Allometric relationships, 115

Jezequel, S. G., Fluconazole interspecies scaling and allometric relationships of pharmacokinetic properties, J. Pharm. Pharmacol. 1994, 46, 196-199. 

Stone KC, Mercer RR, Gehr P, Stockstill B, Crapo JD (1992) Allometric relationships of cell numbers and size in the mammalian lung. Am J Respir Cell Mol Biol 6 235-243... 

Much of the inter-species variation in pharmacokinetic properties can be explained as a consequence of body size (allometry). Consequently it is possible to scale pharmacokinetic parameters to the organism s individual anatomy, biochemistry and/or physiology in such a manner that differences between species are nuUified. Several excellent reviews on allometric scaling are available in the literature [2-7]. Allometric relationships can be described by an equation of the general form ... 

When considering volume of distribution, an allometric relationship is not surprising as this value will be dependent upon the relative affinity for tissue compared to... 

Fig. 9.1 Allometric relationship between body weight and volume of distribution of fluconazole.

When clearance is dependent upon metabolism, species-specific differences in the enzymes of metabolism can clearly prevent any such allometric relationship. An example of this is the absence of a close homologue of the human CYP2C9 enzyme in the dog, hence its inability to hydroxylate drugs such as tolbutamide and tienilic acid [13]. This said, many compounds cleared by metabolism do exhibit allometric relationships (e.g. N-nitrosodimethylamine, [14]). In an extensive analysis of the allometric relationship between clearance in the rat and man for 54 extensively cleared... 

The consideration of clearance in units of volume per maximum life span potential, instead of the traditional volume per weight, provides an allometric relationship for drugs such as antipyrine and phenytoin [17]. Both of these dmgs are essentially low clearance compounds, cleared by P450 metabolism. Ultimately, the successful utility of such factors may be purely serendipitous as they simply exploit unique features of man as a species. 

As observed in Figure 9.4 the intrinsic clearance (as represented by oral unbound clearance CIqu) of UK-147,535 shows an allometric relationship between the rat, dog and man. This would indicate that the transporter protein involved is conserved across these species and has similar affinity. However, marked reduction in clearance in the rabbit suggests the absence, or marked alteration, of the responsible protein in the hepatic sinusoidal membrane of this species. This finding may explain the common observation of reduced biliary excretion of acidic compounds in rabbits compared to other species [24, 25]. 

The values are based on species-specific allometric relationships. 

The intake rates are based on well-characterized allometric relationships. In this example, these variables are treated as random variables without uncertainty. 

Much has been published on the extrapolation of in vivo data from animals to humans. These include pharmacokinetic data (e.g. half-lives, plasma concentrations, clearances and rates of metabolism) and pharmacodynamic data (e.g. effective and toxic doses). Two excellent reviews present many examples and insightful discussions on isometric and allometric relationships, time scales, interspecies pharmacokinetic and pharmacodynamic scaling, and physiological models (Boxenbaum and D Souza, 1990 Chappell and Mordenti, 1991). 

In a study investigating the allometric relationships of pharmacokinetic parameters for five therapeutic proteins, the allometric equations for clearance and volumes of distribution, however, were found to be different for each protein [102]. This variability was attributed to possible species specificity and immune-mediated clearance mechanisms. Species specificity refers to the inherent differences in structure and activity across species. Minute differences in the amino acid sequence may render an agent inactive when administered to foreign species, and may even generate an immunogenic response. Immunogenicity has been clearly demonstrated in a study with the tumor necrosis factor receptor-immunoglobulin fusion protein lenercept. This all-human sequence protein elicits an immune response in laboratory animals which ultimately results in the rapid clearance of the protein [103]. 

Fig. 4.3 Allometric relationship of plasma clearance for ISIS 104838, ISIS 113715, and ISIS 301012. Each point represents the average of three to six individuals. Doses ranged from 2 to 5 mg/kg.

Figure 7.34. Allometric relationship of mitochondrial proton leak and body mass. Proton leak measured at a potential of 170 mV is expressed per unit volume (ji ) of mitochondrial matrix. Numbers refer to the following species (1) mouse, (2) hamster, (3) rat, (4) ferret, (5) Dutch rabbit, (6) New Zealand rabbit, (7) sheep, (8) pig, and (9) horse. (Figure modified after Porter et al. 1996.)...

Sijm DTHM, Van der Linde A. 1995. Size-dependent bioconcentration kinetics of hydrophobic organic chemicals in fish based on diffusive mass transfer and allometric relationships. Environ Sci Technol 29 2769-2777. 

While the interspecies variability in metabolism precludes the possibility of a simple allometric relationship for the plasma kinetics of ARA-C, the non-metabolic clearance by the kidney does exhibit a power-law relationship with body weight. Figure 30.7 shows the kidney clearance of ARA-C and its deami-nated product ARA-U on a log-log plot as a function of body weight for mice, monkeys, dogs, and humans. The slope is 0.80, which is essentially the same as the value of 0.77 for inulin (1). 

Table 13 Allometric relationship between the clearance (ml/min) of some drugs and body weight (kg) of various mammalian species...

Fig. 3.4 Double logarithmic plots showing the allometric relationship between (a) half-life and (b) body (systemic) clearance of HI-6 and body weight of seven animal species. (Reproduced with permission from Baggot (1994).)...

Fig. 3.5 Allometric relationship between unbound antipyrine intrinsic clearance (C/U(int)) per maximum life-span potential (MLP) and body weight. Note that the body weight exponent of the regression equation is close to unity. Units on the ordinate (litres per MLP) are equivalent to C/U(int) (L/min) x MLP (min). (Reproduced with permission from Boxenbaum (1982).)...

Figure 8.3 Allometric relationship between body surface area and species body weight on a log vs. log plot...

Given this representation for the individual rate processes leading to the formation and removal of the system constituents, one can demonstrate that all the well known growth laws and allometric relationships follow by deduction (Savageau, 1979a,b). Thus, it has been proved that this representation is consistent with known systemic behavior. 

This is not the case for the other two formalisms commonly used in biochemistry—the Linear Formalism and the Michaelis-Menten Formalism. The Linear Formalism implies linear relationships among the constituents of a system in quasi-steady state, which is inconsistent with the wealth of experimental evidence showing that these relationships are nonlinear in most cases. The case of the Michaelis-Menten Formalism is more problematic. An arbitrary system of reactions described by rational functions of the type associated with the Michaelis-Menten Formalism has no known solution in terms of elementary mathematical functions, so it is difficult to determine whether or not this formalism is consistent with the experimentally observed data. It is possible to deduce the systemic behavior of simple specific systems involving a few rational functions and find examples in which the elements do not exhibit allometric relationships. So, in... 

Figure 9. Allometric relationship between glycogen accumulation and growth of the chicken (replotted form the data of Wladimirow and Danilina, 1930).

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