Partial least squares Quantitative Structure-Activity

HQSARhologram quantitative structure-activity relationship, MLR multiple linear regression, PCA principal component analysis, PLS-QSAR partial least-squares quantitative structure-activity relationship, TAACF Tuberculosis Antimicrobial Acquisition and Coordinating Facility STATOO Consulting (Berne, Switzerland)... 

Multivariate calibration has the aim to develop mathematical models (latent variables) for an optimal prediction of a property y from the variables xi,..., jcm. Most used method in chemometrics is partial least squares regression, PLS (Section 4.7). An important application is for instance the development of quantitative structure—property/activity relationships (QSPR/QSAR). 

Partial least squares regression analysis (PLS) has been used to predict intensity of sweet odour in volatile phenols. This is a relatively new multivariate technique, which has been of particular use in the study of quantitative structure-activity relationships. In recent pharmacological and toxicological studies, PLS has been used to predict activity of molecular structures from a set of physico-chemical molecular descriptors. These techniques will aid understanding of natural flavours and the development of synthetic ones. 

A relatively recent development in QSAR research is molecular reference (MOLREF). This molecular modelling technique is a method that compares the structures of any number of test molecules with a reference molecule, in a quantitative structure-activity relationship study (27). Partial least squares regression analysis was used in molecular reference to analyse the relation between X- and Y-matrices. In this paper, forty-two disubstituted benzene compounds were tested for toxicity to Daphnia... 

Odor and taste quality can be mapped by multidimensional scaling (MDS) techniques. Physicochemical parameters can be related to these maps by a variety of mathematical methods including multiple regression, canonical correlation, and partial least squares. These approaches to studying QSAR (quantitative structure-activity relationships) in the chemical senses, along with procedures developed by the pharmaceutical industry, may ultimately be useful in designing flavor compounds by computer. 

Quantitative structure-activity/pharmacokinetic relationships (QSAR/ QSPKR) for a series of synthesized DHPs and pyridines as Pgp (type I (100) II (101)) inhibitors was generated by 3D molecular modelling using SYBYL and KowWin programs. A multivariate statistical technique, partial least square (PLS) regression, was applied to derive a QSAR model for Pgp inhibition and QSPKR models. Cross-validation using the leave-one-out method was performed to evaluate the predictive performance of models. For Pgp reversal, the model obtained by PLS could account for most of the variation in Pgp inhibition (R2 = 0.76) with fair predictive performance (Q2 = 0.62). Nine structurally related 1,4-DHPs drugs were used for QSPKR analysis. The models could explain the majority of the variation in clearance (R2 = 0.90), and cross-validation confirmed the prediction ability (Q2 = 0.69) [ 129]. 

When compounds are selected according to SMD, this necessitates the adequate description of their structures by means of quantitative variables, "structure descriptors". This description can then be used after the compound selection, synthesis, and biological testing to formulate quantitative models between structural variation and activity variation, so called Quantitative Structure Activity Relationships (QSARs). For extensive reviews, see references 3 and 4. With multiple structure descriptors and multiple biological activity variables (responses), these models are necessarily multivariate (M-QSAR) in their nature, making the Partial Least Squares Projections to Latent Structures (PLS) approach suitable for the data analysis. PLS is a statistical method, which relates a multivariate descriptor data set (X) to a multivariate response data set Y. PLS is well described elsewhere and will not be described any further here [42, 43]. 

Kimura, T, Miyashita, Y, Funatsu, K. and Sasaki, S.I. (1996). Quantitative Structure-Activity Relationships of the Synthetic Substrates for Elastase Enzyme Using Nonlinear Partial Least Squares Regression. J.Chem.Inf.Comput.Sci., 36,185-189. 

Marengo, E., Carpignano, R., Savarino, P. and Viscardi, G. (1992). Comparative Study of Different Structural Descriptors and Variable Selection Approaches Using Partial Least Squares in Quantitative Structure-Activity Relationships. Chemom.Intell.Lab.Syst., 14,225-233. 

Clark, M. and Cramer, R.D., III (1993) The probability of chance correlation using partial least squares (PLS). Quantitative Structure-Activity Relationships, 12, 137-145. 

Hoffman, B., Cho, S.J., Zheng, W., Wyrick, S.D., Nichols, D.E., Mailman, R.B. and Tropsha, A. (1999) Quantitative structure-activity relationship modeling of dopamine D-1 antagonists using comparative molecular field analysis, genetic algorifhms-partial least-squares, and K nearest neighbor methods./. Mod. Chom., 42, 3217-3226. 

Kimura, T., Miyashita, Y, Eunatsu, K. and Sasaki, S.l. (1996) Quantitative structure-activity relationships of the synthetic substrates for elastase enzyme using nonlinear partial least squares regression. J. Chem. Inf. Comput. Sci., 36, 185—189. 

Quantitative Structure - Activity Relationships (QSARs) are estimation methods developed and used to predict certain effects or properties of chemical substances, which are primarily based on the structure of the chemicals. The development of QSARs often relies on the application of statistical methods such as multiple linear regression (MLR) or partial least squares regression (PLS). However, since toxicity data often include uncertainties and measurements errors, when the aim is to point out the more toxic and thus hazardous chemicals and to set priorities, order models can be used as alternative to statistical methods such as multiple linear regression. 

Hasegawa K, Funatsu K. Partial least squares modeling and genetic algorithm optimization in quantitative structure-activity relationships. SAR QSAR Environ Res 2000 11 189-209. 

All developments of quantitative structure activity relationships (QSARs)/ quantitative structure-property relationships (QSPRs)/QSDRs go through similar steps (1) collection of a database of measured values for model development and validation/evaluation, (2) selection of chemical descriptors (can include connection indices, atom, bond, or functional groups, molecular orbital calculations), (3) development of the model (develop a correlation between the chemical descriptors and the activity/property/degradation values) using a variety of statistical approaches (linear and non-linear regression, neural networks, partial least squares (PLS), etc. [9]), and (4) validate/evaluate the model for predictability (usually try to use a separate set of chemicals other than the ones used to train the model external validation) [10]. 

K. Hasegawa and K. Funatsu, SAR QSAR Environ. Res., 11(3 ), 189-209 (2000). Partial Least-Squares Modeling and Genetic Algorithm Optimization in Quantitative Structure-Activity Relationships. 

In summary, the support vector machine (SVM) and partial least square (PLS) methods were used to develop quantitative structure activity relationship (QSAR) models to predict the inhibitory activity of nonpeptide HIV-1 protease inhibitors. Cenetic algorithm (CA) was employed to select variables that lead to the best-fitted models. A comparison between the obtained results using SVM with those of PLS revealed that the SVM model is much better than that of PLS. The root mean square errors of the training set and the test set for SVM model were calculated to be 0.2027, 0.2751, and the coefficients of determination (R2) are 0.9800, 0.9355 respectively. Furthermore, the obtained statistical parameter of leave-one-out cross-validation test (Q ) on SVM model was 0.9672, which proves the reliability of this model. Omar Deeb is thankful for Al-Quds University for financial support. 

Chemometrics Multivariate View on Chemical Problems Linear Free Energy Relationships (LFER) Partial Least Squares Projections to Latent Structures (PLS) in Chemistry Pharmacophore and Drug Discovery Quantitative Structure-Activity Relationships in Drug Design. 

CAMD = computer-aided molecular design ES = evolutionary strategies GA = genetic algorithm GFA = genetic function approximation LOF = lack of fit LSE = least squares error MARS = multivariate adaptive regression spline PLS = partial least squares QSAR = quantitative structure-activity relationships RMSE = root mean squared error. 

Linear or nonlinear multiple regression analysis is used as a statistical tool to derive quantitative models, to check the significance of these models and of each individual term in the regression equation. Other statistical methods, such as discriminant analysis, principal component analysis (PCA), or partial least squares (PLS) analysis (see Partial Least Squares Projections to Latent Structures (PLS) in Chemistry) are alternatives to regression analysis (see Che mo me tries Multivariate View on Chemical Problems)Newer approaches compare the similarity of molecules with respect to different physicochemical or other properties with their biological activities. 

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