Multi-parameter Linear Regression Research Articles

Amino acid profiles and quantitative structure–property relationship models as markers for Merlot and Torrontés wines

Quantitative structure–property relationships (QSPRs) were applied to the aminograms obtained by HPLC in our laboratories for Torrontés and Merlot wines. Dragon theoretical descriptors were derived for a set of optimized amino acid structures with the purpose of establishing QSPR models. The statistical Replacement Method was used for designing the best multi-parametric linear regression models, which included structural features selected from a pool containing 1497 constitutional, topological, geometrical or electronic molecular descriptors. Predicted QSPR results were in good agreement with experimental amino acid profiles. The developed QSPR approach showed to be of practical value for distinguishing each wine varietal, and for calculating experimentally non-available amino acid concentrations of Torrontés and Merlot wines. It was also useful for assessing wine authenticity; the models were especially suitable for Merlot and Torrontés wines.

Quantitative structure–property relationship analyses of aminograms in food: Hard cheeses

The concentrations of the amino acids of Reggianito Argentino and Goya full-ripened industrial Argentine hard cheeses were subjected to quantitative structure–property relationship (QSPR) models. We used the statistical Replacement Method technique for designing the best multi-parametric linear regression models, which included structural features selected from a pool containing 1497 molecular descriptors. Predicted QSPR values were in good agreement with experimental amino acid profiles carried out in our laboratories. The developed approach is of practical value, especially to assign unknown analyte concentrations for Reggianito Argentino and Goya cheeses, and to establish whether any cheese sample belongs to these kinds of hard cheeses.

Prediction of Sea of Japan (East Sea) acidification over the past 40 years using a multiparameter regression model

A multiparameter linear regression model (MLR) of aragonite saturation state (ΩARG) as a function of temperature, pressure and O2 concentration in the upper 1,000 m of the Sea of Japan (East Sea) was derived with an uncertainty of ±0.020 (1σ). The ΩARG data (n = 1,482) used to derive the basin‐wide ΩARG prediction model were collected during a field survey in 1999 and were corrected for anthropogenic CO2. Some biases were resolved by addition of a pressure and O2 concentration interaction term to the proposed model. Correlation between the two predictor terms, caused by addition of this term, was minimized by centering the data for the three variables (thus subtracting the mean from each individual data point). Validation of the model against data sets obtained in 1992 and 2007 yielded correlation coefficients of 0.995 ± 0.013 for 1992 (n = 64, p ≪ 0.001) and 0.995 ± 0.009 for 2007 (n = 137, p ≪ 0.001) and root mean square errors of ±0.064 for 1992 and ±0.050 for 2007. The strong correlation between measurements and predictions suggests that the model can be used to estimate the distribution of ΩARG in the Sea of Japan (East Sea) (including dynamic coastal waters) on varying time scales when basic hydrographic data on temperature, pressure and O2 concentration are available. Application of the model to past measurements for the Sea of Japan (East Sea) indicated that interdecadal variability (2σ from the mean) in ΩARG corrected for anthropogenic CO2 was generally high (0.1–0.7) in the upper water layer (<200 m depth), and decreased (0.05–0.2) with depth for waters deeper than 500 m. The interdecadal variability is largely controlled by variations in the degree of water column ventilation. Superimposed on this natural variability, the input of CO2 derived from fossil fuels has markedly acidified the upper water layers during the anthropocene and thereby moved the aragonite saturation horizon upward by 50–250 m. The impact of CO2 derived from fossil fuels on upper ocean acidification will increase in the future. The present study indicates that, in combination with other easily measurable parameters, a multifunctional model can be a powerful tool for predicting the temporal evolution of ΩARG in the ocean, including coastal waters that are highly likely to be susceptible to ocean acidification in the future.

QSPR analyses for aminograms in food: Citrus juices and concentrates

Dragon theoretical descriptors were derived for a set of optimised amino acid structures, with the purpose of establishing quantitative structure–property relationship (QSPR) models to predict aminograms for 100% natural fresh juices and concentrates of Navel and Valencia oranges, and Eureka lemon. We used the statistical replacement method technique for designing the best multi-parametric linear regression models, which included structural features selected from a pool containing 1497 constitutional, topological, geometrical, or electronic types of molecular descriptors. The prediction results achieved in this work were in most cases in good agreement with experimental amino acid profiles obtained in our laboratories by a validated HPLC procedure, thus demonstrating the predictive power of the designed QSPR. The developed approach is of practical value, especially when it is not possible to assign the analyte concentration with an accurate degree of certainty.

Formaldehyde and its relation to CO, PAN, and SO<sub>2</sub> in the Houston-Galveston airshed

Abstract. The Houston-Galveston Airshed (HGA) is one of the major metropolitan areas in the US that is classified as a nonattainment area of federal ozone standards. Formaldehyde (HCHO) is a key species in understanding ozone related air pollution; some of the highest HCHO concentrations in North America have been reported for the HGA. We report on HCHO measurements in the HGA from summer 2006. Among several sites, maximum HCHO mixing ratios were observed in the Houston Ship Channel (HSC), a region with a very high density of industrial/petrochemical operations. HCHO levels at the Moody Tower (MT) site close to downtown were dependent on the wind direction: southerly maritime winds brought in background levels (0.5–1 ppbv) while trajectories originating in the HSC resulted in high HCHO (up to 31.5 ppbv). Based on the best multiparametric linear regression model fit, the HCHO levels at the MT site can be accounted for as follows: 38.5±12.3% from primary vehicular emissions (using CO as an index of vehicular emission), 24.1±17.7% formed photochemically (using peroxyacetic nitric anhydride (PAN) as an index of photochemical activity) and 8.9±11.2% from industrial emissions (using SO2 as an index of industrial emissions). The balance 28.5±12.7% constituted the residual which cannot be easily ascribed to the above categories and/or which is transported into the HGA. The CO related HCHO fraction is dominant during the morning rush hour (06:00–09:00 h, all times are given in CDT); on a carbon basis, HCHO emissions are up to 0.7% of the CO emissions. The SO2 related HCHO fraction is significant between 09:00–12:00 h. After 12:00 h HCHO is largely formed through secondary processes. The HCHO/PAN ratios are dependent on the SO2 levels. The SO2 related HCHO fraction at the downtown site originates in the ship channel. Aside from traffic-related primary HCHO emissions, HCHO of industrial origin serves as an appreciable source for OH in the morning.

Amino acid profiles and quantitative structure–property relationships for malts and beers

Experimental amino acid concentrations of blonde and black commercial beers, brewed in Argentina, as well as national malts were subjected for the first time to Quantitative Structure–Property Relationships (QSPRs). Thus, Dragon theoretical descriptors were derived for a set of optimised amino acid structures with the purpose of assessing QSPR models. We used the statistical Replacement Method for designing the best multi-parametric linear regression models, which included structural features selected from a pool containing 1497 constitutional-, topological-, geometrical-, and electronic-type molecular descriptors. In this work QSPR results were in good agreement with experimental amino acid profiles, thus demonstrating the predictive power of the designed QSPRs. QSPR-modelling was used to predict aminograms, and was also used to estimate non-available amino acid concentrations for these malts, and beers. The developed QSPR approach showed to be an useful tool for discriminating among blonde and dark beers, and malts. This is a new application of the QSPR theory to food, in particular to chemical biomarkers of malts and beers.

QSAR analysis on Spodoptera litura antifeedant activities for flavone derivatives

We establish useful models that relate experimentally measured biological activities of compounds to their molecular structure. The pED 50 feeding inhibition on Spodoptera litura species exhibited by aurones, chromones, 3-coumarones and flavones is analyzed in this work through the hypothesis encompassed in the Quantitative Structure–Activity Relationships (QSAR) Theory. This constitutes a first necessary computationally based step during the design of more bio-friendly repellents that could lead to insights for improving the insecticidal activities of the investigated compounds. After optimizing the molecular structure of each furane and pyrane benzoderivative with the semiempirical molecular orbitals method PM3, more than a thousand of constitutional, topological, geometrical and electronic descriptors are calculated and multiparametric linear regression models are established on the antifeedant potencies. The feature selection method employed in this study is the Replacement Method, which has proven to be successful in previous analyzes. We establish the QSAR both for the complete molecular set of compounds and also for each chemical class, so that acceptably describing the variation of the inhibitory activities from the knowledge of their structure and thus achieving useful predictive results. The main interest of developing trustful QSAR models is that these enable the prediction of compounds having no experimentally measured activities for any reason. Therefore, the structure–activity relationships are further employed for investigating the antifeedant activity on previously synthesized 2-,7-substituted benzopyranes, which do not pose any measured values on the biological expression. One of them, 2-(α-naphtyl)-4H-1-benzopyran-4-one, results in a promising structure to be experimentally analyzed as it has predicted pED 50 = 1.162.

Application of a genetic algorithm and an artificial neural network for global prediction of the toxicity of phenols to Tetrahymena pyriformis.

Genetic algorithm (multiparameter linear regression; GA-MLR) and genetic algorithm–artificial neural network (GA-ANN) global models have been used for prediction of the toxicity of phenols to Tetrahymena pyriformis. The data set was divided into 150 molecules for training, 50 molecules for validation, and 50 molecules for prediction sets. A large number of descriptors were calculated and the genetic algorithm was used to select variables that resulted in the best-fit to models. The six molecular descriptors selected were used as inputs for the models. The MLR model was validated using leave-one-out, leave-group-out cross-validation and external test set. A three-layered feed forward ANN with back-propagation of error was generated using six molecular descriptors appearing in the MLR model. Comparison of the results obtained using the ANN model with those from the MLR revealed the superiority of the ANN model over the MLR. The root mean square error of the training, validation, and prediction sets for the ANN model were calculated to be 0.224, 0.202, and 0.224 and correlation coefficients (r 2) of 0.926, 0.943, and 0.925 were obtained. The improvements are because of non-linear correlations of the toxicity of the compounds with the descriptors selected. The prediction ability of the GA-ANN global model is much better than that of previously proposed models.Graphical

Application of genetic algorithm-support vector machine (GA-SVM) for prediction of BK-channels activity

The support vector machine (SVM), which is a novel algorithm from the machine learning community, was used to develop quantitative structure–activity relationship (QSAR) for BK-channel activators. The data set was divided into 57 molecules of training and 14 molecules of test sets. A large number of descriptors were calculated and genetic algorithm (GA) was used to select variables that resulted in the best-fitted for models. A comparison between the obtained results using SVM with those of multi-parameter linear regression (MLR) revealed that SVM model was much better than MLR model. The improvements are due to the fact that the activity of the compounds demonstrates non-linear correlations with the selected descriptors. Also distances between Oxygen and Chlorine atoms, the mass, the van der Waals volume, the electronegativity, and the polarizability of the molecules are the main independent factors contributing to the BK-channels activity of the studied compounds.

Solvent effects on kinetics of an aromatic nucleophilic substitution reaction in mixtures of an ionic liquid with molecular solvents and prediction using artificial neural networks

AbstractKinetics of the reaction between 1‐chloro‐2,4‐dinitrobenzene and aniline was studied in mixtures of 1‐ethyl‐3‐methylimidazolium ethylsulfate ([EMIM][EtSO4]) with methanol, chloroform, and dimethylsulfoxide at 25°C. Single‐parameter correlations of log kA versus normalized polarity parameter (ENT), hydrogen‐bond acceptor basicity (β), hydrogen‐bond donor acidity (α), and dipolarity/polarizability (π*) of media do not give acceptable results. Multiparameter linear regression (MLR) of log kA versus the solvatochromic parameters demonstrates that the reaction rate constant increases with ENT, π*, and β and decreases with α parameter. To predict accurately solvent effects on the rate constant, optimized artificial neural network with three inputs (including α, π*, and β parameters) was applied for prediction of the log kA values in the prediction set. It was found that properly selected and trained neural network could fairly represent the dependence of the reaction rate constant on solvatochromic parameters. Mean percent deviation of 5.023 for the prediction set by the MLR model should be compared with the value of 0.343 by the artificial neural network model. These improvements are due to the fact that the reaction rate constant shows nonlinear correlations with the solvatochromic parameters. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 41: 153–159, 2009

Regionally Specific Cortical Thinning in Children with Sickle Cell Disease

Sickle cell disease (SCD) is a chronic disease with a significant rate of neurological complications in the first decade of life. In this retrospective study, cortical thickness was examined in children with SCD who had no detectable abnormalities on conventional magnetic resonance imaging/magnetic resonance angiography. Regional differences in cortical thickness from SCD were explored using age-matched healthy controls as comparison. A comparison analysis was done for SCD (n = 28) and controls (n = 29) based on age (5-11; 12-21 years), due to the age-dependent variation in cortex maturation. Distinct regions of thinning were found in SCD patients in both age groups. The number, spatial extent, and significance (P < 0.001) of these areas of thinning were increased in the older SCD group. Regions of interest (ROIs) were defined on the areas of highly significant thinning in the older group and then mapped onto the younger cohort; a multiparametric linear regression analysis of the ROI data demonstrated significant (P < 0.001) cortical thinning in SCD subjects, with the largest regions of thinning in the precuneus and the posterior cingulate. The regionally specific differences suggest that cortical thickness may serve as a marker for silent insults in SCD and hence may be a useful tool for identifying SCD patients at risk for neurological sequelae.

QSAR study of the 5-HT1A receptor affinities of arylpiperazines using a genetic algorithm–artificial neural network model

Genetic algorithm–multiparameter linear regression (GA–MLR) and genetic algorithm–artificial neural network (GA–ANN) models have been used for prediction of the 5-HT1A receptor affinities (pK i ) of 66 arylpiperazines. A large number of theoretical descriptors were calculated for each compound. The genetic algorithm (GA) was used for selection of the variables that resulted in the best fit to the MLR and ANN models. The models were generated using seven descriptors as variables. For evaluation of the predictive power of the models, pK i values of 13 compounds in the prediction set were calculated. Mean percentage deviation (MPD) for the GA–MLR and GA–ANN models were 0.344 and 0.065, respectively. Comparison of the results obtained by use of the models reveals the GA–ANN model is superior to the GA–MLR model.

Artificial Neural Network Prediction of Normalized Polarity Parameter for Various Solvents with Diverse Chemical Structures

Artificial neural networks (ANNs) are successfully developed for the modeling and prediction of normalized polarity parameter (ETN) of 216 various solvents with diverse chemical structures using a quantitative-structure property relationship. ANN with architecture 5-9-1 is generated using five molecular descriptors appearing in the multi-parameter linear regression (MLR) model. The most positive charge of a hydrogen atom (q+), total charge in molecule (qt), molecular volume of solvent (Vm), dipole moment (μ) and polarizability term (πI) are input descriptors and its output is ETN. It is found that properly selected and trained neural network with 192 solvents could fairly represent the dependence of normalized polarity parameter on molecular descriptors. For evaluation of the predictive power of the generated ANN, an optimized network is applied for prediction of the ETN values of 24 solvents in the prediction set, which are not used in the optimization procedure. Correlation coefficient (R) and root mean square error (RMSE) of 0.903 and 0.0887 for prediction set by MLR model should be compared with the values of 0.985 and 0.0375 by ANN model. These improvements are due to the fact that the ETN of solvents shows non-linear correlations with the molecular descriptors.

Kinney Revisited: An Improved Group Contribution Method for the Prediction of Boiling Points of Acyclic Alkanes

The classical Kinney method for predicting the boiling points of acyclic alkanes is taken as the starting point for the development of a much more accurate group contribution method developed using multiparametric linear regression. The procedure involves calculating a revised “boiling point number” (YR) from a count of structural features, including the length of the longest carbon chain, the nature and location of substituents, and the overall shape of the molecule. For a combined data set of 198 acyclic alkanes having from 6 to 30 carbon atoms, the correlation of predicted and literature boiling points has an R2 of 0.999 and an average absolute deviation of 1.45 K. Thus, the method reported here is comparable in accuracy to, but much easier to apply than, more elaborate molecular connectivity, nonlinear regression, and neural network methods that were developed for narrower ranges of molecular weights.

Prediction Acidity Constant of Various Benzoic Acids and Phenols in Water Using Linear and Nonlinear QSPR Models

An artificial neural network (ANN) is successfully presented for prediction acidity constant (pKa) of various benzoic acids and phenols with diverse chemical structures using a nonlinear quantitative structure-property relationship. A three-layered feed forward ANN with back-propagation of error was generated using six molecular descriptors appearing in the multi-parameter linear regression (MLR) model. The polarizability term <TEX>$(\pi_1)$</TEX>, most positive charge of acidic hydrogen atom <TEX>$(q^+)$</TEX>, molecular weight (MW), most negative charge of the acidic oxygen atom <TEX>$(q^-)$</TEX>, the hydrogen-bond accepting ability <TEX>$(\epsilon_B)$</TEX> and partial charge weighted topological electronic (PCWTE) descriptors are inputs and its output is pKa. It was found that properly selected and trained neural network with 205 compounds could fairly represent dependence of the acidity constant on molecular descriptors. For evaluation of the predictive power of the generated ANN, an optimized network was applied for prediction pKa values of 37 compounds in the prediction set, which were not used in the optimization procedure. Squared correlation coefficient <TEX>$(R^2)$</TEX> and root mean square error (RMSE) of 0.9147 and 0.9388 for prediction set by the MLR model should be compared with the values of 0.9939 and 0.2575 by the ANN model. These improvements are due to the fact that acidity constant of benzoic acids and phenols in water shows nonlinear correlations with the molecular descriptors.

Application of artificial neural networks for predicting the aqueous acidity of various phenols using QSAR

Artificial neural networks (ANNs) have been successfully trained to model and predict the acidity constants (pK(a)) of 128 various phenols with diverse chemical structures using a quantitative structure-activity relationship. An ANN with 6-14-1 architecture was generated using six molecular descriptors that appear in the multi-parameter linear regression (MLR) model. The polarizability term (pi (I)), most positive charge of acidic hydrogen atom (q+), molecular weight (MW), most negative charge of the phenolic oxygen atom (q-), the hydrogen-bond accepting ability (epsilon(B)) and partial-charge weighted topological electronic (PCWTE) descriptors are inputs and its output is pK(a). It was found that a properly selected and trained neural network with 106 phenols could represent the dependence of the acidity constant on molecular descriptors fairly well. For evaluation of the predictive power of the ANN, an optimized network was used to predict the pK(a)s of 22 compounds in the prediction set, which were not used in the optimization procedure. A squared correlation coefficient (R2) and root mean square error (RMSE) of 0.8950 and 0.5621 for the prediction set by the MLR model should be compared with the values of 0.99996 and 0.0114 by the ANN model. These improvements are due to the fact that the pK(a) of phenols shows non-linear correlations with the molecular descriptors. [Figure: see text].

Anthropogenic CO&lt;sub&gt;2&lt;/sub&gt; in the ocean

The focus of this review article is on the anthropogenic CO 2 taken up by the ocean. There are several methods of identifying the anthropogenic CO 2 signal and quantifying its inventory in the ocean. The ?C* method is most frequently used to estimate the global distribution of anthropogenic CO 2 in the ocean. Results based on analysis of the dataset obtained from the comprehensive surveys of inorganic carbon distribution in the world oceans in the 1990s are given. These surveys were jointly conducted during the World Ocean Circulation Experiment (WOCE) and the Joint Global Ocean Flux Study (JGOFS). This data set consists of 9618 hydrographic stations from a total of 95 cruises, which represents the most accurate and comprehensive view of the distribution of inorganic carbon in the global ocean available today. The increase of anthropogenic CO2 in the ocean during the past few decades is also evaluated using direct comparison of results from repeat surveys and using statistical method of Multi-parameter Linear Regression (MLR). The impact of increasing oceanic anthropogenic CO 2 on the calcium carbonate system in the ocean is reviewed briefly as well. Extensive studies of CaCO 3 dissolution as a result of increasing anthropogenic CO 2 in the ocean have revealed several distinct oceanic regions where the CaCO 3 undersaturation zone has expanded.

Prediction of Solvent Effects on Rate Constant of [2+2] Cycloaddition Reaction of Diethyl Azodicarboxylate with Ethyl Vinyl Ether Using Artificial Neural Networks

predictive power of the generated ANN, the optimized network with 68 various solvents as training set was used to predict log k2 of the reaction in 16 solvents in the prediction set. The results obtained using ANN was compared with the experimental values as well as with those obtained using multi-parameter linear regression (MLR) model and showed superiority of the ANN model over the regression model. Mean square error (MSE) of 0.0806 for the prediction set by MLR model should be compared with the value of 0.0275 for ANN model. These improvements are due to the fact that the reaction rate constant shows non-linear correlations with the descriptors.

QSAR modeling on binding affinity of diverse estrogenic flavonoids: electronic, topological and spatial functions in quantitative approximation

Phytoestrogens have been explored as promising next generation estrogenic drug candidates with minimum cardiovascular risks. Investigating spatial, electronic and topological properties of the molecules, structure-activity relationships were drawn in an endeavor to find out the basic pharmacophore features of flavonoids for binding with the estrogen receptor. Implementing multi-parameter linear regression analysis, a significant relationship ( R 2=0.892 and Q 2=0.805 for n=19) was established that explained 86.097% variance in binding affinity to the receptor. This study revealed the importance of partial charges at atoms C 2′ and C 4′ in the phenyl ring C, electrotoplogical state of atom C 7 in the phenyl ring A and the molecular orientation and conformational stringency factors. It has been found that substitution by an e − donating group in the phenyl ring at C 2′, e − withdrawing groups at C 4′ and C 7 of the molecule in conjunction with minimal conformational rigidity could be important for estrogenic activity.

Estimation of pressure pulse amplification between aorta and brachial artery using stepwise multiple regression models

The pressure pulse is amplified between the aorta and peripheral sites. This study compares two methods to estimate pressure pulse amplification (PPA) between the aorta and the brachial artery. Method 1: PPA was determined from a multi-parameter linear regression of subject parameters (gender, age, height, weight, heart rate (HR), brachial systolic pressure (BSP), diastolic pressure (BDP), mean pressure (MP)). Method 2: PPA was calculated from central aortic pressure waveforms (CW) estimated from the same subject parameters. The sample population (1421 male, 992 female) was selected from a database where aortic pressure was estimated by mathematical transformation of a peripheral (radial) pulse calibrated to sphygmomanometric BSP and BDP. The two methods were consistent in showing HR and MP as the most important parameters to estimate PPA. Correlation coefficients (R2) of 0.48 (method 1) and 0.44 (method 2) were obtained using height, weight, HR, BSP, BDP and age. Inclusion of MP increased R2 to 0.77 (method 1) and 0.71 (method 2). This study shows that databases containing peripheral and central aortic pressure waveforms can be used to construct multiple regression models for PPA estimation. These models could be applied to studies of similar subject groups where peripheral waveforms may not be available.