Design of optimized high-performance liquid chromatographic gradients for the separation of either small or large molecules

New trends in reversed-phase liquid chromatographic separations of therapeutic peptides and proteins: theory and applications

In the pharmaceutical field, there is considerable interest in the use of peptides and proteins for therapeutic purposes. There are various ways to characterize such complex samples, but during the last few years, a significant number of technological developments have been brought to the field of RPLC and RPLC-MS. Thus, the present review focuses first on the basics of RPLC for peptides and proteins, including the inherent problems, some possible solutions and some directions for developing a new RPLC method that is dedicated to biomolecules. Then the latest advances in RPLC, such as wide-pore core-shell particles, fully porous sub-2 μm particles, organic monoliths, porous layer open tubular columns and elevated temperature, are described and critically discussed in terms of both kinetic efficiency and selectivity. Numerous applications with real samples are presented that confirm the relevance of these different strategies. Finally, one of the key advantages of RPLC for peptides and proteins over other historical approaches is its inherent compatibility with MS using both MALDI and ESI sources.

Simple algorithms for fitting and optimisation for multilinear gradient elution in reversed-phase liquid chromatography

The theory of the multilinear gradient elution in reversed-phase liquid chromatography (RP-HPLC) presented in [P. Nikitas, A. Pappa-Louisi, P. Agrafiotou, J. Chromatogr. A 1120 (2006) 299] is modified to increase its flexibility. In addition, it is embodied to simple algorithms for fitting gradient data and especially for resolution optimisation under multilinear gradient conditions. In particular, two new algorithms for fitting and one for optimisation are tested and compared with conventional algorithms. Their performance was examined using 13 o-phthalaldehyde (OPA) derivatives of amino acids with mobile phases modified by acetonitrile. It was found that the new proposed algorithms, a repeated application of the Levenberg-Marquardt (LM) method for fitting (R_LM) and a modified descent algorithm for optimisation (RND_D), in combination with the modified theory of the multilinear gradient elution can lead to high quality predictions of the retention times and optimisation results.

Models and objective functions for the optimisation of selectivity in reversed-phase liquid chromatography

Interpretive methodologies are the most efficient tools for finding the optimal conditions in chromatography. These methodologies are supported by models or algorithms able to infer the system behaviour upon changes in the experimental factors. Once the models are built with data obtained from sets of carefully designed experiments, molecular modelling or other approaches, they can be applied to predict the performance of new conditions. The different elements involved in these methodologies, for both isocratic and gradient elution, are given. Special attention is devoted to the description of retention, owing to its major impact on the prediction of chromatographic resolution. Several models considering the main factors affecting retention (i.e. organic modifiers, pH and temperature), and procedures that enhance the predictions, are presented. Both the existence of skewed peaks and the effect of elution conditions on peak profiles are considered. Finally, the assessment of resolution, as well as other secondary aims that affect the practical suitability of the optimal conditions, is discussed.

Computer-assisted transfer of programmed elutions in reversed-phase high-performance liquid chromatography

Computer-assisted procedures were used to simulate modifications in chromatograms caused by the transfer of elution programmes between instruments with significantly different dwell volumes. Moreover, for the first time the same approach was used to modify the elution programmes to match the chromatograms produced in the different instruments. The process may consist of making minor modifications to gradient programmes or transforming the original gradient programme into a stepwise gradient profile and/or the simultaneous programming of flow and solvent composition. The combination of these approaches has been shown to have an enormous potential for producing matched chromatograms in instrumental systems with dwell volumes that differ by several millilitres. The efficiency and robustness of the proposed procedure is demonstrated with a variety of compounds (two different mixtures of 10 and 11 analytes), mobile phases (methanol and acetonitrile gradients), flow rates (0.5-1.5 mL/min range), temperatures (35-45 degrees C interval) and gradient profiles (linear, multilinear, curved and stepwise).

Multilinear gradient elution optimisation in reversed-phase liquid chromatography using genetic algorithms

The treatment presented in a recent paper [P. Nikitas, A. Pappa-Louisi, J. Chromatogr. A, 1068 (2005) 279] is extended to multilinear gradients, i.e. continuous gradients consisting of a certain number of linear portions. Thus, the experimental lnk versus phi curve, where k is the retention factor of a sample solute under isocratic conditions and phi is the volume fraction of the organic modifier in the water-organic mobile phase, is subdivided into a finite number of linear portions resulting in simple analytical expressions for the solute gradient retention time. These expressions of the retention time are directly used in an optimisation technique based on genetic algorithms. This technique involves first the determination of the theoretical dependence of k upon phi by means of gradient measurements, which in turn is used by the genetic algorithm for the prediction of the best gradient profile. The validity of the analytical expressions and the effectiveness of the optimisation technique were tested using fifteen underivatized amino acids and related compounds with mobile phases modified by acetonitrile. It was found that the adopted methodology exhibits significant advantages and it can lead to high quality predictions of the gradient retention times and optimisation results.

A practical approach to transferring linear gradient elution methods

Attempts to theoretically address the problems involved in transferring linear gradient elution methods have been somewhat ad hoc due to the simplifying assumptions usually made in conventional gradient elution theory. Until now, all equations based on the k* parameter of linear gradient elution theory used as the basis for predicting the separation selectivity have not explicitly included the effect of the dwell volume (VD). Using an exact equation for predicting k*, that is, one which fully accounts in an a priori fashion for VD, we find a set of simple yet exact equations which unequivocally must be satisfied to transfer an optimized linear gradient elution method from one system (column or instrument or both) to another. These relationships absolutely mandate that a change in the instrument dwell volume requires a proportional change in the column volume; in turn, a change in the column volume requires a proportional change in the flow rate and/or gradient time to maintain a constant gradient steepness. Although we are not the first to suggest these guidelines, this work provides a complete theoretical foundation for these exact guidelines for the maintenance of gradient selectivity for the case of transferring a linear gradient elution method between different columns packed with the same particles and/or between different instruments.

New approach to linear gradient elution used for optimisation in reversed-phase liquid chromatography

A new mathematical treatment concerning the gradient elution in reversed-phase liquid chromatography when the volume fraction psi of an organic modifier in the water-organic mobile phase varies linearly with time is presented. The experimental ln k versus psi curve, where k is the retention factor under isocratic conditions in a binary mobile phase, is subdivided into a finite number of linear portions and the solute gradient retention time tR is calculated by means of an analytical expression arising from the fundamental equation of gradient elution. The validity of the proposed analytical expression and the methodology followed for the calculation of tR was tested using eight catechol-related solutes with mobile phases modified by methanol or acetonitrile. It was found that in all cases the accuracy of the predicted gradient retention times is very satisfactory because it is the same with the accuracy of the retention times predicted under isocratic conditions. Finally, the above method for estimating gradient retention times was used in an optimisation algorithm, which determines the best variation pattern of psi that leads to the optimum separation of a mixture of solutes at different values of the total elution time.

Optimisation technique for stepwise gradient elution in reversed-phase liquid chromatography

An optimisation technique of reversed-phase liquid chromatographic separations based on gradient elution with a stepwise variation pattern of the volume fraction phi of the organic modifier in the water-organic mobile phase is presented. It uses a non-linear least-squares programme with a Monte-Carlo search for initial estimates in order to determine the best variation pattern that leads to the optimum separation of a mixture of solutes. The validity of the above methodology was tested by separating eight catechol-related solutes with mobile phases modified by methanol or acetonitrile and variation patterns of two, three or four steps in the psi values. It was found in all cases a very satisfactory accuracy of the predicted gradient elution times, which is of the same order with the accuracy of the retention times predicted under isocratic or linear gradient conditions. In addition, it was shown that the proposed optimisation technique is both effective and flexible but well-shaped chromatograms are obtained under electrochemical detection only if steps with increasing psi are used and the change in psi is programmed to occur at the intermediate of the predicted peaks.

Enhanced calculation of optimal gradient programs in reversed-phase liquid chromatography

The resolution of a mixture of 16 beta-blockers under gradient elution was optimised using both isocratic and gradient training sets, with a reversed-phase column and acetonitrile-water eluents. Error theory was applied to measure the information extracted from different gradient experimental designs. This allows checking the expected accuracy when gradient predictions exceed the initial solvent concentrations tested in the training set. This work applies the results on modelling found in a previous study [J. Chromatogr. A 1018 (2003) 169] where the performance of several retention models was compared. Enhanced retention predictions were applied to the optimisation of gradient programs involving three factors (gradient slope, initial solvent composition and gradient curvature), using the peak purity criterion as resolution assessment. Peak shape parameters required in peak purity evaluation were modelled by adapting previous developments in isocratic mode. The mixture, which required prohibitive analysis times under isocratic elution, was almost baseline resolved in less than 35 min with linear gradients. Curvilinear gradients did not enhance this result significantly.

Peptide mapping by reversed-phase high-performance liquid chromatography employing silica rod monoliths

In this paper, a general procedure is described for the generation of peptide maps of proteins with monolithic silica-based columns. The peptide fragments were obtained by tryptic digestion of various cytochrome c species with purification of the tryptic fragments achieved by reversed-phase high-performance liquid chromatographic methods. Peak assignment of the various peptides was based on evaluation of the biophysical properties of the individual peptides and via mass spectrometric identification. The performance of several different monolithic sorbents prepared as columns of identical cross-sectional dimensions were investigated as part of these peptide mapping studies and the data evaluated by applying solvent strength theory. These studies revealed curvilinear dependencies in the corresponding relative resolution maps. These findings directly impact on the selection of specific sorbent types or column configurations for peptide separations with silica rod monoliths. Moreover, the influence of variations in the amino acid sequence of the cytochrome cs were evaluated with respect to their effect on intrinsic hydrophobicity, the number of experimental observed tryptic cleavage sites, detection limits of the derived fragments in relation to their molecular size, and the chromatographic selectivity and resolution of the various peptides obtained following enzymatic fragmentation of the parent protein. Finally, the scope of these approaches in method development was examined in terms of robustness and efficiency.

Computerized design of separation strategies by reversed-phase liquid chromatography: development of DryLab software

The development of DryLab software is a special achievement in analytical HPLC which took place in the last 16 years. This paper tries to collect some of the historical mile stones and concepts. DryLab, being always subject to change according to the needs of the user, never stopped being developed. Under the influence of an ever changing science market, the DryLab development team had to consider not just scientific improvements, but also new technological achievements, such as the introduction of Windows 1.0 and 3.1, and later Windows NT and 2000. The recent availability of new 32-bit programming tools allowed calculations of chromatograms to be completed more quickly so as to show peak movements which result for example from slight changes in eluent pH. DryLab is a great success of interdisciplinary and intercontinental cooperation by many scientists.

HPLC of peptides and proteins: standard operating conditions

The standard operating conditions for the eight basic modes of HPLC are presented in this unit. They include: size-exclusion chromatography (HP-SEC), ion-exchange chromatography (HP-IEX), normal phase chromatography (HP-NPC), hydrophobic interaction chromatography (HP-HIC), reversed-phase chromatography (RP-HPLC), hydrophilic interaction chromatography (HP-HILIC), immobilized metal ion affinity chromatography (HP-IMAC), and biospecific/biomimetic affinity chromatography (HP-BAC). In addition, some subsets of these chromatographic modes, e.g., mixed mode chromatography (HP-MMC), charge transfer chromatography (HP-CTC), or ligand-exchange chromatography (HP-LEC) are described. Procedures for multimodal column switching are also included, as are guidelines for a systematic approach to method development. Example separations help illustrate the procedures. The standard operating conditions for the eight basic modes of HPLC are presented in this unit.

Computer-assisted high-performance liquid chromatography method development with applications to the isolation and analysis of phytoplankton pigments

We used chromatography modeling software to assist in HPLC method development, with the goal of enhancing separations through the exclusive use of gradient time and column temperature. We surveyed nine stationary phases for their utility in pigment purification and natural sample analysis. For purification, a complex algal matrix was separated on an efficient monomeric column, from which partially purified fractions were collected and purified on polymeric columns that exaggerated resolution between pigments of interest. Additionally, we feature an HPLC method that is simple, fast, demonstrates excellent transferability and is ideal for quantitative analysis of pigments in dilute natural water samples.

Reversed-phase liquid chromatographic separation of complex samples by optimizing temperature and gradient time III. Improving the accuracy of computer simulation

Previous studies have shown that four experimental runs, where both temperature T and gradient time tG are varied, can be used for the reliable prediction of separation as a function of these two variables (two-dimensional optimization). Computer simulation (e.g., DryLab) can then be used to predict "optimized" conditions for maximum sample resolution using either isocratic or gradient elution. Samples that contain a large number of components (e.g., n>15-20) present a greater challenge. Resolution for these more complex samples is often quite sensitive to small changes in T or tG in turn requiring greater accuracy in predictions that result from computer simulation. In the present study of several samples, we have examined computer simulation errors that can arise from inexact expressions for retention time as a function of T, tG or isocratic %B. Resulting conclusions are applicable to both complex and simpler samples, in either one- or two-dimensional optimization. Means to anticipate and minimize the impact of these predictive errors are examined.

Systematic, computer-assisted optimisation of the isolation of Thermus thermophilus 50S ribosomal proteins by reversed-phase high-performance liquid chromatography

Isolation of the 50S ribosomal proteins from Thermus thermophilus has been achieved for the first time using reversed-phase high-performance liquid chromatography based on the use of the non-end-capped LiChrospher RP-18 sorbent and computer-assisted method development for optimisation of the resolution. The separation approach for these basic ribosomal proteins utilised mobile phases of high ionic strength, to suppress silanophilic interactions with this type of reversed-phase sorbent. These conditions were found to be a key requirement for achieving good resolution with minimal peak-tailing. The retention times of the 50S ribosomal proteins of Thermus thermophilus were observed to be in very close agreement with the values predicted by computer simulation procedures based on linear solvent strength concepts, with an average error of only 0.5%, whilst base-line resolution was achieved for most of the adjacent peak zones. Following N-terminal sequencing, the proteins TthL5, TthL9, TthL18, TthL24, TthL29, TthL32, TthL34, TthL35 and TthL36 of Thermus thermophilus were readily identified. This approach thus provided a readily optimised strategy for the isolation of the 50S ribosomal proteins from Thermus thermophilus and should be generally applicable to the corresponding ribosomal proteins from various other species, as well as other classes of basic proteins present in crude extracts derived from other biological sources.

Simultaneous variation of temperature and gradient steepness for reversed-phase high-performance liquid chromatography method development. I. Application to 14 different samples using computer simulation

The optimized reversed-phase HPLC separation of 14 different samples is reported, based on simultaneous changes in temperature and gradient steepness. Four experimental runs are required for each sample, following which preferred conditions can be predicted using computer simulation software (DryLab). The overall accuracy and effectiveness of this method development approach is discussed, with particular attention to the use of resolution maps provided by the software. These maps are useful for maximizing resolution for the total sample, for optimizing the separation of a smaller number of selected sample compounds, and as an initial step in the separation of more demanding samples.

Combined use of temperature and solvent strength in reversed-phase gradient elution. I. Predicting separation as a function of temperature and gradient conditions

It has been shown previously that computer simulation based on two initial experiments can predict separation in reversed-phase gradient elution as a function of gradient conditions (gradient steepness, gradient range and gradient shape) and column conditions (column length, flow-rate and particle size). The present study extends this capability for changes in temperature. Four initial experiments (two different gradient times, two different temperatures) provide input data that allow predictions of separation as a function of temperature as well as gradient and column conditions. A semi-empirical relationship, tR = a + bT, is able to relate gradient retention time tR to column temperature T (other conditions constant). The accuracy of this approach has been evaluated for 102 solutes and a variety of experimental conditions, including the use of five different HPLC instruments (four different models).

Experimental models for optimization of insulin separation on reversed phase columns

Experimentally defined relationships have been found to describe adequately the retention and separation of bovine and porcine insulins as well as their desamido products on reversed phases C4 30 nm and C18 10 nm pore diameter. The equations are valid for a region of initial acetonitrile concentrations from 16 to 31% and gradient rates from 0.04 to 0.60%/min. The peak heights showed an exact non-linear relationship with the time interval between the first and last peak of interest, independent of their retention time. The number of experiments required for obtaining the parametric estimates of the models depends on the particular task, but in all cases is less than eight. The relationships found permit the correct choice to be made in advance both for analysis conditions for a particular column and for different requirements of insulin analysis.

Implementation and use of gradient predictions for optimization of reversed-phase liquid chromatography of peptides. Practical considerations

The options in the implementation of gradient theory for optimization work are critically reviewed and evaluated for the case of the reversed-phase liquid chromatography of peptides. Various models are covered together with methods for the determination of model parameters. Approaches for calculating retention times and band widths from experimental data are discussed. Different kinds of extrapolation are compared with interpolation. This study was aimed at finding the best compromise between number of experiments, accuracy of predictions and simplicity of calculations. Implementation and the use of gradient predictions can be simple, and practical recommendations are given.

Computer simulation as a tool for the rapid optimization of the high-performance liquid chromatographic separation of a tryptic digest of human growth hormone

Computer simulation was used to optimize the separation of a tryptic digest of recombinant human growth hormone using reversed-phase high-performance liquid chromatography in a gradient mode. DryLab G/plus software modelled the retention behavior of the complex tryptic digest mixture as a function of gradient conditions, based on data from two experimental gradient runs. The theoretical optimum separation conditions were rapidly obtained and reproduced experimentally. Resolution did not simply increase as gradient steepness was decreased, rather, an intermediate gradient time provided maximum sample resolution. The simulation results also indicate that the method is reasonably rugged, with little change in the separation expected for different high-performance liquid chromatography systems, and changes in the separation can be compensated by a change in the gradient steepness. Computer simulation can also be useful to quickly reoptimize conditions for a new column, if it fails to provide the same separation.

DryLab computer simulation for high-performance liquid chromatographic method development. II. Gradient elution

Computer simulation (DryLab software) as an aid for the development of gradient high-performance liquid chromatographic methods is reviewed. Several examples of its application are presented and the accuracy of such predictions is discussed.

Reversed-phase chromatographic method development for peptide separations using the computer simulation program ProDigest-LC

A computer program, ProDigest-LC, has been developed that assists scientists in devising methods of size-exclusion, cation-exchange and reversed-phase high-performance liquid chromatography for the analytical separation and purification of biologically active peptides and peptide fragments from enzymatic and chemical digests of proteins. ProDigest-LC accurately predicts the retention behaviour of peptides of known composition, containing 2-50 amino acid residues, and simulates the elution profiles in all three modes of chromatography. In addition, ProDigest-LC is a user-friendly program, designed as a teaching aid for both students and researchers in selecting the correct conditions for chromatography, that is, the mode of chromatography, column selection and mobile-phase selection, and has the ability to examine the effects of gradient-rate, flow-rate and sample size on the separation. The simulation capabilities of ProDigest-LC as they apply to the reversed-phase chromatography of peptides were examined. The development of the reversed-phase simulation features of the program is described, stressing the importance of peptide standards in the development, testing and practical use of ProDigest-LC. The ease of use of the program is clearly demonstrated by presenting a step-by-step procedure to produce several of the simulations illustrated in the paper. The predictive accuracy of the program was rigorously tested by its application to retention time prediction, at different gradient-rates and flow-rates, for a sample mixture containing peptides exhibiting a wide range of size (11-50 residues), charge (+1 to +8 net charge), hydrophobicity and conformation (random coil to considerable alpha-helical structure). The excellent accuracy of these peptide retention time predictions complemented the successful simulation (in terms of peptide retention times, peptide resolution, peak heights and peak widths) of the effects of gradient-rate and flow-rate on the elution profile of a mixture of closely related peptide analogues.