Genomics- The Science and Technology Behind the Human Genome Project. Charles R. Cantor, Cassandra L / genomics1-10 / 6

RELATIONSHIP BETWEEN THE PHYSICAL AND THE GENETIC MAPS

175

mologous chromosome is

copied onto the corresponding region of another homolog. A

schematic

mechanism is

given in Figure 6.11, and the consequences for gene order

are

shown in

Figure 6.12. Gene conversion appears to be relatively frequent

in yeast.

Figure 6.11

An example of gene conversion, an event that destroys the usual 1

:1 segregation pat-

tern seen in typical

Mendelian inheritance.

RELATIONSHIP BETWEEN THE PHYSICAL AND THE GENETIC MAPS

177

BOX 6.2

(Continued)

178

GENETIC ANALYSIS

To distinguish single and multiple crossover events, and gene conversion, large num-

bers of highly informative loci are

very helpful. Several features of

genetic loci

make

them particularly powerful for mapping. Ideally one has many different alleles, and these

occur at reasonable frequencies in the population. Where this occurs, there is a very good

chance that all four parental homologs are distinguishable at the locus because they each

carry different alleles. A major thrust in human genetics has been the systematic collec-

tion of such highly informative loci. This will be discussed in a later section. It is also

helpful to have many offspring in families under study and to have many generations of

family members. Because it is so difficult to satisfy these conditions, human genetics is

often rendered rather impotent compared with the genetics of more easily manipulatable

experimental organisms.

POWER

OF

MOUSE

GENETICS

Mice are among the smallest common mammals. They are relatively inexpensive to main-

tain, have large numbers of offspring, and mature quickly enough to allow many genera-

tions to be examined. However, this alone does not explain why mice form such a power-

ful genetic system. Several reasons exist that make the mouse the preeminent model for

mammalian genetics. First, so much is

already known about so many mouse

genes,

that

an extensive genetic map already exists. Second, many highly inbred strains of laboratory

mice exist. These tend to be homozygous at most alleles, and thus a description of their

phenotype and genotype is relatively simple. Also gene transfer and knockout technology

exist for mice. What is

particularly useful is that rather distant inbred strains of mice can

be interbred to give at

least some fertile offspring. This property dramatically simplifies

the construction of high-resolution genetic maps. Several different sets

of inbred strains

can be used. One of

the earlier

choices was

Mus

musculus,

the common

laboratory

mouse, and

Mus spretus,

a distant cousin.

Figure 6.14 illustrates how crosses between

M. musculus

and

M. spretus

generate very

useful genetic information. Because these mice are so different, the F1 offspring of a di-

rect cross tend to be

heterozygous at almost any locus examined. It turns out that the

males that result from such a cross are sterile, but the females are fertile. When an F1

spretus

musculus

female is bred with an

M. musculus

(a procedure called a

backcross

),

in most regions of the

genome the progeny either resemble wild type

M. musculus

ho-

mozygotes,

or

F1

musculus

spretus

heterozygotes. However,

every time a recombina-

tion event occurs, there is a switch between the homozygous pattern and the heterozygous

pattern

(Fig.

6.14

b ). Given the dense set of genetic markers available in these organisms,

the location of many recombination events can be determined in each set of experimental

animals. The result is that one develops and refines genetic maps extremely rapidly.

WEAKNESS

OF

HUMAN GENETICS

Humans, from

a

genetic

standpoint, are a stark contrast with mice. We have a relatively

long generation time; it precludes the simultaneous availability of large numbers of gen-

erations.

Our

families

are small; most are far too small for effective genetics. Crosses

cannot be controlled, and there are no inbred strains, only the occasional result of very

limited inbreeding in particular cultures that promote such practices as marriages between

WEAKNESS OF HUMAN GENETICS

179

Figure 6.14

Example of the informativeness of a back cross between two

distant mouse

species

M. musculus

and

M. spretus. (a)

Design of the back cross.

(b)

Alleles seen for three loci in the par-

the

trait is linked to any other known trait

in the genome. This is a very tedious task, as

we

will illustrate. However, large numbers of

ongoing studies use this approach because

LINKAGE ANALYSIS IGNORING RECOMBINATION

181

Suppose that the two loci are on different chromosomes. We

then know the genotypes

of the mother and the father unambiguously as shown in Figure 6.16. Independent segre-

gation of alleles on different chromosomes leads to four possible genotypes for the off-

spring of these parents. A priori the probability of occurrence of each of these phenotypes

1

should

be equal, so each

should

occur

with

an expected frequency of

. Thus

the a

priori

4

probability that the family in question should have both children with the same particular

phenotype, AaDd is

1

. We1 need to1

compare this probability, calculated from the

4

4

16

hypothesis that the loci are unlinked, with the probability of seeing the same result if the

loci are linked.

If the two loci are linked, they are on the same chromosome. In this case the genome of

the homozygous father can be described unambiguously, but there

are

two possible

phases

for the mother. These are shown in Figure 6.17

a . Unless we have some a priori knowledge

about the mother’s genotype, we must assume a priori that these two

possible

phases are

1

equally probable. Thus there is a

chance that the 1mother is cis and

that she is trans. Since

2

2

we are not allowing for the possibility of recombination, if the mother is trans, the probability

that she would have an AaDd daughter is zero, since both the A and D alleles have to come

from the mother in the family shown in Figure 6.15, and this

would be impossible in the

trans configuration where the A and D alleles are on different homologs.

If the mother is cis for the two loci, there are two possible genotypes for any offspring.

These are shown in Figure 6.17

b . In the

absence of any intervening factors, the a priori

probability

of

observing

these

genotypes

should

be equal. Thus

the

chance

of

seeing

a

1

child

with

the

genotype

AaDd under

these

circumstances is

. The

chance

of

a

family

2

with two children both of whom are AaDd will be

. However, since1

we have1

no

1

2

2

4

a priori knowledge about the phase of the mother, we must average the chances of seeing

the expected offspring across both possible phases. The overall odds of the observed fam-

ily inheritance pattern is then

1

1

1

1

2

(0) if

(the)two loci are linked.

2

4

8

Figure 6.17

Inheritance patterns with linkage, but no recombination.

(a)

Possible maternal geno-

types

if the two loci

are linked.

(b) Possible offspring if the mother

is cis. For the example

consid-

ered,

other offspring genotypes will be seen only if the loci are not linked.

P

linked

1

odds ratio

8

2

P

unlinked

1

16

In human genetics we frequently know the phase of an individual because this

is available

from data on other generations or other family members. In this case the odds ratio becomes

P

linked

1

odds ratio

4

4

P

unlinked

1

16

P

linked

odds

odds

odds

. . .

P

unlinked

1

2

3

LINKAGE ANALYSIS WITH RECOMBINATION

183

log(A

B C . .

. ) log(A)

log(B)

log(C) . . .

the result is

LOD

log

P

linked

log(odds

1 ) log(odds

2) log(odds 3) . . .

P

unlinked

This is called a

LOD

(rhymes with cod)

score.

The LOD score is calculated from the data

seen with a particular family or set of families. Some feeling for the number of individu-

als

that

must be

examined for a LOD score to be statistically significant can be captured

by

the

expected

LOD score calculated for a particular inheritance model, called an

ELOD. However, the inheritance model we use has to include the possibility of recombi-

nation to be realistic enough to represent actual data.

LINKAGE

ANALYSIS

WITH

RECOMBINATION

Consider

a pair

of markers at loci that appear to be

linked by available

data. There

are

matters if one of these is a locus where

D is an allele of a disease gene

that we are trying

to find. A is an allele at another locus,

and we are interested in testing

the hypothesis

that

in a particular family A and D are linked. The chance that a recombination event occurs

between the two loci in each meiosis is an unknown variable

. We need to calculate the

odds in favor of linkage, for data from a particular family, as a function of

. Actual

LOD( ) calculations are complex. To illustrate the considerations that go into such cal-

culations, we will calculate the expected contribution of a single individual observed to

inherit the disease allele D to the overall LOD score. This contribution is called the ex-

pected LOD or ELOD(

).

We will analyze the case where a parent is AaDd. Usually we are dealing with a rela-

tively rare disease, and the other parent does not have the D allele. We assume for sim-

plicity that the healthy parent

also either has the a allele or some other allele that

we can

distinguish from A and a. We look only at offspring that are detected to carry the disease

allele D. If the two loci are unlinked, the offspring inherit pairs of two different chromo-

somes carrying A or a and D or d at random, as shown in Figure 6.18

a . We look only at

offspring carrying D; thus there is a 0.5 probability that such an offspring will also inherit

A.

Figure 6.18 Analysis of the inheritance of a disease allele D and a possible linked allele A.

(a)

Possible parental contributions to an offspring if no linkage occurs.

(b) Possible parental contribu-

tions to an offspring if the loci are linked but the recombination frequency between them is 0.1.

We will consider the case where

two

loci

are linked

and

the phase

in

the

parent

is

known to be cis (Fig. 6.18

b ). What we want to calculate

is

the

effect

of observing one

child of this parent on the odds in

favor

of

linkage of A

and

D. Suppose that

is 0.1.