Hardy-Weinberg Equilibrium

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Del curso dictado por Novosibirsk State University

From Disease to Genes and Back

28 calificaciones

Novosibirsk State University

From Disease to Genes and Back

28 calificaciones

Human genetics explores the genetically determined similarities and differences between human beings. This scientific discipline encompasses a variety of related fields such as molecular genetics, genomics, population genetics and medical genetics. Study of human genetics can help to find answers to questions regarding the inheritance and development of different human phenotypes. The field of medical genetics is quickly growing and dynamically developing thanks to the new technologies such as the next-generation sequencing. Most human diseases have a genetic component. This genetic component varies by disease. Some rare diseases appear to be completely determined by the genome, whereas more common diseases arise from a complex interplay of many genes, the environment and chance. The understanding of how our genomes contribute to disease susceptibility offers the prospect of large gains: it may guide disease diagnostics and prognostics and help in developing new therapies. The overall goal of this course is to describe how the researchers find genes responsible for different diseases and how this information is used to better understand and fight these diseases. You will learn about current approaches for finding single genetic variants underlying monogenic (Mendelian) diseases and sets of variants responsible for more complex, multifactorial ones. Furthermore, you will learn how the identification of these genetic variants makes it possible to understand how the affected biological pathways lead to disease development. During the final week of the course, we will talk more about clinical applications of the genetic findings. Upon completing the course, you will be able to: - give examples of monogenic and complex disorders - recognise patterns of Mendelian inheritance of monogenic diseases; - understand and describe principles and methods of gene mapping ; - describe the main steps and principles of genome-wide association studies (GWAS); - give examples of modern technologies that are currently used to find variants underlying human diseases; - discuss the approaches to finding causative variants underlying complex disorders; - discuss the possibilities and areas of application of genetic findings.

De la lección

Populational genetics

During this week, Yurii Aulchenko will teach you the basics of population and quantitative genetics. Population genetics is a branch of genetics that deals with genetic variation among individuals in a population. "Nothing in Biology Makes Sense Except in the Light of Evolution" is a quotation from a 1973 essay by the evolutionary biologist Theodosius Dobzhansky. The fundamental importance of population genetics lies in the insights it provides into the mechanisms of evolution, thus allowing geneticists to better understand the drivers behind the organization and functioning of human genomes. You will learn about such phenomena as population structure, selection and genetic drift. You will also learn about quantitative genetics, which studies how the genes and environment control variations in complex phenotypes.

Hardy-Weinberg Equilibrium8:27

Conoce a los instructores

Marianna Bevova
PhD, Director of GIGA Doctoral School
University of Liège (GIGA)
Yurii Aulchenko
PhD, Professor, Head of Theoretical and Applied Functional Genomics Laboratory
Theoretical and Applied Functional Genomics Laboratory
Michel Georges
PhD, Professor, GIGA Research Director
University of Liège
Gert Matthijs
PhD, Professor
Center for Human Genetics, University of Leuven
Lennart Karssen
PhD, Owner and Chief Computational Scientist
PolyOmica
Natalia Aulchenko
M.Sc., Project manager
Theoretical and Applied Functional Genomics Laboratory
Yakov Tsepilov
PhD, Senior Researcher
Theoretical and Applied Functional Genomics Laboratory
Sodbo Sharapov
M.Sc, Junior Researcher
Theoretical and Applied Functional Genomics Laboratory
Alexander Tashkeev
Skolkovo Institute of Science and Technology (Skoltech), Junior Researcher
Laboratory of Computational and Structural Transcriptomics

Now we have defined

the major factors which operate on the genetics of populations,

we can even have the definition of genetic population.

I would like to go to a little bit of more mathematical and specific example.

But before we can put mathematics in practice,

we really need to come up with a concept,

very abstract concept, of a genetic population

with which we could be able to operate in mathematical terms.

So what am I going to assume about this hypothetical population,

which will be subject of our mathematical investigation?

We are going to first assume that it's very large,

it's actually infinitely large.

And this is a very important assumption which will allow us to

operate with the terms of probability theory.

And then secondly, we are going to assume that generations are not overlapping.

So, what is actually going to happen is that one generation is going

to give rise to a pool of gametes,

and from this pool of gametes,

pairs of gametes is going to be sampled to define the next generation.

And the first generation you can think of this as it's dying out or something,

but the generations are not overlapping.

The mating happens only within one generation.

And our third line of assumptions is about segregation and aggregation of alleles.

We will assume random and abandoned segregation of

the alleles and also aggregation of these gametes in forming zygotes.

And this assumption is equivalent to assumption of

panmixia and that Mendel's rules are in place.

Now, if you think of such ideal population,

what kind of expectations would be there for fate of an allele?

So, let's consider a specific system which is made of two alleles, A and B.

And consequently, in the population we could observe three genotypes,

AA, AB and BB,

two homozygous and one heterozygous.

Now, if I want to think like what happens to the frequency of alleles and what are

the expectations of genotypic distributions used in the model we have just formulated?

Then, first from the parental generation,

we need to form a gametic pool.

So, each individual will dump two alleles into this pool.

And then we can easily estimate the frequency of A alleles in this genetic pool

as the probability of homozygote A to be

in parental generation plus half of the probability of heterozygote,

and this falls from the very simple fact that an individual of

the homozygous genotype would generate only gametes of the specific type,

while heterozygous individual is going to generate 50% of gametes A and 50% of gametes B.

So, our frequency of A allele in the genetic pool,

let's denote it as p,

is a probability of AA parental generation plus half the probability of the heterozygotes.

And we can figure out the frequency of the alternative allele B in the same manner,

or actually we can obtain it as one minus the frequency of Allele A,

so one minus B,

let's call the frequency of this allele q.

Now, if you assume that the pairing of gametes to form a generation is at random,

then it's very easy to compute what is going to be

probabilities of different genotypes in next generation.

While the frequency of sampling two gametes at random and that

both gametes are A is simply the p square.

And then for the other homozygous it's q square and for heterozygous is twice pq.

These proportions are known as Hardy-Weinberg equilibrium proportions.

Now, I want you to stop for a moment and think,

this is highly abstract model we have just considered.

We have these infinitely large population,

we have no overlap between generations.

We have a random sampling,

we have gametic pool.

This is very far from reality if you think of

any natural population like population of humans. The generations do

overlap and there is no such thing as gametic pool, and we pick our partners ourselves,

despite of this, it is very interesting that as soon as population is panmictic,

you go there, you sample a random locus,

and you normally you'll see that it's in Hardy-Weinberg equilibrium.

So, there is an incredible power in

this simplistic model which does

describe real things we observe in panmictic populations,

like populations of humans or random bred cats.

Now, we have just considered a system which consist of two alleles.

I would like you to consider a slightly different question.

Let's think of a system which is made of some arbitrary number say N alleles.

And then I would like you to think about two questions.

First, out of N alleles,

how many genotypes could be made?

And secondly, what would be how the Hardy-Weinberg expectations for such a system?

One of the possible ways to approach this problem would be in a graphical manner.

So what we can do, we can draw a matrix where the N alleles which we can see there,

will be on the column and on the long dimension.

And then the cells within this matrix will

represent specific genotypes made of these two alleles.

It is immediately follows that a number of possible homozygous is simply the number of

alleles N. And when we want to consider how many possible heterozygotes are there,

then they are represented by that off-diagonal elements of the matrix.

Now, mind that we are not distinguishing AB heterozygous from BA heterozygotes,

at the moment we don't quite care whether A came from

mother and B came from father or the other way around.

So in that, there are off-diagonal elements,

they are symmetric and equivalent.

And then if you want to count a number off-diagonal elements,

we can do it in this way.

So total number of elements in this matrix is N squared,

and N of them is homozygous.

So if we subtract the N and divide the result by two,

this will give us the number of possible heterozygotes.

So at the end, if you add up the number of homozygous and heterozygotes,

we are going to come up with the figure of a product of

number of alleles by number of alleles plus one divided by two.

And then thinking of Hardy-Weinberg equilibrium,

we can follow exactly the same logic as we did in the biallelic system,

and then the probability of homozygote is simply a square of the frequency of

respective allele and the probability of heterozygote

is twice the product of the frequencies of respective alleles.

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