Abstract
Cassette dosing is a procedure for higher-throughput screening in drug discovery to rapidly assess pharmacokinetics of large numbers of candidate compounds. In this procedure, multiple compounds are administered simultaneously to a single animal. Blood samples are collected, and the plasma samples obtained are analyzed by means of an assay method such as liquid chromatography coupled to tandem mass spectrometry that permits concurrent assay of many compounds in a single sample. Consequently, the pharmacokinetics of multiple compounds can be assessed rapidly with a small number of experimental animals and with shortened assay times. However, coadministration of multiple compounds may result in pharmacokinetic drug-drug interactions. This paper describes a pharmacokinetic description for cassette dosing derived from pharmacokinetic theory. The most important finding from this theoretical treatment is that the potential for drug-drug interactions leading to altered clearances of coadministered drugs depends on both the relative KM values for the metabolic enzymes and the total number of drugs coadministered. However, the theory predicts that the potential for drug-drug interactions is only a weak function of the dose size. Finally, it is also shown that including a benchmark compound within the set of coadministered compounds cannot ensure the detection of errors due to drug-drug interactions. Thus, neither the absolute values of pharmacokinetic parameters nor the rank order obtained from cassette dosing can be accepted without independent confirmation. These theoretical predictions are evaluated with data taken from the literature.
The modern pharmaceutical industry has adopted high-throughput screening for the identification of lead molecules (Fernandes, 1998) and subsequent optimization of chemical structure, leading to clinical candidates with desirable biopharmaceutical and pharmacokinetic properties (e.g., clearance, half-life, and oral bioavailability) (Tarbit and Berman, 1998). Orally active, once-a-day drugs are desirable because of their clinical and commercial advantages. In recent years, several pharmaceutical companies have published reports on the simultaneous administration of several compounds to a single animal (cassette dosing or “ N -in-One” dosing) (Berman et al., 1997; Olah et al., 1997; Allen et al., 1998; Frick et al., 1998a; Shaffer et al., 1999; Wu et al., 2000) as a means to rapidly rank-order compounds on the basis of their pharmacokinetics. Cassette dosing is used to screen compounds in two general ways: for systemic clearance (i.v. dosing) and for oral plasma drug levels (p.o. dosing). Compared with conventional pharmacokinetic studies, this method has the advantage of speed, because the slow steps of animal dosing, blood collection, and sample analysis are minimized. Another advantage is that animal usage is greatly reduced, which is particularly important when dog or monkey is the test species. Cassette dosing also avoids the problem of in vitro-in vivo correlation, which is always present with in vitro methods of rapidly assessing pharmacokinetics. The enabling technology for cassette dosing is liquid chromatography coupled to tandem mass spectrometry which allows many compounds to be simultaneously assayed in a single sample (Berman et al., 1997; McLoughlin et al., 1997; Beaudry et al., 1998; Frick et al., 1998b). The degree of acceleration depends on the number of coadministered compounds (n), but there are practical limitations on n. Most applications of cassette dosing use n of 10 or less (Bayliss and Frick, 1999).
Cassette dosing has been controversial because of concerns over whether there are serious errors. Some reports claim that reliable pharmacokinetic data are obtained (Berman et al., 1997;McLoughlin et al., 1997; Olah et al., 1997; Allen et al., 1998; Frick et al., 1998a; Bayliss and Frick, 1999; Shaffer et al., 1999; Rano et al., 2000; Wu et al., 2000), but only a few have actually demonstrated reasonable correspondence of pharmacokinetic parameters obtained from cassette dosing and conventional single-compound dosing (Berman et al., 1997; Frick et al., 1998a;Shaffer et al., 1999). However, in some of the other reports, large errors are evident (Allen et al., 1998;Bayliss and Frick, 1999), and in several studies no attempt was made to actually assess the reliability of the results (McLoughlin et al., 1997; Rano et al., 2000; Tong et al., 1999; Wu et al., 2000). Although many investigators are aware of the potential for the occurrence of drug-drug interactions to compromise the results, there has been no published assessment of these interactions in terms of their nature, frequency, magnitude, and direction. A majority of the papers focus on the analytical challenges of simultaneously assaying many compounds in a single sample. In the absence of theoretical guidance, a set of intuitive assumptions has arisen regarding the nature of the errors and how to avoid them.
These assumptions are
- 1.
- Drug-drug interactions only occur when one of the dosed compounds is a potent inhibitor of drug-metabolizing enzymes;
- 2.
- One may guard against competitive inhibition of a shared metabolic enzyme by keeping doses small;
- 3.
- The size of the cassette (n) is limited only by the sensitivity of the assay and the solubility of the compounds;
- 4.
- Errors can be detected by including a benchmark compound with known pharmacokinetic characteristics;
- 5.
- Drug-drug interactions can lead only to false positives, which will be discovered later; and
- 6.
- Even if the absolute values are wrong, the correct rank order will be observed.
We applied pharmacokinetic principles to analyze and understand the kinetics of cassette dosing. We then evaluated the above assumptions, both from the viewpoint of theory and by reference to published experimental data. We found that none of these assumptions is always valid.
Results and Discussion
Types of Drug-Drug Interactions.
In the following discussion, we will examine the pharmacokinetics of drug-drug interactions following coadministration of many compounds. To begin, let us enumerate the drug-drug interactions that potentially have pharmacokinetic consequences, as follows:
- 1.
- Competition for clearance pathways (mutual inhibition of metabolic enzymes and transporter proteins);
- 2.
- Competition for net absorption (mutual inhibition of influx and efflux transporter proteins);
- 3.
- Competition for plasma protein binding;
- 4.
- Heteroactivation of clearance pathways (activation of a metabolic enzyme by a second drug acting through an allosteric mechanism);
- 5.
- Pharmacological and toxicological effects on organ blood flows and clearances; and
- 6.
- Enzyme induction phenomena.
Effects 1 through 4 are molecular events involving mutual inhibition at the binding sites of proteins, whereas effect 5 occurs at the physiological level. Effect 6 need not be considered as long as the screening procedure involves only single doses. The following pharmacokinetic analysis will focus on inhibition of clearance (effect 1), with some related discussion of plasma protein binding (effect 3).
Pharmacokinetic Theory.
We can consider cassette dosing to be an extreme case of multiple drug therapy. Our approach is similar to the pharmacokinetic theory of drug-drug interactions in multiple drug therapy elaborated byAarons (1981). A rigorous treatment of drug-drug interactions due to metabolic enzyme inhibition has also been given byIto et al. (1998). Let us consider the case of oral bioavailability, which is often the effective endpoint of cassette dosing screening. Absolute oral bioavailability (F1) is sensitive to effects 1 through 5, as shown in eq. 1:
Assuming for simplicity that all of the dose reaches the liver as unchanged drug (i.e., fa = 1 and EG = 0), the bioavailability F is simply the fraction of the drug that escapes elimination during the first pass through the liver.
If hepatic clearance is due to metabolism, then the rate of metabolism is governed by the Michaelis-Menten equation (Segel, 1975):
As shown under Appendix , when n drugs are present, intrinsic clearance of Drug 1 is given by
Evaluation of Common Assumptions.
In the light of eq. 11, we can now examine the intuitive assumptions that were mentioned in the introduction as the supposed operational characteristics of cassette dosing.
Assumption 1. Drug-drug interactions only occur when one of the dosed compounds is a potent inhibitor of drug-metabolizing enzymes.
Many variations of this very intuitive assumption have been presented in the literature (McLoughlin et al., 1997; Olah et al., 1997; Frick et al., 1998a; Tarbit and Berman, 1998; Rano et al., 2000). While a potent inhibitor can cause serious drug-drug interactions, we will show here that this is not the only source of these interactions. In fact, inhibition of a similar magnitude can be expected whenever a sufficient number of nonpotent inhibitors are present. This number will be seen to be in the range of the number of drugs in a typical cassette.
Let us first show the effect on intrinsic clearance of a drug (Drug 1) due to the presence of a potent inhibitor (Drug 2). Since both K and C have units of concentration, it is not necessary to specify the units. For cassette dosing, we expect that all drugs are given at the same dose, and we will assume for simplicity that all of the doses reach the liver as unchanged drug, so that initial concentrations are equal.4 Thus, setting K1 = 1, K2 = 0.1, and C1 = C2 = 1, by eq. 11 we calculate CL* for Drug 1 = 0.17.
However, eq. 11 predicts that a large reduction in intrinsic clearance will also occur when several drugs are dosed together. To illustrate, take the simplest case first. If Drug 1 is present at a concentration equal to its K value, and only one other drug is present at a concentration equal to its K value, then CL* = 0.67, which is a measurable effect but unlikely to change conclusions.
Assumption 2. One may guard against competitive inhibition of a shared metabolic enzyme by keeping doses small.
This assumption is almost universally cited (Berman et al., 1997; McLoughlin et al., 1997; Olah et al., 1997; Adkison et al., 1998; Allen et al., 1998; Frick et al., 1998a; Tarbit and Berman, 1998; Bayliss and Frick, 1999). We will show that the use of low doses will tend to reduce drug-drug interactions, but meaningful curtailments of these interactions are probably not realized with the typical “low” doses (1 mg/kg) used in reported studies.
Inspection of eq. 11 immediately reveals that, even if C is low but n is high, the ΣD/K term can still be significant, and an appreciably altered intrinsic clearance will still result. To illustrate this effect, let us consider three hypothetical cases.
Case 1. Two drugs, equal values of K (K1 = K2 = 1), concentrations equal to 10% of K.
Case 2. Ten drugs, equal values of K (K1, K2 … K10 = 1), concentrations equal to 10% of K.
Case 3. Ten drugs, K values distributed randomly above and below K1(K1 … K10 = 1, 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10) and concentrations equal to 10% of K1.
In the above examples, we showed the effect of changing K values while holding concentrations constant. Next, we will explore the effect of changing drug concentrations while holding K values constant. Figure 1 shows the dependence of CL* for Drug 1 on drug concentration for the case in which 10 equipotent drugs are dosed simultaneously. Here “drug concentration” refers to the concentration of a single component, with the units of concentration being expressed as multiples of the K for Drug 1. Overall, we can see that reducing the concentration of the drugs does indeed decrease the inhibition. For example, at a concentration of 1, CL* is only 0.18 (82% inhibition), while at a concentration of 0.003, CL* is 0.97 (3% inhibition). However, CL* rises only weakly as the concentration decreases. In fact, we can see that even when no component is present at more than 10% of its K value (i.e., 0.1 in Fig. 1), approximately 50% of the enzyme activity is still inhibited. If we remember that typical K values of drugs are in the 0.1 to 10 μM range, then plasma concentrations would have to be kept quite low to satisfy the criterion of staying well below 0.1 K to avoid noticeable enzyme inhibition, and assay sensitivity would become an important limitation.
Dependence of fractional intrinsic clearance on concentration of the individual compounds in a cassette of 10 drugs.
K values of all drugs were set to 1. CL* was calculated according to eq. 11. Drug concentration is expressed as multiples of the K value of Drug 1. Thus, a drug concentration of 0.1 means that each drug in the cassette was present at a concentration equal to 10% of K1. The horizontal line corresponds to 50% inhibition of intrinsic clearance. The intersection of this line with the inhibition curve (indicated by the arrow) shows that 50% inhibition occurs when concentrations of the 10 drugs are only 10% of K1.
To illustrate this situation in terms of typical practice, assume a cassette of 10 drugs with molecular weights about 500 and volumes of distribution around 2 l/kg. After either a well absorbed p.o. dose or an i.v. dose of 1 mg/kg, maximal plasma concentrations will be on the order of 1 μM. Even if these compounds had an average K value of 10 μM, the average inhibition due to competitive drug-drug interactions would still be 50%. Consequently, to be reasonably assured of avoiding noticeable inhibitions, one should not allow doses to exceed 0.1 mg/kg, a dose that will surely limit most bioanalytical assays. Experimentally, the prediction of theory is borne out, as summarized in Table 1. With doses of only 1 mg/kg, Olah et al. (1997), Allen et al. (1998), and Bayliss and Frick (1999)observed errors as large as 220, 660, and 680%, respectively. Thus, according to both theory and experiment, using 1-mg/kg doses is an ineffective means of avoiding drug-drug interactions.
Results reported for cassette dosing
Assumption 3. The size of the cassette (n) is limited only by the sensitivity of the assay and the solubility of the compounds.
Restrictions on the size of the cassette are sometimes explicitly stated (Olah et al., 1997; Adkison et al., 1998; Bayliss and Frick, 1999) but are more often implicit. Some investigators have used large cassettes and seem to recognize no real restrictions (Frick et al., 1998a;Beaudry et al., 1998; Rano et al., 2000;Wu et al., 2000). In all cases, however, the aggregate inhibitory effect of n coadministered compounds, as predicted by eq. 11, was not appreciated.
To address Assumption 3, we calculated the effect of increasing numbers of simultaneously dosed compounds on CL* by applying eq. 11 (Fig.2). To minimize the drug-drug interactions, concentrations of the compounds were set to only 10% of the K value for Drug 1. Figure 2 displays three curves. The curve marked “Equal K 's” represents the inhibition of enzyme activity toward Drug 1 if the other compounds were equipotent with Drug 1. We can see that as the number of compounds in the cassette grows larger, the aggregate inhibition on any particular component also grows. However, as mentioned before, the assumption of equal K values is not very realistic. We expect to have a dispersion of K values among the coadministered drugs. Thus, the curves marked “Max” and “Min” illustrate the range of values that may be observed among the compounds, assuming that the K values of the compound set the range from 0.1 to 10. Depending on which drug in the set we define as Drug 1, the observed intrinsic clearance may be hardly affected or noticeably reduced. For example, if Drug 1 is the one with the lowest K value of the set, its intrinsic clearance will be minimally affected, as shown by the Min curve. Conversely, compounds with weak potencies (i.e., high K values) will suffer significant inhibition, as shown by the Max curve. Figure 2 also shows the danger of dosing more than about five compounds together. Frick et al. (1998a) clearly observed the effect of large cassette sizes (n = 22 versus n = 90). The half-lives of more than half of the compounds were longer in the 90-compound cassette compared with the 22-compound cassette. Thus, the true limitation on maximum cassette size is the increased danger of pharmacokinetic drug-drug interactions as n increases.
Dependence of fractional intrinsic clearance on the total number of drugs that are coadministered.
Three cases are shown in which the reference compound is the most potent inhibitor (Min; open circles), the weakest inhibitor (Max; closed triangles), or all compounds have equal inhibitory potency (Equal K 's; closed circles). For these simulations, a set of 10 compounds was chosen with K values distributed randomly above and below K1(K1 … K10 = 1, 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10) and concentrations equal to 10% of K1. For the specific n values, subsets of the full set were taken, as follows: (n = 2: 0.1 and 10); (n = 3: 0.1, 1, and 10); (n = 6: 0.1, 0.3, 1, 2, 3, and 10); (n = 10: 1, 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, and 10); (n = 20, 30, 60, and 1000, multiples of the entire set).
Assumption 4. Errors can be detected by including a benchmark compound with known pharmacokinetic characteristics.
Including a benchmark compound (also called a biological internal standard) is commonly used to safeguard the accuracy of the results (McLoughlin et al., 1997; Olah et al., 1997; Adkison et al., 1998; Allen et al., 1998; Frick et al., 1998a; Bayliss and Frick, 1999; Shaffer et al., 1999; Tong et al., 1999; Rano et al., 2000). If the benchmark compound gives comparable data in the cassette experiment versus individual dosing, then it is presumed that no drug-drug interactions occurred. However, this assumption is not always true. Referring again to Fig. 2, we can see that a benchmark compound may show little change in its own clearance if it happens to have one of the lower K values for the drug-metabolizing enzyme involved. With n = 3, the Min curve shows only about 5% error, even though other members of the same cassette could have experienced intrinsic clearance reductions as large as 52%, as shown by the Max curve.
We will refer to the deviation between the pharmacokinetic parameters for the benchmark compound from the cassette-dosed experiment compared with those from the individual dosing as the “benchmark error”. In Table 1, we can see examples of benchmark errors ranging from 0 to 220%. Note that some cassettes with only a small benchmark error may still profoundly inhibit the test compounds (Allen et al., 1998; Shaffer et al., 1999). Conversely, Fig. 2 shows that some compounds in a cassette with a large benchmark error may still give correct results if the benchmark compound had a much higher K value than other members of the cassette. Clearly, then, one cannot absolutely rely on a benchmark compound to detect drug-drug interactions.
Assumption 5. Drug-drug interactions can lead only to false positives, which will be discovered later.
A false positive is a result in which a compound appears to have acceptable pharmacokinetic characteristics when dosed in a mixture but would be identified as unacceptable if dosed singly. Mutually competitive inhibitors of elimination pathways tend to decrease clearance and thereby increase plasma levels and AUC. This may be acceptable in a screening mode, since it will tend to produce false positives, which will be corrected in the later single-compound pharmacokinetics determination.
A false negative is a result in which a compound appears to be unacceptable when dosed in a mixture but would be identified as acceptable if dosed singly. These are more serious than false positives, because there is no mechanism for correction, so that such compounds will be discarded without further testing.
Assumption 5, although stated by several authors (Frick et al., 1998a; Bayliss and Frick, 1999; Watt et al., 2000), is the easiest to dispel. For the purpose of this discussion, we can equate a false negative with an increasein clearance. The inhibitory effects discussed so far result in a decrease in clearance. However, a brief consideration of pharmacokinetics immediately reveals several situations that could lead to false negatives:
- 1.
- For drugs that are restrictively cleared (i.e., only the nonprotein bound fraction is subject to clearance), clearance can be overestimated by displacement from protein binding leading to higher fu and higher effective clearance (see further discussion of this phenomenon below);
- 2.
- If both i.v. and p.o. doses are used, F will be underestimated if AUCiv is increased proportionally more than AUCpo, implying that CLiv is decreased proportionally more than CLpo. Unfortunately, this is exactly what happens when one or more of the drugs has less than complete oral absorption because less total drug is delivered systemically after the oral dose. In that case, less inhibition of intrinsic clearance occurs after the oral dose because the p.o. inhibitor concentration term in eq. 11 is less than the i.v. concentration term, i.e.,
- 3.
- Clearance can be higher in cassette dosing than in single-compound dosing if the compounds being screened are agents, such as vasodilators, that increase liver blood flow. As seen in the clearance equation below, for high-clearance drugs the actual clearance is determined by hepatic blood flow (QH) (Gibaldi and Perrier, 1982). Thus, any effect that increases blood flow will also increase clearance;
- 4.
- If a component of the cassette is an activator of a drug-metabolizing enzyme, the clearance of other components can be increased. For example, Tang et al. (1999) reported an increase in clearance of diclofenac when codosed with quinidine, which was attributed to an allosteric effect of quinidine on CYP 3A;
- 5.
- The clearance of a component could appear to increase in a cassette if it exhibits nonlinear pharmacokinetics and if the cassette dose is much lower than a subsequent single-component dose. For example, a compound with a low KM for the drug-metabolizing enzyme might be in the linear range at the low cassette dose but in the saturated range when dosed singly at a higher, more pharmacologically relevant dose. This apparent clearance increase is not a direct consequence of cassette dosing, since it would occur even if the compound were dosed singly at the low dose. Nonetheless, because the cassette-dosing procedure encourages the use of very low doses, we increase the risk of being misled.
Experimentally, clearance increases are, in fact, common.Olah et al. (1997) observed the clearance of the benchmark compound (as judged by AUC) to be increased more than 2-fold in about 10% of the cassettes. Similarly, Allen et al. (1998) found clearance increases ranging from 37 to 80%, affecting five of nine compounds. Frick et al. (1998a)discovered clearance increases of more than 2-fold for 4 of 21 compounds. Shaffer et al. (1999) observed that 3 of 17 compounds showed a significant increase in clearance (55, 80, and 120%, respectively) when dosed in a cassette. Thus, both theoretically and experimentally, we see that false negatives can occur.
Assumption 6. Even if the absolute values are wrong, the correct rank order will be observed.
In recognition of the unreliability of the parameter values, a frequently discussed tactic is to use cassette dosing merely to rank-order the compounds. Then, the ones with the best plasma levels are taken forward in the drug discovery program, with the assumption, implicit or explicit (Adkison et al., 1998; Allen et al., 1998), that the best compound in the cassette actually is the best compound. It should be clear from the discussion above that the drug-drug interactions have differential effects, so that each compound experiences a different reduction in clearance. Thus, eq. 11predicts that the correct rank order of AUC values will not necessarily be maintained in cassette dosing. We can compare this prediction experimentally. Berman et al. (1997) reported a reasonable maintenance of the correct order of clearances comparing cassette with individual dosing. They found that the correct order (high to low) of 2, 4, 3, 1, 5 was modified to 3, 2, 4, 1, 5 in the cassette experiment. Allen et al. (1998) observed that the correct order (high to low) of rat plasma AUC values for a series of compounds (43, 15, 41, R1, 7, 2, 13, 44, 42) was distorted to 43, R1, 41, 42, 2, 44, 7, 15, 13. Shaffer et al. (1999) also reported some distortion of the order (high to low) of clearance values, from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 to 1, 3, 4, 2, 7, 5, 8, 6, 10, 9. Finally, considerable discrepancy in order was seen in the work of Bayliss and Frick (1999); the compound with the highest plasma level in the cassette experiment was only the ninth highest according to individual dosing. These experiments verify the prediction of eq. 11 that the correct rank order will not necessarily be preserved in cassette dosing.
High- versus Low-Clearance Drugs.
Are the drug-drug interactions predicted by eq. 11 more important for high-clearance or low-clearance drugs? Returning to our original endpoint of absolute bioavailability (eq. 4) and assuming for simplicity no plasma protein binding, we get
As seen in Fig. 3, at all points the F measured for Drug 1 will be an overestimate of the true value in the case of cassette dosing. The inset to Fig. 3 shows that the relative error is highest for high-clearance drugs. However, the significance of the error must also be considered. When we remember that cassette dosing will only be used for screening purposes, we realize that overestimates in most portions of the curve will be of little consequence. Compounds that pass the screen will be measured rigorously later for an accurate determination of F. The purpose of the screening procedure is to quickly identify the compounds with low bioavailability (due to low absorption or high clearance) so that no further resources are wasted on them. Accordingly, Fig. 3 also shows a horizontal dashed line corresponding to an arbitrary cutoff criterion for the screening procedure. In this example, the cutoff has been set at F = 0.1, but it might have any value of F, as determined by the requirements of the therapeutic area. It should be obvious that errors in points near the cutoff linedo have consequences. Specifically, we can see that the compounds with CLi values of 10 and 20 have true F values below the cutoff line and should have been screened out, but would have been retained because the apparent Fvalues were above the line (i.e., they were false positives). The important point to be seen is that, for screening purposes, the only errors of consequence will be those that cause a point to fall on the incorrect side of the cutoff line, and in the case of clearance reductions this occurs with high-clearance compounds. In the example of Fig. 3, only two of eight compounds were misassigned because of their proximity to the cutoff line. However, in a real situation the percentage of false positives is likely to be higher because screening is most likely to be used with a class of compounds that exhibits high clearance and/or low absorption.
Error in estimates of bioavailability of a reference drug in the absence (F) or presence (F*) of nine other competing drugs as a function of intrinsic clearance of the drug.
For this simulation, a set of 10 compounds was chosen with K values distributed randomly above and below K1(K1 … K10 = 1, 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10) and concentrations equal to 10% of K1. Bioavailability for each value of CLi was calculated as shown in the text. The dashed horizontal line corresponds to an arbitrary screening cutoff criterion of 10% bioavailability. Compounds falling below this line would be eliminated by the screening procedure. Inset, relative error was calculated by (F* − F)/F × 100%.
Plasma Protein Binding.
Cassette dosing can potentially cause an increase in clearance if one or more compounds in the cassette are restrictively cleared (i.e., only the unbound fraction in plasma is subject to clearance). This effect arises because competition for binding sites will occur with every protein with which a set of similar compounds interacts. Obviously, just as with the metabolic enzymes, compounds with higher affinity for plasma proteins will displace those with lower binding. However, in exact analogy to binding of compounds to the metabolic enzymes, competition among the cassette components for binding to plasma proteins such as serum albumin will also be governed by a ΣC/K term. Thus, even compounds with lower affinity than Drug 1 will tend to displace when their aggregate concentration is high. Provided that the drug concentration is in the constant protein-binding range, the unbound fraction (fu) is given by eq. 16 (see Appendix
).
Increase of unbound fraction (fu) of a reference drug due to competition by n coadministered drugs.
The value of fu at each value of n was calculated according to eq. 16 by setting all concentrations and all Kd values at 10 μM and assuming 600 μM plasma protein. These values of C and Kd correspond to 98.4% protein binding in the absence of other competing drugs (i.e., n = 1).
Figure 5 shows the effect on clearance of a restrictively cleared drug caused by an increase in free fraction due to multiple competing drugs. In this case, because the intrinsic clearance was assumed to be twice blood flow (i.e., 2 Q), the net clearance asymptotically approaches 0.67 Q. The net clearance changes from 0.03 Q when dosed singly to 0.22 Q when dosed in a set of 10 drugs, a 7-fold increase in clearance, and rises by about 20-fold with cassettes approaching 100. As noted in Table 1, cassettes of this size have already been reported, and the trend seems to be for cassettes to become even larger as analytical capabilities improve. Thus, the increased clearance effect of cassette dosing through decreasing protein binding is similar in magnitude but opposite in direction to the effect on clearance produced by competition for drug-metabolizing enzymes. The increased clearance will be manifest in greater systemic elimination of the affected drugs. To the extent that plasma protein binding is established and equilibrated during the short transit of the drugs through the portal vein during the first pass following absorption, this increase in clearance may also apply to first-pass elimination, thereby affecting F as well.
Increase of CL of a restrictively cleared reference drug due to increase of unbound fraction caused by n coadministered drugs.
Simulation parameters for protein binding were as in Fig. 4. Clearance was calculated according to eq. 13 assuming CLi= 2 QH. Dashed line, the asymptote of 0.67 QH discussed in text.
Reconciliation with Published Results.
The preceding section shows the potential for large errors when applying cassette dosing. However, several accounts have been published in which good results have been claimed, as judged by comparison of pharmacokinetic parameters calculated from multiple- and single-compound dosing (Berman et al., 1997; Olah et al., 1997; Allen et al., 1998; Frick et al., 1998; Shaffer et al., 1999). The available data are compiled in Table 1. How can we reconcile the conclusions from eq. 11 and these published results? To begin, let us explicitly recognize that the derivation of eq. 11 assumed that clearance of all drugs in the set is due to metabolism. Therefore, if other clearance pathways are available to some drugs in the set, net clearance of those drugs may be relatively insensitive to competitive inhibition of only a single enzyme. In addition, eq. 11 refers only to intrinsic clearance, so drugs whose clearance is limited by blood flows may show little effect on net clearance even though their intrinsic clearances have been reduced. Also, many other physiological processes that contribute to the absorption, distribution, and elimination of drugs are potentially subject to the same drug-drug interactions that have been described here for metabolism (see Table2). Each process that is mediated by a protein (i.e., each saturable process) may potentially be modulated by competition between different drugs, and the net result will be difficult to predict.
Potential drug interactions resulting from cassette dosing
A final consideration may be deemed “literature bias,” referring to the fact that the published literature probably does not reflect all instances of the use of cassette dosing. Cases in which the technique has given good results will tend to be published, while those cases in which a poor concordance was observed are unlikely to be published. Nonetheless, examples of considerable discrepancy between pharmacokinetic parameters have been published. For instance,Berman et al. (1997) reported mixed results from dosing of five α1-adrenoceptor antagonists with errors in clearance ranging from −40 to +81%, but with three of the five values within 20% of the true value. Olah et al. (1997)reported that the AUC of a particular compound varied from 2.1 to 10.9 μM · h, depending on the particular cassette of 10 compounds with which it was dosed, while the true value was 3.4 μM · h. Thus, in that study, the errors ranged from −38 to +320%. The largest excursion from the true value reported to date is +660% for a compound dosed in a cassette of five compounds (Allen et al., 1998). Several other studies have been disclosed, but only as abstracts, not full papers (for a compilation, see Bayliss and Frick, 1999).
It is clear from this discussion how different investigators can come to different conclusions regarding the reliability of the data from cassette dosing. However, the reports of distorted data from cassette dosing show that the effects predicted by eq. 11 are real and will occur if the conditions are met. The difficulty, then, in applying cassette dosing to a drug discovery campaign is to know in advance whether the conditions for eq. 11 to be important are present in the case at hand. There is, of course, no way to be assured of the lack of drug-drug interactions without doing extra experimental work, which means that the investigator has to choose between taking a risk with the accuracy of the data or delaying the delivery of results until confirmation can be obtained. Neither of these options is compatible with reliable, high-speed screening. To provide a viable third option, an alternative procedure combining the principle of “one compound per animal” with throughput equal to or exceeding that of cassette dosing has recently been devised (Korfmacher et al., 2001).
“Right Box” Analysis.
Another measure of success of a screening method is the placement of the test compound into the correct category, something we can call the Right Box approach. A pharmacokinetic parameter that can be interpreted in an absolute sense, such as clearance, is divided into three categories: low, medium, and high. For instance, we can (somewhat arbitrarily) define low, medium, and high clearances as <10, 10 to 20, and >20 ml/min/kg, respectively, in dogs based on the hepatic extraction ratios falling into the ranges of 0 to 0.3, 0.3 to 0.7, and 0.7 to 1.0 according to the relationship EH = CL /Q. The observed clearance values calculated from both individual and cassette-dosed experiments are then plotted as shown in Fig. 6. Boxes are defined by the areas enclosed by the boundaries for low, medium, and high clearances. Data points that fall within these areas (the right box) are scored as successful. Three of the published papers provided enough data for a Right Box analysis on clearances5. As seen in Table1, Right Box success rates were 80, 86, and 100% in those studies. This suggests that if one is willing to accept gross categorization as an endpoint of the screening process, then cassette dosing may be an adequate procedure despite large absolute errors. Unfortunately, too little data have been published to allow us to judge whether cassette dosing is always successful in the Right Box approach. This is clearly an area where additional data sets would be a valuable contribution to the literature.
Right Box analysis.
Success of cassette dosing in correct clearance classification of compounds. In this case, only 3 of 21 points did not fall into a box, corresponding to 86% success (data points taken from Frick et al., 1998a).
Conclusions
Although cassette dosing has been reported to yield useful results when used as a screen, especially to rank-order drug candidates, we have shown both theoretically and experimentally the potential for large errors. Consequently, under no circumstances can the pharmacokinetic parameters derived from cassette dosing be accepted as accurate. Potentially affected parameters include F, CL, AUC, t1/2, mean residence time, Vd. High-clearance compounds have the greatest potential for a serious screening error (i.e., false positive, false negative). To detect serious errors, we could use a second dosing episode, either in a different cassette or as a single-compound dose. Obviously, a second dosing defeats the productivity gain of cassette dosing. A better way to detect errors is to include a benchmark compound with known in vivo pharmacokinetics, but we have shown that this is no guarantee. To minimize the potential for errors, one should use the smallest doses detectable and keep the total number of coadministered compounds small.
Acknowledgments
We are grateful to Dr. Anthony Y.H. Lu for encouragement and for critical reading of the manuscript.
Intrinsic Clearance of a Drug in the Presence of Multiple Drugs Which Are Competitive Enzyme Inhibitors
Let D1 represent a drug that is metabolized by an enzyme (E). Let D2, D3, … Dn represent n − 1 other drugs that also bind to E and are present at concentrations C2, C3, … ,Cn. Making the usual assumption of rapid equilibration of binding to the enzyme of all drugs, we can write the concentration of each enzyme-drug complex (ED) in terms of the respective free drug concentration and equilibrium constant (K).
Competitive Plasma Protein Binding by Multiple Drugs
The binding of a drug to a protein with one independent binding site is described by an equilibrium dissociation constant (Kd).
Footnotes
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↵2 An important drug-metabolizing enzyme, CYP3A4, has been shown recently to have non-Michaelis-Menten kinetics (Houston and Kenworthy, 2000; Wang et al., 2000). A different enzyme rate equation applies to CYP3A4, but the general derivation being followed here would still be valid.
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↵3 We can rigorously use the plasma concentration of the drug as a surrogate for the true intracellular concentration of drug seen by the enzyme by assuming rapid equilibration of plasma and hepatic concentrations and by expressing K values in terms of the corresponding plasma concentrations.
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↵4 In general, compounds will not conveniently be at concentrations equal to their K values, and concentrations will not be equal to one another unless the volumes of distribution are equal. However, choosing a special case for ease of calculation does not alter the conclusions, since C is an explicit term for each compound in the equations.
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↵5 A fourth paper, shown in Table 1 (Ward et al., 2001), was not included in this statement because the screening method that was used combined cassette dosing with a pharmacokinetic approximation so that results falling outside the right box (29%) cannot be clearly ascribed to the cassette dosing.
- Abbreviations used are::
- F, oral bioavailability
- AUC, area under the plasma concentration versus time curve
- CL
- plasma clearance
- ED
- enzyme-drug complex
- Received June 6, 2000.
- Accepted March 7, 2001.
- The American Society for Pharmacology and Experimental Therapeutics
