Mendel – AP Biology

Mendel’s Genetics [5]: The dihybrid cross

Last sections we discussed inheritance where only a single gene was involved. The 3:1 ratio is the basic Mendelian ratio and everything that follows depends upon it.

The obvious next step is to look at a situation where the inheritance of two different inherited characters are studied at the same time, a dihybrid cross.

Again, we learn dihybrid cross by experiments. Let’s see what Mendel did:

He crossed two pure-bred starins of pea plants, one producing only round yellow seeds and the other only wrinkled green seeds.Round seeds are dominant over wrinkled ones; yellow seeds are dominant over green ones. Both phenotypes are determined by one single gene.

(Why did Mendel use the seed characteristics as his focus of study instead of other traits of the pea plants? )

A cross between the two parents produced a F1 generation that consisted only of round yellow seeds. Self-fertilization of F1 yielded F2 generation, the seeds of which showing considerable diversity.

Four different phenotypes could be identified. Of 556 seeds analyzed, Mendel found 315 round yellow seeds, 108 round green seeds, 101 wrinkled yellow seeds and 32 round green seeds. Close to a ratio of 9: 3: 3: 1, which is referred to as the dihybrid ratio.

dihybrid cross — THE 9:3:3:1 IN MENDEL’S EXPERIMENTS, image from Instant Notes in Genetics

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Interestingly, if we only focus on the round/wrinkled phenotype, the ratio of round seeds and wrinkled seeds is 3:1. the monohybrid ratio. Similarly, if we only focus on the yellow/green phenotype, the ratio of yellow seeds and green seeds is the monohybrid ratio as well. Just as we said “The 3:1 ratio is the basic Mendelian ratio and everything that follows depends upon it”

Now I want to introduce a little bit mathematics into this section. Let’s see what happens when we use polynomial multiplication to explain the relationship between 9: 3: 3: 1 and 3:1:

(yellow: green)× (round: wrinkled)

= (yellow·round): (yellow·wrinkled): (green·round): (green·wrinkled)

known: yellow: green=3:1; round: wrinkled=3:1

SO: (yellow: green)×(round: wrinkled)=(3:1)×(3:1)

=(3×3):(3×1):(1×3):(1×1)=9:3:3:1

Therefore, (yellow·round): (yellow·wrinkled): (green·round): (green·wrinkled)=9:3:3:1
Does this reasoning inspire you? What happens when it comes to a tri-hybrid ratio?

(3:1)×(3:1)×(3:1)=

(3×3×3):(3×3×1):(3×1×3):(3×1×1):(1×3×3):(1×3×1):(1×1×3):(1×1×1)

=27 : 9 : 9 : 9 : 3 : 3 : 3 : 1

See? Quite easy. The ratios for the three groups of phenotypes are simply multiplied across, and the 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1 ratio is obtained.

SO what happens when it comes to tetra-hybrid, penta-, hex-? What happens when it comes to n-hybrid?

I’m sure the answer is easy for you now, make the n phenotypes multiplied across, and the expected ratio is obtained. In plain mathematics, (3:1)^n

——————————————————————————-As noted before the 3:1 ratio can be distorted by factors such as incomplete dominance or lethal alleles. These also affect the 9:3:3:1 ratio, but other factors can also modify this ratio.

The two different genes must not act on the same character. For instance, if the proteins encoded by the two genes are involved in the same biochemical pathway then the ratios of phenotypes resulting from the genotypes will be altered.
If the two genes lie close together on the same chromosome, linkage happens and the ratio won’t be 9:3:3:1 either, as we mentioned in Review of Mendel’s Genetics, the very beginning of our Genetics study.

Testcross

As with the monohybrid cross, it is also possible to conduct a testcross with F1 generation of the dihybrid cross.

Mendel’s Genetics [4]: examples of mutiple alleles

All the examples used in last classes have employed genes with only two alternative alleles. But the majority of genes exist in several different forms, multiple alleles. This is caused by the mutations of bases at different sites within the same gene, thus affecting different amino acids in the encoded protein.

examples of multiple-allele traits/diseases:

the human β-globin gene where a specific mutation at one site of the gene results in an allele responsible for the hereditary syndrome sickle cell (picture)anaemia, while mutations at several other sited sites in the gene cause a different syndrome, β-thalassemia(beta地中海贫血),
A SICKLE CELL,image from the Internet

Beta-thalassemia, inherited blood disorder caused by reduced or absent synthesis of the beta chains of hemoglobin, resulting in variable phenotypes ranging from severe anemia to clinically asymptomatic individuals.

Although they are alterations of the same gene, the changes are to different codons(a specific sequence of three consecutive nucleotides that is part of the genetic code and that specifies a particular amino acid in a protein or starts or stops protein synthesis). The resulting proteins have variant beta-globins with discrete differences in amino acid sequence and so behave differently.

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In rabbits, multiple alleles of one gene are responsible for a number of different coat color phenotypes.

Here we go, a little confusing but, interesting:

There are four members of the allelic series: agouti, chinchilla, Himalayan and albino. When homozygous, each series produces a distinct coat pattern. When heterozygous, there is a clear pattern of dominance. Agouti is dominant over all the alleles, chinchilla is dominant over Himalayan and albino, while Himalayan is dominant over albino, which fails to produce any pigment and hence is recessive to the others…Hope your mind is still clear!

1, Agouti rabbit: the wild rabbit.

genetics 4 an agouti rabbit — AN AGOUTI RABBIT, image form the Internet

If you blow into the fur of an Agouti rabbit, you will see “bandings” of different colors along the shaft of the hair, being blue, black, tan, fawn. The Agouti also has light tan coloring around the nostrils and at the back of the neck. The belly is cream.(http://rabbit.wikia.com/wiki/Agouti)

2, Chinchilla rabbit: soft, grey fur.

genetics 4 A five-week-old Chinchilla rabbit — A FIVE-WEEK-OLD CHINCHILLA RABBIT, image from the Internet

Chinchilla Rabbits originated in France and were bred to standard by M. J. Dybowski. They were introduced to the United States in 1919. (wikipedia)

3. Himalayan rabbit: white body with colored points, recognized colors are black, blue, chocolate and lilac.

A HIMALAYAN RABBIT, image from the Internet

red eyes; posed stretched out, body to be 3.5 head lengths. They are the ancestors of Californians, one of the most common meat rabbits.(wikipedia: Himalayan_rabbit)

4. Albino rabbit: completely white since it’s missing the melanin which determines the color of their skin, eyes, and fur.

genetics 4 albino rabbits — AN ALBINO RABBIT, image from the Internet

Not all white rabbits are albinos, so you’ll need to check their eyes. If their eyes are red or pink and their hair is totally white, they would be considered an albino. They are not rare.

An albino rabbit may not have the greatest eyesight due to their lack of eye pigment. Since their eyesight is not the best, they should be caged or kept inside since they may not be able to see predators.(http://www.ask.com/question/albino-rabbits)

Having seen so much about rabbits, hope you haven’t forgotten what we were doing before those cute bunnies. We were learning about examples of multiple alleles of one gene.

the human ABO blood group system.

(all form wikipedia: ABO blood group system:)

The ABO blood type is controlled by a single gene (the ABO gene) with three types of alleles inferred from classical genetics: i, I^A, and I^B. The gene encodes a glycosyltransferase— an enzyme that modifies the carbohydrate content of the red blood cell antigens.

The I^A allele gives type A, I^B gives type B, and i gives type O.

Both I^A and I^B are dominant over i, so only ii people have type O blood. Individuals with I^AI^A or I^Ai have type A blood, and individuals with I^BI^B or I^Bi have type B.

I^AI^B people have both phenotypes, because A and B express a special dominance relationship: codominance(we talked about it last class), which means that type A and B parents can have an AB child.

A type A and a type B couple can also have a type O child if they are both heterozygous (I^Bi,I^Ai)

Hope your mind is still clear!

NOTE: the concept of multiple alleles of one gene is totally different from multiple-gene inheritance.

A polygene, multiple factor, multiple gene inheritance, or quantitative gene is a group of, non-allelic, genes that together influence a phenotypic trait.

Mendel’s Genetics[3]: Variations of the 3:1ratio

Variations of the 3:1 ratio

The simple 3-to-1 monohybrid ratio is not always observed in instances where only one gene is responsible for a particular phenotype.

A number of factors:

Partial or incomplete dominance

Complete dominance means the phenotype of first filial generation(heterozygous) is exactly identical to that of one of the parents(both homozygous). Partial or incomplete dominance means the first filial has phenotype somewhere between that of both parents.

For example, When two pure-bred snapdragons, with white and red petals respectively, cross, their first filial generation has pink petal rather than red or white.

In this case, the homozygous phenotypes are red, or white petals while heterozygous one is between white and red: pink petal.

Thus, it is conceivable that when it comes to the second filial generation, which was produced by the self fertilization of the heterozygous F1, F2 should have three different phenotypes, white, pink, and red. And we can also deduce the ratio of them is 1:2:1.

Codominance

Codominance is similar to incomplete dominance, but here the heterozygote displays both alleles(两种等位基因均被表达).

For example, in humans the MN blood group is controlled by a single gene.

In humans the main blood group systems are the ABO system, the Rh system and theMN system.

Only two alleles exist, M and N. Children whose father is an NN homozygote with N blood and whose mother is a MM homozygote with group M blood are MN heterozygotes and have group MN blood.Both phenotypes are identifiable in the hybrid. And the ratio also switches from 3:1 to 1:2:1.

Lethal alleles

Some alleles affect the viability of individuals that carry them.

In most cases the homozygous recessive does not survive but the heterozygotes may have a normal lifespan.

The best-known example of lethal alleles is the inheritance of yellow coat color in mice.

Yellow fur can arise in strain of mice with different colors, or instance, black. Yellow coat color is dominant to black coat. Mice with BB alleles are back, with BB^yare yellow, with B^yB^y alleles are supposed to be yellow as well, but B^yB^y alleles are lethal and any mice with this genotype die in utero(in the uterus : before birth).

SO it is conceivable that when two yellow mices are mated ratio of the different phenotypes of their first generation is 2 : 1, rather than 3 : 1 or 1 : 2 :1.

NOTE: The allele B^yis recessive in its relation to its effect on viability (only homozygous B^yB^ys die, while the heterozygotes survive ), but dominant in relation to coat color(heterozygotes present in yellow fur in stead of black fur.).

Other examples where alleles are lethal when homozygous but have a dominant effect when heterozygous, include :

tailless Manx cats

genetics — a manx cat, image from the Internet

a breed of domestic cat(Felis catus) originating on the Isle of Man, with a naturally occurring mutation that shortens the tail.

The Manx taillessness gene is dominant and highly penetrant; kittens from two Manx parents are generally born without any tail. Being homozygous for the taillessnees gene is lethal in utero.Thus, tailless cats can only be heterzygous. Because of the danger of having homozygous taillessness gene, breeders avoid breeding two entirely tailless Manx cats together.(wikipedia: Manx (cat))

short-legged Creeper chickens.

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(Annie: If none of the homozygous yellow mice can survive before birth, then where did all the heterozygous yellow mice come from in the first place???????)

Answer: Through mutation. The presence of one mutant allele alters development so as to produce characteristic changes to the animal, but when two of the mutant alleles are present, development is so aberrant as to cause death.

This may occur in utero as described above or resulted in shortened life expectancy as found in several examples in humans, such as Tay-Sachs disease, Huntington’s syndrome（亨丁顿舞蹈症） or sickle-cell anemia（镰刀形红血球病）. (from Instant Notes)

Mendel’s Genetics[2]: The monohybrid cross

Keywords:

Phenotype

Any character (trait) which can be shown to be inherited, such as eye color, leaf shape or an inherited disease, such a cystic fibrosis, is referred to as a phenotype.

Description: A fly may be described as having a red-eyed phenotype. A child may be described as displaying the cystic fibrosis phenotype.

Genotype

The pattern of genes that are responsible for a particular phenotype in a individual is referred to as genotype.

Dominance

In hybrids between two individuals displaying different phenotypes, only one phenotype may be observed. This phenotype is referred to as the dominant trait and the un-shown one the recessive.

For instance, if the wife has wide eyes while the husband has small eyes, and their little girl has wide eyes, then the wide eyes are dominant to small eyes.

Pure-breeding lines

Organisms which have been inbred for many generations in which a certain phenotype remain the same.Pedigree breeds of dogs or cats are commonplace examples of pure-breeding lines.

A puppy from two purebred dogs of the same breed, for example, will exhibit the traits of its parents, and not the traits of all breeds in the subject breed’s ancestry.

Homozygous: Individuals with two identical copies of a gene.

“True breeding (pure-breedind) organisms are always homozygous for the traits that are to be held constant.”

Heterozygous: Individuals with two different copies of the gene.
Alleles: The different variants of a gene.

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Mendel made a cross between two pure-breeding lines of pea plants, one of which had violet petals and the other white petals. The hybrids produced in this cross were referred to as the F1 (first filial) generation.

In Mendel’s experiment, the ratio of violet pedals and white ones in the second filial were very close to 3 to 1, which applied to the theoretic reasoning shown above.

He did many other experiments focusing on different types of genotypes of the pea plants and the results were shockingly similar. The hidden phenotype in the first filial reappeared in the second filial and the ratio of the dominant to the recessive phenotype were all close to 3 to 1.

The 3:1 ratio is referred to as the monohybrid ratio and is the basis for all patterns of inheritance in higher organisms.

One simple extension of the 3:1 phenotype ratio is a 1:1 ratio, produced when a heterozygous F1 individual is crossed to the homozygous-recessive parent. The process is known as testcross.

Testcross is useful in any condition when it is necessary to determine whether an individual is heterozygous or homozygous. Conceivable that if F2 all have dominant phenotype, then the tested parent is homozygous-dominant; if F2 have a 1:1 ratio of dominant and recessive phenotype, then the tested parent is heterozygous.

Review of Mendel’s Genetics

Here I found a great page story-telling Mendel’s Genetics.Can’t be more suitable as a revision of what we learned about genetics and inheritance in high school. >>Mendel’s Genetics

I believe by reading the link page you have remembered the principles of Mendel’s Genetics. We’ll summarize these principles again in next posts.

While Mendel’s research was with plants, the basic underlying principles of heredity that he discovered also apply to people and other animals because the mechanisms of heredity are essentially the same for all complex life forms.”

It must be a cliche to summarize the success factors of Mendel’s experiments, but it has to be done, for many of the factors are still important for today’s experimentalists.

Firstly, before the experiment,Mendel spent a long time observing different traits of the peas and decided which traits he was going to focus on in the after experiments. He was prepared, had anticipation and, perhaps already held some hypothesis of what was going to happen.

Then it was the choice of his “lab-rats”. As the link page says,”Mendel picked common garden pea plants for the focus of his research because they can be grown easily in large numbers and their reproduction can be manipulated. ” Based on a large number of offspring, the resulting statistics can be assumed as very close to theoretic statistics. In this case, it’s way more convenient to study the traits of these peas than those of some fragile and rare pole plants.

More important, “pea plants have both male and female reproductive organs. As a result, they can either self-pollinate themselves or cross-pollinate with another plant. In his experiments, Mendel was able to selectively cross-pollinate purebred plants with particular traits and observe the outcome over many generations. This was the basis for his conclusions about the nature of genetic inheritance.”

Reproductive
structures of
flowers

drawing of a flower cross-section showing both male and female sexual structures — the picture is from http://anthro.palomar.edu

Last but not least, Mendel was a pioneer in applying Math(Statistics) to experiment analysis. He rounded the ratio of numbers of different traits to a whole number and discovered the astonishing similarity of all the results.

In high school that’s all the factors, but actually there’s more. For one, Mendel succeeded because all the genes that controlled traits he picked to observe happened to be on different chromosomes. Otherwise, the phenomena of “linkage” would have appeared (which we’ll talk about later)and he should never have had such a groundbreaking discovery.