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 Over
the past decade, investigators have isolated many genes in which mutations
have been shown to be responsible for specific disorders. Genetic linkage
studies, often among the first steps in these efforts, provide a powerful
approach to help elucidate the underlying genetic mechanisms for inherited
disorders. However, the application of genetic linkage studies to more
complex psychiatric disorders has been less than satisfactory. The purpose
of this column is to provide a brief overview of linkage methodology and
to discuss some of the possible reasons why most initial linkage studies
of complex disorders have not been successful.
Genetic
linkage is designed to estimate the distance between genes. Normally,
immediately before the gametes (sperm or eggs) are produced, there is
a lining up of parental chromosomes in preparation for the separation
of genetic material into gametes. An exchange of genetic material occurs
between parental chromosomal pairs, which is termed recombination, or
crossing over between chromosomes. The chromosomes are then separated
and packaged into the gametes.
Two genes that lie on separate chromosomes will be transmitted independently
of each other from parent to child. The child has an equal chance of receiving
the gene from his mother or from his father. This phenomenon is encapsulated
in Mendel’s law of independent assortment.
What
happens when the 2 genes are on the same chromosome? If they are located
at opposite ends, then they will once again be transmitted independently
of each other. This is because they are so far away from each other that
a recombination event is very likely to occur between the 2 loci. However,
the closer the 2 genes lie to each other, the less likely it is that a
genetic crossover will occur between them. Finally, 2 genes may lie so
close that it is much more likely that they will remain together and be
transmitted together into the forming gamete. This is the violation of
Mendel’s law of independent assortment. Two examples should make
this clearer.
If
an individual has genotype A1A2 at locus A and genotype B1B2 at locus
B and the loci are not linked to each other, the alleles at locus A and
locus B will assort independently and 4 different types of gametes (A1B1,
A1B2, A2B1, A2B2) will be produced in equal frequencies. This is termed
independent assortment.
If
locus A is very close to locus B on the same chromosome, an individual
will again produce 4 types of gametes, but now the alleles found will
not be in equal frequencies. The most common types of gametes will be
those that represent the alleles that occurred in each parent. The less
frequent types of gametes will contain a mixture of the parental alleles
that has occurred as a result of infrequent recombination events between
the 2 loci.
Historically,
2 approaches to linkage analyses were developed: (1) the allele sharing
method and (2) the family pedigree method. Each of these methods has been
extended over the past 2 decades and now includes methods that examine
cosegregation of marker alleles and disease as well as allele sharing
between 2 affected individuals that are either sibs or some other relative
pair. The allele sharing method is a model-free procedure and does not
require any assumptions about the nature of transmission involved in the
disease. The family pedigree method examines cosegregation of marker alleles
and disease, and it requires that the mode of inheritance of the trait
under study be specified. The first approach is generally referred to
as a nonparametric method and the second as a parametric one.
Because
the mode of inheritance of any psychiatric disorder is not well understood,
the allele sharing approach would seem to be the method of choice. However,
allele sharing analyses are generally statistically less powerful than
family pedigree analyses and until recently have not been used extensively
in genetic linkage studies. It has become evident that the allele sharing
approach can provide important preliminary evidence for linkage that can
form the basis for more powerful techniques.
Early
linkage studies in human genetics involved inherited disorders with known
patterns of inheritance. The disease in question was clearly passed in
an autosomal dominant or an autosomal recessive fashion, for example.
The family pedigree approach became the more widely used analytic method
to test for linkage between the disorder and a marker locus. That is,
researchers asked whether the 2 genes traveled together within the pedigree
or sorted independently. If they sorted independently, the research team
moved on to the next DNA marker and repeated the analysis. Eventually
they hoped to find a marker that was so close to the gene that caused
the disorder that they no longer sorted independently, but were rather
found together in affected members of the pedigree. All that was needed
were markers evenly scattered throughout the chromosomes, and these are
now available.
The
family pedigree approach became even more widely used after the development
of a computer program (LIPED) that facilitated the analysis of data from
large families. The applicability of this approach to complex disorders
was enhanced when LIPED was modified to allow for the incorporation of
age- and sex-specific variables. The use of this approach has had limited
success, however, in the localization of genes for complex psychiatric
disorders. (Fig. 1)
The
family pedigree parametric method involves the comparisons of likelihoods
for specific genetic linkage hypotheses. First, the likelihood of observing
a specific pattern of transmission in a pedigree is calculated assuming
the null hypothesis of no genetic linkage to be true. That is, the likelihood
of observing the distribution of the disease and a set of marker genotypes
is calculated assuming independent assortment of the disease and marker
alleles. Next, the likelihood of observing the pattern of disease and
marker alleles for each of several alternative hypotheses of linkage is
calculated and compared with the likelihood of the null hypothesis by
means of an “odds ratio.” The odds ratio consists of the likelihood
of an alternative hypothesis divided by the likelihood of the null hypothesis.
An odds ratio greater than 1,000 to 1 is taken as evidence for linkage,
whereas an odds ratio of less than 1 in 100 is taken as evidence against
linkage. For ease of comparison, the base 10 logarithm of the odds ratio
is reported. In linkage analyses, these so-called “lod” scores
(log10 [odds ratio]) are calculated for various hypotheses of linkage.
The
alternative hypotheses of linkage are specified by different values of
the recombination fraction. That is, the alternative hypotheses propose
that (1) linkage is so close that no recombinations have occurred (i.e.,
q = 0.0); (2) linkage is tight, but a one-recombination event has occurred
in 100 meioses (q = 0.01); (3) linkage is quite close, but relatively
more recombinations have occurred (q = 0.05); and so on for as many increments
of q as the investigator specifies. The null hypothesis specifies that
q = 0.50. A lod score greater than 3.0 (log10 [1,000/1]) is taken as evidence
for linkage, and a lod score of less than –2.0 (log10 [1/100]) is
taken as evidence against linkage.
The
replicated demonstration of genetic linkage constitutes proof that a gene
that confers susceptibility to some illness exists. Thus, this approach
has the potential to be extremely powerful in the search for genetic factors
important for the expression of psychiatric illness.
However,
there are limitations to the parametric approach. All of the calculations
of likelihoods assume that the underlying genetic mechanisms for the illnesses
being studied are known. The calculation of the lod scores for these families
requires that the genetic model be specified. For psychiatric disorders,
the underlying genetic mechanisms are not known. Furthermore, in those
cases in which the patterns of transmission within families are consistent
with a single gene, the estimate of penetrance is always less than 1.0.
The ability to estimate correctly and thus detect linkage decreases dramatically
when there is reduced penetrance. If penetrance is reduced from 1.0
to 0.8, 20% of the individuals with the susceptibility
genotype will not manifest the disease. Because these individuals carry
the genetic susceptibility (although they do not manifest the disorder),
they will have the genetic marker associated with the illness.
Because
the individuals are unaffected (and it is not possible to know what their
disease genotype is), it is not possible to know whether they have the
susceptibility genotype or whether there has been a crossover between
the susceptibility locus and the marker locus. It follows, then, that
when there is reduced penetrance, it becomes more difficult to estimate
accurately the strength of linkage. Likewise, the misspecification of
other parameters of the genetic model for the disease results in inaccurate
estimates of the strength of the linkage relationship. Changes in gene
frequency, penetrance estimates, and diagnostic criteria can significantly
affect the results of linkage analyses. Alternative nonparametric analytic
strategies have been and are being developed and will be discussed in
the subsequent column.
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