Simplified methods for the evaluation of the parameters of the time course of plasma concentration in the one-compartment body model with first-order invasion and first-order drug elimination including methods for ascertaining when such rate constants are equal

The many limitations in determining the pharmacokinetic parameters of firstorder invasion of, and elimination from, the onecompartment body model by the method of residuals or by feathering Ct data can be minimized by applying the simplified methods outlined herein. Comparisons of the apparent volumes of distribution, V, calculated on the premises that the Bateman Function represents k_a>k_e or its converse, k_e>k_a,i.e., flip-flop, can permit a proper choice of the correct version. Estimation of k_e can be obtained by regression of (A₀/V)/C(oncentration) on AUC₁/ Cwhere A₀/Vis estimable from knowledge of C_max and t_max since .The ratio of the magnitude of the rate constant of invasion to that of elimination, m=k_a/k_e,is related to k_et_max by the expression k_et_max=ln m/ (m–1)for all possible values of m.A table for the determination of m from values of k_et_max is given. When bioavailability, =A₀/Dose,is known or complete, k_e and Vcan be determined from the respective ordinate and abscissa of the intersection of and Cl(clearance)/k_e,both plotted against arbitrary k_e values. The two functions may not intersect at low values of mdue to errored C-t values but the k_e value when the two curves are closest (k_min)may approximate k_e.The intersections of and k_eAUCT (AUC_trap)plotted against variable k_e values (Method A) provide estimates of k_e from their abscissa values and A/Vfrom their ordinate values when is unknown. Method B appears to give more reliable estimates of k_e at the k_min of the difference plotted against k_e.Since k_min of this plot is 1/t_max when m=1,the identity of the mas unity underlying the C-t data is indicated when either k_mint_max is approximately unity or k_min ispractically synonymous with 1/t_max.This was clearly shown when 12 constructed m=1,C-t cases with 10% random error were evaluated by Method B. Better estimates were effected by all procedures when the raw C-t data were smoothed.We regretfully announce that Dr. Edward Garrett passed away on October 25, 1993, after an extended illness.     

Stability of pipethanate hydrochloride in aqueous solution

In the present investigation, an attempt has been made to apply the methods of classical chemical kinetics to the hydrolytic reaction of pipethanate hydrochloride. By successively keeping all but one variable essentially constant, it has been possible to resolve the overall effect of the individual contributing factors. Since nearly all commercial pipethanate preparations are formulated with antacid, studies were made at several constant hydrogen ion concentration ranging pH 0.4 to 7.5. Rate measurement was also carried out in temperature ranging from 25°C to 60°C. The hydrolysis of pipethanate is found to be of first order with respect to pipethanate concentration over an experimental range of hydrogen ion concentration (pH 0.4–7.5). The apparent activation energy(Ea) at pH 7.5 is 18.30 Kcal/mole and the frequency factor is 1.1408×10⁹ sec^?1. The rate of the hydrolysis has a minimum at pH 2.5–3.5. In this region the half-life of pipethanate was about 15.3 days at 60°C. The catalytic effect of water was found to be \(K_{H^{ + } } = 1.1568 \times 10^{ - 2 } min^{ - 1} \) at 60°C. The catalytic constants of the hydroxyl ions and hydrogen ions at 60°C were also found to be \(K_{OH^ - } = 4.5519 \times 10^5 min^{ - 1} \) and \(K_{H_2 O} = 3.16 \times 10^{ - 5} {\text{ min}}^{{\text{ - 1}}} \) , respectively. This reaction appears to be primarily base catalyzed hydrolysis and pipethanate is relatively reluctant toward acid catalyzed hydrolysis. A positive primary salt effect was noted in the solution of pipethanate at pH 7.5 and at 60°C.     

Molecular modeling studies on structural requirement of diarylpropionitrile for selectivity to estrogen receptor subtypes

Molecular modeling techniques are widely used to discover drug candidates for selective disease. In the present study, ligand-based drug design techniques have been explored to find the structural requirement of diarylpropionitrile derivatives, a group of non-steroidal estrogen receptor (ER) modulators for selective binding to receptor subtypes. 2D/3D quantitative structure activity relationship (QSAR) and pharmacophore space modeling studies have been explored for this purpose. The classical QSAR models (R _α ² ?=?0.870, Q _α ² ?=?0.813, R _α-pred ² ?=?0.636; R _β ² ?=?0.853, Q _β ² ?=?0.745, R _β-pred ² ?=?0.565) show the importance of molecular refractivity, electronic contribution of atoms C₃, C₇, C₁₃ and C₁₄, and R₂ and R₄ substituents (Fig.?1) for specificity. The 3D QSAR, molecular fields (CoMFA, R _α ² ?=?0.999, Q _α ² ?=?0.679, R _α-pred ² ?=?0.678 and R _β ² ?=?0.999, Q _β ² ?=?0.611, R _β-pred ² ?=?0.691) and similarity (CoMSIA, R _α ² ?=?0.999, Q _α ² ?=?0.670, R _α-pred ² ?=?0.686 and R _β ² ?=?0.999, Q _β ² ?=?0.671, R _β-pred ² ?=?0.590) analyses show contour maps of steric, hydrophobic along with hydrogen bond (HB) donor and acceptor are important factors for binding affinity to both α- and β-subtypes. In addition, electronic contribution is crucial for α-subtype binding. Pharmacophore models derive the importance of HB acceptor and donor, aromatic ring, molecular steric, and hydrophobic interactions for selective binding to receptor subtypes. The derived models are correlated with structure-based molecular docking study, explaining the significant interactions between receptor and ligand for selective subtypes binding.

Study on the quantitative structure–toxicity relationships of aconitine compounds basing on PCA-ANN method

Aconitine compounds are diterpenoid alkaloids found in the roots/rhizome of Aconitum napellus, Aconitum carmichaeli, and other Aconitum plants in the family of Ranunculanceae, which have beneficial pharmacological activity along with toxicity. The quantum chemistry parameters of thirty-six aconitine compounds were calculated using Gaussian software, and the quantitative structure–toxicity relationships of aconitine compounds were studied in mice via oral acute toxicity (LD₅₀). A model was built to more accurately predict the toxicity of aconitine compounds in mice versus oral LD₅₀. Twenty-seven aconitine compounds were used as a training dataset for building the principal component analysis combined with artificial neural network model and nine others as a forecasting dataset to test the prediction ability of the model using SAS 9.0 program software and Matlab 7.5 software. The model derived a good forecasting ability (MSE = 0.50, R ² = 0.9818 $ R_{\text{pred}}^{2} $  = 0.9457, $ r_{{{\text{m}}\left( {\text{test}} \right)}}^{2} $  = 0.9130, $ r_{{{\text{m}}\left( {\text{overal}} \right)}}^{2} $  = 0.9207, $ R_{\text{r}}^{2} $  = 0.6561, $ {\text{c}}R_{\text{r}}^{2} $  = 0.5655).     

Surface characterization of 2-hydroxypyrimidine sulphate by inverse gas chromatography

The net retention volumes, V _N , of n-alkanes and polar probes on 2-hydroxypyrimidine sulphate (2-HPS) drug surface are determined at 323.15, 328.15 and 333.15 K using inverse gas chromatography. The dispersive surface free energy, $ \gamma_{S}^{d} $ of 2-HPS are evaluated by applying Schultz method as well as Dorris–Gray method and found that $ \gamma_{S}^{d} $ values are higher by 8 per cent in the latter method. The $ \gamma_{S}^{d} $ values are decreasing in both the methods with increase of temperature. The specific component of the free energy of adsorption, $ \Updelta G_{a}^{S} $ , for polar probes are obtained by three methods proposed by Schultz et al., Saint Flour–Papirer and Sawyer–Brookman. The Lewis acid–base parameters, K _a and K _b , are calculated using $ \Updelta G_{a}^{S} $ values. The surface character value, S = (K _b /K _a ) according to the Schultz et al., is found to be 3.9 whereas the S value in the other two methods are found to be 6.2 and 5.6. The results demonstrate that the 2-HPS powder surface contain relatively more basic sites and can interact strongly in the acidic media.     

Relationship between plasma or serum drug concentration and amount of drug in the body at steady state upon multiple dosing

The average amount of drug in the body at steady state ( \(\bar X\) )upon repetitive dosing in a two-compartment open system is related to the average steady-state plasma level ( \(\bar C\) )by the apparent volume of distribution at steady state V_ss rather than by V_β,the apparent volume of distribution at pseudodistribution equilibrium, despite the fact that \(\bar C\) is directly proportional to 1/V_β.Multiplication of \(\bar C\) by \(\ddot V_\beta \) results in an overestimate of \(\bar X\) the magnitude of which depends on the distribution and elimination parameters of the drug. The significance and utility of the volume parameters, V_β and V_ss,employed in multicompartment systems are considered.     

The pharmacokinetics of furazlocillin in healthy humans

The pharmacokinetics of the novel acylureidopenicillin furazlocillin, 6-[D-2-(3-furfurylidenamino-2-oxo-imidazolidine-1-carboxamido)-2-(4-hydroxyphenyl)-acetamido]-penicillanic acid and of its penicilloic acid derivative were investigated in five healthy male volunteers after intravenous administration of 2 and 4 g dosages. The volunteers were either in a lying or sitting position throughout the duration of the studies. The concentrations of the drug in plasma and urine were measured by two different methods in parallel: a microbiological assay and a newly developed high pressure liquid chromatography method. The latter method was also applicable for quantitation of the penicilloic acid derivative in these biological fluids. The drug's plasma protein binding (66%) and apparent red cell-plasma partition coefficient (0.055) were concentration independent. The pharmacokinetics of the drug were first order only at the lower dose level The apparent half lives of three distinguishable phases were, respectively, 4 \((t_{1/2_1 } )\) , 18 \((t_{1/2_2 } )\) , and 64 \((t_{1/2_z } )\) .     

Bayesian Approach to Estimate AUC,Partition Coefficient and Drug Targeting Index for Studies with Serial Sacrifice Design

Purpose

The current study presents a Bayesian approach to non-compartmental analysis (NCA), which provides the accurate and precise estimate of AUC ₀ ^∞ and any AUC ₀ ^∞ -based NCA parameter or derivation.

Methods

In order to assess the performance of the proposed method, 1,000 simulated datasets were generated in different scenarios. A Bayesian method was used to estimate the tissue and plasma AUC ₀ ^∞ s and the tissue-to-plasma AUC ₀ ^∞ ratio. The posterior medians and the coverage of 95% credible intervals for the true parameter values were examined. The method was applied to laboratory data from a mice brain distribution study with serial sacrifice design for illustration.

Results

Bayesian NCA approach is accurate and precise in point estimation of the AUC ₀ ^∞ and the partition coefficient under a serial sacrifice design. It also provides a consistently good variance estimate, even considering the variability of the data and the physiological structure of the pharmacokinetic model. The application in the case study obtained a physiologically reasonable posterior distribution of AUC, with a posterior median close to the value estimated by classic Bailer-type methods.

Conclusions

This Bayesian NCA approach for sparse data analysis provides statistical inference on the variability of AUC ₀ ^∞ -based parameters such as partition coefficient and drug targeting index, so that the comparison of these parameters following destructive sampling becomes statistically feasible.     

Improved superaugmented eccentric connectivity indices

Topochemical versions of all the four superaugmented eccentric connectivity indices (denoted by: ^SAc ξ₄ ^c, ^SAc ξ₅ ^c, ^SAc ξ ₆ ^c , and ^SAc ξ ₇ ^c ) were utilized for the development of models for prediction of hiCE and hCE1 inhibitory activities. The values of these topochemical indices were computed for each of the 65 analogs constituting the data set using an in-house computer program. Resulting data was analyzed and suitable models were developed after identification of the active ranges by maximization of moving average with regard to active derivatives. Subsequently, two biological activities were assigned to each analog using proposed models, which were then compared with the reported hiCE and hCE1 inhibitory activities. Statistical significance of topological indices/models was investigated through sensitivity, specificity, and Matthews correlation coefficient (MCC). The overall accuracy of prediction varied from a minimum of 81% for a model based upon ^SAc ξ ₄ ^c to a maximum of 92% in case of a model based upon ^SAc ξ ₅ ^c with regard to hiCE inhibitory activity and from a minimum of 85% for a model based upon ^SAc ξ ₄ ^c to a maximum of 94% in case of a model based upon ^SAc ξ ₇ ^c with regard to hCE1 inhibitory activity. An excellent relationship between new generation superaugmented eccentric connectivity topochemical indices ( ^SAc ξ ₄ ^c , ^SAc ξ ₅ ^c , ^SAc ξ ₆ ^c , and ^SAc ξ ₇ ^c ) and hiCE and hCE1 inhibitory activities can be attributed to the sensitivity of the proposed topological indices toward nature, number, and relative position of heteroatom. High predictability amalgamated with high potency of the active ranges offer proposed models a vast potential for providing lead structures for development of potent and selective hiCE and hCE1 inhibitors.     

Receptor and ligand-based 3D-QSAR study on a series of nonsteroidal anti-inflammatory drugs

Self-organizing molecular field analysis (SOMFA) has been used to study the correlation between the molecular properties of a series of 33 stilbene analogs and the cyclooxygenase-2 (COX-2) inhibitory activities. Thus, two different alignments and four charge-assigning methods using grid spacing of 1 Å were investigated to produce eight SOMFA models. The best one derived from the superposition of docked conformation with PM3 charge showed satisfied statistical results. It is characterized by a good noncross-validated r ² (0.806), cross-validated $ r_{\text{cv}}^{ 2} $ (0.799) and F test value (128.673). In addition, the resulted SOMFA model was validated by an external set of ten compounds. The statistical results, predicted correlation coefficient $ r_{\text{Test}}^{ 2} $  = 0.651, metric $ r_{{m({\text{Test}})}}^{ 2} $  = 0.514, and the squared correlation coefficient between observed and predicted values r ² = 0.762, show a satisfied predictive ability. The analysis of SOMFA model, through electrostatic and shape grids, helped in understanding the possible structural modifications of molecules to improve the inhibitory potency.     

Docking-based 3D-QSAR modeling of the inhibitors of IMP metallo-β-lactamase

IMP metallo-β-lactamases (MBLs) confer broad-spectrum resistance to β-lactam antibiotics such as imipenem and escape the action of almost all clinically used β-lactamase inhibitors. We conducted three-dimensional quantitative structure–activity relationships (3D-QSAR) for a series of IMP-1 MBL inhibitors with the aid of docking-based alignment. While the 3D-QSAR models were created based on a training set of 41 compounds, their external predictivity was validated using a test set of eight compounds. The study has resulted in two types of satisfactory 3D-QSAR models for predicting the biological activity of new compounds: CoMFA model (r ² = 0.989; $ r_{\text{pre}}^{ 2} = 0. 8 4 3 $ ) and CoMSIA model (r ² = 0.968; $ r_{\text{pre}}^{ 2} = 0. 9 5 7 $ ). Our work will facilitate the design and optimization of new potential inhibitors.     

k nearest neighbor-molecular field analysis on human HCV NS5B polymerase inhibitors: 2,5-disubstituted imidazo[4,5-c]pyridines

The k nearest neighbor-molecular field analysis (kNN-MFA) is used to study the correlation between the molecular properties and biological activities of the recently reported 2,5-disubstituted imidazo[4,5-c]pyridines as anti-HCV agents. The most predictive kNN-MFA model derived from the superposition of docked conformations, has good cross-validated q ² (0.96) and satisfied predictive ability $ r_{\text{pred}}^{2} $ (0.88). It could rationalize the HCV inhibitory activity profile of many compounds used in the present study as well as the important structural features responsible for activity. Furthermore, the effects of various structural modifications on biological activity are investigated, and biological activities of novel structures are estimated using the developed 3D QSAR model.     

Analysis of the inhibiting activity of presynaptic\alpha _{2^ - } ADRENOCEPTORS against NSAID-induced gastric mucosal lesions in the ratagainst NSAID-induced gastric mucosal lesions in the rat

Clonidine at a dose of 0.00625–0.025 mg/kg (po) inhibited the gastric mucosal lesions induced by indomethacin, acidified aspirin, naproxen and piroxicam. The gastroprotective effect was reversed by the $\alpha _{2^ - } ADRENOCEPTORS$ antagonist yohimbine (5 mg/kg sc) and by the highly selective $\alpha _{2^ - } andrenoceptor$ antagonist berbane derivative, Ch-38083 (3.5 mg/kg sc). Clonidine also decreased the gastric acid secretion in pylorus-ligated rats at a dose of 0.2 mg/kg (given intraduodenally) but not at gastroprotective doses (0.00625–0.025 mg/kg). The antisecretory effect of clonidine was reversed by both yohimbine and Ch-38083. The $\alpha _{2B^ - receptor} $ antagonist prazosin (0.1 mg/kg sc) blocked the gastroprotective effect but failed to influence the antisecretory action of clonidine. Our data suggest that the $\alpha _{2B^ - androceptor} $ subtype might be involved in gastroprotection; however, the antisecretory effect is likely to be mediated by $\alpha _{2A^ - like} $ adrenoceptor subtype.     

Molecular docking and 3D-QSAR studies on the MAPKAP-K2 inhibitors

Mitogen-activated protein kinase-activated protein kinase 2 (MAPKAP-K2) has been identified as a drug target for the treatment of inflammatory diseases. Therefore, there is an urgent need to develop new classes of MAPKAP-K2 inhibitors. To understand the structure activity correlation of MAPKAP-K2 inhibitors, we have carried out a molecular docking study and three-dimensional quantitative structure–activity relationship (3D-QSAR) modeling. Both comparative molecular field analysis ( $r_{\text{cv}}^{2}$  = 0.602, $r_{\text{ncv}}^{2}$  = 0.955) and comparative molecular similarity indices analysis ( $r_{\text{cv}}^{2}$  = 0.546, $r_{\text{ncv}}^{2}$  = 0.891) models were generated using the training set on the basis of the common substructure-based alignment and gave reasonable results. The structural insights obtained from both the 3D-QSAR contour maps and molecular docking help to better interpret the structure activity relationship. The results obtained from this study will be useful in the design of potent MAPKAP-K2 inhibitors.     

3D-QSAR analysis of anti-cancer agents by CoMFA and CoMSIA

Three-dimensional quantitative structure–activity relationships were performed for a series of isatin derivatives as anti-cancer agents using the CoMFA and CoMSIA methods. Statistically significant CoMFA ( $r_{\text{cv}}^{2} = 0.869,\;r_{\text{ncv}}^{2} = 0.962$ ) and CoMSIA ( $r_{\text{cv}}^{2} = 0.865,\;r_{\text{ncv}}^{2} = 0.959$ ) models were generated using the training set on the basis of the common substructure-based alignment. Further, the predictive ability of the CoMFA and CoMSIA models was determined using a test set of nine compounds. Based on the information derived from CoMFA and CoMSIA contour maps, we have identified some key features for increasing the activity of compounds and have been used to design new anti-cancer agents. The newly designed molecules in this series of compounds may be more potent anti-cancer agents.     

Dynamic bioavailability of copper in soil estimated by uptake and elimination kinetics in the springtail Folsomia candida

This study aimed to assess the bioavailability of copper in soil, by measuring its uptake kinetics into a representative soil invertebrate, the collembolan Folsomia candida. The animals were exposed to 25 or 100 μg Cu g^?1 dry LUFA 2.2 soil at nominal $ {\text{pH}}_{{{\text{CaCl}}_{ 2} }} $ 4.5, 5.5, or 6.5 during 14 days after which they were transferred to clean soil for 14 days elimination. Uptake and elimination rate constants were calculated based on total and extractable soil concentrations and porewater concentrations using one-compartment first-order kinetics modelling. Copper was present in the animals at a basal physiological level of 40–90 μg g^?1dry weight, on top of this uptake and elimination kinetics were observed. Uptake rates constants varied between 0.02 and 0.17 g_soil g _animal ^?1  day^?1, being higher at lower exposure level, but did not differ significantly between different soil pH levels. Elimination rate constants ranged between 0.04 and 0.20 day^?1 and were negligible (k₂ < 0.001 day^?1) at pH 4.5 and 6.5. Multiple linear regressions showed that the pH effect on copper uptake was only significant when taking into account cation exchange capacity, or calcium and dissolved organic carbon levels in the pore water. Copper concentrations in the animals however, never were higher than 185 μg g^?1 dry weight, independent of exposure level and pH, suggesting homeostatic regulation. These results show that the chemical composition of the pore water does affect bioavailability of copper in soil, but that copper uptake in collembolans is dominated by homeostatic regulation rather than by soil properties like pH.