Predictive Elution Window Stretching and Shifting as a Generic Search Strategy for Automated Method Development for Liquid Chromatography

Performance of global retention models in the optimisation of the liquid chromatographic separation (II): Complex multi-analyte samples

BACKGROUND

Enhancing the quality control of medicinal plants is a complex challenge due to their rich variety of chemical compounds present at varying and extreme concentrations. Chromatographic fingerprints, which have become essential for characterising these complex natural materials, require achieving optimal separation conditions to effectively maximise the number of detected peaks. The challenges in optimising fingerprints and other complex multi-analyte samples include the unavailability of standards, the presence of unknown constituents and the substantial workload that would require conventional optimisation methods based on models.

RESULTS

This work introduces an interpretive optimisation approach which operates on the premise of predicting chromatograms using global models. Initially, a multi-linear gradient experimental design is sequentially executed to accommodate all peaks in the chromatogram in an adequate time window. Following this, a small set of sample peaks (reference peaks) is selected based on their consistent traceability across all chromatograms in the design. Using this reference dataset, a global model is constructed, initially focused solely on the reference peaks and later extended to encompass all detected peaks in the sample. The aim is to find gradients that maximise resolution while minimising analysis time. These optimised gradients are applied successfully to enhance the separation of medicinal plant extracts, with particular emphasis on peppermint and pennyroyal extracts.

SIGNIFICANCE

The proposed optimisation relying on global models can be applied to highly complex samples even in the absence of standards, or in cases where standards are available but their use is impractical due to workload constraints. Moreover, in discerning the most promising gradients for highly complex samples, peak purity has demonstrated superior reliability and competitiveness compared to peak capacity as chromatographic objective function.

Quantitative description of the quality of size exclusion chromatography separations

Size exclusion chromatography (SEC) is unique among chromatographic methods as it allows separation of non-retained analytes. However, such mechanism often put an analytical scientist in front of relatively poorly resolved set of peaks that may have strikingly different abundance. The description of such chromatograms needs a particular approach to accurately capture the overall quality of separation. Consequently, use of a single parameter description may not be accurate enough and therefore we introduce a dimensionless separation quality factor, which is based on five SEC specific measures (peak-to-valley, elution window width, peak widths, peak-positioning and recovery). Combining several factors allowed detailed differentiation of various simulated separations, clearly correlating column characteristics with specific contributions to separation quality whether they concern a single peak pair or entire peak landscape. The method could be further elaborated by the addition of normalized priority weighting allowing for flexible quality quantification of a relevant portion of real-life nucleic acid separation on different columns. With growing complexity of biotherapeutics to be separated, such a term is predicted to be a useful response function for purposes of factorial method optimization.

A new chromatographic response function with automatically adapting weight factor for automated method development

A critical factor for automated method development in chromatography is the maximization or minimization of an objective function describing the quality (and speed) of the separation. In chromatography, this function is commonly referred to as a chromatographic response function (CRF). Many CRFs have previously been introduced, but many have unfavourable properties such as featuring multiple optima, insufficient discriminatory power, and a too strong dependence on the weight factors needed to balance resolution and time penalty components. To overcome these problems, the present study introduces a new type of CRF wherein the relative weight of the time penalty term is a self-adaptive function of the separation quality. The ability to unambiguously identify the optimal gradient settings of this newly proposed CRF is compared to that of some of the most frequently used CRFs in a study covering 100 randomly composed in silico samples. Doing so, the new CRF is found to flawlessly lead to the correct solution (=linear gradient parameters providing the highest resolution in the shortest potential time) in 100 % of the cases, while the most frequently used literature CRFs were off-target for about 50 to 60 % of the samples, even when considering the availability of spectral peak shape data. Some slight alterations to the proposed CRF are introduced and discussed as well.

Computer-assisted multifactorial method development for the streamlined separation and analysis of multicomponent mixtures in (Bio)pharmaceutical settings

The (bio)pharmaceutical industry is rapidly moving towards complex drug modalities that require a commensurate level of analytical enabling technologies that can be deployed at a fast pace. Unsystematic method development and unnecessary manual intervention remain a major barrier towards a more efficient deployment of meaningful analytical assay across emerging modalities. Digitalization and automation are key to streamline method development and enable rapid assay deployment. This review discusses the use of computer-assisted multifactorial chromatographic method development strategies for fast-paced downstream characterization and purification of biopharmaceuticals. Various chromatographic techniques such as reversed-phase liquid chromatography (RPLC), hydrophilic interaction liquid chromatography (HILIC), ion exchange chromatography (IEX), hydrophobic interaction chromatography (HIC), and supercritical fluid chromatography (SFC) are addressed and critically reviewed. The most significant parameters for retention mechanism modelling, as well as mapping the separation landscape for optimal chromatographic selectivity and resolution are also discussed. Furthermore, several computer-assisted approaches for optimization and development of chromatographic methods of therapeutics, including linear, nonlinear, and multifactorial modelling are outlined. Finally, the potential of the chromatographic modelling and computer-assisted optimization strategies are also illustrated, highlighting substantial productivity improvements, and cost savings while accelerating method development, deployment and transfer processes for therapeutic analysis in industrial settings.

Automated method development in high-pressure liquid chromatography

Method development in liquid chromatography is a crucial step in the optimization of analytical separations for various applications. However, it is often a challenging endeavour due to its time-consuming, resource intensive and costly nature, which is further hampered by its complexity requiring highly skilled and experienced scientists. This review presents an examination of the methods that are required for a completely automated method development procedure in liquid chromatography, aimed at taking the human out of the decision loop. Some of the presented approaches have recently witnessed an important increase in interest as they offer the promise to facilitate, streamline and speed up the method development process. The review first discusses the mathematical description of the separation problem by means of multi-criteria optimization functions. Two different strategies to resolve this optimization are then presented; an experimental and a model-based approach. Additionally, methods for automated peak detection and peak tracking are reviewed, which, upon integration in an instrument, allow for a completely closed-loop method development process. For each of these approaches, various currently applied methods are presented, recent trends and approaches discussed, short-comings pointed out, and future prospects highlighted.

Theory of separation performance and peak width in gradient elution liquid chromatography: A tutorial

Separation performance in chromatography has been extensively studied since the dawn of the technique. Although the basic principles of band broadening and the resulting separation performance in isocratic elution are in general well known and understood, this is much less the case for gradient separations. In this tutorial, first the basic principles, concepts and parameters that determine separation performance, peak width and variance and analysis time in isocratic separations are reviewed. This is subsequently used to discuss the parameters that affect peak width in gradient elution, together with the concepts of plate count and plate height in this elution mode. In addition, the effect of peak compression in gradient elution is elaborated. Finally, the effect of extra-column dispersion on separation performance in gradient elution is discussed, and an overview of how these contributions can be experimentally evaluated is given.

Retention prediction of monoamine neurotransmitters in gradient liquid chromatography

Retention prediction of monoamine neurotransmitters has been compared for the generally applied linear solvent-strength model and quadratic polynomial three-parameter model. The design of experiments protocol has been applied to plan linear gradients within the experimental space with altered gradient time, mobile phase flowrate, and column temperature. Relative prediction errors increased at elevated temperature, which is more significant for the linear solvent-strength model when compared to the polynomial model. On the other hand, the predefined design of experiments space controls the retention time errors, as predictions for LC conditions that are outside of the plan are much less accurate and should be avoided. The final part of the work deals with the effect of extracolumn band dispersion on the peak capacity of linear gradients at various gradient times, mobile phase flowrates, and column temperature. The peak capacity determined for corrected experimental data were consistent with the published results dealing with the optimization of peak capacity in gradient elution. This article is protected by copyright. All rights reserved.

Development of a retention prediction model in ion-pair reversed-phase HPLC for nucleoside triphosphates used as mRNA vaccine raw materials

The International Conference on Harmonization guidelines for quality on pharmaceutical development recommends a systematic development approach including robustness studies which assure performance of manufacturing and analytical method development of drug product. It was demonstrated that the retention prediction model for nucleoside triphosphates (NTPs) on ion-pair reversed-phase HPLC was developed by a highly accurate Kawabe's model which supports the development of robust HPLC methods. As NTPs and its derivatives are typically used for Messenger ribonucleic acid (mRNA) vaccine production, adenosine-5'-triphosphate (ATP), guanosine-5'-triphosphate (GTP), cytidine-5'-triphosphate (CTP), 5-methylcytidine-5'-triphosphate (m5-CTP), uridine-5'-triphosphate (UTP), 5-methyluridine-5'-triphosphate (m5-UTP), pseudouridine-5'-triphosphate (Ψ-UTP) and N1-methylpseudouridine-5'-triphosphate (m1Ψ-UTP) were applied for prediction model development. By a comparison of the predicted retention factor in eight studied samples with the retention factor measured under six isocratic conditions, the absolute prediction error was 0.075 and also the prediction error (%) was 2.70%. In practical examples, analytical method for residual ATP, GTP, CTP, and m1Ψ-UTP in the commercial mRNA-based drugs and purity method for UTP derivatives were optimized by QbD approach. The design space for the minimum resolution between adjacent peaks was simulated with the models developed to evaluate the robustness of peak separation, and the optimal mobile phase condition was also simulated. As a conclusion, the desired peak was successfully separated under the optimized condition, and we thought that these retention models could optimize the mobile phase condition of the NTP analysis method for applying to various quality tests, such as quantity, purity and identity test for NTPs and its derivates in the mRNA-based drugs.

The development of retention time prediction model using multilinear gradient profiles of seven pharmaceuticals

The ICH guidance on pharmaceutical development recommends a systematic development approach including robustness studies which assure performance of manufacturing and analytical method development of drug product. The retention model by T. Kawabe et al have an excellent correlation between observed and predicted retention time in various kinds of pharmaceutical compounds during isocratic elution by the multiple regression modeling of solvent strength parameters. However, it cannot be successfully applied to the predictability of the retention time during multilinear gradient elution and also it does not consider the instrument dependent parameters such as dwell volume. The current study demonstrated that the solution of the fundamental gradient elution equation was applied to T. Kawabe's retention time prediction model to predict the retention time using a multilinear gradient profile with taking the delay volume of HPLC system into account. Seven pharmaceutical compounds were used for evaluation of prediction models for retention time. The predicted retention time was compared with the measured retention time obtained by several multilinear gradient using two HPLC systems with different dwell volume. The evaluated prediction error (%) was 1.10 % and 1.54 % with H-Class and Nexera XR HPLC systems, respectively. In order to evaluate the robustness of the analytical method and to set the system suitability test (SST) for proper method performance, the design space for the ACN/MeOH mixture ratio in the total organic solvent and the full width at half maximum (FWHM) relationship to the minimum resolution was simulated by the developed retention time prediction. The optimized condition of the ACN/MeOH mixture ratio, the acceptance criterion of the SST for achieving the robust separation was estimated based on the simulated design space. As a conclusion, the developed retention time prediction will be useful during analytical method transfer among different manufacturing/analytical sites of the pharmaceuticals with different HPLC systems.

Negative gradient slope methods to improve the separation of closely eluting proteins

In the present work, we describe the fundamental and practical advantages of a new strategy to improve the resolution of very closely eluting peaks within therapeutic protein samples. This approach involves the use of multiple isocratic steps, together with the addition of a steep negative gradient segment (with a decrease in mobile phase strength) to "park" a slightly more retained peak somewhere along the column (at a given migration distance), while a slightly less retained compound can be eluted. First, some model calculations were performed to highlight the potential of this innovative approach. For this purpose, the retention parameters (logk₀ and S) for two case studies were considered, namely the analysis of a mixture of two therapeutic mAbs (simple to resolve sample) and separation of a therapeutic mAb from its main variant (challenging to resolve sample). The results confirm that the insertion of a negative segment into a multi-isocratic elution program can be a good tool to improve selectivity between critical peak pairs. However, it is also important to keep in mind that this approach only works with large solutes, which more or less follow an "on-off" type elution behavior. Two real applications were successfully developed to illustrate the practical advantage of this new approach, including the separation of a therapeutic mAb from its main variant possessing very close elution behavior, and the separation of a carrier protein from an intact mAb as might be encountered in a quantitative bioanalysis assay. These two examples demonstrate that improved selectivity can be achieved for protein RPLC through the inclusion of a negative gradient slope that selectively bifurcates the elution of two or more peaks of interest.

Recent applications of retention modelling in liquid chromatography

Recent applications of retention modelling in liquid chromatography (2015–2020) are comprehensively reviewed. The fundamentals of the field, which date back much longer, are summarized. Retention modeling is used in retention‐mechanism studies, for determining physical parameters, such as lipophilicity, and for various more‐practical purposes, including method development and optimization, method transfer, and stationary‐phase characterization and comparison. The review focusses on the effects of mobile‐phase composition on retention, but other variables and novel models to describe their effects are also considered. The five most‐common models are addressed in detail, i.e. the log‐linear (linear‐solvent‐strength) model, the quadratic model, the log–log (adsorption) model, the mixed‐mode model, and the Neue–Kuss model. Isocratic and gradient‐elution methods are considered for determining model parameters and the evaluation and validation of fitted models is discussed. Strategies in which retention models are applied for developing and optimizing one‐ and two‐dimensional liquid chromatographic separations are discussed. The review culminates in some overall conclusions and several concrete recommendations.

Application of evolutionary algorithms to optimise one- and two-dimensional gradient chromatographic separations

We report on the performance of three classes of evolutionary algorithms (genetic algorithms (GA), evolution strategies (ES) and covariance matrix adaptation evolution strategy (CMA-ES)) as a means to enhance searches in the method development spaces of 1D- and 2D-chromatography. After optimisation of the design parameters of the different algorithms, they were benchmarked against the performance of a plain grid search. It was found that all three classes significantly outperform the plain grid search, especially in terms of the number of search runs needed to achieve a given separation quality. As soon as more than 100 search runs are needed, the ES algorithm clearly outperforms the GA and CMA-ES algorithms, with the latter performing very well for short searches (<50 search runs) but being susceptible to convergence to local optima for longer searches. It was also found that the performance of the ES and GA algorithms, as well as the grid search, follow a hyperbolic law in the large search run number limit, such that the convergence rate parameter of this hyperbolic function can be used to quantify the difference in required number of search runs for these algorithms. In agreement with one's physical expectations, it was also found that the general advantage of the GA and ES algorithms over the grid search, as well as their mutual performance differences, grow with increasing difficulty of the separation problem.

Separation Optimization of a Mixture of Ionized and Non-Ionized Solutes under Isocratic and Gradient Conditions in Reversed-Phase HPLC by Means of Microsoft Excel Spreadsheets

Τhe crucial role of mobile phase pH for optimizing the separation of a mixture of ionized and non-ionized compounds on a Phenomenex extended pH-range reversed-phase column (Kinetex 5 µm EVO C18) was examined. A previously developed Excel-spreadsheet-based software was used for the whole separation optimization procedure of the sample of interest under isocratic conditions as well as under single linear organic modifier-gradients in different eluent pHs. The importance and the advantages of performing a computer-aided separation optimization compared with a trial-and-error optimization method were realized. Additionally, this study showed that the optimized separation conditions for a given stationary phase may be used to achieve successful separations on new columns of the same type and size. In general, the results of this work could give chromatographers a feel of confidence to establish desired separations of a mixture of ionizable and neutral compounds in reversed-phase columns.

Computer assisted liquid chromatographic method development for the separation of therapeutic proteins

This review summarizes the use of computer assisted liquid chromatographic method development for the analytical characterization of protein biopharmaceuticals.

Recent progress in the fundamental understanding of hydrophilic interaction chromatography (HILIC)

With the exponential growth in the application of the HILIC technique, there has been a significant progress in understanding the fundamental aspects of hydrophilic interaction chromatography.

Use of individual retention modeling for gradient optimization in hydrophilic interaction chromatography: separation of nucleobases and nucleosides

In this study, the separation of twelve nucleobases and nucleosides was optimized via chromatogram simulation (i.e., prediction of individual retention times and estimation of the peak widths) with the use of an empirical (reversed-phase) non-linear model proposed by Neue and Kuss. Retention time prediction errors of less than 2% were observed for all compounds on different stationary phases. As a single HILIC column could not resolve all peaks, the modeling was extended to coupled-column systems (with different stationary phase chemistries) to increase the separation efficiency and selectivity. The analytical expressions for the gradient retention factor on a coupled column system were derived and accurate retention time predictions were obtained (<2% prediction errors in general). The optimized gradient (predicted by the optimization software) included coupling of an amide and an pentahydroxy functionalized silica stationary phases with a gradient profile from 95 to 85%ACN in 6 min and resulted in almost baseline separation of the twelve nucleobases and nucleosides in less than 7 min. The final separation was obtained in less than 4h of instrument time (including equilibration times) and was fully obtained via computer-based optimization. As such, this study provides an example of a case where individual retention modeling can be used as a way to optimize the gradient conditions in the HILIC mode using a non-linear model such as the Neue and Kuss model.