On the accuracy of calculation of the mean residence time of drug in the body and its volumes of distribution based on the assumption of central elimination.

1. The steady state and terminal volumes of distribution, as well as the mean residence time of drug in the body (Vss, Vß, and MRT) are the common pharmacokinetic parameters calculated using the drug plasma concentration-time profile (Cp(t)) following intravenous (iv bolus or constant rate infusion) drug administration. 2. These traditional calculations are valid for the linear pharmacokinetic system with central elimination (i.e. elimination rate being proportional to drug concentration in plasma). The assumption of central elimination is not valid in general, so that the accuracy of the traditional calculation of these parameters is uncertain. 3. The comparison of Vss, Vß, and MRT calculated by the derived exact equations and by the commonly used ones was made considering a physiological model. It turned out that the difference between the exact and simplified calculations does not exceed 2%. 4. Thus the calculations of Vss, Vß, and MRT, which are based on the assumption of central elimination, may be considered as quite accurate. Consequently it can be used as the standard for comparisons with kinetic and in silico models.

On the maintenance of hepatocyte intracellular pH 7.0 in the in-vitro metabolic stability assay.

The account of pH difference between hepatocytes (intracellular pH 7.0) and extracellular water (pH 7.4) leads to the novel equation for hepatic clearance (Berezhkovskiy, J Pharma Sci 100:1167-1683, 2011). The metabolic stability assay using hepatocytes is commonly performed in the incubation buffer of pH 7.4. If hepatocytes retain their physiological pH 7.0 in these conditions, then the assay would mimic the in vivo condition, that is pH 7.4 for plasma and extracellular water, and pH 7.0 in hepatocytes. In this case the rate of drug elimination, taken as proportional to unbound drug concentration in buffer, would correspond to the in vivo rate of drug elimination as proportional to the unbound drug concentration in the extracellular water. Consequently the commonly used PBPK equation for the rate of hepatic elimination, and the equation for hepatic clearance would be valid. However, the experiment designed to determine hepatocyte internal pH indicated that it was not maintained in the in vitro stability assay, so that hepatocytes acquire the same pH as the incubation buffer. Thus, the novel equations for hepatic clearance (that include an ionization factor) should be applied regardless if the intrinsic clearance was obtained either from microsomal or hepatocyte stability assay.

Preclinical stereoselective disposition and toxicokinetics of two novel MET inhibitors.

The R- and S-enantiomer of N-(4-(3-(1-ethyl-3,3-difluoropiperidin-4-ylamino)-1H-pyrazolo[3,4-b]pyridin-4-yloxy)-3-fluorophenyl)-2-(4-fluorophenyl)-3-oxo-2,3-dihydropyridazine-4-carboxamide are novel MET kinase inhibitors that have been investigated as potential anticancer agents. The effect of the chirality of these compounds on preclinical in vivo pharmacokinetics and toxicity was studied. The plasma clearance for the S-enantiomer was low in mice and monkeys (23.7 and 7.8 mL min(-1) kg(-1), respectively) and high in rats (79.2 mL min(-1) kg(-1)). The R/S enantiomer clearance ratio was 1.5 except in rats (0.49). After oral single-dose administration at 5 mg kg(-1) the R/S enantiomer ratio of AUC(inf) was 0.95, 1.9 and 0.41 in mice, rats and monkeys, respectively. In an oral single-dose dose-ranging study at 200 and 500 mg kg(-1) and multi-dose toxicity study in mice plasma AUC exposure was approximately 2- to 3-fold higher for the R-enantiomer compared to the S-enantiomer. Greater toxicity of the S-enantiomer was observed which appeared to be due to high plasma C(min) values and tissue concentrations approximately 24 h after the final dose. Both enantiomers showed low to moderate permeability in MDCKI cells with no significant efflux, no preferential distribution into red blood cells and similar plasma protein binding in vitro. Overall, the differences between the enantiomers with respect to low dose pharmacokinetics and in vitro properties were relatively modest. However, toxicity results warrant further development of the R-enantiomer over the S-enantiomer.

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.

Prediction of the possibility of the second peak of drug plasma concentration time curve after iv bolus administration from the standpoint of the traditional multi-compartmental linear pharmacokinetics.

It is shown that the existence of the second peak on the drug plasma concentration time curve C(p)(t) after iv bolus dosing can be explained by considering the traditional multi-compartmental linear pharmacokinetics. It was found that a direct solution of the general three-compartment model yields the second peak of C(p)(t) for the certain values of the rate constants, and C(p)(t) includes the term with oscillating preexponent, that is, K sin(omegat + phi) exp(-lambdat), in this case. The considered model describes the drug entero-hepatic recirculation in the species which do not have gall bladder (rats). The model fit of the experimental data from rat pharmacokinetic studies where the second peak of C(p)(t) was observed, yields the rate of bile production that is consistent with the physiological value ( approximately 0.7 mL/h).

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.

NF-κB inducing kinase is a therapeutic target for systemic lupus erythematosus.

NF-κB-inducing kinase (NIK) mediates non-canonical NF-κB signaling downstream of multiple TNF family members, including BAFF, TWEAK, CD40, and OX40, which are implicated in the pathogenesis of systemic lupus erythematosus (SLE). Here, we show that experimental lupus in NZB/W F1 mice can be treated with a highly selective and potent NIK small molecule inhibitor. Both in vitro as well as in vivo, NIK inhibition recapitulates the pharmacological effects of BAFF blockade, which is clinically efficacious in SLE. Furthermore, NIK inhibition also affects T cell parameters in the spleen and proinflammatory gene expression in the kidney, which may be attributable to inhibition of OX40 and TWEAK signaling, respectively. As a consequence, NIK inhibition results in improved survival, reduced renal pathology, and lower proteinuria scores. Collectively, our data suggest that NIK inhibition is a potential therapeutic approach for SLE.

Scaffold-Hopping Approach To Discover Potent, Selective, and Efficacious Inhibitors of NF-κB Inducing Kinase.

NF-κB-inducing kinase (NIK) is a protein kinase central to the noncanonical NF-κB pathway downstream from multiple TNF receptor family members, including BAFF, which has been associated with B cell survival and maturation, dendritic cell activation, secondary lymphoid organ development, and bone metabolism. We report herein the discovery of lead chemical series of NIK inhibitors that were identified through a scaffold-hopping strategy using structure-based design. Electronic and steric properties of lead compounds were modified to address glutathione conjugation and amide hydrolysis. These highly potent compounds exhibited selective inhibition of LTßR-dependent p52 translocation and transcription of NF-κB2 related genes. Compound 4f is shown to have a favorable pharmacokinetic profile across species and to inhibit BAFF-induced B cell survival in vitro and reduce splenic marginal zone B cells in vivo.

On the determination of the time delay in reaching the steady state drug concentration in the organ compared to plasma.

A problem of substantial delay in reaching the steady state drug concentration in particular organ (compartment) compared to the time of reaching the steady state plasma concentration is considered. It is shown that the ratio of the terminal (V(beta)) and the steady state (V(ss)) volumes of distribution, V(beta)/V(ss), appears to be an indication of possible lag in reaching the steady state in the organ tissue compared to plasma. The estimations of the time of reaching the steady state drug concentration in the organ are suggested. The in vivo based pharmacokinetic model, which uses the experimentally measured drug plasma concentration time course and the appropriate equation for the kinetics of drug distribution into the tissues, is suggested. It is intended to determine the kinetic mechanism of drug distribution into the tissues. The model was applied to interpret the kinetics of drug distribution into the brain. The importance of precise measurement of drug plasma concentration at terminal phase for obtaining accurate values of V(beta) and V(ss) is emphasized: this allows predicting a possible slow plasma-tissue drug transfer and substantial difference in time of reaching the steady state by the body and plasma.

On the calculation of the concentration dependence of drug binding to plasma proteins with multiple binding sites of different affinities: determination of the possible variation of the unbound drug fraction and calculation of the number of binding sites of the protein.

The measurement of the unbound drug fraction in plasma is routinely performed at drug concentrations much less than that of plasma proteins. Commonly, the protein has several binding sites of different affinities. The obtained value of the unbound drug fraction does not yield the affinity of each binding site separately. For drug binding to a single type of protein, it is shown that the assumption that all binding sites of the protein have the same affinity yields the slowest possible concentration increase of the unbound drug fraction, while the assumption that a drug binds to a single binding site yields the highest possible value of the unbound fraction for a given drug concentration. The conditions to be imposed on the affinities of binding sites, to provide the fastest and the slowest possible concentration increase of the unbound drug fraction are also obtained for the case of drug binding to several types of plasma proteins. The suggested approach is applied to the determination of the number of binding sites of the protein from the measured values of the unbound drug fraction at different drug concentrations.

The connection between the steady state (Vss) and terminal (Vbeta) volumes of distribution in linear pharmacokinetics and the general proof that Vbeta >/= Vss.

The steady state and terminal (area) volumes of distribution are important pharmacokinetic parameters defined as the ratio of the total quantity of drug in the body, A(b)(t), to drug plasma concentration C(p)(t) at steady state and the terminal phase of drug elimination, respectively. The general equations for the approach of C(p)(t), A(b)(t) and the distribution volume A(b)(t)/C(p)(t) to the steady state values (for a continuous constant rate drug infusion) are derived. It is shown that the time course of A(b)(t) near the asymptotic steady state value depends on both the terminal and steady state volumes of distribution, and an accurate equation to determine the time required to reach the steady state is obtained. For a general linear pharmacokinetic system (i.e., with possible drug elimination at any state from any compartment and drug exchange between compartments) it is proven that V(beta) >/= V(ss). A physiologically determined feature, which is the drug input into plasma for reaching the steady state or terminal phase, underlies the proof. If the steady state is reached by a continuous input of drug into some compartment other than plasma, and the terminal volume of distribution is considered after dosing of a drug in the same compartment, then both cases V(ss) <> V(beta) are possible. It is shown that the general exponential series for C(p)(t) after intravenous bolus dose may have negative pre-exponents, unlike a common assumption that all pre-exponents should be positive. Its is figured out that the commonly used equations for the estimation of V(ss) and V(beta) (V(ss) = D x AUMC/AUC(2) and V(beta) = D/(AUC x beta) may yield V(ss) > V(beta) for a linear pharmacokinetic system, contrary to the usual statement (V(ss) < V(beta)) and its seemingly simple proof, which has a flaw. It is shown that the time required to reach the steady state concentration of drug in plasma could be much shorter than a commonly used estimation of 5t(1/2), where t(1/2) is the terminal half-life obtained from the intravenous bolus drug plasma concentration time course.

The influence of drug kinetics in blood on the calculation of oral bioavailability in linear pharmacokinetics: the traditional equation may considerably overestimate the true value.

A common calculation of oral bioavailability is based on the comparison of the areas under the concentration-time curves after intravenous and oral drug administration. It does not take into account that after the oral dosing a drug enters the systemic circulation in different states, that is, as free fraction, protein bound and partitioned into blood cells, and plasma lipids, while after intravenous input it is introduced into the systemic circulation only as a free fraction. Consideration of this difference leads to a novel equation for the oral bioavailability. In general, the traditional calculation overestimates the oral bioavailability. For a widely applied model of a linear pharmacokinetic system with central (plasma) drug elimination it is shown that the traditional calculation of the oral bioavailability could substantially overestimate the true value. If the existence of an immediate equilibrium between different drug fractions in blood is assumed, the obtained equation becomes identical to the traditional one. Thus the deviation of oral bioavailability from the value given by a common calculation appears to be a kinetic phenomenon. The difference could be significant for the drugs with the rate constant of elimination from plasma of the same order of magnitude or greater than the dissociation rate constant of drug-protein complexes, or the off-rate constant of partitioning from the blood cells, if the blood concentration profiles were used to calculate the oral bioavailability.

A convenient method for estimating the quantity of drug eliminated by the routes other than hepatic metabolism and renal excretion and the fraction of drug that reaches the "first pass" after oral administration.

The comparison of routine pharmacokinetic data obtained after intravenous and oral drug administration allows to figure out that some quantity of drug, which reached the systemic circulation, was eliminated from the body by routes other than hepatic metabolism and renal excretion. This quantity is equal or exceeds the certain minimum value, which can be calculated from a simple equation obtained in the article. If the minimum value is equal to zero, then the maximum possible fraction of orally administered drug, that is, absorbed into the gut wall and gets through it unchanged, can be calculated. The examples considered indicate that the quantity of drug eliminated not by liver metabolism or kidney excretion could be quite substantial (exceeds half of the dose that reached the circulation).

Exploration of PBPK Model-Calculation of Drug Time Course in Tissue Using IV Bolus Drug Plasma Concentration-Time Profile and the Physiological Parameters of the Organ.

An uncommon innovative consideration of the well-stirred linear physiologically based pharmacokinetic model and the drug plasma concentration-time profile, which is measured in routine intravenous bolus pharmacokinetic study, was applied for the calculation of the drug time course in human tissues. This cannot be obtained in the in vivo pharmacokinetic study. The physiological parameters of the organ such as organ tissue volume, organ blood flow rate, and its vascular volume were used in the calculation. The considered method was applied to calculate the time course of midazolam, alprazolam, quinidine, and diclofenac in human organs or tissues. The suggested method might be applied for the prediction of drug concentration-time profile in tissues and consequently the drug concentration level in the targeted tissue, as well as the possible undesirable toxic levels in other tissues.

Volume of distribution at steady state for a linear pharmacokinetic system with peripheral elimination.

The problem of finding the steady-state volume of distribution V(ss) for a linear pharmacokinetic system with peripheral drug elimination is considered. A commonly used equation V(ss) = (D/AUC)*MRT is applicable only for the systems with central (plasma) drug elimination. The following equation, V(ss) = (D/AUC)*MRT(int), was obtained, where AUC is the commonly calculated area under the time curve of the total drug concentration in plasma after intravenous (iv) administration of bolus drug dose, D, and MRT(int) is the intrinsic mean residence time, which is the average time the drug spends in the body (system) after entering the systemic circulation (plasma). The value of MRT(int) cannot be found from a drug plasma concentration profile after an iv bolus drug input if a peripheral drug exit occurs. The obtained equation does not contain the assumption of an immediate equilibrium of protein and tissue binding in plasma and organs, and thus incorporates the rates of all possible reactions. If drug exits the system only through central compartment (plasma) and there is an instant equilibrium between bound and unbound drug fractions in plasma, then MRT(int) becomes equal to MRT = AUMC/AUC, which is calculated using the time course of the total drug concentration in plasma after an iv bolus injection. Thus, the obtained equation coincides with the traditional one, V(ss) = (D/AUC)*MRT, if the assumptions for validity of this equation are met. Experimental methods for determining the steady-state volume of distribution and MRT(int), as well as the problem of determining whether peripheral drug elimination occurs, are considered. The equation for calculation of the tissue-plasma partition coefficient with the account of peripheral elimination is obtained. The difference between traditionally calculated V(ss) = (D/AUC)*MRT and the true value given by (D/AUC)*MRT(int) is discussed.

Determination of volume of distribution at steady state with complete consideration of the kinetics of protein and tissue binding in linear pharmacokinetics.

The assumption of an instant equilibrium between bound and unbound drug fractions is commonly applied in pharmacokinetic calculations. The equation for the calculation of the steady-state volume of distribution V(ss) from the time curve of drug concentration in plasma after intravenous bolus dose administration, which does not assume an immediate equilibrium and thus incorporates dissociation and association rates of protein and tissue binding, is presented. The equation obtained V(ss) = (Dose/AUC)*MRT(u) looks like the traditional equation, but instead of mean residence time MRT calculated using the total drug concentration in plasma, it contains mean residence time MRT(u) calculated using the plasma concentration of the unbound drug. The equation connecting MRT(u) and MRT is derived. If an immediate equilibrium between bound and unbound drug fractions occurs, MRT(u) and MRT are the same, but in general, MRT(u) is always smaller than MRT. For drugs with high protein affinity and slow dissociation rate MRT(u) may be of an order of several hours smaller than MRT, so that V(ss) can be considerably overestimated in the traditional calculation.

Practical permeability-based hepatic clearance classification system (HepCCS) in drug discovery.

BACKGROUND: The use of liver microsomes and hepatocytes to predict total in vivo clearance is standard practice in the pharmaceutical industry; however, metabolic stability data alone cannot always predict in vivo clearance accurately. RESULTS: Apparent permeability generated from Mardin-Darby canine kidney cells and rat hepatocyte uptake for 33 discovery compounds were obtained. CONCLUSION: When there is underprediction of in vivo clearance, compounds with low apparent permeability (less than 3 × 10(-6) cm/s) all exhibited hepatic uptake. A systematic approach in the form of a classification system (hepatic clearance classification system) and decision tree that will help drug discovery scientists understand in vitro-in vivo clearance prediction disconnect early is proposed.

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(ß), 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(ß) 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(ß)) 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.

On the accuracy of a one-compartment approach for determination of drug terminal half-life.

The drug terminal half-life (t(1/2)) is commonly predicted by a simplified one-compartment approach (t(1/2) = ln 2V(ss)/CL), where V(ss) and CL are the steady-state volume of distribution and the total body clearance of drug, respectively. The analysis of the accuracy of this approach is provided. It turns out that most often a simplified one-compartment calculation underestimates t(1/2) by no more than 25% for human, 26% for dog, 20% for monkey, 19% for rat, and 23% for mouse. Thus, the application of a one-compartment calculation of t(1/2) is well justifiable, except for the rare cases of very high drug clearance (CL/(rQ) ≳ 0.5), where r is the equilibrium blood-plasma concentration ratio, and Q is the cardiac output.

An alternative approach for quantitative bioanalysis using diluted blood to profile oral exposure of small molecule anticancer drugs in mice.

A quantitative bioanalytical method for pharmacokinetic studies using diluted whole blood from serially bled mice was developed. Oral exposure profiles in mice for five model anticancer compounds dacarbazine, gefitinib, gemcitabine, imatinib, and topotecan were determined following discrete and cassette (five-in-one) dosing. Six micro blood samples per animal were collected and added to a fixed amount of water. This dilution served several purposes: the red blood cells were lysed; an anticoagulant was unnecessary and the fluid volume of diluted sample was sufficient for bioanalytical assays. AUC values obtained from blood concentrations were within twofold for discrete and cassette dosing except for imatinib (2.1-fold difference) and in agreement with those obtained from plasma concentrations after discrete dosing. All compounds were stable in plasma and diluted blood samples for at least 2 weeks at approximately -80°C. Matrix and intermatrix effects were evaluated to ensure robustness and integrity of the bioanalytical assays. This method provides significant process improvement by enhancing efficiency for sample collection and processing and reducing resources (e.g., reduced compound, cost, and animal requirement) compared with conventional methods. Our study demonstrates the applicability of using diluted micro blood samples for small molecule quantitative bioanalysis to support mouse studies in drug discovery.