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PROFESSOR: So as you recall last time

we talked about chromatin structure and chromatin

regulation.

And now we're going to move on to genetic analysis.

But before we did that, I want us to touch on two points

that we talked about briefly last time.

One was 5C analysis.

Who was it that brought up-- who was the 5C expert here?

Anybody?

No?

Nobody wants to own 5C.

OK.

But as you recall, we talked about ChIA-PET

as one way of analyzing any to any interactions in the way

that the genome folds up and enhancers talk to promoters.

And 5C is a very similar technique.

I just wanted to show you the flow

chart for how the protocol goes.

There is a cross linking.

A digestion with a restriction enzyme

step, followed by a proximity ligation step,

which gives you molecules that had been brought together

by an enhancer, promoter complex, or any other kind

of distal protein-protein interaction.

And then, what happens is that you design specific timers

to detect those ligation events.

And you sequence the result of what

is known as ligation mediated amplification.

So those primers are only going to ligate

if they're brought together at a particular junction, which

is defined by the restriction sites lining up.

So, 5C is a method of looking at which regions of the genome

interact and can produce these sorts of results,

showing which parts of the genome

interact with one another.

The key difference, I think, between chIA-PET and 5C

is that you actually have to have these primers designed

and pick the particular locations you want to query.

So the primers that you design represent query locations

and you can then either apply the results to a microarray,

or to high throughput sequencing to detect these interactions.

But the essential idea is the same.

Where you do proximity based ligation

to form molecules that contain components

of two different pieces of the genome

that have been brought together for some functional reason.

The next thing I want to touch upon

was this idea of the CpG dinucleotides

that are connected by a phosphate bond.

And you recall that I talked about the idea

that they were symmetric.

So you could have methyl groups on the cytosines in such a way

that, because they could mirror one another,

they could be transferred from one strand of DNA

to the other strand of DNA, during cell replication

by DNA methyltransferase.

So it forms a more stable kind of mark and as you recall,

DNA methylation where something occurred

in lowly expressed genes and typically in regions

of the genome that are methylated.

Other histone marks are not present

and the genes are turned off.

OK.

So those were the points I wanted

to touch upon from last lecture.

Now we're going to embark upon an adventure,

looking for the answer to, wear is missing heritability found?

So it's a big open question now in genetics.

In human genetics, which is that we really

can't find all the heritability.

And as a point of introduction, the narrative

arc for today's lecture is that, generally speaking,

you're more like your relatives than random people

on the planet.

And why is this?

Well obviously you contain components of your mom

and dad's genomes.

And they are providing you with components of your traits.

And the heritability of a trait is

defined by the fraction of phenotypic variance

that can be explained by genetics.

And we're going to talk today about computational models that

can predict phenotype from genotype.

And this is very important, obviously,

for understanding the sources of various traits and phenotypes.

As well as fields such as pharmacogenomics

that try and predict the best therapy for a disease

based upon your genetic makeup.

So, individual loci in the genome

that contribute to quantitative traits

are called quantitative trait locis, or QTLs.

So we're going to talked about how to discover them

and how to build models of quantitative traits using QTLs.

And finally, as I said at the outset,

our models are insufficient today.

They really can't find all of the heritability.

So we're going to go searching for this missing heritability

and see where it might be found.

Computationally, we're going to apply a variety of techniques

to these problems.

A preview is, we're going to build

linear models of phenotype and we're

going to use stepwise regression to learn these models using

a forward feature selection.

And I'll talk about what that is when

we get to that point of the lecture.

We're going to derive test statistics for discovering

which QTLs are significant and which QTLs are not,

to include in our model.

And finally, we're going to talk about how

to measure narrow sense heritability and broad sense

heritability in environmental variance.

OK.

So, one great resource for traits that are fairly simple.

That primarily are the result of a single gene mutation,

or where a single gene mutation plays a dominant role,

is something called Online Mendelian Inheritance in Man.

And it's a resource.

It has about 21,000 genes in it right now.

And it's a great way to explore what human genes function

is in various diseases.

And you could query by disease.

You can query by gene.

And it is a very carefully annotated and maintained

collection that is worthy of study,

if you're interested in particular disease genes.

We're going to be looking at more complex analyses today.

The analyses we're going to look at

are where there are many genes that

influence a particular trait.

And we would like to come up with general methods

for discovering how we can de novo from experimental data--

discover all the different genes that participate.

Now just as a quick review of statistics,

I think that we've talked before about means in class

and variances.

We're also going to talk a little bit

about covariances today.

But these are terms that you should

be familiar with as we're looking today

at some of our metrics for understanding heritability.

Are there any question about any of the statistical metrics that

are up here?

OK.

So, a broad overview of genotype to phenotype.

So, we're primarily going to be working

with complete genome sequences today,

which will reveal all of the variance that

are present in the genome.

And it's also the case that you can subsample a genome

and only observe certain variance.

Typically that's done with microarrays

that have probes that are specific to particular markers.

The way those arrays are manufactured

is that whole genome sequencing is done at the outset, and then

high prevalence variance, at least

common variance, which typically are

at a frequency of at least 5% in the population

are queried by using a microarray.

But today we'll talk about complete genome sequence.

An individual's phenotype, we'll say

is defined by one or more traits.

And a non-quantitative trait is something perhaps as simple as

whether or not something is dead or alive.

Or whether or not it can survive in a particular condition.

Or its ability to produce a particular substance.

A quantitative trait, on the other hand,

is a continuous variable.

Height, for example, of an individual

is a quantitative trait.

As is growth rate, expression of a particular gene,

and so forth.

So we'll be focusing today on estimating quantitative traits.

And as I said, a quantitative trait or loci,

is a marker that's associated with a quantitative trait

and could be used to predict it.

And you can sometimes hear about eQTLs,

which are expression quantitative trait loci.

And they're loci that are related to gene expression.

So, let's begin then, with a very simple genetic model.

It's going to be haploid, which means, of course,

there's only one copy of each chromosome.

Yeast is the model organism we're

going to be talking about today.

It's a haploid organism.

And we have mom and dad up there.

Mom on the left, dad on the right in two different colors.

And you can see that mom and dad in this particular example,

have n different genes.

They're going to contribute to the F1 generation, to junior.

And the relative color is white for mom, black for dad,

are going to be used to describe the alleles,

or the allelic variance that are inherited

by the child, the F1 generation.

And as I said, a specific phenotype

might be alive or dead in a specific environment.

And note that I have drawn the chromosomes to be disconnected.

Which means that each one of those genes

is going to be independently inherited.

So the probability in the F1 generation

that you're going to get one of those from mom or dad

is going to be a coin flip.

We're going to assume that they're

far enough away that the probability of crossing over

during meiosis is 0.5.

And so we get a random assortment

of alleles from mom and dad.

OK?

So let us say that you go off and do an experiment.

And you have 32 individuals that you produce out of a cross.

And you test them, OK.

And two of them are resistant to a particular substance.

How many genes do you think are involved in that resistance?

Let's assume that mom is resistant and dad is not.

OK.

If you had two that were resistant out of 32,

how many different genes do you think were involved?

How do you estimate that?

Any ideas?

Yes?

AUDIENCE: If you had 32 individuals

and say half of them got it?

PROFESSOR: Two, let's say.

One out of 16 is resistant.

And mom is resistant.

AUDIENCE: Because I was thinking that if it was half of them

were resistant, then you would maybe guess one gene,

or something like that.

PROFESSOR: Very good.

AUDIENCE: So then if only eight were

resistant you might guess two genes, or something like that?

PROFESSOR: Yeah.

What you say is, that if mom's resistant, then

we're going to assume that you need

to get the right number of genes from mom to be resistant.

Right?

And so, let's say that you had to get four genes from mom.

What's the chance of getting four genes from mom?

AUDIENCE: Half to the power of four.

PROFESSOR: Yeah, which is one out of 16, right?

So, if you, for example had two that were resistant out of 32,

the chances are one in 16.

Right?

So you would naively think, and properly so,