Enhancing LC×LC separations through multi-task Bayesian optimization

Method development in comprehensive two-dimensional liquid chromatography (LC×LC) is a challenging process. The interdependencies between the two dimensions and the possibility of incorporating complex gradient profiles, such as multi-segmented gradients or shifting gradients, make trial-and-error method development time-consuming and highly dependent on user experience. Retention modeling and Bayesian optimization (BO) have been proposed as solutions to mitigate these issues. However, both approaches have their strengths and weaknesses. On the one hand, retention modeling, which approximates true retention behavior, depends on effective peak tracking and accurate retention time and width predictions, which are increasingly challenging for complex samples and advanced gradient assemblies. On the other hand, Bayesian optimization may require many experiments when dealing with many adjustable parameters, as in LC×LC. Therefore, in this work, we investigate the use of multi-task Bayesian optimization (MTBO), a method that can combine information from both retention modeling and experimental measurements. The algorithm was first tested and compared with BO using a synthetic retention modeling test case, where it was shown that MTBO finds better optima with fewer method-development iterations than conventional BO. Next, the algorithm was tested on the optimization of a method for a pesticide sample and we found that the algorithm was able to improve upon the initial scanning experiments. Multi-task Bayesian optimization is a promising technique in situations where modeling retention is challenging, and the high number of adjustable parameters and/or limited optimization budget makes traditional Bayesian optimization impractical.

Fingerprinting of hydroxy propyl methyl cellulose by comprehensive two-dimensional liquid chromatography-mass spectrometry of monomers resulting from acid hydrolysis

Hydroxypropyl methyl cellulose (HPMC) is a type of cellulose derivative with properties that render it useful in e.g. food, cosmetics, and pharmaceutical industry. The substitution degree and composition of the β-glucose subunits of HPMC affect its physical and functional properties, but HPMC characterization is challenging due to its high structural heterogeneity, including many isomers. In this study, comprehensive two-dimensional liquid chromatography-mass spectrometry was used to examine substituted glucose monomers originating from complete acid hydrolysis of HPMC. Resolution between the different monomers was achieved using a C18 and cyano column in the first and second LC dimension, respectively. The data analysis process was structured to obtain fingerprints of the monomers of interest. The results revealed that isomers of the respective monomers could be selectively separated based on the position of substituents. The examination of two industrial HPMC products revealed differences in overall monomer composition. While both products contained monomers with a similar degree of substitution, they exhibited distinct regioselectivity.

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

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

High-Throughput Liquid Chromatographic Analysis Using a Segmented Flow Injector with a 1 s Cycle Time

High-throughput screening (HTS) workflows are revolutionizing many fields, including drug discovery, reaction discovery and optimization, diagnostics, sensing, and enzyme engineering. Liquid chromatography (LC) is commonly deployed during HTS to reduce matrix effects, distinguish isomers, and preconcentrate prior to detection, but LC separation time often limits throughput. Although subsecond LC separations have been demonstrated, they are rarely utilized during HTS due to limitations associated with the speed of common autosamplers. In this work, these limits are overcome by utilizing droplet microfluidics for sample introduction. In the method, a train of samples segmented by air are continuously pumped into the inlet of an LC injection valve that is actuated once each sample fills the sample loop. Coupled with 2.1 mm diameter × 5 mm long columns packed with 2.7 μm superficially porous C18 particles operated at 5 mL/min, the injector enabled separation of 3 components at 1 s/sample and analysis of a 96-well plate in 1.6 min with <2% peak area relative standard deviation. Analyte-dependent carryover was minimized by including wash droplets composed of organic solvent in between sample droplets. High-throughput LC coupled with mass spectrometric detection using the segmented flow injector was applied to a screen of inhibitors of a cytochrome P450-catalyzed hydroxylation reaction. Measurements of the reaction substrate and product concentrations made using fast LC with the segmented flow injector correlated well with measurements made using a more conventional, 3 min LC method. These results demonstrate the potential for droplet microfluidics to be used for sample introduction during high-throughput LC analysis.

Computer-driven optimization of complex gradients in comprehensive two-dimensional liquid chromatography

Method development in comprehensive two-dimensional liquid chromatography (LC × LC) is a complicated endeavor. The dependency between the two dimensions and the possibility of incorporating complex gradient profiles, such as multi-segmented gradients or shifting gradients, renders method development by "trial-and-error" time-consuming and highly dependent on user experience. In this work, an open-source algorithm for the automated and interpretive method development of complex gradients in LC × LC-mass spectrometry (MS) was developed. A workflow was designed to operate within a closed-loop that allowed direct interaction between the LC × LC-MS system and a data-processing computer which ran in an unsupervised and automated fashion. Obtaining accurate retention models in LC × LC is difficult due to the challenges associated with the exact determination of retention times, curve fitting because of the use of gradient elution, and gradient deformation. Thus, retention models were compared in terms of repeatability of determination. Additionally, the design of shifting gradients in the second dimension and the prediction of peak widths were investigated. The algorithm was tested on separations of a tryptic digest of a monoclonal antibody using an objective function that included the sum of resolutions and analysis time as quality descriptors. The algorithm was able to improve the separation relative to a generic starting method using these complex gradient profiles after only four method-development iterations (i.e., sets of chromatographic conditions). Further iterations improved retention time and peak width predictions and thus the accuracy in the separations predicted by the algorithm.

Algorithm for tracking peaks amongst numerous datasets in comprehensive two-dimensional chromatography to enhance data analysis and interpretation

Analytical data processing often requires the comparison of data, i.e. finding similarities and differences within separations. In this context, a peak-tracking algorithm was developed to compare multiple datasets in one-dimensional (1D) and two-dimensional (2D) chromatography. Two application strategies were investigated: i) data processing where all chromatograms are produced in one sequence and processed simultaneously, and ii) method optimization where chromatograms are produced and processed cumulatively. The first strategy was tested on data from comprehensive 2D liquid chromatography and comprehensive 2D gas chromatography separations of academic and industrial samples of varying compound classes (monoclonal-antibody digest, wine volatiles, polymer granulate headspace, and mayonnaise). Peaks were tracked in up to 29 chromatograms at once, but this could be upscaled when necessary. However, the peak-tracking algorithm performed less accurate for trace analytes, since, peaks that are difficult to detect are also difficult to track. The second strategy was tested with 1D liquid chromatography separations, that were optimized using automated method-development. The strategy for method optimization was quicker to detect peaks that were still poorly separated in earlier chromatograms compared to assigning a target chromatogram, to which all other chromatograms are compared. Rendering it a useful tool for automated method optimization.

A Strategy for assessing peak purity of pharmaceutical peptides in reversed-phase chromatography methods using two-dimensional liquid chromatography coupled to mass spectrometry. Part II: Development of second-dimension gradient conditions

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.

A strategy for assessing peak purity of pharmaceutical peptides in reversed-phase chromatography methods using two-dimensional liquid chromatography coupled to mass spectrometry. Part I: Selection of columns and mobile phases

The current study describes the development of a 2D-LC-MS-based strategy for assessing main peak purity in the analysis of pharmaceutical peptides. The focus is on 2D-LC using reversed-phase (RP) separations in both dimensions, and particularly peptide isomer selectivity, since compounds with the same mass to charge ratio are not readily differentiated by mass spectrometry and therefore must be separated chromatographically. Initially, 30 column / mobile phase combinations were evaluated for both general separation performance (i.e., selectivity and peak shape) and isomer selectivity using forcibly degraded peptide samples and mixtures of synthetic diastereomers. A ranking of more than 300 UV and MS chromatograms suggests that when developing a new method, screening a set of four columns and four volatile mobile phases with differing characteristics should be adequate to both cover the selectivity space, and yield good separation performance. When 2D-LC-MS is to be used to evaluate peak purity for a new method, our results show that a second-dimension separation comprising a C8/C18 column possessing no ionic functionality, and an acetic acid / ammonium acetate mobile phase buffered at pH 5, provides good selectivity at 25 °C for peptide isomers with a MW <10 kDa. Retention data for 29 diverse peptides (1 < MW < 14 kDa, 3.7 < pI < 12.5) measured in this study using a variety of column and mobile phase conditions (i.e., 30 in total) are consistent with the classification of these various chromatographic conditions using the previously reported Peptide RPC Column Characterisation Protocol. For the investigated peptides trifluoroacetic acid was found to reduce selectivity differences between columns of diverse properties, probably due to its potential to form ion-pairs with peptides. Trifluoroacetic acid often improves peak shape for very large peptides (i.e. MW > 10 kDa). In the current dataset which also contain smaller peptides it received the highest ranking for 40% of the column and mobile phase combinations due to better selectivity and/or peak shape. The reported work here constitutes part one of a series of two papers. The second paper focuses on the use of retention modelling for rapid and accurate selection of the shallow gradients (i.e., << 1% ACN/min) required to obtain sufficient peptide isomer retention and separation in the second dimension. The overall results presented in this series of papers provides the guidance needed to develop a 2D-LC-MS method from start to finish for the analysis of main peak purity of therapeutic peptides.

Development of tandem-column liquid chromatographic methods for pharmaceutical compounds using simulations based on hydrophobic subtraction model parameters

The liquid chromatography (LC) analysis of small molecule pharmaceutical compounds and related impurities is crucial in the development of new drug substances, but developing these separations is usually challenging due to analyte structural similarities. Tandem-column LC (TC-LC) has emerged as a powerful approach to achieve alternative separation selectivity compared to conventional single column separations. However, one of the bottlenecks associated with use of tandem column approaches is time-consuming column pair screening and selection. Herein, we compared critical resolution (R_c) in single column vs. TC-LC separations for a given set of small molecule pharmaceutical compounds and developed a column selection workflow that uses separation simulations based on parameters from the hydrophobic subtraction model (HSM) of reversed-phase selectivity. In this study, HSM solute parameters were experimentally determined for a small molecule pharmaceutical (Linrodostat) and ten of its related impurities using multiple linear regression of their retentions on 16 selected RPLC columns against in-house determined HSM column parameters. R_c values were calculated based on HSM database column parameters for a pool of about 200 available stationary phases in both single-phase column (2.1 mm i.d. × 100 mm) or tandem column paired (two 2.1 mm i.d. × 50 mm) formats. Four column configurations (two single and two tandem) were predicted to achieve successful separations under isocratic HSM separation conditions, with a fifth tandem pair predicted to have a single co-elution. Of these five potential candidates, one tandem pair yielded compete baseline resolution of the 11-component mixture in an experimental separation. In this specific case, the tandem column pairs outperformed single-phase columns, with better predicted and experimental R_c values for the Linrodostat mixture under the HSM separation conditions. The results reported in this study demonstrated the enormous selectivity potential of TC-LC in pharmaceutical compound separations and are consistent with our previous study that examined the potential of tandem column approaches using purely computational means, though there is room for substantial improvement in the prediction accuracy. The proposed workflow can be used to prioritize a small number of column combinations by computational means before any experiments are conducted. This is highly attractive from the point of view of time and resource savings considering over 200,000 different tandem column pairings are possible using columns for which there are data in the HSM database.

Essentials of LC Troubleshooting, Part II, Continued: More Misbehaving Retention Times

Some liquid chromatography (LC) troubleshooting topics never get old, because there are some problems that persist in the practice of LC, even as instrument technology improves over time. There are many ways for things to go wrong in an LC system that ultimately manifest as deviations from expected retention times. Lot-to-lot variability in column chemistry, effects of pressure on selectivity, and stationary phase loss are less frequently encountered causes of unexpected retention shifts, but ones that should be included in a comprehensive troubleshooting agenda.

What are Options to Improve My Separation? Part II: Likelihood of Separation, Adjusting Selectivity for Simple Mixtures

When high performance liquid chromatography (HPLC) users are confronted with questions about how to improve upon the performance of an existing or recently developed method, there are many technological options to consider. This series offers guidance for a systematic approach to method improvement that can save time and resources and likely produce more robust methods. Part II explains options adjusting selectivity (peak spacing or elution pattern) when dealing with relatively simple mixtures—which are not always easy to separate—with a focus on reversed-phase LC (RPLC) separations.

What Are My Options to Improve My Separation? Part I: Foundational Concepts

Many high performance liquid chromatography (HPLC) users are confronted with questions about how to improve the performance of an existing or recently developed method. These days, we have many technological options to consider (for example, using higher pressures or temperatures, or both), but how do we choose one (or a few) to try? A systematic approach to method improvement can save time and resources by using methods that are likely to be better, and more robust, than those developed using a trial-and-error approach.

Essentials of LC Troubleshooting, VI: How Wide Should Those Peaks Be?

In this latest installment of our series on recurring challenges in liquid chromatography (LC), we turn our attention to peak widths that are wider than expected. Estimating the expected peak widths can help determine when a column and LC system are not working quite right, and to decide when troubleshooting should be initiated.

Essentials of LC Troubleshooting, Part V: What Happened to My Sensitivity?

Some liquid chromatography (LC) troubleshooting topics never get old because there are some problems that persist in the practice of LC, even as instrument technology improves over time. There are many ways for things to go wrong in an LC system that ultimately manifests as detection sensitivity that is lower than expected. Developing a short list of the likely causes of these results can help streamline our troubleshooting experience when sensitivity-related problems occur.

The Future of Method Development for Two-Dimensional Liquid Chromatography – Work Smarter, Not Just Harder?

The potential for wider use of two-dimensional liquid chromatography (2D-LC) is becoming more evident as the complexity of samples that must be handled continues to increase in application areas ranging from biopharmaceuticals to biosourced consumer products. Although the sophistication and ease of use have improved in recent years for commercial 2D-LC instruments, many analysts are still intimidated by the method development process for 2D methods because of the larger number of variables involved compared to conventional liquid chromatography. In this article, I share my perspective on the trends in this area, and the developments we are likely to see in the field in the near future.

Essentials of LC Troubleshooting, Part IV: What Is Going On with the Baseline?

Some liquid chromatography (LC) troubleshooting topics never get old because there are some problems that persist in the practice of LC, even as instrument technology improves over time. There are many ways for things to go wrong in an LC system that ultimately manifest as detector baselines that do not look right. Developing a short list of the likely causes of these results can help streamline our troubleshooting experience when baseline-related problems occur.

An approach to high throughput measurement of accurate retention data in liquid chromatography

Efforts to model and simulate various aspects of liquid chromatography (LC) separations (e.g., retention, selectivity, peak capacity, injection breakthrough) depend on experimental retention measurements to use as the basis for the models and simulations. Often these modeling and simulation efforts are limited by datasets that are too small because of the cost (time and money) associated with making the measurements. Other groups have demonstrated improvements in throughput of LC separations by focusing on "overhead" associated with the instrument itself - for example, between-analysis software processing time, and autosampler motions. In this paper we explore the possibility of using columns with small volumes (i.e., 5 mm x 2.1 mm i.d.) compared to conventional columns (e.g., 100 mm x 2.1 mm i.d.) that are typically used for retention measurements. We find that isocratic retention factors calculated for columns with these dimensions are different by about 20%; we attribute this difference - which we interpret as an error in measurements based on data from the 5 mm column - to extra-column volume associated with inlet and outlet frits. Since retention factor is a thermodynamic property of the mobile/stationary phase system under study, it should be independent of the dimensions of the column that is used for the measurement. We propose using ratios of retention factors (i.e., selectivities) to translate retention measurements between columns of different dimensions, so that measurements made using small columns can be used to make predictions for separations that involve conventional columns. We find that this approach reduces the difference in retention factors (5 mm compared to 100 mm columns) from an average of 18% to an average absolute difference of 1.7% (all errors less than 8%). This approach will significantly increase the rate at which high quality retention data can be collected to thousands of measurements per instrument per day, which in turn will likely have a profound impact on the quality of models and simulations that can be developed for many aspects of LC separations.

Essentials of LC Troubleshooting, Part III: Those Peaks Don’t Look Right

Some LC troubleshooting topics never get old, because there are some problems that persist in the practice of LC, even as instrument technology improves over time. There are many ways for things to go wrong in an LC system that ultimately manifest as peak shapes that are not good. Developing a short list of the likely causes of these results can help streamline our troubleshooting experience when peak shape-related problems occur.

Trapping-Enrichment Multi-dimensional Liquid Chromatography with On-Line Deuterated Solvent Exchange for Streamlined Structure Elucidation at the Microgram Scale

At the forefront of chemistry and biology research, development timelines are fast-paced and large quantities of pure targets are rarely available. Herein, we introduce a new framework, which is built upon an automated, online trapping-enrichment multi-dimensional liquid chromatography platform (TE-Dt-mDLC) that enables: 1) highly efficient separation of complex mixtures in a first dimension (¹ D-UV); 2) automated peak trapping-enrichment and buffer removal achieved through a sequence of H₂ O and D₂ O washes using an independent pump setup; and 3) a second dimension separation (² D-UV-MS) with fully deuterated mobile phases and fraction collection to minimize protic residues for immediate NMR analysis while bypassing tedious drying processes and minimizing analyte degradation. Diverse examples of target isolation and characterization from organic synthesis and natural product chemistry laboratories are illustrated, demonstrating recoveries above 90 % using as little as a few micrograms of material.

Perspectives on the Use of Retention Modeling to Streamline 2D-LC Method Development: Current State and Future Prospects

The history of multidimensional liquid chromatography (MDLC) has been dominated by methods that have been developed using highly empirical, experience-driven, trial-and-error approaches. These approaches have been sufficient in progressing the field forward scientifically, primarily in academic research laboratories. However, more widespread usage of multidimensional separations will require more systematic approaches to method development that rely less on user experience and lower the barriers to development and use of methods by a wider community of users. In this mini-review, we discuss recent research aimed at developing such systematic, model-driven approaches to streamline method development and speculate about likely advances in the same direction in the near future. It seems likely that such model-driven approaches would be particularly helpful for methods developed for analyzing biopharmaceutical molecules, which tend to be very sensitive to slight changes in method conditions (for example, mobile phase composition).

Essentials of LC Troubleshooting, Part II: Misbehaving Retention Times

Several liquid chromatography (LC) troubleshooting topics never get old because there are some problems that persist in the practice of LC, even as instrument technology improves over time. There are many ways for things to go wrong in an LC system that ultimately manifest as deviations from expected retention times. Developing a short list of the likely causes of these deviations can help streamline our troubleshooting experience when retention-related problems occur.

A Comprehensive 2D-LC/MS Online Platform for Screening of Acetylcholinesterase Inhibitors

The continuous interest in discovering new bioactive molecules derived from natural products (NP) has stimulated the development of improved screening assays to help overcome challenges in NP-based drug discovery. Here, we describe a unique platform for the online screening of acetylcholinesterase inhibitors without the need for pre-treating the sample. In the current study, we have demonstrated the ability to combine reversed-phase separation with a capillary immobilized enzyme reactor (cIMER) in two-dimensional liquid chromatography system coupled with mass spectrometry detection. We systematically investigated the effects of method parameters that are of practical significance and are known to affect the enzyme assay and interfere in the analysis such as: bioreactor dimensions, loop sizes, amount of immobilized enzyme, second dimension flow rates, reaction time, substrate concentration, presence of organic modifier, limit of detection and signal suppression. The performance of this new platform was evaluated using a mixture containing three known AChE inhibitors (tacrine, galanthamine and donepezil) and an ethanolic extract obtained from the dry bulbs of Hippeastrum calyptratum (Amaryllidaceae) was investigated to provide a proof of concept of the applicability of the platform for the analysis of complex mixtures such as those derived from NPs.

But Why Doesn’t It Get Better? Kinetic Plots for Liquid Chromatography, Part II: Making and Interpreting the Plots

Choosing a liquid chromatography (LC) column for a particular application can be a surprisingly challenging task. On the one hand, column manufacturers provide us many options to choose from, including particle types, pore sizes, particle sizes, and different lengths and diameters. On the other hand, we usually do not have time to experimentally evaluate many combinations of these parameters, and sometimes we end up picking something similar to the columns that are already available. The “kinetic plot” is a powerful graphical tool that can help leverage the best available theory to help us understand how different combinations of parameters (that is, particle size, length, among others) will perform in regard to the time needed to get to a particular column efficiency (and thus resolution), and therefore make well-informed decisions when choosing columns.

But Why Doesn’t It Get Better? Kinetic Plots for Liquid Chromatography, Part I: Basic Concepts

Choosing a liquid chromatography (LC) column for a particular application can be a surprisingly challenging task. On the one hand, column manufacturers give us many options to choose from, including particle types, pore sizes, particle sizes, and different lengths and diameters. On the other hand, we usually do not have time to experimentally evaluate many combinations of these parameters, and sometimes we end up picking something similar to the columns that are already in the drawer. The “kinetic plot” is a powerful graphical tool that can help leverage the best available theory to help us understand how different combinations of parameters (such as particle size and length) will perform in relation to the time needed to get to a particular column efficiency (and thus resolution), and therefore make well-informed decisions when choosing columns.

In Silico Multifactorial Modeling for Streamlined Development and Optimization of Two-Dimensional Liquid Chromatography

Continued adoption of two-dimensional liquid chromatography (2D-LC) in industrial laboratories will depend on the development of approaches to make method development for 2D-LC more systematic, less tedious, and less reliant on user expertise. In this paper, we build on previous efforts in these directions by describing the use of multifactorial modeling software that can help streamline and simplify the method development process for 2D-LC. Specifically, we have focused on building retention models for second dimension (²D) separations involving variables including gradient time, temperature, organic modifier blending, and buffer concentration using LC simulator (ACD/Labs) software. Multifactorial retention modeling outcomes are illustrated as resolution map planes or cubes that enable straightforward location of ²D conditions that maximize resolution while minimizing analysis time. We also illustrate the practicality of this approach by identifying conditions that yield baseline separation of all compounds co-eluting from a first dimension (¹D) separation using a single combination of ²D stationary phase and elution conditions. The multifactorial retention models were found to be very accurate for both the ¹D and ²D separations, with differences between experimental and simulated retention times of less than 0.5%. Pharmaceutical applications of this approach for multiple heartcutting 2D-LC were demonstrated using IEC-IEC or achiral RPLC-chiral RPLC for 2D separations of multicomponent mixtures. The framework outlined here should help make 2D-LC method development more systematic and streamline development and optimization for a variety of 2D-LC applications in both industry and academia.

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

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

Surfing on Mobile Phase, Part I: Origins of Mobile-Phase Composition Waves and Their Effects on Detector Baselines

The most commonly used designs for modern liquid chromatography (LC) pumps produce mobile-phase streams with small short-term variations in mobile phase composition. Understanding the origin of these variations and their effects on chromatographic performance can help us develop high-performing methods. In this installment, we focus on the effect of these mobile-phase composition “waves” on detector baselines.

Peak-tracking algorithm for use in comprehensive two-dimensional liquid chromatography - Application to monoclonal-antibody peptides

A peak-tracking algorithm was developed for use in comprehensive two-dimensional liquid chromatography coupled to mass spectrometry. Chromatographic peaks were tracked across two different chromatograms, utilizing the available spectral information, the statistical moments of the peaks and the relative retention times in both dimensions. The algorithm consists of three branches. In the pre-processing branch, system peaks are removed based on mass spectra compared to low intensity regions and search windows are applied, relative to the retention times in each dimension, to reduce the required computational power by elimination unlikely pairs. In the comparison branch, similarity between the spectral information and statistical moments of peaks within the search windows is calculated. Lastly, in the evaluation branch extracted-ion-current chromatograms are utilized to assess the validity of the pairing results. The algorithm was applied to peptide retention data recorded under varying chromatographic conditions for use in retention modelling as part of method optimization tools. Moreover, the algorithm was applied to complex peptide mixtures obtained from enzymatic digestion of monoclonal antibodies. The algorithm yielded no false positives. However, due to limitations in the peak-detection algorithm, cross-pairing within the same peaks occurred and six trace compounds remained falsely unpaired.

Rapid two-dimensional Protein-A size exclusion chromatography of monoclonal antibodies for titer and aggregation measurements from harvested cell culture fluid samples

The success of monoclonal antibody (mAb) therapeutics have increased pharmaceutical investment in mAb production, which has led to a greater demand of technologies to efficiently characterize these biotherapeutics. The large size and heterogeneity of mAbs require the measurement of multiple critical quality attributes (CQAs) during production. The current workflow to measure CQAs of antibodies involves multiple one-dimensional liquid chromatography methods, including Protein-A (ProA), ion-exchange (IEX), reversed-phase, size exclusion (SEC), hydrophilic interaction, and hydrophobic interaction (HIC). Recent advances in commercial two-dimensional liquid chromatography (2D-LC) affords an opportunity to perform two separations at once to measure multiple CQAs in a single assay. Here, we describe the development of a 2D ProA–SEC method using entirely commercially available instrumentation. Each individual separation and the transfer of material between dimensions were optimized to develop a method that measures titer and aggregation of a target antibody from harvested cell culture fluid in under 5 min. We determined the effects of each parameter of the method on mAb recovery and stability, as well as speed, robustness, resolution, and accuracy of the aggregate amount detected in the second dimension (²D). While there are still sources of error caused by hardware limitations, our rapid ProA-SEC method is an effective screening tool with a significant throughput advantage over previously described methods. Additionally, this work serves as a basis for developing other 2D-LC methods with ProA as the first dimension (¹D) separation coupled with different ²D separation, such as ProA-IEX and ProA-HIC.

Implications of dispersion in connecting capillaries for separation systems involving post-column flow splitting

It is common practice in liquid chromatography to split the flow of the effluent exiting the analytical column into two or more parts, either to enable parallel detection (e.g., coupling the separation to two destructive detectors such as light scattering and mass spectrometry (MS)), or to accommodate flow rate limitations of a detector (e.g., electrospray ionization mass spectrometry). In these instances the user must make choices about split ratio and dimensions of connecting tubing that is used between the split point and the detector, however these details are frequently not mentioned in the literature, and rarely justified. In our own work we often split the effluent following the second dimension (²D) column in two-dimensional liquid chromatography systems coupled to MS detection, and we have frequently observed post ²D column peak broadening that is larger than we would expect to result from dispersion in the MS ionization source itself. For the present paper we describe a series of experiments aimed at understanding the impact of the split ratio and post-split connecting tubing dimensions on dispersion of peaks exiting an analytical column. We start with the simple idea - based on the principle of conservation of mass - that analyte peaks entering the split point are split into two parts such that the analyte mass (and thus peak volume) entering and exiting the split point is conserved, and directly related to the ratio of flow rates entering and exiting the split point. Measurements of peak width and variance after the split point show that this simple view of the splitting process - along with estimates of additional dispersion in the post-split tubing - is sufficient to predict peak variances at the detector with accuracy that is sufficient to guide experimental work (median error of about 10% over a wide range of conditions). We feel it is most impactful to recognize that flow splitting impacts apparent post-column dispersion not because anything unexpected happens in the splitting process, but because the split dramatically reduces the volume of the analyte peak, which then is more susceptible to dispersion in connecting tubing that would not cause significant dispersion under conditions where splitting is not implemented. These results will provide practitioners with a solid basis on which rational decisions about split ratios and dimensions of post-split tubing can be made.

LC Troubleshooting Odds and Ends from 2020

Sometimes our approach to troubleshooting specific problems has to change in response to changes in high performance liquid chromatography (HPLC) technology over time. In this installment, we discuss changes in technologies for mobile-phase degassing, silica-based stationary phases, and models for reversed-phase selectivity.

Mapping the Separation Landscape in Two-Dimensional Liquid Chromatography: Blueprints for Efficient Analysis and Purification of Pharmaceuticals Enabled by Computer-Assisted Modeling

Recent developments in two-dimensional liquid chromatography (2D-LC) now make separation and analysis of very complex mixtures achievable. Despite being such a powerful chromatographic tool, current 2D-LC technology requires a series of arduous method development activities poorly suited for a fast-paced industrial environment. Recent introductions of new technologies including active solvent modulation and a support for multicolumn 2D-LC are helping to overcome this stigma. However, many chromatography practitioners believe that the lack of a systematic way to effectively optimize 2D-LC separations is a missing link in securing the viability of 2D-LC as a mainstay for industrial applications. In this work, a computer-assisted modeling approach that dramatically simplifies both offline and online 2D-LC method developments is introduced. Our methodology is based on mapping the separation landscape of pharmaceutically relevant mixtures across both first (¹D) and second (²D) dimensions using LC Simulator (ACD/Labs) software. Retention models for ¹D and ²D conditions were built using a minimal number of multifactorial modeling experiments (2 × 2 or 3 × 3 parameters: gradient slope, column temperature, and different column and mobile phase combinations). The approach was first applied to online 2D-LC analysis involving achiral and chiral separations of complex mixtures of enantiomeric species. In these experiments, the retention models proved to be quite accurate for both the ¹D and ²D separations, with retention time differences between experiments and simulations of less than 3.5%. This software-based concept was also demonstrated for offline 2D-LC purification of drug substances.

Measuring and using scanning-gradient data for use in method optimization for liquid chromatography

The use of scanning gradients can significantly reduce method-development time in reversed-phase liquid chromatography. However, there is no consensus on how they can best be used. In the present work we set out to systematically investigate various factors and to formulate guidelines. Scanning gradients are used to establish retention models for individual analytes. Different retention models were compared by computing the Akaike information criterion and the prediction accuracy. The measurement uncertainty was found to influence the optimum choice of model. The use of a third parameter to account for non-linear relationships was consistently found not to be statistically significant. The duration (slope) of the scanning gradients was not found to influence the accuracy of prediction. The prediction error may be reduced by repeating scanning experiments or - preferably - by reducing the measurement uncertainty. It is commonly assumed that the gradient-slope factor, i.e. the ratio between slopes of the fastest and the slowest scanning gradients, should be at least three. However, in the present work we found this factor less important than the proximity of the slope of the predicted gradient to that of the scanning gradients. Also, interpolation to a slope between that of the fastest and the slowest scanning gradient is preferable to extrapolation. For comprehensive two-dimensional liquid chromatography (LC × LC) our results suggest that data obtained from fast second-dimension gradients cannot be used to predict retention in much slower first-dimension gradients.

Improvements in the predictive accuracy of the hydrophobic subtraction model of reversed-phase selectivity

The hydrophobic subtraction model (HSM) for characterizing the selectivity of reversed-phase liquid chromatography (LC) columns has been used extensively by the LC community since it was first developed in 2002. Continuing interest in the model is due in part to the large, publicly available set of column descriptors that has been assembled over the past 18 years. In the work described in this report, we sought to refine the HSM with the goal of improving the predictive accuracy of the model without compromising its physico-chemical interpretability. The approach taken here has the following facets. A set of retention measurements for 635 columns and the 16 probe solutes used to characterize new columns using the HSM was assembled. Principal components analysis (PCA) was used as a guide for the development of a refined version of the HSM. Several outlying columns (84) were eliminated from the analysis because they were either inconsistent with the PCA model or were outliers from the original HSM model. With the retention dataset for the 16 probe solutes on the remaining 551 columns, we determined that a six-component model is the most sophisticated form of the model that can be used without overfitting the data. In our refined version of the HSM, the S*σ term has been removed. Two new terms have been added, which more accurately account for the molecular volume of the solute (Vv), and the solute dipolarity (Dd), and the remaining terms have been adjusted to accommodate these changes. The refined model described here provides improved prediction of retention factors, with the model standard error being reduced from 1.0 for the original HSM to 0.35 for the refined model (16 solutes, 551 columns). Furthermore, the number of retention factors with errors greater than 10% are reduced from 231 to 25. A revised metric for column similarity, F, is also proposed as a part of this work.

Separation and Identification of Isomeric and Structurally Related Synthetic Cannabinoids Using 2D Liquid Chromatography and High Resolution Mass Spectrometry

Novel psychoactive substances (NPS) are emerging drugs of abuse that are variations of existing compounds intended to cause a CNS psychotropic effect. Some NPS are so comparable in structure and physicochemical properties that they co-elute using traditional single column chromatographic techniques and therefore will not be detected as individual compounds. 2D liquid chromatography (2D-LC) has demonstrated applicability in difficult separations of small molecules and compounds in complex mixtures. It was hypothesized that this technique could also be used to separate co-eluting isomeric and structurally related, non-isomeric NPS, including synthetic cannabinoids (SC). Initial studies assessed several parameters, including column type, mobile phase, analysis time, gradient and flow rate, to optimize a 2D-LC method for separation and analysis of SC. The final comprehensive on-line 2D-LC method employed a Bonus-RP column in the first dimension (1D) coupled with UV detection and a biphenyl column in the second dimension (2D) coupled with QTOF-MS detection in full scan positive mode. To test the utility of the method, three SC mixes were created, each containing five compounds that were unresolvable in a traditional, 1D-LC separation; one mix with isomeric compounds and two with structurally related but non-isomeric compounds. Contour plots of UV absorbance in 1D and MS ion intensity in 2D demonstrated that all components in each mixture were successfully resolved using the 2D-LC separation method. This research serves as proof-of-concept for the application of 2D-LC to the separation of isomeric and structurally related SC. With further optimization and validation, 2D-LC may be a generally useful tool for separation of complex mixtures of NPS.

Comparison of short- and long-term exposure effects of cruciferous and apiaceous vegetables on carcinogen metabolizing enzymes in Wistar rats

Cruciferous and apiaceous vegetables may be chemopreventive due to their ability to modulate carcinogen-metabolizing enzymes but whether the effects on such enzymes are sustained over time is unknown. To examine the short- and long-term effects of the vegetables, rats were fed one of four diets for 7, 30, or 60 d: AIN-93G, CRU (21% cruciferous vegetables-fresh broccoli, green cabbage, watercress), API (9% apiaceous vegetables - fresh parsnips, celery), or API + CRU (10.5% CRU + 4.5% API). Although CRU increased activity and protein expression of cytochrome P450 (CYP) 1A1 and CYP1A2 after 7 d, only activity was sustained after 30 and 60 d. There was a trend towards an interaction between the length of feeding period and CRU for CYP1A1 activity; activity increased with greater time of feeding. API increased CYP1A2 activity but decreased sulfotransferase 1A1 activity after 7 d, although not at later times. Altogether, increased CYP1A activity by CRU was maintained with long term feeding while protein amount decreased, suggesting influence by mechanisms other than, or in addition to, transcriptional regulation. Thus, response patterns and interactions with length of feeding may differ, depending upon the types of vegetables and enzymes, requiring caution when interpreting the results of short-term feeding studies.

Comparison of originator and biosimilar therapeutic monoclonal antibodies using comprehensive two-dimensional liquid chromatography coupled with time-of-flight mass spectrometry

As research, development, and manufacturing of biosimilar protein therapeutics proliferates, there is great interest in the continued development of a portfolio of complementary analytical methods that can be used to efficiently and effectively characterize biosimilar candidate materials relative to the respective reference (i.e., originator) molecule. Liquid phase separation techniques such as liquid chromatography and capillary electrophoresis are powerful tools that can provide both qualitative and quantitative information about similarities and differences between reference and biosimilar materials, especially when coupled with mass spectrometry. However, the inherent complexity of these protein materials challenges even the most modern one-dimensional (1D) separation methods. Two-dimensional (2D) separations present a number of potential advantages over 1D methods, including increased peak capacity, 2D peak patterns that can facilitate unknown identification, and improvement in the compatibility of some separation methods with mass spectrometry. In this study, we demonstrate the use of comprehensive 2D-LC separations involving cation-exchange (CEX) and reversed-phase (RP) separations in the first and second dimensions to compare 3 reference/biosimilar pairs of monoclonal antibodies (cetuximab, trastuzumab and infliximab) that cover a range of similarity/disimilarity in a middle-up approach. The second dimension RP separations are coupled to time-of-flight mass spectrometry, which enables direct identification of features in the chromatograms obtained from mAbs digested with the IdeS enzyme, or digestion with IdeS followed by reduction with dithiothreitol. As many as 23 chemically unique mAb fragments were detected in a single sample. Our results demonstrate that these rich datasets enable facile assesment of the degree of similarity between reference and biosimilar materials.

Retention projection enables accurate calculation of liquid chromatographic retention times across labs and methods

Identification of small molecules by liquid chromatography-mass spectrometry (LC-MS) can be greatly improved if the chromatographic retention information is used along with mass spectral information to narrow down the lists of candidates. Linear retention indexing remains the standard for sharing retention data across labs, but it is unreliable because it cannot properly account for differences in the experimental conditions used by various labs, even when the differences are relatively small and unintentional. On the other hand, an approach called "retention projection" properly accounts for many intentional differences in experimental conditions, and when combined with a "back-calculation" methodology described recently, it also accounts for unintentional differences. In this study, the accuracy of this methodology is compared with linear retention indexing across eight different labs. When each lab ran a test mixture under a range of multi-segment gradients and flow rates they selected independently, retention projections averaged 22-fold more accurate for uncharged compounds because they properly accounted for these intentional differences, which were more pronounced in steep gradients. When each lab ran the test mixture under nominally the same conditions, which is the ideal situation to reproduce linear retention indices, retention projections still averaged 2-fold more accurate because they properly accounted for many unintentional differences between the LC systems. To the best of our knowledge, this is the most successful study to date aiming to calculate (or even just to reproduce) LC gradient retention across labs, and it is the only study in which retention was reliably calculated under various multi-segment gradients and flow rates chosen independently by labs.