Hardy Weinberg Analysis of Isoniazid Metabolism

A definitive study of isoniazid metabolism was performed on 267 members of 53 complete Caucasian families.32 The concentration of free isoniazid (measured biochemically) was bimodally distributed because of differences in individual acetylating capacity (see Figure 2.1), Metabolic studies had shown that acet-ylation was the most important factor in the elimination of isoniazid, and the inheritance patterns in families suggested that individual differences in acetyla-tion measured in vivo were controlled by a single gene with two major alleles.

Among 291 unrelated subjects tested, 152 or 52.23% were slow acetylators. The frequency of the slow acetylator allele estimated from the Hardy-Weinberg law is p = H0.5223 = 0.7227. The frequency of the alternative character, the rapid acetylator allele, is thus q = 1 - 0.7227 = 0.2773. The hypothesis that slow acetylation is a recessive character was tested by David Price Evans and colleagues according to the Hardy-Weinberg law (1) by comparing the number of matings observed with those expected in the population sample as shown in Table

5.8, and (2) by comparing the number of children observed with those expected from 53 matings as shown in Table 5.9. Both comparisons show that the data fit the hypothesis (1) that the division into rapid and slow acetylator phenotypes is due to two major alleles and (2) that the slow acetylator phenotype is due to homozygosity of the slow acetylator allele. A test of the alternative hypothesis that rapid acetylation is the homozygous recessive character results in unsatisfactory agreement of observed and expected numbers.

Shortly after the Caucasian study but independent of it, S. Sunahara and co-workers performed a similar analysis of the pharmacogenetics of isoniazid metabolism on Japanese persons and families. It gave results that differed dramatically from those obtained on Caucasians. In the Japanese study, free isoni-azid in blood was measured microbiologically instead of biochemically. The more sensitive assay enabled the separation of intermediate rapid (heterozygous) acetylator phenotypes from the homozygous rapid acetylator phenotypes to yield a trimodal frequency distribution (Figure 5.7)33 instead of the bimodal frequency distribution found for Caucasians (Figure 2.1). Tests of the same hypotheses were performed on the Japanese data by the Hardy-Weinberg law. Comparisons of the observed and expected numbers of matings (Table 5.10) and of the children of each acetylator phenotype for Japanese subjects (Table 5.11) confirmed the conclusions reached for Caucasians even though there are major ethnic differences in the frequencies of the two acetylator phenotypes.

The checkerboard diagram in Figure 5.8 provides an alternative display of the genetic data that complements its presentation in tabular form (Tables 5.8,

5.9, 5.10, and 5.11). The checkerboard helps to explain the Hardy-Weinberg

Table 5.9 Expected Numbers of Children of Each Acetylator Phenotype Compared with Those Observed in 53 Caucasian Matings3

Number of children of each phenotype

Rapid Slow

Table 5.9 Expected Numbers of Children of Each Acetylator Phenotype Compared with Those Observed in 53 Caucasian Matings3

Number of children of each phenotype

Rapid Slow

Phenotypic

Number

Number

0 0

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