Simultaneous Nonlinear Regression Research Articles

Biotransformation of Polycyclic Aromatic Hydrocarbons by Trout Liver S9 Fractions: Evaluation of Competitive Inhibition Using a Substrate Depletion Approach.

Environmental contaminants frequently occur as part of a chemical mixture, potentially resulting in competitive inhibition among multiple substrates metabolized by the same enzyme. Trout liver S9 fractions were used to evaluate the biotransformation of 3 polycyclic aromatic hydrocarbons (PAHs): phenanthrene, pyrene, and benzo[a]pyrene, tested as binary mixtures. Initial rates of biotransformation were determined using a substrate-depletion approach. The resulting data were then fitted by simultaneous nonlinear regression to a competitive inhibition model. In each case, the PAH possessing the lower Michaelis-Menten affinity constant (KM ) competitively inhibited biotransformation of the other compound. Inhibition constants determined for the lower-KM compound were generally close to previously determined KM values, consistent with the suggestion that phase I biotransformation of PAHs is largely catalyzed by one or a small number of cytochrome P450 enzymes. The use of a substrate-depletion approach to perform enzyme-inhibition studies imposes practical limitations on experimental design and complicates the interpretation of derived kinetic constants. Nevertheless, the resulting information may have utility for chemical hazard assessments as well as the design and interpretation of controlled laboratory studies. Depletion experiments informed by measured chemical concentrations in tissues may also provide a means of determining whether enzyme inhibition occurs under relevant environmental conditions. Environ Toxicol Chem 2019;38:2729-2739. Published 2019 Wiley Periodicals, Inc. on behalf of SETAC. This article is a US government work, and as such, is in the public domain in the United States of America.

Effect of fluvastatin, lovastatin, nifedipine and verapamil on the systemic exposure of nateglinide in rabbits

A diabetic patient may suffer simultaneously from cardiovascular disease; thus, lipid-lowering or anti-hypertensive agents could be given together with nateglinide. The pharmacokinetics of nateglinide were investigated in the presence and absence of HMG-CoA reductase inhibitors (fluvastatin, lovastatin) and calcium channel blockers (verapamil, nifedipine) in rabbits. A pharmacokinetic modeling approach was used to quantify the effects of the drugs that significantly influenced the pharmacokinetics of nateglinide. Fluvastatin and nifedipine shifted the time course of serum nateglinide concentrations upwards; there was no significant change with verapamil or lovastatin. The C(max) and AUC(inf) increased 1.5- (p<0.05) and 1.3-fold in the presence of fluvastatin and 1.8- (p<0.01) and 2.4-fold (p<0.01) in the presence of nifedipine, respectively. In a simultaneous nonlinear regression, fluvastatin and nifedipine decreased the elimination rate constant, by 76% and 32%, respectively. Fluvastatin and nifedipine increased the systemic exposure of nateglinide in rabbits, probably due to their inhibitory action on the metabolism of nateglinide by CYP2C5 (human CYP2C9). The concomitant use of fluvastatin and/or nifedipine with nateglinide is quite likely; therefore, the clinical consequences of long-term treatments must be considered.

Methodological Comparison of In Vitro Binding Parameter Estimation: Sequential vs. Simultaneous Non-linear Regression

Analysis of simulated data was compared using sequential (NLR) and simultaneous non-linear regression (SNLR) to evaluate precision and accuracy of ligand binding parameter estimation. Commonly encountered experimental error, specifically residual error of binding measurements (RE), experiment-to-experiment variability (BEV) and non-specific binding (B(NS)), were examined for impact of parameter estimation using both methods. Data from equilibrium, dissociation, association and non-specific binding experiments were fit simultaneously (SNLR) using NONMEM VI compared to the common practice of analyzing data from each experiment separately and assigning these as exact values (NLR) for estimation of the subsequent parameters. The greatest contributing factor to bias and variability in parameter estimation was RE of the measured concentrations of ligand bound; however, SNLR provided more accurate and less bias estimates. Subtraction of B(NS) from total ligand binding data provided poor estimation of specific ligand binding parameters using both NLR and SNLR. Additional methods examined demonstrated that the use of SNLR provided better estimation of specific binding parameters, whereas there was considerable bias using NLR. NLR cannot account for BEV, whereas SNLR can provide approximate estimates of BEV. SNLR provided superior resolution of parameter estimation in both precision and accuracy compared to NLR.

Pharmacokinetic evaluation and modeling of formulated levodopa intranasal delivery systems

Levodopa ( l-dopa), the metabolic precursor of dopamine, has primarily been used for the treatment of Parkinson's disease (PD) in combination with carbidopa (C-dopa). This study aims to investigate the feasibility of l-dopa nasal delivery systems prepared using maleic acid solution containing 2-hydroxypropyl-β-cyclodextrin, and to develop pharmacokinetic models. Following oral or intravenous administration of l-dopa plus C-dopa and intranasal dosing of l-dopa in the presence and absence of C-dopa to the rat, the concentrations of l-dopa in plasma and brain were determined using HPLC. The pharmacokinetic profiles were analyzed using non-compartmental and compartmental modeling approaches. Simultaneous nonlinear regression was performed to improve the identifiability of model parameters. l-Dopa was rapidly absorbed into blood and brain. The absolute bioavailabilities of oral and nasal preparations containing C-dopa were 17.7 and 45.4%, respectively. C-dopa caused a 1.2-fold decrease in the elimination rate of l-dopa, indicating decreased metabolism. Although the half-life after nasal administration was relatively short (less than 30 min) in both blood and brain regardless of C-dopa addition, the systemic exposure was promising due to rapid absorption. In conclusion, the l-dopa nasal delivery system could be used as a good rescue therapy for PD patients who experience symptom fluctuation with oral l-dopa administration.

Kinetic analysis of saturable hepatic uptake of digoxin and its inhibition by rifampicin

Although the organic anion transporter Oatp2 plays a critical role in determining the hepatic clearance of some drugs, little quantitative information exists about its functional characteristics in relation to inhibition of sinusoidal drug uptake. We investigated the uptake kinetics of the Oatp2 substrate digoxin in the isolated perfused rat liver. In the single-pass perfused liver three consecutive digoxin doses of 15, 30 and 45 μg were administered in the presence or absence of rifampicin (100 μM), an inhibitor of Oatp2. Digoxin was determined in the outflow samples by HPLC and all data were analyzed by simultaneous nonlinear regression assuming a Michaelis–Menten uptake mechanism. Hepatocellular uptake of digoxin was concentration-dependent with a Michaelis constant ( K M) of 577.8 ng/ml. Rifampicin significantly reduced uptake ( K M increased 2.5-fold) without affecting other parameters.

Determining RuBisCO activation kinetics and other rate and equilibrium constants by simultaneous multiple non-linear regression of a kinetic model

The forward and reverse rate constants involved in carbamylation, activation, carboxylation, and inhibition of D-ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) have been estimated by a new technique of simultaneous non-linear regression of a differential equation kinetic model to multiple experimental data. Parameters predicted by the model fitted to data from purified spinach enzyme in vitro included binding affinity constants for non-substrate CO2 and Mg2+ of 200+/-80 microM and 700+/-200 microM, respectively, as well as a turnover number (k(cat)) of 3.3+/-0.5 s(-1), a Michaelis half-saturation constant for carboxylation (K(M,C)) of 10+/-4 microM and a Michaelis constant for RuBP binding (K(M,RuBP)) of 1.5+/-0.5 microM. These and other constants agree well with previously measured values where they exist. The model is then used to show that slow inactivation of RuBisCO (fallover) in oxygen-free conditions at low concentrations of CO2 and Mg2+ is due to decarbamylation and binding of RuBP to uncarbamylated enzyme. In spite of RuBP binding more tightly to uncarbamylated enzyme than to the activated form, RuBisCO is activated at high concentrations of CO2 and Mg2+. This apparent paradox is resolved by considering activation kinetics and the fact that while RuBP binds tightly but slowly to uncarbamylated enzyme, it binds fast and loosely to activated enzyme. This modelling technique is presented as a new method for determining multiple kinetic data simultaneously from a limited experimental data set. The method can be used to compare the properties of RuBisCO from different species quickly and easily.

Kinetic analysis of saturable myocardial uptake of idarubicin in rat heart: effect of doxorubicin and hypothermia.

Little is known of how anthracyclines are transported into the heart. Our previous kinetic study suggested saturable myocardial uptake of idarubicin. This study sought to determine the effects of temperature reduction and of doxorubicin coadministration on the transport process. In Langendorff-perfused rat hearts, a 0.5 mg dose of idarubicin was infused over 10 min. The outflow concentration-time curve as well as the residual amounts in cardiac tissue of idarubicin and its active metabolite idarubicinol were measured after temperature reduction (from 37 degrees C to 30 degrees C) and in the presence of doxorubicin (20 microM) in the perfusate. The outflow concentration-time profile of idarubicin was analyzed by a four-compartment model and simultaneous nonlinear regression. Doxorubicin significantly inhibited the Michaelis-Menten-like uptake process of idarubicin in the heart (50% decrease in Vmax), leading to a decreased net tissue uptake of idarubicin. Kinetic analysis of sensitivity to temperature reduction revealed a 2.6-fold increase in KM; however, this inhibition of idarubicin uptake was counterbalanced by a decrease in efflux rate. These data confirm the existence of a saturable myocardial uptake mechanism for idarubicin and might provide useful information for optimizing anthracycline dosage regiments.

P-glycoprotein inhibitors enhance saturable uptake of idarubicin in rat heart: pharmacokinetic/pharmacodynamic modeling.

Little is known about cardiac uptake kinetics of idarubicin, including a possible protective role of P-glycoprotein (Pgp)-mediated transport. This study therefore investigated uptake and negative inotropic action of idarubicin in the single-pass isolated perfused rat heart by using a pharmacokinetic/pharmacodynamic modeling approach. Idarubicin was administered as a 10-min constant infusion of 0.5 mg followed by a 70-min washout period in the absence and presence of the Pgp antagonists verapamil or amiodarone. Outflow concentration and left ventricular developed pressure were measured and the model parameters were estimated by simultaneous nonlinear regression. The results indicate the existence of a saturable, Michaelis-Menten type uptake process into the heart (K(m) = 3.06 microM, V(max) = 46.0 microM/min). Verapamil and amiodarone significantly enhanced the influx rate (V(max) increased 1.8-fold), suggesting that idarubicin is transported by Pgp directly out of the membrane before it gets into the cell. Verapamil and amiodarone attenuated the negative inotropic action of idarubicin, which was linked to the intracellular concentration of idarubicin.

Calculation of immobilized enzyme reaction progress curves from nested ordered-sequential rate expressions

A method for estimating immobilized enzyme reaction progress curves, using simultaneous non-linear regression analysis of 2–3 substrate concentrations with time, is presented. These facile procedures involve using nested Gauss–Newton curve fitting algorithms on a Microsoft EXCEL spreadsheet. We refer to our technique as "nested" because the analysis consists of two or three mutually parameter-dependent sets of computations associated with bi- or termolecular enzyme-catalyzed reactions, respectively. We have applied the method to immobilized glucose oxidase-catalyzed reactions ([ d-glucose] and [O 2] with time) and found that the kinetic parameters from initial velocity data were similar to those determined by the nested curve fitting method discussed herein.

Use of a spreadsheet to quantitate the equilibrium binding of an allosteric modulator

Using the program Microsoft excel, a spreadsheet was developed for constrained, simultaneous analysis of multiple datasets obtained from equilibrium binding experiments, according to an allosteric model of interaction. This approach was used to quantitate the interaction between the modulator (heptane-1,7-bis (dimethyl 3′-phthalimidopropyl) ammonium bromide) (C 7/3-phth) and the radioligands [ 3 H]N- methylscopolamine and [ 3 H] quinuclidinyl benzilate at cortical and atrial muscarinic receptors. The interaction between various concentrations of the radioligands and C 7/3-phth, in the guinea pig atrium and in the rat cerebral cortex, could be well described by the allosteric model. The affinity of C 7/3-phth for unoccupied atrial receptors was significantly higher than for cortical receptors. The negative cooperativity between [ 3 H] quinuclidinyl benzilate and the modulator was higher in cortex than that between the modulator and [ 3 H]N- methylscopolamine . It is suggested that the described method has wide applicability because of the extensive availability of spreadsheet programs, the analytical advantages offered by constrained, simultaneous nonlinear regression and the ability to adapt the spreadsheet to almost any model of ligand–receptor interaction.

A Kinetic Oxymoron: Concentration-Dependent First-Order Rate Constants for Hydrolysis of Ceftazidime

□ The influence of pH, temperature, and buffers on the hydrolysis of 10–4 M ceftazidime was previously reported. The pH– rate profiles showed that maximum stability occurred in the pH- independent region from 4.5 to 6.5. In the present study, hydrolysis rates of 0.031, 0.14, 0.25, and 0.35M ceftazidime were measured at 30 and 65°C, pH5.5–6.2. The data were consistent with β-lactam hydrolysis and the rapid release of pyridine. The sum of the time- dependent concentrations of ceftazidime and pyridine provided mass balance. Simultaneous nonlinear regression for ceftazidime loss and pyridine formation provided similar rate constants (K) to those determined from first-order plots of ceftazidime loss. Although the loss of ceftazidime was first-order for each initial concentration, the K values increased as the initial concentrations increased. Plots of K versus initial concentration were linear with intercepts similar to the K values for 10–4 M solutions, thus implying that ceftazidime catalyzed its own degradation. At the pH of these studies ceftazidime exists as a base. The ceftazidime catalytic constant, calculated from the slope of the plot, was similar to that found for the general-base catalyst, HPO42–. Therefore, it is feasible that ceftazidime also behaved as a intermolecular general-base catalyst. However, first-order plots exhibited excellent linearity even though the catalyst (ceftazidime) was consumed. This would require that the catalytic moieties on ceftazidime remained relatively constant throughout its hydrolysis. This hypothesis was shown to be consistent with literature reports which indicate that the general-base catalytic groups can remain relatively constant during cephalosporin hydrolysis.

Dynamic energy budgets affect kinetics of xenobiotics in the marine mussel Mytilus edulis

A dynamic energy budget model is applied to describe uptake and elimination kinetics of xenobiotics in the mussel Mytilus edulis. A multi-compartment pharmaco-kinetic model is used in simultaneous non-linear regression analysis of existing experiments. Data on Cd, PCB's and PAH's are analyzed. The contribution of physiological determined variables as body size and tissue composition are evaluated on its influence on the pharmaco-kinetics of the xenobiotics. Internal partitioning over body fractions is related to log K ow values of the organic compounds. Values of the bioconcentration factor (BCF) are evaluated in relation to physiological determined variables as body size, stored energy reserves and accumulated reproductive output.

Simultaneous determination of kinetic and diffusion parameters for the water-gas shift reaction

The water-gas shift reaction was studied at 563–638 K over an industrial ferrochrome catalyst. The reaction rate data could be described by first order kinetics coupled to a diffusional resistance model for isothermal pellets. The model parameters were determined by simultaneous nonlinear regression.

Brain and cerebrospinal fluid uptake of zidovudine (AZT) in rats after intravenous injection

Uptake kinetics of zidovudine into cerebrospinal fluid (CSF) and brain tissue were determined in adult Sprague Dawley male rats after single intravenous injection of 6.7 mg/kg (25 μmol/kg). The drug kinetics in plasma followed biexponential disposition with an initial distribution half-life of approximately 11 minutes and an elimination half-life of 40 minutes. Over the plasma concentration range of 0.2 to 10 μg/ml, the cerebrospinal fluid to plasma ratio averaged 14.8±1.9% whereas the mean brain tissue to plasma ratio was 8.2±1.2% (uncorrected) or 2.3±1.8% (corrected) for the brain vascular space contribution. Simultaneous nonlinear regression analysis of brain, CSF and plasma concentration data indicate that the overall rate constant for efflux of drug from brain is ∼75-fold higher and from CSF is 8-fold higher than the respective rate constants for influx. Thus, the ratio of the efflux to influx appears to be the predominant factor in determining the net accumulation of drug into CSF and brain parenchymal tissue.

Pharmacokinetic Prodrug Modeling: In Vitro and In Vivo Kinetics and Mechanisms of Ancitabine Bioconversion to Cytarabine

Conversion rates of the prodrug ancitabine to the antileukemic cytarabine have been measured in vivo (rabbits) and in vitro (in the presence of rabbit blood and human red blood cells, blood, and plasma) using HPLC analyses for the prodrug, drug, and its inactive metabolite, 1‐β‐D‐arabinosyluracil. These observed pH‐dependent in vitro rate constants were consistent with those for chemical hydrolysis determined from controls using Tris buffers. Hydrolysis of ancitabine to cytarabine is chemically, not enzymatically, mediated. The blood concentration‐time course for administered compound was described by a two‐compartment open model following a rapid intravenous injection of prodrug, drug, or metabolite in each of three rabbits. The in vivo conversion rate constant (kc) following a rapid intravenous prodrug injection was estimated by simultaneous nonlinear regression of ancitabine and cytarabine blood concentration‐time courses using equations for two‐compartment prodrug and drug with all possible models describing potential conversion sites. The best fit was obtained for the case allowing simultaneous conversion of the prodrug in both central and peripheral compartments to the drug in the central compartment with a common value for kc. The resulting kc value (0.09h−1, three rabbits) is similar to that for chemical hydrolysis (0.07h−1) at 38.8°C. Reasons why this agreement is regarded as fortuitous are discussed.

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Little is known about cardiac uptake kinetics of idarubicin, including a possible protective role of P-glycoprotein (Pgp)-mediated transport. This study therefore investigated uptake and negative inotropic action of idarubicin in the single-pass isolated perfused rat heart by using a pharmacokinetic/pharmacodynamic modeling approach. Idarubicin was administered as a 10-min constant infusion of 0.5 mg followed by a 70-min washout period in the absence and presence of the Pgp antagonists verapamil or amiodarone. Outflow concentration and left ventricular developed pressure were measured and the model parameters were estimated by simultaneous nonlinear regression. The results indicate the existence of a saturable, Michaelis-Menten type uptake process into the heart (<i>K</i>_m = 3.06 μM,<i>V</i>_max = 46.0 μM/min). Verapamil and amiodarone significantly enhanced the influx rate (<i>V</i>_max increased 1.8-fold), suggesting that idarubicin is transported by Pgp directly out of the membrane before it gets into the cell. Verapamil and amiodarone attenuated the negative inotropic action of idarubicin, which was linked to the intracellular concentration of idarubicin.