Human Gene Mapping

1

• Human Gene Mapping
• Disease Gene Identification

2
Overview

• This chapter provides an overview of how
  geneticists use the familial nature of disease to
  identify the responsible genes and gene variants.
  
• Whether a disease is inherited in a recognizable
  mendelian pattern or just occurs at a higher
  frequency in relatives of affected individuals,
  the genetic contribution to disease must result
  from genotypic differences among family members
  that either cause disease outright or increase or
  decrease disease susceptibility.

3

• The Human Genome Project, has provided
  geneticists with a complete list of all human
  genes, knowledge of their location and structure,
  and a catalogue of some of the millions of
  variants in DNA sequence found among individuals
  in different populations.
• Some of these variants are common, others are
  rare, and still others differ in frequency among
  different ethnic groups.
• Whereas some variants clearly have functional
  consequences, others are certainly neutral. For
  most, their significance for human health and
  disease is unknown.

4

• In this chapter we discuss how meiosis, acting
  over both time and space, determines the
  relationships b/w genes and polymorphic loci with
  their neighbors
• Two fundamental approaches to disease gene
  identification
• linkage analysis, is family-based. Linkage
  analysis takes explicit advantage of family
  pedigrees to follow the inheritance of a disease
  over a few generations by looking for consistent,
  repeated inheritance of a particular region of
  the genome whenever disease is passed on in a
  family.

5

• Association analysis, is population-based.
  Association analysis does not depend explicitly
  on pedigrees but instead looks for increased or
  decreased frequency of a particular allele or set
  of alleles in a sample of affected individuals
  taken from the population, compared with a
  control set of unaffected people.

6
How Does Gene Mapping Contribute to Medical
Genetics?

• Disease gene mapping has immediate clinical
  application by providing information about a
  gene's location that can be used to develop
  indirect linkage methods for use in prenatal
  diagnosis, pre-symptomatic diagnosis, and carrier
  testing
• Disease gene mapping is a critical first step in
  identifying a disease gene. Mapping the gene
  focuses attention on a limited region of the
  genome in which to carry out a systematic
  analysis of all the genes so we can find the
  mutations or variants that contribute to the
  disease (known as positional cloning).

7

• Positional cloning of a disease gene provides an
  opportunity to characterize the disorder as to
  the extent of
• locus heterogeneity,
• the spectrum of allelic heterogeneity,
• the frequency of various disease-causing or
  predisposing variants in various populations,
• the penetrance and positive predictive value of
  mutations,
• the fraction of the total genetic contribution to
  a disease attributable to the variant at any one
  locus, and
• the natural history of the disease in
  asymptomatic at-risk individuals.

8

• Characterization of a gene and the mutations in
  it furthers our understanding of
• disease pathogenesis
• development of specific and sensitive diagnosis
  by direct detection of mutations,
  population-based carrier screening to identify
  individuals at risk for disease in themselves or
  their offspring,
• development of cell and animal models,
• drug therapy to prevent or ameliorate disease or
  to slow its progression, and
• treatment by gene replacement

9
Independent Assortment and Homologous
Recombination in Meiosis
The effect of recombination on the origin of
various portions of a chromosome. Because of
crossing over in meiosis, the copy of the
chromosome the boy (generation III) inherited
from his mother is a mosaic of segments of all
four of his grandparents' copies of that
chromosome.
10

• Since homologous chromosomes look identical under
  the microscope, we must be able to differentiate
  them in order to trace the grandparental origin
  of each segment, and to determine if and where
  recombination has occurred.
• Genetic marker any characteristic located at the
  same position on a pair of homologous chromosomes
  and allows distinguishing them.
• Millions of genetic markers are now available
  that can be genotyped by PCR.

11
Alleles at Loci on Different Chromosomes Assort
Independently
Independent assortment of alleles at two loci, 1
and 2, when they are located on different
chromosomes. Assume that alleles D and M were
inherited from one parent, d and m from the
other Half (50) of gametes will be parental (DM
or dm) and half (50) will be non-parental (dM or
Dm).
12

• Assume D and M are paternally derived and d and m
  are maternally derived.
• Gametes containing DM or dm are non-recombinant
• Alleles at Loci on the Same Chromosome Assort
  Independently if at Least One Crossover Occurs
  Between Them in Every Meiosis

Note Genes that reside on the same chromosome
are said to be syntenic
13
recombinant chromosome
If crossing over occurs at least once in the
segment between the loci, the resulting
chromatids may be either nonrecombinant or Dm and
dM, which are not the same as the parental
chromosomes such a nonparental chromosome is
therefore a recombinant chromosome
14

• The ratio of recombinant to nonrecombinant
  genotypes will be, on average, 1 1, just as if
  the loci were on separate chromosomes and
  assorting independently

15
Recombination Frequency and Map Distance

• Crossing over between homologous chromosomes in
  meiosis is shown in the quadrivalents on the
  left. Crossovers result in new combinations of
  maternally and paternally derived alleles on the
  recombinant chromosomes present in gametes.
• If no crossing over occurs in the interval
  between loci 1 and 2, only parental
  (nonrecombinant) allele combinations, DM and dm,
  occur in the offspring.
• If one or two crossovers occur in the interval
  between the loci, half the gametes will contain a
  nonrecombinant and half the recombinant
  combination. The same is true if more than two
  crossovers occur between the loci.

16
The smaller the recombination frequency, the
closer together two loci are.
17

• A common notion for recombination frequency is ?,
  where ? varies from 0 (no recombination at all)
  to 0.5 (independent assortment).

18

• Detecting the recombination events between loci
  requires that (1) a parent be heterozygous
  (informative) at both loci and (2) we know which
  allele at locus 1 is on the same chromosome as
  which allele at locus 2.
• Alleles on the same homologue are in coupling (or
  cis), whereas alleles on the different homologues
  are in repulsion (or trans).

19
Effect of Heterozygosity and Phase on Detecting
Recombination Events
Possible phases of alleles M and m at a marker
locus with alleles D and d at a disease locus
20

• Co-inheritance of the gene for an autosomal
  dominant form of retinitis pigmentosa, RP9, with
  marker locus 2 and not with marker locus 1.
• Only the mother's contribution to the children's
  genotypes is shown. The mother (I-1) is affected
  with this dominant disease and is heterozygous at
  the RP9 locus (Dd) as well as at loci 1 and 2.
  She carries the A and B alleles on the same
  chromosome as the mutant RP9 allele (D). The
  unaffected father is homozygous normal (dd) at
  the RP9 locus as well as at the two marker loci
  (AA and BB) his contributions to his offspring
  are not considered further.

21

• All three affected offspring have inherited the B
  allele at locus 2 from their mother, whereas the
  three unaffected offspring have inherited the b
  allele. Thus, all six offspring are
  nonrecombinant for RP9 and marker locus 2.
• However, individuals II-1, II-3, and II-5 are
  recombinant for RP9 and marker locus 1,
  indicating that meiotic crossover has occurred
  between these two loci.

22

• Determine the phase in the II.1.
• How many recombinants/Non-recombinants

23

• Phase known/unknown

24

• Detecting the recombination events between loci
  requires informative parent and knowing the phase
  

25
Linkage and Recombination Frequency

• Linkage is the term used to describe a departure
  from the independent assortment of two loci, or,
  in other words, the tendency for alleles at loci
  that are close together on the same chromosome to
  be transmitted together, as an intact unit,
  through meiosis.
• Analysis of linkage depends on determining the
  frequency of recombination as a measure of how
  close different loci are to each other on a
  chromosome. If two loci are so close together
  that ? 0 between them, they are said to be
  tightly linked if they are so far apart that ?
  0.5, they are assorting independently and are
  unlinked.

26

• Suppose that among the offspring of informative
  meioses (i.e., those in which a parent is
  heterozygous at both loci), 80 of the offspring
  are non-recombinant and 20 are recombinant. At
  first glance, the recombination frequency is
  therefore 20 (? 0.2). the accuracy of this
  measure of depends on the size of the family used
  to make the measurement.

27

• The map distance between two loci is a
  theoretical concept that is based on real data,
  the extent of observed recombination, ?, between
  the loci.
• Map distance is measured in units called
  centimorgans (cM), defined as the genetic length
  over which, on average, one crossover occurs in
  1 of meioses.
• Therefore, a recombination fraction of 1 ( ?
  0.01) translates approximately into a map
  distance of 1 cM
• As the map distance between two loci increases,
  however, the frequency of recombination we
  observe between them does not increase
  proportionately (Fig. 10-7). This is because as
  the distance between two loci increases, the
  chance that the chromosome carrying these two
  markers could undergo more than one crossing over
  event between these loci also increases.
• As a rule of thumb, recombination frequency
  begins to underestimate true genetic distance
  significantly once rises above 0.1.

28

• The relationship between map distance in
  centimorgans and recombination fraction,?.
  Recombination fraction (solid line) and map
  distance (dotted line) are nearly equal, with 1
  cM 0.01 recombination, for values of genetic
  distance below 10 cM, but they begin to diverge
  because of double crossovers as the distance
  between the markers increases. The recombination
  fraction approaches a maximum of 0.5 no matter
  how far apart loci are the genetic distance
  increases proportionally to the distance between
  loci.

29
Genetic maps and physical maps

• To measure true genetic map distance between two
  widely spaced loci accurately, therefore, one has
  to use markers spaced at short genetic distances
  in the interval between these two loci and add up
  the values of ? between the intervening markers.
  (Fig. 10-8).
• For example, human chromosome 1 is the largest
  human chromosome in physical length (283 Mb) and
  also has the greatest genetic length, 270 cM
  (0.95 cM/Mb) the q arm of the smallest
  chromosome, number 21, is 30 Mb in physical
  length and 62 cM in genetic length (2.1 cM/Mb).
• Overall, the human genome, which is estimated to
  contain about 3200 Mb, has a genetic length of
  3615 cM, for an average of 1.13 cM/Mb.
• Furthermore, the ratio of genetic distance to
  physical length is not uniform along a chromosome
  as one looks with finer and finer resolution at
  recombination versus physical length.

30
A diagram showing how adding together short
genetic distances, measured as recombination
fraction,? , between neighboring loci A, B, C,
and so on allows accurate determination of
genetic distance between the two loci A and H
located far apart. The value of between A and H
is not an accurate measure of genetic distance.
31
Sex Differences in Map Distances

• Just as male and female gametogenesis shows sex
  differences in the types of mutations and their
  frequencies, there are also significant
  differences in recombination between males and
  females.
• Across all chromosomes, the genetic length in
  females, 4460 cM, is 72 greater than the genetic
  distance of 2590 cM in males, and it is
  consistently about 70 greater in females on each
  of the different autosomes.
• The reason for increased recombination in females
  compared with males is unknown, although one
  might speculate that it has to do with the many
  years that female gamete precursors remain in
  meiosis I before ovulation.

32
Linkage Equilibrium and Disequilibrium

• When a disease allele first enters the population
  (by mutation or a founder), the particular set of
  alleles at markers linked to the disease locus
  constitutes a disease-containing haplotype
• The degree to which this haplotype will persist
  as such over time depends on probability of
  recombination

33

• The speed with which recombination will move
  disease allele onto a new haplotype is the
  product of two main factors
• The number of generations, and therefore the
  number of opportunities for recombination
• The frequency of recombination between the loci
• A third factor, selection for or against a
  particular haplotype, but its effect has been
  difficult to prove in humans

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35

• The shorter the time since the disease allele
  appeared and the smaller the value of ?, the
  greater is the chance that the disease-containing
  haplotype will persist intact.
• With longer time periods and greater values of ?,
  shuffling will go to completion and the allele
  frequencies for marker alleles in the haplotype
  that includes the disease allele will come to
  equal the frequencies of these marker alleles in
  all chromosomes in the population i.e., alleles
  in the haplotype will have reached equilibrium.

36
The Haplotype Map (HapMap)

• One of the biggest human genomics efforts to
  follow completion of the sequencing is a project
  designed to create a haplotype map (HapMap) of
  the genome. The goal of the HapMap project is to
  make LD measurements between a dense collection
  of millions of single nucleotide polymorphisms
  (SNPs) throughout the genome to delineate the
  genetic landscape of the genome on a fine scale.
• To accomplish this goal, geneticists collected
  and characterized millions of SNP loci, developed
  methods to genotype them rapidly and
  inexpensively, and used them, one pair at a time,
  to measure LD between neighboring markers
  throughout the genome.
• The measurements were made in samples that
  included both unrelated population samples and
  samples containing one child and both parents,
  obtained from four geographically distinct
  groups a primarily European population, a West
  African population, a Han Chinese population, and
  a population from Japan

37

• The study showed that
• 1) More than 90 of all SNPs are shared among
  such geographocally disparate populations, with
  allele frequencies that are quite similar in the
  different populations
• This finding indicates that most SNPs are old and
  predate the waves of emigration out of East
  Africa that populated the rest of the world
• Differences in allele frequencies in a small
  fraction of SNPs may be the result of either
  genetic drift/founder effect or selection in
  localized geographical regions after migration
  out of Africa.

38

• Such SNPs, termed ancestry informative markers,
  are used in studies of human origin, migration
  and gene flow.
• In forensic investigations, to determine the
  likely ethnic background when the only available
  evidence is DNA

39

• 2) When pairwise measurements of LD were made for
  neighboring SNPs across the genome, contiguous
  SNPs can be grouped into clusters of varying size
  in which SNPs in any one cluster shows high
  levels of LD with each other.
• These clusters of SNPs in high LD, located across
  segments of a few kb to a few dozen Kb are termed
  LD blocks.
• The sizes of LD blocks are not identical in all
  populations. African populations have smaller
  blocks as compared to other populations.

40
A 145-kb region of chromosome 4 containing 14
SNPs. In cluster 1, containing SNPs 1 through 9,
five of the 29 512 theoretically possible
haplotypes are responsible for 98 of all the
haplotypes in the population, reflecting
substantial linkage disequilibrium among these
SNP loci. Similarly, in cluster 2, only three of
the 24 16 theoretically possible haplotypes
involving SNPs 11 to 14 represent 99 of all the
haplotypes found. In contrast, alleles at SNP 10
are found in linkage equilibrium with the SNPs in
cluster 1 and cluster 2.
41

• 3) Pairwise measurements of recombination between
  closely neighboring SNPs revealed that the ratio
  of map distance to base pairs was not constant
  (1 cM/Mb). Instead ranged from far below 0.01
  cM/Mb to more than 60 cM/Mb.
• - This indicates that rate of recombination
  between polymorphic markers which was thought to
  be uniform is, in fact, the result of an
  averaging of hotspots of recombination
  interspersed among regions of little or no
  recombination.

42
B, A schematic diagram in which each box contains
the pairwise measurement of the degree of linkage
disequilibrium between two SNPs (e.g., the arrow
points to the box, outlined in black, containing
the value of D' for SNPs 2 and 7). The higher the
degree of LD, the darker the color in the box,
with maximum D' values of 1.0 occurring when
there is complete LD. Two LD blocks are
detectable, the first containing SNPs 1 through
9, and the second SNPs 11 through 14. In the
first block, pairwise measurements of D' reveal
LD. A similar level of LD is found in block 2.
Between blocks, the 14-kb region containing SNP
10 shows no LD with neighboring SNPs 9 or 11 or
with any of the other SNP loci. Below is a graph
of the ratio of map distance to physical distance
(cM/Mb) showing that a recombination hotspot is
present in the region around SNP 10 between the
two blocks, with values of recombination that are
50- to 60-fold above the average of approximately
1.13 cM/Mb for the genome.
43
MAPPING HUMAN GENES BY LINKAGE ANALYSIS
Determining Whether Two Loci Are Linked

• Linkage analysis is a method of mapping genes
  that uses family studies to determine whether two
  genes show linkage (are linked) when passed on
  from one generation to the next.
• To decide whether two loci are linked, and if
  so, how close or far apart they are, we rely on
  two pieces of information.
• First, we ascertain whether the recombination
  fraction between two loci deviates significantly
  from 0.5
• Second, if ? is less than 0.5, we need to make
  the best estimate we can of ? since that will
  tell us how close or far apart the linked loci
  are.

44

• For these determinations, a statistical tool
  called the likelihood ratio is used.
• Likelihoods are probability values odds are
  ratios of likelihoods.
• One proceeds as follows
• examine a set of actual family data, count the
  number of children who show or do not show
  recombination between the loci,
• calculate the likelihood of observing the data at
  various possible values of ? between 0 and 0.5.
• Calculate a second likelihood based on the null
  hypothesis that the two loci are unlinked, that
  is, ? 0.50.
• take the ratio of the likelihood of observing the
  family data for various values of ? to the
  likelihood the loci are unlinked to create an
  odds ratio.

45
The computed odds ratios for different values of
are usually expressed as the log10 of this ratio
and are called a LOD score (Z) for "logarithm of
the odds."
46

• Model-Based Linkage Analysis of Mendelian
  Diseases
• Linkage analysis is called model-based (or
  parametric) when it assumes that there is a
  particular mode of inheritance (autosomal
  dominant, autosomal recessive, or X-linked) that
  explains the inheritance pattern.
• LOD score analysis allows mapping of genes in
  which mutations cause diseases that follow
  mendelian inheritance.
• The LOD score gives both a best estimate of the
  recombination frequency, ?max, between a marker
  locus and the disease locus and

47

• an assessment of how strong the evidence is for
  linkage at that value of ?max. Values of the LOD
  score above 3 are considered strong evidence.
• Linkage at a particular ? max of a disease gene
  locus to a marker with known physical location
  implies that the disease gene locus must be near
  the marker

48

• The odds ratio is important in two ways.
• First, it provides a statistically valid method
  for using the family data to estimate the
  recombination frequency between the loci.
• If ? max differs from 0.50, you have evidence of
  linkage. However, even if ? max is the best
  estimate you can make, how good an estimate is
  it? The odds ratio also provides you with an
  answer to this question because the higher the
  value of Z, the better an estimate ?max is.
• Positive values of Z (odds gt1) at a given ?
  suggest that the two loci are linked, whereas
  negative values (odds lt1) suggest that linkage is
  less likely than the possibility that the two
  loci are unlinked. By convention, a combined LOD
  score of 3 or greater (equivalent to greater
  than 10001 odds in favor of linkage) is
  considered definitive evidence that two loci are
  linked.

49

• Mapping genes by linkage analysis provides an
  opportunity to localize medically relevant genes
  by following inheritance of the condition and the
  inheritance of alleles at polymorphic markers to
  see if the disease locus and the polymorphic
  marker locus are linked.
• Return to the family shown in Figure 10-6. The
  mother has an autosomal dominant form of
  retinitis pigmentosa. She is also heterozygous
  for two loci on chromosome 7, one at 7p14 and one
  at the distal end of the long arm.
• One can see that transmission of the RP mutant
  allele (D) invariably "follows" that of allele B
  at marker locus 2 from the first generation to
  the second generation in this family.
• All three offspring with the disease (who
  therefore must have inherited their mother's
  mutant allele D at the RP locus) also inherited
  the B allele at marker locus 2. All the offspring
  who inherited their mother's normal allele, d,
  inherited the b allele and will not develop RP.
  The gene encoding RP, however, shows no tendency
  to follow the allele at marker locus 1.

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51

• Suppose we let ? be the "true" recombination
  fraction between RP and locus 2, the fraction we
  would see if we had unlimited numbers of
  offspring to test.
• Because either a recombination occurs or it does
  not, the probability of a recombination, ?, and
  the probability of no recombination must add up
  to 1. Therefore, the probability that no
  recombination will occur is 1 -? .
• There are only six offspring, all of whom show
  no recombination. Because each meiosis is an
  independent event, one multiplies the probability
  of a recombination, ?, or of no recombination, (1
  -? ), for each child.
• The likelihood of seeing zero offspring with a
  recombination and six offspring with no
  recombination between RP and marker locus 2 is
  therefore (?)0(1 -? )6. The LOD score between RP
  and marker 2, then, is

The maximum value of Z is 1.81, which occurs when
0, and is suggestive of but not definite
evidence for linkage because Z is positive but
less than 3.
52
Combining LOD Score Information Across Families

• In the same way that each meiosis in a family
  that produces a nonrecombinant or recombinant
  offspring is an independent event, so too are the
  meioses that occur in other families.
• We can therefore multiply the likelihoods in the
  numerators and denominators of each family's
  likelihood odds ratio together.
• An equivalent but more convenient calculation is
  to add the log10 of each likelihood ratio,
  calculated at the various values of ?, to form an
  overall Z score for all families combined.

53

• In the case of RP in Figure 10-6, suppose two
  other families were studied and one showed no
  recombination between locus 2 and RP in four
  children and the third showed no recombination in
  five children. The individual LOD scores can be
  generated for each family and added together
  (Table 10-1). In this case, one could say that
  the RP gene in this group of families is linked
  to locus 2. Because the chromosomal location of
  polymorphic locus 2 was known to be at 7p14, the
  RP in this family can be mapped to the region
  around 7p14, which is near RP9, an already
  identified locus for one form of autosomal
  dominant RP.

54

• Table 10-1. LOD Score Table for Three Families
  with Retinitis Pigmentosa

?0.4 ?0.3 ?0.2 ?0.1 ?0.05 ?0.01 ?0
0.48 0.88 1.22 1.53 1.67 1.78 1.8 Family 1
0.32 0.58 0.82 1.02 1.11 1.19 1.2 Family 2
0.39 0.73 1.02 1.28 1.39 1.48 1.5 Family 3
1.19 2.19 3.06 2.83 4.17 4.45 4.5 Total
Zmax 4.5 at ? max 0
55

• If, however, some of the families being used for
  the study have RP due to mutations at another
  locus, the LOD scores between families will
  diverge, with some showing a trend to being
  positive at small values of ? and others showing
  strongly negative LOD scores at these values. One
  can still add the Z scores together, but the
  result will show a sharp decline in the overall
  LOD score. Thus, in linkage analysis involving
  more than one family, unsuspected locus
  heterogeneity can obscure what may be real
  evidence for linkage in a subset of families.

56

• Phase information is important in linkage
  analysis. Figure 10-14 shows two pedigrees of
  autosomal dominant neurofibromatosis, type 1
  (NF1).
• In the three-generation family on the left, the
  affected mother, II-2, is heterozygous at both
  the NF1 locus (D/d) and a marker locus (M/m), but
  we have no genotype information on her parents.
  Her unaffected husband, II-1, is homozygous both
  for the normal allele d at the NF1 locus and
  happens to be homozygous for allele M at the
  marker locus. He can only transmit to his
  offspring a chromosome that has the normal allele
  (d) and the M allele.

57

• By inspection, then, we can infer which alleles
  in each child have come from the mother. The two
  affected children received the m alleles along
  with the D disease allele, and the one unaffected
  has received the M allele along with the normal d
  allele. Without knowing the phase of these
  alleles in the mother, either all three offspring
  are recombinants or all three are
  nonrecombinants.

58
Figure 10-14 Two pedigrees of autosomal dominant
neurofibromatosis, type 1 (NF1). A, Phase of the
disease allele D and marker alleles M and m in
individual II-2 is unknown. B, Availability of
genotype information for generation I allows a
determination that the disease allele D and
marker allele M are in coupling in individual
II-2. NR, nonrecombinant R, recombinant.
59

• Which of these two possibilities is correct?
  There is no way to know for certain, and thus we
  must compare the likelihoods of the two possible
  results.
• Given that II-2 is an M/m heterozygote, we
  assume the correct phase on her two chromosomes
  is D-m and d-M half of the time and D-M and d-m
  the other half.
• If the phase of the disease allele is D-m, all
  three children have inherited a chromosome in
  which no recombination occurred between NF1 and
  the marker locus. If the probability of
  recombination between NF1 and the marker is ?,
  the probability of no recombination is (1 - ?),
  and the likelihood of having zero recombinant and
  three nonrecombinant chromosomes is ?0 (1-?)3.

60

• The contribution to the total likelihood,
  assuming this phase is correct half the time, is
  1/2 ?0 (1-?)3.The other half of the time,
  however, the correct phase is D-M and d-m, which
  makes each of these three children recombinants
  the likelihood, assuming this phase is correct
  half the time, is 1/2 ?3(1-?)0.
• To calculate the overall likelihood of this
  pedigree, we add the likelihood calculated
  assuming one phase in the mother is correct to
  the likelihood calculated assuming the other
  phase is correct. Therefore, the overall
  likelihood 1/2(1-?)3 1/2 (?3)/1/8

61

• By evaluating the relative odds for values of ?
  from 0 to 0.5, the maximum value of the LOD
  score, Zmax, is found to be log(4) 0.602 (when
  ? 0.0) Table 10-2. Because this is far short of
  a LOD score greater than 3, we would need at
  least five equivalent families to establish
  linkage (at ? 0.0) between this marker locus
  and NF1.
• With slightly more complex calculations (made
  much easier by computer programs written to
  facilitate linkage analysis), one can calculate
  the LOD scores for other values of ? (see Table
  10-2).

62

• Why are the two phases in individual II-2 in the
  pedigree shown in Figure 10-14A equally likely?
• First, unless the marker locus and NF1 are so
  close together as to produce linkage
  disequilibrium between alleles at these loci, we
  would expect them to be in linkage equilibrium.
• Second, new mutations represent a substantial
  fraction of all the alleles in an autosomal
  dominant disease with reduced fitness, such as
  NF1. If new mutations are occurring independently
  and repeatedly, the alleles that happened to be
  present at the neighboring linked loci when each
  mutation occurred in the NF1 gene will then be
  the alleles in coupling with the new disease
  mutation. A group of unrelated families are
  likely to have many different mutant alleles,
  each of which is as likely to be in coupling with
  one polymorphic marker allele at a linked locus
  as with any other.

63

• Suppose now that additional genotype information,
  shown in Figure 10-14B, becomes available in the
  family in Figure 10-14A. By inspection, it is now
  clear that the maternal grandfather, I-1, must
  have transmitted both the NF1 allele (D) and the
  M allele to his daughter.
• This finding does not require any assumption
  about whether a crossover occurred in the
  grandfather's germline all that matters is that
  we can be sure the paternally derived chromosome
  in individual II-2 must have been D-M and the
  maternally derived chromosome was d-m.

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• The availability of genotypes in the first
  generation makes this a phase-known pedigree.
• The three children can now be scored definitively
  as nonrecombinant and we do not have to consider
  the opposite phase.
• The probability of having three children with the
  observed genotypes is now (1 -? )3. As in the
  previous phase-unknown pedigree, the probability
  of the observed data if there is no linkage
  between the loci is (1/2)3 1/8.
• Overall, the relative odds for this pedigree are
  (1 - ?)3 1/8 in favor of linkage, and the
  maximum LOD score Z at ? 0.0 is 0.903 or 8 to 1
  (see Table 10-2).
• Thus, the strength of the evidence supporting
  linkage (8 to 1) is twice as great in the
  phase-known situation as in the phase-unknown
  situation (4 to 1).

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Determining Phase from Pedigrees

• As shown in the pedigree in Figure 10-14B, having
  grandparental genotypes may be helpful in
  establishing phase in the next generation.
• However, depending on what the genotypes are,
  phase may not always be definitively determined.
  For example, if the grandmother, I-2, had been an
  M/m heterozygote, it would not be possible to
  determine the phase in the affected parent,
  individual II-2.

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Determining Phase from Pedigrees

• For linkage analysis in X-linked pedigrees, the
  mother's father's genotype is particularly
  important because, as illustrated in Figure
  10-15, it provides direct information on linkage
  phase in the mother.
• Because there can be no recombination between
  X-linked genes in a male and because the mother
  always receives her father's only X, any X-linked
  marker present in her genotype, but not in her
  father's, must have been inherited from her
  mother.
• Knowledge of phase, so important for genetic
  counseling, can thus be readily ascertained from
  the appropriate male members of an X-linked
  pedigree, if they are available for study.

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Pedigree of X-linked hemophilia.
The affected grandfather in the first generation
has the disease (mutant allele h) and is
hemizygous for allele M at an X-linked locus. No
matter how far apart the marker locus and the
factor VIII gene are on the X, there is no
recombination involving the X-linked portion of
the X chromosome in a male, and he will pass the
hemophilia mutation h and allele M together. The
phase in his daughter must be that h and M are in
coupling
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MAPPING OF COMPLEX TRAITS

• Two major approaches to locate and identify genes
  that predispose to complex disease or contribute
  to genetic variance of quantitative traits
• Affected pedigree member method if a region of
  genome is shared more frequently than expected by
  relatives concordant for a particular disease,
  the inference is alleles predispose to disease at
  one or more loci in that region.
• Association looks for increased frequency of
  particular alleles in affected compared with
  unaffected in the pop.

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Model-Free Linkage Analysis of Complex Traits

• Linkage analysis is called model-free (or
  nonparametric) when it does not assume any
  particular mode of inheritance to explain the
  inheritance pattern.
• Nonparametric LOD (NPL) score analysis allows
  mapping of genes in which variants contribute to
  susceptibility for diseases (so-called
  qualitative traits) or to physiological
  measurements (known as quantitative traits) that
  do not follow a straightforward mendelian
  inheritance pattern.

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MAPPING OF COMPLEX TRAITS

• NPL scores are based on testing for excessive
  allele-sharing among relatives, such as pairs of
  siblings, who are both affected with a disease or
  who show greater similarity to each other for
  some quantitative trait compared with the average
  for the population.

71
MAPPING OF COMPLEX TRAITS

• The NPL score gives an assessment of how strong
  the evidence is for increased allele sharing near
  polymorphic markers. A value of the NPL score
  greater than 3.6 is considered evidence for
  increased allele-sharing an NPL score greater
  than 5.4 is considered strong evidence.

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Model-Free Linkage Analysis of Qualitative
(Disease) Traits

• One type of model-free analysis is the affected
  sibpair method.
• Only siblings concordant for a disease are used
• No assumptions need be made about the number of
  loci involved or the inheritance pattern.
• Sibs are analyzed to determine whether there are
  loci at which affected sibpairs share alleles
  more frequently than expected by chance alone
• In this method, DNA of affected sibs is
  systematically analyzed by use of hundreds of
  polymorphic markers throughout the entire genome
  in a search for regions that are shared by the
  two sibs significantly more frequently than is
  expected on a purely random basis.

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• When elevated degrees of allele-sharing are found
  at a polymorphic marker, it suggests that a locus
  involved in the disease is located close to the
  marker.
• Whether the degree of allele-sharing diverges
  significantly from the expected by chance alone
  can be assessed by use of a maximum likelihood
  odds ratio to generate a nonparametric LOD score
  for excessive allele sharing.

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Model-Free Linkage Analysis of Quantitative Traits

• Model-free linkage methods based on
  allele-sharing can also be used to map loci
  involved in quantitative complex traits. Although
  a number of approaches are available, one
  interesting example is the highly discordant
  sibpair method.
• Once again, no assumptions need be made about the
  number of loci involved or the inheritance
  pattern.
• Sibpairs with values of a physiological
  measurement that are at opposite ends of the
  bell-shaped curve are considered discordant for
  that quantitative trait and can be assumed to be
  less likely to share alleles at loci that
  contribute to the trait.
• The DNA of highly discordant sibs is then
  systematically analyzed by use of polymorphic
  markers throughout the entire genome in a search
  for regions that are shared by the two sibs
  significantly less frequently than is expected on
  a purely random basis. When reduced levels of
  allele-sharing are found at a polymorphic marker,
  it suggests that the marker is linked to a locus
  whose alleles contribute to whatever
  physiological measurement is under study.

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Disease Association

• An entirely different approach to identification
  of the genetic contribution to complex disease
  relies on finding particular alleles that are
  associated with the disease.
• The presence of a particular allele at a locus at
  increased or decreased frequency in affected
  individuals compared with controls is known as a
  disease association.
• In an association study, the frequency of a
  particular allele (such as for an HLA haplotype
  or a particular SNP or SNP haplotype) is compared
  among affected and unaffected individuals in the
  population

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Disease Association
total control patients
ab b a With allele
cd d c Without allele
bd ac total
The RRR is approximately equal to the odds ratio
when the disease is rare (i.e., a lt b and c lt d).
(Do not confuse RRR (relative risk ratio) with
?r, the risk ratio in relatives. ?r is the
prevalence of a particular disease phenotype in
an affected individual's relatives versus that in
the general population.)
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• If the study design is a case-control study in
  which individuals with the disease are selected
  in the population, a matching group of controls
  without disease are then chosen, and the
  genotypes of individuals in the two groups are
  determined an association between disease and
  genotype is then calculated by an odds ratio.
• Odds are ratios. With use of the above table, the
  odds of an allele carrier's developing the
  disease is the number of allele carriers that
  develop the disease (a) divided by the number of
  allele carriers who do not develop the disease
  (b). Similarly, the odds of a noncarrier's
  developing the disease is the number of
  noncarriers who develop the disease (c) divided
  by the number of noncarriers who do not develop
  the disease (d). The disease odds ratio is then
  the ratio of these odds, that is, a ratio of
  ratios.

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• If the study was designed as a cross-sectional or
  cohort study, in which a random sample of the
  entire population is chosen and then analyzed
  both for disease and for the presence of the
  susceptibility genotype, the strength of an
  association can be measured by the relative risk
  ratio (RRR).
• The RRR compares the frequency of disease in all
  those who carry a susceptibility allele (a/(a
  b) with the frequency of disease in all those
  who do not carry a susceptibility allele (c/(c
  d).

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• The RRR is approximately equal to the odds ratio
  when the disease is rare (i.e., a lt b and c lt d).
  
• The significance of any association can be
  assessed in one of two ways
• One is simply to ask if the values of a, b, c,
  and d differ from what would be expected if there
  were no association by a ?2 test.
• The other is determined by a 95 confidence
  interval for the relative risk ratio. This
  interval is the range in which one would expect
  the RRR to fall 95 of the time that you genotype
  a similar group of cases and controls by chance
  alone. If the frequency of the allele in question
  were the same in patients and controls, the RRR
  would be 1. Therefore, when the 95 confidence
  interval excludes the value of 1, then the RRR
  deviates from what would be expected for no
  association with P value lt0.05.

80
, Example suppose there were a case-control
study in which a group of 120 patients with
cerebral vein thrombosis(CVT)
Total Controls without CVT Patients with CVT
27 4 23 20210G gt A allele present
213 116 97 20210G gt A allele absent
240 120 120 Total
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• For example, suppose there were a case-control
  study in which a group of 120 patients with
  cerebral vein thrombosis (CVT) and 120 matched
  controls were genotyped for the 20210G gt A allele
  in the prothrombin gene.
• There is clearly a significant increase in the
  number of patients carrying the 20210 G gt A
  allele versus controls (?2 15 with 1 df P lt
  10-10). Since this is a case-control study, we
  use an odds ratio (OR) to assess the strength of
  the association.

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Genome-Wide Association and the Haplotype Map

• Association studies for human disease genes have
  been limited to particular sets of variants in
  restricted sets of genes. For example,
  geneticists might look for association with
  variants in genes encoding proteins thought to be
  involved in a pathophysiological pathway in a
  disease.
• Many such association studies were undertaken
  before the Human Genome Project era, with use of
  the HLA loci, because these loci are highly
  polymorphic and easily genotyped in case-control
  studies.

83
Genome-Wide Association and the Haplotype Map

• A more powerful approach, however, would be to
  test systematically for association genome-wide
  between the more than 10 million variants in the
  genome and a disease phenotype, without any
  preconception of what genes and genetic variants
  might be contributing to the disease.

84
Tag SNPs

• By examining all the haplotypes within an LD
  block and measuring the degree of LD between
  them, it is possible to identify the most useful,
  minimum set of SNP alleles (so-called tag SNPs)
  that are capable of defining most of the
  haplotypes contained in each LD with minimum
  redundancy.
• In theory, a set of well-chosen tag-SNPs
  constitutes the minimal numbers of SNPs that need
  to be genotyped to provide nearly complete info
  on which haplotypes are present on any chromosome
  

85

• In practice, genotyping a few hundred thousand
  tag SNPs is only a bit less useful for an
  association study than is genotyping more than 10
  million SNP genotypes at every known variant in
  the genome.
• Tag SNPs need to be examined and refined before
  we know if the results based on the four
  populations studied in the Hap-Map project are
  applicable world-wide.

86
From Gene Mapping to Gene Identification

• Positional cloning Mapping location of a disease
  gene by linkage analysis or other means, followed
  by identifying the gene on basis of its map
  position
• This strategy has led to identification of genes
  associated with hundreds of mendelian disorders
  and to a small but increasing number of genes
  associated with complex disorders.

87
Autozygosity mapping

• The method of choice for the discovery of
  autosomal recessive gene loci.
• Autozygosity is a term used to describe
  homozygosity for markers identical by descent
  (IBD) i.e., the two alleles are both copies of
  one specific allele that was present in a recent
  ancestor.
• An individual who is homozygous for two such
  alleles is said to be autozygous at that
  particular locus.

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• Autozygosity mapping

89

• The methodology seeks homozygous regions in
  consanguineous families.
• The rarer the alleles are in a population, the
  more likely the homozygosity represents
  autozygosity.
• The greater the number of affected individuals
  who have a shared homozygous region and the
  greater the size of the region, the more likely
  it is to harbor the mutation that causes the
  disease.
• DNA from the affected individuals is genotyped
  using SNP arrays/STRs and regions of homozygosity
  highlighted using IBD ?nder software.
• Linkage is confirmed using polymorphic more
  microsatellite markers
• Candidate genes within these haplotype regions
  are screened for pathogenic mutations.