Principles of Inheritance - Mendelian Genetics
Gregor
Johann Mendel is known as "father of modern genetics" for his
contributions. He conducted hybridization
experiments on garden peas for nearly 8 years (1856-1863) and proposed the laws
of inheritance, a simple theory to explain the transmission of hereditary
traits from generation to generation. During this time, he grew over 10,000 pea
plants, and recorded every single progeny number and details. Even though the
results of his genetic experiments were published in 1865, his Laws of
Inheritance did not receive due appreciation. It was only in 1900, his laws
were rediscovered and understood.
Mendel
selected the pea plant since
• The pea plants were easy to grow and
maintain, is an annual plant
• Pea plants have clearly distinct and
contrasting characters.
• Peas can be self-pollinated as well
as cross-pollinated.
Mendel studied the
inheritance of the following 7 traits that had 2 forms:
- Pea
shape (round or wrinkled)
- Pea
colour (yellow or green)
- Flower
colour (purple or white)
- Flower
position (terminal or axial)
- Plant
height (tall or short)
- Pod
shape (inflated or constricted)
- Pod
color (yellow or green).
Mendel studied pure-breeding pea plants. These plants always produced progeny with the
same characteristics as the parent plant. Mendel designed his experiments so
that only one pair of contrasting characters was observed at one time.
He cross-pollinated two pure lines for contrasting characters and
the resultant off springs were called F1 generation (the first filial
generation). The F1 generations were then self-pollinated which gave rise to
the F2 generation or second filial generation.
Mendel conducted 2 main experiments to determine the laws of
inheritance. These experiments were:
1. Monohybrid Cross
2. Dihybrid Cross
Monohybrid
Cross
In this experiment, Mendel took two
pea plants of opposite traits (one short and one tall) and crossed them. The
first generation offsprings, the F1 progeny were tall. Then he self - crossed
F1 progeny and obtained both tall and short plants in the ratio 3:1 in F2
progeny.
www.pinkmonkey.comMendel conducted this experiment with
other contrasting traits like green peas vs yellow peas, round vs wrinkled,
etc. In all the cases, he found that results were similar. From this, he
formulated the law of Segregation and law of Dominance.
Dihybrid Cross
In a dihybrid cross experiment, Mendel
considered two traits, each having two alleles. He crossed wrinkled-green seed
and round-yellow seeds and observed that all the first generation progeny (F1
progeny) were round-yellow. He then self-pollinated the F1 progeny and obtained
4 different traits, wrinkled-yellow, round-yellow, wrinkled-green seeds and
round-green in the ratio 9:3:3:1.
https://www.quora.com/With the other traits too the results
were found to be similar. From this experiment, Mendel formulated his second
law of inheritance, law of Independent Assortment.
1.
Law of Dominance
This law
states that in a heterozygous condition, the allele whose characters are
expressed over the other allele is called the dominant allele and the
characters of this dominant allele are called dominant characters. The
characters that appear in the F1 generation are called as dominant characters.
The recessive characters appear in the F2 generation.
2.
Law of Segregation
This law
states that when two traits come together in one hybrid pair, the two
characters do not mix with each other and are independent of each other. Each
gamete receives one of the two alleles during meiosis of the chromosome.
3.
Law of Independent Assortment
This means
that at the time of gamete formation, the two genes segregate independently of
each other as well as of other traits. Law of independent assortment emphasizes
that there are separate genes for separate traits and characters and they
influence and sort themselves independently of the other genes. This law also says that at the time of gamete
and zygote formation, the genes are independently passed on from the parents to
the offspring.
Differences between
monohybrid and dihybrid cross:
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Monohybrid
Cross
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Dihybrid
Cross
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1. It is a cross between two pure
organisms to study the inheritance of a single pair of contrasting character.
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1. It is a cross between two pure
organisms to study the inheritance of two pairs of contrasting characters.
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2. It produces a phenotypic
monohybrid ratio of 3:1 in F2 generation.
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2. It produces a phenotypic
dihybrid ratio of 9:3:3:1 in F2 generation.
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3. It produces a genotypic ratio
of 1:2:1 in F2 generation.
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3. It produces a genotypic ratio
of 1:2:1:2:4:2:1:2:1 in F2 generation.
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4. Example: Cross between tall and
dwarf pea plants.
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4. Example: Cross of pea plants
having round and yellow seeds and plants with wrinkled and green seeds.
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Back cross- When F1 individuals are crossed with one of the two
parents from which they were derived, it is called a back cross. Backcross is a cross of
a hybrid (F1) with any one of its parents, in order to achieve offspring with a
genetic identity closer to that of the parent. It is used in horticulture,
animal breeding and in the production of gene knockout organisms.
Test cross- A test cross is a cross used
to test whether an
individual is homozygous ie pure or heterozygous ie hybrid. It is always crossed with a recessive parent. Test cross is done to
identify the unknown genotype. It is a
cross between an organism (unknown genotype for a certain trait) and another
organism that is homozygous recessive for that trait. This cross is used to
determine whether the individual in question is heterozygous or homozygous for
a certain allele. It is also used as a method to test for linkage, i.e. to
estimate recombination fraction.
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Punnett
square and laws of
probability
The Punnett square is a square diagram that is used to predict
the genotypes of a particular cross or breeding experiment. It is named after
Reginald C. Punnett, who devised the approach. The diagram is used by
biologists to determine the probability of an offspring having a particular
genotype. The Punnett square is a tabular summary of possible combinations of
maternal alleles with paternal alleles. These tables can be used to examine the
genotypical outcome probabilities of the offspring of a single trait (allele),
or when crossing multiple traits from the parents. The Punnett Square is a
visual representation of Mendelian inheritance.
The probability of an individual offspring's having the genotype
BB is 25%, Bb is 50%, and bb is 25%. The ratio of the phenotypes is 3:1,
typical for a monohybrid cross.
A dihybrid cross between two double-heterozygote pea
plants. R represents the dominant allele for shape (round), while r represents
the recessive allele (wrinkled). A represents the dominant allele for color
(yellow), while a represents the recessive allele (green). If each plant has
the genotype RrAa, and since the alleles for shape and color genes are
independent, then they can produce four types of gametes with all possible
combinations: RA, Ra, rA, and ra.
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RA
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Ra
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rA
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ra
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RA
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RRAA
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RRAa
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RrAA
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RrAa
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Ra
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RRAa
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RRaa
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RrAa
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Rraa
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rA
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RrAA
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RrAa
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rrAA
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rrAa
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ra
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RrAa
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Rraa
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rrAa
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rraa
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The forked-line method (also known as the
tree method and the branching system) can also solve dihybrid and
multihybrid crosses.
The Punnett square is a valuable tool,
but it's not ideal for every genetics problem. For instance, suppose you were
asked to calculate the frequency of the recessive class for an AaBbCcDdEe x AaBbCcDdEe cross
you would need to complete a Punnett square with 1024 boxes.Punnett square is a visual way of representing probability
calculations and with more number of genes, it become slow and cumbersome. The
alternate way is the use of probability principles.
Probabilities are mathematical way of quantifying how likely something
is to happen. Probabilities can be either empirical, meaning that they are
calculated from real-life observations, or theoretical, meaning that they are
predicted using a set of rules or assumptions.
·
The empirical probability of an event is
calculated by counting the number of times that event occurs and dividing it by
the total number of times that event could have occurred.
·
The theoretical probability of an event is
calculated based on information about the rules and circumstances that produce
the event. It reflects the number of times an event is expected to occur relative to the number of times
it could possibly occur.
The product rule
One probability rule
that's very useful in genetics is the product rule,
which states that the probability of two (or more) independent events occurring
together can be calculated by multiplying the individual probabilities of the
events. For example, if a six-sided die is rolled once, there is a 1/6 chance of getting a six. If two dice are rolled at once, the chance of
getting two sixes is: (probability of a six on die 1) x (probability of a six
on die 2) = (1/6) X (1/6) =1/36.
The product rule is the
“and” rule: if both event X and event Y
must happen in order for a certain outcome to occur, and if X and Y are
independent of each other, then product rule can be used to calculate the
probability of the outcome by multiplying the probabilities of X and Y.
The product rule can be
used to predict frequencies of fertilization events. For example, in a cross
between two heterozygous (Aa) individuals,
the chance of getting an aa individual
in the next generation can be calculated.
It can happen when the mother contributes an a gamete and the father contributes an a gamete. Each parent has a 1/2 chance of making
an a gamete. Thus, the chance of an aa offspring is: (probability of mother
contributing a) x (probability of father
contributing a) = (1/2) X (1/2) = 1/4.
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This is the same result as can be
obtained from a Punnett square. In the
Punnett square, the calculation is done visually using columns and rows.
The sum rule of probability
Sometimes the
probability that any one of several events may occur need to be calculated. In
this case the sum rule is used. According to the sum rule, the probability that any of several
mutually exclusive events will occur is equal to the sum of the events’
individual probabilities.
For example, if a
six-sided die is rolled, there is a 1/6 chance of
getting any given number, but only one number per roll. We will never get both
a one and a six at the same time, since these outcomes are mutually exclusive.
Thus, the chances of getting either a one or a six are:
(probability of getting a 1) + (probability of getting a 6) = (1/6) +(1/6) = 1/3.
The sum rule is the
“or” rule: if an outcome requires that either event X or event Y occur, and if X and Y are mutually
exclusive (if only one or the other can occur in a given case), then the
probability of the outcome can be calculated by adding the probabilities of X
and Y.
For example, the sum
rule can be used to predict the fraction of offspring from an Aa x Aa cross that
will have the dominant phenotype (AA or Aa genotype). In this cross, there are three
events that can lead to a dominant phenotype:
·
Two A gametes meet (giving AA genotype), or
·
A gamete from Mother meets a gamete
from Father (giving Aa genotype), or
·
a gamete from Mother meets A gamete
from Father (giving Aa genotype)
In any one
fertilization event, only one of these three possibilities can occur.
Since this is an “or”
situation where the events are mutually exclusive, we can apply the sum rule.
Using the product rule, we know that each individual event has a probability
of 1/4. So, the probability of offspring with a dominant
phenotype is: (probability of A from Mother and A from Father) + (probability of A from Mother and a from Father) + (probability of a from Mother and A from Father) = (1/4) + (1/4) + (1/4) = 3/4.
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This result can be obtained from a Punnett
square too. In punnett square, one out of the four boxes holds the dominant
homozygote, AA and two more boxes represent
heterozygotes, one with a maternal A and a
paternal a. Each box is 1 out of the 4 boxes in the whole Punnett square, and since the
boxes do not overlap as they are mutually exclusive, they can be added up (1/4 + 1/4 + 1/4 = 3/4) to get the probability of offspring with the
dominant phenotype.
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Pedigree Analysis
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Term
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Meaning
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Pedigree
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Chart that shows the presence or absence of a trait within a
family across generations
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Genotype
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The genetic makeup of an organism (ex: TT)
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Phenotype
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The physical characteristics of an organism (ex: tall)
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Dominant allele
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Allele that is phenotypically expressed over another allele
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Recessive allele
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Allele that is only expressed in absence of a dominant allele
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Autosomal trait
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Trait that is located on an autosome (non-sex chromosome)
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Sex-linked trait
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Trait that is located on one of the two sex chromosomes
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Homozygous
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Having two identical alleles for a particular gene
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Heterozygous
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Having two different alleles for a particular gene
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Pedigrees are used to analyze the pattern of inheritance of a
particular trait throughout a family. Pedigrees show the presence or absence of
a trait as it relates to the relationship among parents, offspring, and
siblings.
Reading a pedigree
Pedigrees represent family members and relationships using
standardized symbols.
By analyzing a pedigree, we can determine genotypes,
identify phenotypes, and predict how a trait will be passed on in
the future. The information from a pedigree makes it possible to determine how
certain alleles are inherited: whether they are dominant, recessive, autosomal,
or sex-linked.
To start reading a pedigree:
1.
Determine whether the trait is dominant or
recessive. If the trait is dominant, one of the parents must have
the trait. Dominant traits will not skip a generation. If the trait is
recessive, neither parent is required to have the trait since they can be
heterozygous.
2.
Determine if the chart shows an autosomal or
sex-linked (usually X-linked) trait. For example, in
X-linked recessive traits, males are much more commonly affected than females.
In autosomal traits, both males and females are equally likely to be affected
(usually in equal proportions).
Simple rules for pedigree analysis
To study the inheritance pattern in human
beings, controlled experimental mating is not possible and instead we study the
inheritance pattern in families by pedigree analysis.
The simple rules for pedigree analysis are:
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Autosomal recessive
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affects males and females equally
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both parents must carry allele
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parents may not display trait (carriers)
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~1/4 of children affected (if both parents are
carriers)
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Autosomal dominant
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affects males and females equally
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only one parent must carry alllele
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if child displays trait, at least one parent
must also display trait
§
~1/2 of children affected (if one parent
displays trait)
§
X-linked recessive
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typically affects only males
§
affected male passes allele to daughters, not
to sons
§
trait skips a generation
