The kinetic plot method applied to gradient chromatography: Theoretical framework and experimental validation

Characterization of hybrid organo-silica monoliths for possible application in the gradient elution of peptides

We characterized thermally polymerized organo-silica hybrid monolithic capillaries to test their applicability in the gradient elution of peptides. We have used a single-pot approach utilizing 3-(methacryloyloxy)propyltrimethoxysilane (MPTMS), ethylene dimethacrylate (EDMA), and n-octadecyl methacrylate (ODM) as functional monomers. The organo-silica monolith containing MPTMS and EDMA was compared with the stationary phase prepared by adding ODM to the original polymerization mixture. Column prepared using a three-monomer system provided a lower accessible volume of flow-through pores, a higher proportion of mesopores, and higher efficiency. We utilized isocratic and gradient elution data to predict peak widths in gradient elution. Both protocols provided comparable results and can be used for peptide peak width prediction. However, applying gradient elution data for peak width prediction seems simpler. Finally, we tested the effect of gradient time on achievable peak capacity in the gradient elution of peptides with a column prepared with a three-monomer system providing a higher peak capacity. However, the performance of hybrid organo-silica monolithic stationary phases in gradient elution of peptides must be improved compared to other monolithic stationary phases. The limiting factor is column efficiency in highly aqueous mobile phases, which needs to be focused on.

Theory of linear focusing in chromatographic columns with exponential retention. Part 1: Basic solutions

This report is the first of 2-part study of the effect of gradients in column parameters on the column performance. If t, x and p are, respectively, time since sample introduction, distance from column inlet and some parameter of solute migration along the column then ∂p/∂t and ∂p/∂x are, respectively, the rate of changing p and the gradient of p. Unified approach to study of gradients and rates in different chromatographic techniques (LC, GC, etc.) has been developed. To facilitate a unified approach, the umbrella term mobilization (y) representing column temperature (T) in GC, solvent composition (ϕ) in LC, etc. is introduced. Differential equations for migration of a solute band (collection of solute molecules) under the following conditions are formulated and solved:The key solutions describe the time of migration of a solute band and the band width - both as functions of the distance traveled by the band. The solutions are used in Part 2 for the study of the effects of the negative gradients in y on column performance in several practically important cases. A reduction of the key general solutions to much simpler equations for gradient LC has been demonstrated herein as an example.

Reversed-Phase Liquid Chromatography of Peptides for Bottom-Up Proteomics: A Tutorial

The performance of the current bottom-up liquid chromatography hyphenated with mass spectrometry (LC-MS) analyses has undoubtedly been fueled by spectacular progress in mass spectrometry. It is thus not surprising that the MS instrument attracts the most attention during LC-MS method development, whereas optimizing conditions for peptide separation using reversed-phase liquid chromatography (RPLC) remains somewhat in its shadow. Consequently, the wisdom of the fundaments of chromatography is slowly vanishing from some laboratories. However, the full potential of advanced MS instruments cannot be achieved without highly efficient RPLC. This is impossible to attain without understanding fundamental processes in the chromatographic system and the properties of peptides important for their chromatographic behavior. We wrote this tutorial intending to give practitioners an overview of critical aspects of peptide separation using RPLC to facilitate setting the LC parameters so that they can leverage the full capabilities of their MS instruments. After briefly introducing the gradient separation of peptides, we discuss their properties that affect the quality of LC-MS chromatograms the most. Next, we address the in-column and extra-column broadening. The last section is devoted to key parameters of LC-MS methods. We also extracted trends in practice from recent bottom-up proteomics studies and correlated them with the current knowledge on peptide RPLC separation.

Kinetic performance comparison of superficially porous, fully porous and monolithic reversed-phase columns by gradient kinetic plots for the separation of protein biopharmaceuticals

To find the best performing column for the analysis of protein-based biopharmaceuticals is a significant challenge as meanwhile numerous modern columns with distinct stationary phase morphologies are available for reversed-phase liquid chromatography. Especially when besides morphology also several other column factors are different, it is hard to decide about the best performing column a priori. To cope with this problem, in the present work 13 different reversed-phase columns dedicated for protein separations were systematically tested by the gradient kinetic plot method. A comprehensive comparison of columns with different morphologies (monolithic, fully porous and superficially porous particle columns), particle sizes and pore diameters as well as column length was performed. Specific consideration was also given to various monolithic columns which recently shifted a bit out of the prime focus in the scientific literature. The test proteins ranged from small proteins starting from 12 kDa, to medium sized proteins (antibody subunits obtained after IdeS-digestion and disulphide reduction) and an intact antibody. The small proteins cytochrome c, lysozyme and β-lactoglobulin could be analysed with similar performance by the best columns of all three column morphologies while for the antibody fragments specific fully porous and superficially porous particle columns were superior. A 450 Å 3,5 µm superficially porous particle column showed the best performance for the intact antibody while a 1.7 µm fully porous particle column with 300 Å showed equivalent performance to the best superficially porous column with thin shell and 400 Å pore size for proteins between 12 and 25 kDa. While the majority of the columns had C4 bonding chemistry, the silica monolith with C18 bonding and 300 Å mesopore size approximated the best performing particle columns and outperformed a C4 300 Å wide-pore monolith. The current work can support the preferred choice for the most suitable reversed-phase column for protein separations.

Mass Fabrication of Capillary Columns Based on Centrifugal Packing

Packed capillary columns have become the standard front-end separation device for mass spectrometry-based proteomics. The development of simple, fast, and robust capillary column technology, especially that with mass-fabrication capacity, can greatly improve analytical throughput and reproducibility in omics research. In this technical note, we report a centrifugal packing technology, which has the capability to mass fabricate high quality capillary columns with a 2886 columns/day fabrication throughput. The centrifugally packed columns presented significantly improved efficiency (reduced plate height h_min = 1.6, 37%-40% improvement compared with slurry packed columns), advanced kinetic performance limit, and excellent column-to-column reproducibility (2.0% RSD for retention time, 50 columns). Such columns enabled ∼5300 HeLa proteins identified in single-shot proteomic analysis, displaying both intercolumn and inter-run retention time stability (retention time RSD = 0.94% between nine replicates on three columns for probing peptide sequence). The mass-fabrication technology reported in this technical note may support disposable use of high quality chromatographic columns in large-scale bioanalysis.

But Why Doesn’t It Get Better? Kinetic Plots for Liquid Chromatography, Part III: Pulling It All Together

Choosing a liquid chromatography (LC) column for a particular application can be a surprisingly challenging task. On 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 don’t 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 (that is, particle size and length) will perform in terms of 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 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.

Measurement of optimal flow rate in gradient elution liquid chromatography

Method development in gradient LC relies upon the selection of a solvent time program and a mobile phase flow rate. The flow rate, optimal for gradient separation cannot be inherently predicted by the isocratic value optimal for a given analyte, and rather should be identified independently to ensure the highest separation performance of gradient analysis. The optimal flow rate (F_opt) is defined herein as the solvent volumetric flow rate (F) maximizing the separation (Δs) of a predetermined peak-pair or the separation capacity (s_c) of the entire LC analysis. The theoretical background and the experimental technique of measurement of F_opt in gradient elution analysis were considered and experimentally demonstrated. The technique of measuring F_opt is based on translatable changes of F where the product Ft_G (t_G is the gradient time) was the same for all values of F. The F_opt was found as F corresponding to the maximum in Δs or in s_c.

Three-dimensional graphing representing six variables for speed and separation performance in liquid chromatography

The two variables, flow rate and column length, enable naive determination of the number of theoretical plates (N) in isocratic elution; this, in turn, enables the formation of a three-dimensional graph with N as the z-axis. An alternate three-dimensional graph with N as the z-axis can be drawn, then, with the alternate basal plane illustrating the pressure drop and hold-up time. In this article, the pressure drop and hold-up time are formulated so as to be represented unitarily in the former graph, because the flow rate and column length interact simultaneously as operational variables. This formulation manipulates both the pressure drop and the hold-up time as logarithmic axes, to evaluate the landscape. Also of use is the representation, in the same graph, of the height equivalent to a theoretical plate, as the fundamental property of the packing supports. For this purpose, the number of theoretical plates per unit length are here introduced as the sixth variable, instead of the height equivalent to a theoretical plate. Representing the six variables in three-dimensional graphs enables a clear understanding both of the separation condition optimization methods and the relation among variables for the speed and separation performance. The linear velocity, column length, N, velocity-length product, hold-up time, and number of theoretical plates per unit length, are here selected as the six elementary variables for the three-dimensional graphs; and, based on the packing supports of 2, 3, and 5-μm particle and monolithic columns. Finally, the usage of logarithmic three-dimensional graph is illustrated for understanding the speed and separation performance.

Segmented Microfluidics-Based Packing Technology for Chromatographic Columns

Nanoflow liquid chromatography-mass spectrometry (NanoLC-MS) has become the method of choice for the analysis of complex biological systems, especially when the available sample amount is limited. The preparation of high-performance capillary columns for nanoLC use is still a technical challenge. Here, we report a segmented microfluidic method for the preparation of packed capillary columns, where liquid segments were used as soft, dynamic, and well-dispersed slurry reservoirs for carrying and delivering micrometer packing particles. Based on this microfluidic packing technology, the column bed was assembled layer-by-layer at a 50 μm resolution, and ultralong capillary columns of 3, 5, and 10 m were fabricated in such a manner. The microfluidically packed columns demonstrated excellent separation efficiencies of 116 000 plates/m. The higher efficiencies obtained at higher slurry concentrations also indicate that a high-quality packed bed can be obtained without sacrificing the packing speed. Kinetic performance limit analysis shows that the microfluidic packed columns have higher peak capacity production efficiency in the high-resolution region, presenting an improved separation impedance of 2800, which is significantly better than columns packed with the conventional slurry packing method. In comparison with a commercial nanoLC column, a 5 m long microfluidic packed column was evaluated for proteomic analysis using a standard HeLa protein digest and presented 261% improvement in peptide identification capability, resulting in significantly enhanced protein identification confidence.

Assessment of the resolving power of hydrophobic interaction chromatography for intact protein analysis on non-porous butyl polymethacrylate phases

This study reports on the assessment of the separation performance of hydrophobic interaction chromatography for intact protein analysis using non-porous butyl polymethacrylate phases. The maximum peak capacity in inverse gradient mode was reached at a volumetric flow rate which was significantly (10-20 times) higher than the flow rate yielding the minimum plate height in isocratic mode, as the gradient volume dominates the peak-capacity generation. The flow rate yielding the maximum peak capacity increased with decreasing gradient volume, i.e., steeper gradients, and also depends on the magnitude of the mass-transfer contribution to peak dispersion (affected by particle size and molecular diffusion coefficient of proteins) at these high flow rates. The maximum peak capacity using a 100 mm long column packed with 4 µm particles for steep 7.5 min gradients was determined to be 60. Increasing the column length by coupling columns leads to better gradient performance than increasing the gradient duration for gradients of 60 min and longer. Using a coupled column system (2 × 100 mm long columns packed with 4 µm particles), the maximum peak capacity was determined to be 105, which was 33% higher compared to that of a single column while applying a similar gradient volume. Decreasing the particle size to 2.3 µm leads to higher peak capacities even though the column was operated at lower volumetric flow rate. The maximum peak capacity obtained with the 2.3 µm column was 128% higher than was obtained with the coupled column. Even at suboptimal conditions, the 2.3 µm column yields a higher peak capacity (14%) than when using two coupled columns packed with 4 µm at optimal conditions (gradient time of 120 min and a flow rate of 0.5 mL/min).

Assessing effects of ultra-high-pressure liquid chromatography instrument configuration on dispersion, system pressure, and retention

This study involves the systematic assessment of the effects of system configuration on dispersion, pressure, and retention characteristics while operating a 1500 bar UHPLC system with 2.1 mm i.d. × 100 mm long columns packed with 1.5 µm core-shell particles in isocratic and gradient mode. Altering the system configuration by changing the i.d. of connection tubing and flow cells affects the elution time, dispersion characteristics, and the kinetic performance limits of the system. The gain in separation efficiency when decreasing tubing i.d. from 100 to 75 µm was found to contribute more to the decrease in separation impedance and the position of the kinetic performance curve than the loss in available column pressure induced by the narrower tubing. When applying steep gradients, characterized by gradient-to-column dead-time ratio < 7, optimizing instrument configuration leads to either a significant time gain factor of 3.9 without compromising peak capacity, or a gain in peak capacity with a gain factor of 1.3 while maintaining the analysis time constant. Due to the reduced fluidic volume of connection tubing of smaller i.d., a decrease in residence time is obtained. At the same time, an increase in k was observed due to a pressure-induced retention effect, and this effect is significant for late-eluting analytes.

Three approaches to improving performance of liquid chromatography using contour maps with pressure, time, and number of theoretical plates

Attempts to improve HPLC performance often focus on increasing the speed or separation performance. In this article, both the flow rate and column length are optimized as separation conditions, while observing the number of theoretical plates and hold-up time with isocratic elutions. In addition, the upper pressure limit must be simultaneously considered as the boundary condition. Approaches based on the optimal velocity (Opt.) are often adopted; but the kinetic performance limit (KPL) in Desmet's method can also be utilized for three-dimensional graphing with axes of pressure, time, and number of theoretical plates. Here, two approaches involving pressure increase are introduced, beginning with the condition of optimal linear velocity: one aimed at greater speed and the other at higher resolution. Coefficients of pressure-application are derived to measure the effectiveness of the intermediate conditions between the Opt. and KPL methods. In the third approach, the hold-up time is extended while maintaining a fixed pressure. Coefficients of time-extension are also derived, to determine the effectiveness to improve the separation performance.

Methods to determine the kinetic performance limit of contemporary chromatographic techniques

By combining separation efficiency data as a function of flow rate with the column permeability, the kinetic plot method allows to determine the limits of separation power (time vs. efficiency) of different chromatographic techniques and methods. The technique can be applied for all different types of chromatography (liquid, gas, or supercritical fluid), for different types of column morphologies (packed beds, monoliths, open tubular, micromachined columns), for pressure and electro-driven separations and in both isocratic and gradient elution mode. The present contribution gives an overview of the methods and calculations required to correctly determine these kinetic performance limits and their underlying limitations.

Migration and elution equations in gradient liquid chromatography

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

Optimizing separations in online comprehensive two-dimensional liquid chromatography

Online comprehensive two-dimensional liquid chromatography has become an attractive option for the analysis of complex nonvolatile samples found in various fields (e.g. environmental studies, food, life, and polymer sciences). Two-dimensional liquid chromatography complements the highly popular hyphenated systems that combine liquid chromatography with mass spectrometry. Two-dimensional liquid chromatography is also applied to the analysis of samples that are not compatible with mass spectrometry (e.g. high-molecular-weight polymers), providing important information on the distribution of the sample components along chemical dimensions (molecular weight, charge, lipophilicity, stereochemistry, etc.). Also, in comparison with conventional one-dimensional liquid chromatography, two-dimensional liquid chromatography provides a greater separation power (peak capacity). Because of the additional selectivity and higher peak capacity, the combination of two-dimensional liquid chromatography with mass spectrometry allows for simpler mixtures of compounds to be introduced in the ion source at any given time, improving quantitative analysis by reducing matrix effects. In this review, we summarize the rationale and principles of two-dimensional liquid chromatography experiments, describe advantages and disadvantages of combining different selectivities and discuss strategies to improve the quality of two-dimensional liquid chromatography separations.

Application of two-dimensional chromatography to the characterization of macromolecules and biomacromolecules

Modern polymeric materials are heterogeneous with respect to different structural features, for instance molar mass, composition, and architecture. One-dimensional separation methods such as size-exclusion chromatography (SEC) are insufficient to fully resolve the multidimensional distributions of such complex materials. Therefore, two-dimensional separation methods are increasingly employed to characterize macromolecules. The present article describes in detail the advantages and experimental aspects of two-dimensional macromolecular separations. Selected examples will be discussed to explain the strategies used to separate macromolecules with respect to specific structural features.

Are sub-2 μm particles best for separating small molecules? An alternative

Superficially porous particles (SPP) in the 2.5-2.7 μm range provide almost the same efficiency and resolution of sub-2 μm totally porous particles (TPP), but at one-half to one-third of the operating pressure. The advantage of SPP has led to the introduction of sub-2 μm SPP as a natural extension of this technology. While short columns of both SPP and TPP sub-2 μm particles allow very fast separations, the efficiency advantages of these very small particles often are not realized nor sufficient to overcome some of the practical limitations and disadvantages of such small particles. Advantages and disadvantages of columns packed with sub-2 μm particles are described for comparison with the characteristics of larger particles. The authors conclude that while sub-2 μm particles have utility in research studies, columns of larger particles are often better suited for most applications. A suggested 2.0 μm superficially porous particle diameter retains many of the advantages of sub-2 μm particles, but minimizes some of the disadvantages. The characteristics of these new 2.0 μm SPP are described in studies comparing some present sub-2 μm SPP commercial columns for efficiency, column bed homogeneity and stability.