Introduction

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In recent years, kinetic measurements using liver microsomes have been increasingly used as a measure of the rate of metabolic drug oxidation in drug discovery. The results from these in vitro assays are then frequently processed, through a variety of methods, to produce predictions of the in vivo metabolic clearance of compounds in humans (Iwatsubu et al., 1997; Obach et al., 1997; Lave et al., 1999). Methods that are often used for scaling such in vitro data to in vivo predictions are the well stirred model and the parallel tube model, and these models contain plasma free fraction terms that account for the effect of plasma binding on the clearance of compounds (Pang and Rowland, 1977). However, it is frequently found that inclusion of the plasma binding correction can lead to underprediction of the in vivo clearance, particularly for nonacidic compounds, and better performance can often be obtained by ignoring the correction altogether (Obach 1997, 1999; Obach et al., 1997). It has been recognized that nonspecific microsomal binding in the in vitro metabolic assays can significantly affect the observed kinetics of metabolism and hamper the accurate prediction of clearance, and there are now several examples where knowledge of the extent of microsomal binding can lead to a better understanding of the relationship between in vitro metabolism and in vivo pharmacokinetics (Lin et al., 1978, 1980; Bäärnhielm et al., 1986; St-Pierre and Pang, 1995; Obach, 1996, 1997, 1999; Carlile et al., 1999). It has been reinforced by several studies (Houston, 1994; Obach, 1996; Iwatsubu et al., 1997) that unbound intrinsic clearance (CL_int,U) is for many compounds not the same as the experimentally observed intrinsic clearance (CL_int) and that the two are related by eq. 1:

(1)

where V_max is the maximum velocity, K_M is the Michaelis constant based on free substrate concentrations, and fu_inc is the free fraction of compound in the microsomal incubation. CL_int is not a constant for a particular compound, but is a function of the microsome concentration, and is not an ideal parameter for use in predictions of in vivo clearance. However, for some compounds, the observed CL_int does fortuitously lead to good predictions of in vivo clearance (Obach et al., 1997; Obach, 1999). When eq. 1 is substituted into the well stirred model, the predicted in vivo clearance is given by eq. 2 (Obach, 1996):

(2)

where A is a constant representing the milligrams of microsomes per gram of liver, B is a constant describing the grams of liver per kilogram of body weight, Q represents liver blood flow, fu_p is the free fraction of the compound in plasma, and fu_inc is the free fraction of the compound in the microsomal incubation. From eq. 2, an interpretation of why CL_int can provide good predictions of clearance can be given, because such good predictions could be the result of a compound that has similar binding to plasma and to microsomes at the microsomal concentration used for the measurement of CL_int, leading to the cancellation of the fu_p/fu_inc ratios in eq. 2. Using measured values of fu_p and fu_inc, it has been shown that eq. 2 could be of more general utility in the prediction of clearance than either the well stirred model containing no free fraction corrections or only the fu_p correction (Obach, 1999).

Knowledge of fu_inc has also been shown to be important for the prediction of in vivo drug-drug interactions, where inhibition constants (K_i) have been converted to unbound K_i values followed by plasma binding corrections, leading to improved predictions of changes in area under the curve upon coadministration of drugs (Ishigam et al., 2001).

If eq. 2 is to be more widely used for clearance predictions and if unbound K_i values are going to be more commonly used then it would be advantageous to be able to predict the fu_inc term from readily available physicochemical properties of compounds such as lipophilicity. Several studies have examined the extent of nonspecific microsomal binding of various compounds, and how this binding affects the observed kinetics of turnover of these compounds by the microsomes, and the quality of in vivo prediction (Obach, 1997, 1999; Carlile et al., 1999; Mclure et al., 2000; Venkatakrishnan et al., 2000; Kalvass et al., 2001). However, these studies have used a variety of microsomal protein concentrations, and the resulting data are consequently unsuitable for finding predictive quantitative relationships between the physicochemical properties of the compounds and the extent of microsomal binding. To find such relationships, data are required on a set of compounds with a variety of physicochemical properties, and where the binding is measured under identical conditions of microsomal protein concentration, which is the main purpose of this work.

	Materials and Methods

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Materials. Frozen hepatic microsomes from male Sprague-Dawley rats at a protein concentration of 20 mg/ml were obtained from In Vitro Technologies (Baltimore, MD). The same batch of microsomes was used for all of the studies and was stored at 80°C. 1-Octanol was obtained from Fisher Scientific (Loughborough, UK). -NADPH, 2-ethoxybenzamide, albendazole, alprazolam, amiodarone, astemizole, bumetanide, carbamazepine, cinoxacin, clomipramine, clozapine, colchicine, desipramine, glipizide, glyburide, ibuprofen, indapamide, indomethacin, ketoprofen, mebendazole, methocarbamol, methoxsalen, metyrapone, pimozide, piroxicam, prednisone, promethazine, propafenone, propranolol, quinidine, sulindac, tamoxifen, thioridazine, tolbutamide, tolmetin, triazolam, trimeprazine, trioxsalen, verapamil, and warfarin were obtained from Sigma Chemical (Poole, Dorset, UK). Oxaprozin was obtained from Maybridge Chemicals (Trevillet, UK). Betaxolol, cerivastatin, chlorpromazine, diazepam, dichloralphenazone, diclofenac, diltiazem, diphenhydramine, imipramine, isradipine, losartan, phensuximide, and sulfadoxine were obtained from the AstraZeneca compound collection.

Instrumentation. All sample handling was performed using a Genesis RSP 100 liquid handling robot (Tecan, Durham, NC) fitted with disposable tips and controlled by Gemini software. Centrifugations were carried out using an Allegra R6 (Beckman Coulter, Inc., Fullerton, CA). A Dianorm (Munich, Germany) system with cells of 1-ml volume was used for equilibrium dialysis experiments, along with cellulose membranes (Diachema AG, Zurich, Switzerland) with molecular weight cut off of 5 kDa. All HPLC¹analyses were carried out using a 2700 autosampler, a 2690 separations module (both from Waters, Milford, MA) and a ZMD mass spectrometer (Micromass, UK Ltd., Manchester, UK) using a selected ion recording quantitation method. Symmetry C₈ (5 µm × 3.9 mm × 20-mm columns; Waters) were used along with a gradient of 1% actonitrile/99% 0.05% aqueous ammonium acetate to 99% actonitrile/1% 0.05% aqueous ammonium acetate at a flow rate of 2 ml/min over 3.5 min.

Microsomal Incubations. Five microliters of 100 µM compound solutions in DMSO was transferred to glass vials held in a thermostatically controlled metal incubation block heated at 37°C. To these same vials was also added 395 µl of microsomes of the appropriate concentration suspended in 0.1 M phosphate buffer, pH 7.4. The drug and microsome mixtures were then mixed thoroughly and left to equilibrate for approximately 3 min. After this equilibration period, the metabolic reactions were initiated by the addition of 100 µl of -NADPH solution at a concentration of 50 mM in 0.1 M phosphate buffer, pH 7.4. At eight time points, covering a range of 3 min for the most rapid reactions, and up to 90 min for the slowest reactions, 50-µl aliquots of this mixture were then removed and quenched by addition to 300 µl of methanol that contained an appropriate internal quantification standard compound (indomethacin or 2-ethoxybenzamide) at a concentration of about 0.25 µM. The plate of quenched samples was then centrifuged at 300g and 5°C for 20 min to sediment the precipitated proteins before quantitation using HPLC/MS. The kinetic data were analyzed using a linear fit of the natural logarithm of the ratio of the compound peak area to the internal standard peak area against time. Using the assumption that the substrate concentration of 1 µM is well below the apparent K_m, CL_int values were then calculated from the negative slope of the linear fit divided by the microsomal concentration (Obach et al., 1997).

Measurement of Microsomal Binding. The extent of binding of compounds to microsomes was determined using equilibrium dialysis of five compounds (each at a concentration of 1 µM) simultaneously in each dialysis cell. The mixtures of compounds were chosen such that all compound masses were at least 5 Da apart, allowing resolution of the compounds during MS quantification.

Measurement of LogD_7.4. Partitioning of compounds (40-400 µM) between 1-octanol and 0.02 M phosphate buffer, pH 7.4, at 20°C was determined using a standard shake flask method (Leo et al., 1971). Samples were analyzed by HPLC with MS quantitation of both layers of the partition mixture.

Model for Microsomal Binding. The most simple model for describing the binding of drugs to microsomes is to treat the system as a phase equilibrium, in the same way that drug binding to liposomes is normally described (Austin et al., 1995). The drug is assumed to be in equilibrium between an aqueous phase and a microsomal phase, and the equilibrium is described by a partition coefficient K_mics given by eq. 3:

(3)

where [drug]_mics and n_mics are the concentrations and amounts of drug in the microsomal phase, [drug]_aq and n_aq are the concentrations and amounts of drug in the aqueous phase, V_aq is the volume of the aqueous phase and V_mics is the volume of the microsomal phase. If we now let r be equal to the ratio of aqueous to microsomal phase volumes V_aq/V_mics at a 1 mg/ml microsomal concentration then eq. 3 becomes the following:

(4)

where C_mics is the microsomal concentration in micrograms per milliliter. Equation 4 can now be used to relate the value of n_mics/n_aq at one microsomal concentration (C₁) to the value of n_mics/n_aq at another microsomal concentration (C₂) as shown by eq. 5:

(5)

Equation 5 now needs to be expressed in terms of free fractions rather than ratios of amounts in each phase. The definition of free fraction is given by eq. 6:

(6)

because V_aq V_mics at typical microsomal concentrations, eq. 6 can be simplified to give eq. 7:

(7)

Equation 7 can now be rearranged to give eq. 8:

(8)

Equation 8 can now be substituted into eq. 5, followed by rearrangement, to give eq. 9, which is an expression for the free fraction at a second microsomal concentration (fu₂) in terms of the observed free fraction at a first microsomal concentration (fu₁) and the second and first microsomal concentrations (C₂ and C₁):

(9)

	Results

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A set of 13 compounds was selected that covers a range of lipophilicity (logD_7.4 ranges from 0.3 to >5) and ionization class (five neutral, four acidic, and four basic). Acids are defined as compounds with a pK_a for the formation of an anion of <7.4, and bases are defined as compounds with a pK_a for the formation of a cation of >7.4. The kinetics of metabolism of these compounds was determined using the in vitro half-life approach (Obach et al., 1997) with rat liver microsomal protein concentrations of 0.25, 1, and 4 mg/ml. The extent of binding of compounds, fu_inc, was determined at these same microsomal protein concentrations using equilibrium dialysis. In the dialysis experiments, -NADPH was omitted such that metabolism of the compounds did not occur. The results of these experiments are listed in Table 1.

Of the 13 compounds in Table 1 it was found that some of them had an approximately constant CL_int at the three different microsomal concentrations. An example of this type of behavior is given by bumetanide where CL_int = 157 ± 6 (microliters per minute per milligram of protein) at 0.25 mg/ml, 122 ± 7 at 1 mg/ml, and 121 ± 21 at 4 mg/ml. The other extreme of observed behavior is exemplified by compounds such as astemizole, where the CL_int values decrease with increasing microsomal concentration. These different types of behavior correspond to differing propensity for microsomal binding. According to eq. 1 the correctly defined intrinsic clearance, which is equal to the observed intrinsic clearance divided by the free fraction of compound in the incubation medium, should be constant. The data in Table 1 shows that such values of CL_int,U are much closer to being constant than the values of CL_int. Figure 1A shows a plot of logCL_int at 1 mg/ml microsomal protein against logCL_int at 0.25 mg/ml, where the error bars indicate 95% confidence intervals calculated from the four replicate data points. If logCL_int were constant then the points would lie along the indicated line of unity, but clearly several of the compounds deviate away from the line of unity, often very strongly. In contrast, Fig. 1B is a plot of logCL_int,U at 1 mg/ml microsomal protein against logCL_int,U at 0.25 mg/ml, where the error bars indicate 95% confidence intervals propagated from the 95% confidence intervals calculated from the four replicate CL_int values and the four replicate fu_inc values. Most of the compounds lie on the indicated line of unity within experimental error, whereas the remaining compounds only show small deviations.

View larger version (10K): [in this window] [in a new window]   Fig. 1.   Plots of intrinsic clearance data, and unbound intrinsic clearance data using different concentrations of rat liver microsomes.

The microsomal binding data in Table 1 can be used to develop a better understanding of how the extent of microsomal binding depends on microsomal protein concentration. A simple model for microsomal binding has been developed that treats the system as a microsome/buffer phase equilibrium (under Materials and Methods, eqs. 3-9). From this model of binding, it is possible to estimate the extent of microsomal binding at one microsomal concentration from the observed extent of binding at a different microsomal concentration using eq. 9. From the data in Table 1, eq. 9 was used to estimate fu_inc at one microsomal concentration from that observed at a different concentration, and Fig. 2 shows a plot of the resulting predictions. The data points scatter fairly evenly about the indicated line of unity, and the average deviation in the predicted fu_inc values is only 15%. The simple phase equilibrium model therefore seems be a good model for microsome binding.

View larger version (16K): [in this window] [in a new window]   Fig. 2.   Plot of observed fuinc against fuinc predicted from measurement at different microsomal concentrations using eq. 9.

The binding data at 1 mg/ml microsomal protein concentration in Table 1 was augmented with binding measurements on a further set of 25 compounds, and with logD_7.4 measurements on the full set of 38 compounds. Microsomal binding data for the full set of compounds is shown in Table 2 along with logP, logD_7.4, and pK_a data. Table 2 also contains microsome binding data from Obach (1997, 1999). Most of the additional data from Obach is from human liver microsomes, whereas the current study has used rat liver microsomes. However, it has been shown that the extent of microsome binding shows very little difference between human, rat, dog, and monkey (Obach, 1997). The Obach data were determined using a variety of microsomal protein concentrations between 0.3 and 10 mg/ml, and any data not determined at 1 mg/ml have been converted to an estimated extent of binding at 1 mg/ml using eq. 9. The combination of our data with Obach's produces a microsomal binding data set on 56 compounds of diverse structure where all of the data are either measured at 1 mg/ml microsomal protein or have been converted to 1 mg/ml using a method that has been shown to work reliably.

The extent of nonspecific binding to microsomes is expected to be dominated by lipophilicity. Figure 3 shows a plot of log((1  fu_inc)/fu_inc) against logD_7.4. The microsomal binding data are plotted in this way because (1  fu_inc)/fu_inc is similar to an equilibrium constant (eq. 8), which is the appropriate property to use when searching for linear free energy relationships. Figure 3 shows a strong relationship between microsomal binding and logD_7.4. The extent of microsomal binding generally increases with increasing lipophilicity, but basic compounds clearly show enhanced binding over neutral or acidic compounds of similar lipophilicity. This is expected because it has been shown that basic compounds exhibit enhanced affinity for phospholipid membranes, compared with octanol, as demonstrated by liposome binding studies (Austin et al., 1995; Krämer et al., 1998). To account for the pattern shown in Fig. 3, a modified lipophilicity descriptor has been introduced that accounts for the enhanced microsomal binding of basic compounds. This descriptor will be called logP/D and corresponds to logP for basic compounds and logD_7.4 for acidic and neutral compounds (note, logD_7.4 = logP for neutral compounds). Figure 4 shows a plot of log((1  fu_inc)/fu_inc) against logP/D, where only those compounds with fu_inc < 0.9 have been included. This is because it is very difficult to discriminate between compounds with free fractions between 0.9 and 1.0 using equilibrium dialysis, and it is not important to model this range of binding because all of these compounds are close to 100% free. Using the logP/D descriptor, Fig. 4 shows a much better correlation than that in Fig. 3. The logP/D descriptor has collapsed the separate acid/base/neutral behavior shown in Fig. 3 into a single trend of high statistical significance. The equation of the least-squares regression line in Fig. 4 is given by eq. 10:

View larger version (13K): [in this window] [in a new window]   Fig. 3.   Plot of log((1  fuinc)/fuinc) against logD7.4 from data in Table 2.

View larger version (13K): [in this window] [in a new window]   Fig. 4.   Plot of log((1  fuinc)/fuinc) against logP/D from data in Table 2 where fuinc < 0.9.

	Discussion

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When one wishes to scale in vitro metabolic kinetic data to in vivo clearances, the issue of nonspecific microsomal binding needs to be addressed in addition to the plasma or blood binding that is more frequently incorporated into the scaling method. It has been demonstrated that eq. 2 could be of more general utility in the prediction of clearance than either the well stirred model containing no free fraction corrections, or only the fu_p correction (Obach, 1999). Cancellation of the fu_p/fu_inc ratios cannot be relied upon, particularly because fu_inc can depend strongly on the microsomal protein concentration that one chooses to use as shown in Table 1 and by other studies (Obach, 1996, 1997; Mclure et al., 2000; Venkatakrishnan at. al., 2000). If eq. 2 is to become more widely used for in vivo clearance prediction, a better understanding of how nonspecific microsomal binding depends on microsomal protein concentration and on chemical structure is required. The ultimate goal would be to predict the extent of microsomal binding at any microsomal concentration purely from properties calculated from chemical structure, but the ability to estimate microsomal binding using commonly measured properties such as octanol-water partition coefficients would be very useful. The fact that equilibrium dialysis experiments have not nearly reached the high capacity and highly automated efficiency of microsomal intrinsic clearance assays is also a strong driving force for the generation of an alternative method for the estimation of fu_inc.

The important role that microsomal binding has in influencing the observed rate of in vitro metabolism has been clearly illustrated by the results in Table 1 and Fig. 1, A and B. For some compounds CL_int can differ from CL_int,U by a very large amount. For example, at 4 mg/ml microsomal protein amiodarone seems to be metabolically rather stable with CL_int = 3 µl min¹ mg protein¹, whereas CL_int,U was ~16,000 µl min¹ mg protein¹, a greater than 5000-fold deviation. Amiodarone is therefore intrinsically very metabolically labile, presumably a consequence of its high lipophilicity, leading to high affinity for the binding sites of metabolizing enzymes. However, the high lipophilicity also leads to a very large amount of nonspecific binding to the microsomes, which leads to a huge reduction in the observed rate of metabolism. The importance and validity of eq. 1 have previously been demonstrated using full determinations of V_max and apparent K_m (Obach, 1997; Venkatakrishnan et al., 2000; Kalvass et al., 2001) on limited numbers of compounds. This study has used the in vitro t_1/2 method, the most frequently used method for metabolic screening in drug discovery research, to further highlight the importance of eq. 1 using a wider set of compounds.

In addition to the well established dependence of fu_inc on microsomal protein concentration, it is also possible that fu_inc depends on the compound concentration, and also that the binding is saturable. It has been shown that the microsomal binding of phenytoin and tolbutamide (Carlile et al., 1999), amitriptyline (Venkatakrishnan et al., 2000), and imipramine and propranolol (Obach, 1997) is independent of compound concentration over the range of concentration studied (up to 1000 µM). Evidence for concentration dependence has been shown for nortriptyline (Mclure et al., 2000) and for warfarin (Obach, 1997). However, the observed concentration dependence is weak in both cases. It therefore seems that nonspecific microsomal binding is normally independent of compound concentration and that saturation of the binding does not occur at the low micromolar concentration levels used in modern metabolic assays, which use sensitive MS detection. If strong concentration dependence were frequently observed then the commonly used description of the process as nonspecific microsomal binding would clearly be inappropriate. The type of model involving defined binding sites (Romer and Bickel, 1979) that has been suggested as appropriate for modeling microsomal binding of drugs (Mclure et al., 2000; Kalvass et al., 2001) seems to be unnecessarily complicated. Binding that is independent of compound concentration is indicative of a phase equilibrium-type process, where clearly defined individual binding sites do not exist, much like organic/aqueous partitioning systems. The success of this model of microsomal binding (eq. 9) is shown by the quality of the predictions in Fig. 2. It therefore seems that eq. 9 represents a suitable general model for the description of microsomal binding, particularly when the drug concentration is low, and should be of general use for converting microsomal binding data between different microsomal protein concentrations.

Equation 9 has been used to augment our own microsomal binding data set of 38 compounds all measured at 1 mg/ml microsomal protein with literature data on 18 further compounds, leading to a fairly large data set suitable for finding a structure-binding relationship. The enhanced binding shown by basic compounds in Fig. 3 led us to search for a more suitable lipophilicity-related descriptor. The enhanced phospholipid binding of compounds containing protonated basic groups is thought to be due to a favorable electrostatic interaction between the protonated base and phosphate groups on the phospholipid (Austin et al., 1995; Krämer et al., 1998). A result of this is that phospholipid membrane affinity at pH 7.4 for basic compounds is much closer to the octanol-water logP of the molecule than to logD_7.4, whereas for acidic molecules (where only the neutral form of the molecule has significant membrane affinity) the membrane affinity at pH 7.4 is much closer to the octanol-water logD_7.4 than logP (Austin et al., 1995). Therefore, because the affinity of compounds for microsomes is likely to be dominated by the affinity for the phospholipid membrane content of the microsomes, this should be best modeled by octanol-water logP for bases and by logD_7.4 for acidic and neutral (note, logD_7.4 = logP for neutral compounds) compounds. This descriptor will be called logP/D and does indeed lead to a much better correlation with extent of microsomal binding (Fig. 4; eq. 10).

The correlation shown in Fig. 4 seems to be of higher quality where logP/D > 2, and this may be due the equilibrium dialysis method not being able to accurately distinguish between the low levels of binding (50-100% free) of hydrophilic compounds. For predicting the binding of more lipophilic molecules it might be better to only fit the data in Fig. 4 where logP/D > 2, and simply state that for less lipophilic molecules fu_inc > 0.5. This approach should lead to better predictions for more lipophilic molecules where fu_inc can be very small (hence corrections to CL_int would be large). Accurate prediction of microsomal binding of hydrophilic molecules is not so important because the resulting corrections to CL_int would be less than a factor of 2 (of the 56 compounds in Table 2, 28 have logP/D < 2 and none of these has fu_inc < 0.5). The correlation in Fig. 4 also seems to be better for basic compounds than for neutral or acidic compounds. Again this is likely to be due to the fact that most of the basic compounds exhibit higher binding than the neutral or acidic compounds (a large proportion of the bases have logP/D > 2), which is more easily discriminated by the equilibrium dialysis method. Equation 10 shows that microsomal binding is only significant for rather lipophilic neutral and acidic compounds (logD_7.4 > 3), but will be significant for many more basic compounds. For example, a basic compound with logD_7.4 of only 1 and pK_a of 10 will have logP = 3.6 and from eq 10 will have fu_inc of about 0.2.

The fact that the literature microsomal binding data and the data from the current study both fit well in the correlation in Fig. 4 adds validation to two important facts about microsomal binding that are emerging. First, it is consistent with the observation that microsome binding is independent of species (Obach, 1997); and second, it gives further evidence of the general utility of eq. 9 for converting data between different microsomal concentrations. Equation 10 can only predict the extent of binding to microsomes with a concentration of 1 mg/ml. However, the good correlations shown in Figs. 2 and 4 suggest that eqs. 9 and 10 can be combined to give a reliable prediction of fu_inc at any microsomal concentration from lipophilicity using eq. 11

(11)

where C is the microsomal protein concentration in milligrams per milliliter, logP/D is the logP of the molecule if it is a base (basic pK_a > 7.4), and logP/D is the logD_7.4 of the molecule if it is neutral or an acid (acidic pK_a < 7.4). Along with a knowledge of lipophilicity and ionization, eq. 11 should prove to be useful for gaining better insight into observed kinetics of microsomal metabolism, for converting CL_int data to CL_int,U, for further testing and validating models for clearance prediction such as eq. 2, and for conversion of K_i to unbound K_i as part of the process of predicting in vivo drug-drug interactions.