Chemical Multi-way Calibration Fundamental Theories And Their Applications To Quantitative Analysis In Complex Systems

Chemical multi-way calibration methods based on multilinear components models are gaining more and more attention in the field of analytical science. Based on the “mathematical separation”, multi-way calibration methods enable one to achieve direct quantitative analysis of multiple analytes of interest in complex systems even in the presence of multiple unknown, uncalibrated interferents and multiple varying background interferents, which is known as the “second-order advantage”. When combined with advanced analytical instruments capable of generating higherorder tensor data arrays, multi-way calibration methods can be an efficient and green quantitative analysis strategy for complex chemical systems, based on the “mathematical separation”. Additionally, multi-way calibration methods can provide some other advantages, such as higher sensitivity.The research works in this thesis mainly focus on chemical multi-way calibration fundamental theories and their applications to static and dynamic quantitative analysis in complex systems. The research works are organized into six chapters, which follow the brief introduction in Chapter 1.Chapter 2: A flexible trilinear decomposition algorithm for three-way calibration based on the trilinear component model and a theoretical extension of the algorithm to the multilinear component modelThere is a great deal of interest in decompositions of multilinear component models in the field of multi-way calibration, especially the three-way case. A flexible novel trilinear decomposition algorithm of the trilinear component model as a modification of an alternating least squares algorithm for three-way calibration(Second-order tensor calibration) is proposed. The proposed algorithm(Constrained alternating trilinear decomposition, CATLD) is based on an alternating least squares scheme, in which two extra terms are added to each loss function, making it more efficient and flexible. The analysis of simulated three-way data arrays shows that it converges fast, is insensitive to initialization, and is insensitive to the overestimated number of components used in the decomposition. The analysis of real excitation emission matrix fluorescence spectroscopy(EEMs) and real high performance liquid chromatography-diode array detector(HPLC-DAD) data arrays confirms the results of the simulation studies, and shows that the proposed algorithm is favorable not only for EEMs but also for HPLC-DAD data. The three-way calibration method based on the CATLD algorithm is very efficient and flexible for direct quantitative analysis of multiple analytes of interest in complex systems, even in the presence of uncalibrated interferents and varying background interferents. Additionally, a theoretical extension of the proposed algorithm to the multilinear component model(Constrained alternating multilinear decomposition, CAMLD) is developed for multi-way calibration(Higher-order tensor calibration).Chapter 3: Simultaneous determination of aromatic amino acids in different systems using three-way calibration coupled with EEM fluorescenceA practical analytical method based on intrinsic fluorescence is proposed for simultaneous determination of L-phenylalanine, L-tyrosine, and L-tryptophan in cell culture and human plasma. By using three-way calibration method coupled with excitation-emission matrix fluorescence, the proposed method has successfully achieved quantitative analysis of the three aromatic amino acids in the two different complex systems simultaneously, even in the presence of three unknown, uncalibrated serious interferents. The method needs little preparation by using “mathematical separation” instead of chemical or physical separation, which makes it efficient and environmentally friendly. Satisfactory results have been achieved for calibration, validation, and prediction sets. For phenylalanine, tyrosine, and tryptophan, the calibration ranges are 6.00–60.00, 0.40–4.00, and 0.10–1.00 μg m L-1 respectively. The average spike recoveries(mean ± standard deviation) are 98.5±7.8%, 103.7±6.9%, and 102.3±7.9% respectively. The relative errors are-4.2%, 6.3%, and-0.8% for predicting real contents of phenylalanine, tyrosine, and tryptophan in cell culture respectively. Additionally, the potentiality of three-way calibration method for determining analytes of interest in different systems simultaneously is discussed, to further explore the second-order advantages. The paired t-test results indicate that the predicted results between predicting in two systems simultaneously and predicting in single system individually have no significant difference. The satisfactory results obtained in this work indicate that the use of three-way calibration method coupled with EEMs data array is a promising tool for multi-component simultaneous determination in multiple complex systems containing uncalibrated spectral interferents.and FAD in human plasma using three- or four-way calibration capable of providing the second-order advantage Chapter 4: Real-time fluorescence kinetic analysis of metabolic coenzymes NADHThe metabolic coenzymes reduced nicotinamide adenine dinucleotide(NADH) and flavin adenine dinucleotide(FAD) are the primary electron donor and acceptor respectively, participate in almost all biological metabolic pathways. This work studies the real-time kinetic analysis of the degradation reaction of NADH and the formation reaction of FAD in human plasma containing an uncalibrated interferent, by using three-way calibration based on multi-way fluorescence technique. In the threeway data analysis, by using the calibration set in a static manner, the concentrations of both analytes in the mixture at any time after the start of their reactions were directly predicted, even in the presence of an uncalibrated spectral interferent and a varying background interferent. The satisfactory quantitative results indicate that one can directly monitor the concentration of each analyte in the mixture as the function of time in real-time and nondestructively, instead of determining the concentration after the analytical separation. Thereafter, the first-order rate law was fitted to their concentration data throughout their reactions. Additionally, a four-way calibration procedure is developed as an alternative for highly collinear systems. The results of the four-way data analysis confirm the results of the three-way data analysis and reveal that both the degradation reaction of NADH and the formation reaction of FAD in human plasma fit the first-order rate law. The proposed methods could be expected to provide promising tools for simultaneous kinetic analysis of multiple reactions in complex systems in real-time and nondestructively.Chapter 5: An alternative quadrilinear decomposition algorithm for four-way calibration with application to analysis of four-way fluorescence excitationemission-p H data arrayA novel quadrilinear decomposition algorithm for four-way calibration(Thirdorder tensor calibration), which is called as regularized self-weighted alternating quadrilinear decomposition(RSWAQLD), has been developed in this work. It originates from the alternating trilinear decomposition(ATLD) algorithm, and inherits the philosophy behind self-weighting operation from the self-weighted alternating trilinear decomposition(SWATLD) algorithm. The RSWAQLD algorithm is based on the least squares scheme, in which two extra terms are added to each loss function, making it more stable and flexible. The results of simulated data arrays show that RSWAQLD has the features of fast convergence and being insensitive to the overestimated number of components in the model. Owing to its unique optimizing approach, RSWAQLD is much more efficient than four-way PARAFAC. Moreover, the performance of RSWAQLD is quite stable as the number of components used in calculation varies(As long as it is no less than the true number of factors). Such a feature will simplify the analysis of four-way data arrays, since it is unnecessary to spend a lot of time and effort on accurately determining the appropriate number of components in the chemical system. In addition, the results of four-way fluorescence excitation-emission-p H data, as well as that of simulated data arrays, illustrate that RSWAQLD can not only remain the "higher-order advantage" but also provide a satisfactory result even in high collinear systems.Chapter 6: Direct quantitative analysis of aromatic amino acids in human plasma by four-way calibration using intrinsic fluorescenceA novel intrinsic fluorescence method for the direct determination of Lphenylalanine, L-tyrosine, and L-tryptophan in human plasma is presented. By using fluorescence excitation-emission-p H-sample data array in combination with four-way calibration method based on the quadrilinear component model, the proposed approach has successfully achieved quantitative analysis of the aromatic amino acids in human plasma, even in the presence of an unknown, uncalibrated serious interferent. It needs little preparation, uses the “mathematical separation” instead of “analytical separation”, what makes it simple, fast and environmentally friendly. Satisfactory results have been achieved for calibration set, validation set, and prediction set. The ranges for phenylalanine, tyrosine, and tryptophan are 2.0×103–20.0×103, 50.0–500.0, and 20.0–200.0 ng m L-1 respectively. Average spike recoveries(mean ± standard deviation) are 93.3±7.7%, 104.3±6.6%, and 99.5±9.0% respectively. The predicted real concentrations in human plasma are 10.2±0.3, 6.6±0.1, and 5.3±0.1 μg m L-1 respectively, which are consistent with the results obtained by the approved liquid chromatography-tandem mass spectrometry(LC-MS/MS) method and reference values. In addition, the third-order advantages have been explored by the real four-way data array; it has shown that more resolving power is one of the main advantages of higherorder tensor calibration methods. These results demonstrate that the proposed method is sensitive, accurate, and efficient for direct quantitative analysis of aromatic amino acids in human plasma.calibration Chapter 7: Direct quantitative analysis of metabolic coenzymes FAD and FMN in the cell by using a novel strategy of intrinsic fluorescence coupled with four-wayThe direct quantitative analysis of metabolic coenzymes flavin adenine dinucleotide(FAD) and flavin mononucleotide(FMN) in the cell is very important because they participate in many electron-transfer reactions of metabolism. However, the direct quantitative analysis of FAD and FMN is hard to be achieved by traditional methods. This work reports a novel strategy of intrinsic fluorescence coupled with four-way calibration method for the direct quantitative analysis of metabolic coenzymes FAD and FMN in the cell. With the mathematical separation, the proposed method has successfully achieved the direct quantitative analysis of metabolic coenzymes FAD and FMN in the cell, even in the presence of an uncalibrated spectral interferent. The predicted concentrations of FAD and FMN in the cell are 217.0±6.9 and 155.0±1.7 pmol/106 cells respectively, which are validated by the approved liquid chromatography-tandem mass spectrometry(LC-MS/MS) method. The proposed method only needs the cell solution to be diluted directly by a buffer for sample preparation, which makes the method simple and efficient. The proposed method with nondestructive sample preparation introduces a very promising strategy for direct quantitative analysis in complex systems, and shows excellent potential for in situ quantitative analysis in complex systems. In addition, the third-order advantages of four-way calibration have been explored by a comparative study based on this real fluorescence data array. The comparisons indicate that the third-order advantages can not only maintain the second-order advantage, but also provide higher sensitivity and more resolving power.