Theory of Analytical Chemistry

PARAFAC under non-negativity constraint is adapted to recover the underlying Beer-Lambert law of the excitation-emission fluorescence matrix measurements acquired from analyte-triggered semiconductor QDs photoluminescence modulation. When and why?

BACKGROUND

Analyte-triggered semiconductor quantum dots (QDs) modulation in the presence of non-consistently responsive fluorescent species represents a challenging analytical issue in concrete multi-way data handling. QDs with heterogeneous sizes and/or uneven distribution of functional moieties on their surfaces exhibit significant fluctuations in the fluorescent response components, known as chemical rank, across different excitation/emission modes. This phenomenon may lead to a substantial deviation from the proportionality prescribed by Beer-Lambert law. Nonetheless, even in the presence of such deviation, a multi-way model may be successfully selected after determining a proper chemical rank in a QDs system.

RESULTS

We show that in a valid PARAllel FACtor (PARAFAC) model under properly determined chemical rank, meaningfully resolved pure spectral profiles can be reached for each fluorescent responsive constituent in the original excitation-emission fluorescence matrix (EEFM) measurements. This was thoroughly illustrated by applying PARAFAC trilinear decomposition of a three-way data array of two distinct datasets acquired from semiconductor QDs sensing systems with low-rank trilinear assumption. The first dataset, presented here for the first time, comprises EEFM measurements of the ligand-driven quenching of thiomalic acid (TMA)-capped AgInS2 (AIS) QDs by vomitoxin. The second dataset, employed for illustrative purposes, comprises EEFM measurements of the quenching, via cation bridging, of glutathione (GSH)-capped CdTe QDs by Pb(II). The results of this study enabled the determination of vomitoxin at a ppb level in real samples of fish feeds, showcasing the efficacy of the PARAFAC model in resolving spectral signatures (loadings) and pure concentration profiles (scores).

SIGNIFICANCE

PARAFAC under a properly examined chemical rank can be easily adapted for retrieval the underlying Beer-Lambert law of the original EEFM measurements with a low-rank trilinear structure through the chemically meaningful information either when (i) no deviation of Beer-Lambert law was observed as deeply discussed in connection with the dataset acquired from vomitoxin-driven molecular sensing through TMA-capped AIS QDs, or when (ii) substantial deviations of the Beer-Lambert law are evident, as discussed in connection with the dataset collected from sensing ionic species through Pb(II) bridging of GSH-capped CdTe QDs.

Contribution of multiway calibration to White Analytical Chemistry

In this article, the compatibility between second- and third-order calibration and White Analytical Chemistry (WAC) is exposed and discussed. The WAC concept and the principles on which it is based are briefly presented. Multiway calibration methods, which consist of performing analyte(s) quantification by processing second- or higher-order instrumental data using chemometric models, are analyzed in light of their contribution to the whiteness of an analytical method. Special emphasis is directed towards the chemometric property called "second-order advantage," which offers the possibility of modeling sample interferences without either needing to remove them nor knowing their identity. With the purpose of illustrating to the analytical community the valuable contribution of multiway calibration to the development of white methodologies, some examples selected from our laboratory are here presented.

DC vs AC Electrokinetics-Driven Nanoplasmonic Raman Monitoring of Charged Analyte Molecules in Ionic Solutions

Electrokinetic surface-enhanced Raman spectroscopy (EK-SERS) is an emerging high-order analytical technique that combines the plasmonic sensitivity of SERS with the electrode interfacial molecular control of electrokinetics. However, previous EK-SERS works primarily focused on non-Faradaic direct current (DC) operation, limiting the understanding of the underlying mechanisms. Additionally, developing reliable EK-SERS devices with electrically connected plasmonic hotspots remains challenging for achieving high sensitivity and reproducibility in EK-SERS measurements. In this study, we investigated the use of two-tier nanolaminate nano-optoelectrode arrays (NL-NOEAs) for DC and alternating current (AC) EK-SERS measurements of charged analyte molecules in ionic solutions. The NL-NOEAs consist of Au/Ag/Au multilayered plasmonic nanostructures on conductive nanocomposite nanopillar arrays (NC-NPAs). We demonstrate that the NL-NOEAs exhibit high SERS enhancement factors (EFs) of ∼106 and can be used to modulate the concentration and orientation of Rhodamine 6G (R6G) molecules at the electrode surface by applying DC and AC voltages. We also performed numerical simulations to investigate the ion and R6G dynamics near the electrode surface under DC and AC voltage modulation. Our results show that AC EK-SERS can provide additional insights into the dynamics of molecular transport and adsorption processes compared to DC EK-SERS. This study demonstrates the potential of NL-NOEAs for developing high-performance EK-SERS sensors for a wide range of applications.

The advantages behind the efforts of performing higher-order calibration methods - A case study

BACKGROUND

Across numerous investigations delved into second- and higher-order data, an undoubted finding emerges: models based on such data can effectively exploit the second-order advantage. However, whether further benefits can be achieved by modeling data of higher dimensions remains a subject of inquiry. In this regard, a prevailing question emerges in third-order data-based applications regarding the fundamental need to increase the data dimension and, hence, the data analysis complexity. This study aims to provide meaningful evidence to support the advantages inherent in employing third-order calibration methods despite the associated efforts, such as instrumentation and data analysis complexity.

RESULTS

This study compares the analytical performance achieved using a third-order calibration method with those obtained from most of the possible second-order calibration approaches derived from the same dataset. This work delves into the structural properties of the data, modeling limitations, and analytical characteristics associated with each model. Additionally, it includes a comprehensive statistical comparison of the models based on their recovery performance. First, the outcomes demonstrate the importance of capitalizing on all available chemical information and harnessing the full potential of data to maximize its benefits. Moreover, the results provide evidence that asserts the fact that third-order calibration methods bring the opportunity to increase the number of analytes that can be simultaneously determined, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.

SIGNIFICANCE

this research marks the first extensive comparison of third-order data calibration models with possible second-order calibration methods. Moreover, this work pioneers the incorporation of highly challenging non-multilinear data. The advancements detailed in this study emphasize the advantages of third-order data acquisition, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.

An exhaustive analysis of the use of image moments for second-order calibration. A comparison with multivariate curve resolution-alternating least-squares

BACKGROUND

the chemometric processing of second-order chromatographic-spectral data is usually carried out with the aid of multivariate curve resolution-alternating least-squares (MCR-ALS). Recently, an alternative procedure was described based on the estimation of image moments for each data matrix and subsequent application of multiple linear regression after suitable variable selection.

RESULTS

The analysis of both simulated and experimental data leads to the conclusion that the image moment method, although can cope with chromatographic lack of reproducibility across injections, it only performs well in the absence of uncalibrated interferents. MCR-ALS, on the other hand, provides good analytical results in all studied situations, whether the test samples contain uncalibrated interferents or not.

SIGNIFICANCE

The results are useful to assess the real usefulness of newly proposed methodologies for second-order calibration in the case of chromatographic-spectral data sets, especially when samples contain unexpected chemical constituents.

Detection and Quantification of Bisphenol A in Surface Water Using Absorbance-Transmittance and Fluorescence Excitation-Emission Matrices (A-TEEM) Coupled with Multiway Techniques

In the present protocol, we determined the presence and concentrations of bisphenol A (BPA) spiked in surface water samples using EEM fluorescence spectroscopy in conjunction with modelling using partial least squares (PLS) and parallel factor (PARAFAC). PARAFAC modelling of the EEM fluorescence data obtained from surface water samples contaminated with BPA unraveled four fluorophores including BPA. The best outcomes were obtained for BPA concentration (R2 = 0.996; standard deviation to prediction error's root mean square ratio (RPD) = 3.41; and a Pearson's r value of 0.998). With these values of R2 and Pearson's r, the PLS model showed a strong correlation between the predicted and measured BPA concentrations. The detection and quantification limits of the method were 3.512 and 11.708 micro molar (µM), respectively. In conclusion, BPA can be precisely detected and its concentration in surface water predicted using the PARAFAC and PLS models developed in this study and fluorescence EEM data collected from BPA-contaminated water. It is necessary to spatially relate surface water contamination data with other datasets in order to connect drinking water quality issues with health, environmental restoration, and environmental justice concerns.

A smartphone digital image colorimetric method based on nanoparticles for determination of lamotrigine

Aim: A colorimetric approach for quantification of lamotrigine using spectrophotometric and smartphone image analysis is described in this study. Methods: For full optimization and validation procedures, UV-visible spectroscopy was used, and image analysis was carried out with the help of an app (PhotoMetrix PRO®). Then, as a multivariate calibration method, parallel factor analysis was used for data analysis. Results: The results demonstrated the capacity of these methods to estimate lamotrigine concentrations in the range of 0.1-7.0 μg.ml-1 in exhaled breath condensate, indicating the value of using digital images and smartphone applications in combination with chemometric tools. Conclusion: The image analysis can be superior for its fast and reliable lamotrigine analysis in biological samples.

First-Order Individual Gas Sensors as Next Generation Reliable Analytical Instruments

It is conventionally expected that the performance of existing gas sensors may degrade in the field compared to laboratory conditions because (i) a sensor may lose its accuracy in the presence of chemical interferences and (ii) variations of ambient conditions over time may induce sensor-response fluctuations (i.e., drift). Breaking this status quo in poor sensor performance requires understanding the origins of design principles of existing sensors and bringing new principles to sensor designs. Existing gas sensors are single-output (e.g., resistance, electrical current, light intensity, etc.) sensors, also known as zero-order sensors (Karl Booksh and Bruce R. Kowalski, Analytical Chemistry, DOI: 10.1021/ac00087a718). Any zero-order sensor is undesirably affected by variable chemical background and sensor drift that cannot be distinguished from the response to an analyte. To address these limitations, we are developing multivariable gas sensors with independent responses, which are first-order analytical instruments. Here, we demonstrate self-correction against drift in two types of first-order gas sensors that operate in different portions of the electromagnetic spectrum. Our radiofrequency sensors utilize dielectric excitation of semiconducting metal oxide materials on the shoulder of their dielectric relaxation peak and achieve self-correction of the baseline drift by operation at several frequencies. Our photonic sensors utilize nanostructured sensing materials inspired by Morpho butterflies and achieve self-correction of the baseline drift by operation at several wavelengths. These principles of self-correction for drift effects in first-order sensors open opportunities for diverse emerging monitoring applications that cannot afford frequent periodic maintenance that is typical of traditional analytical instruments.

Interference-free quantitation of aromatic amino acids in two complex systems by three-way calibration with ultraviolet-visible spectrophotometer: Exploration of trilinear decomposition of spectrum-pH data

Aromatic amino acids play an extremely important role in life activities and participate in many biological processes. Their concentration levels are associated with a variety of diseases, such as phenylketonuria and colorectal cancer. Therefore, the quantification of aromatic amino acids is an important task. In the present work, a novel and rapid three-way analytical method was proposed to detect the levels of aromatic amino acids in prostate cancer cells (PC3 cells) and Dulbecco's modified minimal essential medium (DMEM cell culture), by using the affordable ultraviolet-visible spectrophotometer. First, spectrum-pH second-order data were designed per sample; Second, properties of the resulted spectrum-pH-sample three-way data were investigated by utilizing the parallel factor analysis (PARAFAC), alternating trilinear decomposition (ATLD), and constrained alternating trilinear decomposition (CATLD) algorithms, and a flexible scanning approach for determining the constraint parameters of CATLD was proposed; Third, a three-way calibration method based on the CATLD algorithm with the proposed scanning approach was developed for interference-free quantification of aromatic amino acids in these systems. The average relative predictive errors of validation (ARPEV) for phenylalanine, tyrosine, and tryptophan were 1.4%, 3.0%, and 0.7% in prostate cancer cells, and ARPEV for phenylalanine, tyrosine, and tryptophan were 4.1%, 1.2%, and 0.7% in DMEM cell culture. The predicted contents of tyrosine and tryptophan in DMEM cell culture were 64.2 ± 2.9 μg mL^-1, 5.6 ± 0.3 μg mL^-1, there are no significant differences in the concentrations between the developed analytical method and high performance liquid chromatography method. The proposed spectrum-pH-sample three-way calibration method based on CATLD algorithm can provide an interesting analytical strategy with high selectivity and accuracy for ultraviolet-visible spectrophotometer.

Practical and comparative application of efficient data reduction - Multivariate curve resolution

The term 'Big Data' has recently attracted much attention in science. Working with big data sets can be both challenging and rewarding. The complexity and big data sets make the analysis difficult to deal with, and the increasing volume of data sets requires the development of new practical methods for their handling. In this contribution, we explored the efficient data reduction-multivariate curve resolution (EDR-MCR) strategy based on the convex hull theory for quantitative and qualitative analysis of large chemical data sets. For the quantitative example, the potential of the EDR-MCR method for selecting a representative calibration set was investigated, and the results were compared with the widely used Kennard-Stone (KS) algorithm. The EDR-MCR strategy strongly limits the number of calibration samples with a high potency of prediction performance. The priority of EDR-MCR over KS is its ability to find informative variables and eliminate redundant features. Moreover, the EDR-MCR strategy was also applied for the qualitative analysis of a large-scale metabolomic data set. The comparable analysis results of EDR-MCR with the region of interest (ROI) method confirmed the ability of this method for quantitative analysis of big mass spectrophotometer data sets.

Detection of protein oxidation products by fluorescence spectroscopy and trilinear data decomposition: Proof of concept

Current analytical methods studying protein oxidation modifications require laborious sample preparation and chromatographic methods. Fluorescence spectroscopy is an alternative, as many protein oxidation products are fluorescent. However, the complexity of the signal causes misinterpretation and quantification errors if single emission spectra are used. Here, we analyzed the entire fluorescence excitation-emission matrix using the trilinear decomposition method parallel factor analysis (PARAFAC). Two sample sets were used: a calibration set based on known mixtures of tryptophan, tyrosine, and four oxidation products, and a second sample set of oxidized protein solutions containing UV-illuminated β-lactoglobulin. The PARAFAC model succeeded in resolving the signals of the model systems into the pure fluorophore components and estimating their concentrations. The estimated concentrations for the illuminated β-lactoglobulin samples were validated by liquid chromatography-mass spectrometry. Our approach is a promising tool for reliable identification and quantification of fluorescent protein oxidation products, even in a complex protein system.

A tutorial on multi-way data processing of excitation-emission fluorescence matrices acquired from semiconductor quantum dots sensing platforms

This tutorial demonstrates how to exploit the second-order advantage on excitation-emission fluorescence matrices (EEFMs) acquired from sensing platforms based on analyte-triggered semiconductor quantum dots (QDs) fluorescence modulation (quenching/enhancing). The advantage in processing such second-order EEFMs data from complex samples, seeking successful quantification, is comprehensively addressed. It is worth emphasizing that, aiming to exploit the second-order advantage, the selection of the most appropriate advanced chemometric model should rely on the matching between the data structure and the physicochemical chemometric model assumption. In this sense, the achievement of second-order advantage after EEFMs' processing is extensively addressed throughout this tutorial taking into consideration three different analytical situations, each involving a specific data structure: i) parallel factor analysis (PARAFAC), which is applied in a real dataset stacked in a three-way data array containing a trilinear data structure acquired from QDs-based detection with non-selective species; ii) multivariate curve resolution - alternating least-squares (MCR-ALS), which is also employed in a real dataset arranged in an augmented data matrix containing non-trilinear data structure acquired from QDs-based detection with a single breaking mode caused by background signals; iii) unfolded partial least-squares with residual bilinearization (U-PLS/RBL), which is applied in a dataset containing non-trilinear data acquired from a classical fluorescence system with two breaking modes caused by inner filter effect (IFE) in both instrumental modes (excitation and emission). The latter challenging data structure can be acquired via fluorescence quenching from IFE-based sensing platforms and chemometrically handled in two main steps. First, a set of calibration EEFMs data is converted into an unfolded data matrix during the unfolding process, followed by applying U-PLS model. Second, a post-calibration procedure using RBL analysis is applied to a test sample of EEFM maintained in its matrix form, in order to handle potential interferents. In the last section, the state-of-the-art of second-order EEFMs data acquired from semiconductor QDs-based sensing platforms and coupled to multi-way fluorescence data processing to accomplish a successful quantification, even with substantial interfering species, is critically reviewed.

Radial basis function-artificial neural network (RBF-ANN) for simultaneous fluorescent determination of cysteine enantiomers in mixtures

The determination of chiral compounds is critically important in chemical and pharmaceutical sciences. Cysteine amino acid is one of the important chiral compounds where each enantiomer (L and D) has different effects on fundamental physiological processes. The unique optical properties of nanoparticles make them a suitable probe for the determination of different analytes. In this work, the water-soluble thioglycolic acid (TGA)-capped cadmium-telluride (CdTe) quantum dots (QDs) were applied as optical nanoprobe for the simultaneous determination of cysteine enantiomers. The difference in the kinetics of the interactions between L- and D-cysteine with CdTe QDs is used for multivariate quantitative analysis. Multivariate methods are superior to univariate methods in determining the concentration of each enantiomer in the mixture without the information about the total chiral analyte concentration. As a nonlinear calibration method the radial basis function -artificial neural network (RBF-ANN) model was more successful in predicting L-and D-cysteine concentrations than the linear partial least squares regression (PLS) model.

Orthogonality constrained inverse regression to improve model selectivity and analyte predictions from vibrational spectroscopic measurements

In analytical chemistry spectroscopy is attractive for high-throughput quantification, which often relies on inverse regression, like partial least squares regression. Due to a multivariate nature of spectroscopic measurements an analyte can be quantified in presence of interferences. However, if the model is not fully selective against interferences, analyte predictions may be biased. The degree of model selectivity against an interferent is defined by the inner relation between the regression vector and the pure interfering signal. If the regression vector is orthogonal to the signal, this inner relation equals zero and the model is fully selective. The degree of model selectivity largely depends on calibration data quality. Strong correlations may deteriorate calibration data resulting in poorly selective models. We show this using a fructose-maltose model system. Furthermore, we modify the NIPALS algorithm to improve model selectivity when calibration data are deteriorated. This modification is done by incorporating a projection matrix into the algorithm, which constrains regression vector estimation to the null-space of known interfering signals. This way known interfering signals are handled, while unknown signals are accounted for by latent variables. We test the modified algorithm and compare it to the conventional NIPALS algorithm using both simulated and industrial process data. The industrial process data consist of mid-infrared measurements obtained on mixtures of beta-lactoglobulin (analyte of interest), and alpha-lactalbumin and caseinoglycomacropeptide (interfering species). The root mean squared error of beta-lactoglobulin (% w/w) predictions of a test set was 0.92 and 0.33 when applying the conventional and the modified NIPALS algorithm, respectively. Our modification of the algorithm returns simpler models with improved selectivity and analyte predictions. This paper shows how known interfering signals may be utilized in a direct fashion, while benefitting from a latent variable approach. The modified algorithm can be viewed as a fusion between ordinary least squares regression and partial least squares regression and may be very useful when knowledge of some (but not all) interfering species is available.

Rapid determination of sulfamethoxazole and trimethoprim illegally added to health products using excitation-emission matrix fluorescence coupled with the second-order calibration method

In this work, a simple and fast analytical method based on a self-weighted alternating trilinear decomposition (SWATLD) algorithm coupled with excitation-emission matrix (EEM) fluorescence was developed for the simultaneous determination of sulfamethoxazole (SMZ) and trimethoprim (TMP) illegally added to health products. With the second-order advantage, the proposed method obtained satisfactory results in the presence of peak overlap and unknown interferences. The analysis time for a single sample is only 0.8 minutes. The average spiked recoveries of SMZ and TMP in three health product spiked samples were in the range of 91.0-106.2% and 86.8-107.8%, respectively. The relative standard deviations (RSDs) were lower than 8.6%. In addition, verification parameters including sensitivity (SEN), selectivity (SEL), the limit of detection (LOD), the limit of quantification (LOQ), intra-day precision, and inter-day precision were calculated, and the results show that the proposed method is feasible. The quantitative results of the proposed method were further confirmed by the LC-MS/MS method, which proved that the proposed method was efficient and green for drug-abuse monitoring of SMZ and TMP in health products.

Chromatographic Applications in the Multi-Way Calibration Field

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

Multi-Way Analysis Coupled with Near-Infrared Spectroscopy in Food Industry: Models and Applications

Near-infrared spectroscopy (NIRS) is a fast and powerful analytical tool in the food industry. As an advanced chemometrics tool, multi-way analysis shows great potential for solving a wide range of food problems and analyzing complex spectroscopic data. This paper describes the representative multi-way models which were used for analyzing NIRS data, as well as the advances, advantages and limitations of different multi-way models. The applications of multi-way analysis in NIRS for the food industry in terms of food process control, quality evaluation and fraud, identification and classification, prediction and quantification, and image analysis are also reviewed. It is evident from this report that multi-way analysis is presently an attractive tool for modeling complex NIRS data in the food industry while its full potential is far from reached. The combination of multi-way analysis with NIRS will be a promising practice for turning food data information into operational knowledge, conducting reliable food analyses and improving our understanding about food systems and food processes. To the best of our knowledge, this is the first paper that systematically reports the advances on models and applications of multi-way analysis in NIRS for the food industry.

Multilinear Mathematical Separation in Chromatography

Chromatography is a powerful and generally applicable method for the analytical separation and quantification of the chemical constituents in complex mixtures because chromatographic separation can provide high selectivity by isolating all analytes from interferences. Multiway analysis based on the multilinear model is an increasingly widely used method for interference-free and fast determination of the chemical constituents also in complex mixtures because multilinear mathematical separation can provide high selectivity by extracting the pure signal of the analyte from the mixed signal of a real sample. By combining chromatographic separation with mathematical separation, multiway calibration method, multiway standard additions method, and multiway internal standard method can be established. Chromatography assisted by multiway analysis can reduce the requirements for complete chromatographic separation, save elution time, and decrease the consumption of the mobile phase, particularly when the peak coelution problem is difficult to solve. This review presents the fundamentals and analytical applications of multilinear mathematical separation in chromatography.

Three-way calibration using PARAFAC and MCR-ALS with previous synchronization of second-order chromatographic data through a new functional alignment of pure vectors for the quantification in the presence of retention time shifts in peak position and shape

In the present contribution is shown the application of the recently developed functional alignment of pure vectors (FAPV) as a proper algorithm to align second-order chromatographic data with severe retention time shifts in peak position and shape. FAPV decomposed a three-way chromatographic data array in their three modes (sample, spectral and elution time vectors), using a basis function to pre-process the non-linear mode (elution time) and then it aligns the functionalized pure vectors and reshapes the transformed vectors into matrices, restoring the trilinearity of second-order chromatographic data. The well-aligned three-way chromatographic data array is then successfully decomposed by advanced chemometric models such as parallel factor analysis (PARAFAC) and multivariate curve resolution - alternating least-squares (MCR-ALS) with the trilinearity constraint. The performance of this innovative analytical strategy based on PARAFAC and MCR-ALS with previous synchronization of data through FAPV algorithm is properly evaluated using real second-order chromatographic data with multiple artifacts, i.e., shifts in peak position and shape for the simultaneous quantification of amoxicillin and potassium clavulanate in commercial medicinal drugs. The present contribution compares some analytical results achieved by: (1) the usual MCR-ALS as a bilinear model applied in augmented data matrix without previous synchronization and with interval correlation optimized shifting (ICOSHIFT) and FAPV and (2) trilinear models using PARAFAC with ICOSHIFT and FAPV and trilinearity constraint in MCR-ALS with FAPV. Available results suggest that these strongly shifted and warped elution time profiles cause for the loss of trilinearity, which can be adequately restored by FAPV algorithm. PARAFAC performed a successful trilinear decomposition of three-way chromatographic data array with law values of relative prediction error (REP) in the order of 1.34-1.42% in both analytes.

A simple self modelling curve resolution (SMCR) method for two-component systems

Multivariate self-modeling curve resolution (SMCR) methods are the best choice for analyzing chemical data when there is not any prior knowledge about the chemical or physical model of the process under investigation [[1Q3: The reference '1' is only cited in the abstract and not in the text. Please introduce a citation in the text.]]. However, the rotational ambiguity is the main problem of SMCR methods, yielding a range of feasible solutions. It is, therefore, important to determine the range of all feasible solutions of SMCR methods. Different methods have been presented in the literature to find feasible solutions of two, three, and four component systems. Here, a novel simple SMCR method is presented for calculating the boundaries of feasible solutions of two-component systems. At first, the simple strategy is presented for calculating the feasible solutions of two-component systems. Next, four different experimental two-component systems are analyzed in detail for calculating the boundaries of feasible solutions in both spaces, including complex formation equilibrium, keto-enol tautomerization kinetic, lipidomics data, and a case for quantification of an analyte in gray systems. In all cases, the boundaries of range of feasible solutions are properly determined by the proposed simple strategy.

Simultaneous, Rapid and Nondestructive Determination of Moisture, Fat Content and Storage Time in Leisure Dried Tofu Using LF-NMR

Leisure dried tofu is a kind of small packaged food which is popular with consumers in China. However, during the storage of leisure dried tofu, moisture and fat may be lost and deteriorate. For their own benefit, bad business operators might forge or mark the production date and shelf life. Therefore, it is necessary to explore a method to determine simultaneously the moisture, fat content, and storage time of leisure dried tofu. Samples were measured for obtaining transverse relaxation data by using low-field nuclear magnetic resonance (LF-NMR) spectrometer. The experimental data were analyzed and modeled by methods including partial least squares (PLS) or back-propagation artificial neural network (BP-ANN). The results show that the models can be used to predict the moisture, fat content, and storage time rapidly, nondestructively, accurately, and simultaneously. Furthermore, in order to explore the changes of nutrients in leisure dried tofu with the storage time, the storage dynamics of moisture and fat was considered by a using corresponding calibration model.

Standardization of chromatographic signals - Part I: Towards obtaining instrument-agnostic fingerprints in gas chromatography

One of the main causes for the sparse use of multivariate analytical methods in routine laboratory work is the dependency on the measuring instrument from which the analytical signal is acquired. This issue is especially critical in chromatographic equipment and results in limitations of their applicability. The solution to this problem is to obtain a standardized instrument-independent signal -or instrument-agnostic signal- regardless of the measuring instrument or of the state of the same instrument from which it has been acquired. The combined use of both internal and external standard series, allows us to have external and transferable references for the normalization of both the intensity and the position of each element of the data vector being arranged from the raw signal. From this information, a simple mathematical data treatment process is applied and instrument-agnostic signals can be secured. This paper describes and applies the proposed methodology to be followed for obtaining standardized instrumental fingerprints from two significant fractions of virgin olive oil (volatile organic compounds and triacylglycerols), obtained by gas chromatography coupled to mass spectrometry (GC-MS) and analysed with two temperature conditions (conventional and high-temperature, respectively). The results of both case studies show how the instrument-agnostic fingerprints obtained are coincidental, regardless of the state of the chromatographic system or the time of acquisition.

A chemometric comparison of different models in fluorescence analysis of dabigatran etexilate and dabigatran

In this paper, a simple, rapid, low-cost and potential method was established for the simultaneous quantitative analysis of dabigatran etexilate (DABE) and dabigatran (DAB) in spiked biological fluids. It combined excitation-emission matrix fluorescence (EEMF) with different second-order calibration methods, including the self-weighted alternating normalized residue fitting (SWANRF) algorithm based on trilinear decomposition model, the multivariate curve resolution - alternating least-squares (MCR-ALS) based on bilinear decomposition model and the unfolded partial least-square coupled with residual bilinearization (U-PLS/RBL) based on latent variables model. The proposed method showed "second-order advantage", that is, satisfactory quantitative results were successfully obtained even in the presence of unknown interferences and serious spectral overlap. The recoveries of DABE and DAB in spiked biological fluids were 91.7%-101.7% for SWANRF, 95.9%-117.8% for MCR-ALS, 83.0%-109.6% for U-PLS/RBL, respectively. Figures of merit and other statistical parameters were also calculated to assess the performance of the proposed method. Moreover, the modeling procedures and characteristics of three different models in EEMF analysis were discussed and compared.

A down-to-earth analyst view of rotational ambiguity in second-order calibration with multivariate curve resolution - a tutorial

Rotational ambiguity is a phenomenon with the potential of generating an uncertainty in the estimation of analyte concentrations in protocols based on matrix instrumental data processed by multivariate curve resolution - alternating least-squares (MCR-ALS). This is particularly relevant when the second-order advantage is to be achieved, i.e., when selected analytes are determined in unknown samples having unexpected constituents, not considered in the calibration set of samples. It is therefore imperative that analytical chemists developing second-order multivariate calibration methods using MCR-ALS acknowledge the relevance of this issue, and more importantly, have access to the required tools to size the relative impact of this potential source of uncertainty on the estimated analyte concentrations. The purpose of this tutorial is to provide a down-to-earth view of rotational ambiguity, by studying in detail a synthetic example mimicking a typical chromatographic-spectral experiment, where a set of calibration samples is joined with an unknown sample having an uncalibrated interference. After explaining the background information needed to understand the origin of the phenomenon, the available tools for the estimation of the feasible MCR-ALS solutions and the derived uncertainty on analyte predictions will be discussed. A multi-component experimental system will also be discussed, stressing the fact that rotational ambiguity uncertainties, however small, should always be estimated and reported.

Exploring the potential of combining chemometric approaches to model non-linear multi-way data with quantitative purposes - A case study

Second-order based calibration methods have been widely investigated capitalizing on the inherent benefits of the data structure and the decomposition models, demonstrating that second-order advantage is a property that conspires to a high likelihood success in the resolution of systems of varying complexity. This work aims to demonstrate the applicability of a combined chemometric strategy to solve non-linear multivariate calibration systems in the presence of non-multilinear multi-way data. The determination of histamine by differential pulse voltammetry at different pH is presented as case study. The experimental system has the outstanding difficulty arisen from the large displacement along the potential axis by the pH, which was successfully overcome by implementation of the presented combined strategy. For data modeling, MCR-ALS, U-PLS/RBL and U-PCA/RBL-RBF were used. MCR-ALS allowed unraveling the non-linear behavior between the signal and the concentration, and extracting the underlying profiles of the constituent. Quantitative analysis was performed through the three models, and a comparative evaluation of the predictive performance was done. The best results were achieved with U-PCA/RBL-RBF (mean recovery = 101%) whereas, MCR-ALS yield the lowest mean recovery for all samples (70%).

Determination of ochratoxin A in coffee and tea samples by coupling second-order multivariate calibration and fluorescence spectroscopy

A new method to quantify the mycotoxin ochratoxin A (OTA) in coffee and tea samples is proposed based on second-order multivariate calibration and excitation-emission fluorescence matrix (EEFM) data. Experimental conditions were optimized by studying the effect of pH and various organized media on the fluorescence signal of OTA. For each analysed matrix (coffee grains and tea leaves), several sample pretreatments and calibration methods (external or standard addition) and data processing by chemometric models (e.g., parallel factor analysis/PARAFAC and multivariate curve resolution-alternating least squares/MCR-ALS) were evaluated and discussed. The MCR-ALS algorithm provided an adequate fit to the data for both samples, while PARAFAC was satisfactory only for the tea samples. Regarding the figures of merit, the limits of detection were in the range of 0.2-0.3 ng mL^-1; furthermore, low relative prediction errors, between 2% and 4%, were achieved in both the fortified and real samples. Accordingly, the proposed methodology was applied to analyse fortified roasted and green coffee and real tea leaf samples. Satisfactory recoveries were achieved (ranging from 92 to 110%), and the obtained concentrations were in agreement with the values obtained by the reference method (based on high-performance liquid chromatography with fluorescence detection/HPLC-FLD). In addition, all samples contained OTA levels lower than the maximum permissible levels. Finally, the proposed strategy allows the use of green analytical chemistry principles; for instance, the use of organic solvents and the generation of waste products were significantly lower than for similar analytical methods reported in the literature.

Simultaneous Determination of Medicinal Drugs with Overlapping Profiles Contained in Low Chromatographic Resolution Data using HPLC-DAD and Multivariate Curve Resolution

Background:

The increasing demand of effective pharmaceutical products directed to fight against malaria lead to the combination of at least two antimalarial drugs. This combination aims to minimize the Plasmodium falciparum resistance which is found when the most frequently used drugs are taken individually. Within this context, proguanil hydrochloride and chloroquine phosphate which have independent modes of action are taken together to prevent malaria. This paper aims to develop a fast and powerful analytical method for the simultaneous determination of proguanil hydrochloride and chloroquine phosphate in the commercial Paludrine/Avloclor dosage forms using a multi-way chromatographic calibration based on high-performance liquid chromatography with diode array detection (HPLC-DAD) and multivariate curve resolution – alternating leastsquares (MCR-ALS).

Methods:

A rapid and powerful analytical method based on HPLC-DAD and MCR-ALS was developed for the simultaneous quantification of proguanil hydrochloride and chloroquine phosphate in the commercial Paludrine/Avloclor antimalarial drugs. An isocratic mobile phase composed by 0.2 M ammonium acetate, acetonitrile, and methanol (40:25:35) and a flow rate of 1.2 mL min-1 were employed in the chromatographic runs with an elution time about 5 min.

Results:

This approach demonstrates that chromatographic analysis may become considerably simpler and economical in terms of time, cost, and organic solvent consumption when coupled to multiway calibration models such as MCR-ALS. In fact, this multi-way chromatographic calibration based on second-order HPLC-DAD data matrices (with extremely low chromatographic resolution) and MCR-ALS allows the development of greener analytical methods for complex samples. The proposed analytical method allowed the simultaneous quantification of two antimalarial APIs present in the commercial Paludrine/Avloclor drugs with low REP values below 8% for the simultaneous determination of proguanil hydrochloride and chloroquine phosphate.

Conclusion:

The proposed multi-way chromatographic strategy can be used for routine control of pharmaceutical dosage forms. It should be highlighted that MCR-ALS allowed to: (a) achieve the second- order advantage and the quantification of analytes in the presence of uncalibrated compounds such as coeluted profile measured in different magnitude of the signal in each successive chromatographic run and significant overlapping profiles and (b) separate the contribution of several components from chromatographic runs with extremely low separation of peaks through the deconvolution of the signal obtained, performing the so-called mathematical chromatography.

Comparing the performance of three methods to assess DOM dynamics within two distinct glacierized watersheds of the tropical Andes

Dissolved organic matter (DOM) is recognized as a good indicator of water quality as its concentration is influenced by land use, rainwater, windborne material and anthropogenic activities. Recent technological advances make it possible to characterize fluorescent dissolved organic matter (FDOM), the fraction of DOM that fluoresces. Among these advances, portable fluorometers and benchtop fluorescence excitation and emission spectroscopy coupled with a parallel factor analysis (EEM-PARAFAC) have shown to be reliable. Despite their rising popularity, there is still a need to evaluate the extent to which these techniques can assess DOM dynamics at the watershed scale. We compare the performance of in-situ measurements of FDOM with laboratory measurements of fluorescence spectroscopy within the context of two distinct glacierized watersheds in Peru. Glacierized watersheds represent unique testing environments with contrasting DOM conditions, flowing from pristine, vegetation-free headwaters through locations with obvious anthropogenic influences. We used an in-situ fluorometer and a portable multimeter to take 38 measurements of FDOM, pH and turbidity throughout the two catchments. Additionally, samples were analyzed in the laboratory using the EEM-PARAFAC method. Results were compared to dissolved organic carbon (DOC) measurements using standard high-temperature catalytic oxidation. Our results show that the three techniques together were able to capture the DOM dynamics for both studied watersheds. Taken individually, all three methods allowed detection of the watershed DOM main points of sources but in a more limited way. Due to the narrow bandwidth of the portable fluorometer used in the study, FDOM measurements were almost non-detectable to protein-like substances. Indeed, the more demanding EEM-PARAFAC was able to both differentiate between potential sources of DOM and provide an estimate of relative concentrations of different organic components. Finally, similar to FDOM but to a lesser extent, the DOC measurements showed some limits where protein-like substances make up most of the DOM composition.

N-Way NIR Data Treatment through PARAFAC in the Evaluation of Protective Effect of Antioxidants in Soybean Oil

The use of chemometric tools is progressing to scientific areas where analytical chemistry is present, such as food science. In analytical food evaluation, oils represent an important field, allowing the exploration of the antioxidant effects of herbs and seeds. However, traditional methodologies have some drawbacks which must be overcome, such as being time-consuming, requiring sample preparation, the use of solvents/reagents, and the generation of toxic waste. The objective of this study is to evaluate the protective effect provided by plant-based substances (directly, or as extracts), including pumpkin seeds, poppy seeds, dehydrated goji berry, and Provençal herbs, against the oxidation of antioxidant-free soybean oil. Synthetic antioxidants tert-butylhydroquinone and butylated hydroxytoluene were also considered. The evaluation was made through thermal degradation of soybean oil at different temperatures, and near-infrared spectroscopy was employed in an n-way mode, coupled with Parallel Factor Analysis (PARAFAC) to extract nontrivial information. The results for PARAFAC indicated that factor 1 shows oxidation product information, while factor 2 presents results regarding the antioxidant effect. The plant-based extract was more effective in improving the frying stability of soybean oil. It was also possible to observe that while the oxidation product concentration increased, the antioxidant concentration decreased as the temperature increased. The proposed method is shown to be a simple and fast way to obtain information on the protective effects of antioxidant additives in edible oils, and has an encouraging potential for use in other applications.

Simultaneous Double-Pass Absorption and Fluorescence Excitation-Emission Matrix Spectroscopy for Measurements of Reaction Kinetics

A novel Hadamard-transform excitation-emission matrix (EEM) spectrometer generates two-dimensional (2D) fluorescence matrices at a data acquisition rate of over 6 EEMs per minute and with a spectral resolution of 5.3 nm. Using Fresnel reflections from the sample cell, we could record optical transmission spectra synchronously with the 2D EEMs. The spectrometer was integrated into a custom-designed stopped-flow injection device to collect visible absorption and fluorescence EEM spectra of reacting solutions. Two different kinetic studies on two rapidly evolving chemical reactions with multiple overlapping spectral components were conducted by collecting over 8400 absorption spectra and EEMs. The third-order rate constant for the demetalation of chlorophyll-a to pheophytin-a was experimentally determined to be 450 ± 20 M^-2·s^-1 as derived from a parallel factor (PARAFAC) analysis where absorption and fluorescence data were combined. A PARAFAC analysis of data collected from the insertion of a copper atom into pheophytin-a resulted in several absorbing components and only a single fluorescing component. A reaction model with an association complex and a sitting-a-top (SAT) complex as intermediates explained the absorption data, resulting in a sequence of second-order reactions with rate constants of 4.0 ± 0.4, 2.7 ± 0.3, and 0.28 ± 0.02 M^-1·s^-1, respectively. The rate constant of the fluorescence decrease was determined to be 1.7 ± 0.2 M^-1·s^-1, which is consistent with the fluorescence component being attributed to both the pheophytin-a and the association complex.

Spectrophotometric and Multivariate Calibration Techniques for Simultaneous Determination of Different Drugs in Pharmaceutical Formulations and Human Urine: Evaluation of Greenness Profile

Eco-friendly, rapid, and cost-effective two spectrophotometric methods were developed and validated for the determination of atenolol, paracetamol, hydrochlorothiazide, and levofloxacin. The first method is the newly developed extended derivative ratio (EDR) and the second method is multivariate curve resolution-alternating least squares (MCR-ALS). In the EDR method, the extended derivative ratio amplitudes at 281.6, 237.6, 279.2, and 282.8 nm were used for quantification of atenolol, paracetamol, hydrochlorothiazide, and levofloxacin, respectively. In the MCR-ALS method, calibration model was developed and correlation constraint was employed. External validation data set composed of seven mixtures was used, and different figures of merits such as root mean square error of prediction, standard error of prediction, bias, and relative error of prediction were calculated, and satisfactory results were obtained. Both methods provided comparable results. The methods were validated and applied for the determination of the target analytes in dosage forms, spiked and real human urine. Thereafter, the obtained results were statistically compared to the published methods and revealed no significant difference regarding accuracy and precision. Furthermore, the greenness profile of the methods was evaluated using the National Environmental Methods Index "NEMI" and Analytical Eco-Scale. The developed methods can be used as a valid eco-friendly and simple cost-effective alternative to the commonly used chromatographic methods for the routine analysis of the studied drugs in dosage forms and human urine.

Second-order universal calibration

Quantification and qualification of an analyte of interest in pharmaceutical tablets from different manufacturers/companies are a hard task because of the potential presence of various interfering molecules. Indeed, the composition of the tablets covers a wide range of interferents which can be even unknown. As a consequence, we propose to determine the concentration of an analyte of interest regardless of the interferents using the concept of universal calibration. Universal calibration paves the way to the quantification of a specific chemical entity in samples with various compositions and different interferents. This is possible by the trilinear structure of analyte's signal. In fact, the second-order advantage resulting from the second-order universal calibration models is exploited. However, a new second-order calibration strategy was conducted in this work using Trilinear Factor Extraction (TFE). A simulated data set was exemplified to highlight the ability of the proposed procedure in order to accurate extraction of the analyte's concentration profile. Additionally, two real data sets were also explored in order to test the TFE method. In the first case, Acetaminophen was quantified using fluorescence spectroscopy in tablets with different formulations from 6 companies. In the second experimental data, a peptide (Valine-Tyrosine-Valine) was successfully quantified in different samples using spectrofluorimetric data. Finally, these real data sets were analyzed by Multivariate Curve resolution - Alternating Least-Squares (MCR-ALS) under non-negativity and trilinearity constraints for the sake of comparison. The calculated Root Mean Square Error of Predictions (RMSEP) of Acetaminophen were 0.028 and 0.026 for the MCR-ALS and TFE models, respectively. On the other hand, for the second experimental data set, the RMSEP were 0.216 and 0.165, respectively. Finally, based on a paired t-test, the results of MCR-ALS and TFE were not significantly different.