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Lets Go Blog: THE PUNNETT SQUARE APPROACH FOR A MONOHYBRID CROSS...
Lets Go Blog: THE PUNNETT SQUARE APPROACH FOR A MONOHYBRID CROSS...: When fertilization occurs between two true-breeding parents that di f fer in only one characteristic, the process is called a monohybrid c...
THE PUNNETT SQUARE APPROACH FOR A MONOHYBRID CROSS
When fertilization occurs between two
true-breeding parents that differ in
only one characteristic, the process is called a monohybrid cross, and the resulting offspring are monohybrids. Mendel performed seven monohybrid
crosses involving contrasting traits for each characteristic. On the basis of his results in F1 and F2 generations, Mendel postulated that each
parent in the monohybrid cross contributed one of two paired unit factors to each offspring, and every possible
combination of unit factors was
equally likely.
To
demonstrate a monohybrid cross, consider the case of true-breeding pea plants with yellow versus
green pea seeds. The dominant seed color is yellow; therefore, the parental genotypes
were YY for the plants with yellow seeds and yy for the plants with green seeds,
respectively. A Punnett square, devised
by the British geneticist Reginald Punnett, can be drawn that applies the rules
of probability to predict the possible outcomes of a genetic cross or mating
and their expected frequencies. To
prepare a Punnett square, all possible combinations of the parental alleles are
listed along the top (for one parent) and side (for the other parent) of a
grid, representing their meiotic segregation into haploid gametes. Then the
combinations of egg and sperm are made in the boxes in the table to show which
alleles are combining. Each box then represents the diploid genotype of a zygote, or fertilized egg, that could result from this mating. Because each possibility
is equally likely, genotypic ratios
can be determined from a Punnett square. If the pattern of inheritance
(dominant or recessive) is known, the phenotypic ratios can be inferred as
well. For a monohybrid cross of two true-breeding parents, each parent
contributes one type of allele. In this case, only one genotype is possible.
All offspring are Yy and have yellow seeds (Figure 1).
Figure 1 In the P generation, pea
plants
that are true-breeding for the dominant yellow phenotype are crossed with plants with
the recessive green phenotype. This cross produces F1
heterozygotes with a yellow
phenotype. Punnett square analysis
can be used to predict the genotypes of the F2
generation.
A self-cross of one of the Yy heterozygous offspring can be represented in a 2 × 2 Punnett square because each parent
can donate one of two different
alleles. Therefore, the offspring
can potentially have one of four allele combinations: YY, Yy, yY,
or yy (Figure 1). Notice that there are two ways to obtain the Yy genotype: a Y from the egg
and a y from the sperm, or a y from the egg and a Y from the sperm. Both of these
possibilities must be counted. Recall that Mendel’s pea- plant characteristics behaved
in the same way in reciprocal crosses.
Therefore, the two possible heterozygous combinations produce offspring
that are genotypically and phenotypically identical despite their dominant and
recessive alleles deriving from different
parents. They are grouped together.
Because fertilization is a random event, we expect each combination to be equally
likely and for the offspring to exhibit a ratio of YY:Yy:yy genotypes of 1:2:1 (Figure 1). Furthermore, because the YY and Yy offspring have yellow seeds
and are phenotypically identical, applying the sum rule of probability, we expect the offspring to exhibit a phenotypic ratio of 3 yellow:1 green.
Indeed, working with large sample
sizes, Mendel observed approximately this
ratio in every F2 generation resulting from
crosses for individual traits.
Mendel validated these
results by performing an F3 cross in which he
self-crossed the dominant- and recessive-expressing F2 plants.
When he self-crossed the plants expressing green seeds, all of the offspring had green seeds, confirming that
all green seeds had homozygous genotypes of yy.
When he self-crossed the F2 plants expressing
yellow seeds, he found that one-third of the plants bred true, and two-thirds of the plants segregated at a 3:1 ratio of yellow:green seeds. In this case,
the true-breeding plants
had homozygous (YY) genotypes, whereas the segregating plants corresponded to the heterozygous (Yy) genotype. When these plants self-fertilized, the outcome was just
like the F1 self-fertilizing cross.
The Test Cross Distinguishes the Dominant Phenotype
Beyond predicting the offspring of a cross between known homozygous or heterozygous parents,
Mendel also developed a way to determine whether an organism that expressed a dominant trait
was a heterozygote or a homozygote. Called the test cross, this
technique is still used by plant and animal breeders. In a test cross, the
dominant-expressing organism is
crossed with an organism
that is homozygous recessive for the same characteristic. If the dominant-expressing organism is a
homozygote, then all F1 offspring will be heterozygotes expressing
the dominant trait (Figure 2). Alternatively,
if the dominant expressing organism
is a heterozygote, the F1 offspring will exhibit a 1:1 ratio of
heterozygotes and recessive homozygotes (Figure
2). The test cross further validates Mendel’s postulate that pairs of unit factors segregate equally.
Figure 2 A test cross can
be performed to
determine whether an organism expressing
a dominant trait is a homozygote
or a heterozygote.
In
pea plants, round peas (R) are dominant to wrinkled peas (r). You do a test cross between
a pea plant with wrinkled peas (genotype rr) and
a plant of unknown genotype that has round peas. You end up with three plants,
all which have
round peas. From this data, can
you tell if the round
pea parent plant is homozygous dominant or
heterozygous? If the round pea parent plant is heterozygous, what is the probability that a random sample of
3 progeny peas will all
be round?
Many
human diseases are genetically inherited. A healthy person in a family in which some members suffer from a recessive genetic disorder may want to
know if he or she has the disease-causing gene and what risk exists of passing
the disorder on to his or her offspring. Of course, doing
a test cross in humans
is unethical and impractical. Instead,
geneticists use pedigree analysis to study the inheritance pattern
of human genetic diseases (Figure 3).
Figure 3 Alkaptonuria is a recessive genetic
disorder in which two amino
acids,
phenylalanine and
tyrosine, are not properly metabolized. Affected
individuals may have
darkened skin and brown urine,
and may suffer joint damage and other complications. In this pedigree, individuals with the disorder are indicated in blue and have the genotype aa. Unaffected individuals are indicated in yellow and
have
the genotype AA or Aa. Note that it is often possible to
determine a person’s genotype
from the genotype of
their offspring.
For example, if neither
parent has the disorder but their child does, they must be heterozygous.
Two individuals on the pedigree have
an unaffected
phenotype but unknown genotype. Because they do not have the disorder, they must have at least
one
normal allele, so their genotype
gets the “A?” designation.
Friday, September 16, 2016
MENDEL’S EXPERIMENTS AND THE LAWS OF PROBABILITY
Johann Gregor Mendel (1822–1884) (Figure 1)
was a lifelong learner, teacher, scientist, and man of faith. As a young
adult, he joined the Augustinian Abbey of St. Thomas in Brno in what is now the
Czech Republic. Supported by the monastery,
he taught physics, botany, and
natural science courses at the secondary and university levels. In 1856, he
began a decade-long research pursuit involving inheritance patterns in
honeybees and plants, ultimately settling on pea plants as his primary model system (a system with convenient
characteristics used to study a specific biological phenomenon to be applied to
other systems). In 1865, Mendel presented the results of his experiments with
nearly 30,000 pea plants to the local Natural History Society. He demonstrated that traits are
transmitted faithfully from parents to offspring
independently [1] of other traits and in dominant
and recessive patterns.
In 1866, he published his work, Experiments in Plant Hybridization, in the proceedings of the Natural History Society of
Brünn.
Figure 1. Johann Gregor Mendel
is considered the father of genetics.
Mendel’s
work went virtually unnoticed by the scientific community that believed,
incorrectly, that the process of
inheritance involved a blending of parental traits that produced an
intermediate physical appearance in offspring;
this hypothetical process appeared to be correct because of what we know now as
continuous variation. Continuous
variation results from the action of many genes to determine a
characteristic like human height. Offspring
appear to be a “blend” of their parents’ traits when we look at characteristics
that exhibit continuous variation. The blending
theory of inheritance asserted that the original parental traits were lost
or absorbed by the blending in the offspring,
but we now know that this is not the case. Mendel was the first researcher to
see it. Instead of continuous characteristics, Mendel worked with traits that
were inherited in distinct classes (specifically, violet versus white flowers); this is referred to as discontinuous variation. Mendel’s choice of these kinds of traits allowed
him to see experimentally that the traits were not blended in the offspring, nor were they absorbed, but
rather that they kept their distinctness and could be passed on. In 1868,
Mendel became abbot of the monastery
and exchanged his scientific pursuits for his pastoral duties. He was not recognized
for his extraordinary scientific contributions during his lifetime. In
fact, it was not until 1900 that his work was rediscovered, reproduced, and
revitalized by scientists on the brink of discovering the chromosomal basis of heredity.
Mendel’s Model
System
Mendel’s seminal work was accomplished using the garden pea, Pisum sativum, to study inheritance. This species naturally self-fertilizes, such that
pollen encounters ova within individual flowers. The flower petals remain
sealed tightly until after pollination, preventing pollination from other
plants. The result is highly inbred, or “true-breeding,” pea plants. These are
plants that always produce offspring
that look like the parent. By experimenting with true-breeding pea plants,
Mendel avoided the appearance of unexpected traits in offspring that might occur if the plants were not true breeding.
The garden pea also grows to maturity within one season, meaning that several
generations could be evaluated over a relatively short time. Finally, large
quantities of garden peas could be cultivated simultaneously, allowing Mendel to conclude that his
results did not come about simply by chance.
Mendelian Crosses
Mendel performed hybridizations, which
involve mating two true-breeding individuals that have different traits.
In the pea, which is naturally
self-pollinating, this is done by manually transferring pollen from the anther of a mature pea plant of
one variety to the stigma of a separate mature pea plant of the second variety. In plants, pollen carries the male
gametes (sperm) to the stigma, a sticky organ
that traps pollen and allows the sperm to move down the pistil to the female
gametes (ova) below. To prevent the pea plant that was
receiving pollen from self-fertilizing and confounding his results, Mendel
painstakingly removed all of the
anthers from the plant’s flowers before they had a chance to mature.
Plants used in first-generation crosses were called P0, or parental generation one, plants (Figure 2). Mendel collected
the seeds belonging to the P0 plants that resulted from each cross and grew them the following season.
These offspring were called the F1, or the first filial (filial = offspring, daughter
or son), generation. Once Mendel examined
the characteristics in the F1 generation of plants, he allowed
them to self-fertilize naturally. He
then collected and grew the seeds from the F1 plants to produce the F2, or second filial, generation. Mendel’s experiments extended beyond the F2 generation to the F3 and
F4 generations, and so on, but it was
the ratio of characteristics in the P0−F1−F2 generations
that were the most intriguing and became the
basis for Mendel’s postulates.
Figure 2. In one of his experiments on inheritance patterns, Mendel crossed plants that
were
true-breeding for
violet flower
color with plants true-breeding for white flower color (the P generation). The resulting hybrids in the F1 generation all had violet flowers. In the F2 generation, approximately three quarters of
the plants had violet flowers,
and one quarter had white flowers.
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