Chromatographic fingerprint-based analysis of extracts of green tea, lemon balm and linden: II. Simulation of chromatograms using global models

Medicinal plants contain a large variety of chemical compounds in highly variable concentrations, so the quality control of these materials is especially complex. With this purpose, regulatory institutions have accepted chromatographic fingerprints as a valid tool to perform the analyses.

Journal of Chromatography A 1684 (2022) 463561 Contents lists available at ScienceDirect Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma Chromatographic fingerprint-based analysis of extracts of green tea, lemon balm and linden: II Simulation of chromatograms using global models A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta, J.R Torres-Lapasió∗ , M.C García-Alvarez-Coque Department of Analytical Chemistry, Faculty of Chemistry, University of Valencia, C/ Dr Moliner 50, Burjassot 46100, Spain a r t i c l e i n f o Article history: Received 23 February 2022 Revised 30 March 2022 Accepted 11 October 2022 Available online 13 October 2022 Keywords: Medicinal plants Global retention models Bandwidth models Multi-linear gradient elution Prediction of chromatographic fingerprints a b s t r a c t Medicinal plants contain a large variety of chemical compounds in highly variable concentrations, so the quality control of these materials is especially complex With this purpose, regulatory institutions have accepted chromatographic fingerprints as a valid tool to perform the analyses In order to improve the results, separation conditions that maximise the number of detected peaks in these chromatograms are needed This work reports the extension of a simulation strategy, based on global retention models previously developed for selected compounds, to all detected peaks in the full chromatogram Global models contain characteristic parameters for each component in the sample, while other parameters are common to all components and describe the combined effects of column and solvent The approach begins by detecting and measuring automatically the position of all peaks in a chromatogram, obtained preferably with the slowest gradient Then, the retention time for each detected component is fitted to find the corresponding solute parameter in the global model, which leads to the best agreement with the measured experimental value The process is completed by developing bandwidth models for the selected compounds used to build the global retention model based on gradient data, which are applied to all peaks in the chromatogram The usefulness of the simulation approach is demonstrated by predicting chromatographic fingerprints for three medicinal plants with specific separation problems (green tea, lemon balm and linden), using several multi-linear gradients that lead to problematic predictions © 2022 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Introduction In traditional medicine, preparations derived from plant tissues have been used for thousands of years in the prevention and treatment of diseases The therapeutic activity of medicinal plants is due to the presence of biologically active chemical compounds, which can act synergistically [1,2] Due to the efficacy of treatments based on these natural products and their low toxicity, its use has been extended in recent years [3] Several factors can affect the quality of medicinal plants, such as soil type, geographical location, environmental conditions during growth, harvest season and methods, storage conditions, and procedures for their preparation Therefore, the products must follow a quality control that certifies the consumer their safety and pharmacological efficacy ∗ Corresponding author E-mail address: jrtorres@uv.es (J.R Torres-Lapasió) However, the high chemical diversity of natural products, in very different concentrations, makes quality control extremely difficult [2] To solve the problems found in the sanitary control of medicinal plants, due to their complex composition, the World Health Organization (WHO), the United States Food and Drug Administration (FDA), and the State Food and Drug Administration of China (SFDA), have accepted chromatographic fingerprints as a valid tool to guarantee their quality [4–7] Probably, the most problematic aspect that prevents the development of methods to optimise fingerprint resolution is finding retention models that describe all the components in the samples, in situations where there are no standards [8–11] Recently, we have developed an approach to describe the retention behaviour of unknown compounds in a chromatogram using global models [12,13] The purpose is to get a set of model parameters to predict the behaviour of a group of compounds (known or unknown), as an alternative to the use of parameters focused to each compound In global models, some parameters are specific of each solute, while https://doi.org/10.1016/j.chroma.2022.463561 0021-9673/© 2022 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 other parameters describe the combined effects of column and solvent, and are common for all solutes Our proposal consists in, once the chromatograms of the sample are obtained according to a certain experimental design described in Part I, the peaks for several compounds (which we have called “reference peaks”) are selected to get the chromatographic information required to build the global model The peaks for the reference compounds are preferably those with the highest intensity, or at least peaks that can be tracked in all training gradients For this purpose, the identity of these compounds is not needed There are some rules for the selection of the reference peaks: they are only subjected to the condition that the equivalent peaks should be easily recognizable in all gradients For instance, reference peaks could be very intense peaks that stand out from the others due to their intensity or position, or that give rise to easily identifiable patterns with their neighbouring peaks The presence of outliers or abnormal scattering in the correlation plots of the individual models reveal incidental mistakes in peak identification Part I of this work [13] reports the construction of global retention models for the reference compounds in chromatographic fingerprints of extracts of medicinal plants, using the information obtained from appropriate experimental designs The applied designs were based on a common scouting linear gradient and consist of several related multi-linear gradients, which also facilitated peak tracking [14] In Part II, the global retention models obtained with the reference compounds are extended to include all other components in the chromatogram giving rise to detectable peaks The information required to update the global retention model is preferably obtained from the chromatogram corresponding to the slowest experimental condition, amongst those in the training design after baseline correction [15] The extended model including all detectable peaks in that chromatogram was used to predict full chromatograms at any new arbitrary experimental condition The construction of bandwidth models for the reference compounds allows full chromatogram predictions in gradient elution Simulated chromatograms were tested with extracts of Camellia sinensis (green tea), Melissa officinalis (lemon balm), and Tilia platyphyllos (linden), with satisfactory results (Acros Organics, Fair Lawn, NJ, USA) Peak monitoring was carried out between 210 and 280 nm with 10 nm increments Other details are given in Part I [13] To establish the acetonitrile working limits in the experimental design for each medicinal plant, a preliminary scouting gradient was used where the modifier concentration was increased linearly from to 100% (v/v) in 60 [13] Sets of training gradients were proposed attending to the peak distribution in the chromatograms observed with the scouting gradient All the gradients included the necessary additional steps for column cleaning to remove the most hydrophobic components, and re-equilibration before the next injection For each medicinal plant, a training experimental design, consisting of 6–7 multi-linear gradients with an intermediate node of variable position (Fig 1), was used These designs allowed exploring extreme compositions, without giving rise to excessive retention times for the most hydrophobic components, or too short for the most hydrophilic A final advantage is that this type of designs facilitates tracking the identity of the peaks of the reference compounds when the elution conditions are varied In Fig 1, it can be seen that the modifier concentration ranges, covered by the gradients for each medicinal plant, are rather different, reflecting the differences in the nature of the components in each sample, and consequently, in the distribution of chromatographic peaks The construction of the training experimental design for each type of sample, as well as other details for the chromatographic separation, are given in Part I [13] To verify the prediction performance of the global models, several gradients not included in the experimental design (validation gradients) were used (gradients tagged as E in Fig 1) 2.3 Software All data treatment was carried out with Matlab 2020a (The MathWorks Inc., Natick, MA, USA) Baseline subtraction in the experimental chromatograms was done with the BEADS algorithm [15] Automatic peak detection and measurement was carried out using Matlab functions developed in our laboratory [16] These functions automatically analyse baseline-free signals to locate the peaks and obtain the values of retention times, half-widths and peak areas, together with other additional information Experimental 2.1 Preparation of extracts of medicinal plants Theory The reversed-phase liquid chromatographic (RPLC) separation of extracts of three medicinal plants (green tea, lemon balm and linden) was studied Lemon balm and linden were purchased in bulk from a local store, while green tea was marketed in individual bags in a supermarket The extracts of the three plants were processed following the recommendations of Alvarez-Segura et al [16] Due to sample heterogeneity, dry portions of each plant were grinded One gram of the powder was weighted and transferred to a Falcon tube, to which 15 ml of a solution prepared with nanopure water (Adrona B30 Trace, Burladingen, Germany), and 70% (v/v) methanol (Scharlau, Barcelona, Spain) was added The Falcon tube content was sonicated during 60 at 80 °C Finally, the solution was centrifuged at 30 0 rpm during 3.1 Global retention models for the reference compounds The approach proposed in this work to simulate chromatographic fingerprints needs previous fitting of a global model for a set of selected compounds, with peaks distributed along the chromatogram (i.e., the so-called “reference compounds”) Knowledge of the chemical nature of these compounds is not needed, but their identity should be established unequivocally in the chromatograms run with all training gradients Also, the peaks should be intense enough for a proper detection under weak elution conditions Guidelines for selecting the peaks for the reference compounds are given in Part I of this research [13] There, the performance of global retention models based on the equations proposed by Snyder [17], Schoenmakers [18], and Neue-Kuss [19], was compared From these, the Neue-Kuss equation: 2.2 Chromatographic separation The supernatant was taken from the Falcon tube with a syringe, and filtered through a 0.45 μm pore size Nylon membrane (Micron Separations, Westboro, MA, USA) into a vial, before injection The separation was performed using gradient elution with hydroorganic mixtures, prepared by mixing nanopure water and HPLC grade acetonitrile (Scharlau), both containing 0.1% (v/v) formic acid −bϕ ki = k0,i (1 + cϕ )2 e + cϕ (1) offered the best results Therefore, only this equation will be considered in Part II of this work, reformulated as: −bϕ ki = 10log k0,i (1 + cϕ )2 e + cϕ (2) A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 to get model parameters less dissimilar in scale, which facilitates convergence [13] The global model can be represented by the [b, c, log k0,1 , log k0,2 , …, log k0, ns ] vector, where b and c are the common column/solvent parameters, and log k0, i , the specific solute parameters The steps needed to fit the global model are briefly outlined below (see Part I for more details): (i) First, the retention data for each reference compound i are individually fitted to Eq (2), in order to obtain the values of the bi , ci and log k0, i parameters For this purpose, the whole set of experimental retention times measured with all training gradients is used (ii) The medians of the parameters that describe the behaviour of column and solvent for each reference compound, obtained in step (i) (bm and cm ), are taken as initial estimates of the global parameters, while the log k0, i values for each compound i are fitted (iii) Parameters b and c are then fitted, this time keeping fixed the values of log k0, i found in the previous step, and attending simultaneously to the prediction of all solutes and training gradients (iv) Finally, all parameters defining the [b, c, log k0,1 , log k0,2 , …, log k0, ns ] vector in the global retention model are altogether optimised using all available data (v) If necessary, the process is repeated from step (ii) until convergence 3.2 Extension of global retention models to all detected peaks in the medicinal plants The global retention models obtained for the reference compounds allow predictions exclusively involving the reference compounds, for any arbitrary gradient However, the goal of this research is the prediction of full chromatograms for the medicinal plants, which can include several hundred compounds Therefore, we developed an approach to extend the global models fitted with the data of the reference compounds, to the prediction of retention for all detected peaks in the chromatograms The global retention model, initially established with the reference compounds, was modified to include other components in the chromatogram, as follows: (i) First, a chromatogram obtained with a gradient belonging to the training design is selected, preferably that one with the largest number of detectable peaks, which is usually the gradient with the lowest initial slope in the design Before being processed, the baseline is subtracted from the experimental chromatogram using an adequate algorithm This chromatogram will be referred to as “base chromatogram” (ii) Next, the position of all detected peaks in the base chromatogram is measured, using an automatic analysis function These peaks are those exceeding certain acceptability thresholds, such as a critical height or bandwidth The autodetection software developed in our laboratory was applied for this purpose [16] (iii) The retention times for all detected peaks (tR, i ) (the reference peaks or any other exceeding the detection thresholds) are obtained, together with other measurements that define the bandwidths and areas (iv) The process followed to extend the global model, to all detected peaks, consists of least-squares fitting, where the column and solvent parameters (b and c) are kept fixed to the values found with the reference peaks, whereas the specific parameters log k0, i (related to solute hydrophobicity) describe the experimental retention times (tR, i ) for all solutes (reference com- Fig Training (G) and validation (E) gradients, used to obtain the global models and evaluate the accuracy of the predictions of chromatographic fingerprints, respectively, for: (a) green tea, (b) lemon balm, and (c) linden A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 pounds or any other), when they elute with the gradient associated with the base chromatogram (v) With this information (b and c and log k0, i ), the chromatogram for any other arbitrary gradient can be predicted solute leaves the column, and hence, isocratic retention times are calculated The isocratic time corresponding to ϕ j will be referred here as “equivalent isocratic time” The sequence of operations needed to obtain the parameters of the bandwidth global models (ω0 , ω1 and ω2 in Eq (3)) is the following: Following this protocol, the effect of the modifier was determined with several gradients with very different profiles and some representative solutes, whereas the effect of the solute hydrophobicity (which ideally should be mobile-phase independent) was obtained only with the gradient in the design showing a maximal number of peaks A vector gathering the parameters of the global model [b, c, log k0,1 , log k0,2 , ] is thus obtained This vector can be rearranged into a collection of smaller [b, c, log k0, i ] vectors, each of them associated to the individual retention model for solute i In order to speed up and favour the convergence of the extended global model, several options were tried The best one was carrying out a sequential fitting, where the specific solute parameters are determined solute-by-solute in decreasing hydrophobicity order, so that the log k0 value found for solute i is used as an initial estimate for solute i – This operation mode accelerates considerably the regression process, and increases the chances of obtaining a good fitting in a single attempt Other options that were tried with less success were: (i) independent fittings using the same initial estimate (log k0 ) for all solutes, and (ii) sequential fittings, where the solution found for solute i was used in increasing hydrophobicity order (i) The retention data for each solute and gradient are calculated by solving the fundamental equation for gradient elution [26– 28], with either analytical or numerical integration Once found the time along the gradient that makes the sum of integrals match the dead time, the instant composition ϕ j at which the solute leaves the column is collaterally obtained (ii) The equivalent isocratic retention time (at which each solute would leave the column if it migrated at ϕ j ) can be determined by substituting the composition into the retention model (e.g., Eq (2)) (iii) The gradient bandwidth for solute i in gradient j is obtained straightforwardly by introducing tiso in Eq (3) (iv) Finally, the bandwidth global model is fitted by modulating the parameters in Eq (3), trying to obtain the best matching between the observed bandwidths and the corresponding predictions, using the reference compounds and all training gradients Results and discussion 4.1 Measurement of the chromatographic signal 3.3 Global bandwidth models for the reference compounds As indicated in Section 2.2, peak monitoring was carried out in the wavelength range between 210 and 280 nm (using nine acquisition channels separated each other by 10 nm) The detection wavelength was selected according to two approaches The first one made use of the “total chromatogram”, where the maximal absorbance in a certain wavelength domain is plotted versus the retention time This chromatogram can be processed and used further as a conventional chromatogram In the second approach, a compromise wavelength was selected balancing detectability and noise This approach was finally preferred, and the most suitable wavelength was found to be 230 nm At higher values, the chromatograms showed fewer peaks (i.e., the absorption was more selective), while below 230 nm the background was too disturbing, making peak tracking more difficult Before processing the chromatograms, the baseline was removed using a Matlab function developed in our laboratory, which automates and applies the BEADS (Baseline Estimation and Denoising using Sparsity) algorithm [15] BEADS performs a frequencybased signal decomposition to obtain three contributions: baseline, noise and net signal The built-in laboratory software applies the algorithm in a very flexible way, allowing a successful treatment of highly complex chromatograms Fig shows a representative chromatogram for the linden extract, obtained with gradient G3 (see Fig 1c) As can be observed, the assisted BEADS algorithm was successful for baseline suppression, removing almost completely the perturbation associated with the sudden increase in the gradient slope at 40 Fig depicts the chromatogram for the linden extract, once processed by the automatic detection algorithm after eliminating the baseline The simulated signals included the real peak size, which was automatically measured with the MATLAB function developed for signal analysis To be realistic and practical, the simulation of chromatograms requires not only the prediction of peak location, for each component in the sample as the elution conditions change, but also the peak bandwidths Although some peaks present anomalous bandwidths, often due to partial co-elution or other phenomena, what really matters is that most peaks in fingerprints are well predicted In this work, chromatographic peak profiles were simulated using a modified Gaussian model, where the standard deviation depends on the distance to the retention time [20,21] (see Supplementary material) The parameters of the Gaussian model can be related to the peak retention time, area and widths (or halfwidths) In turn, the bandwidths can be correlated with the retention times, giving rise to a family of global models based on the generalisation of the concept of chromatographic efficiency (N) [22–24] Bandwidth models describe the trend of chromatographic peaks to broaden, as the retention time increases In this work, the measurement of bandwidths was carried out when the signal was attenuated to 10% of the maximal peak height If the starting data are isocratic, the experimental bandwidths are directly correlated with the respective retention times Parabolic trends are usually obtained [23]: w = ω0 + ω1 tiso + ω2 tiso (3) which can be often assimilated to a linear behaviour In Eq (3), w can be the peak width (or the left or right half-widths), and tiso is the isocratic retention time For gradient elution, the relationship between the bandwidths and retention time is not direct However, enough accuracy can be obtained by applying the Jandera approximation [25], although it is only strictly valid for linear gradients This approximation postulates that, under gradient elution, the bandwidth of a solute i is the same as that obtained if it migrated isocratically using a mobile phase at the instant composition ϕ j , reached by gradient j when the solute leaves the column Although the source data come from gradient experiments, the prediction of gradient retention times provides collaterally the instant composition when the 4.2 Construction of global bandwidth models to simulate chromatograms As commented, the simulation of chromatograms requires, besides the availability of retention models (Section 3.2), the con4 A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 Fig Chromatogram obtained for the linden extract using gradient G3 (see Fig 1c), before (a) and after (b) baseline subtraction with the assisted BEADS algorithm Fig Peak detection analysis carried out with the automatic algorithm developed in the laboratory, for one of the fingerprint replicates obtained with gradient G3 for linden, after subtracting the baseline The abscissa axis corresponds to the indices of the time vector (data acquisition frequency of five points per second) Section 3.3 describes the protocol to obtain the parameters ω0 , ω1 and ω2 in the global bandwidth model (Eq (3)), based on gra- struction of bandwidth models to describe the peak profiles of the sample components In this work, bandwidths were predicted based on correlations with the isocratic retention times (see Section 3.3) However, there is no direct correspondence between the bandwidths and the retention times for gradient elution; thus, an inner relationship should be established with the times the solute would experience, if it migrated isocratically at the solvent composition when it leaves the column under a given gradient (the equivalent isocratic times) dient data Similarly to isocratic data, the bandwidths of a set of compounds eluted under several gradients offers a parabolic trend when represented versus the equivalent isocratic retention times Fig 4a to c shows the bandwidth trends for the peaks of the reference compounds in the chromatograms of the extracts of the three medicinal plants The data represented in the figure correspond to the whole set of reference compounds, eluted using all gradients in A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 Fig Width plots for: (a) green tea, (b) lemon balm, (c) linden, and (d) a set of sulphonamides See text for details the training designs For comparison purposes, the bandwidth data for some structurally-related compounds (a set of sulphonamides), eluted under isocratic elution, have been represented in Fig 4d As will be shown, the plots built for the reference compounds show trends, which can be useful for the prediction of peak profiles for the chromatographic fingerprints, in spite of the intrinsically larger scattering Medicinal plants contain compounds with a high diversity in chemical nature, which gives rise to diverse interaction kinetics with the chromatographic column This is one of the reasons of the larger scattering observed in the correlations, compared to sulphonamides The second reason that explains the larger scattering is that, in gradient elution, the isocratic retention times correspond to the instant the solutes leave the column It should be noted that this happens at the beginning of the gradient at short times for solutes of low hydrophobicity, and at the end of the gradient for solutes of high hydrophobicity, where the elution strength is higher, giving rise to a reduction in retention times Thus, the shorter retention times, characteristic of gradient elution, make the scattering more apparent Note, however, that the simulations show good agreement with the experimental peaks (see Figs to 7) It should be noted that the global bandwidth models for the reference peaks are valid for any peak in the chromatogram (the reference peaks or any other) This is not the case for the global retention models, which are initially obtained with reference peaks and must be adapted to predict the retention of any other component in the sample, as explained in Section 3.2 A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 Fig Comparison of the experimental chromatographic fingerprint for lemon balm, corresponding to gradient G1 (b), with the chromatograms predicted using two different base chromatograms: (a) gradient G7, and (c) gradient G3, which include a faster and a slower initial steps, respectively See Fig for the identity of gradient profiles 4.3 Some factors affecting the simulation of chromatograms based on global models G3, again for lemon balm), the peaks would be better resolved, but the longer analysis time can make the signals with the smallest size less detectable However, if the slow ramp were followed by a steeper linear segment (as in gradient G3), the loss of perceptibility for the most hydrophobic components in the chromatogram will not happen There are other factors to consider when choosing the base chromatogram, such as the differences in the prediction uncertainty of peaks eluting close to sections of the gradient with strong changes in slope The specific log k0, i parameters in the global models, used to predict the chromatographic fingerprints, were calculated from the values of the retention times for all the peaks found in the base chromatogram, using the automatic peak detection and signal analysis function The set of log k0, i solute parameters and the parameters associated with column and solvent (which are common for all solutes) can be used to predict the chromatograms under any other gradient included inside the experimental region covered by the training design It is interesting to note that, in total, 162, 205 and 203 peaks were detected for green tea, lemon balm and linden, respectively, with the respective base chromatograms (i.e., obtained with the slowest gradients in their experimental designs) Fig shows the experimental chromatogram for the lemon balm extract eluted with gradient G1, together with two predicted chromatograms (also for G1) obtained with the global model, but using two different base chromatograms: G7 and G3 (Fig 1b) Figs 5a and 5c show the respective predictions for both gradients: the fastest (G7) and the slowest (G3) in the experimental design In general terms, the predictions were more accurate with the global model developed with G3 As can be observed, the agreement between the experimental and predicted chromatograms is excellent It should be indicated that the acquisition of chromatograms was carried out along a period of two months In all the experiments, a vial containing the same extract was used, so that any The quality of the predictions, using global models, was checked by comparison of experimental and predicted chromatograms for: (i) Multi-linear gradient programs belonging to the experimental training design (Fig 1, gradients G) (ii) External validation gradients, with compositions exceeding the range covered by the training design (Fig 1, gradients E) These gradients were also multi-linear, with profiles very different from those in the training design In some cases, isocratic segments were included Validation gradients were used to check the prediction performance of the global models, under unfavourable prediction conditions This is the case of those gradients where the program starts at modifier concentrations exceeding those used in the training design, or gradients that include isocratic segments, more prone to prediction errors 4.3.1 Influence of the base chromatogram on the predictions The construction of a global retention model, valid to predict the retention for all the components in a sample, requires the arbitrary selection of an experimental chromatogram with the maximal number of peaks (the base chromatogram, see Section 3.3) The choice of the base chromatogram is a point that very critically affects the quality of predictions If the selected chromatogram were associated to the gradient with the highest initial slope in the experimental design (e.g., gradient G7 for lemon balm, Fig 1b), the smallest signals in the chromatogram will be higher due to the compression effect of the gradient However, this would also favour the undesirable co-elution of neighbouring peaks Conversely, if the chromatogram with the slowest gradient were used (e.g., gradient A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 chemical change in the sample produced by degradation or formation of new compounds during this period, would be beyond the fitted model Another factor to consider is that the number of peaks in the predicted chromatogram depends on the peaks detected in the base chromatogram Thus, in the experimental chromatogram obtained with gradient G7 (where the peaks are closer), only two intermediate peaks are shown in region (Fig 5a) Consequently, if this chromatogram is used as base chromatogram, any prediction would include only two peaks within this region However, the experimental chromatogram with gradient G1 shows at least seven peaks in region (Fig 5b) If the base chromatogram would have been that obtained with gradient G3 (Fig 5c), it would have been possible to predict the seven peaks for gradient G1 and in Fig 6b On the other hand, the refractive signals that appear at the end of the gradient (region in Fig 6b) are displaced when the gradient composition changes, as they are processed as genuine sample components Consequently, a fictitious value of log k0, i is assigned to these signals, and changes in composition affect their location In the example, the simulation only includes positive areas, and therefore, both refractive peaks are positive These signal can be easily identified and removed if wished 4.4 Validation of chromatograms obtained with external multi-linear gradients Experimental chromatograms corresponding to multi-linear gradients outside the training design (i.e., not used to build the global models) were also simulated with the aim of verifying the prediction performance under less favourable conditions These validation gradients are shown in Fig for the samples of green tea (gradient E8), lemon balm (E8) and linden (E7 and E8) The external validation runs were carried out after the acquisition and modelling steps, usually two weeks after the experimental design was completed For a more realistic comparison, the baseline contribution, initially subtracted by the BEADS algorithm, was added to the predicted chromatograms (Fig 7) In the chromatogram for green tea, some experimental peaks are observed, whose prediction is abnormally narrower (e.g., peaks and in Fig 7a), since they are processed as genuine peaks associated to a single component when they are predicted with the global bandwidth model Observe that the bandwidths of these experimental signals show differences with the trend observed for the neighbouring peaks Therefore, the abnormally broader peaks may be the result of co-elution of two or more components Other medicinal plants and gradients also showed sporadic broader peaks (e.g., peak in gradient E8 for linden, in Fig 7d) The shift towards shorter times of the peaks associated to the refractive signals, at the end of the gradient, is equally perceptible in the chromatograms The profile and position of the experimental refractive disturbance R1 , for the three plants, must be compared with the R2 + R3 signals in the predicted chromatograms These chromatograms were obtained by adding the fictitious peaks that model the refractive disturbance to the baseline found by BEADS Some differences observed between experimental and predicted chromatograms may be attributed to a slow degradation of the samples along weeks, which would have been solved by the periodic renewal of the solutions It should be noted that the base chromatograms were acquired several days before performing the validation experiments Therefore, certain peaks are present in some experimental chromatograms, but not in others However, most peaks retain their original presence and intensity It should be also taken into account that the validation gradients include isocratic segments, followed by other segments with strong increases in slope This type of configuration makes the position of the signals more uncertain, being the effects cumulative along the gradient Region in the chromatogram of linden, obtained with gradient E8 (Fig 7d), illustrates this behaviour as a shift in the sequence of peaks The magnitude and sign of the shift depends on the particular gradient configuration A similar effect (region in Fig 7b), but amplified due to a steeper gradient slope (gradient E8, see Fig 1b), is observed around the node for lemon balm, close to 40 This strong variation in the eluent composition, together with the progressively higher uncertainties in peak position (typical of slower solutes) results in dissimilar bandwidths for relatively close peaks It can be seen that the first two peaks in region for the experimental chromatogram (Fig 7b), which elute in the isocratic segment of the gradient program (before the change in slope), give rise to broader bandwidths According to the global model, the compounds associated to these 4.3.2 Prediction of signals not associated to retained solutes The automatic function for signal analysis naturally does no distinguish between genuine peaks and some other signals not associated to retained solutes: (i) Signals close to the hold-up time: Present at the start of the chromatogram as refractive fluctuations or signals appearing before the hold-up time region, which are associated to carryover phenomena or incomplete column stabilisation from a previous injection If these signals are not discarded, they will be processed as corresponding to a fictitious solute Since they not follow the global retention model, the incidental prediction will fail (e.g., see region in Fig 5) (ii) Signals associated to the sudden stop of the ramp at the end of the gradient: The sudden stabilisation of the slope at the end of the gradient (e.g., region in Fig 5) also produces refractive fluctuations, which appear at a fixed position These signals not correspond to the elution of any solute, but to the sudden stop of the modifier increase at the end of the gradient Therefore, they are insensitive to changes in the gradient, as long as the gradient time tG remains constant However, when the peaks in this region are incorrectly associated with fictitious solutes, their position becomes susceptible to changes when a gradient different from the base chromatogram is used Therefore, these signals should be ignored or removed from the simulation Analogously, sudden changes in slope in multi-linear gradients may give rise to fake peaks that should be removed 4.3.3 Peaks with abnormal bandwidth Some peaks, whose bandwidths are wider than expected according to the retention, can be found often associated to coelution of two or more unresolved components, although these peaks can have another origin Since the bandwidth model is established with the information of peaks for single compounds, an abnormally wide peak will be predicted according to the common width trend for a single compound eluting at that position Consequently, when global bandwidth models are applied, to keep the same area the simulated peaks will appear with a larger height than its experimental counterparts (compare the experimental and simulated peaks in Fig 5) In order to evaluate the quality of the predictions of bandwidths, removing the consequences of eventual biases in the prediction of retention times, the chromatogram for a selected gradient was predicted using itself as base chromatogram Therefore, the peak positions were not actually predicted, only the peak profiles According to this idea, the chromatograms associated to gradients G3 and G7 were predicted with the global retention models that included all peaks present in the experimental signal The experimental and predicted chromatograms are compared for both gradients G3 and G7 in Fig 6a and b, respectively As expected, abnormally wide peaks are predicted thinner and more intense This is the case of regions and in Fig 5, and peaks A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 Fig Comparison between the experimental (above, blue) and predicted (below, red) chromatograms for lemon balm, obtained with gradients: (a) G7, and (b) G3 (see Fig 1) The same gradients were also used as base chromatograms peaks are slightly more hydrophobic with regard to the experimental ones; therefore, they are predicted with longer retention However, since these peaks are located close to a steep change in gradient slope, the slightly higher value of the predicted log k0,i (related to solute hydrophobicity) implies being reached by the next segment of steeper slope in the gradient when they leave the column This accelerates the elution of these peaks, and consequently, they are compressed Therefore, the five peaks in region for gradient E8 are correctly predicted considering their bandwidth, but experience gradual biases in position Finally, it should be noted that for green tea and lemon balm, the composition range scanned by the validation set at the beginning of the gradient is out of the domain covered by the training design (16.4% acetonitrile for green tea and 23% for lemon balm, see gradient E8 in Fig 1a and 1b) This means that for the least retained compounds, the gradients will not reach such high concentrations in the first few minutes, and therefore, prediction of the retention for these compounds will be based on extrapolations The more polar components in the samples, which elute at the start of the gradient, are more sensitive to the lack of information, being thus affected by larger uncertainties Since the validation gradients for green tea and lemon balm start with isocratic elution, this problem is magnified Nevertheless, in spite of this limitation, the predicted and experimental chromatograms show good agreement can be useful for optimisation purposes In Part II, the global retention models, obtained in Part I [13] for selected compounds in chromatographic fingerprints, are extended to include all components in the sample To this, the retention data for all detected peaks, found in the chromatogram associated to the assayed gradient containing the lowest initial slope, were included in the model Global models allow the prediction of highly complex chromatograms under different gradient conditions, with a remarkable level of approximation to reality The approach has been verified with excellent results for the extracts of three medicinal plants, with chromatograms affected of specific problems In order to get safer detection of the smallest peaks, a baseline correction algorithm was applied, followed by an unsupervised, laboratory-built MATLAB function for peak detection In the construction of conventional individual retention models, all the parameters obtained by fitting the retention data are specific of a given solute, since each is fitted independently As a consequence, when the specific solute parameters (log k0, i ) are compared, these are unevenly affected by their chemical nature In contrast, in global models, the regression process isolates the common column/solvent effects from those specific of each solute This makes the estimation of solute hydrophobicity less dependant on the particular interactions of the analytes Consequently, the contribution of each solute to retention is better ranked [13] Although the prediction of the retention behaviour using a global model implies losing some solute specificity, which is distinctive of the individual models, the loss in prediction performance is acceptable The main limitation of our proposal (and in general of global models in its current state) is that changes in the elution order of the components in the sample, with the com- Conclusions This work deals with the suitability of global models to simulate chromatograms containing hundreds of components, which A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 Fig Comparison between the experimental (above, blue) and predicted (below, red) chromatograms obtained for the three medicinal plants, corresponding to validation gradients: (a) green tee obtained with gradient E8 (see Fig 1), (b) lemon balm with gradient E8, (c) linden with gradient E7, and (d) linden with gradient E8 10 A Gisbert-Alonso, A Navarro-Martínez, J.A Navarro-Huerta et al Journal of Chromatography A 1684 (2022) 463561 position, would require identifying all peaks present in a second base chromatogram, in order to relate them to the first base chromatogram It should be indicated that unassisted chromatogram processing would consider any detected signal as a genuine component of the sample Thus, in the initial and final regions of the chromatograms, positive and negative peaks with a refractive nature are often observed Consequently, the prediction of these signals will be affected by changes in the gradient program, and if they are not eliminated from the simulations, the associated peaks will be predicted with shifts proportional to their apparent hydrophobicity The same can happen with residual signals associated with: (i) imperfect baseline correction, (ii) calculation artifacts produced by the BEADS baseline correction algorithm, or (iii) presence of peaks that co-elute with abnormally broader bandwidths In this step of the work, these abnormal signals have been preserved to show their effects The aim of Part I and Part II was to study comprehensively all the relevant aspects and limitations of global models for the simulation of chromatograms The usefulness of global models goes beyond the field of chromatographic fingerprints: there are many separation problems where there are no standards available, or even the identity of most components is unknown Global models would allow unknown compounds in any sample to be included in the simulations Finally, this work opens the possibility of optimising the separation of chromatographic fingerprints by interpretive methods, which remains for future 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Enhancement in the computation of gradient retention times in liquid chromatography using root-finding methods, J Chromatogr A 1600 (2019) 137–147 Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Acknowledgments Work supported by Grant PID2019-106708GB-I00 funded by MCIN (Ministery of Science and Innovation of Spain)/AEI/10.13039/50110 011033 José Antonio Navarro-Huerta thanks the University of Valencia for the pre-doctoral grant UVINV-PREDOC18F1-742530 We thank the Universitat de València for paying the APC to publish as Open Access Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.chroma.2022.463561 References [1] H Sun, X Chen, A Zhang, T Sakurai, J Jiang, X Wang, Chromatographic fingerprinting analysis of Zhizhu Wan preparation by high-performance 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Chromatographic fingerprint-based analysis of extracts of green tea, lemon balm and linden: I Development of global retention models without the use of standards, J Chromatogr A 1672 (2022) 463060... comprehensively all the relevant aspects and limitations of global models for the simulation of chromatograms The usefulness of global models goes beyond the field of chromatographic fingerprints: there... and validation (E) gradients, used to obtain the global models and evaluate the accuracy of the predictions of chromatographic fingerprints, respectively, for: (a) green tea, (b) lemon balm, and