Michaelis–Menten kinetic analysis of drugs of abuse to estimate their affinity to human P-glycoprotein

The pharmacokinetics of various important drugs are known to be significantly influenced by the human ABC transporter P-glycoprotein (P-gp), which may lead to clinically relevant drug–drug interactions. In contrast to therapeutic drugs, emerging drugs of abuse (DOA) are sold and consumed without any safety pharmacology testing. Only some studies on their metabolism were published, but none about their affinity to the transporter systems. Therefore, 47 DOAs from various classes were tested for their P-gp affinity using human P-gp (hP-gp) to predict possible drug–drug interactions. DOAs were initially screened for general hP-gp affinity and further characterized by modeling classic Michaelis–Menten kinetics and assessing their K_m and V_max values. Among the tested drugs, 12 showed a stimulation of ATPase activity. The most intensive stimulating DOAs were further investigated and compared with the known P-gp model substrates sertraline and verapamil. ATPase stimulation kinetics could be modeled for the entactogen 3,4-methylenedioxy-α-ethylphenethylamine (3,4-BDB), the hallucinogen 2,5-dimethoxy-4-iodoamphetamine (DOI), the abused alkaloid glaucine, the opioid-like drugs N-iso-propyl-1,2-diphenylethylamine (NPDPA), and N-(1-phenylcyclohexyl)-3-ethoxypropanamine (PCEPA), with K_m and V_max values within the same range as for verapamil or sertraline. As a consequence interactions with other drugs being P-gp substrates might be considered to be very likely and further studies should be encouraged.     

Dose correction for the Michaelis–Menten approximation of the target-mediated drug disposition model

The Michaelis–Menten (M–M) approximation of the target-mediated drug disposition (TMDD) pharmacokinetic (PK) model was derived based on the rapid binding (RB) or quasi steady-state (QSS) assumptions that implied that the target and drug binding and dissociation were in equilibrium. However, the initial dose for an IV bolus injection for the M–M model did not account for a fraction bound to the target. We postulated a correction to an initial condition that was consistent with the assumptions underlying the M–M approximation. We determined that the difference between the injected dose and one that should be used for the initial condition is equal to the amount of drug bound to the target upon reaching the equilibrium. We also observed that the corrected initial condition made the internalization rate constant an identifiable parameter that was not for the original M–M model. Finally, we performed a simulation exercise to check if the correction will impact the model performance and the bias of the M–M parameter estimates. We used literature data to simulate plasma drug concentrations described by the RB/QSS TMDD model. The simulated data were refitted by both models. All the parameters estimated from the original M–M model were substantially biased. On the other hand, the corrected M–M is able to accurately estimate these parameters except for equilibrium constant K_m. Weighted sum of square residual and Akaike information criterion suggested a better performance of the corrected M–M model compared with the original M–M model. Further studies are necessary to determine the importance of this correction for the M–M model applications to analysis of TMDD driven PK data.     

Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis–Menten model

Journal of Pharmacokinetics and Pharmacodynamics - Nonlinear ordinary differential equations (ODEs) are common in pharmacokinetic–pharmacodynamic systems. Although their exact solutions...     

Effects of chronic cirrhosis induced by intraperitoneal thioacetamide injection on the protein content and Michaelis–Menten kinetics of cytochrome P450 enzymes in the rat liver microsomes

Chronic intraperitoneal injection of thioacetamide (TAA) in rats has been used as an animal model of human cirrhosis to study the effects of the disease on drug metabolism. However, TAA inhibits P450 enzymes directly and independently of cirrhosis. We investigated the effects of chronic cirrhosis in rats, induced by 10 weeks of intraperitoneal TAA, on the P450 enzymes after a 10-day washout period to eliminate TAA. Liver histology and serum biomarkers of hepatic function confirmed cirrhosis in all animals. Microsomal total P450 content, P450 reductase activity and ethoxycoumarin O-deethylase activity, a general marker of P450 activity, were significantly reduced by 30%–50% in cirrhotic animals. Additionally, the protein content and Michaelis–Menten kinetics of the activities of CYP2D, CYP2E1 and CYP3A were investigated. Whereas cirrhosis reduced the microsomal protein contents of CYP2D and CYP3A by 70% and 30%, respectively, the protein contents of CYP2E1 were not affected. However, the activities of all the tested isoenzymes were substantially lower in the cirrhotic livers. It is concluded that the TAA model of cirrhosis that incorporates a 10-day washout period after intraperitoneal injection of the chemical to rats produces isoenzyme-selective reductions in the P450 proteins or activities, which are independent of the direct inhibitory effects of TAA.     

Application of the Kuenz–Leuenberger Equation as a Predictive Model of the Direct Tablet Compression Process

Pharmaceutical Chemistry Journal - Mathematical models, the most widely applied of which are the Heckel and Kawakita models, are used in modern research on the compression process to estimate...     

Are Polymorphisms in Genes Relevant to Drug Disposition Predictors of Susceptibility to Drug-Induced Liver Injury?

Despite considerable progress in identifying specific HLA alleles as genetic risk factors for some forms of drug-induced liver injury, progress in understanding whether genetic polymorphisms relevant to drug disposition also contribute to risk for developing this serious toxicity has been more limited. Evidence from both candidate-gene case control studies and genome-wide association studies is now discussed. In the case of genes relevant to drug metabolism, polymorphisms in cytochromes P450, UDP-glucuronosyltransferases, N-acetyltransferases and glutathione S-transferases as risk factors for DILI are assessed. The relevance of ABC transporters to drug-induced liver injury is also considered, together with data showing associations of particular ABCB11, ABCB1 and ABCC2 polymorphisms with some forms of drug-induced liver injury. Very few of the associations with genes relevant to drug disposition that have been reported have been well replicated. Even apparently well-studied associations such as that between isoniazid liver injury and N-acetyltransferase 2 slow acetylators remain problematic, though it seems likely that polymorphisms in drug metabolism genes do contribute to risk for some specific drugs. A better understanding of genetic risk factors for drug-induced liver injury will require further genome-wide association studies with larger numbers of cases, especially for forms of drug-induced liver injury where HLA genotype does not appear to be a risk factor.     

Analysis of Dissolution Data Using Modified Versions of Noyes–Whitney Equation and the Weibull Function

PURPOSE: The aim of the study is to develop modified, branched versions of the Noyes-Whitney and the Weibull equations, including explicitly the solubility/dose parameter, for the analysis of dissolution data, which reach the plateau either at infinite or finite time. METHODS: The modified Weibull function is applied to the analysis of experimental and literature dissolution data. To demonstrate the usefulness of the mathematical models, two model drugs are used: one highly soluble, metoprolol, and one relatively insoluble, ibuprofen. RESULTS: The models were fitted successfully to the data performing better compared with their classic versions. The advantages of the use of the models presented are several. They fit better to a large range of datasets, especially for fast dissolution curves that reach complete dissolution at a finite time. Also, the modified Weibull presented can be derived from differential equations, and it has a physical meaning as opposed to the purely empirical character of the original Weibull equation. The exponent of the Weibull equation can be attributed to the heterogeneity of the process and can be explained by fractal kinetics concepts. Also, the solubility/dose ratio is present explicitly as a parameter and allows to obtain estimates of the solubility even when the dissolution data do not reach the solubility level. CONCLUSION: The use of the developed branched equations gives better fittings and specific physical meaning to the dissolution parameters. Also, the findings underline the fact that even in the simplest, first-order case, the speed of the dissolution process depends on the dose, a fact of great importance in biopharmaceutic classification for regulatory purposes.     

Comparison between recombinant P450s and human liver microsomes in the determination of cytochrome P450 Michaelis–Menten constants

1. Non-linear dose–exposure (supra-proportionality) occurs when plasma drug concentrations increase in a non-linear fashion with increasing dose. To predict the likelihood of this, an understanding is required of the K_M, which reflects a drug ability to saturate a specific enzyme involved in its metabolism.

2. This study assessed the accuracy of K_M and V_max determinations for compounds using a substrate-depletion approach with those determined using the product-formation approach, using both recombinant human cytochrome P450 (CYP) enzymes and human liver microsomes.

3. For the vast majority of the compounds studied, the K_M’s using recombinant CYPs and human liver microsomes in the two approaches predicted within two-fold. Further comparisons between the K_M and V_max-values were made between those measured using the product-formation approach and those estimated following simultaneous fitting of the Michaelis–Menten equation to all substrate depletion plots. In each case values were comparable.

4. In conclusion, the current study showed the substrate-depletion approach can be used to estimate K_M and V_max using both human liver microsomes and recombinant P450s. Estimation of these parameters during early discovery will aid in the understanding of dosages at which non-linearity may occur, but potentially aid predictions of likely clinical drug–drug interactions.

     

Application of Box–Behnken Design to Optimize the Osmotic Drug Delivery System of Metoprolol Succinate and its In Vivo Evaluation in Beagle Dogs

The objective of this study was to develop osmotic pump tablets of metoprolol succinate (MS) using water-soluble pore formers in the semipermeable membrane in place of orifice drilled on the membrane thereby abolishing the shortcomings associated with laser drilling technique. The formulation was optimized for coating variables such as semipermeable membrane level (X ₁) and pore former level (X ₂) by response surface methodology using Box–Behnken design (BBD) employing design expert software. The developed osmotic pump tablet was found to sustain the drug release up to 20 h at zero-order rate. The pharmacokinetic study in Beagle dogs showed delayed T _max and lower C _max compared to marketed brand TOPROL XL, indicating a slow and more sustained release behavior of MS from the optimized osmotic tablets in comparison with the existing matrix-based marketed dosage form. Thus, a novel approach for the controlled release of MS from osmotic pump tablets has been successfully developed using BBD, which is valuable for the advancement of controlled drug delivery of other water-soluble drugs.     

Analysis of Clinical Dose–Response in Small-Molecule Drug Development: 2009–2014

A meta-analysis of dose–response studies is reported for small-molecule drugs approved by the U.S. Food and Drug Administration (FDA) between January 2009 and May 2014. Summaries of the study designs are presented, including the number of studies conducted for each drug, dosing range, and the number of doses evaluated. Most drugs were studied on a ? 4-fold range. Most of the study designs and their analyses focused on a small number of pairwise comparisons of dose groups to placebo. For the meta-analysis, efficacy endpoints were evaluated at a single landmark time. Safety endpoints were not collected. The commonly used E_max? model was fit for each drug. Due to the limited number of doses and dosing ranges, maximum likelihood estimation applied to drugs separately performed poorly. Bayesian hierarchical models were successfully fit producing E_max? curves that represented the data well. The distributions of the E_max? model parameters were consistent with previously reported distributions estimated from a sponsor-specific meta-analysis of dose response. Assessment of model fit, which focused on potential nonmonotone loss of efficacy at the highest doses, supported the use of the E_max? curves. The meta-analysis provides additional empirical basis for Bayesian prior distributions for model parameters. Supplementary materials for this article are available online.     

Mathematical analysis and drug exposure evaluation of pharmacokinetic models with endogenous production and simultaneous first-order and Michaelis–Menten elimination: the case of single dose

Drugs with an additional endogenous source often exhibit simultaneous first-order and Michaelis–Menten elimination and are becoming quite common in pharmacokinetic modeling. In this paper, we investigate the case of single dose intravenous bolus administration for the one-compartment model. Relying on a formerly introduced transcendent function, we were able to analytically express the concentration time course of this model and provide the pharmacokinetic interpretation of its components. Using the concept of the corrected concentration, the mathematical expressions for the partial and total areas under the concentration time curve (AUC) were also given. The impact on the corrected concentration and AUC is discussed as well as the relative contribution of the exogenous part in presence of endogenous production. The present findings theoretically elucidate several pharmacokinetic issues for the considered drug compounds and provide guidance for the rational estimation of their pharmacokinetic parameters.     

An In Silico Transwell Device for the Study of Drug Transport and Drug–Drug Interactions

PURPOSE: Validate and exemplify a discrete, componentized, in silico, transwell device (ISTD) capable of mimicking the in vitro passive transport properties of compounds through cell monolayers. Verify its use for studying drug-drug interactions. METHODS: We used the synthetic modeling method. Specialized software components represented spatial and functional features including cell components, semi-porous tight junctions, and metabolizing enzymes. Mobile components represented drugs. Experiments were conducted and analyzed as done in vitro. RESULTS: Verification experiments provided data analogous to those in the literature. ISTD parameters were tuned to simulate and match in vitro urea transport data; the objects representing tight junction (effective radius of 6.66 A) occupied 0.066% of the surface area. That ISTD was then tuned to simulate pH-dependent, in vitro alfentanil transport properties. The resulting ISTD predicted the passive transport properties of 14 additional compounds, individually and all together in one in silico experiment. The function of a two-site enzymatic component was cross-validated with a kinetic model and then experimentally validated against in vitro benzyloxyresorufin metabolism data. Those components were used to exemplify drug-drug interaction studies. CONCLUSIONS: The ISTD is an example of a new class of simulation models capable of realistically representing complex drug transport and drug-drug interaction phenomena.     

Multiple Inhibition Mechanisms and Prediction of Drug–Drug Interactions: Status of Metabolism and Transporter Models as Exemplified by Gemfibrozil–Drug Interactions

Purpose To assess the consequences of multiple inhibitors and differential inhibition mechanisms on the prediction of 12 gemfibrozil drug–drug interactions (DDIs). In addition, qualitative zoning of transporter-related gemfibrozil and cyclosporine DDIs was investigated. Methods The effect of gemfibrozil and its acyl-glucuronide on different enzymes was incorporated into a metabolic prediction model. The impact of CYP2C8 time-dependent inhibition by gemfibrozil acyl-glucuronide was assessed using repaglinide, cerivastatin, loperamide, rosiglitazone and pioglitazone DDIs. Gemfibrozil and cyclosporine inhibition data obtained in human embryonic kidney cells expressing OATP1B1 and hepatic input concentration ([I]in) were used for qualitative zoning of 14 transporter-mediated DDIs. Results Incorporation of time-dependent inhibition by gemfibrozil glucuronide showed no significant improvement in the prediction, as CYP2C8 contributed <65% to the overall elimination of the victim drugs investigated. Qualitative zoning of OATP1B1 DDIs resulted in no false negative predictions; yet the magnitude of observed interactions was significantly over-predicted. Conclusions Time-dependent inhibition by gemfibrozil glucuronide is only important for victim drugs eliminated predominantly (>80%) via CYP2C8. Qualitative zoning of OATP1B1 inhibitors based on [I]in/K _i is valid in drug screening to avoid false negatives. Refinement of the transporter model by incorporating the fraction of drug transported by a particular transporter is recommended.     

A Bayesian Meta-Analysis on Published Sample Mean and Variance Pharmacokinetic Data with Application to Drug–Drug Interaction Prediction

In drug-drug interaction (DDI) research, a two-drug interaction is usually predicted by individual drug pharmacokinetics (PK). Although subject-specific drug concentration data from clinical PK studies on inhibitor or inducer and substrate PK are not usually published, sample mean plasma drug concentrations and their standard deviations have been routinely reported. Hence there is a great need for meta-analysis and DDI prediction using such summarized PK data. In this study, an innovative DDI prediction method based on a three-level hierarchical Bayesian meta-analysis model is developed. The three levels model sample means and variances, between-study variances, and prior distributions. Through a ketoconazle-midazolam example and simulations, we demonstrate that our meta-analysis model can not only estimate PK parameters with small bias but also recover their between-study and between-subject variances well. More importantly, the posterior distributions of PK parameters and their variance components allow us to predict DDI at both population-average and study-specific levels. We are also able to predict the DDI between-subject/study variance. These statistical predictions have never been investigated in DDI research. Our simulation studies show that our meta-analysis approach has small bias in PK parameter estimates and DDI predictions. Sensitivity analysis was conducted to investigate the influences of interaction PK parameters, such as the inhibition constant Ki, on the DDI prediction.     

Bias in the Wagner–Nelson Estimate of the Fraction of Drug Absorbed

Purpose. To examine and quantify bias in the Wagner-Nelson estimate of the fraction of drug absorbed resulting from the estimation error of the elimination rate constant (k), measurement error of the drug concentration, and the truncation error in the area under the curve. Methods. Bias in the Wagner-Nelson estimate was derived as a function of post-dosing time (t), k, ratio of absorption rate constant to k (r), and the coefficient of variation for estimates of k (CV _k), or CV _c for the observed concentration, by assuming a one-compartment model and using an independent estimate of k. The derived functions were used for evaluating the bias with r= 0.5, 3, or 6; k= 0.1 or 0.2; CV _c = 0.2 or 0.4; and CV _k =0.2 or 0.4; for t= 0 to 30 or 60. Results. Estimation error of k resulted in an upward bias in the Wagner-Nelson estimate that could lead to the estimate of the fraction absorbed being greater than unity. The bias resulting from the estimation error of k inflates the fraction of absorption vs. time profiles mainly in the early post-dosing period. The magnitude of the bias in the Wagner-Nelson estimate resulting from estimation error of k was mainly determined by CV _k. The bias in the Wagner-Nelson estimate resulting from to estimation error in k can be dramatically reduced by use of the mean of several independent estimates of k, as in studies for development of an in vivo-in vitro correlation. The truncation error in the area under the curve can introduce a negative bias in the Wagner-Nelson estimate. This can partially offset the bias resulting from estimation error of k in the early post-dosing period. Measurement error of concentration does not introduce bias in the Wagner-Nelson estimate. Conclusions. Estimation error of k results in an upward bias in the Wagner-Nelson estimate, mainly in the early drug absorption phase. The truncation error in AUC can result in a downward bias, which may partially offset the upward bias due to estimation error of k in the early absorption phase. Measurement error of concentration does not introduce bias. The joint effect of estimation error of k and truncation error in AUC can result in a non-monotonic fraction-of-drug-absorbed-vs-time profile. However, only estimation error of k can lead to the Wagner-Nelson estimate of fraction of drug absorbed greater than unity.     

Determination of Association Constants in Cyclodextrin/Drug Complexation Using the Scatchard Plot: Application to β-Cyclodextrin-Anilinonaphthalenesulfonates

The appropriate Scatchard equation was developed for a system involving the formation of 1:1 and 1:2 substrate: cyclodextrin complexes. Simulation of this system was performed under the most common experimental conditions encountered in this type of study. The use of the equation allows for nonlinear least-squares estimation of the association constants. The interaction of the model compounds 1-anilino-8-naphthalenesulfonate (1,8-ANS) and 2(p-toluidinyl)-6-naphthalenesulfonate (2,6-TNS) with -cyclodextrin (-CD) was used to evaluate the theoretical model. Binding experiments were performed using either potentiometric titration or fluorimetric detection. The experimental data for 1,8-ANS/-CD fit well to the 1:1 binding model, with an association constant of 87 ± 1 M–1. The association constants of the 1:1 and 1:2 2,6-TNS/-CD complexes utilizing direct potentiometry were 3737 ± 6 and 149 ± 2 M–l. It is shown that fluorimetry can give biased estimates for the association constants of the complexation 2,6-TNS/-CD, since the assumption of an equivalent quantum yield of bound species is not valid.     

Analysis of the constituents of aqueous preparations of Stachys recta by HPLC–DAD and HPLC–ESI-MS

In the present study a method based on liquid chromatography with diode array detection (HPLC/DAD) coupled to an electrospray ionization (ESI) interface for the simultaneous determination of phenolic constituents in three aqueous preparations of the herbal medicinal drug Stachys recta. The developed assay was simple and effective and permitted the quality control of S. recta decoctions and infusion. Overall, 30 constituents were detected and identified, belonging mainly to three classes of compounds: caffeoylquinic acids, phenylethanol glycosides and flavonoids. 15 of them were quantified having a lower limit not less than 0.02% of the lyophilized extracts. Only seven of them were previously reported in this species, while 23 were identified for the first time as constituents of S. recta. HPLC–DAD–ESI-MS analysis provided evidence for the certain identification of the main constituents and in some cases of their isomers. Eight constituents were isolated and their structure elucidated by HPLC–ESI-MS and 1D- and 2D-NMR spectroscopy. Among the investigated preparations, the infusion seems to be the best method to extract the native constituents of the plant, while decoction is a more aggressive treatment and causes partial degradation of some acylated flavonoids.     

Pharmacokinetic Drug–Drug Interaction of the Novel Anticancer Agent E7070 and Acenocoumarol

E7070 is a novel sulfonamide anticancer agent that arrests cancer cells at the G1/S boundary of the cell cycle. Three patients receiving chronic therapy with the oral anticoagulant acenocoumarol experienced bleeding and/or a prolonged prothrombin time after treatment with E7070 at a dose of 700mg/m² given as a 1-h infusion. In vitro studies have shown that E7070 has the potential to inhibit several cytochrome P450 (CYP)-enzymes, including CYP2C9, CYP2C19, CYP2D6, CYP2E1, and CYP3A4. The major enzyme involved in the metabolism of acenocoumarol in man is CYP2C9. This study was performed to investigate the interaction between E7070 and acenocoumarol.Blood samples were obtained from two patients receiving daily oral maintenance treatment with acenocoumarol both prior to and following treatment with E7070. In addition, we incubated acenocoumarol enantiomers with pooled human microsomes with and without E7070 and measured the in vitro plasma protein binding of acenocoumarol after incubation with E7070. Pharmacokinetic parameters of acenocoumarol were calculated by noncompartmental analysis and revealed that in both patients the area under the concentration–time curve up to 24h after the acenocoumarol administration was higher following E7070 (2.56 and 1.58h*mol/L) compared to the systemic exposure in the absence of E7070 (1.87 and 1.23h*mol/l). The formation of acenocoumarol metabolites was retarded by E7070 at already low concentrations (2.1M). The plasma protein binding of acenocoumarol was reduced at higher concentrations of E7070 (259M).These results indicate that E7070 may primarily interact with acenocoumarol by reducing its systemic clearance. Displacement of acenocoumarol's plasma protein binding by E7070 may also occur but to a minor extent. In the absence of careful monitoring this drug–drug interaction may result in hypoprothrombinemia and a hemorrhagic tendency.