Transcript Inheritance Patterns of Individual Genes (1)

Inheritance Patterns of Individual Genes (1)
1) MITOSIS
We will use the alleles A and a as "typical" alleles of a gene. We can represent gene duplication and
segregation as follows:
Haploid cells can be of
Genotype A
genotype A or a, and the
diploids can be
homozygous, A/A and
Genotype a
a/a, or heterozygous, A/a.
Because each of the
chromosomes is
Genotype A/A replicated faithfully, the
genotypes of the daughter
cells must be identical
Genotype A/a with the progenitor.
Genotipe A/a
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Inheritance Patterns of Individual Genes (2)
2) MEIOSIS
Meiosis in homozygous meiocytes can produce only one genotype in the four haploid
products of meiosis (the tetrad), whereas starting with a meiocyte of genotype A/a,
meiosis produces four haploid cells, of which half are A and half are a, as follows:
The reason for this is that
in the A/a meiocyte, the A
chromosome produces a
pair of sister chromatids
Genotype A/A A/A, and the homologous
chromosome produces a
pair a/a. These four
copies of the gene end up
in the four meiotic
Genotype A/a product cells. This result,
was first observed by
Mendel.
Genotipe A/a
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Mendel’s experiments
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Mendel’s experiments were devised to explain the mechanisms of inheritance: “The
object of the experiment was to observe these variations in the case of each pair of
differentiating characters, and to deduce the law according to which they appear in
successive generations”.
Mendel's studies constitute an outstanding example of good scientific technique. He
chose research material well suited to the study of the problem at hand, designed his
experiments carefully, collected large amounts of data, and used mathematical
analysis to show that the results were consistent with his explanatory hypothesis.
The predictions of the hypothesis were then tested in a new round of
experimentation.
The techniques of analysis used by Mendel remained unchanged for most part of the
XX century; model organisms changed with time, but the basic methodology
remained always the same. The existence of genes was originally inferred (and is
still inferred today) by observing precise mathematical ratios in the descendants of
two genetically different parental individuals.
Only with the advent of fast DNA sequencing in the 1980’s, genes could be
analyzed directly without performing experimental crosses.
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The reasons of a choice
Mendel
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studied the garden pea (Pisum sativum) for two main reasons
Peas were available in a wide array of varieties that could be easily identified and
analyzed.
Peas can either self (self-pollinate: the male parts - pollen, contained in anthers –
can fertilize the female parts – ovules, contained in pistils) or be cross-pollinated
(the anthers from one plant are removed before they have opened to shed their
pollen, and pollen from the other plant is transferred to the receptive stigma with
a paintbrush). Thus, the experimenter can choose to self or to cross the pea
plants.
Other
practical reasons for Mendel's choice of peas were:
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they are inexpensive and easy to obtain,
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take up little space,
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have a short generation time,
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produce many offspring.
Such
considerations enter into the choice of organism for any piece of
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Differences among plant peas
The various forms of pea plants available for crossing showed differences in:
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length and color of the stem;
size and form of the leaves;
position, color, size of the flowers;
length of the flower stalk;
color, form, and size of the pods;
form and size of the seeds;
color of the seed-coats and of the albumen [cotyledons].
Some of these characters do not permit of a sharp and certain separation, since the
difference is of a "more or less" nature, which is often difficult to define. Such
characters could not be utilized for the separate experiments; these could only be
applied to characters which stand out clearly and definitely in the plants. Lastly, the
result must show whether they, in their entirety, observe a regular behavior in their
hybrid unions, and whether from these facts any conclusion can be reached regarding
those characters which possess a subordinate significance in the type.
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Characters selected for experiments
1.
Form of the seeds
The depressions, if any, occur on the surface, or they are irregularly angular and deeply wrinkled
2.
Color of the seed albumen (endosperm)
The albumen is either pale yellow, or it possesses an intense green tint. This difference of color is seen in the
seeds as their coats are transparent
3.
Color of the seed-coat/ color of the flower
This is either white, with which character white flowers are constantly correlated; or it is gray, gray-brown,
leather-brown, with or without violet spotting, in which case the color of the standards is violet, that of the
wings purple, and the stem in the axils of the leaves is of a reddish tint
4.
Form of the ripe pods
These are either simply inflated, not contracted in places; or they are deeply constricted between the seeds and
more or less wrinkled (P. saccharatum)
5.
Color of the unripe pods
They are either light to dark green, or vividly yellow, in which coloring the stalks, leaf-veins, and calyx
participate
6.
Position of the flowers
They are either axial, that is, distributed along the main stem; or they are terminal, that is, bunched at the top
of the stem and arranged almost in a false umbel; in this case the upper part of the stem is more or less
widened in section (P. umbellatum)
7.
Length of the stem
The length of the stem is very various in some forms; it is, however, a constant character for each, in so far
that healthy plants, grown in the same soil, are only subject to unimportant variations in this character. In
experiments with this character, in order to be able to discriminate with certainty, the long axis of 6 to 7 ft. was
always crossed with the short one of 3/4 ft. to 1 and 1/2 ft
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Plants differing in one character
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Mendel chose seven different characters to study. The word character in this regard
means a specific property of an organism; geneticists use this term as a synonym for
characteristic or trait.
For each of the characters that he chose, Mendel obtained lines of plants, which he
grew for two years to make sure that they were pure. A pure line is a population that
shows no variation in the particular character being studied; that is, all offspring
produced by selfing or crossing within the population are identical for this character.
These two characters can be
directly scored in the crossed
plants
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Dichotomous phenotypes
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Each pair of Mendel's plant lines can be said to show a character
difference, i.e. a contrasting difference between two lines of
organisms (or between two organisms) in one particular character.
Contrasting phenotypes for a particular character are the starting point
for any genetic analysis. The differing lines (or individuals) represent
different forms that the character may take: they can be called
character forms, character variants, or phenotypes.
The term phenotype (derived from Greek) literally means "the form
that is shown"; it is the term used by geneticists today.
The description of characters is somewhat arbitrary. For example, we
can state the color-character difference in at least three ways:
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Reciprocal crosses
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In one of his early experiments, Mendel pollinated a purple-flowered plant with
pollen from a white-flowered plant. Individuals from which an experiment is started
are called the parental generation (P).
All the plants resulting from this cross had purple flowers. This progeny generation
is called the first filial generation (F1 ). The subsequent generations produced by
selfing are symbolized F2 , F3 , and so forth.
Mendel made reciprocal crosses. In most plants, any cross can be made in two ways,
depending on which phenotype is used as male or female.
For example, the following
two crosses are reciprocal
crosses:
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Monohybrid crosses
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Next, Mendel selfed the F1 plants (the pollen of each flower fertilized
its own stigma). He obtained 929 pea seeds from this selfing (the F2
individuals) and planted them.
Some of the resulting plants were white flowered; the white
phenotype had reappeared.
Mendel then did something that, more than anything else, marks the
birth of modern genetics: he counted the numbers of plants with each
phenotype.
Mendel counted 705 purple-flowered plants and 224 white-flowered
plants. He noted that the ratio of 705:224 is almost exactly a 3:1 ratio
(in fact, it is 3.1:1).
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Dominance defined
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Mendel repeated the experiment for the six other character differences. He found the
same 3:1 ratio in the F2 generation for each pair. In all cases, one parental phenotype
disappeared in the F1 and reappeared in one-fourth of the F2 .
Mendel used the terms dominant and recessive to describe this phenomenon. The
purple phenotype is dominant to the white phenotype and the white phenotype is
recessive to purple. Thus the operational definition of dominance is provided by the
phenotype of an F1 established by intercrossing two pure lines. The parental
phenotype that is expressed in such F1 individuals is by definition the dominant
phenotype.
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A diagram of Mendel’s monohybrid experiments
P
F1
F2
F3
All the F2 greens were
x
evidently pure breeding, like
the green parental line; but,
of the F2 yellows, two-thirds
were like the F1 yellows
(producing yellow and green
self
seeds in a 3:1 ratio) and one6022 yellow peas
2001 green peas
third were like the purebreeding yellow parent. Thus
519 sampled and selfed
self
the study of the individual
selfings revealed that
underlying the 3:1
166 peas
353 peas with
green peas
with yellow
3:1 yellow/green
with green
phenotypic ratio in the F2
progeny
progeny
progeny
generation was a more
only
only
fundamental 1:2:1 ratio
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Mendel’s theory
Mendel's explanation is a classic example of a creative model or hypothesis derived
from observation and suitable for testing by further experimentation. He deduced the
following explanation:
1. The existence of genes.
There are hereditary determinants of a particulate nature.
2. Genes are in pairs.
Alternative phenotypes of a character are determined by different forms of a single type
of gene. In adult pea plants, each type of gene is present twice in each cell, constituting a
gene pair. In different plants, the gene pair can be of the same alleles or of different
alleles of that gene.
3. The principle of segregation.
The members of the gene pairs segregate (separate) equally into the gametes, or eggs
and sperm.
4. Gametic content.
Consequently, each gamete carries only one member of each gene pair.
5. Random fertilization.
The union of one gamete from each parent to form the first cell (zygote) of a new
progeny individual is random; that is, gametes combine without regard to which member
of a gene pair is carried.
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The 1:2:1 ratio
These points can be illustrated diagrammatically for a general case by
using A to represent the allele that determines the dominant phenotype
and a to represent the gene for the recessive phenotype (as Mendel did).
The use of A and a is similar to the way in which a mathematician uses
symbols to represent abstract entities of various kinds.
In this figure, these symbols are used to
illustrate how the preceding five points
explain the 1:2:1 ratio. The members of a
gene pair are separated by a slash (/). This
slash is used to show us that they are
indeed a pair; the slash also serves as a
symbolic chromosome to remind us that
the gene pair is found at one location on a
chromosome pair
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The backcross
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Mendel's next job was to test his model. He did so in the seed-color crosses by
taking an F1 plant that grew from a yellow seed and crossing it with a plant grown
from a green seed.
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This type of cross, of an individual of uncertain genotype with a fully recessive
homozygote, is now called a testcross or a backcross. Because one of the parents
contributes only recessive alleles, the gametes of the unknown individual can be deduced
from progeny phenotypes
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A 1:1 ratio of yellow to green seeds could be
predicted in the next generation. If Y stand for the
allele that determines the dominant phenotype
(yellow seeds) and y stand for the allele that
determines the recessive phenotype (green seeds),
we can diagram Mendel's predictions, as in the
figure beside.
•
In this experiment, Mendel obtained 58 yellow
(Y /y ) and 52 green (y /y ), a very close
approximation to the predicted 1:1 ratio and
confirmation of the equal segregation of Y and y
in the F1 individual.
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Dihybrid crosses
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Mendel went on to analyze the descendants of pure lines that differed
in two characters.
Here we need a general symbolism to represent genotypes including
two genes. If two genes are on different chromosomes, the gene pairs
are separated by a semicolon, for example, A /a ; B /b . If they are on
the same chromosome, the alleles on one chromosome are written
adjacently and are separated from those on the other chromosome by a
slash, for example, A B /a b or A b /a B.
An accepted symbolism does not exist for situations in which it is not
known whether the genes are on the same chromosome or on different
chromosomes. For this situation, we will separate the genes with a
dot, for example, A /a ·B /b . A double heterozygote, A /a · B /b , is
also known as a dihybrid. From studying dihybrid crosses (A /a · B /b
× A /a · B /b ), Mendel came up with another important principle of
heredity.
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Yellow/green-round/wrikled seeds
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The two specific characters that he began working with were seed
shape and seed color.
To perform a dihybrid cross, Mendel started with two parental pure
lines. One line had yellow, wrinkled seeds; because Mendel had no
concept of the chromosomal location of genes, we must use the dot
representation to write this genotype as Y /Y · r /r . The other line had
green, round seeds, the genotype being y /y · R /R .
The cross between these two lines produced dihybrid F1 seeds of
genotype R /r · Y /y , which he discovered were round and yellow.
This result showed that the dominance of R over r and of Y over y was
unaffected by the presence of heterozygosity for either gene pair in the
R /r · Y /y dihybrid.
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DiHybrid-cross F2 ratios
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Next Mendel made the dihybrid cross by selfing the dihybrid F1 to
obtain the F2 generation. The F2 seeds were of four different types in
the following proportions:
What could be the explanation? Mendel added up
the numbers of individuals in certain F2 phenotypic
classes to determine if the monohybrid 3:1 F2
ratios were still present. He noted that, in regard to
seed shape, there were 423 round seeds (315+108)
and 133 wrinkled seeds (101+32). This result is
close to a 3:1 ratio. Next, in regard to seed color,
there were 416 yellow seeds (315+101) and 140
green (108+32), also very close to a 3:1 ratio. The
presence of these two 3:1 ratios hidden in the
9:3:3:1 ratio was undoubtedly a source of the
insight that Mendel needed to explain the 9:3:3:1
ratio, because he realized that it was nothing more
than two independent 3:1 ratios combined at
random.
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Visualizing the 9:3:3:1 ratio
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One way of visualizing the random
combination of these two ratios is with a
branch diagram, as follows:
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The combined proportions are
calculated by multiplying along the
branches in the diagram because, for
example, 3/4 of 3/4 is calculated as 3/4
× 3/4, which equals 9/16 These
multiplications give us the following
four proportions:
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The Punnett square
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The four female gametic types will be fertilized
randomly by the four male gametic types to
obtain the F2 , and the best way of showing this
graphically is to use a 4×4 grid called a Punnett
square, which is depicted in Figure 2-10 . Grids
are useful in genetics because their proportions
can be drawn according to genetic proportions or
ratios being considered, and thereby a visual data
representation is obtained. In the Punnett square
in Figure 2-10 , for example, we see that the areas
of the 16 boxes representing the various gametic
fusions are each one-sixteenth of the total area of
the grid, simply because the rows and columns
were drawn to correspond to the gametic
proportions of each. As the Punnett square shows,
the F2 contains a variety of genotypes, but there
are only four phenotypes and their proportions are
in the 9:3:3:1 ratio.
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Chi-square analysis of Mendel’s single-plant observations
Mendel reported the following results for the F2 progeny of single plants:
Seed shape
Expectations
Round Wrinkled
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Total
1
2
3
4
5
6
7
8
9
Total
Round Wrinkled
Chi-squares
Total
Chi1
Chi2
Chisq
0.474
0.086
0.097
1.391
0.008
0.667
0.762
0.667
0.980
5.130
0.823
45
27
24
19
32
26
88
22
28
12
8
7
10
11
6
24
10
6
57
35
31
29
43
32
112
32
34
42.8
26.3
23.3
21.8
32.3
24.0
84.0
24.0
25.5
14.3
8.8
7.8
7.3
10.8
8.0
28.0
8.0
8.5
57
35
31
29
43
32
112
32
34
0.118
0.355
0.021
0.064
0.024
0.073
0.348
1.043
0.002
0.006
0.167
0.500
0.190
0.571
0.167
0.500
0.245
0.735
Chi-square (9 df)
Probability
311
94
405
303.8
101.25
405
0.173
0.519 0.692
Chi-square (1 df) 0.692
Probability
0.405
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