The utility of statistical moments in chromatography using trapezoidal and Simpson's rules of peak integration

Influence of theoretical and semi-empirical peak models on the efficiency calculation in chiral chromatography

Height equivalent to theoretical plate (H) equations, such as the van Deemter or Knox-Saleem equations, and other efficiency vs. linear velocity equations (u), provide kinetic insights into chromatographic separations phenomena and column performance. In enantioselective separations, the peak shape of the two enantiomers can differ significantly and are often asymmetric. The peak efficiency calculations heavily impact these efficiency-flow profiles, leading to erroneous estimations of eddy diffusion, longitudinal diffusion, and mass transfer terms. In this work, new asymmetric peak functions are employed for modeling enantiomer peaks based on the Haarhoff-Van der Linde function, its generalized variant (GHVL), once Generalized Asymmetric Gaussian (AGN), and Twice Generalized Gaussian (TGN). The new models (AGN, TGN, and GHVL) incorporate higher statistical moments besides the zeroth, first, and second moments to account for two-sided asymmetry (fronting or tailing). The fit results are compared with the traditional efficiency calculation methods endorsed by official pharmacopeia and numerical estimation of moments from the raw data. Enantiomeric separations of ibuprofen and dl-homophenylalanine were chosen as probe molecules. The results demonstrate that non-linear least squares fitted functions provide better estimations of peak efficiency data even in the presence of high noise. In particular, the generalized models consistently offered the best quality fits for various peak shapes in chiral separations. Conversely, the half-height Gaussian method greatly overpredicted skewed peak efficiencies. This investigation reveals that the commonly held assumptions of peak shape and numerical integration of raw data are highly insufficient for chiral chromatography. The impact of asymmetry on plate height should not be overlooked when accurate data from efficiency-flow rate curves is derived. We advocate for the broader adoption of these new generalized peak (AGN, TGN, GHVL) models because they provide robustness at various SNRs that account for right or left asymmetry while accurately representing peak geometry.

Insights into the synthesis of NHC-stabilized Au nanoclusters through real-time reaction monitoring

Atomically precise gold nanoclusters (AuNCs) are interesting nanomaterials with potential applications in catalysis, bioimaging and optoelectronics. Their compositions and properties are commonly evaluated by various analytical techniques, including UV-vis spectroscopy, NMR spectroscopy, ESI mass spectrometry, and single-crystal X-ray diffraction. While these techniques have provided detailed insights into the structure and properties of nanoclusters, synthetic methods still suffer from a lack of in situ and real-time reaction monitoring methodologies. This limits insight into the mechanism of formation of AuNCs and hinders attempts at optimization. We have demonstrated the utility of HPLC-MS as a monitoring methodology in the synthesis of two NHC-protected gold nanoclusters: [Au13(NHC)9Cl3]2+ and [Au24(NHC)14Cl2H3]3+. Herein we show that HPLC coupled with mass spectrometry and 13C NMR spectroscopy of labelled derivatives enables new insight into critical reaction dynamics of AuNCs synthesis and rapid reaction optimization.

Quantitative LC-MS/MS. 1. Impact of Points across a Peak on the Accuracy and Precision of Peak Area Measurements

The number of points across a chromatographic peak has long been recognized as a key determinant of the accuracy and precision of the measured peak area. In LC-MS-based quantitation experiments in drug discovery and development, the "rule-of-thumb" has been to use 15 or more points. This "rule" is based on the literature describing chromatographic methods where the goal was to achieve the lowest possible imprecision in the measurements, especially when unknown analytes are being detected. Restricting methods to the requirement of at least 15 points across a peak can be detrimental to the development methods that fully optimize the signal-to-noise ratio for the assay using longer dwell times and/or transition summing. This study aims to show that 7 points across the peak for peaks that are 9 s or less wide provide more than sufficient accuracy and precision for drug quantitation studies. Data from simulated Gaussian curves using a sampling interval of 7 points across the peak gave peak area calculations within 1% of the expected total peak area using the Trapezoidal and Riemann rules and 0.6% for the Simpson rule. Low and high concentration samples (n = 5) were assayed using three different LC methods on three different days on two different instruments (API5000 and API5500). The difference in peak area (%ΔPA) and relative standard deviation of the peak areas (%RSD) was less than ∼5%. No significant difference was observed from the data that were obtained from different sampling intervals, different peak widths, different days, different peak sizes, and different instruments. Three core analytical runs were performed on three different days. In each core run, the lower limit of quantitation (LLOQ, n = 5), low quality control (LQC, n = 5), middle quality control (MQC, n = 5), and high-quality control samples (HQC, n = 5) were processed and run simultaneously with a standard curve. The range of the intra- and interday accuracy and precision for 3 core runs was 98.0-105% and 0.9-3.0% for 7 data points and 97.5-105% and 0.8-4.3% for 17 data points, respectively. No significant difference was observed for the different sampling intervals. The results show a sampling interval of 7 points for peaks up to 9 s wide is sufficient to define a peak accurately and precisely for drug quantitation studies in drug discovery and development.

Packed modulation loops to reduce band broadening in two-dimensional liquid chromatography

Modulation interfaces employing sample loops are applied in many hyphenated separations such as two-dimensional liquid chromatography (2D-LC). When the first-dimension effluent in 2D-LC is eluted from the modulation loop, dispersion effects occur due to differences in the laminar flow velocity of the filling and emptying flow. These effects were recently studied by Moussa et al. whom recommended the use of coiled loops to promote radial diffusion and reduce this effect. In the 1980s, Coq et al. investigated the use of packed loops, which also promote radial diffusion, in large volume injection 1D-LC. Unfortunately, this concept was never investigated in the context of 2D-LC modulation. Our work evaluates use of packed loops in 2D-LC modulation and compares them to unpacked coiled and uncoiled modulation loops. The effect of the solvents, loop volume, differences in filling and emptying rates, and loop elution direction on the elution profile was investigated. Statistical moments were used as a pragmatic tool to quantify elution profile characteristics. Decreased dispersion was observed in all cases for the packed loops compared to unpacked loops and unpacked coiled loops. In particular for larger loop volumes the dispersion was reduced significantly. Furthermore, countercurrent elution resulted in narrower elution profiles in all cases compared to concurrent elution. We found that packed modulation loops are of high interested when analytes are not refocussed in the second-dimension separation (e.g. for size-exclusion chromatography). Moreover, our work suggests that the use of packed loops may aid in prevention of loop overfilling.

Direct Construction of Peaks from Free Induction Decay Curves for Gas Chromatography-Molecular Rotational Resonance Spectroscopy without Fourier Transforms

The concept of coupling gas chromatography with molecular rotational resonance spectroscopy (GC-MRR) was introduced in 2020, combining the separation capabilities of GC with the unparalleled specificity of MRR. In this study, we address the challenge of the high data throughput of MRR spectrometers, as GC-MRR spectrometers can generate thousands to millions of data points per second. In the previous GC-MRR studies, a free induction decay (FID) measurement was Fourier transformed to generate each point on the chromatogram. Such extensive calculations limit the performance, sensitivity, and speed of GC-MRR. A direct approach is proposed here to extract peak intensity from FID using the Gram-Schmidt vector orthogonalization method. First, analyte-free FIDs are used to construct a basis set representing the instrument's background noise, and then the remaining FIDs are orthogonalized to this fixed basis set. Each FID yields a single intensity value after Gram-Schmidt orthogonalization. The magnitude of the orthogonalized analyte FID is the signal intensity plotted in the chromatogram. This approach is computationally much faster (up to 10 times) than the conventional Fourier transform algorithm, is at least as sensitive as the FT algorithm, and maintains or improves the chromatographic peak shape. We compare the sensitivity, linearity, and chromatographic peak shapes for the Fourier transform and Gram-Schmidt approaches using both synthetically generated FIDs and instrumental data. This approach would allow the summed peak intensity to be displayed essentially in real-time, following which identified peaks can be further investigated to identify and quantify the species associated with each.

Iterative Multivariate Peaks Fitting—A Robust Approach for The Analysis of Non-Baseline Resolved Chromatographic Peaks

Selectivity in separation science is defined as the extent to which a method can determine the target analyte free of interference. It is the backbone of any method and can be enhanced at various steps, including sample preparation, separation optimization and detection. Significant improvement in selectivity can also be achieved in the data analysis step with the mathematical treatment of the signals. In this manuscript, we present a new approach that uses mathematical functions to model chromatographic peaks. However, unlike classical peak fitting approaches where the fitting parameters are optimized with a single profile (one-way data), the parameters are optimized over multiple profiles (two-way data). Thus, it allows high confidence and robustness. Furthermore, an iterative approach where the number of peaks is increased at each step until convergence is developed in this manuscript. It is demonstrated with simulated and real data that this algorithm is: (1) capable of mathematically separating each component with minimal user input and (2) that the peak areas can be accurately measured even with resolution as low as 0.5 if the peak’s intensities does not differ by more than a factor 10. This was conclusively demonstrated with the quantification of diterpene esters in standard mixtures.

Evaluation of gas chromatography for the separation of a broad range of isotopic compounds

The separation of deuterated compounds from their protiated counterparts is essential in areas of drug discovery and development, investigating kinetic isotope effects and quantitative methods of non-mass spectrometry-based stable isotope dilution assay (non-MS SIDA). The separations of 47 isotopologue pairs of common compounds and drugs were achieved by gas-liquid chromatography, employing twelve different stationary phases. Polydimethylsiloxane phase, phenyl substituted polydimethylsiloxane phases, wax phases, ionic liquid phases, and chiral stationary phases were selected to encompass a wide polarity range and diverse chemical interactions. The best-performing stationary phases are presented for separation of protic-polar, aprotic-dipolar, nonpolar analytes. Overall, the IL111i, SPB-20, and PAG stationary phases were remarkable in their ability to separate the isotopologues. The isotope effect was also evaluated. It was observed that nonpolar stationary phases often exhibit an inverse isotope effect in which heavier isotopic compounds elute earlier than their lighter counterparts. Conversely, polar stationary phases often show a normal isotope effect, while those of intermediate polarities can show both effects depending on the isotopologues. The location of deuterium atoms, however, affects isotopologue retention times. Deuterium substituted aliphatic groups appear to have a greater inverse isotope effect on retention than aromatic substituents.

Nutritional Controlled Preparation and Administration of Different Tomato Purées Indicate Increase of β-Carotene and Lycopene Isoforms, and of Antioxidant Potential in Human Blood Bioavailability: A Pilot Study

The isoforms of lycopene, carotenoids, and their derivatives including precursors of vitamin A are compounds relevant for preventing chronic degenerative diseases such as cardiovascular diseases and cancer. Tomatoes are a major source of these compounds. However, cooking and successive metabolic processes determine the bioavailability of tomatoes in human nutrition. To evaluate the effect of acute/chronic cooking procedures on the bioavailability of lycopene and carotene isoforms in human plasma, we measured the blood levels of these compounds and of the serum antioxidant potential in volunteers after a meal containing two different types of tomato sauce (rustic or strained). Using a randomized cross-over administration design, healthy volunteers were studied, and the above indicated compounds were determined by HPLC. The results indicate an increased bioavailability of the estimated compounds and of the serum antioxidant potential with both types of tomato purée and the subsequently derived sauces (the increase was greater with strained purée). This study sheds light on the content of nutrient precursors of vitamin A and other antioxidant compounds derived from tomatoes cooked with different strategies. Lastly, our study indicates that strained purée should be preferred over rustic purée.

Chromatographic study of electron acceptor-donor properties of of 4-(trans-4'-n-alkylcyclohexyl) benzoates

A new approach of characterizing the specific properties of 4-(trans-4'-n-alkylcyclohexyl) benzoates, based on the interaction of the acidic and basic testing substances, for their form Crystalline, Smectic B and Nematic have been proposed. The testing substances selected for our study have been considered in the light of the results obtained in the previous research and the data available in the literature for other liquid crystals with different structures. The DN values denoting the electron donor number in the Gutmann scale and the AN* values indicating the acceptor number in the Riddle-Fowkes scale have been chosen in the estimation of the electron acceptor parameter K_A and electron donor parameter K_D values. The temperature-dependent quotients of K_A to K_D are employed for the assessment of the electron donor-acceptor properties of 4-(trans-4'-n-alkylcyclohexyl) benzoates. The 4-(trans-4'-n-alkyl cyclohexyl) benzoates tested have the affinity to act as a donor of electrons concerning electron acceptor of the testing substance. The sizes and shapes effects of the testing substances (or penetrants) and the LCs tested (or solvents while in mesophases) are taken into account. The inverse gas chromatography tests were supported by the Quantitative Structure-Activity Relationship modelling technique to determine which part (or group) of liquid crystals tested was dominant in the interaction with the testing substances.

Mining for Peaks in LC-HRMS Datasets Using Finnee - A Case Study with Exhaled Breath Condensates from Healthy, Asthmatic, and COPD Patients

Separation techniques hyphenated to high-resolution mass spectrometry are essential in untargeted metabolomic analyses. Due to the complexity and size of the resulting data, analysts rely on computer-assisted tools to mine for features that may represent a chromatographic signal. However, this step remains problematic, and a high number of false positives are often obtained. This work reports a novel approach where each step is carefully controlled to decrease the likelihood of errors. Datasets are first corrected for baseline drift and background noise before the MS scans are converted from profile to centroid. A new alignment strategy that includes purity control is introduced, and features are quantified using the original data with scans recorded as profile, not the extracted features. All the algorithms used in this work are part of the Finnee Matlab toolbox that is freely available. The approach was validated using metabolites in exhaled breath condensates to differentiate individuals diagnosed with asthma from patients with chronic obstructive pulmonary disease. With this new pipeline, twice as many markers were found with Finnee in comparison to XCMS-online, and nearly 50% more than with MS-Dial, two of the most popular freeware for untargeted metabolomics analysis.

Recent applications of chemometrics in one- and two-dimensional chromatography

The proliferation of increasingly more sophisticated analytical separation systems, often incorporating increasingly more powerful detection techniques, such as high-resolution mass spectrometry, causes an urgent need for highly efficient data-analysis and optimization strategies. This is especially true for comprehensive two-dimensional chromatography applied to the separation of very complex samples. In this contribution, the requirement for chemometric tools is explained and the latest developments in approaches for (pre-)processing and analyzing data arising from one- and two-dimensional chromatography systems are reviewed. The final part of this review focuses on the application of chemometrics for method development and optimization.

Development of a Two-Compartment System In vitro Dissolution Test and Correlation with In vivo Pharmacokinetic Studies for Celecoxib

The objective of this study was to develop a novel open-mode two-compartment system dissolution apparatus to simulate the dissolution and absorption of poorly soluble drugs and to establish an in vitro-in vivo correlation (IVIVC). Celecoxib (CEB) was selected as a model drug, and in vitro dissolution was performed using the novel dissolution apparatus with acetate buffers at pH 4.5 containing Tween 80 (0.15%, w/v), at a flow rate of 30 mL/min and an agitation rate of 50 rpm. Cumulative release of all formulations was incomplete at approximately 70-80%, which likely reflected in vivo dissolution. Corresponding pharmacokinetic studies were performed in which twelve healthy male subjects from two bioequivalence studies received either one immediate release (IR) dose of the test (test 1 or test 2) or the reference formulation (Celebrex®, 200 mg). Individual plasma profiles of the formulations were deconvoluted via the Wanger-Nelson method to obtain the mean absorption fractions. A level A correlation was successfully developed with a good R². The Weibull equation was used to describe the in vitro dissolution and in vivo absorption kinetics. In vitro dissolution correlated with in vivo absorption was applied successfully to predict the in vivo plasma concentrations-time profiles of the CEB formulations. Compared with conventional methods, the novel dissolution device showed great potential for discriminating the dissolution between formulations and generic drugs, which may provide a tool for making in vivo predictions for next bioequivalence trials.