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Thulfeqar Alrubai’eyGenetics Sheet #11 6/5/2014

A student asked the following question about the previous lecture and the professor answered the following:

What is the meaning of genetic linkage?

When there are two genes that are close to each other, they will not be separated by crossing over during meiosis. In other words, they will be segregated together because the chance of having crossing in the area between these two genes is very small.

How can we analyze this?

First, we have to know on which chromosome this gene is located (chromosome 1, chromosome 2 …etc). To do this, we use special markers. Markers are artificial segments of DNA that we make and each chromosome has a specific marker. We found on each chromosome a segment of DNA that is unique to that chromosome only and we made a marker complementary to that segment. Then we look to see which marker the gene is segregated with. For example, if a gene is always segregated with the marker for chromosome 5, this means the gene is found on chromosome 5.

Then we want to see where on chromosome 5 for example this gene is; q arm or p arm, which band. Each chromosome has even more specific markers (around 20 markers for each chromosome). Each marker is complementary to a specific segment of the chromosome. We use these markers to see which part of the chromosome the gene is segregated with. If, for example, it’s segregated with markers 12 and 20 that means this gene is found in that specific area of the chromosome.

Then we cut this segment of the chromosome using specific endonucleases (restrictive enzymes). So now we know that this specific marker is close to a specific gene. After that, we find out the specific sequence of the gene. This is what we mean by linkage analysis.

We use this linkage analysis to diagnose a disease but the mutated gene of this disease is unknown. We use restrictive enzymes to segregate the mutated gene, then we compare the result with the father and mother to see if they’re carriers or not.

Using linkage analysis, we can see whether or not a person has a mutation, but we cannot know the specific type of that mutation.

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This lecture is going to be about Population Genetics:

-What is the meaning of population? It’s a group of people, animals, or plants living in a certain geographical area.

-Subpopulation: A part of the population within which migration is restricted. For example, the population of Jordan is considered to be the people living within the borders of Jordan, and a subpopulation would be the people living in Amman.

When we study the genetics of a population, we do not mean specific individuals of the population, rather the population is a whole.

Gene pool: The sum of all genes in a population. For example if we want to study the thalassemia gene pool we take all the patients that have the thalassemia gene.

Gene Flow: The genes which pass from one generation or population to the other. For example, if we have a generation with a specific gene pool, the generation after it may have the same gene pool or a slightly different gene pool.

Population Genetics: The study of the rules governing the maintenance and transmission of genetic variation in natural populations.

What are the things affecting our gene pool?

1. The change in allele frequencies2. The change in genotype frequencies3. The change in phenotype frequencies

We can use these three conditions to study population genetics.

Where does this genetic variation come from?

Evolution: which depends on genetic mutations to create new alleles. If the genome is stable (no mutations) then we wouldn’t get new alleles. The environment around us and other things we are exposed to will cause mutations to develop, and as a result there will be a change in the frequency of some alleles.

The main factor which contributes to genetic variation is mutation. This mutation usually ends up with clinical pictures. For example, a change in the color, or a symptom that we can see and measure.

Some mutation are associated with disease. Others improve the ability of the species to survive changes in the environment.

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If we have a dominant mutation and a recessive mutation, which one will stay in the population more than the other? The recessive mutation will stay in the population. The dominant mutation will end up with the death of the individual at an early age so this mutated gene will be eliminated from the population. However, if the mutation is recessive, it will not be expressed in the heterozygous state so the person with the mutation will reproduce and the mutated allele will be passed on.

How can we observe variation in characteristics?

1- We can observe variation in the diversity of the genes. (How much variety in this gene is there between individuals).

2- If there is high adaptation to new environments or not.3- How much variation there is4- The level of reproductivity (high or low reproductivity). Usually, if the level of reproductivity

is high, the chance of survival of the offspring will be lower because the offspring will have malnutrition and will struggle for existence. This is seen more in animals and plants than in humans. For example, if a tree dispersed a high number of seeds in a small area of land, then the survival rate will be low (because of high competition for nutrients) so the offspring will be very weak and some of them will die. On the other hand, the less the number of offspring, the better the survival rate.

The outcome of natural selection depends on:

1- Relationship between phenotype and fitness: If we have a phenotype that is more fit than another phenotype, the chances of survival of the individual with the fit genotype will be higher.

2- Relationship between phenotype and genotype. Genetic variation will result in different phenotypes which we can see and measure.

These two factors determine whether a phenotype is more fit than other phenotypes or not, as a result of these two factors, we either have evolution or don’t have evolution. In other words, if there is a variation which resulted in a fit phenotype, then we will have evolution, and vice versa. This new fit phenotype will be passed on to future generations.

What are the conditions which affect the population?

1- Mutation: It will have a positive effect on the population.2- Migration: Could be positive or negative. Migration means when a new population enters or

comes with the existing one. This results in changes in gene frequency. This may be good or bad depending on which gene has entered the population.

3- Drift: When a small population keeps reproducing together (without mating from outside this population) they will all end up with very similar phenotypes because some alleles will be eliminated. This effects the population negatively.

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Thulfeqar Alrubai’eyGenetics Sheet #11 6/5/20144- Selection in mating: choosing to mate specific people. For example someone marries his first

cousin, and his children and grandchildren will do the same. This will end up with characteristics like drift. Selection would affect the population negatively.

Population differentiation:

Mutations will increase the genetic diversity. The population will acquire a new gene or allele.

Selection could increase or decrease the genetic diversity. If the population selects to mate with relatives, the genetic diversity will be decreased. On the other hand, if this population selects to mate with non-relatives the genetic diversity will be increased.

Genetic drift will decrease the genetic diversity. Migration could increase or decrease the genetic diversity. Non-random mating will decrease the genetic diversity.

Mutations, mating selection, genetic drift, migration, and natural selection are the forces responsible for maintaining the genetic equilibrium.

Genetic equilibrium refers to stable genetic pool (constant gene frequencies), and in order to have a stable genetic pool, the previously mentioned factors should be stable (constant).

How can we calculate allele frequency in a population?

Allele frequency= (number of particular allele) / (total number of alleles in the population).

For example if we want to calculate the LDL receptors allele frequency in a group of 100 people. We have a total of 200 alleles because each individual will have one allele from the father and another allele from the mother. We take the number of alleles that are positive for the LDL receptor (not the number of people who are positive for LDL receptor) and we divide it by 200. The result would represent the allele frequency.

The allele frequency calculations are affected by both homozygous and heterozygous genotypes. If someone is homozygous for the allele that we want to calculate its frequency, then we count this as two alleles and for the heterozygous we count it as 1 allele, and if someone doesn't have this allele at all we count it as zero.

Allele frequencies affect the genotype frequencies (frequency of each type of homozygote and heterozygote) in the population.

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The frequencies of certain alleles are not always the same in different populations.

Example: frequencies of phenylketoneuria (PKU) in different populations

We can see that in the Turks there is a higher frequency of PKU.

Frequency for any allele is not the same in different populations (not only PKU).

What can affect allele frequency?

1. Non-random mating: individuals reproduce more often with each other rather than random reproduction between all individuals (in other words, someone marries his cousin and his son will also marry his cousin etc.)

2. Migration: Individuals migrate between populations3. Genetic drift: A small group of individuals within the population keep reproducing with each

other leading to a change in allele frequency 4. Mutation: production of new alleles.5. Selection: Individuals with a particular genotype are more likely to have viable, fertile

offspring.

The calculation of allele frequency was first introduced by two scientists named Hardy and Weinberg, and this calculation was named Hardy-Weinberg principle/equilibrium.

Hardy-Weinberg principle equilibrium states:

1. Allele frequencies remain constant from generation to generation unless some outside force is acting to change them. Examples of outside forces are migration and natural disasters.

2. When an allele is rare, there are many more heterozygotes than homozygotes.

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In order to apply the Hardy-Weinberg principle, we have to assume that the population is in genetic equilibrium. For this population to be in equilibrium we have to have the following:

There is no selection There is no mutation (genes do not change from one allele state to another) There is no migration and no gene flow There are no chance events (no natural disasters) Individuals choose their mates randomly (there is no non-random mating) The population is large

If all these conditions are met, then the Hardy-Weinberg principle can be applied.

The Hardy-Weinberg Law can be used to:

Estimate frequencies of autosomal dominant and recessive alleles in a population

Detect when allele frequencies are shifting in a population (evolutionary change)

Measure the frequency of heterozygous carriers of deleterious recessive alleles in a population

Slides 22+23: Example

The parents and the zygote are diploid, so they will have 2 alleles. On the other hand, the gametes are haploid so they will have only one allele. These parents will produce offspring and a large gene pool containing two alleles on the same locus; these two alleles are A and a.

If we have two parents with "Aa" alleles, what are the possibilities of the alleles of their offspring?

("A" is referred to as "p" and "a" is referred to as "q").

The possibilities of their offspring's alleles will be:

AA (homozygous) or p2

aa (homozygous) or q2

Aa (heterozygous) or pq

These are the possibilities which will be generated if we are talking about an individual with two alleles.

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Thulfeqar Alrubai’eyGenetics Sheet #11 6/5/2014If we have 2 alleles, the sum of the two allele frequencies = 1. So the sum of the allele frequency of A and the allele frequency of a = 1.

In this example, the sum of p2+q2+2pq=1 (allele frequency of AA+aa+2Aa=1).

(2pq because we have two offspring with the genotype pq).

Slides 26+27+28 are about the same idea.

Hardy-Weinberg Problem: In a population of 747 individuals (1494 alleles).

Problem:

Step 1: Find the allele frequencies for A and a (which are represented by Mm and Mn in the following example). Equation for allele frequency is p+q=1

Step 2: Find the genotypic frequencies of AA, Aa, and aa. The equation for genotype (genotype=2 alleles) frequency is p2+q2+2pq=1.

Step 1: In this example, we are testing blood groups. We took a population of 747 individuals. This means we have 1494 alleles (747x2). We want to test the m and n blood groups in these individuals. The possible genotypes of these individuals are MmMm or MmMn or MnMn.

To test the genotypes in this population we carry out lab tests.

Refer to the table in slide 31: The results of the test showed that 233 or the individuals have MmMm and 385 have MmMn and 129 have MnMn.

Each one of the 233 people who have MmMm have 2 Mm's.

Each one of the 385 people with MmMn have 1 Mm and 1 Mn

Each one of the 129 with MnMn have 2 Mn's.

To calculate the total of both alleles:

Total Mm alleles = (2 x 233) + (1 x 385) = 851 Total Mn alleles = (2 x 129) + (1 x 385) = 643

Total of both alleles =1494 (total number of alleles)

To calculate allele frequency:

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Thulfeqar Alrubai’eyGenetics Sheet #11 6/5/2014Frequency of the Mm allele = 851/1494 = 0.57 or 57% Frequency of the Mn allele = 643/1494 = 0.43 or 43%

0.57+0.43=1 (p+q=1)

This was the first step to solve this problem which is finding the individual allele frequencies. Note that these allele frequencies are the same for both the father and mother.

Now the 2nd step: Using the allele frequencies that we found to:

Predict the genotype frequencies in the next generationIn other words, finding the expected frequencies of MmMm and MmMn and MnMn

Verify that the present population is in genetic equilibrium

Remember: p2+q2+2pq=1 or frequencies of MmMm+ MnMn + 2MmMn =1

In this table, we took the allele frequencies that we calculated in step 1 and multiplied them together to find the expected frequency of each genotype in the next generation.

0.32+0.18+0.25+0.25=1

Here we have calculated the expected frequencies of the genotypes. This step is also used to verify that there is genetic equilibrium. To say that there is equilibrium, we do a test for the genotypes in this generation and compare it to the expected genotypes that we have calculated, and the difference between the expected and the observed genotype frequencies should be negligible.

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MnMn 0.18

MmMn

0.25

MmMn

0.25

MmMm 0.32

Mn 0.43

Mm 0.57

Mn 0.43

Mm 0.57

SPERMS

EGGS

Genotypes Expected frequencies

Observed frequencies

MmMm

0.32 233 ¸ 747 = 0.31

MmMn

0.50 385 ¸ 747 = 0.52

MnMn

0.18 129 ¸ 747 = 0.17

Thulfeqar Alrubai’eyGenetics Sheet #11 6/5/2014In the previous table, it is seen that the difference between the observed and expected genotype frequencies is very small, so this population or these genes are in equilibrium.

Remember:

p2 = homozygous dominant 2pq = heterozygous q2 = homozygous recessive

Another example:

If we went to a garden and observed the flowers, we will find red, white, and pink flowers. The red represents a homozygous dominant genotype, the white represents a homozygous recessive genotype and the pink represents and heterozygous genotype.

Assume that Red is RR, white is rr, and pink is Rr.

If we have 1000 flowers: 200 white (rr) , 500 pink (Rr), and 300 red (RR); the genotype frequencies will be:

White: 200/1000=0.2

Pink: 500/1000=0.5

Red: 300/1000=0.3

In this population of 1000 flowers, we have 2000 alleles.

To find the allele frequencies:

White (rr) : 400r [the same as 200 rr]

Pink (Rr) : 500 R and 500 r [because each pink flower has 1 R and 1 r]

Red (RR) : 600 R [each red flower has 2 R's]

Frequency for "r" allele = (400+500)/2000 = 0.45 Frequency for "R" allele = (500+600)/2000 = 0.55

From here, we can predict the genotype frequency of the next generation depending on which two flowers mated to give the next generation (whether 2 white flowers mated or 2 red or 1 pink 1 red etc). This is done exactly like the previous example: by putting the values in a table and multiplying them together.

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Thulfeqar Alrubai’eyGenetics Sheet #11 6/5/2014To sum up: First we test the current generation that we have and find their genotypes. Using these tested genotypes, we calculate the allele frequencies. Then, we use these allele frequencies to predict the genotype frequencies for the next generation. When we get the next generation, we test them to find their actual genotype frequencies. We then compare the predicted and actual genotype frequencies to test whether or not the population is in genetic equilibrium.

To calculate the frequency of a dominant allele (p) in the population:

We count the number of individuals with the homozygous recessive genotype (aa). The frequency of this genotype is calculated in the population by:

number of people with "aa"/total number of people in the population. This will give us q2.

The frequency of the "a" allele can be calculated by taking the square root of q2 [√q2 = q]

p+q=1 so p= 1 – q. "p" is the frequency of the dominant allele (A).

Calculating the frequency for alleles of an X-linked trait:

In a population, we have 3 X chromosomes (2 in the female and 1 in the male). So an X-linked trait will have 3 alleles (2 in the female and 1 in the male).

The equation we use for the male: p+q=1 This is because males only have 1 X chromosome. The equation we use for females: p2+q2+2pq=1 This is because females have 2 X chromosomes.

If we take hemophilia as an example (hemophilia is X linked):

Males with hemophilia is "q" and males without hemophilia is "p" If the incidence of hemophilia for males is 1/10,000; q= 0.0001 , then p=1-0.0001=0.999

Here, the genotype frequency is the same as the allele frequency since the male only has 1 allele due to only 1 X chromosome. The male will have either p (non-affected) or q (affected); there is no carrier for males.

However, for females, they have 2 alleles because they have 2 X chromosomes so the genotype will be either p2 or q2 or pq.

If we want to know the genotype frequency for females (which females are carriers [pq] and which females are affected [q2] and which females are not affected at all [p2]) we use the same p and q values calculated for the male because this is stable in the gene pool and the allele frequencies are the same.

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Thulfeqar Alrubai’eyGenetics Sheet #11 6/5/2014So to find the frequency of female carriers (pq) -> 2× p×q=2 (0.999 ) (0.0001 )=0.0002 This means 0.0002 of the population are carriers (1 in 5000 are carriers).

Frequency of affected females (q2)¿ (0.0001 )2¿0.0000001 or 1 in 100,000,000 females are affected.

To sum up: Every gene has 2 alleles, and the sum of these 2 alleles in the population is equal to 1. In X-linked traits, we use incidence in males to find p and q, since the equation for males is p+q=1. We then use these values of p and q to calculate q2 (affected females) and 2pq (carrier females) and p2 (non affected females) by using the equation p2+q2+2pq=1. p and q are allele frequencies, while p2 and q2 and 2pq are genotype frequencies for females.

In X linked traits, males are much more affected than females.

In the previous example, we are talking about 2 alleles. How can we calculate these frequencies if we are taking co-dominancy into consideration? Co-dominancy means more than 2 alleles; for example blood groups.

In blood groups, there are 3 alleles: A, B and O. Here there are 6 different genotypes: AA, AO, BB, BO, AB, OO. The O allele codes for no antigen (so we have an allele but no antigen).

Allele frequency for A=p, allele frequency for B=q, and allele frequency for O=r.

Allele frequencies should add up to 1, so: p+q+r=1.

Genotype frequencies should also add up to 1, so: (p+q+r)2=1.

(p+q+r)2 is the same as p2 (AA) + 2pq (AB) + 2pr (AO) + q2 (BB) + 2qr (BO) + r2 (OO) = 1

This is called the expanded Hardy-Weinberg equation.

Remember: the Hardy-Weinberg equation is (p+q)2 which is p2+2pq+q2 (this is the form which we used for the examples involving 2 alleles).

RULE: THE TOTAL ALWAYS EQUALS 1.

So, in general, the gene pool of a population is affected either by intrinsic factors or extrinsic factors.

The intrinsic factors are:

Segregation Recombination Transposition Mutation

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The extrinsic factors are:

Population size Patterns of mating Geographic distribution Migration Natural selection

Thanks to Khalid Araim

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