Global retention models and their application to the prediction of chromatographic fingerprints

Analysis and classification of tea varieties using high-performance liquid chromatography and global retention models

As a result of their metabolic processes, medicinal plants produce bioactive molecules with significant implications for human health, used directly for treatment or for pharmaceutical development. Chromatographic fingerprints with solvent gradients authenticate and categorise medicinal plants by capturing chemical diversity. This work focuses on optimising tea sample analysis in HPLC, using a model-based approach without requiring standards. Predicting the gradient profile effects on full signals was the basis to identify optimal separation conditions. Global models characterised retention and bandwidth for 14 peaks in the chromatograms across varied elution conditions, facilitating resolution optimisation of 63 peaks, covering 99.95 % of total peak area. The identified optimal gradient was applied to classify 40 samples representing six tea varieties. Matrices of baseline-corrected signals, elution bands, and band ratios, were evaluated to select the best dataset. Principal Component Analysis (PCA), k-means clustering, and Partial Least Squares-Discriminant Analysis (PLS-DA) assessed classification feasibility. Classification limitations were found reasonable due to tea processing complexities, involving drying and fermentation influenced by environmental conditions.

Experimental design and re-parameterization of the Neue-Kuss model for accurate and precise prediction of isocratic retention factors from gradient measurements in reversed phase liquid chromatography

The present work describes a re-parameterization of the Neue Kuss (NK) model for describing retention in liquid chromatography, and this re-parameterized model is used to fit a large set of isocratic retention measurements with improved convergence properties relative to the original parameterization of the model. Next, an experimental design for retention measurements using mobile phase gradient elution conditions is proposed for the purpose of obtaining accurate and precise NK parameters. Simulated retention data for mobile phase gradient elution conditions with two different levels of noise, as well as an essentially zero noise level were fit with the re-parameterized model. The results showed that the re-parameterized fits yielded average (absolute value) prediction errors for the parameters at the highest noise level of 7.2 % for S1,ref, 18 % for S2,ref and 6.2 % for kref (the re-parameterized NK model parameters). These errors were significantly smaller than those for the original parameterization of the NK model, where the errors were 23 % for S1, 25 % for S2 and 160 % for kw (the original NK model parameters). Furthermore, isocratic retention factors predicted using these model parameters were found to have an average magnitude of error of 0.51 % for the re-parameterized model, as opposed to 6800 % for the model with the original parameterization. A further test of this approach was carried out for independent experimental measurements for five solutes on a C18 column. The average magnitude of error of the isocratic retention factors predicted from parameters obtained from fits of gradient data was 1.6 %, provided that the range of organic solvent compositions that the solute sampled in the mobile phase gradient experiments was consistent with the isocratic experiments. These results indicate that the re-parameterization of the NK model allows for significant improvements in the fitting process, and that the proposed experimental design allows for NK parameters to be extracted from mobile phase gradient experiments, with prediction accuracies of isocratic retention factors on the order of 1-2 %.

Performance of global retention models in the optimisation of the chromatographic separation (I): Simple multi-analyte samples

Conventional retention models lead to accurate descriptions of the elution behaviour from the fitting of data for single solutes or from a set of solutes, one by one. However, the simultaneous fitting of several solutes through a regression process that separates the contributions of column and solvent from those of each solute is also possible. The result is a global retention model constituted by a set of equations with some common parameters (those associated with column and solvent), whereas others, specific to each solute, differ for each equation. This work explores the possibilities, advantages, and limitations of global models when they are applied to the optimisation of chromatographic resolution. A set constituted by 13 drugs (diuretics and β-blockers) and a training experimental design of seven multi-linear gradients are considered. Since standards for all compounds were available, the optimisation based on global models could be compared with the conventional optimisation, which is based on individual models. In their current state, global models do not predict changes in elution order, but they do allow for incorporating additional solutes (e.g., new analytes or matrix peaks) with only one new experiment. This possibility is explored by extending the model for the 13 analytes to include 26 peaks associated with a contamination in the injector. The combination of individual and global models allows an optimisation where the effects of matrix peaks on the separation of analytes can be integrated.

Simultaneous effect of different chromatographic conditions on the chromatographic retention of pentapeptide derivatives (HGRFG and NPNPT)

Introduction: Oligopeptides exhibit great prospects for clinical application and its separation is of great importance in new drug development. Methods: To accurately predict the retention of pentapeptides with analogous structures in chromatography, the retention times of 57 pentapeptide derivatives in seven buffers at three temperatures and four mobile phase compositions were measured via reversed-phase high-performance liquid chromatography. The parameters ( k H A , k A , and p K a ) of the acid-base equilibrium were obtained by fitting the data corresponding to a sigmoidal function. We then studied the dependence of these parameters on the temperature (T), organic modifier composition (φ, methanol volume fraction), and polarity ( P m N parameter). Finally, we proposed two six-parameter models with (1) pH and T and (2) pH and φ or P m N as the independent variables. These models were validated for their prediction capacities by linearly fitting the predicted retention factor k-value and the experimental k-value. Results: The results showed that log k H A and log k A exhibited linear relationships with 1 / T , φ or P m N for all pentapeptides, especially for the acid pentapeptides. In the model of pH and T, the correlation coefficient (R²) of the acid pentapeptides was 0.8603, suggesting a certain prediction capability of chromatographic retention. Moreover, in the model of pH and φ or P m N , the R² values of the acid and neutral pentapeptides were greater than 0.93, and the average root mean squared error was approximately 0.3, indicating that the k-values could be effectively predicted. Discussion: In summary, the two six-parameter models were appropriate to characterize the chromatographic retention of amphoteric compounds, especially the acid or neutral pentapeptides, and could predict the chromatographic retention of pentapeptide compounds.

Solvent strength of organic phase for two biphasic solvent systems in high speed countercurrent chromatography

In this work, relationships between solvent strength of organic phase (ψ) for two biphasic solvent systems in high speed countercurrent chromatography, hexane-ethyl-acetate-methanol-water (HEMWat) and ethyl acetate-n-butanol-water (EBuWat), and partition coefficient (K) were investigated using four retention models, including Jandera's model (ABM), Neue-Kuss model (NK), linear-solvent-strength model (LSS) and quadratic-solvent-strength model (QSS). Experimental results showed that ABM model had the best fitting results for HEMWat system while NK model and QSS model had good fitting results in EBuWat system. Thus, a mathematical relationship between partition coefficient (K) and solvent strength of organic phase (ψ) could be obtained by measurement of partition coefficients of the target compounds with three different volume ratios of organic phase. At the same time, a functional map was proposed to construct to get a maneuverable region so that an optimal two-phase solvent system for separation of a target compound could be selected easily, which saved a lot of manpower for high speed countercurrent chromatographic separation. The application of this new method was declared by successful separation of two components, apigenin-6-C-β-D-xylopyranosyl-8-C-α-L-arabinopyranoside and vicenin-3, from dried leaves of Dendrobium officinale Kimura et Migo using high speed countercurrent chromatography.

Testing experimental designs in liquid chromatography (II): Influence of the design geometry on the prediction performance of retention models

In liquid chromatography, the reliability of predictions carried out with retention models depends critically on the quality of the training experimental design. The search of the best design is more complex when gradient runs are used instead of isocratic experiments. In Part I of this work (JCA 1624 (2020) 461180), a general methodology based on the error propagation theory was developed and validated for assessing the quality of training designs involving gradients. The treatment relates the mathematical properties of a retention model with the geometry of the training designs and their subsequent predictions. In that work, only five usual designs were considered. Part II investigates in detail the effects on predictions when the features of the training design (number and distribution of the experiments, initial and final modifier content, gradient slope(s), and location of gradient nodes and pulses) are varied systematically. Several groups of related designs containing one or more isocratic steps, linear or multi-linear gradients, or mixed isocratic/gradient runs, among others (in total 38 designs) were evaluated. Box and whiskers and triple plots of expected relative uncertainties were used to evidence the differences in prediction performance. The purpose was to give recommendations to construct designs with good prediction performance. The best designs sample (considering all runs) concentrations as diverse as possible, at any gradient time.

Closed form approximations to predict retention times and peak widths in gradient elution under conditions of sample volume overload and sample solvent mismatch

Closed form expressions for the prediction of retention times and peak widths for gradient liquid chromatography are particularly useful in understanding, rationalizing and optimizing separations. These expressions are obtained by integrating differential equations, in conjunction with a model of the variation of the retention factor as a function of mobile phase composition. Two of these models, the linear solvent strength (LSS) model and the Neue-Kuss (NK) model are explored in the present work. Here, we expand on these closed form expressions to account for effects of sample volume overload and a mismatch between the sample solvent and the initial mobile phase composition for the gradient. We show that there have been errors in expressions reported in the literature, and we have evaluated the accuracy of the predictions from the closed form expressions reported here using a recently developed liquid chromatography simulator. The expressions assume a constant plate height and consider elution across four zones of the gradient profile - elution in the sample solvent, elution in the initial (isocratic) mobile phase caused by the gradient delay volume, elution during a linear gradient, and elution post-gradient at the final (isocratic) mobile phase composition. The expressions generally give reasonably accurate predictions for retention times and peak widths, except for cases where the solute elutes during transitions between the different zones. The average magnitude of the prediction errors for retention time and peak width relative to simulation were 0.093% and 0.40% for the LSS expressions for ten amphetamine solutes at 36 different separation conditions, and 0.22% and 1.8% for the NK expressions for eight alkylbenzene solutes at 36 different separation conditions, respectively.