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6. MENDELIAN GENETICS.
LINKAGE AND GENETIC MAPS.
The Mendelian laws. Types of inheritance. The two
components of recombination: crossing over and
independent assortment. Test cross. Linkage and
genetic maps.
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over the short one that was called recessive.
(Naturally, the first Mendelian law refers to
individuals that derive from crosses with true
breeding strains.)
INTRODUCTION
Inheritance of traits has long kept the interest of
people. The rules of inheritance were first described by
the Augustinian monk, Gregor Johann Mendel in
1865. Thomas Hunt Morgan and his co-workers
(1913) showed that genes are inherited in linkage
groups and that one linkage group corresponds to one
chromosome. The genes, like beads on a string, are
linearly arranged on the chromosomes. Their sequence
and distance can be determined and arranged into
so-called genetic maps. This chapter deals with the
laws of inheritance, describes general principles of
inheritance of traits and the construction of genetic
maps.
A brief glossary:
Gene: the unit of heredity and genetic function.
Locus: the site of a gene in a chromosome.
Genotype: the genetic constitution of an individual
with respect to a single or several traits.
Phenotype: the observable properties of an individual
as developed under the combined influence of its
genetic constitution and the environmental factors.
Allele: a particular form of a gene that is
distinguishable from other forms or alleles of the same
gene.
Heterozygous: diploid organism having different
alleles of a gene on the homologous chromosomes.
Homozygous: diploid organism having identical
alleles of a given gene on both homologous
chromosomes.
Hemizygous: condition for genes present in a single
copy in the otherwise diploid organisms. (Examples
are X-linked genes in the XY individuals.)
Recessive: the allele which has an effect on the
phenotype only in a homozygous condition.
Dominant: the ability of one allelic form of a gene to
determine the phenotype of a heterozygous
individual.
Wild type: the most frequent allele in a population.
Expressivity: the degree of expression of a trait in the
phenotype at the individual level.
Penetrance: the percentage of carriers expressing the
phenotype at the population level.
The Mendelian laws
1. The Law of Uniformity
Mendel made use of true breeding, i.e. genetically
homogeneous strains in which every individual is
homozygous for one (or more) trait(s). In the first
sets of experiments, Mendel crossed tall garden pea
plants with short ones (Figure 6.1). He noticed that
in the offspring, the so-called F1 generation, the
plants were uniformly tall and the short feature
seemingly disappeared. According to the Mendel's
first law, the law of uniformity, individuals in the F1
generation are uniform. The tall trait is dominant
Figure 6.1. Principles of Mendel's experimental
procedure.
2. The Law of Segregation
Mendel crossed F1 individuals with one another and
produced the so-called F2 generation. He noticed
that tall and short plants segregated at the 3:1 ratio in
the F2 generation. According to Mendel's second
law, the law of segregation, the parental traits
segregate in the F2 generation at the 3:1 ratio.
Mendel studied inheritance of 7-pairs of alleles
(Table 6.1). Based on the 3:1 segregation ratio
Mendel concluded that the height of the plants are
controlled by two factors (what we call genes). He
further concluded that (i) gamete carried only one of
the two factors (either T = tall or t = short) and (ii)
that the male and female gametes combine randomly
(Figure 6.2). The random combination of germ cells
will lead to the formation of TT individuals who are
homozygous for the dominant allele, Tt and tT
heterozygous as well as tt homozygous ones that are
homozygous for the recessive allele. The first three
types carry the T dominant allele and are thus tall,
the fourth one is tt and is short. Segregation of the
genotypes is 1 TT : 2 Tt and 1 tt (Figure 6.2).
Table 6.1. A summary of Mendel's results with
seven pairs of alleles.
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Figure 6.2. Germ cells carry only one of the two
factors and combine randomly.
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chloride ion channel (Figure 6.3). Mutant alleles lead
to abnormal chloride channel function, disease and
death. (2) The Tay-Sachs disease is caused by an
absence of the hexosaminidase-A enzyme, leading to
gradual degeneration of the nervous system resulting
in death before the age of 5. The frequency is 1/3600
births among Ashkenazi Jews. (3) Phenylketonuria
develops due to the inability to metabolize
phenylalanine. Mental retardation develops in the
homozygotes that usually die before the age of 30. (4)
Sickle cell anemia develops due to a single amino acid
chain of the ß-hemoglobin. (5) Albinism is the
consequence, due to mutations, of the absence of the
failure of pigment synthesis. (Details of human genetic
disorders will be discussed in the course on human
genetics.)
For convenience, Reginald Punnett developed a
system that graphically depicts the genotypes of the
parental germ cells. The genotypes of the germ cells
are presented in the heading and in the first column of
the so-called Punnett table. Possible combinations of
the zygotes are arranged in the squares of the Punnett
table as shown here.
Germ cell
genotype
T
t
T
TT
Tt
t
Tt
tt
Examples for the dominant-recessive mode of
inheritance in humans
Traits and genetic disorders linked to autosomes
There are several traits that follow the
dominant-recessive mode of inheritance. For example,
brown eyes are dominant to blue, woolly hair is
dominant to straight. Inheritance of several human
genetic disorders follows the pattern described for the
T and t allele pair. In cases like brachydactylism (short
fingers) and polydactylism (extra fingers) the disorder
is caused by the Bd and the Pd dominant mutations,
respectively. Perhaps surprising, but not all the Pd/+
people possess polydactyly: penetrance of the Pd
mutation is not 100%. Expressivity of polydactyly is
also less than 100%: there are people with 4x6 fingers;
others have only one extra finger.
In other cases the genetic disorder develops in
individuals homozygous for the recessive mutation
(like tt). We shall mention briefly five of these
mutations. (1) Cystic fibrosis is the most frequent
hereditary disease in European populations (1 in 2000,
the heterozygote frequency is 1/22). Thick mucus
forms and persists in the lungs of the cf homozygous
people. The liver, pancreas and digestive systems fail
to function properly, resulting in death between the
ages of 20-30. The CF gene (and also its mutant
alleles) is linked to the 7th chromosome. The CF gene
encodes a protein composed from 1480 amino acids.
The CF protein is membrane-bound regulator of a
Figure 6.3. Structure of the cystic fibrosis gene and
the CF protein.
Incomplete dominant and co-dominant modes of
inheritance
We are aware of the fact that the T allele is linked to
one, the t allele is to the other member of the
homologous chromosomes. In case of semi-dominant
inheritance (also called intermediate or incomplete
dominant inheritance) phenotype of the heterozygotes
is between those characteristic for the dominant and
the recessive ones. The phenotype determined by the
dominant allele is incomplete, semi-dominant or
intermediate. In case of co-dominant inheritance, both
alleles make equal contribution to the phenotype. The
best known example is the inheritance of A and B
blood group in the AB0 system. The phenotype of the
AA individuals, with respect to the A character, is
equal to those of A0's and AB's.)
Sex linkage
In any of Menedel's crosses phenotype of the offspring
did not depend on sex of the parents. When Morgan
and his co-workers crossed red eyed fruit fly
(Drosophila melanogaster) females with white eyed
males, eyes of the offspring were uniformly red, as
expected (Figure 6.4). Surprisingly, in the reciproc
cross, in which white eyed females were mated with
red eyed males, all the females had red eyes and all the
males had white eyes (Figure 6.4). The Morgan group
concluded that the males received a white mutation
carrying chromosome from the females and the males
did not carry the homologue of that chromosome.
They called the chromosome X, a sex chromosome
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characteristic for the females. Females received an X
chromosome with the normal (red) gene and hence
their eyes were red. They also called the male-specific
(sex) chromosome Y. Naturally the red/white females
gave rise to 50% red and 50% white eyed males.
XX
XX
x
XY
XY
Reciproc
XX
XX
x
XY
XY
X = chromosome with the red eyes encoding gene
X = chromosome with the white eyes encoding allele
Figure 6.5. Pedigre od some of the descendants of
Queen Victoria demonstrating the sex-linked
inheritance of hemophilia. The symbols are as follows:
= male, = male possessing the symptoms, =
female, = carrier (heterozygous) female.
Figure 6.4. Reciproc crosses between red and white
eyed fruit flies.
There are about 2200 genes on the fruit fly X
chromosome. The eye color-coding gene is one of the
genes linked to the X chromosome. (In most birds and
moths the males are ZZ and the females are ZW. Z
and W are symbols of the sex chromosomes.)
The X chromosome in humans, like in the fruit flies,
contains many genes. The X-linked genes are in
hemizygous condition in the XY men, i.e. present in
one copy. Mutations in the X-linked genes affect
males usually and possess a characteristic pattern of
inheritance: the disease affects males in every other
generation and the encoding mutation is transmitted by
the heterozygous females (Figure 6.5).
There are only a few dominant mutations know to
be X-linked. (They will be discussed in the human
genetics course.) Some of the diseases caused by
X-linked recessive mutations in humans are quite well
know. We shall mention briefly five of these
mutations. (1) The Lesch-Nyhan syndrome develops
due to the absence of the enzyme hypoxanthine
guanine phosphoribosyl transferase (HPRT). HPRT it
is an essential enzyme of purine and ATP
biosynthesis. The absence of the HPRT enzyme leads
to abnormal mental functions, self-mutilation and
paralysis. (2) Patients who carry mutation in the
corresponding X-linked gene are hemophilic due to
failure of blood clotting. (3) Muscular dystrophy is
caused by mutations in the dystrophin gene, that is the
largest known human gene (composed of some 2.4
million base pairs). The normal dystrophin protein
establishes contact between the cytoskeleton and the
extracellular matrix through a large transmembrane
glycoprotein complex (Figure 6.6). Mutations in the
dystrophin gene induce progressive muscular
deterioration usually following the age of 3. (4) Color
blindness or Daltonism and (5) ichthyosis (epidermal
scaling) are also caused by X-linked mutations.
It is often claimed that hairy ear rims are caused by
a mutation linked to the Y chromosome.
Figure 6.6. Dystrophin protein establishes contact
between the cytoskeleton and the extracellular matrix.
The so-called sex limited inheritance refers to genes
that can be expressed only in one sex. Inherited
variations in primary and secondary sex characteristics
are obvious examples. (It is very difficult to study the
inheritance of breast shape and udder characteristics in
males, although males transmit genes influencing
breast development.)
Characteristics known in both sexes but different in
their degree of expression possess sex-influenced
inheritance. Inheritance of pattern baldness is a typical
example of sex-influenced inheritance (Fig. 6.7).
Figure 6.7. Inheritance of pattern baldness is a typical
example of sex-influenced inheritance. It is dominant
in males and recessive in females.
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Two factorial crosses
3. The Law of Independent Assortment
Mendel conducted experiments in which he followed
the inheritance of two genes, e.g. Yy and the Rr (Y =
yellow seeds, y = green seeds, R = round seeds, r =
cube-shaped seeds. While Y and R are the dominant, y
and r are the recessive alleles). He crossed YY; RR
garden peas with yy; rr ones. Seeds in the F1
generation were homogenously yellow and round
shaped. He than crossed the F1 generation Yy; Rr
individuals with each other and generated the next
generation as shown in Table 6.2. In the F2 generation
the phenotypic ratios were as follows: yellow and
round : green and round : yellow and cube-shaped :
green and cube-shaped = 9 : 3 : 3 : 1. Mendel
concluded, based on the 9 : 3 : 3 : 1 proportions, that
the yellow/green and the round/cube-shaped factors
combine freely, as we say, they possess independent
assortment. The above phenomenon is natural when
the seed color and the shape determining genes are
linked to different autosomes. The 3rd Mendelian law,
i.e. the law of independent assortment, states that
genes linked to different chromosomes assort
independently.
Table 6.2. Genotypes, as presented in a Punnett table,
in the F2 generation following a cross between Y/y: R/r
individuals
Female
germ
cells
Y; R
Male germ cells
Outcome of a test cross is simple, because (1) only
four classes of offspring develop and (2) the ratio of
different phenotypes is 1 : 1 : 1 : 1.
Note that while in the Y; R and in the y; r
combinations the parental chromosomes appear (and
hence are called parental , they are recombined
(mixed) in the y; R and in the y; R combinations (and
are thus called recombinant ). The proportion of the
recombinant offspring among the total is thus = 2/4 =
0.5.
Linkage
It was mostly the Morgan group that conducted several
crosses with two genes and two alleles each. To their
surprise, the proportion of the four classes from the
test crosses was not always 1:1:1:1 (Table 6.4). The
parental classes (A B and the a b in the example in
Table 6.4) were more frequent than the recombinant
classes (A b and a B). The ratio of the two parental
classes is 1 (A B : a b = 1). Similarly the ratio of the
recombinant classes is also one (A b : a B = 1),
indicating that they are reciprocal products of one
event, the crossing over.
Table 6.4. Result of a test cross with two genes with
two alleles each. Genes on the same chromosome.
Female germ cells
A; B parental
Male germ cells
a; b
Aa; Bb
Y; R
Y; r
y; R
y; r
A; b recombinant
Aa; bb
YY; RR
YY; Rr
Yy; RR
Yy; Rr
a; B recombinant
aa; Bb
Y; r
YY; Rr
YY; rr
Yy; Rr
Yy; rr
a; b parental
aa; bb
y; R
Yy; RR
Yy; Rr
yy; RR
yy; Rr
y; r
Yy; Rr
Yy; rr
yy; Rr
yy; rr
The phenotypes: = yellow and round; = green and
round; = yellow and cube-shaped;
= green and
cube-shaped.
The Punnett table in Table 6.2 appears rather
complicated. To make crosses the least complicated,
geneticists use test crosses, in which one of the
partners is homozygous for the recessive alleles as
shown in Table 6.3.
Table 6.3. Result of a test cross with two genes with
two alleles each. The genes are on different
chromosomes.
Female germ cells
Y; R parental
Male germ cells
y; r
Yy; Rr
Y; r recombinant
Yy; rr
y; R recombinant
yy; Rr
y; r parental
yy; rr
The phenotypes are the same as in Table 6.2.
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When two genes are linked, the distance between
them is measured by the frequency (in %) of the
recombinats in the offspring and is determined by
the following formula:
number of recombinants x 100
total number of offspring
and is measured in centiMorgans (cM).
Based on the frequency of the recombinants in the
offspring, A. H. Sturtevant elaborated a method to
measure the genetic distance between the linked genes.
The unit of map distance is cM (Table 6.4).
The maximum measurable distance is 50 cM. When
the distance is 50 cM, the proportion of both
recombinants and parental classes is 50%, as if the two
genes were located on different chromosomes. The
relationship between the measured and the actual map
distances is described be the Haldane equation:
r = 1 (1 - e
2m
)
where r = proportion of the recombinant chromosomes
and m = distance between two points (in cM; Figure
6.8). Note that even numbered crossing overs decrease
the map distance.
Observed recombination
frequency
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50
40
30
20
10
50
100
150
200
Corrected map units
Figure 6.8. The relationship between the observed
recombination frequency and the actual map distance
as determined by JBS Haldane s equation.
In the actual practice the map distances are
determined in bits of less than 10 cM. The genetic map
of the long chromosomes is often longer than 100 cM,
for shorter chromosomes can be only a few cM long.
Genetic maps
Sturtevant also showed that genes, like beads on a
string, are linearly arranged and comprise a so-called
linkage group. The mapping studies showed that the
number of linkage groups is four in Drosophila,
identical with the haploid number of chromosomes. It
become apparent during early 20th century that one
chromosome corresponds to one linkage group and
that chromosomes carry the material that determine
the heritable characteristics of the organisms. The
chromosomal basis of inheritance, as well as the laws
of inheritance proved to be universal for all the
eukaryotic organisms.
Detailed genetic maps are available for not only
fruit flies, but also yeast, corn, mouse, humans and
many others (Figure 6.9). The genetic maps, along
with the physical and molecular ones provide access
to understand the molecular basis of heritable
characteristics, modify the genes for practical purposes
and cure it in gene therapy.
Pedigree analysis
Inheritance of the characters thorough generations is
depicted in pedigrees (Figure 6.5). The pedigrees
illustrate the inheritance of one or only a few
characteristics. Pedigree analysis helps to understand
the mode of inheritance of traits and provide basis for
genetic counseling, predicting the likelihood of
affected offspring.
SUMMARY
The laws of inheritance are universal in all the
eukaryotes and are in full harmony with chromosome
"mechanics" during the two meiotic divisions. The
marker mutations, i.e. alleles with visible phenotypes,
made possible the identification of linkage groups and
the construction of genetic maps. Genetic maps serve
as basis for molecular genetics.
Figure 6.9. Genetic map of part of the human X
chromosome.
REFERENCES
1. Sadava, D. et al., Life the Science of Biology, 9th
edition, 237-259, 2011.
2. Griffiths, A.J.F. et al. Genetic Analysis, 31-180,
2008.
3. Fristrom, J.W. and Clegg, M.T., Principles of
Genetics, 147-177, 201-252, 1989.
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