
particular contingency table set of values would
occur at random. So if people talk about
Fisher’s Exact Test– you know, tonight at that cocktail party. “Oh yeah, I know about that. Yeah, it’s like
the hypergeometric. It’s no big deal.” You know? Right. All right. So now let us suppose that
we do an association test and you do the following design. You say, well, I’ve
got all my cases. They’re all at Mass General and
I want to genotype them all. And Mass General
is the best place for this particular disease,
so I’m going to go up there. I need some controls but I’m
running out of budgetary money, so I’m going to do all my
controls in China, right? Because I know it’s going
to be less expensive there to genotype them. And furthermore–
as a little aside, I was once meeting
with this guy who is like one of the ministers
of research in China. He came to my office. I said, so what do
you do in China? And he said, well, I guess
the best way to describe it is that I’m in charge of the
equivalent of the NSF, DARPA, and the NIH. I said, oh. I said, would like to
meet the president? Because I’d be happy to
call MIT’s president. I’m sure they’d be
happy to meet with you. He said, no. He said, I like going direct. So, at any rate,
I told him I was working in stem cell research. He said, you know, one thing I
can say about China– in China, stem cells, ethics, no problem. [LAUGHTER] At any rate, so you go to
China to do your controls, OK? And why is that a bad
experimental design? Can anybody tell me? You do all your cases here,
you do your controls in China. Yes? AUDIENCE: Because
the SNPs in China are not necessarily the same. PROFESSOR: Yes. The Chinese population’s
going to have a different set of SNPs,
right, because it’s been a contained population. So you’re going to
pick up all these SNPs that you think are going to
be related to the disease that are simply a consequence of
population stratification, right? So what you need to do
is to control for that. And the way you do that is you
pick a bunch of control SNPs that you think are
unrelated to a disease and you do a Chi-square
test on those to make sure that they’re
not significant, right? And methodologies for
controlling for population stratification by picking
apart your individuals and re-clustering
them is something that is a topic of
current research. And finally, the good news
about age-related macular degeneration is that
there are three genes with five common variants
that explain 50% of the risk. And so it has been viewed as
sort of a very successful study of a polygenic– that
is, multiple gene– genetic disorder that
has been dissected using this methodology. And with these genes, now
people can go after them and see if they can come up
appropriate therapeutics. Now using the same idea– cases,
controls– you look at each SNP individually and you
query it for significance based upon a null model. You can take a wide
range of common diseases and ask whether or
not you can detect any genetic elements that
might influence risk. And so here are a set
of different diseases, starting with bipolar
disorder at the top, going down to type 2
diabetes at the bottom. This is a so-called
Manhattan plot, because you see the buildings
along the plot, right? And when there are
skyscrapers, you go, whoa, that could be
a problem, all right? And so this is the
style– you see, this came out in
2007– of research that attempts to do genome
wide scans for loci that are related to
particular diseases. OK, now, I’d like to go on
and talk about other ways that these studies can
be influenced, which is the idea of linkage
disequilibrium. So for example, let us say that
I have a particular individual who’s going to produce a
gamete and the gamete’s going to be haploid, right? And it’s going have one
allele from one of these two chromosomes and one allele from
one of these two chromosomes. We’ve talked about
this before last time. And there are four
possibilities– AB, aB, Ab, and ab, OK? And if this was a
coin flip, then each of these genotypes
for this gamete would be identical, right? But let us suppose
that I tell you that there are only two
that result– this one, AB, and the small one, ab, OK? If you look at this, you
say, aha, these two things are linked and they’re
very closely linked. And so, if they’re always
inherited together, we might think that the distance
between them on the genome is small. So in the human genome,
what’s the average distance between crossover events
during a meiotic event? Does anybody know, roughly
speaking, how many bases? Hm? AUDIENCE: A megabase? PROFESSOR: A megabase. Little low. How many centimorgans
long is the human genome? All right? Anybody know? 3,000? 4,000? Something like that? So maybe 50 to 100 megabases
between crossover events, OK? So if these markers
are very closely organized along the genome,
the likelihood of a crossover is very small. And therefore, they’re going
to be in very high LD, right? And a way to measure that is
with the following formula, which is that if you link the
two locuses– we have L1 and L2 here. And now we’re talking about
the population instead of a particular individual. If the likelihood of the
capital allele A is piece of A and the probability
of the big B allele is piece of B, then if they
were completely unlinked, then the likelihood of
inheriting both of them together with would be
piece of A times piece of B, showing independence. However if they
aren’t independent, we can come up
with a single value D which allows us to quantify
the amount of disequilibrium between those two alleles. And the formula for D
is given on the slide. And furthermore, if it’s
more convenient for you to think about in terms
of r-squared correlation, we can define the
r-squared correlation as D squared over
PA, QA, PB, QB, as shown in the lower left
hand part of this slide, OK? This is simply a
way of describing how skewed the
probabilities are from being independent for
inheriting these two different loci in a population. Are there any questions
at all about that, the details of that? OK. So just to give you an example,
if you look at chromosome 22, the physical distance on
the bottom is in kilobases, so that’s from 0 to 1
megabase on the bottom. And you look at the
r-squared values, you can see things that
are quite physically close, as we suggested earlier,
have a high r-squared value. But there are still
some things that are pretty far away
that have surprisingly high r-squared values. There are recombination
hot spots in the genome. And it’s, once again, a topic
of current research trying to figure out how the genome
recombines and recombination is targeted. But suffice it to say, as you
can see, it’s not uniform. Now what happens as
a consequence of this is that you get regions
of the genome where things stick together, right? They’re all drinking
buddies, right? They all hang out together, OK? But here’s what I’m going to ask
you– how much of your genome came from your dad? Half. How much came from
your dad’s dad? AUDIENCE: A quarter. PROFESSOR: And from
your dad’s dad’s dad? AUDIENCE: An eighth. PROFESSOR: An eighth, OK? So the amount of your genome
going back up the family tree is falling off exponentially
up a particular path, right? So if you think about groups
of things that came together from your great,
great grandfather or his great, great
grandfather, right, the further back you go, the
less and less contribution they’re going to
have to your genome. And so the blocks are
going to be smaller– that is, the amount
of information you’re getting from
way back up the tree. So if you think about
this, the question of what blocks of things
are inherited together is not something that you
can write an equation for. It’s something that you
study in a population. You go out and you
ask, what things do we observe coming together? And generally, larger
blocks of things are inherited together, occur
in more recent generations, because there’s less
dilution, right? Whereas if you go way
back in time– not quite to where the dinosaurs
roamed the land, but you get the idea– the
blocks are, fact, quite small. And so, the HapMap project
went about looking at blocks and how they were
inherited in the genome. And what suffices to know is
that they found blocks– here you can see three
different blocks. And these are called
haplotype blocks and the things that
are colored red are high r-squared
values between different genetic markers. And we talked earlier
about how to compute that r-squared value. So those blocks typically
are inherited together. Yes? AUDIENCE: Are these blocks
like fuzzy boundaries? PROFESSOR: No. Well, remember in this
particular example, we’re only querying at
specified markers which are not necessarily at regular
intervals along the genome. So in this case, the blocks
don’t have fuzzy boundaries. As we get into
sequencing-based approaches, they could have
fuzzier boundaries. But haplotype
blocks are typically thought to be discrete blocks
that are inherited, OK? Good question. Any other questions? OK. So I want to impress
upon the idea that this is empirical, right? There’s no magic here in
terms of fundamental theory about what things should
be haplotype blocks. It’s simply that you
look at a population and you’re look at what
markers are drinking buddies and those make haplotype blocks
and you empirically categorize and catalog them– which can
be very helpful, as you’ll see. And thus, when we think
about genetic studies, when we think about the
length of shared segments, if you’re thinking
about studying a family, like a trio– a trio is a mom,
a dad, and a child, right? They’re going to share a
lot of genetic information, and so the haplotype blocks that
are shared amongst those three individuals are going
to be very large indeed. Whereas if you go
back generations, the blocks– like the
second cousins or things like that– the
blocks get smaller. So the x-axis on this
plot is the median length of a shared segment. And as an association
study, which is taking random people
out of the population, has very small shared
blocks indeed, OK? And so the techniques
that we’re talking about today are applicable
almost in any range, but they’re particularly
useful where you can’t depend upon
the fact that you’re sharing a lot of information
along the genome proximal to where the marker
is that’s associated with a particular disease. Now the other thing
that is true is that we should note that
the fact that markers have this LD associated
with them means that it may be that a particular
marker is bang on– what’s called a causative SNP. Or something that,
for example, sits in the middle of a gene
causing a missense mutation. Or it sits right in the middle
of a protein binding site, causing the factor
not to bind anymore. But also it could be something
that is actually a little bit away, but is highly correlated
to the causative SNP. So just keep in mind that
when you have an association and you’re looking at a SNP, it
may not be the causative SNP. It might be just linked
to the causative SNP. And sometimes these things
are called proxy SNPs. OK, so we’ve talked
about the idea of SNPs and discovering them. Let me ask you one more question
about where these SNPs reside and see if you
could help me out. OK, this is a really
important gene, OK? Call it RIG for short, OK? Now let us suppose that
you know that there are some mutations here. And my question for you is,
does it matter whether or not the two mutations look
like this or the mutations look like this, in your opinion? That is, both mutations
occur in one copy or on one chromosome
of the gene, whereas in the other case, we
see two different SNPs that are different than
reference, but they’re referring in both
mom and dad alleles. Is there a difference
between those two cases? Yeah? AUDIENCE: In terms of
the phenotype displayed? PROFESSOR: In terms of
the phenotype, sorry. AUDIENCE: It depends. PROFESSOR: It depends? AUDIENCE: Yes. PROFESSOR: OK. AUDIENCE: So if it causes a
recessive mutation, then no, because other genes will
be able to rescue it. But if it’s dominant,
then it’ll still– PROFESSOR: It’s actually
the other way around. If it’s recessive,
this does matter. AUDIENCE: Oh, I see. PROFESSOR: Because in this
case, with the purple ones, you still have one good
copy of the gene, right? However, with the
green ones, it’s possible that you have
ablated both good copies of the gene, this
really important gene, and therefore, you’re
going to get a higher risk of having a
genetic disorder. So when you’re scanning down
the genome then– you know, we’ve been asking where
are there differences from reference or from
between cases and controls down the genome, but we
haven’t asked whether or not they’re on mom or dad, right? We’re just asking,
are they there? But it turns out that
for questions like this, we have to know whether or
not the mutation occurred in only in mom’s chromosome
or in both chromosomes in this particular
neighborhood, all right? This is called phasing
of the variants. Phasing means
placing the variants on a particular chromosome. And then, by phasing
the variants, you can figure out some
of the possible phenotypic consequences of them. Because if they’re not
they phased, in this case, it’s going to be much less
clear what’s going on. So then the question
becomes, how do we phase variants, right? So phasing assigns alleles
to the parental chromosomes. And so, the set of alleles along
a chromosomes is a haplotype. We’ve talked about the
idea of haplotypes. So imagine one way to phase
is that if I tell you, by magic, in this population
you’re looking at, here are all the
haplotypes and these are the only ones that exist. You look in your
haplotypes and you go, aha, this haplotype exists but
this one does not, right? That this is a haplotype–
this two purples together is a haplotype, and
this green without one is another haplotype. So you see which
haplotypes exist– that is, what patterns of inheritance
of alleles along a chromosome you can detect. And using the established
empirical haplotypes, you can phase the variants, OK? Now the other way to
phase the variants is much, much simpler
and much better, right? The other way to
phase variants is you just have a single read that
covers the entire thing, right? And then the read, it
will be manifest, right? The read will cover
the entire region and then you see
the two mutations in that single
region of the genome. The problem we’re up against
is that most of our reads are quite short and we’re
reassembling our genotypes from a shattered genome. If the genome wasn’t
shattered, then we wouldn’t have this problem. So everybody’s
working to fix this. Illumina has sort of a
cute trick for fixing this. And PacBio, which is
another sequence instrument manufacturer, can produce reads
that are tens of thousands of bases long, which allows
you to directly phase the variants from the reads. But if somebody,
once again, comes up to you at the cocktail party
tonight and says, you know, I’ve never understood why
you have to phase variants. You know, this is a popular
question I get all the time. [LAUGHTER] You can tell them,
hey, you know, you have to know whether or
not mom and dad both have got big problems or just all
the problems are with mom, OK? Or dad. So you can put
their mind at ease as you’re finishing
off the hors d’oeuvres. OK, so I wanted just to tell
you about phasing variants because we’re about to go on to
the next part of our discussion today. We are leaving the very
clean and pristine world of very defined SNPs,
defined by microarrays, into the wild and woolly world
of sequencing data, right? Which is all bets are off. It’s all raw
sequencing data and you have to make sense
of it– hundreds of millions of sequencing reads. So today’s lecture is drawn from
a couple of different sources. I’ve posted some of
them on the internet. There’s a very nice article
by Heng Li on the underlying mathematics of SNP calling and
variation which I’ve posted. In addition, some of
the material today is taken from the Genome
Analysis Toolkit, which is a set of tools
over at the Broad, and we’ll be talking about
that during today’s lecture. The best possible case when
you’re looking at sequence data today is that you get
something like this, all right? Which is that you have
a collection of reads for one individual and you
align them to the genome and then you see that
some of the reads have a C at a particular base
position and other of the reads have a T at that base position. And so it’s a very
clean call, right? You have a CT heterozygote
at that position– that is, whatever person that
is is a heterozygote there. You can see the reference genome
at the very bottom, right? So it’s very difficult for
you to read in the back, but C is the reference allele. And the way that
the IGV viewer works is that it shows non-reference
alleles in color, so all those are the T alleles
you see there in red, OK? And it’s very, very
beautiful, right? I mean you can tell
exactly what’s going on. Now we don’t know whether
or not the C or the T allele are a mom and dad
respectively, right? We don’t know which of the
chromosomes they’re on, but suffice to say,
it’s very clean. And the way that all of
this starts, of course, is with a BAM file. You guys have seen
BAM files before. I’m not going to belabor this. There’s a definition
here and you can add extra
annotations on BAM files. But the other thing
I wanted to point out is that you know that BAM
files include quality scores. So we’ll be using those quality
scores in our discussion. The output of all
this typically is something called a variant
call file or a VCF file. And just so you are
not completely scared by these files, I want to
describe just a little bit about their structure. So there’s a header
at the top telling you what you actually did. And then chromosome 20 at this
base location has this SNP. The reference allele is
G, the alternative allele is A. This is some
of the statistics as described by this
header information, like DP is the read depth. And this tells you the status
of a trio that you processed. So this is the
allele number for one of the chromosomes,
which is 0, which is a G. The other one’s
a G, and so forth. And then this data right
here is GT, GQ, GP, which are defined up here. So you have one person,
second person, third person, along with which one
of the alleles, 0 or 1, they have on each of
their chromosomes, OK? So this is the output. You put in raw reads
and what you get out is a VCF file that for
bases along the genome calls variance, OK? So that’s all there
is to it, right? You take in your read data. You take your genome, throw
it through the sequencer. You take the BAM file,
you call the variants, and then you make your
medical diagnosis, right? So what we’re going to
talk about is what goes on in the middle there,
that little step– how do you actually
call the variants? And you might say, gee,
that does not seem too hard. I mean, I looked at
the slide you showed me with the CT heterozygote. That looked beautiful, right? I mean, that was just gorgeous. I mean, these sequencers are
so great and do so many reads, what can be hard
about this, after all? You know, it’s a quarter
to 2:00, time to go home. Not quite, OK? Not quite. The reason is actual
data looks like this. So these are all reads
aligned to the genome and, as I told you
before, all the colors are non-reference bases. And so you can see that
the reads that come out of an individual are
very messy indeed. And so we need to deal with
those in a principled way. We need to make good,
probabilistic assessments of whether or not there’s a
variant at a particular base. And I’m not going to belabor
all the steps of the Genome Analysis Toolkit,
suffice to say, here is a flow chart of all
the steps that go through it. First, you map your reads. You recalibrate the scores. You compress the
read set and then you have read sets for
n different individuals. And then you jointly call
the variants and then you improve upon the variants
and then you evaluate, OK? So I’ll touch upon some of
the aspects of this pipeline, the ones that I think
are most relevant, so that you can appreciate
some of the complexity in dealing with this. Let me begin with the
following question. Let us suppose that you have
a reference genome here, indicated by this line,
and you align a read to it. And then there’s some base
errors that are non-reference, so it’s variants calls down
at this end of the read, OK? So this is the five
prime, three prime. And then you align a read
from the opposite strand and you have some variant
calls on the opposite end of the read like this. And you’ll say to yourself,
what could be going on here, you know? Why is it that they’re
not concordant, right, when they’re mapped, but
they’re in the same region of the genome? And then you think
to yourself, well, what happens if I map this
successfully here correctly to the reference genome
and this correctly to the reference genome here,
but this individual actually had a chromosome that had
a deletion right here, OK? Then what would happen would
be that all these reads down here are going to be
misaligned, all of these bases are going to be misaligned
with the reference. And so you’re going
to get variant calls. And these bases will be also
misaligned with the reference, you’ll get variant calls. So deletions in
an individual can cause things to
be mapped but you get variant calls at the end. And so that is shown
here, where you have reads that are being mapped
and you have variant calls at the end of the reads. And it’s also a
little suspicious because in the middle here is
a seven-base pair homopolymer which is all T’s. And as we know,
sequencers are notoriously bad at correctly
reading homopolymers. So if you then
correct things, you discover that some
fraction of the reads actually have one of the T’s
missing and all the variants that were present
before go away. So this is a process
of INDEL adjustment when you are mapping the
region looking for variants. Now this does not occur we’re
talking about SNP microarrays. So this is a problem
that’s unique to the fact that we’re making many
fewer assumptions when we map reads to
the genome de novo. The second and another
very important step that they’re very proud
of is essentially– I guess how to put this
politely– finding out that manufacturers of
sequencing instruments, as you know, for every
base that they give you, they give you an estimate
of the probability that the base is correct–
or it’s wrong, actually. A so-called Phred score–
we’ve talked about that before. And as you would imagine,
manufacturers’ instruments are sometimes optimistic,
to say the least, about the quality of their scores. And so they did a survey of
a whole bunch of instruments and they plotted the reported
score against the actual score, OK? And then they have a whole
step in their pipeline to adjust the scores, whether
you be a Solexa GA instrument, a 454 instrument, a SOLiD
instrument, a HiSeq instrument, or what have you. And there is a way to adjust the
score based upon the raw score and also how far down
the read you are, as the second line shows. The second line is a
function of score correction versus how far down the read or
number of cycles you have gone. And the bottom is adjustments
for dinucleotides, because some
instruments are worse a certain dinucleotides
than others. As you can see, they’re very
proud of the upper left hand part. This is one of the major
methodological advances of 1000 Genome
Project, figuring out how to recalibrate quality
scores for instruments. Why is this so important? The reason it’s important
is that the estimate of the veracity of
bases figures centrally in determining whether or
not a variant is real or not. So you need to have as best
an estimate as you possibly can of whether or not a base
coming out of the sequencer is correct, OK? Now if you’re doing
lots of sequencing of either individuals
or exomes– I should talk about exome
sequencing for a moment. Up until recently,
it has not really been practical to
do whole genome sequencing of individuals. That’s why these SNP arrays
were originally invented. Instead, people sequenced the
expressed part of the genome, right? All of the genes. And they can do this
by capture, right? They go fishing. They create fishing poles out of
the genes that they care about and they pull out the
sequences of those genes and they sequence them. So you’re looking at a
subset of the genome, but it’s an important part. Nonetheless, whether or
not you do exome sequencing or you do sequencing
of the entire genome, you have a lot of reads. And so the reads that you
care about are the reads that are different from reference. And so you can reduce the
representation of their BAM file simply by throwing all
the reads on the floor that don’t matter, right? And so here’s an example of
the original BAM file and all the reads, and what
you do is you just trim it to only the
variable regions, right? And so you are
stripping information around the variant regions
out of the BAM file and things greatly compress
and the downstream processing becomes much more efficient. OK. Now let’s turn to the
methodological approaches once we have gotten the
data in as good a form as we possibly can get it, we
have the best quality scores that we can possibly
come up with, and for every base position,
we have an indication of how many reads say
that the base is this and how many reads say
the base is that, OK? So we have these raw read counts
of the different allelic forms. And returning to this,
we now can go back and we can attempt
to take these reads and determine what the
underlying genotypes are for an individual. Now I want to be clear
about the difference between a genotype
for an individual and an allelic spectrum
for a population. A genotype for an
individual thinks about both of the alleles
that that individual has, and they can be phased
or unphased, right? If they’re phased,
it means you know which allele belongs to mom and
which allele belongs to dad, so to speak, right? If they’re unphased, you
simply know the number of reference alleles that
you have in that individual. Typically, people think about
there being a reference allele and an alternative allele,
which means that a genotype can be expressed as
0, 1, or 2, which is the number of
reference alleles present at a particular base
if it’s unphased, right? 0, 1, or 2– 0 mean there are
no reference alleles there, 1 meaning that it’s
a heterozygote, 2 mean there are two reference
alleles in that individual. OK? So there are different ways
of representing genotype, but once again, it represents
the different allelic forms of the two chromosomes. And whatever form you
choose, the probability over those genotypes
has to sum to 1. You can think about
the genotype ranging over all the possible bases from
mom and from dad or over 0, 1, and 2. Doesn’t really matter,
depending upon which way you want to simplify the problem. And what we would like to do
is, for a given population– let’s say cases
or controls– we’d like to compute the
probability over the genotypes with high veracity, OK? So in order to do
that, we’ll start by taking all the
reads for each one of the individuals
in a population, OK? And we’re going to compute
the genotype likelihoods for each individual. So let’s talk about
how to do that. Now everything I’ve written on
the board is on the next slide. The problem is, if I
put it on the slide, it will flash in front
of you and you’ll go, yes, I understand that, I think. This way, I’ll put
it on the board first and you’ll look at
it and you’ll say, hm, maybe I don’t
understand that, I think. And then you’ll
ask any questions and we can look at the
slide in a moment, OK? But here’s the fundamental
idea, all right? At a given base in the
genome, the probability of the reads that we see based
upon the genotype that we think is there can be expressed
in the following form, which is that we take the product over
all the reads that we see, OK? And the genotype is going to
be a composition of the base we get from mom and the base
that we get from dad, or it could simply
be 0, 1, and 2. We’ll put that
aside for a moment. So what’s the chance that
we inherited something from a particular base from mom? It’s this base over
a particular read. What’s the chance
a particular read came from mom’s chromosome? That’s one half
times the probability of the data given
the base that we see. And once again, since
it could be a coin flip whether the read came
from mom or dad’s chromosome, divide it by 2– the
probability of the data that we see with dad’s version
of that particular base. So once again, for
all the reads we’re going to compute the
probability of the read set that we see given a particular
hypothesized genotype by looking at what’s the
likelihood or the probability of all those reads. And for each read,
we don’t know if it came from mom or from dad. But in any event, we’re going
to compute the probability on the next blackboard,
this bit right here. OK? Yes? AUDIENCE: So if you assume
that mom and dad have a different phase at
a particular base, couldn’t that possibly
skew the probability of getting a read from mom’s
chromosome or dad’s chromosome? PROFESSOR: A different phase? AUDIENCE: So the composition
of bases affect what you get. I think certain
base compositions are more likely to be
sequenced, for example. PROFESSOR: Yes. AUDIENCE: Could that bias– PROFESSOR: Yes. In fact, that’s why on,
I think, the third slide, I said non-random genotyping
error was being excluded. AUDIENCE: Oh. PROFESSOR: Right? From our discussion today? But you’re right that it might
be that certain sequences are more difficult to
see, but we’re going to exclude that
for the time being. OK? So this is the
probability of the reads that we see given a
hypothesized genotype. And I’ll just show you,
that’s very simple. That we have a read, let’s
call the read D sub j, and we have the base that
we think we should see. And if the base is correct,
then the probability that that’s correct is 1
minus the error, right, that the machine reported. And if it isn’t
correct, the probability is just the error at that base
that the machine reported. So we’re using the error
statistics from the machine and if it matches what we
expect, it’s 1 minus the error. And if it doesn’t match,
it’s just simply going to be the error
that’s reported, OK? So this is the probability of
seeing a particular read given a hypothesized base
that should be there. Here’s how we use that, looking
at all the possible bases that could be there given a
hypothesized genotype. Remember, this genotype is
only going to be one pair. It’s only going to be AA or
TT or what have you, right? So it’s going to be one pair. So we’re going to be testing
for either one or two bases being present. And finally, we want to
compute the posterior of the genotype given the
data we have observed, OK? So we want to compute what’s
the probability of the genotype given the reads that
we have in our hand. This is really important. That is what that genotype
likelihood is up there. It’s the probability of the read
set given the genotype times the probability of
the genotype– this is a prior– over the
probability of the data. This is simply Bayes’ Rule. So with this, for
an individual now, we can compute the
posterior of the genotype given the read set. Very simple concept. So in another form, you can
see the same thing here, which is the Bayesian model. And we’ve talked about this
haploid likelihood function, which was on the
blackboard I showed you. And we’re assuming all
the reads are independent and that they’re
going to come equally from mom and dad, more
or less, et cetera, OK? And the haploid likelihood
function, once again, just is using the error
statistics for the machine. So I’m asking if the
machine says this is an A and I think it’s an A, then the
probability that that’s correct is 1 minus the error
of the machine. If the two are not
in agreement, it’s simply the error in the
machine that I’m using. So this allows me now to
give a posterior probability of a genotype given a
whole bunch of reads. And the one part that
we haven’t discussed is this prior,
which is how do we establish what we think is
going on in the population and how do we set that? So if you look back
at the slide again, you can see that we
have these individuals and there’s this magic step
on the right-hand side, which is that somehow we’re
going to compute a joint estimate
across all the samples to come up with an estimate
of what the genotypes are in a particular SNP position. And the way that we can do
that is with an iterative EM procedure– looks
like this– so we can estimate the probability
of the population genotype iteratively using this
equation until convergence. And there are various tricks. As you’ll see if you
want to delve further into this in the
paper I posted, there are ways to deal with some
of the numerical issues and do allele count
frequencies and so forth. But fundamentally,
in a population we’re going to
estimate a probability over the genotypes for
a particular position. And just to keep
it simple, you can think about the
genotypes being 0, 1, or 2– 0, no reference
alleles present; 1, one reference allele present
to that site; 2, two reference alleles present
to that site, OK? So we get a
probability of each one of those states for
that population. Any questions at all about that? The details or anything at all? People get the general idea
that what we’re just doing is we’re taking a bunch of
reads at a particular position for an individual and
computing the posterior probability of a genotype
seeing all of those reads and then, when we think about
the entire population– say either the cases
or the controls– we’re computing the
probability over the genotypes within that population
using this kind of iterative procedure. OK, so going on then, if
we go back to our 0, 1, 2 kind of genotype
representation, we can marginalize psi,
which is the probability of the reference allele
being in the population, and 1 minus psi
being the probability of the non-reference allele,
where the capital alleles are reference and the little
ones are non-reference. And then we could also
for epsilon 0, epsilon 1, And Epsilon 2, those
are the probabilities of the various allelic
forms, the various genotypes. And actually, I think
epsilon 0 should be little A, little A. Must have
got the two of them flipped, but it’s not
really that important. OK, so what do we know
about a population? Who’s heard about
Hardy-Weinberg before? Hardy-Weinberg equilibrium? OK. So Hardy-Weinberg equilibrium
says that, for example, in a population, if the allelic
frequency of the reference allele is psi, right, what’s
the chance that an individual should be AA, big A, big
A, reference, reference? In a population? Pardon? I think I heard it. Psi squared, right? We’re going to assume
diploid organisms, we’re going to
assume random mating, we’re going to
assume no selection, we’re going to assume no
bottlenecks, and so forth, right? That over time, the population
will come to its equilibrium in the exchange of alleles. However, if there’s
strong selection or if part of the
population gets up and moves to a different continent
or something of that sort, you can get out of equilibrium. And so one question,
whenever you’re doing a genetic
study like this– is your population in
equilibrium or not? And we have a direct way for
testing for that because we’re actually estimating
the genotypes, right? So what we can do is this test. We can do a log likelihood
test directly, right? And we can compare the
probability of the observed genotypes– these are E1 and
E2, where the number indicates the number of reference
copies– over the probability of the genotypes being
composed directly from the frequency of
the reference allele. And this will tell
us whether or not these are concordant or not. And if the Chi-square
value is large enough, we’re going to say that this
divergence couldn’t have occurred at random and
therefore the population is not in equilibrium. And you might say,
well, gee, why do I really care if it’s
in equilibrium or not? I mean, you know,
what relevance does that have to me when
I’m doing my test? Well, here’s the issue. The issue is this– you’re going
to be testing whether or not genotypes are different
between a case and a control population, let’s say, OK? And you have a couple
different tests you can do. The first test is
the test on the top and the second test is
the test on the bottom. Let’s look at the test on
the bottom for a moment, OK? The test in the bottom
is saying you consider the likelihood of
the data in group one and group two
multiplied together over the probability of the
data with the groups combined and you ask whether or not the
increased likelihood– you’re willing to pay for that given
the two degrees of freedom that model implies, right? Because you have to have two
additional degrees of freedom to pay for that in the bottom. On the other hand,
in the top, you only have one degree of
additional freedom to pay for the difference in
simply the reference allele frequency. And so these are two
different metrics you can use to test
for associations for a particular SNP in two
different case and control populations. The problem comes is that if the
population is in equilibrium, then the bottom has too many
degrees of freedom, right? Because the bottom,
in some sense, can be computed
directly from the top. You can compute the epsilons
directly from the size if it’s in equilibrium. So you need to
know whether or not you’re in equilibrium or not
to figure out what kind of test to use to see whether or not a
particular SNP is significant. OK, so just a brief review where
we’ve come to at this point. I’ve handed you a
basket of reads. We’re focusing on a particular
location in the genome. For an individual, we can
look at that basket of reads and compute a posterior
probability of the genotype at that location. We then asked if we take
all of the individuals in a given interesting
population, like the cases, we could compute the
posterior or the probability of the genotype over
all those cases. We then can take the
cases and the controls and test for associations using
this likelihood ratio, OK? So that is the way to go
at the question of SNPs. And I’ll pause here
and see if there any other questions about this. OK, now there are
lots of other ways of approaching
structural variation. I said I would touch upon it. There is another
method which is– we’ve not been here assigning
what haplotypes to things or paying attention to
which chromosome or mom or dad a particularly
allele came from. But suffice to
say– I’ll let you read this slide
at your leisure– the key thing is that, imagine
you have a bunch of reads. What you can do in
a particular area there’s going to
be a variant is you can do local assembly
of the reads. We want to do local assembly
because local assembly handles general cases of
structural variation. And if you then take
the most likely cases of the local assembly
supported by reads, you have the different possible
haplotypes or collections of bases along the
genome from the assembly. And we’ve already talked
about, earlier in class, how to take a given
sequence of bases and estimate the probability
of the divergence from another string. So you can estimate
the divergence of each one of those
assemblies from the reference and compute likelihoods, like
we did before for single bases, although it’s
somewhat more complex. And so another way
to approach this is, instead of asking
about individual bases and looking at the likelihood
of individual bases, you can look at doing
localized assembly of the reads that handle
structural variation. And if you do that,
what happens is that you can recover
INDEL issues that appear to call SNP variants that
actually are actually induced by insertions and deletions
in one of the chromosomes. So as you can see, as things
get more sophisticated in the analysis of
human genome data, one needs a variety
of techniques, including local assembly,
to be able to recover what’s going on. Because of course,
the reference genome is only an approximate
idea of what’s there and is being
used as a scaffold. So we’ve already talked
about the idea of phasing, and we talked about why phasing
is important, especially when we’re trying to
recover whether or not you have a loss of
function event, right? And so the phasing
part of genomics right now is highly
heuristic, relies partly upon empirical data from
things like the HapMap Project and is outside the
scope of what we’re going to talk about,
because we could talk about phasing for
an entire lecture. But suffice it to
say, it’s important. And if you look at
what actually goes on, here’s a trio, mom,
dad, and the daughter. You can see down at the
bottom, you see mom’s reads. And you see dad actually
has two haplotypes. He got one haplotype
from one of his parents and the other haplotype
from both of his parents. And then the daughter actually
has the haplotype number one from dad and no haplotype
number one from mom. So you can see how these
blocks of mutations are inherited through the
generation in this form. And finally, if you
look at a VCF file, if you see a
vertical bar, that’s telling you that the
chromosomal origin is fixed. So it tells you, for
example, in this case, the one where the
arrow’s pointed to is that variant
number one, which is the alternative
variant T came from mom and a T came from dad. So VCF, when it has
slashes between the two different alleles of a
genotype is unphased, but you can actually have
a phased VCF version. And so there’s a whole
phase in the GATK tool kit that does phasing. And finally, we get
through all this, the question is how important
are the variants you discover? And so there’s a
variant analysis phase and it will go through and
annotate all the variants. For example, this is a
splice site acceptor variant which is in a
protein coating gene and it’s thought
to be important. And so at the end
of this pipeline, what’s going to
happen is you’re going to be spitting out not
only the variants but, for some of them, what
their annotated function is. OK, so that ends the
part of our lecture where we’re talking about
how to process raw read data. And I encourage you to look
at the GATK and other websites to actually look at
the state of the art. But as you can see, it’s
an evolving discipline that has a kernel of principal
probabilistic analysis in part of its core surrounded by
a whole lot of baling wire, right, to hold it all together. And you get the
reads marshalled, organized, compressed,
aligned properly, phased, and so forth, OK? Let’s talk now about how
to prioritize variants. And I just wanted to show you
a very beautiful result that is represented by this paper,
which came out very recently. And here is a portion
of the genome. And we’re looking
here at– you see here– a pancreatic disorder. And there is an enhancer
on the right-hand side of the screen where that
little red square is. And recall that we said that
certain histone marks were present typically
over active enhancers. And so you can see the
H3K4 mono-methyl mark being present over that little
red box as well as the binding of two pancreatic
regulators, FoxA2 and Pdx1. And within that
enhancer you can see there are a whole lot of
variants being called. Well, not a whole lot. There are actually
five different variants being called. And in addition to those
five specific SNP variants, there’s also another
variation that was observed in the population of a 7.6-kb
deletion right around that enhancer. And if you look at the
inheritance of those mutations with disease
prevalence, you can see that there’s a very
marked correlation. That when you inherit
these variants, you get this Mendelian disorder. So it’s a single
gene disorder really. And in order to confirm this,
what the authors of this study did was they took
that enhancer and they looked at all the different
SNPs and they mutated it. And in the upper
left-hand corner, you can see that the five little
asterisks note the decrease in activity of that
enhancer when they mutated the bases indicated
at SNP positions. The three C’s on the
panel on the right with the y-axis being
relative interaction shows that that
enhancer is interacting with the promoter of that gene. And they further
elucidated the motifs that were being interacted with
and the little arrows point to where the mutations
in those motifs occur. So they’ve gone
from an association with that particular disease
to the actual functional characterization
of what’s going on. I’ll leave you with a final
thought to think about. This is the thing
that caused the brawls in the bars I told you about
at the beginning of today’s lecture. Let’s suppose you look
at identical twins, monozygotic twins, and you
ask the following question. You say, OK, in
monozygotic twins, the prevalence of a particular
disease is a 30% correlative. That is, if one individual
in a twin has the disease, there’s a 30% chance that the
other twin’s going to get it. Now there are two
possibilities here, which is that for
all pairs of twins, there’s a very low risk
that you’re going to get it, or that there are some
subset of genotypes where if one twin has it, the other
one’s always going to get it. So the author of the
study actually looked at a block of identical twin
data and asked two questions. The first was if you look at
the percentage of cases that would test positive, making
no assumptions about genotype, using twin data, you
can see the percentage of people that actually
have a disease that will test positive
is actually fairly low for a wide
variety of diseases. All these diseases were
studied in the context of identical twins. And this suggested to
them that, in fact, personal genomic
sequencing might not be as predictive
as one might like. That is, if you have a disease,
for over half of these, the test will not be positive. And furthermore, if you test
negative for the disease, your relative risk–
that is, the chance you’re going to get this
disease to the chance you get it at random in the population–
is not really reduced that much. And so, since this study
relied solely on twin data and didn’t make any
other assumptions, it raised the question in
the field of to what extent is personal genome sequencing
going to be really helpful? So on that note, we’ve
talked a lot today about the analysis of
human genetic variation. I hope you’ve enjoyed it. Once again, on Thursday
we have Ron Weiss coming. Thank you very much. This concludes lecture 20 of the
formal material in the course and we’ll see you in lecture. Thank you very much.

19 comments

  1. I feel bad because the class is very unresponsive to the point where the teacher starts to disengage about 20 minutes in. At which point the lecturer and the students lose a connection (my hypothesis), and he starts to doubt how interested everyone is. We appreciate you Mr David Gifford, don't ever forget that! Always believe in yourself and don't let the dulled minds of the mob get you down!

  2. 4:13 A lot of correlational gobbledegook, given the claims that some corners of this field keep making – that lead no where

  3. 19:15 Polygenetics (maybe, nearly, w/no follow up replication or Tx/Rx) comes up w/the win for 50& genetic loading for associated risk, maybe probably.

  4. 32:44 In recessive illness, taking out primary in x+y line = bad news [phasing of varience]

  5. 57:25 assuming independant reads, eq from ma/da (Haplo lily pi fcnt)[Bayes Inf]

  6. 1:14:03 Association Variant Pedigrees (enhancers & mutating NSP position tests to elucidate promoter of gene proper) [causality claims of fctn]

  7. 1:16:30 Ident twins studies show no great personal genome med promise in path, nor risk reduction in neg findings. <3

  8. Lecture Outline Available | Chimera Embedded
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