The Research On Multi-way Chemometric Methodologies And Their Applications In Pharmaceutical And Pharmacological Sciences

Chemometrics is a developing composite discipline. It uses the methods of mathematics, statistics and computer sciences to extracting the optimal scheme for chemical measurements and to elucidating the data collected from chemical measurements. Chemometric methodologies not only comprehensively expand the fundamental theory of modern analytical chemistry, but also provide a variety of powerful techniques for direct and on-line analysis of complex chemical systems, which are generally hard to handle by conventional analytical techniques. With the development of high-order analytical instrumentation, multi-way data analysis has become an active domain with practical significance. Studies presented in the thesis primarily deals with the following aspects of multi-way data analysis in chemometrics.1. The multilinear component model (Chapter 2):In order to further understand the decomposition algorithms based on multilinear component model and the application of these algorithms in practice, it is necessary to realize and explore the characteristics and advantages of multilinear decomposition algorithms. Based on the mathematical and graphic expressions of multilinear component model, the nature of these decomposition algorithms were analyzed in detail. Especially in the graphic expression, the algorithms of multi-way arrays and methodologies provide interesting hints to develop multilinear algebra in mathematics.2. The trilinear decomposition algorithms (Chapter 3 to Chapter 5):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. However, the sources of three-way data are becoming richer and research systems are becoming more and more complex, limited algorithms are difficult to guarantee to obtain satisfying results in all circumstances. The alternating fitting residue method (AFR) and the alternating normalization-weighted error method (ANWE) are also proposed for three-way data analysis. Coupled with some practical examples of direct and rapid determinations of drugs, such as fluoroquinolone, daunorubicin and psoralen, both these algorithms and the PARAFAC algorithm can obtain good results. They retain the second-order advantage of quantification for analytes of interest in thepresence of potentially unknown interferents and can escape the two-factor degeneracy and relieve the slow convergence problem compared with PARAFAC. Furthermore, in practical application, they perform well and can directly and rapidly carry out quantitative analysis of actual complex systems.3. The quadrilinear decomposition algorithm (Chapter 6):A novel algorithm, alternating penalty quadrilinear decomposition (APQLD), is developed as an extension of alternating penalty trilinear decomposition (APTLD) for decomposition of quadrilinear data and applied to third-order calibration. The proposed method as well as four-way parallel factor analysis (PARAFAC) not only retains the second-order advantage possessed second-order calibration but also holds additional advantage, for example, with trilinear data from one sample, the intrinsic profiles in each order can be determined uniquely for each species in the samples. From simulations, it is observed that another advantage is that the introduction of fourth mode can relieve the serious problem of collinearity. It can be defined the'third-order advantage'. It was shown a much higher convergence rate compared with four-way PARAFAC. Moreover, it is generally insensitive to the overestimates of the component number chosen. This offers the advantage that in third-order calibration one need not pay much attention to determining a proper component number for the model, and it is difficult for four-way PARAFAC to avoid it. By treating simulated and real data sets, the results indicated that both APQLD and PARAFAC work well, but the performance of APQLD is better than that of PARAFAC in the prediction of concentration even if the component number chosen is the same as the actual number of underlying factors in the real system.4. The chemical rank estimation of high-way data arrays (Chapter 7):A novel method, a subspace projection of pseudo high-way data array (SPPH), was developed for estimating the chemical rank of high-way data arrays. The proposed method determines the chemical rank through performing singular value decomposition (SVD) on the slice matrices of original high-way data array to produce a pseudo high-way data array and employing the idea of the difference of the original truncated data set and the pseudo one. Compared with the traditional methods, it uses the information from eigenvectors combined with the projection residual to estimate the rank of the three-way data arrays instead of using the eigenvalue. In order to demonstrate the good performance of the new method, simulated and real trilinear data arrays are carried out by the proposed method. The results showed that the proposed method could accurately and quickly determine the chemical rank to fit the trilinear model. It was found that the proposed method can deal with more complex situations with existence of severe collinearity and trace concentration than many other methods can and performs well in practical application. However, only the estimate of the chemical rank of trilinear data will be discussed here, but the method can be extended straightforwardly to the estimate of the chemical rank of higher-way data as well.5. The applications of three-way data analysis in pharmacology and pharmaceutical research (Chapter 8 to Chapter 9):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. 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.A new kinetic spectrofluorimetric method was proposed for the direct determination of adrenaline in human plasma. It is based on the facts that weak fluorescent adrenaline can be oxidized into the strong fluorescent intermediate product, indole derivative and that second-order calibration methods in chemometric methodologies have the second-order advantage, which is the ability to get accurate concentration estimates of interested analytes even in the presence of uncalibrated interfering components. The second-order calibration algorithms to handle the recorded data are the parallel factor analysis (PARAFAC) and the alternating penalty trilinear decomposition (APTLD) in this paper. The emission spectra and time profiles as well as the relative concentrations of co-existing species in reaction mixtures can be directly and conveniently obtained by the PARAFAC and APTLD treatments. The results obtained are valuable for providing a deeper insight into the oxidation reaction mechanism of adrenaline and show that the adrenaline in complex human plasma mixtures can be accurately determined using the new method. Furthermore, compared with PARAFAC, APTLD can acquire more satisfactory results.