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In this work a multi-objective quantitative structure-property relationship (QSPR) analysis approach was reported based on the study on three partition properties of 50 aromatic sulfur-containing carboxylates. Here multi-objectives (properties) were taken as a vector for QSPR modeling. The quantitative correlations for partition properties were developed using a genetic algorithm-based variable-selection approach with quantum chemical descriptors derived from AMl-based calculations. With the QSPR models, the aqueous solubility, octanol/water partition coefficients and reversed-phase HPLC capacity factors of sulfur-containing compounds were estimated and predicted. Using GA-based multivariate linear regression with cross-validation procedure, a set of the most promising descriptors was selected from a pool of 28 quantum chemical semi-empirical descriptors, including steric and electronic types, to integrally build QSPR models. The selected molecular descriptors included the net charges on carboxyl group (Qoc), the 2nd power of net charges on nitrogen atoms (Q2N), the net atomic charge on the sulfur atoms (Qs), the van der Waals volume of molecule (V), the most positive net atomic charge on hydrogen atoms (QH) and the measure of polarity and polarizability (π), which were main factors affecting the distribution processes of the compounds under study. The statistically best QSPR models of six descriptors were simultaneously obtained by GA-based linear regression analysis. With the selected descriptors and the QSPR equations, mechanisms of partition action of the Sulfur-containing carboxylates were able to be investigated and interpreted.

Selective inhibition of cyclooxygenase-2 (COX-2) might avoid the side effects of current available nonsteroidal antiinflammatory drugs while retaining their therapeutic efficacy. A novel variable selection and modeling method based on prediction is developed to construct the quantitative structure-activity relationships (QSAR) between the molecular electronegativity distance vector (MEDV) based on 13 atomic types and the biological activities of a set of selective cyclooxygenase-2 inhibitory molecules, 3,4-diarylcycloxazolones (DAA) plus indomethacin, naproxen, and celecoxib. Using multiple linear regression, a 5-variable linear model is developed with the calibrated correlation coefficient of 0.9271 and root mean square error of 0.17 in modeling stage and the validated correlation coefficient of 0.9030 and root mean square error of 0.20 in leave-one-out validation step, respectively. To further test the predictive ability of the model, 20 DAA compounds are picked up to construct a training set which is used to build a QSAR model and then the model is employed to predict the biological activities of the balance compounds. The predicted correlation coefficient and root mean square error are 0.9332 and 0.19, respectively.

Molecular structures of polychlorinated naphthalenes were numerically described with a simple but efficient encoding method. Correspondingly a set of structural parameters were obtained for these compounds and linearly correlated with their gas chromatography retention indexes. A quantitative structure-retention relationship Model (M1) was developed by using multiple linear regression (MLR) with correlation coefficient R = 0.9880 between the numeric structural codes and the gas chromatography retention indexes of 62 polychlorinated naphthalenes. If the "leave-one-out" cross-validation procedure was employed to construct QSPR model for all samples, the second model M2 with the correlation coefficient being R = 0.9839 was generated. The structural codes of polychlorinated naphthalenes were tested with MLR for estimation and prediction of the GC RI by models M1 and M2, and the results obtained were satisfactory.

The molecular holographic distance vector (MHDV) is employed to characterize the structures of 51 substituted benzenes. 29 descriptors from 91 MHDV ones have nonzero values where 3 descriptors have only one nonzero sample and 1 descriptor only two nonzero samples. A genetic algorithm is used to select an optimal combination of the variables from the remaining 25 nonzero descriptors. Then the optimal descriptors are employed to relate to the relative biodegradability using multiple linear regression method. The 6-variable linear model developed has high quality where the correlation coefficient of estimations and the root mean square error of estimations are 0.9604 and 0.280, respectively, and the correlation coefficient of predictions and the root mean square error of predictions for leave-one-out procedure are 0.9471 and 0.324, respectively.

A molecular electronegativity–distance vector (MEDV) has been proposed to describe the structure of polycyclic aromatic hydrocarbons (PAHs) and relate to their retention indices (RI) for programmed temperature SE-52 capillary-column gas chromatography. The 209 PAHs investigated contain not only one or two heteroatoms such as nitrogen, oxygen and sulfur but also one, two or more conjugated rings. Applying multiple linear regression (MLR) in combination with the cross-validation (CV) technique, a four-parameter quantitative structure–retention relationship (QSRR) of 209 PAHs is developed with the correlation coefficient ( R ) of 0.9812 and the root mean square error (RMS) of 15.533 between the estimated and experimental retention indices (RI). It was found that the errors for oxygen-containing PAHs are often positive and for sulfur-containing PAHs, negative. Thus, MEDV is modified by lengthening the CO or CO bond and by shortening the CS bond. Leaving out several outliers, a better QSRR is described with R =0.9936 and RMS=9.212 for 172 PAHs.

A set of novel graph theoretical parameters, called the atomic distance–edge vector (ADEV), was developed in our laboratories. A regression equation linking the carbon-13 chemical shift (CS) to an ADEV containing 16 descriptor variables of various chemically non-equivalent carbon atoms in a molecule was obtained using multiple linear regression (MLR). The regression model was used to predict the carbon-13 nuclear magnetic resonance (13C NMR) spectra of unknown alkanes. It was found that the estimated CS values were in good agreement with the experimental CS values. Copyright © 2001 John Wiley & Sons, Ltd.

A new method of quantitative structure-retention relationship (QSRR) is proposed for estimating and predicting gas chromatographic retention indices of alkanes by using a novel molecular distance-edge vector, called μ vector, containing 10 elements. The QSRR model (Ml), between the μ vector and chromatographic retention indices of 64 alkanes, was developed by using multiple linear regression (MLR) with the correlation coefficient being R = 0.9992 and the root mean square (RMS) error between the estimated and measured retention indices being RMS = 5.938. In order to explain the equation stability and prediction abilities of the M1 model, it is essential to perform a cross-validation (CV) procedure. Satisfactory CV results have been obtained by using one external predicted sample every time with the average correlation coefficient being R = 0.9988 and average RMS = 7.128. If 21 compounds, about one third drawn from all 64 alkanes, construct an external prediction set and the 43 remaining construct an internal calibration set, the second QSRR model (M2) can be created by using calibration set data with statistics being R = 0.9993 and RMS = 5.796. The chromatographic retention indices of 21 compounds in the external testing set can be predicted by the M2 model and good prediction results are obtained with R = 0.9988 and RMS = 6.508.

Models that estimate and predict the normal boiling point (NBP) of alkanes based on a molecular distance-edge (MDE) vector, λ, have been developed by using multiple linear regression (MLR) methods. The structures of the examined compounds are selectively described by an MDE vector structure descriptor, a novel molecular distance-edge vector recently developed in our laboratory. MLR was used to develop a linear model containing ten variables with a high precision root mean squares error (RMS = 4.985K) and a good correlation with the correlation coefficient (R = 0.9948). In addition, a predictive model has been developed by using 125 isomers in alkanes as the training set, and its performance was certified by employing 25 alkanes chosen randomly as the test set from a total of 150 alkane compounds; excellent predicted results were obtained with the RMS and R values found between the calculated value and observed NBP being RMS = 4.486K and R = 0.9945.

The MEDV-13, molecular electronegativity distance vector based on 13 atomic types, has at best 91 descriptors. It is impossible to indirectly use multiple linear regression (MLR) to derive a quanti...

Only from the primary structures of peptides, a new set of descriptors called the molecular electronegativity edge-distance vector (VMED) was proposed and applied to describing and characterizing the molecular structures of oligopeptides and polypeptides, based on the electronegativity of each atom or electronic charge index (ECI) of atomic clusters and the bonding distance between atom-pairs. Here, the molecular structures of antigenic polypeptides were well expressed in order to propose the automated technique for the computerized identification of helper T lymphocyte (Th) epitopes. Furthermore, a modified MED vector was proposed from the primary structures of polypeptides, based on the ECI and the relative bonding distance of the fundamental skeleton groups. The side-chains of each amino acid were here treated as a pseudo-atom. The developed VMED was easy to calculate and able to work. Some quantitative model was established for 28 immunogenic or antigenic polypeptides (AGPP) with 14 (1-14) A(d) and 14 other restricted activities assigned as "1"(+) and "0"(-), respectively. The latter comprised 6 A(b)(15-20), 3 A(k)(21-23), 2 E(k)(24-26), 2 H-2(k)(27 and 28) restricted sequences. Good results were obtained with 90% correct classification (only 2 wrong ones for 20 training samples) and 100% correct prediction (none wrong for 8 testing samples); while contrastively 100% correct classification (none wrong for 20 training samples) and 88% correct classification (1 wrong for 8 testing samples). Both stochastic samplings and cross validations were performed to demonstrate good performance. The described method may also be suitable for estimation and prediction of classes I and II for major histocompatibility antigen (MHC) epitope of human. It will be useful in immune identification and recognition of proteins and genes and in the design and development of subunit vaccines. Several quantitative structure activity relationship (QSAR) models were developed for various oligopeptides and polypeptides including 58 dipeptides and 31 pentapeptides with angiotensin converting enzyme (ACE) inhibition by multiple linear regression (MLR) method. In order to explain the ability to characterize molecular structure of polypeptides, a molecular modeling investigation on QSAR was performed for functional prediction of polypeptide sequences with antigenic activity and heptapeptide sequences with tachykinin activity through quantitative sequence-activity models (QSAMs) by the molecular electronegativity edge-distance vector (VMED). The results showed that VMED exhibited both excellent structural selectivity and good activity prediction. Moreover, the results showed that VMED behaved quite well for both QSAR and QSAM of poly-and oligopeptides, which exhibited both good estimation ability and prediction power, equal to or better than those reported in the previous references. Finally, a preliminary conclusion was drawn: both classical and modified MED vectors were very useful structural descriptors. Some suggestions were proposed for further studies on QSAR/QSAM of proteins in various fields.

The MEDV-13, molecular electronegativity distance vector based on 13 atomic types, has at best 91 descriptors. It is impossible to indirectly use multiple linear regression (MLR) to derive a quantitative structure-activity relationship (QSAR) model. Although principal component regression (PCR) or partial least-squares regression (PLSR) can be employed to develop a latent QSAR model, it is still difficult how to determine the principal components (PCs) and depict the physical meaning of the PCs. So, a genetic algorithm (GA) is first employed to select an optimal subset of the descriptors from original MEDV-13 descriptor set. Then MLR is utilized to build a QSAR model between the optimal subset and the biological activities of three sets of compounds. For 31 benchmark steroids, a 5-descriptor QSAR model (M1) between the corticosteroid-binding globulin (CBG) binding affinity of the steroids and 5-descriptor subset is developed. The root-mean-square error of estimations (RMSEE) and the correlation coefficient of estimations (r) between the CBG binding affinity (BA) observed and the BA estimated by M1 are 0.422 and 0.9182, respectively. The root-mean-square error of predictions (RMSEP) and the correlation coefficient of predictions (q) between the BA observed and the BA predicted by leave-one-out cross validations are 0.504 and 0.8818, respectively. For 58 dipeptides inhibiting angiotensin-converting enzyme (ACE), a 5-variable QSAR model (M2) between the pIC(50) of peptides and 5-descriptor subset is derived. The M2 has a high quality with RMSEE = 0.339 and r = 0.9398 and RMSEP = 0.370 and q = 0.9280. For 16 indomethacin amides and esters (ImAE) inhibiting cyclooxygenase-2 (COX-2), a 6-variable QSAR model (M3) with RMSEE = 0.079 and r = 0.9839 and RMSEP = 0.151 and q = 0.9413 is built.

Several quantitative structure-property relationship (QSPR) models between 15 basic physical properties or thermodynamic functions of alkanes and their molecular electronegative distance vectors (MEDV) are developed. For six of the properties-boiling point (BP), density (D) at 25 degrees C, refraction index (RI) at 25 degrees C, critical temperature (CT), critical pressure (CP), and surface tension (ST) at 20 degrees C-logarithmic models are found to give better results than conventional (linear) models since the values of these properties all tend to a limit with increasing carbon chain length. All models are created using multiple linear regression (MLR). Conventional models are proposed for the remaining nine physical properties or thermodynamic functions: molar volume (MV) at 20 degrees C, molar refraction (MR) at 20 degrees C, heat capacity (HC) at 300 K, enthalpy (E) at 300 K, heats of vaporization (HV) at 25 degrees C, heat of atomization (HA) at 25 degrees C, standard heat of formation (HF) at 25 degrees C, heat of formation in liquid (HFL) at 25 degrees C, and heat of formation in gas (HFG) at 25 degrees C.