Three-Mode Abstracts, Part X

INDEX

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• Xia, A. L., Wu, H. L., Fang, D. M., Ding, Y. J., Hu, L. Q., & Yu, R. Q. (2005).
  Alternating penalty trilinear decomposition algorithm for second-order calibration with application to interference-free analysis of excitation-emission matrix fluorescence data. Journal of Chemometrics, 19, 65-76.
  A new method, alternating penalty trilinear decomposition (APTLD), is developed for the decomposition of three-way data arrays. By utilizing the alternating least squares principle and alternating penalty constraints to minimize three different alternating penalty errors simultaneously, the intrinsic profiles are found. The APTLD algorithm can avoid the two-factor degeneracy problem and relieve the slow convergence problem, which is difficult to handle for the traditional parallel factor analysis (PARAFAC) algorithm. It retains the second-order advantage of quantification for analytes of interest even in the presence of potentially unknown interferents. In additions, it is insensitive to the estimated component number, thus avoiding the difficulty of determining a correct component number for the model, which is intrinsic in the PARAFAC algorithm. The results of treating one simulated and one real excitation-emission spectral data set showed that the proposed algorithm performs well as long as the model dimensionality chosen is not less than the actual number of components. Furthermore, the performance of the APTLD algorithm sometimes surpasses that of the PARAFAC algorithm in the prediction of concentration profiles even if the component number chosen is the same as the actual number of underlying factors in real samples.

• Xia, A. L., Wu, H. L., Fang, D. M., Ding, Y. J., Hu, L. Q., & Yu, R. Q.
  Determination of daunomycin in human plasma and urine by using an interference-free analysis of excitation-emission matrix fluorescence data with second-order calibration. Analytical Sciences, 22, 1189-1195.
  Daunorubicin (DNR) is a significant antineoplastic antibiotic, which is usually applied to a chemotherapy of acute lymphatic and myelogenous leukaemia. Unfortunately, cardiotoxicity research in animals has indicated that DNR is cardiotoxic. Therefore, it is important to quantify DNR in biological fluids. A new algorithm, the alternating fitting residue (AFR) method, and the traditional parallel factor analysis (PARAFAC) have been utilized to directly determine DNR in human plasma and urine. These methodologies fully exploit the second-order advantage of the employed three-way fluorescence data, allowing the analyte concentrations to be quantified even in the presence of unknown fluorescent interferents. Furthermore, in contrast to PARAFAC, more satisfactory results were gained with AFR.

• Xia,A. L., Wu, H. L., Li, S. F., Zhu, S. H., Zhang, Y., Han, Q. J., & Yu, R. Q. (2003).
  Study of the interactions of berberine and daunorubicin with DNA using alternating penalty trilinear decomposition algorithm combined with excitation-emission matrix fluorescence data. Talanta, 73, 606-612.
  Studies of interactions between drugs and DNA are very interesting and significant not only in understanding the mechanism of interaction, but also for guiding the design of new drugs. However, until recently, mechanisms of interactions between drug molecules and DNA were still relatively little known. It is necessary to introduce more simple methods to investigate the mechanism of interaction. In this study, the interactions of daunorubicin (DNR) or berberine (BER) with DNA and the competitive interactions of DNR and BER with DNA have been studied by alternating penalty trilinear decomposition algorithm (APTLD) combined with excitation-emission matrix fluorescence data. The excitation and emission spectra as well as the relative concentrations of co-existing species in different reaction and equilibrium mixtures can be directly and conveniently obtained by the APTLD treatment. The results obtained are valuable for providing a deeper insight into the interaction mechanism of DNR and BER with DNA. It is proved that the fluorescence spectrum of complex DNR-DNA is different from that of DNR. Furthermore, the present method provides a new way to search for a new non-toxic, highly efficient fluorescent probe. For controversial interaction mechanism of the drugs and DNA, it can provide a helpful verification.

• Xian, B., Li, T. H., Kai, C., Cao, T. C., Huang, J. R., & Qi, Y. P. (2004).
  A novel preprocessing algorithm for three-way HPLC data. Journal of Mathematical Chemistry, 36,129-138.
  Orthogonal signal correction (OSC) was a data preprocessing algorithm. It ensured that the filtered information was irrelevant to concentration data while using it to filter the noise from the original data. This paper extended the OSC application range from two-way data to three-way data. Two drug data sets, Enoxacin, Norfloxacin, Ciprofloxacin and Betamethasone, cortisone acetate, prednisone acetate, showed that the application of the OSC algorithm to three-way HPLC data was feasible and needed further research.

• Xiao, Y. D., Wei, L. H., Wang, J. T., Zhang, J. B., Lin, S. F., & Zhou, Z. H. (1999).
  Study of 3D-quantitative structure-activity relationship on a set of 1,2,4-triazole compounds. Chemometrics and Intelligent Laboratory Systems, 45, 277-280.
  In this article, 3D-quantitative structure–activity relationship on a set of 1,2,4-triazole compounds is studied. A set of 16 derivatives of triazole that have different biological activities to wheat black rust as inhibitors are characterized by molecular mechanics. The analysis result by PLS agrees with the study of 2D-QSAR, and it offers useful 3-dimensional information for designing high activity compounds.

• Xie, H. P., Jiang, J. H., Chu, X., Cui, H., Wu, H. L., Shen, G. L. & Yu, R. Q. (2002).
  Competitive interaction of the antitumor drug daunorubicin and the fluorescence probe ethidium bromide with DNA as studied by resolving trilinear fluorescence data: the use of PARAFAC and its modification Analytical and Bioanalytical Chemistry, 373, 159-162.
  The competitive interaction with DNA of daunorubicin (DR), being present in the clinical anti-tumor drug daunoblastina, and the fluorescence probe ethidium bromide (EB) has been studied by parallel-factor analysis (PARAFAC) and full-rank parallel-factor analysis (FRAPARAFAC) of a fluorescence excitation-emission threeway data array. The PARAFAC algorithm can furnish stable resolution results for the data array studied, if the estimated number of chemical components is consistent with the real number. The FRA-PARAFAC algorithm is not sensitive to the estimated number of components of the fluorescence data array if the estimated number is not less than the real number. Both algorithms gave identical resolution for the three components concerned DR, EB, and the complex EB-DNA. Variations of the equilibrium concentrations of free DR, EB, and the complex EB-DNA were resolved by both algorithms. Experimental observation confirms the hypothesis that DR is an intercalator of DNA and that the binding interactions of DR and EB with DNA are a pair of parallel competitive intercalation reactions on same base sites of DNA. The method exemplified by this study provides a useful approach for studying competitive interactions of different drugs with DNA in the presence of interferents.

• Xie, H. P., Jiang, J. H., Long, N., Shen, G. L., Wu, H. L.& Yu, R. Q. (2003).
  Estimation of chemical rank of a three-way array using a two-mode subspace comparison approach. Chemometrics and Intelligent Laboratory Systems, 66, 101-115.
  When two matrices are formed by unfolding a three-way array along two full-rank modes and when two subspaces with the same size are constructed by taking the first principal component vectors of the same mode space in these two unfolded matrices, the principal components corresponding to the chemical species should behave identically in both subspaces, while the components corresponding to the noise contribution should behave differently in these two subspaces. Based on the difference of the behavior of the chemical signal and noise components, the two-mode subspace comparison (TMSC) approach has been proposed to estimate the chemical rank of a three-way array with two full-rank modes. Two outstanding features of the proposed method have been demonstrated. It is robust to a very high degree of collinearity between the spectra or chromatograms involved, or to a very high level of noise contained in a three-way array. The method has been shown to be useful for the treatment of three-way analytical data sets obtained by high-performance liquid chromatography-diode array detector (HPLC)-DAD and excitation-emission fluorescence spectroscopy. (C) 2003 Elsevier Science B.V. All rights reserved.

• Xie, H. P., Chu, X., Jiang, J. H., Cui, H., Shen, G. L. & Yu, R. Q. (2003).
  Competitive interactions of adriamycin and ethidium bromide with DNA as studied by full rank parallel factor analysis of fluorescence three-way array data Spectrochimica acta part a-molecular and biomolecular spectroscopy, 59, 743-749.**
  The competitive interactions of adriamycin (AMC) and a fluorescence probe of ethidium bromide (EB) with DNA have been studied by full rank parallel factor analysis (FRA-PARAFAC) of fluorescence excitation-emission three-way data array. The excitation and emission spectra as well as the equilibrium concentrations of co-existing species in different reaction mixtures can be directly obtained by the FRA-PARAFAC treatment. The concordance of the resolved excitation and emission spectra of AMC, EB and EB-DNA with The standard spectra of these species confirmed the reliability of the equilibrium concentrations of these components in the reaction mixtures studied. The results obtained are valuable for providing a deeper insight into the competitive interaction mechanism of AMC and EB with DNA. The conclusion was directly given out that the interaction of AMC with DNA is the intercalating model. The FRA-PARAFAC method as exemplified by the present study provides an useful approach for studying the interaction of clinical drugs with DNA in the presence of disturbance of drug assistants. (C) 2002 Elsevier Science B.V. All rights reserved.

• Xie, Y.-L., Baeza-Baeza, J.J., & Ramis-Ramos, G. (1995).
  Kinetic spectrophotometric resolution of binary mixtures using three-way partial least squares. Chemometrics and Intelligent Laboratory Systems, 27, 211-220.
  Three-way partial least squares (PLS) was applied to kinetic-spectrophotometric data. The coupling reaction of diazotized sulfanilamide with o-, m- and p-amino benzoic acid (ABA), and with orciprenaline (ORC), to give azodyes was monitored. Three binary mixtures of substrates, i.e., o-ABA/ORC, m-ABA/p-ABA and o- ABA/m-ABA, with different values of the rate constant ratio and spectra which overlapped seriously were studied. The spectra of the mixtures were scanned with a 2 nm resolution every 30 s during ca. 15 min. The data sets contained from 30 x 36 to 30 x 48 time-wavelength data. Nine mixtures of each binary combination of substrates were used for calibration, thus the three-way calibration data sets contained from 9 x 30 x 36 to 9 x 30 x 48 concentration-time-wavelength data. The two-way PLS modelling was constructed on the basis of single wavelength kinetic curves, and the three-way PLS modelling was applied to series of three-way data arrays consisting of a number of selected wavelengths each (up to the whole spectra). The results based on three-way data arrays were better than that of ordinary PLS, particularly with mixtures having both a low rate constant ratio and small spectral differences.

• Xie, Y.-L., Baeza-Baeza, J.J., & Ramis-Ramos, G. (1996a).
  Second-order tensorial calibration for kinetic spectrophotometric determination. Chemometrics and Intelligent Laboratory Systems, 32, 215-232.
  Kinetic-diode array spectrophotometric detection, as well as other multichannel techniques when used in non-equilibrium conditions, constitute second-order instrumentation. The second-order response provided will be bilinear, under certain conditions even trilinear, thus allowing the use of the generalized rank annihilation method (GRAM) and the trilinear decomposition method (TLD). Both numerically simulated and experimental data were used to evaluate the performance of these calibration techniques. The conditions in which the 'second-order advantage' (the possibility of quantifying the analytes in the presence of unknown reactions or interferences) is preserved were investigated. The coupling reaction of diazotized sulfanilamide with p-, o- and m-amino benzoic acid, and with orciprenaline, to give azodyes was monitored. Binary mixtures of these substrates with different values of the rate constant ratio, and with various degrees of spectral overlap, were resolved. The advantages and limitations of higher-order data analysis techniques such as GRAM and TLD for the treatment of second-order kinetic data are discussed.

• Xie, Y.-L., Baeza-Baeza, J. J., & Ramis-Ramos, G. (1996b).
  A compariative study of several chemometric methods applied to the treatment of two-way kinetic-spectral data for mixture resolution. Analytica Chimica Acta, 321, 75-95.
  A comparative study was conducted to investigate the performance of several chemometric methods applied to the treatment of two-way kinetic-spectral data with the aim of resolving mixtures. The methods involved are non-linear least squares regression performed using the Powell algorithm, the linear and extended Kalman filter, and partial least squares regression. Both simulated and experimental data were processed. The coupling reaction of diazotized sulfanilamide with arylamines to give azodyes was monitored spectrophotometrically. Binary mixtures of the substrates with different values of the rate constant ratio and with varied degrees of spectral overlap were resolved. The effects of several influence factors have been studied using numeric simulation. The advantages and the limitations of each method have been evaluated.

• Xie, Y.L., Hopke, P.K., & Paatero, P. (1998).
  Positive matrix factorization applied to a curve resolution problem. Journal of Chemometrics, 12, 357-364.
  Positive matrix factorization (PMF) is a least squares approach to factor analysis which was originally developed for environmental data analysis and has been applied to several problems in resolving sources of environmental pollutants. PMF has been used as both a two-way and three-way data analysis tool. In this investigation, three-way data arrays were used to explore the ability of PMF in curve resolution. Pulsed gradient spin echo (PGSE) nuclear magnetic resonance (NMR) data were measured for spectral mixtures where the concentrations of the compounds decay exponentially. Three-way data arrays were constructed by packing different parts of the data from single experiments and were analyzed with three-way PMF to obtain the NMR spectra, decay profiles and the self-diffusion coefficients of constituents.

• Xie, Y.L., Hopke, P.K., Paatero, P., Barrie, L.A., & Li, S.M. (1999a).
  Identification of source nature and seasonal variations of Arctic aerosol by positive matrix factorization. Journal of the Atmospheric Sciences, 56,, 249-260.
  Week-long samples of airborne particulate matter were obtained at Alert, Northwest Territories, Canada, between 1980 and 1991. The concentrations of 24 particulate constituents have some strong, persistent seasonal variations that depend on the transport from their sources. In order to explore the nature of the cyclical variation of the different processes that give rise to the measured concentrations, the observations were arranged into both a two-way matrix and a three-way data array. For the latter the three modes consist of chemical constituents, weeks within a year, and years. The two-way bilinear model and a three-way trilinear model were used to fit the data and a new data analysis technique, positive matrix factorization (PMF), has been used to obtain the solutions. PMF utilizes the error estimates of the observations to provide an optimal pointwise scaling data array far weighting, which enables it to handle missing data, a common occurrence in environmental measurements. It can also apply nonnegative constraints to the factors. Five factors have been obtained that reproduce the data quite well for both two-way and three-way analyses. Each factor represents a probable source with a compositional profile and distinctive seasonal variations. Specifically, there are (i) an acid photochemical factor typified by Br^-, H⁺, and SO₄^2- and characterized by a concentration maximum around April, or shortly after polar sunrise; (ii) a soil factor representing by Si, Al, and Ca and having its main seasonal maximum in September and October; (iii) an anthropogenic factor dominated by SO₄^2- together with metallic species like Pb, Zn, V, As, Sb, Se, In, etc., peaking from December to April; (iv) a sea salt factor consisting mainly of Cl, Na, and K with maximum concentrations during the period from October to April: And (v) a biogenic factor characterized by methane-sulfonate and having a primary maximum at May and a secondary maximum in August. The results obtained by both two-way and three-way PMF analyses are generally consistent with one another. However, there are differences because of additional constraints on the solution imposed by the three-way analysis. The results also help to confirm the hypotheses regarding the origins of the Arctic aerosol.

• Xie, Y-L., Hopke, P.K., Paatero, P., Barrie, L.A., & Li, S-M. (1999b).
  Identification of source nature and seasonal variations of Arctic aerosol by the multilinear engine. Atmospheric Environment, 33, 2549- 2562.
  The multilinear engine is introduced in this study to estimate a mixed 2-way/3- way model for the Alert aerosol data. Five 2-way and two 3-way factors have been found to provide the best fit and interpretation of the data. Each factor represented probable source with a distinctive compositional profile and seasonal variations. The results obtained are consistent with those obtained in the previous study (Xie, 1999a) and agree with the current understanding of the Arctic aerosol.

• Xie, Y-L., Hopke, P.K., Paatero, P., Barrie, L.A., & Li, S-M. (1999c).
  Locations and preferred pathways of possible sources of Arctic aerosol. Atmospheric Environment, 33, 2229-2239.
  In this investigation, potential source contribution function (PSCF) analysis was applied to the source contributions derived from the ME (Multilinear Engine) analysis by incorporating meteorological information in the form of 5-d air parcel back trajectories. The potential locations and/or the preferred pathways of these possible sources were then determined by the PSCF analysis.

                         

• Xu, Q., & Liang, Y. (1999).
  On the equivalence of window factor analysis and orthogonal projection resolution. Chemometrics and Intelligent Laboratory Systems, 45, 335-338.
  Window factor analysis (WFA) and orthogonal projection resolution (OPR) are two factor analytical techniques for extracting component concentration profiles from two-way evolutionary data. Both methods take advantage of the fact that each component lies in a special region along the evolutionary axis. Theoretical equations are derived to prove that WFA is equivalent to OPR, if errors are ignored.

           

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