Second- and third-order multivariate calibration: data, algorithms and applications

Angle Distribution of Loading Subspace (ADLS) for estimating chemical rank in multivariate analysis: Applications in spectroscopy and chromatography

Multivariate analyses are increasingly popular to explore the underlying structure of multivariate datasets, which are more and more prevalent in analytical chemistry. However, difficulties can be associated with estimating the number of components for the data with considerable coherence and noise. The method of Angle Distribution of Loading Subspace (ADLS) has been proposed to estimate the number of components for Principal Component Analysis (PCA) and PARAllel FACtor analysis (PARAFAC), which showed some advantages, in particular in the case of datasets with high coherence, over the commonly used methods (scree plot and cross-validation in PCA, and core consistency diagnostics (CORCONDIA) in PARAFAC). In this paper, we systematically improved and applied ADLS to estimate the number of components in different multivariate methods including, Multivariate Curve Resolution (MCR), PARAFAC and four-way PARAFAC. Firstly, we showed that ADLS performed better when estimating the chemical rank for MCR analysis, compared with scree plots. As well as this, we improved ADLS in multi-way analysis (three- and four-way PARAFAC) by calculating the loading subspace in advance using the Khatri-Rao product. The improved ADLS in multi-way analysis provided the correct result for the simulated three-way fluorescence datasets with unevenly distributed coherence at different dimensions, while the previous version of ADLS showed biased results and CORCONDIA / split-half analysis provided relatively unstable results. Moreover, ADLS was used to estimate the chemical rank for a four-way real-life fluorescence dataset analyzed by four-way PARAFAC. In this case the result of chemical rank results from ADLS was more precise and informative compared with CORCONDIA /split-half analysis in four-way analysis.

The registration of aptamer-ligand (ochratoxin A) interactions based on ligand fluorescence changes

The fluorescent properties of ligands can change when they bind to specific receptors. Modulated by the transition of the ligand from the free to the bound state, fluorescence makes it possible both to detect this ligand and quantitatively register its binding. We characterized the interaction of ochratoxin A (OTA) with the specific G-quadruplex aptamer through excitation-emission matrix fluorescence spectroscopy. It was shown that the formation of the complex changes the OTA fluorescence spectrum both in the region of the main peak at λ_ex/λ_em 380/430 nm and in the region of peak at λ_ex/λ_em 265/425 nm. At pH 8.5 and OTA concentration of 30 nM, this peak is smaller in intensity than the main peak of fluorescence. The formation of the complex with the aptamer leads to an increase of the fluorescence at λ_ex/λ_em 265/425 nm up to 6.5 times, which makes it up to 4.9 times more intense than fluorescence at 380/430 nm. Fluorescence of the G-quadruplex aptamer (donor) takes part in increasing of the OTA (acceptor) emission at λ_ex/λ_em 265/425 nm due to the resonance energy transfer. The concentration regularities of the modulated fluorescence of OTA at λ_ex/λ_em 265/425 nm have been studied. Their correspondence to the calculations of complexation conducted on the basis of the dissociation constant is shown.

Designing Algorithms To Aid Discovery by Chemical Robots

Recently, automated robotic systems have become very efficient, thanks to improved coupling between sensor systems and algorithms, of which the latter have been gaining significance thanks to the increase in computing power over the past few decades. However, intelligent automated chemistry platforms for discovery orientated tasks need to be able to cope with the unknown, which is a profoundly hard problem. In this Outlook, we describe how recent advances in the design and application of algorithms, coupled with the increased amount of chemical data available, and automation and control systems may allow more productive chemical research and the development of chemical robots able to target discovery. This is shown through examples of workflow and data processing with automation and control, and through the use of both well-used and cutting-edge algorithms illustrated using recent studies in chemistry. Finally, several algorithms are presented in relation to chemical robots and chemical intelligence for knowledge discovery.

A green chemometrics-assisted fluorimetric detection method for the direct and simultaneous determination of six polycyclic aromatic hydrocarbons in oil-field wastewaters

Oil-field wastewaters contain high level of polycyclic aromatic hydrocarbons (PAHs), which have to be analyzed to assess the environmental effects before discharge. In this work, a green fluorimetric detection method that combines excitation-emission matrix (EEM) fluorescence with parallel factor analysis (PARAFAC) algorithm was firstly developed to achieve the direct and simultaneous determination of six U.S. EPA PAHs in two different kinds of complex oil-field wastewaters. Due to the distinctive "second-order advantage", neither time-consuming sample pretreatments nor toxic organic reagents were involved in the determination. By using the environment-friendly "mathematical separation" of PARAFAC, satisfactory quantitative results and reasonable spectral profiles for six PAHs were successfully extracted from the total EEM signals of oil-field wastewaters without need of chromatographic separation. The limits of detection of six PAHs were in the range of 0.09-0.72ngmL^-1, and the average spiked recoveries were between (89.4±4.8)% and (109.1±5.8)%, with average relative predictive errors <2.93%. In order to further confirm the accuracy of the proposed method, the same batch oil-field wastewater samples were analyzed by the recognized GC-MS method. t-test demonstrated that no significant differences exist between the quantitative results of the two methods. Given the advantages of green, fast, low-cost and high-sensitivity, the proposed method is expected to be broadened as an appealing alternative method for multi-residue analysis of overlapped PAHs in complex wastewater samples.

Simultaneous determination of binary solution of triphenylmethane dyes in complex matrices onto magnetic amino-rich SWCNT using second-order calibration method

This study suggested a new method for simultaneous quantification of two dyes in complex matrices using second-order data by spectrophotometry. Second-order data was generated simply without any expensive instrument using two independent variables including wavelength and the monotonic addition of sodium dodecyl sulfate. Solid-phase extraction (SPE) based on amino-rich magnetic single-walled carbon nanotube as an adsorbent was employed prior to second-order data generation. SPE optimization was performed by Box-Behnken design, and parameters and their interaction which were dependent on the simultaneous extraction of dyes were examined. Competitive Langmuir and Freundlich isotherms for a binary system and individual dyes could all represent the equilibrium data well. The second-order data was processed by parallel factor analysis (PARAFAC and PARAFAC2) and multivariate curve resolution-alternating least squares (MCR-ALS). Figures of merit of the model including a limit of detection of 3.0 and 2.5 ng mL^-1 for crystal violet and malachite green, respectively, were estimated using the MCR-ALS method. The combination of the second-order calibration and SPE presents an easy and versatile method for determination of the mixture of two dyes in the presence of uncalibrated interferences in environmental water, synthetic, and fish samples with the recoveries of 94-104.

Interference-free spectrofluorometric quantification of aristolochic acid I and aristololactam I in five Chinese herbal medicines using chemical derivatization enhancement and second-order calibration methods

A rapid interference-free spectrofluorometric method combined with the excitation-emission matrix fluorescence and the second-order calibration methods based on the alternating penalty trilinear decomposition (APTLD) and the self-weighted alternating trilinear decomposition (SWATLD) algorithms, was proposed for the simultaneous determination of nephrotoxic aristolochic acid I (AA-I) and aristololactam I (AL-I) in five Chinese herbal medicines. The method was based on a chemical derivatization that converts the non-fluorescent AA-I to high-fluorescent AL-I, achieving a high sensitive and simultaneous quantification of the analytes. The variables of the derivatization reaction that conducted by using zinc powder in acetose methanol aqueous solution, were studied and optimized for best quantification results of AA-I and AL-I. The satisfactory results of AA-I and AL-I for the spiked recovery assay were achieved with average recoveries in the range of 100.4-103.8% and RMSEPs <0.78ngmL^-1, which validate the accuracy and reliability of the proposed method. The contents of AA-I and AL-I in five herbal medicines obtained from the proposed method were also in good accordance with those of the validated LC-MS/MS method. In light of high sensitive fluorescence detection, the limits of detection (LODs) of AA-I and AL-I for the proposed method compare favorably with that of the LC-MS/MS method, with the LODs <0.35 and 0.29ngmL^-1, respectively. The proposed strategy based on the APTLD and SWATLD algorithms by virtue of the "second-order advantage", can be considered as an attractive and green alternative for the quantification of AA-I and AL-I in complex herbal medicine matrices without any prior separations and clear-up processes.

A systematic study on the effect of noise and shift on multivariate figures of merit of second-order calibration algorithms

In the present study, multivariate analytical figures of merit (AFOM) for three well-known second-order calibration algorithms, parallel factor analysis (PARAFAC), PARAFAC2 and multivariate curve resolution-alternating least squares (MCR-ALS), were investigated in simulated hyphenated chromatographic systems including different artifacts (e.g., noise and peak shifts). Different two- and three-component systems with interferences were simulated. Resolved profiles from the target components were used to build calibration curves and to calculate the multivariate AFOMs, sensitivity (SEN), analytical sensitivity (γ), selectivity (SEL) and limit of detection (LOD). The obtained AFOMs for different simulated data sets using different algorithms were used to compare the performance of the algorithms and their calibration ability. Furthermore, phenanthrene and anthracene were analyzed by GC-MS in a mixture of polycyclic aromatic hydrocarbons (PAHs) to confirm the applicability of multivariate AFOMs in real samples. It is concluded that the MCR-ALS method provided the best resolution performance among the tested methods and that more reliable AFOMs were obtained with this method for the studied chromatographic systems with various levels of noise, elution time shifts and presence of unknown interferences.

Characterization and quantification of humic substances 2D-Fluorescence by usage of extended size exclusion chromatography

In this article, two methods for in-depth analysis of humic substances fluorescence are presented. The first one allows the combined analysis of fluorescence excitation-emission matrix (EEM) with chromatography technique. The main issue is the coupling of size exclusion chromatography (SEC) with spectroscopy by the use of an absorption and a fluorescence spectrometer as additional detectors. These allow a detailed characterization of humic substances depending on their molecular size, concentration and optical properties. For the evaluation of the resulting complex data, a model based on non-negative matrix factorization, which is also presented in this article, was developed. From the results of the examined humic substances standards, the second method was developed. It allows the characterization and quantification of humic substances fluorescence of a natural water sample solely on the basis of an excitation-emission matrix. The validation of the model is carried out within the framework of extensive analysis of real water samples.

Chemometric applications to assess quality and critical parameters of virgin and extra-virgin olive oil. A review

Today virgin and extra-virgin olive oil (VOO and EVOO) are food with a large number of analytical tests planned to ensure its quality and genuineness. Almost all official methods demand high use of reagents and manpower. Because of that, analytical development in this area is continuously evolving. Therefore, this review focuses on analytical methods for EVOO/VOO which use fast and smart approaches based on chemometric techniques in order to reduce time of analysis, reagent consumption, high cost equipment and manpower. Experimental approaches of chemometrics coupled with fast analytical techniques such as UV-Vis spectroscopy, fluorescence, vibrational spectroscopies (NIR, MIR and Raman fluorescence), NMR spectroscopy, and other more complex techniques like chromatography, calorimetry and electrochemical techniques applied to EVOO/VOO production and analysis have been discussed throughout this work. The advantages and drawbacks of this association have also been highlighted. Chemometrics has been evidenced as a powerful tool for the oil industry. In fact, it has been shown how chemometrics can be implemented all along the different steps of EVOO/VOO production: raw material input control, monitoring during process and quality control of final product.

Second order advantage obtained by spectroelectrochemistry along with novel carbon nanotube modified mesh electrode: Application for determination of acetaminophen in Novafen samples

A matrix-augmentation multivariate curve resolution-alternating least-squares (MA-MCR-ALS) has been conducted on the spectroelectrochemical data of acetaminophen oxidation in order to quantify acetaminophen in Novafen capsule in the presence of unknown interferences. The experiments were carried out using new cheap mesh electrode, namely carbon nanotube modified mesh electrode (CNMME) as optically transparent thin layer electrode (OTTLE). For each sample, a second order spectroelectrochemical data was obtained and MA-MCR-ALS method was applied to analyze these data. Unlike full trilinear models such as PARAFAC, MCR-ALS is flexible in applying trilinearity constraint for each component, a fact which makes it manage deviations from trilinearity of data effectively. This method was employed in both spectral and kinetic augmentation mode of data under examining different trilinear components. However, spectral augmentation was the only setting which allows MA-MCR-ALS to solve the analytical problem achieving the second order advantage. Therefore, here the results of the augmentation in this mode have been described. In order to obtain the best analytical figures of merit in the analysis, different constraints were investigated. The results indicated the accuracy of the proposed method.

Bioelectronic tongues: New trends and applications in water and food analysis

Over the last years, there has been an increasing demand for fast, highly sensitive and selective methods of analysis to meet new challenges in environmental monitoring, food safety and public health. In response to this demand, biosensors have arisen as a promising tool, which offers accurate chemical data in a timely and cost-effective manner. However, the difficulty to obtain sensors with appropriate selectivity and sensitivity for a given analyte, and to solve analytical problems which do not require the quantification of a certain analyte, but an overall effect on a biological system (e.g. toxicity, quality indices, provenance, freshness, etc.), led to the concept of electronic tongues as a new strategy to tackle these problems. In this direction, to improve the performance of electronic tongues, and thus to spawn new application fields, biosensors have recently been incorporated to electronic tongue arrays, leading to what is known as bioelectronic tongues. Bioelectronic tongues provide superior performance by combining the capabilities of electronic tongues to derive meaning from complex or imprecise data, and the high selectivity and specificity of biosensors. The result is postulated as a tool that exploits chemometrics to solve biosensors' interference problems, and biosensors to solve electronic tongues' selectivity problems. The review presented herein aims to illustrate the capabilities of bioelectronic tongues as analytical tools, especially suited for screening analysis, with particular emphasis in water analysis and the characterization of food and beverages. After briefly reviewing the key concepts related to the design and principles of electronic tongues, we provide an overview of significant contributions to the field of bioelectronic tongues and their future perspectives.

Solving signal instability to maintain the second-order advantage in the resolution and determination of multi-analytes in complex systems by modeling liquid chromatography-mass spectrometry data using alternating trilinear decomposition method assisted with piecewise direct standardization

The application of calibration transfer methods has been successful in combination with near-infrared spectroscopy or other tools for prediction of chemical composition. One of the developed methods that can provide accurate performances is the piecewise direct standardization (PDS) method, which in this paper is firstly applied to transfer from one day to another the second-order calibration model based on alternating trilinear decomposition (ATLD) method built for the interference-free resolution and determination of multi-analytes in complex systems by liquid chromatography-mass spectrometry (LC-MS) in full scan mode. This is an example of LC-MS analysis in which interferences have been found, making necessary the use of second-order calibration because of its capacity for modeling this phenomenon, which implies analytes of interest can be resolved and quantified even in the presence of overlapped peaks and unknown interferences. Once the second-order calibration model based on ATLD method was built, the calibration transfer was conducted to compensate for the signal instability of LC-MS instrument over time. This allows one to reduce the volume of the heavy works for complete recalibration which is necessary for later accurate determinations. The root-mean-square error of prediction (RMSEP) and average recovery were used to evaluate the performances of the proposed strategy. Results showed that the number of calibration samples used on the real LC-MS data was reduced by using the PDS method from 11 to 3 while producing comparable RMSEP values and recovery values that were statistically the same (F-test, 95% confidence level) to those obtained with 11 calibration samples. This methodology is in accordance with the highly recommended green analytical chemistry principles, since it can reduce the experimental efforts and cost with regard to the use of a new calibration model built in modified conditions.

Chemometrics-assisted determination of amiloride and triamterene in biological fluids with overlapped peaks and unknown interferences

Background: Amiloride (AMI) and triamterene (TRI) are both potassium-saving diuretics, which are ordinarily used as doping to enhance the performance of athletes in sports. For the similar structures and complex matrices existence, chromatography and extraction are commonly employed to realize the determination of AMI and TRI in biological fluids, which are very time-consuming and laborious. Results: A novel method is presented to simultaneous interference-free determination of AMI and TRI in complex biological fluids samples using excitation–emission matrix fluorescence coupled with second-order calibration method based on alternating normalization-weight error algorithm. Conclusion: The proposed method can obtain accurate qualitative and quantitative information of the analytes, even in the presence of the interference from complex biological fluids, which requires few prior purification and separation procedures.

A chemometric-assisted method for the simultaneous determination of malachite green and crystal violet in water based on absorbance-pH data generated by a homemade pH gradient apparatus

An attractive method of generating second-order data was developed by a dropping technique to generate pH gradient simultaneously coupled with diode-array spectrophotometer scanning. A homemade apparatus designed for the pH gradient. The method and the homemade apparatus were used to simultaneously determine malachite green (MG) and crystal violet (CV) in water samples. The absorbance-pH second-order data of MG or CV were obtained from the spectra of MG or CV in a series of pH values of HCl-KCl solution. The second-order data of mixtures containing MG and CV that coexisted with interferents were analyzed using multidimensional partial least-squares with residual bilinearization. The method and homemade apparatus were used to simultaneously determine MG and CV in fish farming water samples and in river ones with satisfactory results. The presented method and the homemade apparatus could serve as an alternative tool to handle some analysis problems.

The application of a Tchebichef moment method to the quantitative analysis of multiple compounds based on three-dimensional HPLC fingerprint spectra

A Tchebichef moment method was proposed and used to successfully quantify four compounds based on 3D HPLC-PAD spectra.

Second-order advantage maintenance with voltammetric data modeling for quantitation of ethiofencarb in the presence of interferences

This work presents the development of a method based on a voltammetric determination coupled to second-order data modeling with multivariate curve resolution-alternating least-square (MCR-ALS) and unfolded partial least squares regression followed by residual bilinearization (U-PLS/RBL) for the quantitation of the pesticide ethiofencarb in the presence of interferences in tap water. The determination of ethiofencarb by voltammetry is possible on the basis that this pesticide is hydrolysed in alkaline media giving rise to a compound which shows an oxidation peak at Ep=0.80 V. But some other pesticides belonging to the same family can be considered as interferences due to the high overlapping in their signals. The two such interferences are fenobucarb and bendiocarb, which have not been included in the calibration step. The possibility of second-order multivariate calibration was studied by using the hydrolysis time as the third variable, and MCR-ALS and U-PLS/RBL. Good results were obtained in this determination in spite of the high overlapping in voltammetric signals.

Second-order data obtained by beta-cyclodextrin complexes: a novel approach for multicomponent analysis with three-way multivariate calibration methods

This research reports the first application of β-cyclodextrin (β-CD) complexes as a new method for generation of three way data, combined with second-order calibration methods for quantification of a binary mixture of caffeic (CA) and vanillic (VA) acids, as model compounds in fruit juices samples. At first, the basic experimental parameters affecting the formation of inclusion complexes between target analytes and β-CD were investigated and optimized. Then under the optimum conditions, parallel factor analysis (PARAFAC) and bilinear least squares/residual bilinearization (BLLS/RBL) were applied for deconvolution of trilinear data to get spectral and concentration profiles of CA and VA as a function of β-CD concentrations. Due to severe concentration profile overlapping between CA and VA in β-CD concentration dimension, PARAFAC could not be successfully applied to the studied samples. So, BLLS/RBL performed better than PARAFAC. The resolution of the model compounds was possible due to differences in the spectral absorbance changes of the β-CD complexes signals of the investigated analytes, opening a new approach for second-order data generation. The proposed method was validated by comparison with a reference method based on high-performance liquid chromatography photodiode array detection (HPLC-PDA), and no significant differences were found between the reference values and the ones obtained with the proposed method. Such a chemometrics-based protocol may be a very promising tool for more analytical applications in real samples monitoring, due to its advantages of simplicity, rapidity, accuracy, sufficient spectral resolution and concentration prediction even in the presence of unknown interferents.

Second order multivariate curve resolution of Fourier transform infrared spectroscopic data of the photo-induced crosslinking of thymine functionalized polymers

A meaningful characterization of the photo-induced curing process of materials based on styrene monomers functionalized with thymine and charged ionic groups was accomplished using FT-IR spectroscopy in combination with second-order multivariate calibration algorithms. The polymer composition as well as the irradiation dose effects on the photo-crosslinking of copolymer films was experimentally determined. Each FT-IR absorption spectra was decomposed into the contribution of individual species by means of chemometric algorithms. A second-order strategy involving a three-way array for each sample and analyzing all arrays simultaneously was used. Temperature and solvent frequently have a strong influence on the FT-IR peak producing shifts and trilinearity lost. A new methodology to properly pre-align the spectroscopic matrix data is used based on the decomposition of a three-way array via a suitably initialized and constrained PARAFAC model. The chemical reaction mechanism describing the underlying process in terms of identifiable steps was determined. Associated key parameters and equilibrium rate constants that characterize the interconversion and stability of diverse species were predicted. Additionally, it was possible to quantify all the species even in the presence of a non-calibrated compound.

Simultaneous determination of eight flavonoids in propolis using chemometrics-assisted high performance liquid chromatography-diode array detection

A fast analytical strategy of second-order calibration method based on the alternating trilinear decomposition algorithm (ATLD)-assisted high performance liquid chromatography coupled with a diode array detector (HPLC-DAD) was established for the simultaneous determination of eight flavonoids (rutin, quercetin, luteolin, kaempferol, isorhamnetin, apigenin, galangin and chrysin) in propolis capsules samples. The chromatographic separation was implemented on a Wondasil™ C18 column (250mm×4.6mm, 5μm) within 13min with a binary mobile phase composed of water with 1% formic acid and methanol at a flow rate of 1.0mLmin(-1) after flavonoids were only extracted with methanol by ultrasound extraction for 15min. The baseline problem was overcome by considering background drift as additional compositions or factors as well as the target analytes, and ATLD was employed to handle the overlapping peaks from analytes of interest or from analytes and co-eluting matrix compounds. The linearity was good with the correlation coefficients no less than 0.9947; the limit of detections (LODs) within the range of 3.39-33.05ngmL(-1) were low enough; the accuracy was confirmed by the recoveries ranged from 91.9% to 110.2% and the root-mean-square-error of predictions (RMSEPs) less than 1.1μg/mL. The results indicated that the chromatographic method with the aid of ATLD is efficient, sensitive and cost-effective and can realize the resolution and accurate quantification of flavonoids even in the presence of interferences, thus providing an alternative method for accurate quantification of analytes especially when the complete separation is not easily accomplished. The method was successfully applied to propolis capsules samples and the satisfactory results were obtained.

Competitive interactions of anti-carcinogens with serum albumin: a spectroscopic study of bendamustine and dexamethasone with the aid of chemometrics

Interactions between the anti-carcinogens, bendamustine (BDM) and dexamethasone (DXM), with bovine serum albumin (BSA) were investigated with the use of fluorescence and UV-vis spectroscopies under pseudo-physiological conditions (Tris-HCl buffer, pH 7.4). The static mechanism was responsible for the fluorescence quenching during the interactions; the binding formation constant of the BSA-BDM complex and the binding number were 5.14×10(5)Lmol(-1) and 1.0, respectively. Spectroscopic studies for the formation of BDM-BSA complex were interpreted with the use of multivariate curve resolution - alternating least squares (MCR-ALS), which supported the complex formation. The BSA samples treated with site markers (warfarin - site I and ibuprofen - site II) were reacted separately with BDM and DXM; while both anti-carcinogens bound to site I, the binding constants suggested that DXM formed a more stable complex. Relative concentration profiles and the fluorescence spectra associated with BDM, DXM and BSA, were recovered simultaneously from the full fluorescence excitation-emission data with the use of the parallel factor analysis (PARAFAC) method. The results confirmed that on addition of DXM to the BDM-BSA complex, the BDM was replaced and the DXM-BSA complex formed; free BDM was released. This finding may have consequences for the transport of these drugs during any anti-cancer treatment.

Second-order advantage obtained from standard addition first-order instrumental data and multivariate curve resolution-alternating least squares. Calculation of the feasible bands of results

In order to achieve the second-order advantage, second-order data per sample is usually required, e.g., kinetic-spectrophotometric data. In this study, instead of monitoring the time evolution of spectra (and collecting the kinetic-spectrophotometric data) replicate spectra are used to build a virtual second order data. This data matrix (replicate mode×λ) is rank deficient. Augmentation of these data with standard addition data [or standard sample(s)] will break the rank deficiency, making the quantification of the analyte of interest possible. The MCR-ALS algorithm was applied for the resolution and quantitation of the analyte in both simulated and experimental data sets. In order to evaluate the rotational ambiguity in the retrieved solutions, the MCR-BANDS algorithm was employed. It has been shown that the reliability of the quantitative results significantly depends on the amount of spectral overlap in the spectral region of occurrence of the compound of interest and the remaining constituent(s).