Leonid M. Berezhkovskiy

On the influence of protein binding on pharmacological activity of drugs

The effect of variable protein binding (taken as independent parameter) on pharmacological activity of drugs is considered in terms of the exposure or the steady state concentration of unbound drug at targeted tissue. Based on the application of the parallel tube or dispersion models it is shown that for the most common case of orally administered drugs eliminated mainly by hepatic metabolism the increase of protein binding may be beneficial for drug action. In contrary, consideration of this case using the well-stirred model suggests that changes in protein binding do not influence drug efficiency. The relatively simplistic well-stirred model appears not accurate enough to reveal the influence of variation in protein binding on drug exposure. The conclusion in favor of the predictions based on parallel tube or dispersion models is supported by experimental data. In case of the oral dosing of drugs that are subjected to nonhepatic elimination as well as for parenteral drug administration with arbitrary routes of elimination the decrease in protein binding would lead to the increase of unbound drug exposure and thus may enhance drug efficiency. An advanced approach to evaluation of drug activity based on the assumption of the necessity to exceed certain minimal drug concentration at action site is implied. Such a consideration leads to the conclusion that there should be an optimal value of protein binding which provides maximum drug activity. The case when drug action is determined by binding to targeted receptors is discussed in terms of equilibrium binding and kinetics.

Some features of the kinetics and equilibrium of drug binding to plasma proteins

The reaction of drug–protein binding is considered based on the common calculations of chemical equilibrium (using the mass action and mass balance laws) and formal chemical kinetics. The calculative and theoretical aspects presented in the review are pertinent to routine drug development. Numerous real-life examples are provided throughout the article to illustrate the practical utility of the presented concepts. This may be very helpful in the interpretation of protein binding and pharmacokinetic data. Considerable resources may be saved by the proper setting of protein binding experiments, using relatively simple calculations and estimations instead of doing experimental measurements, and also avoiding ‘improvements’ that are destined to failure. The presented material may be also useful for the simulations of pharmacokinetics and pharmacodynamics, which attempt the complete account of drug–protein binding. A complete description of the considered topics is given in the last paragraph of the Introduction

On the Accuracy of Estimation of Basic Pharmacokinetic Parameters by the Traditional Noncompartmental Equations and the Prediction of the Steady-State Volume of Distribution in Obese Patients Based Upon Data Derived from Normal Subjects

The steady-state and terminal volumes of distribution, as well as the mean residence time of drug in the body (V(ss), V(β), and MRT) are the common pharmacokinetic parameters calculated using the drug plasma concentration-time profile C(p) (t) following intravenous (i.v. bolus or constant rate infusion) drug administration. These calculations are valid for the linear pharmacokinetic system with central elimination (i.e., elimination rate being proportional to drug concentration in plasma). Formally, the assumption of central elimination is not normally met because the rate of drug elimination is proportional to the unbound drug concentration at elimination site, although equilibration between systemic circulation and the site of clearance for majority of small molecule drugs is fast. Thus, the assumption of central elimination is practically quite adequate. It appears reasonable to estimate the extent of possible errors in determination of these pharmacokinetic parameters due to the absence of central elimination. The comparison of V(ss), V(β), and MRT calculated by exact equations and the commonly used ones was made considering a simplified physiologically based pharmacokinetic model. It was found that if the drug plasma concentration profile is detected accurately, determination of drug distribution volumes and MRT using the traditional noncompartmental calculations of these parameters from C(p) (t) yields the values very close to that obtained from exact equations. Though in practice, the accurate measurement of C(p) (t), especially its terminal phase, may not always be possible. This is particularly applicable for obtaining the distribution volumes of lipophilic compounds in obese subjects, when the possibility of late terminal phase at low drug concentration is quite likely, specifically for compounds with high clearance. An accurate determination of V(ss) is much needed in clinical practice because it is critical for the proper selection of drug treatment regimen. For that reason, we developed a convenient method for calculation of V(ss) in obese (or underweight) subjects. It is based on using the V(ss) values obtained from pharmacokinetic studies in normal subjects and the physicochemical properties of drug molecule. A simple criterion that determines either the increase or decrease of V(ss) (per unit body weight) due to obesity is obtained. The accurate determination of adipose tissue-plasma partition coefficient is crucial for the practical application of suggested method.

A valid equation for the well-stirred perfusion limited physiologically based pharmacokinetic model that consistently accounts for the blood-tissue drug distribution in the organ and the corresponding valid equation for the steady state volume of distribution.

A consistent account of the assumptions of the well-stirred perfusion limited model leads to the equation for the organ tissue that does not coincide with that often presented in books and papers. The difference in pharmacokinetic profiles calculated by the valid and the commonly used equations could be quite significant, particularly due to contribution of the organs with relatively large perfusion volume, and especially for drugs with small tissue-plasma partition coefficient and high blood-plasma concentration ratio. Application of the valid equation may result in much faster initial drop of drug plasma concentration time curve and significantly longer terminal half-life, especially for low extraction ratio drugs. An equation for the steady state volume of distribution consistent with the well-stirred model described by the valid equation is provided.

Determination of Mean Residence Time of Drug in Plasma and the Influence of the Initial Drug Elimination and Distribution on the Calculation of Pharmacokinetic Parameters

The equation for the calculation of mean residence time of drug in plasma, t(p), is obtained. It is shown that the previously suggested calculation of t(p) considerably overestimates the true value in most cases. It is suggested that due to the possible initial (before establishing the uniform drug mixing in plasma) fast elimination of drug, the commonly calculated total body clearance (Cl = D/AUC) may substantially overestimate the clearance in the linear range of elimination of well-stirred drug. This would result in the high in vivo Cl values that are not supported by the in vitro studies of drug metabolism and stability in tissues. It is shown that the mean residence time of drug in the body, volumes of distribution, oral bioavailability and distribution clearance estimated with the account of initial drug distribution and elimination, may substantially deviate from the values obtained by the traditional calculations.

On the prediction of hepatic clearance using the diluted plasma in metabolic stability assay

It was suggested that in vivo hepatic clearance, CL(h), may be predicted rather accurately with the in vitro values of intrinsic clearance, CL(int), obtained using the microsomal incubation mix containing diluted plasma, and consequently calculated by the well-stirred model equation. Conceivably the improvement could be due to the direct account of plasma protein binding in the measured values of CL(int). It is shown in this article that the prediction of CL(h) done in this manner may not yield accurate results, both substantial underestimation or overestimation of the true value is possible. The procedure may be useful to reduce the overestimation of CL(h) for highly protein bound drugs, though the obtained value of CL(h) may be far off from the correctly calculated one. The accurate way of calculating CL(h), based on the value of CL(int) obtained in diluted plasma, is presented. It takes into account both the drug protein binding in diluted plasma and microsomal binding, as well as blood-plasma concentration ratio. The prediction of CL(h) by the suggested calculation using the experimental data on CL(int), measured at different plasma dilutions for several drugs, yields consistent (dilution independent) values of hepatic clearance. It does not seem possible to avoid the measurement of plasma protein binding, microsomal binding and blood-plasma concentration ratio for an accurate and consistent prediction of CL(h), even if the value of CL(int) were obtained in the pure (undiluted) plasma. In an early stage screening using plasma in the microsomal incubation mix may be beneficial for fast metabolizing drugs with relatively high protein binding. This would reduce a possible overestimation CL(h), and also lead to the increase of the half-life in the microsomal incubation, so that it could be measured more accurately.

The influence of hepatic transport on the distribution volumes and mean residence time of drug in the body and the accuracy of estimating these parameters by the traditional pharmacokinetic calculations

The influence of hepatic uptake and efflux, which includes passive diffusion and transporter-mediated component, on drug distribution volumes [steady-state volume of distribution (V(ss)) and terminal volume of distribution (V(β))], mean residence time (MRT), clearance, and terminal half-life is considered using a simplified physiologically based pharmacokinetic model. To account for hepatic uptake, liver is treated as two-compartmental unit with drug transfer from extracellular water into hepatocytes. The exactly calculated distribution volumes and MRT are compared with that obtained by the traditional equations based on the assumption of central elimination. It was found that V(ss) may increase more than 10-fold and V(β) more than 100-fold due to the contribution of transporter-mediated uptake. The terminal half-life may be substantially shortened (more than 100-fold) due to transporters. It may also decrease significantly due to the increase of intrinsic hepatic clearance (CL(int)), whereas hepatic clearance has already reached saturation (and stays close to the possible maximum value). It is shown that in case of transporter-mediated uptake of compound into hepatocytes, in the absence of efflux and passive diffusion (unidirectional uptake), hepatic clearance is independent of CL(int) and is determined by hepatic blood flow and uptake rate constant. The effects of transporter-mediated uptake are mostly pronounced for hydrophilic acidic compounds and moderately lipophilic neutral compounds. For basic compounds and lipophilic neutral compounds the change of distribution volumes due to transporters is rather unlikely. It was found that the traditional equations provide very accurate values of V(ss), V(β), and MRT in the absence of transporter action even for very low rates of passive diffusion. On the other hand, the traditional equations fail to provide the correct values of these parameters when the increase of distribution volumes due to transporters takes place, and actually yield the values substantially smaller than the true ones (up to an order of magnitude for V(ss) and MRT, and three orders of magnitude for V(β)).

On the possibility of self-induction of drug protein binding

The equilibrium unbound drug fraction (f(u)) is an important pharmacokinetic parameter, which influences drug elimination and distribution in the body. Commonly the drug plasma concentration is substantially less then that of drug binding proteins, so that f(u) can be assumed constant independent of drug concentration. A general consideration of protein binding based on the mass-action law provides that the unbound drug fraction increases with the increase of drug concentration, which is also a usual experimental observation. For several drugs, though, a seemingly unusual sharp decrease of the unbound drug fraction with the increase of total drug concentration (R(o)) in the interval 0 < R(o) less, similar 5 microM was experimentally observed. A possible explanation of this apparently strange phenomenon is presented. The explanation is based on the consideration of a two-step mechanism of drug protein binding. The first step occurs as a drug binding to the site with relatively low affinity. Consequently this binding leads to the activation of a high affinity site, which otherwise is not available for binding. The suggested binding scheme yields the curves for f(u) dependence on the total drug concentration that are in good agreement with experimental measurements. The interpretation of pharmacokinetic data for the drugs with such unusual concentration dependence of f(u) appears to be a formidable problem.

Prediction of Drug Terminal Half-Life and Terminal Volume of Distribution After Intravenous Dosing Based on Drug Clearance, Steady-State Volume of Distribution, and Physiological Parameters of the Body

The steady state, V(ss), terminal volume of distribution, V(β), and the terminal half-life, t(1/2), are commonly obtained from the drug plasma concentration-time profile, C(p)(t), following intravenous dosing. Unlike V(ss) that can be calculated based on the physicochemical properties of drugs considering the equilibrium partitioning between plasma and organ tissues, t(1/2) and V(β) cannot be calculated that way because they depend on the rates of drug transfer between blood and tissues. Considering the physiological pharmacokinetic model pertinent to the terminal phase of drug elimination, a novel equation that calculates t(1/2) (and consequently V(β)) was derived. It turns out that V(ss), the total body clearance, Cl, equilibrium blood-plasma concentration ratio, r; and the physiological parameters of the body such as cardiac output, and blood and tissue volumes are sufficient for determination of terminal kinetics. Calculation of t(1/2) by the obtained equation appears to be in good agreement with the experimentally observed vales of this parameter in pharmacokinetic studies in rat, monkey, dog, and human. The equation for the determination of the pre-exponent of the terminal phase of C(p)(t) is also found. The obtained equation allows to predict t(1/2) in human assuming that V(ss) and Cl were either obtained by allometric scaling or, respectively, calculated in silico or based on in vitro drug stability measurements. For compounds that have high clearance, the derived equation may be applied to calculate r just using the routine data on Cl, V(ss), and t(1/2), rather than doing the in vitro assay to measure this parameter.

Preclinical absorption, distribution, metabolism, excretion, and pharmacokinetic-pharmacodynamic modelling of N-(4-(3-((3S,4R)-1-ethyl-3-fluoropiperidine-4-ylamino)-1H-pyrazolo[3,4-b]pyridin-4-yloxy)-3-fluorophenyl)-2-(4-fluorophenyl)-3-oxo-2,3-dihydropyridazine-4-carboxamide, a novel MET kinase inhibitor.

GNE-A (AR00451896; N-(4-(3-((3S,4R)-1-ethyl-3-fluoropiperidine-4-ylamino)-1H-pyrazolo[3,4-b]pyridin-4-yloxy)-3-fluorophenyl)-2-(4-fluorophenyl)-3-oxo-2,3-dihydropyridazine-4-carboxamide) is a potent, selective MET kinase inhibitor being developed as a potential drug for the treatment of human cancers. Plasma clearance was low in mice and dogs (15.8 and 2.44 mL/min/kg, respectively) and moderate in rats and monkeys (36.6 and 13.9 mL/min/kg, respectively). The volume of distribution ranged from 2.1 to 9.0 L/kg. The mean terminal elimination half-life ranged from 1.67 h in rats to 16.3 h in dogs. Oral bioavailability in rats, mice, monkeys, and dogs were 11.2%, 88.0%, 72.4%, and 55.8%, respectively. Allometric scaling predicted a clearance of 1.3–7.4 mL/min/kg and a volume of distribution of 4.8–11 L/kg in human. Plasma protein binding was high (96.7–99.0% bound). Blood-to-plasma concentration ratios (0.78–1.46) indicated that GNE-A did not preferentially distribute into red blood cells. Transporter studies in MDCKI–MDR1 and MDCKII–Bcrp1 cells suggested that GNE-A is likely a substrate for MDR1 and BCRP. Pharmacokinetic–pharmacodynamic modelling of tumour growth inhibition in MET-amplified EBC-1 human non-small cell lung carcinoma tumour xenograft mice projected oral doses of 5.6 and 13 mg/kg/day for 50% and 90% tumour growth inhibition, respectively. Overall, GNE-A exhibited favourable preclinical properties and projected human dose estimates.