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Genetic Variation in
Individuals and Populations:
Mutation and Polymorphism
INHERITED VARIATION AND
POLYMORPHISM IN PROTEINS

Although all polymorphism is ultimately the result of
differences in DNA sequence, some polymorphic loci
have been studied by examining the variation in the
proteins encoded by the alleles rather than by
examining the differences in DNA sequence of the
alleles themselves.
 Any one individual is likely to be heterozygous for
alleles determining structurally different polypeptides
at approximately 20% of all loci; when individuals
from different ethnic groups are compared, an even
greater fraction of proteins has been found to exhibit
detectable polymorphism.

A striking degree of biochemical
individuality exists within the human
species in its makeup of enzymes and other
gene products.
 As the products of many of the encoded
biochemical pathways interact, each
individual, regardless of state of health, has
a unique, genetically determined chemical
makeup and thus responds in a unique
manner to environmental, dietary, and
pharmacological influences.

Examples of polymorphisms of medical significance:
the ABO and Rh blood groups, the major
histocompatibility complex (MHC).

Studying variation in proteins has real utility, the
variant protein products of various polymorphic alleles
are often what is responsible for different phenotypes
and therefore are likely to dictate how genetic
variation at a locus affects the interaction between an
individual and the environment.
Blood Groups and Their Polymorphisms
 Genetically determined protein variation detected
as antigens found in blood, the so-called blood
group antigens.
 Numerous polymorphisms are known to exist in
the components of human blood, especially in the
ABO and Rh antigens of red blood cells.
 In particular, the ABO and Rh systems are
important in blood transfusion, tissue and organ
transplantation, and hemolytic disease of the
newborn.
The ABO System
 Human
blood can be assigned to one of four
types according to the presence on the
surface of red blood cells of two antigens, A
and B, and the presence in the plasma of the
two corresponding antibodies, anti-A and
anti-B.
Table 9-4. ABO Genotypes and Serum Reactivity
RBC Phenotype
Reaction with
Anti-A
Reaction with
Anti-B
Antibodies In
Serum
O
-
-
Anti-A, anti-B
A
+
-
Anti-B
B
-
+
Anti-A
AB
+
+
Neither

One feature of the ABO groups not shared by other
blood group systems is the reciprocal relationship, in
an individual, between the antigens present on the red
blood cells and the antibodies in the serum.
 When the RBCs lack antigen A, the serum contains
anti-A; when the cells lack antigen B, the serum
contains anti-B.
 The reason for this reciprocal relationship is
uncertain, but formation of anti-A and anti-B is
believed to be a response to the natural occurrence of
A-like and B-like antigens in the environment (e.g.,
in bacteria).

The ABO blood groups are determined by a
locus on chromosome 9.
 The A, B, and O alleles at this locus are a
classic example of multiallelism in which
three alleles, two of which (A and B) are
inherited as a codominant trait and the third
of which (O) is inherited as a recessive trait,
determine four phenotypes.
 The A and B antigens are made by the
action of the A and B alleles on a red blood
cell surface glycoprotein called H antigen.

The antigenic specificity is conferred by the
specific terminal sugars, added to the H
substance.
– The B allele codes for a glycosyltransferase adds
d-galactose to the end H antigen  B antigen.
– The A allele codes for an enzyme that adds Nacetylgalactosamine to the precursor H  A
antigen.
– The O allele codes for a mutant version of the
transferase that lacks transferase activity, does not
detectably affect H substance at all.

The molecular differences in the
glycosyltransferase gene
– Four nucleotide differences between the A and B
alleles result in amino acid changes that alter
specificity of the glycosyltransferase.
– The O allele has a single-base pair deletion in the
coding region, a frameshift mutation that eliminates
the transferase activity in type O individuals.

Now ABO blood group typing can be
performed genotype level, especially when
there are technical difficulties in serological
analysis, as is often the case in forensic
investigations or paternity testing.

ABO blood group is medically important in
blood transfusion and tissue or organ
transplantation.
 A compatible combination is one in which
the RBCs of a donor do not carry an antigen
that corresponds to the antibodies in the
recipient's serum.
 Although theoretically there are universal
donors (group O) and universal recipients
(group AB), a patient is given blood of his
or her own ABO group, except in
emergencies.

In case of incompatibility antibodies can
cause immediate destruction of ABOincompatible cells.
 In tissue and organ transplantation, ABO
compatibility of donor and recipient, human
leukocyte antigen (HLA) compatibility, is
essential to graft survival.
The Rh System

The Rh system is clinically important because of
its role in hemolytic disease of the newborn and in
transfusion incompatibilities.
 The name Rh comes from Rhesus monkeys that
led to the discovery of the system.
 In simplest terms, the population is separated into
Rh-positive who express on their RBCs the
antigen Rh D, a polypeptide encoded by a gene
(RHD) on chromosome 1, and Rh-negative
individuals, who do not express this antigen.

The Rh-negative phenotype usually
originates from homozygosity for a
nonfunctional allele of the RHD gene.
 The frequency of Rh-negative individuals
varies in different ethnic groups. For
example, 17% of whites and 7% of African
Americans are Rh-negative, whereas the
frequency among Japanese is 0.5%.
Hemolytic Disease of the Newborn (HDN)

Rh-negative persons can readily form anti-Rh
antibodies after exposure to Rh-positive RBCs.
 A problem when an Rh-negative pregnant woman is
carrying an Rh-positive fetus.
 Normally during pregnancy, small amounts of fetal
blood cross the placental barrier and reach the
maternal blood stream.
 If the mother is Rh-negative and the fetus Rh-positive,
the mother will form antibodies that return to the fetal
circulation and damage the fetal RBCs, causing HDN
with consequences that can be severe if not treated.

The risk of immunization by Rh-positive fetal
RBCs can be minimized with an injection of Rh
immune globulin at 28 to 32 weeks of gestation
and again after pregnancy.
 Rh immune globulin serves to clear any Rhpositive fetal cells from the mother's circulation
before she is sensitized.
 Rh immune globulin is also given after
miscarriage, termination of pregnancy, or invasive
procedures such as chorionic villus sampling or
amniocentesis, in case any Rh-positive cells
gained access to the mother's circulation.

The discovery of the Rh system and its role in
hemolytic disease of the newborn has been a
major contribution of genetics to medicine.
 At one time ranking as the most common human
genetic disease, hemolytic disease of the newborn
is now relatively rare because of preventive
measures that have become routine practice in
obstetrical medicine.
The Major Histocompatibility Complex

The MHC is composed of a large cluster of
genes located on the short arm of
chromosome 6.
 On the basis of structural and functional
differences, these genes are categorized into
three classes, two of which, the class I and
class II genes, correspond to the human
leukocyte antigen (HLA) genes, originally
discovered by virtue of their importance in
tissue transplantation between unrelated
individuals.

The HLA class I and class II genes encode cell
surface proteins that play a critical role in the
initiation of an immune response and specifically
in the "presentation" of antigen to lymphocytes,
which cannot recognize and respond to an antigen
unless it is complexed with an HLA molecule on
the surface of an antigen-presenting cell.
 Many hundreds of different alleles of the HLA
class I and class II genes are known and more are
being discovered, making them by far the most
highly polymorphic loci in the human genome.

Figure 9-7 A schematic of the MHC complex on chromosome
6p. DP, DQ, and DR, class II antigen genes; B, C, and A, class I
antigen genes; LMP, genes encoding components of large
multifunctional protease; DM, heterodimer of DMA and DMB
genes encoding the antigen-processing molecule required for
binding peptide to MHC class II antigens; other genes encode
TAP, transporter associated with antigen processing; TNF,
tumor necrosis factor; Bf, properdin factor B; C2, C4A, C4B,
complement components; 21-OH, 21-hydroxylase. (One of the
21-OH loci is a pseudogene.)

The class I genes (HLA-A, HLA-B, and HLA-C)
encode proteins that are an integral part of the
plasma membrane of all nucleated cells.
 A class I protein consists of two polypeptide
subunits, a variable heavy chain encoded within
the MHC and a nonpolymorphic polypeptide, β2microglobulin, that is encoded by a gene outside
the MHC, mapping to chromosome 15.
 Peptides derived from intracellular proteins are
generated by proteolytic degradation by a large
multifunctional protease; the peptides are then
transported to the cell surface and held in a cleft
formed in the class I molecule to display the
peptide antigen to cytotoxic T cells.
The Major Histocompatibility Complex

Figure 9-8 The interaction between MHC class I and class II
molecules, foreign proteins, and T-cell receptors. LMP, large
multifunctional protease; TAP, transporter associated with antigen
processing; Ii, invariant chain; DM, heterodimer encoded by the DMA
and DMB genes; CD8+, cytotoxic T cells; CD4+, helper T cells.

The class II region is composed of several
loci, such as HLA-DP, HLA-DQ, and HLADR, that encode integral membrane cell
surface proteins.
 Each class II molecule is a heterodimer,
composed of α and β subunits, both of
which are encoded by the MHC.
 Class II molecules present peptides derived
from extracellular proteins that had been
taken up into lysosomes and processed into
peptides for presentation to T cells.

Other gene loci are present within the MHC
but are functionally unrelated to the HLA
class I and class II genes and do not
function to determine histocompatibility or
immune responsiveness.
 Some of these genes are, however,
associated with diseases, such as congenital
adrenal hyperplasia, caused by deficiency
of 21-hydroxylase, and hemochromatosis,
a liver disease caused by iron overload.
HLA Alleles and Haplotypes

According to the older, traditional system of HLA
nomenclature, the different alleles were
distinguished from one another serologically. An
individual's HLA type was determined by seeing
how a panel of different antisera or reactive
lymphocytes reacted to his or her cells.
 These antisera and cells were obtained from
hundreds of multiparous women who developed
immune reactivity against the paternal type I and
type II antigens expressed by their fetuses during
the course of their pregnancies.

If cells from two unrelated individuals evoked the
same pattern of reaction in a typing panel of
antibodies and cells, they would be considered to
have the same HLA types and the allele they
represented would be given a number, such as B27
in the class I HLA-B locus or DR3 in the class II
DR locus.
 However, as the genes responsible for encoding
the class I and class II MHC chains were
identified and sequenced, single HLA alleles
initially defined serologically were shown to
consist of multiple alleles defined by different
DNA sequence variants even within the same
serological allele.

The 100 serological specificities at HLA-A, B, C, DR,
DQ, and DP now comprise more than 1300 alleles
defined at the DNA sequence level.
 For example, more than 24 different nucleic acid
sequence variants of the HLA-B gene exist in what
was previously defined as "the" B27 allele by
serological testing.
 Most but not all of the DNA variants change a triplet
codon and therefore an amino acid in the peptide
encoded by that allele.
 Each allele that changes an amino acid in the HLA-B
peptide is given its own number, so allele number 1,
number 2, and so on in the group of alleles
corresponding to what used to be a single B27 allele
defined serologically, is now referred to as HLAB*2701, HLA-B*2702, and so on.

The set of HLA alleles at the different class I and class
II loci on a given chromosome together form a
haplotype.
 The alleles are codominant; each parent has two
haplotypes and expresses both. These loci are located
close enough to each other that, in an individual family,
the entire haplotype can be transmitted as a single block
to a child.
 As a result, parent and child share only one haplotype,
and there is a 25% chance that two sibs inherit matching
HLA haplotypes.
 Because acceptance of transplanted tissues largely
correlates with the degree of similarity between donor
and recipient HLA haplotypes (and ABO blood
groups), the favored donor for bone marrow or organ
transplantation is an ABO-compatible and HLAidentical sibling of the recipient.

Figure 9-9 The inheritance of HLA haplotypes. A
haplotype is usually transmitted, as a unit. In extremely
rare instances, a parent will transmit a recombinant
haplotype to the child, as seen in individual II-5, who
received a haplotype that is recombinant between the
class I and class II loci.

Within any one ethnic group, some HLA alleles are
found commonly; others are rare or never seen.
Similarly, some haplotypes are much more frequent
than expected, whereas others are exceptionally rare or
nonexistent.
 For example, most of the 3 × 107 allelic combinations
that could theoretically occur to make a haplotype
among white individuals have never been observed.
 This restriction in the diversity of haplotypes possible
in a population results from a situation referred to as
linkage disequilibrium and may be explained by a
complex interaction between a number of factors:

These factors include:
– low rates of meiotic recombination in the small
physical distance between HLA loci;
– environmental influences that provide positive
selection for particular combinations of HLA
alleles forming a haplotype; and
– historical factors, such as how long ago the
population was founded, how many founders
there were, and how much immigration has
occurred.

Major differences in allele and haplotype
frequencies exist between populations as well.
What may be a common allele or haplotype in one
population may be very rare in another.
 Once again, the differences in the distribution and
frequency of the alleles and haplotypes within the
MHC are the result of complex genetic,
environmental, and historical factors at play in
each of the different populations.
HLA and Disease Association

With the increasing delineation of HLA alleles has
come an appreciation of the association between
certain diseases and specific HLA alleles and
haplotypes.
 The etiological basis for most of the HLA-disease
associations remains obscure. Most but not all of
these disorders are autoimmune, that is,
associated with an abnormal immune response
apparently directed against one or more self
antigens that is thought to be related to variation in
the immune response resulting from
polymorphism in immune response genes.
Ankylosing Spondylitis

Ankylosing spondylitis, a chronic inflammatory
disease of the spine and sacroiliac joints, is one
example.
 In older studies that relied on serologically defined
B27 alleles, only 9% of Norwegians, for example,
are B27-positive, whereas more than 95% of those
with ankylosing spondylitis are B27-positive. Thus,
the risk of developing ankylosing spondylitis is at
least 150 times higher for people who have HLAB27 than for those who do not.
 Although less than 5% of B27-positive individuals
develop the disease, as many as 20% of B27-positive
individuals may have subtle, subclinical
manifestations of the disease without any symptoms
or disability.

One explanation for why some B27-positive
individuals do not develop disease rests in part on
that fact that DNA sequencing has revealed more
than two dozen different alleles within "the" HLAB27 allele originally defined serologically.
 The frequency of each of these different alleles
varies within a given ethnic group and between
ethnic groups.
 *If only certain of these B27 alleles predispose to
disease, while others may actually be protective,
studies in different ethnic groups that lump all the
B27 alleles into a single allele will find quite
different rates of disease in B27-positive
individuals.
Table 9-5. HLA Alleles with Strong Disease Association
Frequency
(%)*
Disease
HLA Allele
(Serological)
Patients
Controls
Odds Ratio†
Ankylosing spondylitis
B27
>95
9
>150
Reiter syndrome
B27
>80
9
>40
Acute anterior uveitis
B27
68
9
>20
Subacute thyroiditis
B35
70
14
14
Psoriasis vulgaris
Cw6
87
33
7
Narcolepsy
DQ6
>95
33
>38
Graves disease
DR3
65
27
4
Rheumatoid arthritis
DR4
81
33
9
Frequency
(%)*
Disease
HLA Allele
(Serological)
Patients
Controls
Odds Ratio†
Juvenile rheumatoid
arthritis
DR8
38
7
8
Celiac disease
DQ2
99
28
>250
Multiple sclerosis
DR2, DQ6
86
33
12
Type I diabetes
DQ8
81
23
14
Type I diabetes
DQ6
<1
33
0.02
Hemochromatosis
A3
75
13
20
25
0.2
80-150
CAH (21-hydroxylase B47
deficiency)

In other cases, the association between a particular
HLA allele or haplotype and a disease is not due
to functional differences in immune response
genes encoded by the HLA alleles.
 Instead, the association is due to a particular MHC
allele being present at a very high frequency on
chromosomes that also happen to contain diseasecausing mutations in another gene within the
MHC, because of linkage disequilibrium.
 As mentioned earlier, the autosomal recessive
disorders congenital adrenal hyperplasia due to
21-hydroxylase deficiency and primary
hemochromatosis result from mutations in genes
that lie within the MHC.


Analysis of 21-hydroxylase mutations responsible
for adrenal hyperplasia has revealed that certain
of the mutations at this locus originally occurred
on chromosomes with particular haplotypes and
were subsequently inherited through multiple
generations along with these specific haplotype
markers as a block.
Another example is hemochromatosis, a common
autosomal recessive disorder of iron overload.
More than 80% of patients with hemochromatosis
are homozygous for a common mutation,
Cys282Tyr, in the hemochromatosis gene (HFE)
and have HLA-A*0301 alleles at their HLA-A
locus. The association is not the result of HLAA*0301 somehow causing hemochromatosis.

HFE is involved with iron transport or metabolism
in the intestine; HLA-A, as a class I immune
response gene, has no effect on iron transport. The
association is due to proximity of the two loci and
the linkage disequilibrium between the Cys282Tyr
mutation in HFE and the A*0301 allele at HLA-A.

The functional basis of most HLA-disease
associations is unknown. HLA molecules are
integral to T-cell recognition of antigens.
 Perhaps different polymorphic alleles result in
structural variation in these cell surface molecules,
leading to differences in the capacity of the
proteins to interact with antigen and the T-cell
receptor in the initiation of an immune response,
thereby affecting such critical processes as
immunity against infections and self-tolerance to
prevent autoimmunity.
HLA and Tissue Transplantation

As the name major histocompatibility complex
implies, the HLA loci are the primary
determinants of transplant tolerance and graft
rejection and therefore play an important role in
transplantation medicine.
 Despite the impressive progress in the design of
powerful immunosuppressive drugs to suppress
rejection of organ transplants, only an absolutely
perfect match for all HLA and blood group alleles,
such as occurs between monozygotic twins, can
provide a 100% transplantation success rate
without immunosuppressive therapy.

For the transplantation of solid organs, such as
kidneys, the percentage of grafts surviving after 10
years when the recipient and the donor are HLAidentical siblings is 72% but falls to 56% when the
donor is a sibling who has only one HLA haplotype
in common with the recipient.
 Bone marrow transplantation is a greater challenge
than solid organ transplantation; not only can the
host reject the graft, but also the graft, which
contains immunocompetent lymphocytes, can attack
the host in what is known as graft-versus-host
disease (GVHD).

Survival to 8 years after BMT for patients with chronic
myelogenous leukemia following chemotherapy is
60% if graft and host mismatch at no more than one
class I or class II locus but falls to 25% when there are
both class I and class II mismatches. GVHD is also
less frequent and severe the better the class I match.
 Given the obvious improvement in the success of
BMT with the greater number of matches, and the
tremendous diversity of HLA haplotypes within a
population and between different ethnic groups,
millions of HLA-typed unrelated BM donors have
been registered in databases that can be searched to
look for the best possible match for a patient needing a
BMT.
GENOTYPES AND PHENOTYPES IN POPULATIONS
Genetic Variation in Populations

Population genetics is the quantitative study of
the distribution of genetic variation in populations
and of how the frequencies of genes and
genotypes are maintained or change.
 Population genetics is concerned both with genetic
factors, such as mutation and reproduction, and
with environmental and societal factors, such as
selection and migration, which together determine
the frequency and distribution of alleles and
genotypes in families and communities.

At present, human geneticists are using the principles
and methods of population genetics to address the
history and genetic structure of human populations, the
flow of genes between populations and between
generations, and, very importantly, the optimal
methods for identifying genetic susceptibilities to
common disease.
 In medical genetic practice, population genetics
provides the knowledge about different disease genes
that are common in different populations, information
that is needed for clinical diagnosis and genetic
counseling, including determining the allele
frequencies required for risk calculations.
Genetic Factors in Human Immunodeficiency
Virus Resistance

An important example of a common autosomal trait
governed by a single pair of alleles can be used to
illustrate the basic principles that determine allele
and genotype frequencies in populations.
 Consider the gene CCR5, which encodes a cell
surface cytokine receptor that serves as an entry
point for certain strains of the HIV that causes
AIDS.
 A 32-base pair deletion in this gene results in an
allele (ΔCCR5) that encodes a nonfunctional protein
due to a frameshift and premature termination.
Individuals homozygous for the ΔCCR5 allele do not
express the receptor on their cell surface and, as a
consequence, are resistant to HIV infection.
 Loss of function of CCR5 appears to be a benign trait,
and its only known phenotypic consequence is
resistance to HIV infection.
 The normal allele and the 32-base pair deletion allele,
ΔCCR5, are easily distinguished by PCR analysis of
the gene.
 A sampling of 788 individuals from Europe provides
absolute numbers of individuals who were
homozygous for either allele or heterozygous.

Table 9-6. Genotype Frequencies for Normal CCR5 Allele and the
Deletion ΔCCR5 Allele
Genotype
Number of People Observed
Relative
Genotype
Frequency
Allele
Derived Allele
Frequencies
CCR5/CCR5
647
0.821
CCR5/ΔCCR5
134
0.168
CCR 5
0.906
ΔCCR5/ΔCCR5
7
0.011
ΔCCR 5
0.094
Total
788
1.000

On the basis of the observed genotype frequencies,
we can directly determine the allele frequencies by
simply counting the alleles.
 When we refer to the population frequency of an
allele, we are considering a hypothetical gene pool
as a collection of all the alleles at a particular
locus for the entire population.
 For autosomal loci, the size of the gene pool at
one locus is twice the number of individuals in the
population because each autosomal genotype
consists of two alleles, that is, a ΔCCR5/ΔCCR5
individual has two ΔCCR5 alleles, and a
CCR5/ΔCCR5 individual has one of each. In this
example, then, the observed frequency of the
CCR5 allele is:

Similarly, one can calculate the frequency
of the ΔCCR5 allele as 0.094, either by
adding up the number of ΔCCR5 alleles
directly [(2 × 7) + (1 × 134) = 148 of a total
of 1576 alleles] or simply by subtracting the
frequency of the normal CCR5 allele, 0.906,
from 1, because the frequencies of the two
alleles must add up to 1.
The Hardy-Weinberg Law

As we have shown with the CCR5 cytokine
receptor gene example, we can use a sample of
individuals with known genotypes in a population
to derive estimates of the allele frequencies by
simply counting the alleles in individuals with
each genotype.
 How about the converse? Can we calculate the
proportion of the population with various
genotypes once we know the allele frequencies?
 Deriving genotype frequencies from allele
frequencies is not as straightforward as counting
because we actually do not know in advance how
the alleles are distributed among homozygotes and
heterozygotes.

If a population meets certain assumptions,
however, there is a simple mathematical
relationship known as the Hardy-Weinberg law for
calculating genotype frequencies from allele
frequencies.
 This law, the cornerstone of population genetics,
was named for Geoffrey Hardy, an English
mathematician, and Wilhelm Weinberg, a German
physician, who independently formulated it in
1908.
The Hardy-Weinberg Law
The Hardy-Weinberg law rests on these assumptions:
 The population is large and matings are random with
respect to the locus in question.
 Allele frequencies remain constant over time
because:
– There is no appreciable rate of mutation
– Individuals with all genotypes are equally capable of
mating and passing on their genes, that is, there is no
selection against any particular genotype.
– There has been no significant immigration of individuals
from a population with allele frequencies very different
from the endogenous population.
The Hardy-Weinberg law has two critical components.
(1) The first is that under certain ideal conditions, a
simple relationship exists between allele frequencies
and genotype frequencies in a population.
 Suppose p is the frequency of allele A and q is the
frequency of allele a in the gene pool and alleles
combine into genotypes randomly; that is, mating in
the population is completely at random with respect
to the genotypes at this locus.
 The chance that two A alleles will pair up to give the
AA genotype is p2; the chance that two a alleles will
come together to give the aa genotype is q2; and the
chance of having one A and one a pair, resulting in
the Aa genotype, is 2pq.

The Hardy-Weinberg law states that the
frequency of the three genotypes AA, Aa,
and aa is given by the terms of the binomial
expansion of (p + q)2 = p2 + 2pq + q2.
(2) A second component of the Hardy-Weinberg
law is that if allele frequencies do not change from
generation to generation, the relative proportion of
the genotypes will not change either; that is, the
population genotype frequencies from generation
to generation will remain constant, at equilibrium,
if the allele frequencies p and q remain constant.
 More specifically, when there is random mating in
a population that is at equilibrium and genotypes
AA, Aa, and aa are present in the proportions p2 :
2pq : q2, then genotype frequencies in the next
generation will remain in the same relative
proportions, p2 : 2pq : q2.

Proof of this equilibrium is shown in Table 9-7. It
is important to note that Hardy-Weinberg
equilibrium does not specify any particular values
for p and q; whatever allele frequencies happen to
be present in the population will result in genotype
frequencies of p2 : 2pq : q2, and these relative
genotype frequencies will remain constant from
generation to generation as long as the allele
frequencies remain constant and other conditions
are met.
Table 9-7. Frequencies of Mating Types and Offspring for a Population in HardyWeinberg Equilibrium with Parental Genotypes in the Proportion p2 : 2pq : q2
Types of
Matings
Offspring
Mother
Father
Frequency
AA
AA
AA
p2 × p2 = p4
(p4)
AA
Aa
p2 × 2pq =
2p3 q
1/2(2p3 q)
1/2(2p3 q)
Aa
AA
2pqxp2=2p3q
1/2(2p3 q)
1/2(2p3 q)
AA
aa
p2xq2=p2q2
p2q2
aa
AA
q2xp2=p2q2
p2q2
Aa
Aa
2pqx2pq=4p2
q2
Aa
aa
aa
aa
¼(4p2q2)
Aa
aa
½(4p2q2)
1/4(4p2q2)
2pqxq2=2pq3
1/2(2pq3)
1/2(2pq3)
Aa
q2x2pq=2pq3
1/2(2pq3)
1/2(2pq3)
aa
q2xq2=q4
(q4)

Applying the Hardy-Weinberg formula to the CCR5
example given earlier, with relative frequencies of the
two alleles in the gene pool of 0.906 (for the normal
allele CCR5) and 0.094 (for ΔCCR5), then the HardyWeinberg law states that the relative proportions of the
three combinations of alleles (genotypes) are p2 =
0.906 × 0.906 = 0.821, q2 = 0.094 × 0.094 = 0.009, and
2pq = (0.906 × 0.094) + (0.094 × 0.906) = 0.170.
 When these genotype frequencies are applied to a
population of 788 individuals, the derived numbers of
people with the three different genotypes (647 : 134 :
7) are, in fact, identical to the actual observed numbers
in Table 9-6. As long as the assumptions of the HardyWeinberg law are met in a population, we would
expect these genotype frequencies (0.821 : 0.170 :
0.009) to remain constant generation after generation in
that population.

As we have seen, Hardy-Weinberg distributions of
genotypes in populations are simply a binomial
distribution (p + q)n, where symbols p and q
represent the frequencies of two alternative alleles
at a locus (where p + q = 1), and n = 2,
representing the pair of alleles at any autosomal
locus or any X-linked locus in females.
 If a locus has three alleles, with frequencies p, q,
and r, the genotypic distribution can be
determined from (p + q + r)2.
 In general terms, the genotypic frequencies for any
known number of alleles an with allele
frequencies p1, p2, … pn can be derived from the
terms of the expansion of (p1 + p2 + … pn)2.
The Hardy-Weinberg Law in Autosomal
Recessive Disease

The major practical application of the HardyWeinberg law in medical genetics is in genetic
counseling for autosomal recessive disorders. For
a disease such as phenylketonuria, the frequency
of affected homozygotes in the population can be
determined accurately because the disease is
identified through newborn screening programs.
 Heterozygotes, however, are asymptomatic silent
carriers, and their population incidence is
impossible to measure directly from phenotype.
 The Hardy-Weinberg law allows an estimate of
heterozygote frequency to be made and used
subsequently for counseling.

E.g,, the frequency of PKU is approximately
1/4500 in Ireland. Affected individuals are
usually compound heterozygotes for different
mutant alleles rather than homozygotes for the
same mutant allele. In practice, however, we
usually lump all disease-causing alleles together
and treat them as a single allele, with frequency
q, even when there is significant allelic
heterogeneity in disease-causing alleles.

Then the frequency of affected individuals =
1/4500 = q2, q = 0.015, and 2pq = 0.029 or
approximately 3%. The carrier frequency in the
Irish population is therefore 3%, and there would
be an approximately 3% chance that a parent
known to be a carrier of PKU through the birth of
an affected child would find that a new mate of
Irish ethnicity would also be a carrier.
 If the new mate were from Finland, however,
where the frequency of PKU is much lower
(~1/200,000), his or her chance of being a carrier
would be only 0.6%.

Recall that for X-linked genes, there are only two
possible male genotypes but three female
genotypes. To illustrate gene frequencies and
genotype frequencies when the gene of interest is
X-linked, we use the trait known as red-green
color blindness, which is caused by mutations in
the series of red and green visual pigment genes
on the X chromosome.
 Color blindness is a good example because it is
not a deleterious trait (except for possible
difficulties with traffic lights), and color-blind
persons are not subject to selection. As discussed
later, allowing for the effect of selection
complicates estimates of gene frequencies.

cb for all the mutant color-blindness alleles and + for
the normal allele, with frequencies q and p,
respectively.
 The frequencies of the normal and mutant alleles can
be determined directly from the incidence of the
corresponding phenotypes in males by simply counting
the alleles.
 Because females have two X chromosomes, their
genotypes are distributed like autosomal genotypes,
but because color-blindness alleles are recessive, the
normal homozygotes and heterozygotes are not
distinguishable.
 The frequency of color blindness in females is much
lower than that in males, even though the allele
frequencies are, of course, the same in both sexes. Less
than 1% of females are color-blind, but nearly 15% are
carriers of a mutant color-blindness allele.
The Hardy-Weinberg Law in X-Linked Disease
Table 9-8. X-Linked Genes and Genotype Frequencies (Color Blindness)
Sex
Genotype
Phenotype
Incidence (Approximate)
Male
X+
Normal color vision
p = 0.92
Xcb
Color blind
q = 0.08
X+/X+
Normal (homozygote)
p2 = (0.92)2 = 0.8464
X+/Xcb
Normal (heterozygote)
2pq = 2(0.92)(0.08) = 0.1472
Normal (total)
p2 + 2pq = 0.9936
Color blind
q2 = (0.08)2 = 0.0064
Female
Xcb/Xcb