Two-point linkage analysis

The follow ing exam ple introduces m any of the basic principles of linkage analysis. Consider tw o loci, A and B; each parent carries two alleles at each of these tw o lo d and, w ith 0.50 probability, transm its one of the two alleles

from each locus in the gam ete and on into the offspring. W hen the two non­ allelic genes tend to be transm itted together to the offspring, there is a deviation from the ratio expected. This, then, serves as the definition of genetic hnkage - the tw o loci are said to be genetically hnked. Since it is u n u su al for tw o lo d to be completely linked, the occurrence of cross-overs betw een the tw o loci can be used to calculate the recombination fraction. For unlinked loci, compliance w ith the expected 1:1:1:1 ratio will generate a recom bination fraction of 0.5 since 50% of the progeny will be recombinants. The recom bination fraction can be denoted by 0. For tightly linked loci, parental combinations will account for the vast majority of progeny and correspondingly, the recom bination fraction, 0, will be very small.

Linkage analysis is used to try to estimate the recombination fraction between tw o lod. This requires observations of the transm ission of the alleles at the tw o lo d through the m em bers of a family pedigree. Additionally, in order to dem onstrate which of the tw o alleles at lo d is passed on from parent to child, the parent m ust have tw o different alleles at each of the two lo d , that is, they m ust be double heterozygotes. For a m ating to be informative for linkage analysis at these two lo d , at least one of the parents m ust be doubly heterozygous.

Figure 1.4: O rdering of th ree genes on the basis of tw o factor crosses. A B B C A C X X X a b b e a e G enotype of progeny parental A B B C A C (93) (85) (80) a b b e a c recom binant A b B e A e (7) (15) (20) a B b C a C

(The figures in brackets represent % of progeny displaying the genotype in this example)

Figure 1.5: Assignm ent of the tentative order of the three genes on the basis of the two-factor crosses

A B C

--- , ^ ----

7% 15%

Figure 1.6: The use of three - factor crosses to confirm gene order

A B C This class arises from no

crossovers occurring. a b c

A b c This class arises from a

crossover occurring between A and B.

a B C A B C

X

a b c

A B c This class arises from a

crossover occurring betw een B and C

a b C

A b C This class arises from crossovers occurring between A and B, and B and C - a double crossover a B c

In order for linkage analysis to be perform ed there are three basic requirem ents; the exact m ode of inheritance m ust be know n, the loci m ust be polym orphic, and lastly, the genotype m ust be observable in the phenotype. Each of these requirem ents is explored separately.

The m ode of inheritance is usually know n for a m arker locus, b u t this m ay not so for the disease locus. The com puter program s designed for complex linkage analysis will allow for various m odes of inheritance to be explored, b u t obviously, the m ore that is know n about the disease inheritance, the more can be extracted from the results of the analysis.

Secondly, it is obvious that the loci need to be polym orphic w ith appreciable frequencies for each allele. If the frequency of one allele is very close to one or zero, there is an increased likelihood that all the parents in the pedigree will be hom ozygous for the sam e allele and reduce the informativity of the analyses. So, the m ore polym orphic the locus is the more useful it will be for linkage analysis.

O ne m ethod of m easuring the degree of polym orphism is the polym orphism inform ation content (PIC) described by Botstein (1980). The PIC represents the probability that an offspring of a random m ating betw een a carrier of a rare dom inant gene and a non-carrier will be informative for linkage between the locus of the dom inant gene and a m arker locus. It is expressed as

n n-1 n

1 - (S Pi") - Z Z 2pi" Pj"

i= l i= l j=i+l

w here p^ is the frequency of the ith allele and n is the num ber of alleles at the m arker locus.

The PIC can be interpreted practically as follows, if the grandparents are not typed, the PIC is the probability that phase can be established for the first child. Once this has been established, the PIC is the probability that an offspring is inform ative for establishing or rejecting linkage.

Lastly, the phenotype m ust resolve the genotype. For example, this is not the case if the ABO blood grouping is considered. An individual w hose phenotype is th at of blood group B, m ay be expressing either two B alleles or one B allele an d one O allele. For reasons of ease of analysis it is preferable to use m arker lo d th at equivocally exhibit the tw o alleles present in that individual.

Linkage data in families is analyzed according to the Lod score m ethod generated by M orton (1955). This m ethod compares the probability of obtaining any given result if the two loci considered are linked w ith a recom bination fraction, 0, w ith the probability th at the tw o loci are unlinked, th at is w ith a 0 of 0.5. This likelihood is calculated for a range of 0 values from 0.0 to 0.5. The results are expressed as log^o, allowing data from several families to be calculated together. The Lod score (Z) is therefore defined by the following expression

probability of observing the result in this family if the lo d are linked w ith a recom bination fraction 0

probability of observing this result if the lo d are unlinked, i.e. w ith 0=0.5

Z=

Z= logio[L(0)/L(O.5)

This is exemplified in the pedigree in Figure 1.7 show ing the segregation of an autosom al dom inant condition in a three generation family that have been typed w ith a polym orphic m arker that gives rise to tw o alleles, A1 and A2.

A 1,A 2 II III A I,A 2 A 1,A 2

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