Reliability evaluation of the design space of the granulation process of mefenamic acid tablets using a bootstrap resampling technique.

The design space of the granulation process of mefenamic acid tablets, based on Box and Behnken design datasets, was described by a response surface method incorporating multivariate spline interpolation. The reliability of the optimal solutions and the acceptance ranges were evaluated by a bootstrap (BS) resampling technique. The distribution of the BS optimal solutions was almost symmetrical; however, several solutions, which were quite different from the original solution, were mixed. The reason for this problem was considered to be the mixing of the global and the local optima. Therefore, we applied self-organizing map (SOM) clustering for dividing data into several clusters and identified the cluster containing the global optima. The accuracy and reproducibility of the optimal solution in the cluster containing the optimal solution were quantitatively evaluated. In addition, the response surfaces modeled from all the BS datasets contained in the cluster were plotted into the same coordinates with the original response surface. The plots of BS optimal solutions were distributed around the original solution. Moreover, the average of all the BS response surfaces sufficiently corresponded with the original response surface. The conservative limits of the 95% confidence intervals of the acceptance ranges in three response variables could be calculated using the standard deviations of the BS response surfaces. Consequently, it was considered that a novel evaluation method based on BS resampling and SOM could be used for quantitatively evaluating the precision of the nonlinear response surface model.

Effect of an experimental design for evaluating the nonlinear optimal formulation of theophylline tablets using a bootstrap resampling technique.

The optimal solutions of theophylline tablet formulations based on datasets from 4 experimental designs (Box and Behnken design, central composite design, D-optimal design, and full factorial design) were calculated by the response surface method incorporating multivariate spline interpolation (RSM(S)). Reliability of these solutions was evaluated by a bootstrap (BS) resampling technique. The optimal solutions derived from the Box and Behnken design, D-optimal design, and full factorial design dataset were similar. The distributions of the BS optimal solutions calculated for these datasets were symmetrical. Thus, the accuracy and the reproducibility of the optimal solutions enabled quantitative evaluation based on the deviations of these distributions. However, the distribution of the BS optimal solutions calculated for the central composite design dataset were almost unsymmetrical, and the basic statistic of these distributions could not be conducted. The reason for this problem was considered to be the mixing of the global and local optima. Therefore, self-organizing map (SOM) clustering was applied to identify the global optimal solutions. The BS optimal solutions were divided into 4 clusters by SOM clustering, the accuracy and reproducibility of the optimal solutions in each cluster were quantitatively evaluated, and the cluster containing the global optima was identified. Therefore, SOM clustering was considered to reinforce the BS resampling method for the evaluation of the reliability of optimal solutions irrespective of the dataset style.

Prediction of the aqueous solvation free energy of organic compounds by using autocorrelation of molecular electrostatic potential surface properties combined with response surface analysis.

Several quantitative structure-property relationship (QSPR) approaches have been explored for the prediction of aqueous solubility or aqueous solvation free energies, DeltaG(sol), as crucial parameter affecting the pharmacokinetic profile and toxicity of chemical compounds. It is mostly accepted that aqueous solvation free energies can be expressed quantitatively in terms of properties of the molecular surface electrostatic potentials of the solutes. In the present study we have introduced autocorrelation molecular electrostatic potential (autoMEP) vectors in combination with nonlinear response surface analysis (RSA) as alternative 3D-QSPR strategy to evaluate the aqueous solvation free energy of organic compounds. A robust QSPR model (r(cv)=0.93) has been obtained by using a collection of 248 organic chemicals. An external test set based on 23 molecules confirmed the good predictivity of the autoMEP/RSA model suggesting its further applicability in the in silico prediction of water solubility of large organic compound libraries.

Linear and nonlinear 3D-QSAR approaches in tandem with ligand-based homology modeling as a computational strategy to depict the pyrazolo-triazolo-pyrimidine antagonists binding site of the human adenosine A2A receptor.

The integration of ligand- and structure-based strategies might sensitively increase the success of drug discovery process. We have recently described the application of Molecular Electrostatic Potential autocorrelated vectors (autoMEPs) in generating both linear (Partial Least-Square, PLS) and nonlinear (Response Surface Analysis, RSA) 3D-QSAR models to quantitatively predict the binding affinity of human adenosine A3 receptor antagonists. Moreover, we have also reported a novel GPCR modeling approach, called Ligand-Based Homology Modeling (LBHM), as a tool to simulate the conformational changes of the receptor induced by ligand binding. In the present study, the application of both linear and nonlinear 3D-QSAR methods and LBHM computational techniques has been used to depict the hypothetical antagonist binding site of the human adenosine A2A receptor. In particular, a collection of 127 known human A2A antagonists has been utilized to derive two 3D-QSAR models (autoMEPs/PLS&RSA). In parallel, using a rhodopsin-driven homology modeling approach, we have built a model of the human adenosine A2A receptor. Finally, 3D-QSAR and LBHM strategies have been utilized to predict the binding affinity of five new human A2A pyrazolo-triazolo-pyrimidine antagonists finding a good agreement between the theoretical and the experimental predictions.

Evaluation of the reliability of nonlinear optimal solutions in pharmaceuticals using a bootstrap resampling technique in combination with Kohonen's self-organizing maps.

The response surface method incorporating multivariate spline interpolation (RSM-S) is a powerful technique for the formulation optimization of pharmaceuticals. However, no satisfactory method has been developed to evaluate the reliability of the optimal solution. We integrated bootstrap (BS) resampling and Kohonen's self-organizing maps (SOM) into RSM-S using the formulation optimization of theophylline tablets as the model experiment. The hardness and the 63.2% drug-release times of the tablets were measured as response variables. Based on the data set obtained, the simultaneous optimal solution was estimated using RSM-S. Leave-one-out cross-validation showed the optimal solution to be reliable. Concurrently, a large number of BS samples were generated from the original data set using BS resampling, and simultaneous optimal solutions for each BS sample (BS optimal solutions) were estimated. The distribution of the BS optimal solutions was far from a normal distribution, suggesting a mixture of global and local optimal solutions. SOM clustering was used to identify the set of global optimal solutions. SOM clustering divided the BS optimal solutions into several clusters, and the reliability of the optimal solution was evaluated from the cluster that included the optimal solution. This study offers a promising method for evaluating the reliability of nonlinear optimal solutions. .

Bootstrap re-sampling technique to evaluate the optimal formulation of theophylline tablets predicted by non-linear response surface method incorporating multivariate spline interpolation.

Optimal solutions of theophylline tablet formulations were derived from three types of experimental datasets, composed of different numbers of data-points using the response surface method incorporating multivariate spline interpolation (RSM(S)). The reliability of these optimal solutions was evaluated by a bootstrap re-sampling technique. Different levels of three causal factors were used as factors of response surface analysis: the lactose/cornstarch ratio (X(1)), the amount of carmellose calcium (X(2)), and the amount of hydroxypropylcellulose (X(3)). The target responses were the dissolution ratio of theophylline for the first 15 min (Y(1)) and the hardness (Y(2)) of each of the prepared tablets. Similar optimal solutions were estimated in three different sizes of datasets. A bootstrap re-sampling with replacements from the original dataset was applied, and optimal solutions for each bootstrap dataset were estimated. The frequency of the distribution of the optimal solution generated by the bootstrap re-sampling technique demonstrated almost normal distribution. The average and standard deviation of the optimal solution distribution were calculated as evaluation indices reflecting the accuracy and reproducibility of the optimal solution. It was confirmed that the accuracy was sufficiently high, irrespective of the dataset size; however, the reproducibility worsened with a decrease in the number of the experimental datasets. Consequently, it was considered that the novel evaluation method based on the bootstrap re-sampling technique was suitable for evaluating the reliability of the optimal solution.

Application of QSAR analysis to organic anion transporting polypeptide 1a5 (Oatp1a5) substrates.

Organic anion transporting polypeptide 1a5, Slco1a5 (previously called Oatp3, Slc21a7) is a multispecific transmembrane transport protein that belongs to the OATP/SLCO superfamily of solute carriers. It is expressed in several epithelial barriers such as the small intestine and the choroid plexus where it might play an important role in the disposition of numerous endogenous and exogenous organic compounds. Since the molecular basis of the multispecificity of Oatp1a5 is not known and the three-dimensional structure not solved yet, we used three-dimensional quantitative structure-activity relationship (3D-QSAR) techniques to obtain topological information on the substrate binding site of the protein. We aligned a heterogeneous data set of 18 Oatp1a5 substrates using the Genetic Algorithm Similarity Program (GASP) and performed comparative molecular field analysis (CoMFA) using this alignment. This resulted in a reasonable QSAR model including steric and electrostatic fields with a leave-one-out cross-validated r(cv)2 value of 0.705 and a no-cross-validated regression coefficient r2 value of 0.949. Based on the derived model we identified new potential Oatp1a5 substrates and confirmed their predicted apparent affinity values experimentally.