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• A model-based approach was shown for gradient elution liquid-liquid chromatography. • The elution profiles of the modifier and solutes were described with a stage model. • Only a few experiments were necessary for model parameter determination. • Pre-selected gradient shapes were optimized by maximizing productivity and yield. • The approach is applicable for systems with constant stationary phase composition. Liquid-liquid chromatography (LLC) is a separation technique that utilizes a biphasic solvent system as the mobile and stationary phases. The components are separated solely due to their different distributions between the two liquid phases. Gradient change in the mobile phase composition during the chromatographic process is a powerful method for improving the resolution of separation or shortening the process time. Gradient elution readily applies to LLC with biphasic solvent systems in which the stationary phase composition remains nearly constant when the mobile phase composition changes. This work proposes a model-based approach to optimize gradients in LLC and circumvent tedious trial-and-error experiments. The solutes' distribution constant depends on the mobile phase composition. Thus, the distribution constants were described as a function of the content of one of the solvents (= modifier) in the mobile phase. The dispersive and mass-transfer effects in the tubing and the column are modeled with a stage model. Only a few experiments are required to determine the model parameters. After the validation of the model and its parameters, the model can be used for LLC gradient optimization. The proposed approach was demonstrated for a gradient LLC separation of a mixture of four cannabinoids. Two different gradient shapes, one-step and linear gradient, were considered. For a pre-selected minimal purity requirement, the gradient was optimized for maximum process efficiency, defined as the product of productivity and yield. An experiment conducted with the optimized gradient conditions was in good agreement with the simulation, showing the potential of the proposed method. [ABSTRACT FROM AUTHOR]

• Re-parameterized Neue-Kuss model is reported. • Re-parameterization improves accuracy and precision of results. • Experimental design for gradient elution is reported. • Reported design allows for accurate prediction of isocratic retention factors. 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 S 1,ref , 18 % for S 2,ref and 6.2 % for k ref (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 S 1 , 25 % for S 2 and 160 % for k w (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 %. [ABSTRACT FROM AUTHOR]

• a dimensionless measure of the particle size gradient steepness was introduced. • about 15–20% gain in efficiency can be expected with particle size gradient. • too large particle size gradient can result in lower efficiencies than monodisperse packing. • large molecules (peptides, proteins) can in principle see the highest gain in efficiency. In this paper, the benefits of using columns packed with particles of decreasing size (particle size gradient) in liquid chromatography was investigated from a theoretical point of view. It is indeed well known that such columns may be useful in gradient elution, since the decrease of particle size along the chromatographic column can provide extra peak focusing effect. In the present contribution, several parameters (i.e., mobile phase gradient steepness, retention times and operating pressures) were considered and the kinetic performance of various types of columns packed with particle size gradient were evaluated. In the best case, about 15–20% gain in efficiency can be expected at a given retention time when utilizing a particle size gradient, compared to constant particle size. Conversely, when fixing efficiency, the analysis time can be decreased by about 15% with an optimal particle size gradient. However, it is also important to keep in mind that a too large a particle size gradient can result in lower efficiencies than a column packed with monodisperse packing. We have introduced the g d value, which is a dimensionless measure of the particle size gradient steepness that measures the relative variation of particle diameter throughout the column with respect to the average. We finally observed that g d = 0.3 - 0.4 provides the highest gain under practically useful conditions. [ABSTRACT FROM AUTHOR]

What is known in the literature as the fundamental equation for gradient elution (FEGE) was previously proven only for conventional gradient LC – uniform (the same at any distance from the inlet) static (fixed in time) solvent velocity (u m) in a column of uniform and static internal structure, cross-section and thermodynamic properties. A published alternative to the FEGE – the general migration equation – is valid for any column-based linear chromatography (GC, LC, SFC etc.). It allows one to theoretically or numerically predict a solute migration time to any location along the column. Starting from that general equation, several migration equations in gradient LC under different operational conditions including non-uniform non-static u m , Neue-Kuss retention model and others have been developed in this report. It has been shown that the conditions of validity of the FEGE can be expanded to include non-uniform u m. On the other hand, the FEGE is not valid for other unconventional operations of LC including gradient LC with dynamic (changing in time) u m. This implies that FEGE cannot be applied to, e.g., gradient LC operating at constant pressure where, due to the change in solvent composition, the solvent viscosity changes causing the change in u m with time. Applications of newly developed equations to other unconventional operations of gradient LC were also considered. Several new time parameters of the mobile phase flow were identified, interpreted, and evaluated. [ABSTRACT FROM AUTHOR]

• Ultra-short columns offer some clear advantages for the analysis of large biomolecules. • 10–20 mm columns are ideal for protein analysis. • Chromatographic instrumentation still needs to be improved to realise the full potential of short columns. • Ultra-short columns can be used in any chromatographic mode under gradient elution conditions. Today, reverse phase liquid chromatography (RPLC) analysis of proteins is almost exclusively performed on conventional columns (100–150 mm) in gradient elution mode. However, it was shown many years ago that large molecules present an on/off retention mechanism, and that only a very short inlet segment of the chromatographic column retains effectively the large molecules. Much shorter columns - like only a few centimetres or even a few millimetres - can therefore be used to efficiently analyse such macromolecules. The aim of this review is to summarise the historical and more recent works related to the use of very short columns for the analysis of model and therapeutic proteins. To this end, we have outlined the theoretical concepts behind the use of short columns, as well as the instrumental limitations and potential applications. Finally, we have shown that these very short columns were also possibly interesting for other chromatographic modes, such as ion exchange chromatography (IEX), hydrophilic interaction chromatography (HILIC) or hydrophobic interaction chromatography (HIC), as analyses in these chromatographic modes are performed in gradient elution mode. [ABSTRACT FROM AUTHOR]

• Pulses largely reduce retention of hydrophobic solutes at low modifier contents. • Intra-column delays should be considered to get good predictions close to the pulses. • Designs with pulses provide model parameters that agree with isocratic experiments. • Out-of-domain predictive capability of pulse designs is excellent. • Analysis times and solvent consumption are also competitive. The advantages and disadvantages of the use of isocratic experimental designs including transient increments of organic solvent (i.e., pulses) in the mobile phase(s) of lowest elution strength are explored with modelling purposes. For retained solutes, this type of mixed design offers similar or better predictive capability than gradient designs, shorter measurement time than pure isocratic designs, and retention model parameters that agree with those derived from pure isocratic experiments, with similar uncertainties. The predicted retention times are comparable to those offered by models adjusted from pure isocratic designs, and the solvent waste is appreciably lower. Under a practical standpoint, mixed designs including pulse(s) can be easily constructed by replacing the slowest isocratic runs with runs containing a pulse of short duration at an intermediate time. This allows the elution of the fastest solutes with appreciable retention in the initial sector of the elution program, previous to the pulse, and the elution of the slow solutes after the pulse, also in acceptable times. The fitting of the retention data obtained with pulses is simpler compared to gradient elution, and involves solving the integral equation of gradient elution, simplified by the presence of isocratic sectors. Experiments involving pulses reveal the existence of discrepancies in the predictions for solutes eluting in the nearby of the pulse, offered by the fundamental equation of gradient elution when this is solved using numerical integration. The correction of such discrepancies implies the inclusion of intra-column delays, in the arrival of changes in the concentration of organic modifier in the gradient to the instantaneous position of the solute, along the whole migration. [ABSTRACT FROM AUTHOR]

Highlights • Sample dispersion through a frit in narrow-bore columns was measured. • Four independent experimental approaches were used to increase data accuracy. • Peak volume variance due to state-of-the-art column frit were from 0.15 to 0.50 μL2. • Frit dispersion is larger than post-column dispersion of least dispersive UHPLC systems. • Observed high throughput LC gradient peak capacity is only 50% of the theoretical value. Abstract The impact of porous frits (2.1 mm i.d. × 1 mm thick, 0.2 μm porosity, 20% void, 0.69 μL) in short 0.5–5 cm long × 2.1 mm i.d. columns packed with sub-2 μm superficially porous particles on gradient performance was investigated using a low dispersive i-class ACQUITY UPLC system (25 cm × 75 μm outlet tube + 250 nL optical cell). In order to maximize data accuracy, the sample dispersion through a single frit was measured from four independent methods: (1) plate height subtraction, (2) peak capacity versus efficiency plot, (3) flow reversal, and (4) direct measurement. Frit dispersion increases non-linearly with increasing flow rate. The corresponding volume variances of small molecules were measured at 0.16 ± 0.04, 0.24 ± 0.05, and 0.31 ± 0.06 μL2 at flow rates of 0.1, 0.2, and 0.3 mL/min, respectively. These observed variances are lower than and consistent with the maximum volume variance of 0. 692 ∼ 0.5 μL2 expected for a mixer-like behavior. The peak capacity of short columns were then calculated for mixtures of peptides using a general model of gradient elution by considering (or not) the actual analyte dispersion taking place in the outlet frit, in the post-column connecting tube, and in the detection cell. The results show that the sole presence of the outlet frit is responsible for about 50% loss in peak capacity (relative to the expected gradient performance in absence of frit and post-column tube) for a 1 cm long column operated under standard gradient steepness. The actual structure and volume of column frits needs adjustment if one wants to take full advantage of the true performance of short high-throughput columns packed with sub-2 μm particles. [ABSTRACT FROM AUTHOR]

• Equation for peak width in gradient LC with solvent composition program having initial isocratic hold has been derived. • Special case of the hold of balanced duration considered. • Newly derived equation for the balanced hold is equivalent to previously published one. Expression for peak width in gradient elution liquid chromatography with exponential dependence of solute retention on linearly programmed solvent composition preceded by initial isocratic hold has been derived. A special case of previously defined balanced hold has been considered and compared with published results. [ABSTRACT FROM AUTHOR]

• Two-dimensional separations enable peak purity analysis of pharmaceutical peptides. • Strategy to derive second-dimension gradient conditions. • Preferred gradient conditions discovered by retention modelling. The importance of therapeutic peptides continues to increase in the marketplace for treating a range of diseases including diabetes and obesity. Quality control analyses for these pharmaceutical ingredients usually depends on reversed-phase liquid chromatography, and it is critically important to ensure that no impurities coelute with the target peptide at levels that would compromise the safety or effectiveness of the drug products. This can be challenging due to the broad range of properties of impurities that can be present on one hand (e.g., amino acid substitutions, chain cleavages, etc.), and the similarity of other impurities on the other hand (e.g., d -/ l -isomers). Two-dimensional liquid chromatography (2D-LC) is a powerful analytical tool that is well suited to address this particular problem; the first dimension can be used to detect impurities over a broad range in properties, while the second dimension can be used to focus specifically on those species that might coelute with the target peptide in the first dimension. While hundreds of papers have been published on the use of 2D-LC for proteomics applications, there are very few papers that have focused on its use for characterisation of therapeutic peptides. This paper is the second in a two-part series. In Part I of the series, we studied several different column / mobile phase combinations that could be useful in 2D-LC separations of therapeutic peptides, with a focus on selectivity, peak shape, and complementarity to other combinations, particularly for isomeric peptides under mass spectrometry-friendly conditions (i.e., volatile buffers). In this second part in the series, we describe a strategy to derive second-dimension (2D) gradient conditions that both, ensure elution from the 2D column, and increase the likelihood of resolving peptides with very similar properties. We find that a two-step process yields conditions that place the target peptide in the middle of the 2D chromatogram. This process begins with two scouting gradient elution conditions in the second dimension of a 2D-LC system, followed by building and refining a retention model for the target peptide using a third separation. The process is shown to be generically useful by developing methods for four model peptides, and application to a sample of degraded model peptide to demonstrate its utility for resolving impurities in a real sample. [ABSTRACT FROM AUTHOR]

• The electrostatic theory applied for modeling gradient elution of oligonucleotides. • Unified retention time model developed for co-solvent and ion-pair gradient modes. • The retention time model was extensively verified for both types of gradient modes. • A unified adsorption isotherm model was developed for both gradient modes. • The isotherms predicted well overloaded elution bands using both gradient modes. Ion-pair chromatography is the de facto standard for separating oligonucleotides and related impurities, particularly for analysis but also often for small-scale purification. Currently, there is limited understanding of the quantitative modeling of both analytical and overloaded elution profiles obtained during gradient elution in ion-pair chromatography. Here we will investigate a recently introduced gradient mode, the so-called ion-pairing reagent gradient mode, for both analytical and overloaded separations of oligonucleotides. The first part of the study demonstrates how the electrostatic theory of ion-pair chromatography can be applied for modeling gradient elution of oligonucleotides. When the ion-pair gradient mode is used in a region where the electrostatic surface potential can be linearized, a closed-form expression of retention time can be derived. A unified retention model was then derived, applicable for both ion-pair reagent gradient mode as well as co-solvent gradient mode. The model was verified for two different experimental systems and homo- and heteromeric oligonucleotides of different lengths. Quantitative modeling of overloaded chromatography using the ion-pairing reagent gradient mode was also investigated. Firstly, a unified adsorption isotherm model was developed for both gradient modes. Then, adsorption isotherms parameter of a model oligonucleotide and two major synthetic impurities were estimated using the inverse method. Secondly, the parameters of the adsorption isotherm were then used to investigate how the productivity of oligonucleotide varies with injection volume, gradient slope, and initial retention factor. Here, the productivity increased when using a shallow gradient slope combined with a low initial retention factor. Finally, experiments were conducted to confirming some of the model predictions. Comparison with the conventional co-solvent gradient mode showed that the ion-pairing reagent gradient leads to both higher yield and productivity while consuming less co-solvent. [ABSTRACT FROM AUTHOR]

• Method combining separation defined by space and the conventional elution-based separation is presented. • Theoretical model describing the proposed two-dimensional separation is developed. • Monolithic capillary columns and commercially available particulate columns are combined. • Experimental setup is applied to separate neurotransmitters contained in human urine. The separation in liquid chromatography is defined either by the space domain where it proceeds until the least retained analyte reaches the outlet of the column or by the time when individual analytes elute out of the column. These two approaches lead to the four possible combinations of two-dimensional liquid chromatography with online space x time coupling being the least experimentally feasible. Here, we show the development of a novel two-dimensional liquid chromatography method combining separation defined by space and the conventional elution-based separation. First-dimension column consisted of four capillary segments coupled serially via two-position six-port valves allowing an online and comprehensive transfer of analytes from the first to the second dimension. After initial experiments using homemade monolithic capillary columns, we tested commercially available columns in both dimensions. We ended with the combination of packed capillary columns in the first dimension and monolithic capillary column in the second dimension. We used a reversed-phase retention mechanism in the first spatial dimension, while HILIC was in the second, time-based dimension. We also developed a theoretical model to describe the proposed two-dimensional separation that was further confirmed by utilizing both an isocratic and gradient elution in the second dimension. Finally, we applied our experimental setup to separate neurotransmitters contained in human urine. [Display omitted] [ABSTRACT FROM AUTHOR]

• Automation and control for a multi-step polishing process has been demonstrated. • Customized Python control layer was developed to schedule and automate BioSMB. • Inline conditioning achieved using inbuilt pumps and sensors available on BioSMB. • pH, conductivity inputs are used for real-time automated control of pumps and valves. • Complex polishing step combinations were carried out in continuous processing trains. We propose a strategy for automation and control of multi-step polishing chromatography in integrated continuous manufacturing of monoclonal antibodies. The strategy is demonstrated for a multi-step polishing process consisting of cation exchange chromatography in bind-and-elute mode followed by mixed-mode chromatography in flowthrough mode. A BioSMB system with a customized Python control layer is used for automation and scheduling of both the chromatography steps. Further, the BioSMB valve manifold is leveraged for in-line conditioning between the two steps, as tight control of pH and conductivity is essential when operating with multimodal resins because even slight fluctuations in load conditions adversely affect the chromatography performance. The pH and conductivity of the load to the multimodal chromatography columns is consistent, despite the elution gradient of the preceding cation exchange chromatography step. Inputs from the BioSMB pH and conductivity sensors are used for real-time control of the 7 pumps and 240 valves to achieve in-line conditioning inside the BioSMB manifold in a fully automated manner. This is confirmed by showcasing different elution strategies in cation exchange chromatography, including linear gradient, step gradient and process deviations like tubing leakage. In all the above cases, the model was able to maintain the pH and conductivity of multimodal chromatography load within the range of 6 ± 0.1 pH and 7 ± 0.3 mS/cm conductivity. The strategy eliminates the need for using multiple BioSMB units or integrating external pumps, valves, mixers, surge tanks, or sensors between the two steps as is currently the standard approach, thus offering a simple and robust structure for integrating multiple polishing chromatography steps in continuous downstream monoclonal antibody purification trains. [ABSTRACT FROM AUTHOR]

• Hydrophobic interaction chromatography (HIC) isotherms employed for anionic multimodal modeling. • Model parameters analytically determined using negative linear gradient elution (LGE). • Standardized modeling workflow validated for four different antibody formats. Multimodal chromatography offers an increased selectivity compared to unimodal chromatographic methods and is often employed for challenging separation tasks in industrial downstream processing (DSP). Unfortunately, the implementation of multimodal polishing into a generic downstream platform can be hampered by non-robust platform conditions leading to a time and cost intensive process development. Mechanistic modeling can assist experimental process development but readily applicable and easy to calibrate multimodal chromatography models are lacking. In this work, we present a mechanistic modeling aided approach that paves the way for an accelerated development of anionic mixed-mode chromatography (MMC) for biopharmaceutical purification. A modified multimodal isotherm model was calibrated using only three chromatographic experiments and was employed in the retention prediction of four antibody formats including a Fab, a bispecific, as well as an IgG1 and IgG4 antibody subtype at pH 5.0 and 6.0. The chromatographic experiments were conducted using the anionic mixed-mode resin Capto adhere at industrial relevant process conditions to enable flow through purification. An existing multimodal isotherm model was reduced to hydrophobic interactions in the linear range of the adsorption isotherm and successfully employed in the simulation of six chromatographic experiments per molecule in concert with the transport dispersive model (TDM). The model reduction to only three parameters did prevent structural parameter non-identifiability and enabled an analytical isotherm parameter determination that was further refined by incorporation of size exclusion effects of the selected multimodal resin. During the model calibration, three linear salt gradient elution experiments were performed for each molecule followed by an isotherm parameter uncertainty assessment. Lastly, each model was validated with a set of step and isocratic elution experiments. This standardized modeling approach facilitates the implementation of multimodal chromatography as a key unit operation for the biopharmaceutical downstream platform, while increasing the mechanistic insight to the multimodal adsorption behavior of complex biologics. [ABSTRACT FROM AUTHOR]

• Optimisations based on individual and global models are compared. • Global models offer good predictions of the global separation. • Global models allow including unknown matrix peaks in the optimisation. • Extension to several unknowns requires only an additional experiment. • Optimisations combining individual and global models are possible. 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. [ABSTRACT FROM AUTHOR]

Various high-throughput systems and strategies are employed by the biopharmaceutical industry for early to late-stage process development for biologics manufacturing. The associated increases to experiment productivity and reduction in material consumption makes high throughput tools integral for bioprocess development. While these high-throughput systems have been successfully leveraged to generate high quality data representative of manufacturing scale processes, their data interpretation often requires complex data transformation and time-intensive system characterization. With respect to high throughput purification development, RoboColumns by Repligen operated on Tecan automated liquid handling systems offer superior performance scalability, but lack an optimized liquid delivery system that is representative of preparative chromatography. Particularly, stock Tecan liquid handling systems lack the capability to provide high-capacity continuous liquid flow and ideal linear gradient chromatography conditions. These limitations impact protein chromatography performance and hinder the application of high-throughput gradient elution experiments. In this work, we describe a Tecan Freedom EVO high-throughput purification tool that provides more continuous liquid delivery enabling continuous gradient elution capability for RoboColumn experiments as demonstrated by generation of highly linear conductivity gradients. Results demonstrate that the tool can provide RoboColumn performance and product quality data that is in agreement with larger, bench scale chromatography formats for two model purification methods. The described gradient purification method also provides more consistent performance between RoboColumns and larger column formats compared to step elution methods using the same optimized Tecan system. Lastly, new insights into the impact of discontinuous flow on RoboColumn elution performance are introduced, which may help further improve application of these data towards bioprocess development. [ABSTRACT FROM AUTHOR]

• Model calibration is cumbersome process involving estimation of model input values of column and binding kinetic parameters • In order to reduce the computational efforts required in model calibration, the present work proposes an accelerated approach for obtaining the input values for binding kinetic parameters in the extended Langmuir binding model from the two Yamamoto coefficient values. • The equations that can relate the two Yamamoto coefficients to the extended Langmuir model equation binding kinetic parameters were derived • The two Yamamoto coefficient values are obtained by Yamamoto method directly from the model calibration linear gradient elution runs and validated from isocratic runs performed at low loadings • The proposed approach not only accelerates model calibration process but also avoids multiple solutions for the binding kinetic parameters. With growing demands for therapeutic monoclonal antibodies, in silico downstream process development based on mechanistic modeling of chromatography separation process is being increasingly used for process optimization and process characterization. Application of mechanistic modeling in biopharmaceutical industry has been sparse due to the significant investment of time and resources that are required for performing model calibration. Mechanistic modeling of the chromatography process involves a large number of mass transport and binding parameters and their initial input values are required for simulations. These input values of column parameters can be easily obtained either from experiments or from empirical correlations available in literature. On the other hand, obtaining the model input valves for binding kinetic parameters is usually a cumbersome process as it involves performing batch experiments which are not only tedious but also require significant quantities of purely isolated main product and its related impurities, which is challenging as the product related impurities are typically present in smaller quantities and hence are difficult to obtain as pure species. In the present work, a mechanistic model that is based on the general rate model coupled with extended Langmuir binding model has been used for prediction of linear gradient elution peaks of monoclonal antibody on cation exchanger chromatography. The present work describes an accelerated approach for obtaining the input values for binding kinetic parameters in the extended Langmuir binding model from the two Yamamoto coefficient A and B values obtained by Yamamoto method directly from the model calibration linear gradient elution runs of different gradient slopes and at low to moderate protein loadings. The equations that can relate the two coefficients to the extended Langmuir model equation binding kinetic parameters were derived. Therefore, once A and B are determined, the binding kinetic parameter values were determined straightforward, thereby avoiding the problem of multiple solutions for the model parameters. The estimated binding parameters were successfully validated from isocratic elution experiments performed at low loading. What we demonstrate is that the proposed approach allows us to estimate binding kinetic parameters in a significantly more efficient and accelerated manner than presently used approaches, thereby accelerating development and implementation of mechanistic modeling for process chromatography. [ABSTRACT FROM AUTHOR]

• Bayesian optimization and Gaussian processes used for chromatography parameter estimation. • Up to two orders of magnitude faster than multi-start gradient descent and genetic algorithms. • Combination of multiple objective functions. The modeling of chromatographic separations can speed up downstream process development, reducing the time to market and corresponding development costs for new products such as pharmaceuticals. However, calibrating such models by identifying suitable parameter values for mass transport and sorption is a major, time-consuming challenge that can hinder model development and improvement. We therefore designed a new approach based on Bayesian optimization (BayesOpt) and Gaussian processes that reduced the time required to compute relevant chromatography parameters by up to two orders of magnitude compared to a multistart gradient descent and a genetic algorithm. We compared the three approaches side by side to process several internal and external datasets for ion exchange chromatography (based on a steric mass action isotherm) and hydrophobic interaction chromatography (a modified version of a recently published five-parameter isotherm) as well as different input data types (gradient elution data alone vs gradient elution and breakthrough data). We found that BayesOpt computation was consistently faster than the other approaches when using either single-core or 12-cores computer processing units. The error of the BayesOpt parameter estimates was higher than that of the competing algorithms, but still two orders of magnitude less than the variability of our experimental data, indicating BayesOpts applicability for chromatography modeling. The low computational demand of BayesOpt will facilitate rapid model development and improvement even for large datasets (e.g., > 100 proteins) and increase its suitability for research laboratories or small and medium enterprises lacking access to dedicated mainframe computers. [ABSTRACT FROM AUTHOR]

Cation-exchange chromatography is widely used in the purification of therapeutic antibodies, wherein parameters such as elution pH and counterion concentration require optimization for individual antibodies across different chromatography resins. With a growing number of antibodies in clinical trials and the pressure to expedite process development, we developed and automated a high-throughput batch-binding screen to more efficiently optimize elution conditions for cation-exchange chromatography resins. The screen maps the binding behavior of antibodies and impurities as a function of pH and counterion concentration in terms of a partition coefficient ( K p ). Using this approach, the binding behavior of a library of antibodies was assessed on Poros 50HS and SP Sepharose Fast Flow resins. The diversity in binding behavior between antibodies and across resins translated to the requirement of a variable counterion concentration to elute each antibody. This requirement can be met through the use of a gradient elution. However, a gradient of increasing counterion concentration spans the transition from binding to non-binding for impurities as well as the antibody, resulting in the elution of impurities within the antibody elution peak. Step elution conditions that selectively elute the antibody while retaining impurities on the resin can now be rapidly identified using our high-throughput approach. We demonstrate that by correlating antibody K p to elution pool volume and yield on packed-bed columns and through the calculation of a separation factor, we can efficiently optimize step elution conditions that maximize impurity clearance and yield for each antibody. [ABSTRACT FROM AUTHOR]

• Catechin and epicatechin were enantioseparated by HPLC with aqueous β-CD eluents. • Ten catechins were separated by HPLC with an aqueous β-CD linear gradient elution. • Catechins in a green tea infusion were separated by the present method. • Epimerization of (+)-catechin was suppressed by addition of D-fructose. Catechin and epicatechin were enantioseparated by high-performance liquid chromatography (HPLC) with a phenyl column and aqueous mobile phases containing 0.05% (w/v) and 0.6% (w/v) of β-cyclodextrin for catechin and epicatechin, respectively. β-Cyclodextrin was found to be scarcely retained on a phenyl column. Consequently, it was suggested that catechin, which was eluted earlier than epicatechin, formed more stable inclusion complex with β-cyclodextrin than epicatechin and earlier eluted enantiomers, (−)-catechin and (+)-epicatechin, formed more stable diastereomer complexes with β-cyclodextrin than the respective enantiomers. This was confirmed by β-cyclodextrin-modified micellar electrokinetic chromatography and Benesi−Hildebrand plots by fluorescence spectrophotometry. Effect of sugars (D-sucrose, D-glucose, and D-fructose) on the epimerization of (+)-catechin and (+)-epicatechin by heating was investigated by HPLC with a β-cyclodextrin stepwise elution mode, in which two kinds of aqueous eluents containing different concentrations of β-cyclodextrin were used by turns. The epimerization of the two enantiomers was suppressed only when D-fructose was added. Separation of ten kinds of catechins including catechin and epicatechin enantiomers was investigated by a β-cyclodextrin linear gradient HPLC elution mode without using organic solvents, where two kinds of aqueous eluents containing different concentrations of β-cyclodextrin were used with changing their ratio gradually. These catechins in a green tea infusion could be separated successfully by this method. [ABSTRACT FROM AUTHOR]

Highlights: [•] Effects of eluent temperature and elution bandwidth on detector response are studied. [•] Eluent temperature has little effect on response of ELSD and CCAD. [•] Both ELSD and CCAD detectors show increased response as elution bandwidth decreases. [•] Use of a temperature gradient gives uniform elution bandwidth and uniform detector response. [Copyright &y& Elsevier]

• Direct measurement of optimal flow rate (F opt) in gradient LC. • Theoretical basis and experimental technique. • F opt in gradient LC can be substantially different from that in isocratic LC. Method development in gradient LC relies upon the selection of a solvent time program and a mobile phase flow rate. The flow rate, optimal for gradient separation cannot be inherently predicted by the isocratic value optimal for a given analyte, and rather should be identified independently to ensure the highest separation performance of gradient analysis. The optimal flow rate (F opt) is defined herein as the solvent volumetric flow rate (F) maximizing the separation (Δ s) of a predetermined peak-pair or the separation capacity (s c) of the entire LC analysis. The theoretical background and the experimental technique of measurement of F opt in gradient elution analysis were considered and experimentally demonstrated. The technique of measuring F opt is based on translatable changes of F where the product Ft G (t G is the gradient time) was the same for all values of F. The F opt was found as F corresponding to the maximum in Δ s or in s c. [ABSTRACT FROM AUTHOR]

• The classical isocratic recycling chromatography is extended to gradient elution. • The theory of gradient elution is applied to automate the gradient recycling process • The gradient recycling process is applied to semi-preparative liquid chromatography. • The application proof-of-concept is demonstrated for complex sample mixtures. • Separation of vitamins D 2 and D 3 from milk extract is achieved in less than two hours. Twin column recycling semi-preparative liquid chromatography (TCRLC) is revived to prepare small amount (∼ 1 mg) of a pure targeted compound, which cannot be isolated by conventional preparative liquid chromatography. In this work, TCRLC is extended to gradient elution. The first step of this modified process consists of a gradient step, which eliminates both early and late impurities. If not discarded, some late impurities could echo during the second isocratic recycling step of the process and compromise the purity level required for the targeted compound. Additionally, the entire gradient TCRLC (GTCRLC) process is automated regarding the eluent composition programmed and the actuation times of two valves: one two-position four-port divert valve enables to shave the targeted compound from early and late impurities during the initial gradient step. The second two-position six-port recycling valve ensures the complete baseline resolution between the band of the targeted compound and those of the closest impurities, which are not fully eliminated after the initial gradient step. The automation of the whole GTCRLC process is achieved by running four preliminary scouting gradient runs (at four different relative gradient times, t g t 0 = 2, 6, 18, and 54, where t 0 is the hold-up column time) for the accurate determination of the thermodynamics (ln k versus φ plots of the retention factor as a function of the mobile phase composition) of the first impurity, the targeted compound(s), and of the last impurity. The automated GTCRLC process was successfully applied for the isolation of a polycyclic aromatic hydrocarbon (PAH), chrysene, from a complex mixture of PAHs containing two nearly co-eluting impurities (benzo[a]anthracene and triphenylene) and nine other early/late impurities (sample volume injected: 1 mL, 7.8 mm × 150 mm Sunfire-C 18 column, acetonitrile/water eluent mixtures, T = 55 ∘ C, 20 cycles, baseline separation in less than two hours). Additionally, the GTCRLC process is advantageously used to isolate and baseline separate the vitamins D 2 and D 3 initially present in a milk extract mixture (0.3 mL sample injection volume, 7.8 mm × 150 mm Sunfire-C 18 column, methanol/water eluent mixtures, T = 65 ∘ C, 14 cycles needed in 1.5 hours). These results open promising avenues toward an effective preparation of unknown targeted compounds before further physico-chemical characterization and unambiguous identification. [ABSTRACT FROM AUTHOR]

• C18-modified monolithic silica separates different end-functionalized PEtOx. • Resolution of subpopulations according to their degree of polymerization. • Electrospray ionization mass spectrometry hyphenation enables peak assignment. • Quantification of chain transfer products is demonstrated with example PEtOx. Hydrophilic poly(2-oxazoline)s represent a promising alternative to replace poly(ethylene glycol) in the biomedical field. For that purpose, reliable analytical protocols to confirm identity and quantity of impurities are required. In particular, side products deriving from chain transfer reactions occurring during the cationic ring-opening polymerization and incomplete end-capping processes may be present. The analytical approach must hence be capable of separating polymers according to minor changes regarding their end group. We demonstrate that liquid chromatography, relying on a monolithic C18-modified silica column and isocratic as well as gradient elution using water / acetonitrile mixtures and varying detectors, can accomplish such demanding high resolution separations. Poly(2-ethyl-2-oxazoline)s (PEtOx) with acetyl, hydroxyl, and phthalimide ω-end groups were investigated. Identification of side products was achieved through coupling with electrospray ionization mass spectrometry. UV / Vis detection was applied to quantify chain transfer products in PEtOx comprising biphenyl moieties. In addition, gradient elution enabled the separation of PEtOx into macromolecules according to their specific degrees of polymerization in molar mass ranges around 2,000 g mol-1. [ABSTRACT FROM AUTHOR]

• Influence of injection volume based on comprehensive data. • Differentiation between isocratic and gradient elution. • Utilization of sub 2 µm reverse phase material. • Significant volume overloading possible without sacrificing efficiency. The injection volume and the associated column volume overload is one of the most common issues in miniaturized chromatography. The injection volume should not exceed 10% of the effective column volume. A further reduction of the injection volume leads to an increase in chromatographic efficiency. However, the signal intensity must be above a certain threshold to generate a chromatographic peak that can be detected. Therefore, the injection volume has to be optimized to reach the ideal balance between chromatographic efficiency and sensitivity. This study examined the general influence of the injection volume for both isocratic and gradient elution, depending on the retention factor and peak standard deviation. For this purpose, substances of different polarity were selected to represent a broad elution spectrum. Besides the model analyte naphthalene, these were mainly pharmaceuticals. For all measurements a microbore column with an ID of 300 µm and packed with 1.9 μm fully porous particles was used. For isocratic elution, the injection volume was varied between 4 and 16% of the effective column volume. The retention factors were adjusted between 2 and 10. For gradient elution, the injection volume was varied between 4 and 160% of the effective column volume. The observed effects were further investigated using the gradient kinetic plot theory. In isocratic elution, a loss in plate height up to 50% was observed for components that elute near the void time. A significant reduction of the chromatographic efficiency was noticed up to a retention factor of 4. In gradient elution, a reduction in peak capacity could only be observed if the injection volume exceeded 40% of the effective column volume. For some substances, only a slight loss in peak capacity was noticed even with a volume overload of 160%. [ABSTRACT FROM AUTHOR]

• Procedure proposed for the fitting of several solutes to the same retention model • Five equations in isocratic and gradient elution and two types of sample were studied • Performance was comparable to the individual models for all equations • Chromatographic fingerprints were successfully predicted with five one-node gradients • log P o/w was estimated based on global models The resolution of samples containing unknown compounds of different nature, or without standards available, as is the case of chromatographic fingerprints, is still a challenge. Possibly, the most problematic aspect that prevents systematic method development is finding models that describe without bias the retention behaviour of the compounds in the samples. In this work, the use of global models (able to describe the whole sample) is proposed as an alternative to the use of individual models for each solute. Global models contain parameters that are specific for each solute, while other parameters ‒related to the column and solvent‒ are common for all solutes. A special regression procedure is presented for the construction of global models, which are applied to predict highly complex chromatograms, such as chromatographic fingerprints, for diverse experimental conditions in isocratic and gradient elution. Another interesting application is the prediction of molecular properties, such as log P o/w , from the specific solute parameters of the global models. The examined adapted models are based on the equations proposed by Snyder, Schoenmakers, Neue and Kuss, Jandera, and Bosch Rosés to describe the retention. In all cases, the predictive capability was very satisfactory. Two cases of study were considered: chromatograms of camomile extracts analysed using acetonitrile gradients, and a set of 145 known compounds in a wide range of structures and functionalities, eluted isocratically with acetonitrile/water mobile phases. [ABSTRACT FROM AUTHOR]

• Multilinear gradient elution under quadratic solvent strength model is studied • Analytical expressions for retention time in above case are presented • Analytical expressions for peak compression factor are also presented • A program for the optimization of multilinear gradient profile is presented • The predicted and experimental chromatograms are well consistent Analytical expressions for retention time and peak compression factor are deduced by assuming quadratic solvent strength model and multilinear gradient elution. Based on these expressions, a program for the optimization of multilinear gradient profile is written with Visual Basic for Applications in Excel using genetic algorithm. The program is applied to search for a gradient profile for the separation of twelve compounds that are degraded from lignin. It is shown that the predicted and experimental chromatograms are well consistent. A better separation of the compounds is achieved under an S-shaped multilinear gradient profile than that obtained under linear gradient profile. [ABSTRACT FROM AUTHOR]

• A radical new way to prepare aqueous buffers for column chromatography • The solid compounds is directly dosed to the aqueous solution • Buffers can be prepared on demand • The method is suited for linear and step gradients Buffer preparation and storage requires a significant facility footprint in large scale bioprocessing and together with the costs of supply chain management can have a substantial economic impact. In-line buffer mixing in chromatography is commonly performed by blending different buffer solutions using at least two pumps and a static or dynamic mixer. We developed a device for an in-line gradient delivery of buffering agents directly from solids to be applied for chromatographic separation processes. A solid feeding device with a screw conveyor and a hold tank for the solids was designed and a miniaturized system was 3D printed. The coefficient of variation for the precision of the solid feeding of 5 different buffering agents was below 5% even for very small solid flow rates necessary for lab-scale chromatography. Stability was demonstrated by a constant linear solid feed at a very low dosing rate of 0.05 g.min−1 over 24 hours. We demonstrated the suitability for chromatography by directly connecting the system to a standard chromatography workstation for protein chromatography. The solids were fed into a miniaturized continuously stirred tank reactor connected to an ÄKTA purification system. The performance of the in-line gradient delivery of buffering agents directly from solids was compared to conventional in-line buffer mixing. We were able to achieve highly linear gradients for elution using only one pump of a chromatographic system, generating the gradient by the direct addition of solids avoiding the necessity of additional pumps and hold tanks. By direct conditioning of buffers and the addition of solids a simple, just in time, at site preparation of buffers was possible. The design of the feeding unit for solid addition for buffer preparation is easily scalable and adaptable to work with or as a replacement for already existing in-line dilution or conditioning units. [ABSTRACT FROM AUTHOR]

• Glyphosate and AMPA were quantified in tap water samples without derivatization. • Glyphosate and AMPA analysis in water by low-cost method without preconcentration. • Analysis of glyphosate, AMPA and ions of public health concern in drinking water. • Glyphosate and AMPA analysis by ion chromatography with conductivity detection. The herbicide glyphosate and its main metabolite aminomethylphosphonic acid (AMPA) are generally studied in environmental samples in the investigation of contamination of soil, plants, water and food. Many analytical methods are based on liquid chromatography or high-performance liquid chromatography, with pre-column or post-column derivatization; in addition, the chromatograph can be coupled to mass spectrometers for detection and quantification. Gas chromatography and spectroscopic and electrochemical methods have also been used. In this work, a simple low-cost method is presented for the analysis of water intended for human consumption with the quantification not only of glyphosate and AMPA, but also of other ions of interest to public health (fluoride, chlorite, bromate, chloride, nitrite, nitrate, sulfate and phosphate). Based on ion chromatography with conductivity detection (chemical suppression of eluent conductivity), the key point in this method is the use of gradient elution with two eluents of different pH and ionic strength, not requiring derivatization. There is no interference from the other ions at higher concentrations. The detection limits obtained for glyphosate and AMPA were 15 μg L −1 and 80 μg L −1, respectively. As the method allows the analysis of a large number of samples, it has been successfully applied to monitoring the quality of tap water in 89 municipalities in the northeast region of the State of São Paulo, Brazil. [ABSTRACT FROM AUTHOR]

• Antibody monomer-dimer separation achieved by gradient elution with hydroxyapatite. • 99% antibody monomer purity and 90% recovery obtained starting with 30% dimer. • Hybrid model predicts performance as a function of protein load and gradient slope. • Optimized protein loads lead to high productivity. Modeling the chromatographic separations of proteins at manufacturing scale is important since downstream processing costs are often dominant. At such scales, the columns are highly overloaded heightening the challenge of predicting performance. In this work, the separation of a monoclonal antibody monomer-dimer mixture is conducted by gradient elution chromatography with ceramic hydroxyapatite (CHT) columns Type I and Type II under overloaded conditions. Phosphate gradients are shown to be preferable over sodium chloride gradients since the latter result in undesirable pH transitions generated within the column itself. Using sodium phosphate gradients separation is obtained with both CHT types, achieving approximately 90% recovery at 99% monomer purity starting with a mixture containing 30% dimer at total protein loads up to 30 mg/mL. Because of its higher binding capacity, even higher loadings can be obtained with CHT Type I without monomer breakthrough. A hybrid model is developed to describe the separation. The model, based on an empirical description of two-component, competitive isotherms at low sodium phosphate concentration coupled with the stoichiometric displacement model at higher sodium phosphate concentrations, is in good agreement with the experiments using the linear driving force (LDF) approximation to describe adsorption/desorption kinetics. The same LDF rate coefficient predicts the separation at loadings between 0.8 and 30 mg/mL. The model developed in this work can be used as a general tool to optimize operating conditions, understand what factors limit performance, and compare different operating modes. [ABSTRACT FROM AUTHOR]

• LC×LC separations can be performed using similar separation mechanisms in both dimensions. • Different types of gradients were compared using emulated and real on-line systems. • Parallel gradients provide the best results when the separation mechanisms are correlated. Comprehensive two-dimensional liquid chromatography (LC×LC) offers increased peak capacity, resolution and selectivity compared to one-dimensional liquid chromatography. It is commonly accepted that the technique produces the best results when the separation mechanisms in the two dimensions are completely orthogonal, which necessitates the use of gradient elution for each second-dimension fraction. Recently, the use of similar separation mechanisms in both dimensions has been gaining popularity, but full or shifted gradients are still used for each second dimension fraction. Herein, we argue that when the separation mechanisms are correlated in the two dimensions, the best results can be obtained with the use of parallel gradients in the second dimension, which makes the technique nearly as user-friendly as comprehensive two-dimensional gas chromatography. This has been illustrated through the separation of a mixture of 39 pharmaceutical compounds using reversed phase in both dimensions. Different selectivity in the second dimension was obtained through the use of different stationary phase chemistries and/or mobile phase organic modifiers. The best coverage of the separation space was obtained when parallel gradients were applied in both dimensions, and the same was true for practical peak capacity. [ABSTRACT FROM AUTHOR]

• Separation optimization in HPLC analysis is implemented in R programming language. • Two different modes (automatic and manual) are offered for selection of optimal separation conditions. • The R software is validated in separation optimization under isocratic, monolinear and/or bilinear conditions governed by variations of φ and/or pH. • The proposed R software is expected to be a valuable tool for simulating and optimizing separation conditions for ionizable and neutral compounds. A complete package of functions in the R-language has been written for professional separation optimization of complex mixtures of ionized and/or non-ionized solutes. The package includes functions for (a) base-line correction of experimentally recorded chromatograms, (b) modeling of chromatographic peak shapes and retention data, (c) prediction of the retention time of the test analytes and/or their chromatograms, and (d) separation optimization under either isocratic or single and/or double gradient elution conditions by changing the organic modifier(s) content and/or eluent pH. The optimization functions presented in this study offer two different modes for selection of optimal separation conditions: automatic and manual mode. In the automatic mode, the optimal separation conditions are determined by maximizing the resolution within separation time preset by the analyst. In the manual mode, the optimal separation conditions are selected via scatter or contour plots. The foreknowledge of the precise dependence of resolution and separation time upon one or two retention parameters of interest, provided by the proposed computer-assisted separation optimization method, gives chromatographers a feel of confidence for the selection of the optimal conditions for a desired separation. An illustrative video given in the Supplementary material may encourage a novice practitioner in R (software) programming language to follow the proposed separation optimization procedure in a real HPLC analysis. [ABSTRACT FROM AUTHOR]

• Adsorption behavior of octreotide has been modeled in gradient elution RP-LC. • Inverse Method allows to get fundamental information by using only a few milligrams. • Study of thermodynamics is necessary for the optimization of continuous separations. • This approach can be adopted when a reduced amount of peptide is available. The thermodynamic behavior of octreotide, a cyclic octapeptide with important pharmaceutical functions, has been simulated under reversed-phase gradient elution conditions. To this end, adsorption behavior was firstly investigated in isocratic conditions, under a variety of water/acetonitrile + 0.02% (v/v) trifluoroacetic acid (TFA) mixtures as mobile phase by using a Langmuir isotherm. Organic modifier was varied in the range between 23 and 28% (v/v). Adsorption isotherms were determined by means of the so-called Inverse Method (IM) with a minimum amount of peptide. The linear solvent strength (LSS) model was used to find the correlation between isotherm parameters and mobile phase composition. This study contributes to enlarge our knowledge on the chromatographic behavior under nonlinear gradient conditions of peptides. In particular, it focuses on a cyclic octapeptide. [ABSTRACT FROM AUTHOR]

• Screening of drugs in urine samples with direct injection is carried out. • Retention models are developed for micellar eluents with extended solvent domains. • Isocratic, linear and multi-linear separations are interpretively optimised. • Consequences of surfactant desorption in C8 and C18 columns by a gradient are shown. • Excellent agreement between predictions and experimental chromatograms is found. Micellar liquid chromatography (MLC) is a reversed-phase mode with mobile phases containing an organic solvent and a micellised surfactant. Most procedures developed in MLC are implemented in the isocratic mode, since the general elution problem in chromatography is less troublesome. However, gradient elution may be still useful in MLC to analyse mixtures of compounds within a wide range of polarities, in shorter times. MLC using gradients is attractive to determine by direct injection moderate to low polar compounds in physiological samples. In these analyses, the use of initial micellar conditions (isocratic or gradient) with a fixed amount of surfactant above the critical micellar concentration, keeping the organic solvent content low, will provide better protection of the column against the precipitation of the proteins in the physiological fluid. Once the proteins are swept away, the elution strength can be increased using a positive gradient of organic solvent to reduce the analysis time. This may give rise to the transition from the micellar to the submicellar mode, since micelles are destroyed at sufficiently high concentration of organic solvent. In this work, several retention models covering extended solvent domains in MLC are developed and tested, and applied to investigate the performance in isocratic, linear and multi-linear gradient separations. The study was applied to the screening of β-adrenoceptor antagonists in urine samples, using mobile phases prepared with sodium dodecyl sulphate and 1-propanol. Predicted chromatograms were highly accurate in all situations, although suffered of baseline problems and minor shifts for peaks eluting close to a steep gradient segment. Two columns (C18 and C8) were investigated, with the C8 column being preferable owing to the smaller amount of adsorbed surfactant. [ABSTRACT FROM AUTHOR]

• Free amino acids analyzed in unified chromatography from SFC to HPLC. • Adapted operating conditions to optimize run time and efficiency. • Separation of isobaric isomers of leucine and isoleucine. • Quantification with ESI(+)-MS detection in dietary supplements. Amino acids are most often analyzed in reversed-phase liquid chromatography after a derivatization procedure to render them sufficiently hydrophobic and detectable with UV or fluorimetric detection. Simpler methods should be possible to avoid additional chemical reactions. We present an improved method to analyze free amino acids with unified chromatography, that is to say with a wide elution gradient starting with supercritical fluid chromatography (SFC) conditions (high percentage of carbon dioxide) and ending with high-performance liquid chromatography (HPLC) conditions (100% co-solvent). The mobile phase composition was carefully adjusted to permit the elution of 21 natural amino acids (among which 19 proteinogenic) with very good peak shapes from a zwitterionic cinchona-based stationary phase (Chiralpak ZWIX(+)). Chiral separation was not desired. The mobile phase finally selected comprised carbon dioxide and a co-solvent (methanol containing 2% water and 20 mM methanesulfonic acid), ranging from 10 to 100% in 7 min followed by 3 min re-equilibration at 25 °C. A reversed pressure gradient (15 to 11 MPa) and a reversed flow rate gradient (3 to 1 mL/min) were applied to avoid reaching the upper pressure limit of the pumping system (40 MPa) and to favor high chromatographic efficiency at every stage of the elution gradient. Detection was achieved with electrospray ionization-mass spectrometry (ESI(+)-MS). The method is then fast and straightforward as no derivatization step is necessary, and all isobaric species were chromatographically resolved. To demonstrate the applicability of the method, it was applied to the quantitation of amino acids in food supplements commonly consumed by sportsmen, containing taurine (a common natural amino acid) or branched-chain amino acids (BCAA), namely valine, and the isobaric leucine and isoleucine. A standard addition method was examined for sensitivity, linearity, repeatability and intermediate precision. [ABSTRACT FROM AUTHOR]

• An extension of the linear solvent strength model is proposed. • A parameter that describes the changes in elution strength is included. • A general equation to calculate the compression factor in gradient elution is given. • Data obtained from several chromatographic modes are fitted to the model. Modelling the retention behaviour of solutes in liquid chromatography, based on the composition of the mobile phase is a common task in the chromatographic practice. Along the development of liquid chromatography (LC), several models have been proposed to help in understanding the retention mechanisms, and especially, allow the prediction of retention times with optimisation purposes. Particular models are used for different LC modes, such as normal phase (NPLC), reversed phase (RPLC), hydrophilic interaction (HILIC), and micellar (MLC). In this work, a general equation is proposed that includes a parameter (the elution degree, g), which characterises the way the elution strength varies with the modifier concentration. The elution degree adopts the value g = 1 when the system follows the linear solvent strength (LSS) model, where the elution strength is constant. When g > 1, the elution strength decreases, and for g < 1, it increases with the modifier concentration. The proposed equation was applied to experimental retention data obtained for several chromatographic systems in RPLC, HILIC, MLC, and microemulsion LC. It was found that values in the 1 < g < 2 range are most usual. The general behaviour of the proposed equation was studied for isocratic and gradient elution. A general expression to calculate the compression factor of chromatographic peaks in gradient elution was also developed. It is shown that an increasing g value makes retention factors close to zero more difficult, since the elution strength decreases as the modifier concentration increases. For this reason, the larger the g value, the harder it is to reach significant peak compression. In contrast, an elution mode with g < 1 would yield increased elution strength with the modifier concentration, giving rise to significant peak compression. [ABSTRACT FROM AUTHOR]

• The plate model is solved for gradient elution. • A general dispersion equation is proposed for isocratic and gradient elution. • Gradients with ramp of stationary phase and mobile phase are considered. • Peak compression is verified with a ramp of mobile phase within the column. • Experimental and predicted values agree satisfactorily. Gradient elution in liquid chromatography reduces the analysis time, improves the efficiency and increases the peak capacity. The study of this chromatographic mode has been based mainly on kinetic dispersion models. The plate model has been applied to a lesser extent, despite being the basis for the concepts of plate height and chromatographic efficiency. In this work, a general equation describing peak dispersion in HPLC gradient elution is derived from the plate model. This equation is studied and validated for three types of gradients: (i) a reference gradient without ramp in which the retention factor varies with time identically throughout the column, (ii) a gradient of stationary phase in which the nature of the stationary phase varies continuously inside the column, resulting in a ramp of constant retention factor over time, and finally, (iii) a mobile phase gradient, which produces a retention factor ramp that varies over time. In the latter case, the results are similar to those derived from the mass-transport equation in linear solvent gradients when the linear solvent strength model is applied. The final equations are expressed based on the initial and final instantaneous retention factors, thus they can be applied independently of the deviation of the elution model, being fully compatible with isocratic elution. Results predicted with the proposed equations are identical to those obtained by numerical resolution of the elution differential equation system. The additional compression due to the presence of a ramp of modifier is also verified. However, useful compressions will appear only when the retention factor changes with time. Finally, the study indicates that the extra-column variance undergoes a compression process when the retention factor varies over time, whether or not there is a ramp inside the column. [ABSTRACT FROM AUTHOR]

• Adsorption enthalpy values of polyphenols in polymer chromatography were obtained. • Isothermal titration calorimetry (ITC) and van't Hoff (VH) plots were used. • Linear gradient elution (LGE) and isocratic elution (IE) were used for VH plots. • Enthalpy values obtained by VH plots using LGE and IE and by ITC were similar. • Adsorption enthalpy values obtained with ITC and VH plots were exothermic. Temperature effect on the adsorption enthalpy of polyphenols was analyzed with van't Hoff plots using the distribution coefficient, K, determined with isocratic and gradient elution chromatography. Catechin and epigallocatechin gallate (EGCG) were used as model polyphenols. The stationary phase was polystyrene-divinylbenzene (PS-DVB) resin particles and the mobile phase was an ethanol-water mixture. The values of adsorption enthalpy determined by chromatography and isothermal titration calorimetry were obtained in the temperature range of 283 and 318 K. The results obtained by van't Hoff plots were consistent with the ones obtained with the isothermal titration calorimetry (ITC). The interaction between PS-DVB particles and the polyphenols was found to be exothermic with negative values of enthalpy, –30.1 and –37.7 kJ/mol for catechin and EGCG, respectively. [ABSTRACT FROM AUTHOR]

• HILIC columns are attractive for 2D-LC because their selectivities complement RP-LC. • The re-equilibration of HILIC columns has been perceived to be too slow for 2D-LC. • We have studied the effects of practical variables on re-equilibration of HILIC phases. • Highly repeatable retention can be obtained with re-equilibration as short as 3 s. In recent years there has been increasing interest in the use of HILIC separations in two-dimensional liquid chromatography (2D-LC), mainly because the selectivity of HILIC separations complement that of reversed-phase separations for a variety of molecules. Historically, the re-equilibration of HILIC phases following gradient elution has been perceived as too slow to be useful in the second dimension of 2D-LC separations in particular. Recent studies of re-equilibration of HILIC phases by McCalley and coworkers using a limited set of conditions showed that highly repeatable gradient separations could be obtained with re-equilibration times as short as 4.3 min [1,2]. In this study we aimed to study re-equilibration of HILIC phases under a broader set of conditions, and at much shorter re-equilibration times, in the interest of determining whether or not HILIC separations can be generally considered as a viable option for use in the second dimension of 2D-LC separations. To this end we studied the effects of mobile phase pH, buffer concentration, and preparation method, flow rate, analyte and stationary phase chemistry, column length, and re-equilibration time on retention of a variety of small molecule probe solutes following gradient elution. In general, we have found that excellent separation repeatability can be obtained with quite short (≪10 min) re-equilibration times, even when progress toward full equilibration of the column is quite slow (≫10 min). In other words, even if the stationary phase is not fully equilibrated, as long as it is partially equilibrated in a highly precise manner, highly repeatable retention times can be obtained. Higher flow rate has a positive effect on both the rate of progress toward full equilibration and the repeatability of separation. No significant, consistent effects of eluent pH or buffer concentration on repeatability of gradient separation were observed for the stationary phases studied. Excellent gradient separation repeatability was obtained with shorter columns (30 mm length) with re-equilibration times as short as 3 s. A proof-of-concept 2D-LC separation of several small molecule probes using HILIC separations in both dimensions was performed to illustrate that re-equilibration of these columns can be fast enough for HILIC columns to be considered as a viable option for the second dimension of comprehensive 2D-LC separations. [ABSTRACT FROM AUTHOR]