Esterase Units

Figure 3.3 Frequency distributions for serum cholinesterase activity levels among 135 members of seven families. The black bars indicate esterase levels of sera with dibucaine numbers below 70.1 With permission from the NRC Research Press.

responses of several genetic phenotypes may overlap, and the overlap may be increased by environmental factors that contribute to the variability within a phenotype. Consequently, genetically heterogeneous populations may appear to be distributed normally, or near normally, with large variability about the average. The distribution of serum cholinesterase activities of individuals provides an example of a unimodal distribution of a quantitative variable that contains hidden genetic modes (Figure 3.3).1 In this case, even though the average of the serum cholinesterase activities of succinylcholine-sensitive persons (dibucaine numbers below 70) is shifted to a lower value, the shift is not great enough to separate normal from abnormal responders. This distribution of enzyme activities is to be contrasted with the distribution of dibucaine numbers that divides the same individuals into three distinct modes (see Figure 2.1A). The dibucaine number, which denotes the sensitivity of serum cholinesterase to dibucaine inhibition, measures a qualitative difference between usual and atypical cholin-esterase variants. The modes with average dibucaine numbers of approximately 16, 60, and 80 correspond to succinylcholine-sensitive responders, heterozygous carriers of this trait, and homozygous normal responders to succinylcholine, respectively.

Graded Dose-Response Relationships

The graded response relationship affords an experimental approach that may shed light on the pharmacodynamic mechanism responsible for a modified drug response. Graded measurements are often preferred to quantal measurements for this reason. When a direct relationship exists between the receptor binding of the xe-nobiotic and the response, changes in the dose-response relationship for the drug would be expected if either the abundance (i.e., the number of receptor sites) or the affinity of the receptor sites is altered (Figure 3.1); the abundance and affinity of receptor proteins are, like half-lives and Kms, individual characteristics that may exhibit considerable person-to-person variation. If the abundance of receptors is decreased, elementary receptor theory predicts that the maximum response that could be attained would be decreased, while the concentration of the drug at which a half-maximal response is attained would be unchanged; conversely, if the abundance increased, the maximal response would theoretically increase without a change in the drug concentration at the half-maximal response. On the other hand, if the affinity of the receptor for the xenobiotic is increased, the maximal response would theoretically not increase, but the concentration of the drug needed to attain that response would decrease, and vice versa.

The application of these concepts to a real situation is illustrated in the analysis of the pharmacological mechanism for hereditary resistance to coumarin anticoagulant drugs such as warfarin. In this case, the absorption, distribution, and elimination of the drug as well as other pharmacokinetic mechanisms were not found to be aberrant in warfarin-resistant individuals. A comparison of the dose-response relations of the normal responder to that of the resistant responder showed that the slopes of the dose-response lines are nearly identical, but the line for the resistant subject is shifted to the right. This observation indicates that the resistant responder requires a larger amount of the drug than the normal responder to achieve a given anticoagulant response (Figure 3.4). The study revealed the affinity of the receptor for warfarin in resistant subjects is much lower, some 20 times lower than that in normal responders. This trait was described by O'Reilly and colleagues in the 1960s prior to the advent of recombinant DNA technology, and the molecular basis of a putative receptor was not defined.2

Hormetic Dose-Response Relationships

Hormesis refers to a biphasic dose-response phenomenon characterized by low-dose stimulation and high-dose inhibition, resulting in a U- or inverted U-shaped dose-response (Figure 3.2). The term hormesis associated with this relationship was coined in 1943 by investigators who were apparently unaware that biphasic dose-response relationships had been characterized well over a century earlier. Historically, researchers, including pharmacogenetic researchers, have placed a strong emphasis on high-dose evaluation, as these doses are more definitive for establishing and reporting the drug level of NOAEL (no observed adverse effect level). Additionally there is the long-standing belief that responses below the NOAEL are, because of their modest nature, not reproducible effects but are most z o t-

ZS 50 POO 200 4-00 700 ISOO DOSE OF WARFARIN IN mg

Figure 3.4 Human dose-response relationships for resistant (solid symbols) and nonresistant (open symbols) responders to warfarin.2

ZS 50 POO 200 4-00 700 ISOO DOSE OF WARFARIN IN mg a.

Figure 3.4 Human dose-response relationships for resistant (solid symbols) and nonresistant (open symbols) responders to warfarin.2

likely due to normal variation. For this reason, only a small fraction of studies has the appropriate dosage design necessary to assess this controversial hypothesis.3-5

Some of the concerns and limitations of this concept are addressed by Ca-labrese and Baldwin who find in assessing the frequency of U-shaped dose-responses in the toxicological literature that hormetic responses are commonly encountered if the study design is appropriate.6 Features that are important and necessary to more properly determine the dose-response in the low-dose zone include multiple and carefully spaced doses below the NOAEL, and possibly a temporal component within the study design if the hormetic mechanism represents an overcompensation response. For assessments of endpoints such as mutagenicity, carcinogenicity, and teratogenicity within a hormetic framework, models with zero or negligible background/control incidence cannot be used.

Most of the prior investigations have focused on toxicologically derived data. Even so, sufficient data exist to suggest that biphasic dose-response relationships are quite common in toxicology and pharmacology, and for a large number of endpoints, including cancer risks, longevity, growth, and more, are common across the spectrum of biological, pharmacological, and biomedical disciplines.7 It seems reasonable to suggest that future modeling of biological responses, including pharmacogenetic study designs, should consider incorporating features for detecting hormetic dose-responses.

Analyzing Dose-Response Relationships

Plots of quantal or graded data, i.e., a plot of frequencies, or intensities, of responses (y-axis) vs. log concentration or dose (x-axis) for normally distributed data, resemble the bell-shaped (Gaussian) curve. These data can also be graphed as cumulative plots because a high dose of drug affects less responsive individuals (or cells) as well as more susceptible individuals for whom a lower dose would have been sufficient. Cumulative plots are sigmoidal for normally distributed measurements.8-10

The probit (probability) plot provides a simpler approach to the graphic analysis of dose-response data. Table 3.1 shows that probit values correspond to "normal equivalent deviate'' (NED) values plus 5, and the relation of percent response, NED, and probit values. Probits were originally introduced to simplify numerical calculation by eliminating negative numbers for NED values.

Certain advantages accrue to probit plots in pharmacogenetics. First, for a set of normally distributed data that has been transformed to probits, a graph of probits vs. dose (log dose) is linear; second, the greater the variability (standard deviation), the lesser the slope of the probit plot; and third, the occurrence of nonlinearity in probit plots indicates there is heterogeneity in the population sample of responders tested.

Although probit plots may clearly reveal heterogeneity among responders, they may be inefficient for this purpose, particularly if the fraction of unusual responders is small, say a few percent or less, of the total sample tested. This point is evident from the distribution of thiopurine methyltransferase activity in human red blood cells (see Figure 2.1C). The red cells with very low or undetectable activity comprise only about 1 in 300 individuals, or about 0.3% of the population; the nonlinearity would hardly be evident in a probit plot. The differential plot shown in Figure 2.1C is better to demonstrate such a small fraction of unusual responders.

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