Prediction of in Vivo Carbamazepine 10,11-Epoxidation from in Vitro Metabolic Studies with Human Liver Microsomes: Importance of Its Sigmoidal Kinetics

Abstract

Hepatic intrinsic clearance (CL_int) of drugs is often predicted based on in vitro data that are obtained from the Michaelis–Menten analysis. While most of the metabolic rate-substrate concentration kinetic curves fit to the Michaelis–Menten equation, cytochrome P450 (CYP) and uridine 5′-diphosphate (UDP)-glucuronosyltransferases exhibit sigmoidal kinetics for certain drugs. In our study, the kinetics of CYP3A4-catalyzed carbamazepine 10,11-epoxidation in human liver microsomes was sigmoidal and fitted to the Hill equation, revealing the S₅₀ value of 358 µM, n of 2.0, and the V_max value of 463 pmol/min/mg. While the intrinsic clearance calculated from Michaelis–Menten parameters (CL_int) overestimated the observed in vivo intrinsic clearance (CL_{int, in vivo}), the maximum intrinsic clearance calculated based on the Hill equation (CL_max) exhibited better predictions of CL_{int, in vivo}. Such better prediction using the CL_max was also observed for other four drugs, all of which also exhibited sigmoidal metabolic rate-concentration curves, according to the literature data. However, even if we assume such Hill equation, intrinsic clearances predicted at their therapeutic concentrations from in vitro data were still much lower than their CL_{int, in vivo}, suggesting the existence of unknown factors causing discrepancy between in vitro intrinsic clearance in human liver microsomes and in vivo data. Thus, even if we assume sigmoidal kinetics, that would not be enough for accurate prediction of CL_{int, in vivo}, and it would be preferable to use CL_max to quantitatively extrapolate the in vitro data to in vivo clearance.

One of the ultimate goals of in vitro drug metabolism research is the prediction of in vivo clearance of drugs from in vitro data. Phase I and II drug-metabolizing enzymes such as cytochrome P450 (CYP) and uridine 5′-diphosphate (UDP)-glucuronosyltransferases (UGT) metabolize drugs to generate metabolites, which are generally pharmacologically inactive and more hydrophilic than the parent compounds, and are therefore easily excreted from the body through the kidney or the liver.^1,2) Since these metabolic processes play a central role in the clearance of drugs, the metabolic clearance of drugs, which is commonly described as an intrinsic clearance (CL_int—often estimated as the ratio of V_max to K_m), is calculated from in vitro research to estimate the in vivo clearance of the drugs.³⁾ Carbamazepine (5-carbamoyl-5H-dibenz-[b,f]azepine) is a widely used anti-epileptic drug, and the first-line drug of choice in partial epilepsy. Since its increased concentration in the blood is tightly linked to the onset of adverse effects of carbamazepine including drug addiction, the blood levels of carbamazepine are monitored so as not to exceed the therapeutic range, which is normally 4–12 µg/mL.⁴⁾ Carbamazepine is metabolized to over 30 metabolites in humans such as carbamazepine 10,11-epoxide, 2- and 3-hydroxy carbamazepine, and carbamazepine N-glucuronide.⁵⁾ Among the 30 metabolites, carbamazepine 10,11-epoxide is the major metabolite, which accounts for approximately 40% of carbamazepine metabolism.⁶⁾ The metabolism of carbamazepine to its 10,11-epoxide is mediated mainly by CYP3A4, while CYP2C8 partially contributes to the epoxidation reaction.⁷⁾ Due to the fact that carbamazepine is eliminated by hepatic metabolism, determination of the hepatic metabolism rate is especially important to predict its clearance from the body. Since CYPs and UGTs are enzymes expressed in the endoplasmic reticulum, human liver microsomes (HLMs) are used in the in vitro metabolic research to obtain the kinetic parameters of carbamazepine 10,11-epoxidation in the human liver. Recombinant systems, such as insect cells expressing human CYP3A4, are also useful to conduct in vitro kinetic analysis of drugs.

When kinetics of drug metabolism is typical and follows Michaelis–Menten kinetics, the relationship between substrate concentration and velocity is described by the Michaelis–Menten equation (Eq. 1):

  

(1)

where V is the velocity of the metabolic reaction, and S is the substrate concentration. The V_max is the maximum rate of metabolism and K_m is the Michaelis constant, which is defined as the substrate concentration at 1/2 the maximum velocity. The ratio of V to S provides the clearance (Eq. 2):

  

(2)

While the clearance is substrate concentration-dependent, it is constant when the substrate concentration is much smaller than K_m, providing the parameter, intrinsic clearance (CL_int) (Eq. 3):

  

(3)

In contrast, sigmoidal kinetics can be described by the Hill equation (Eq. 4):

  

(4)

where S₅₀ is the substrate concentration showing the 1/2 V_max and n is the Hill coefficient. The clearance of drugs whose kinetic profiles are sigmoidal can be described by Eq. 5:

  

(5)

While the clearance is substrate concentration-dependent, the maximum clearance, CL_max, can be described by Eq. 6 as demonstrated by Houston and Kenworthy⁸⁾:

  

(6)

In the present study, we carried out the kinetic analysis of carbamazepine 10,11-epoxidation in HLM and predicted the in vivo clearance of carbamazepine from data obtained in vitro.

MATERIALS AND METHODS

Chemicals and Reagents

Carbamazepine was purchased from Sigma-Aldrich (St Louis, MO, U.S.A.). Carbamazepine 10,11-epoxide was purchased from Tronto Research Chemicals, Inc. (Ontario, Canada). Glucose-6-phosphate (G6P), glucose-6-phosphate dehydrogenase (G6PD), nicotinamide adenine dinucleotide phosphate (NADP) were purchased from Roche Applied Science (Indianapolis, IN, U.S.A.). HLM was purchased from BD Gentest (Woburn, MA, U.S.A.). All other chemicals and solvents were of analytical grade or the highest grade commercially available.

Carbamazepine 10,11-Epoxidation in HLM

Incubation time (30 min) and protein concentration (0.1 mg/mL) were within the linear range for carbamazepine 10,11-epoxidation. Each incubation mixture (200 µL) contained HLM (0.1 mg/mL), reduced nicotinamide adenine dinucleotide phosphate (NADPH) regenerating system (0.33 mM NADP, 6 mM MgCl₂, 0.1 U/mL G6PD, and 8 mM G6P), and carbamazepine (125 µM to 1.5 mM) in phosphate buffer (100 mM, pH 7.4). After 5 min preincubation without carbamazepine, the reaction was started by addition of carbamazepine, and the reaction mixture was incubated for 30 min at 37°C. Carbamazepine was dissolved in methanol and the final concentration of the organic solvent in the incubation mixture was 1%. To understand the inhibitory effects of different types of organic solvents on the carbamazepine 10,11-epoxidation activities in HLM, carbamazepine was dissolved in acetonitrile or methanol and the final concentration of the organic solvents in the incubation mixture was in the range of 0.25 to 4%. The reaction was stopped by adding 200 µL of ice-cold acetonitrile. The samples were then centrifuged at 10000×g for 10 min at 4°C and a 100 µL-portion of the supernatant was subjected to high performance liquid chromatography (HPLC) to quantitate the formation of carbamazepine 10,11-epoxide.

HPLC Conditions

HPLC was performed using an LC-10AD pump (Shimadzu, Kyoto, Japan), a SPD-10A ultraviolet detector (Shimadzu), a SIL-10A autosampler (Shimadzu), a SLC-10A system controller (Shimadzu), and a Mightysil RP-18 GP column (4.6×150 mm, 5 µm; Kanto Chemical, Tokyo, Japan). The flow rate was 1.0 mL/min and the detection was accomplished with an ultraviolet detector at a wavelength of 210 nm. The mobile phase was 20 mM phosphate buffer (pH 7.4)–acetonitrile (6 : 4, v/v). Quantification of carbamazepine 10,11-epoxide was carried out by comparing the HPLC peak area to that of the authentic standard.

Calculation of Parameters

Observed CL_{int, in vivo} of carbamazepine 10,11-epoxidation was estimated to be 40% of total carbamazepine hepatic clearance (CL_H), 0.40 mL/min/kg,^6,9) with the equation; CL_H=Q_H×f_u×CL_int/(Q_H+f_u×CL_int), in which blood unbound fraction (f_u) is 0.31⁹⁾ and hepatic blood flow (Q_H) is 20 mL/min/kg.

Data Analysis

Kinetic parameters were estimated from Michaelis–Menten and Hill equations by using the fitted curve using a computer program (KaleidaGraph, Synergy Software, Reading, PA, U.S.A.) as previously described.¹⁰⁾ Data are expressed as the means±S.D. of three independent determinations. Statistical significances were determined by analysis of variance followed by Dunnett’s test. A value of p<0.05 was considered statistically significant.

RESULTS

Carbamazepine 10,11-Epoxidation in HLM

To obtain the optimal condition for carbamazepine 10,11-epoxide formation in HLM, the formation rate was determined in incubation conditions using final methanol or acetonitrile concentrations of 1 to 4%. While acetonitrile was found to strongly inhibit the enzymatic activity (Supplementary Fig. 1A), the inhibitory effect of methanol on the enzyme activity was less than that of acetonitrile (Supplementary Fig. 1B). Because a wide range of the substrate concentration is required for the kinetic analysis, we determined the kinetic parameters in the incubation condition at a final concentration of 1% methanol. In the present study, the kinetic curve was better fitted to the Hill equation with an Akaike’s information criteria (AIC) value of 60.44, revealing the S₅₀ value of 358±8 µM, n of 2.0±0.1, and the V_max value of 463±6 pmol/min/mg (Eq. 4), while the Michaelis–Menten analysis revealed a K_m value of 808±48 µM and a V_max value of 726±28 pmol/min/mg (Eq. 1) with an Akaike’s information criteria (AIC) value of 76.79 (Fig. 1A), which are in agreement with values from previous reports (Supplementary Table 1).^7,11–15) Eadie–Hofstee plots were not linear (Fig. 1B), confirming that carbamazepine 10,11-epoxide formation in HLM was sigmoidal.

Fig. 1. Kinetic Analyses of Carbamazepine 10,11-Epoxidation in HLM

Carbamazepine 10,11-epoxidation was determined at 1% methanol as described under Materials and Methods. Solid and dashed lines represent Hill and Michaelis–Menten plots, respectively (A). Eadie–Hofstee plots were obtained from carbamazepine 10,11-epoxidation in HLM at final concentration of 31.25 µM to 1.5 mM carbamazepine (B). Data are the means±S.D. of three independent determinations. Clearance of carbamazepine 10,11-epoxidation in HLM was calculated based on the sigmoidal analysis with Eq. 5 (solid line) or the Michaelis–Menten analysis with Eq. 2 (dashed line) (C). While the maximum clearance, CL_max, was obtained at the substrate concentration equal to S₅₀, the clearance was concentrate-dependent in the sigmoidal analysis.

Table 1. Comparison of Clearance of Drugs at Therapeutic Concentrations

Drug	Therapeutic concn.	fu*	Clearance at therapeutic concn.†,†† (mL/min/kg)	CLint, in vivo* (mL/min/kg)	CLmax* (mL/min/kg)
Carbamazepine	8 µg/mL	0.31	0.032	0.52	0.58
Alprazolam	20 ng/mL	0.29	0.14	3.4	2.2
Diazepam	0.4 µg/mL	0.022	0.15	24	4.4
Flunitrazepam	15 ng/mL	0.22	0.0044	20	5.4
Nordiazepam	0.3 µg/mL	0.033	0.04	7.3	0.57

* The therapeutic concentrations, f_u values, CL_{int, in vivo}, and CL_max of alprazolam, diazepam, flunitrazepam, and nordiazepam were from the literature.^{4,16–19) †} Clearance at therapeutic concentrations of drugs was calculated with Eq. 5 by using kinetic parameters, such as S₅₀, V_max, and n, reported preiously.¹⁶⁾ The clearance of each multiple metabolic pathway (1′-hydroxylation and 4-hydroxylation for alprazolam, N-demethylation and 3-hydroxylation for diazepam, 3-hydroxylation and demethylation for flunitrazepam, and 3-hydroxylation for nordiazepam) was combined to obtain the clearance of drugs. ^†† The clearance was calculated from microsome data in vitro.

Difference of Predicted Clearance of Carbamazepine between Typical and Atypical Kinetic Analyses

When the metabolism of drugs shows typical Michaelis–Menten kinetics, Eq. 3 is used to predict CL_{int, in vivo}. While CL_int is constant when the substrate concentration is much smaller than K_m, the clearance is substrate concentration-dependent at higher substrate concentrations, as shown in Fig. 1C (broken line). On the other hand, Eq. 5 is used to obtain the clearance of drugs whose metabolism is sigmoidal. The clearance is substrate concentration-dependent as shown in Fig. 1C (solid line), while the maximum clearance, CL_max, can be obtained with Eq. 6. Since it has been reported that CL_max correlates well to the observed hepatic intrinsic clearance, CL_{int, in vivo},¹⁶⁾ we calculated the CL_max value of carbamazepine 10,11-epoxidation in HLM. The CL_max value of carbamazepine 10,11-epoxidation was 0.65±0.01 µL/min/mg (0.58 mL/min/kg body weight) (Eq. 6), while CL_int calculated based on the Michaelis–Menten analysis was 0.90±0.02 µL/min/mg (0.81 mL/min/kg body weight) (Eq. 3). To convert from µL/min/mg HLM to mL/min/kg body weight, the following parameters were used: normal human body weight of 70 kg with a 1.4-kg liver; 45 mg HLM per gram liver. Reported in vivo hepatic clearance (CL_H) and CL_{int, in vivo} of carbamazepine is 0.40 mL/min/kg body weight and 1.32 mL/min/kg body weight, respectively.^6,9) Since approximately 40% of carbamazepine is metabolized to its 10,11-epoxide to be cleared from the body, partial CL_{int, in vivo} of carbamazepine to its 10,11-epoxide was estimated to be 0.52 mL/min/kg body weight. It was shown that calculation of CL_int based on the Michaelis–Menten analysis resulted in a 1.5-fold overestimation of CL_{int, in vivo} (0.81 mL/min/kg body weight to 0.52 mL/min/kg body weight). In contrast, the CL_max value obtained by the sigmoidal analysis correlated well to the CL_{int, in vivo} (0.58 mL/min/kg body weight to 0.52 mL/min/kg body weight).

Prediction of Clearance at Therapeutic Concentrations

This and other studies have demonstrated that CL_max can be used for the prediction of in vivo CL_int of drugs whose kinetics are sigmoidal. However, it should be noted that generally, therapeutic concentrations of drugs are much lower than their S₅₀ and K_m values. Although the clearance calculated from each equation (Eqs. 2, 5) is similar at the substrate concentration around the S₅₀ or K_m value, the rate could be significantly different at lower substrate concentrations as shown in Fig. 1C. Alprazolam, diazepam, flunitrazepam, and nordiazepam are also drugs whose metabolism is sigmoidal.¹⁶⁾ While their S₅₀ values range from 208 µM to 607 µM,¹⁶⁾ their therapeutic concentrations are much lower than those S₅₀ values^4,16–19) (Table 1). Therefore, predicted clearance rates of those drugs at the therapeutic concentrations using equation 5 significantly underestimated the observed in vivo CL_int (Table 1). The therapeutic concentration of carbamazepine, which is 10 µM,⁴⁾ is also much lower than its S₅₀ value. As with the drugs described above, the predicted clearance of carbamazepine at therapeutic concentrations using Eq. 5 also significantly underestimated the observed in vivo CL_int (Table 1). These results suggest the possibility of the existence of factor(s) causing the discrepancy between predicted and observed in vivo clearances of drugs, whose metabolism is sigmoidal, at therapeutic concentrations, while CL_max can be used for the prediction of CL_{int, in vivo}.

DISCUSSION

The kinetic curve of carbamazepine 10,11-epoxide formation has been analyzed with the Hill equation and the Michaelis–Menten equation (Supplementary Table 1). The accumulated evidence suggests that the enzymatic property is different in the recombinant systems due to different protein modification, such as glycosylation.²⁰⁾ Sigmoidal kinetics were mainly observed in human liver microsomes, while Michaelis–Menten kinetics were mainly observed in the recombinant systems. This indicates that the sigmoidal kinetics of carbamazepine 10,11-epoxidation observed in HLM is more reliable than the Michaelis–Menten kinetics. The comparison of AIC values also supported the usage of the Hill equation for the analysis of carbamazepine 10,11-epoxidation in human liver microsomes.

To predict the in vivo clearance of carbamazepine, its hepatic clearance needs to be estimated from the in vitro data. However, CL_int calculated from the Michaelis–Menten kinetics overestimated the actual clearance, because the metabolic rate-carbamazepine concentration curve is sigmoidal and therefore the clearance is relatively smaller than that estimated from the Michaelis–Menten analysis (Fig. 1C). In accordance with previous studies, CL_max was in excellent agreement with CL_{int, in vivo} in our study. In spite of the fact that carbamazepine 10,11-epoxidation in HLM has been reported to be sigmoidal, K_m and V_max values, which are obtained from the Michaelis–Menten analysis, were still used in a study in 2006 to predict its in vivo clearance,²¹⁾ which can result in an overestimation. Thus, it should be re-emphasized here that CL_max needs to be obtained for the prediction of in vivo CL_int of drugs whose metabolic kinetics are sigmoidal.

While CL_max values correlate well to in vivo CL_int, the predicted clearance of drugs at the therapeutic concentrations using Eq. 5 was significantly lower than the observed in vivo CL_int values (Table 1). This discrepancy between predicted and observed in vivo clearances of drugs might be caused by the following:

1. Presence of factor(s) that can activate the CYP3A4-catalyzed carbamazepine 10,11-epoxidation in vivo. CYPs have been known to possess an activator-binding site along with a substrate-binding site.⁸⁾ Testosterone is one of the endogenous compounds that can activate CYP3A4-catalyzed metabolism of drugs. It was reported that 150 µM testosterone fully activated CYP3A4-catalyzed metabolism of diazepam, whose metabolic kinetics is sigmoidal, resulting in a dramatically increased maximum clearance.⁸⁾ However, the effect of testosterone on CYP3A4 activity was moderate at the physiological concentration of testosterone in human plasma.⁸⁾ It was also reported that other endogenous compounds such as androstenedione and dehydroepiandrosterone 3-sulfate can activate CYP3A4 activities.²²⁾ Taking these findings together, it can be speculated that endogenous compounds might be activating the sigmoidal metabolism of drugs in vivo, causing the discrepancy of clearance parameters between in vitro and in vivo.

2. Accumulation of carbamazepine in hepatocytes. While the predicted plasma concentration of free carbamazepine is 10 µM, there is a possibility that the drug further accumulates in hepatocytes, possibly by active drug transporters expressing in the plasma membrane, causing an even higher clearance in the hepatocytes. Although it was not in the liver, the presence of multiple transporters that can transport carbamazepine was reported.²³⁾ Indeed, a two-fold higher concentration of carbamazepine was observed in the liver of rats, which intraperitoneally received 2.5 mg/kg carbamazepine, compared to concentration in the blood.²⁴⁾

It was also reported that liver concentrations of drugs, such as diazepam and alprazolam, greatly exceed total plasma concentrations.²⁵⁾

We have simply extrapolated the in vitro data to in vivo CL_int based on the assumption of 45 mg microsomal protein per g liver, in the current study. However, nowadays, it is widely accepted that such extrapolation of the absolute values for intrinsic clearance may have large bias, leading miscalculation of predicted values probably because of the quality of microsomes and other factors. An extrapolation using a scaling factor estimated from in vivo and in vitro data for reference compounds might be an alternatively way to predict in vivo clearance accurately. In addition, because approximately 40% of carbamazepine is metabolized to its 10,11-epoxide to be cleared from the body, we compared 40% of the total clearance of carbamazepine in vivo with the clearance of carbamazepine 10,11-epoxidation in vitro. However, there could be a discrepancy in the proportion of carbamazepine 10,11-epoxide formation in total carbamazepine metabolism between in vivo and in vitro. This discrepancy might partially contribute to the inaccurate prediction of in vivo clearance of carbamazepine at the therapeutic concentration.

In conclusion, while the intrinsic clearance calculated from Michaelis–Menten parameters (CL_int) overestimated the observed in vivo intrinsic clearance (CL_{int, in vivo}), the intrinsic clearance calculated based on the Hill equation (CL_max) exhibited better predictions of CL_{int, in vivo}. Predicted clearances of not only carbamazepine, but also of other drugs whose metabolic rate–concentration curves are sigmoidal, are significantly lower at their therapeutic concentrations than CL_{int, in vivo}, while intrinsic clearance at a therapeutic concentration should be close to that observed in humans in vivo. This suggests the existence of factors, such as endogenous CYP3A4 activators and drug transporters, causing the discrepancy between predicted and observed in vivo clearances at therapeutic concentrations. Even if we assume sigmoidal kinetics, that would not be enough for accurate prediction of CL_{int, in vivo}. Therefore, we should use CL_max to quantitatively extrapolate the in vitro data to in vivo data instead of using intrinsic clearance at therapeutic concentration. Further studies are required to fully understand the mechanism causing discrepancies between predicted and observed in vivo clearances of drugs whose metabolism is sigmoidal.

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