Principal component analysis of carbon-13 substituent-induced chemical shifts of some unsaturated compounds

Principal component analysis (PCA) is applied to 32 disubstituted unsaturated compounds (Y–CH₂–X): cyanides, oximes and propenes; bearing 12 -substituents: F, Cl, Br, I, OMe, OEt, SMe, SEt, NMe₂, NEt₂, Me, and Et. The experimental ¹³C chemical shifts for the -carbon and functional carbon atoms are correlated with theoretically derived molecular properties, i.e. partial charges, electronegativity, hardness, dipole moments and the nuclear repulsion energies. In the first PCA, the clustering of these three classes of organic compounds occurred mostly because of the chemical shifts and partial charges, and also of the dipole moments, hardness and electronegativity parameters as confirmed by loading graph. A strong grouping is observed in the second PCA, showing the chemical shift dependence on the type of heteroatom substituents. Therefore, sulfur, nitrogen, oxygen and neutral groups exhibit four types of C-13 SCS influences, indicating that the heteroatom (Y) properties play a significant role on the effects on chemical shifts. The -halogenated compounds represent a very heterogeneous group due to possible orbital interactions between the functional group and the substituent. The third PCA shows the grouping of F, Cl, Br and I derivatives, confirming the second PCA results that same halogen presents the same or very similar effects on the chemical shifts.     

Structural and dynamic variations in DNA hexamers containing T-T and F-F single and tandem internal mispairs

Molecular dynamics simulations of double-helical DNA oligomers have been performed to investigate differences in the structure, dynamics, and hydration of F-F and T-T mispairs. Hexamers containing F-F pairs were found to be more dynamic, especially in the region of the mispair itself. This dynamic variability derives from greater flexibility of F-F pairs. The T-T mispairs, on the other hand, were found to be comparatively tightly bound as wobble pairs. The major and minor groove edges of the T-T pairs were observed to be solvated at exposed carbonyl positions by at least one water molecule, while F-F pairs lacked solvating waters. Stacking interactions were nearly identical for T-T and F-F pairs, leading to similar average structures, even though F stacking was more dynamically variable. Solvation differences between F-F and T-T therefore support the steric exclusion model for nucleotide incorporation in DNA replication. Large differences in the orientation of minor groove functional groups, in addition to differences in solvation, further rationalize why F bases present during DNA extension events induce stalls. Two novel nucleotides are proposed to further elucidate minor groove interactions of DNA with polymerase molecules.Electronic Supplementary Material This Material consists of equilibration protocol, plots of center-of-mass stacking, water radial distribution functions, helical parameter dynamics, and dynamics data for a control AT sequence. Supplementary material is available in the online version of this article at Contribution to the Jacopo Tomasi Honorary Issue     

Applications of maximum likelihood principal component analysis: incomplete data sets and calibration transfer

The application of a new method to the multivariate analysis of incomplete data sets is described. The new method, called maximum likelihood principal component analysis (MLPCA), is analogous to conventional principal component analysis (PCA), but incorporates measurement error variance information in the decomposition of multivariate data. Missing measurements can be handled in a reliable and simple manner by assigning large measurement uncertainties to them. The problem of missing data is pervasive in chemistry, and MLPCA is applied to three sets of experimental data to illustrate its utility. For exploratory data analysis, a data set from the analysis of archeological artifacts is used to show that the principal components extracted by MLPCA retain much of the original information even when a significant number of measurements are missing. Maximum likelihood projections of censored data can often preserve original clusters among the samples and can, through the propagation of error, indicate which samples are likely to be projected erroneously. To demonstrate its utility in modeling applications, MLPCA is also applied in the development of a model for chromatographic retention based on a data set which is only 80% complete. MLPCA can predict missing values and assign error estimates to these points. Finally, the problem of calibration transfer between instruments can be regarded as a missing data problem in which entire spectra are missing on the ‘slave’ instrument. Using NIR spectra obtained from two instruments, it is shown that spectra on the slave instrument can be predicted from a small subset of calibration transfer samples even if a different wavelength range is employed. Concentration prediction errors obtained by this approach were comparable to cross-validation errors obtained for the slave instrument when all spectra were available.     

Chemometric data analysis of pollutants in wastewater—a case study

In this study, chemometric techniques such as cluster analysis (CA), discriminant analysis (DA), principal component analysis (PCA) and partial least squares (PLS) were used to analyse the wastewater dataset to identify the factors which affect the composition of sewage of domestic origin, spatial and temporal variations, similarity/dissimilarity among the wastewater characteristics of cis- and trans-drains and discriminating variables. Samples collected from 24 wastewater drains in Lucknow city and from three sites on Gomti river in the month of January/February, May, August and November during the period of 5 years (1994-1999) were characterized for 32 parameters. The multivariate techniques successfully described the similarities/dissimilarities among the sewage drains on the basis of their wastewater characteristics and sources signifying the effect of routine domestic/commercial activities in respective drainage areas. Spatial and seasonal variations in wastewater composition were also determined successfully. CA generated six groups of drains on the basis of similar wastewater characteristic. PCA provided information on seasonal influence and compositional differences in sewage generated by domestic and industrial waste dominated drains and showed that drains influenced by mixed industrial effluents have high organic pollution load. DA rendered six variables (TDS, alkalinity, F, TKN, Cd and Cr) discriminating between cis- and trans-drains. PLS-DA showed dominance of Cd, Cr, NO₃, PO₄ and F in cis-drains wastewater. The results suggest that biological-process based STPs could treat wastewater both from the cis- as well as trans-drains, however, prior removal of toxic metals will be required from the cis-drains sewage. Further, seasonal variations in wastewater composition and pollution load could be the guiding factor for determining the STPs design parameters. The information generated would be useful in selection of process type and in designing of the proposed sewage treatment plants (STPs) for safe disposal of wastewater.     

Chemometric analysis of groundwater quality data of alluvial aquifer of Gangetic plain, North India

Water quality data set from the alluvial region in the Gangetic plain in northern India, which is known for high fluoride levels in soil and groundwater, has been analysed by chemometric techniques, such as principal component analysis (PCA), discriminant analysis (DA) and partial least squares (PLS) in order to investigate the compositional differences between surface and groundwater samples, spatial variations in groundwater composition and influence of natural and anthropogenic factors. Trilinear plots of major ions showed that the groundwater in this region is mainly of Na/K-bicarbonate type. PCA performed on complete data matrix yielded six significant PCs explaining 65% of the data variance. Although, PCA rendered considerable data reduction, it could not clearly group and distinguish the sample types (dug well, hand-pump and surface water). However, a visible differentiation between the water samples pertaining to two watersheds (Khar and Loni) was obtained. DA identified six discriminating variables between surface and groundwater and also between different types of samples (dug well, hand pump and surface water). Distinct grouping of the surface and groundwater samples was achieved using the PLS technique. It further showed that the groundwater samples are dominated by variables having origin both in natural and anthropogenic sources in the region, whereas, variables of industrial origin dominate the surface water samples. It also suggested that the groundwater sources are contaminated with various industrial contaminants in the region.     

Laser-induced fluorescence microscopic system using an optical parametric oscillator for tunable detection in microchip analysis

A laser-induced fluorescence microscopic system based on optical parametric oscillation has been constructed as a tunable detector for microchip analysis. The detection limit of sulforhodamine B (Ex. 520 nm, Em. 570 nm) was 0.2 mol, which was approximately eight orders of magnitude better than with a conventional fluorophotometer. The system was applied to the determination of fluorescence-labeled DNA (Ex. 494 nm, Em. 519 nm) in a microchannel and the detection limit reached a single molecule. These results showed the feasibility of this system as a highly sensitive and tunable fluorescence detector for microchip analysis.     

Study of gas-liquid partitioning of alkane solutes in several organic solvents by using principal component analysis and linear solvation energy relationships

Principal component analysis (PCA) was used to extract the number of factors which can describe the 737 gas-liquid partition coefficients of five linear, four branched, and two cyclic alkanes in 67 common solvents. Based on the reconstruction of partition coefficient data matrix, we concluded that the experimental dataset could readily be reduced to two relevant factors. Using only these two factors, there were no errors larger than 3%, 7 cases had errors larger than 2%, and in 34 cases, errors were between 1 and 2%. n-Hexane and ethylcyclohexane were chosen as the test factors, and all other partition coefficients were expressed in terms of these two test factors. Prediction of the logarithmic partition coefficient of these alkanes in seven chemically different solvents, which were originally excluded from the data matrix, was excellent: the root mean square error was 0.064, only in 11 cases the errors were larger than 1%, and only 3 had errors larger than 4%.Linear solvation energy relationships (LSERs) using both theoretical and empirical solvent parameters were used to explain the molecular interactions responsible for partition. Several combinations of parameters were tried but the standard deviations were not less than 0.31. This could be attributed to the model itself, imprecisions in the data matrix or in some of the LSER parameters. Solvent cohesive parameters and surface tension in combination with polarity-polarizability or dispersion parameters perform the best.Finally, the two principal component factors were rotated onto the most relevant physicochemical parameters that control the gas-liquid partitioning phenomena.     

曲率流的参数化有限元逼近

许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战.