Likelihood of total resolution in liquid chromatography: Evaluation of one-dimensional, comprehensive two-dimensional, and selective comprehensive two-dimensional liquid chromatography

A simulation-guided approach to the selection of RPLC columns for platform small molecule separations

Simulations were conducted to evaluate the potential of several hundred reversed-phase columns to separate small molecules. By calculating the retention factor of compounds in randomly generated virtual mixtures via the HSM (hydrophobic subtraction model) and applying basic chromatography theory, the simulation can estimate the retention time and peak width of every virtual compound and calculate the resolution between every adjacent pair of compounds. A preferred column set based on the number of successful separations of randomly generated virtual mixtures was developed. The tandem-column liquid chromatography (TC-LC) approach can separate 53.2 % of the 16-compound samples using 20 tandem-column pairs, while a single-column approach can only separate 42.6 % of the 16-compound samples with 20 single columns. The preferred set of columns obtained from the simulation was almost the same as the empirical set of columns previously obtained. In screening applications, TC-LC can achieve a comparably successful separation factor (selectivity) with a smaller column inventory (nine 50-mm columns) compared to the larger inventory needed by single-column LC (twenty-one 100-mm columns).

Techniques and application in comprehensive multidimensional gas chromatography - mass spectrometry

In contrast to the well-known comprehensive two-dimensional gas chromatography (GC×GC) method, it is possible to define comprehensive multidimensional gas chromatography. 'Comprehensiveness' relates to analysis of the whole sample. Two-dimensional and multidimensional here refer to the use of at least two separation stages for analysis, however comprehensive 2DGC now appears to be reserved for the GC×GC method. This may be differentiated from comprehensive MDGC (CMDGC) simply by the analysis time assigned to the second (²D) column, although there does not appear to be a specific definition that relates to this analysis time parameter. A number of different implementation protocols for comprehensive MDGC are described here, that may involve either a single, or multiple, injection(s). In all cases, independent retention must be achieved on each dimension to ensure the probability of enhanced separation. An original application of a crude oil sample is presented to illustrate development of the MDGC approach that incorporates two Deans switches (DS) and a cryogenic trapping approach, performed using a sequential heart-cut (H/C) event method incremented by 0.5 min for each injection; a total of 40 injections is used to analyse the total sample. The higher peak capacity and consequently greater resolution on the long ²D column is illustrated, compared with that expected for conventional GC×GC, with tentative identification in order to classify chemical classes. Incorporating an approach to acquiring retention indices may be implemented, although its utility for petroleum hydrocarbons is limited. Structured groupings of different chemical classes, as exemplified by mono and diaromatics for the crude oil sample, were noted.

Theory of the probability of total resolution in chromatograms with systematic variation of average peak spacing and peak width

An equation is proposed for the probability that all mixture constituents are separated, when the density (i.e., average number of eluting constituents per time) and width of single-component peaks (SCPs) vary systematically. The probability Pr that m SCPs are separated is modeled as the product of the m - 1 probabilities that adjacent pairs of SCPs are separated. Pr is then expressed as the geometric mean of the probability product raised to the power of m - 1. This geometric mean is approximated by an arithmetic mean equaling the probability that adjacent SCPs are separated, as calculated from previously developed statistical overlap theory (SOT) for variable SCP density and width. The theory is tested using previously reported and current in-house simulations of isocratic chromatograms of SCPs with random differences in standard chemical potential. In such chromatograms, more SCPs elute at short times than long times, and their widths are less at short times than long times. The average difference between 179 previously reported and currently predicted values of 100 x Pr is about 0.6, when 100 x Pr > 5. The theory requires numerical computation of one integral but can be approximated by an analytic equation for SOT probabilities close to one. For SCPs having retention times exceeding twice the void time, this equation simplifies to a previous SOT expression, with the gradient peak capacity replaced by the isocratic peak capacity. The versatility of the Pr theory is tested using three other models of chromatograms, in which the density and width of SCPs vary. The Pr predictions agree with simulation for all three models.

Enhancing the Possibilities of Comprehensive Two-Dimensional Liquid Chromatography through Hyphenation of Purely Aqueous Temperature-Responsive and Reversed-Phase Liquid Chromatography

Comprehensive two-dimensional liquid chromatography (LC × LC) allows for substantial gains in theoretical peak capacity in the field of liquid chromatography. However, in practice, theoretical performance is rarely achieved due to a combination of undersampling, orthogonality, and refocusing issues prevalent in many LC × LC applications. This is intricately linked to the column dimensions, flow rates, and mobile-phase compositions used, where, in many cases, incompatible or strong solvents are introduced in the second-dimension (²D) column, leading to peak broadening and the need for more complex interfacing approaches. In this contribution, the combination of temperature-responsive (TR) and reversed-phase (RP) LC is demonstrated, which, due to the purely aqueous mobile phase used in TRLC, allows for complete and more generic refocusing of organic solutes prior to the second-dimension RP separation using a conventional 10-port valve interface. Thus far, this was only possible when combining other purely aqueous modes such as ion exchange or gel filtration chromatography with RPLC, techniques which are limited to the analysis of charged or high MW solutes, respectively. This novel TRLC × RPLC combination relaxes undersampling constraints and complete refocusing and therefore offers novel possibilities in the field of LC × LC including temperature modulation. The concept is illustrated through the TRLC × RPLC analysis of mixtures of neutral organic solutes.

Likelihood of total resolution in selective comprehensive two-dimensional liquid chromatography with parallel processing: Simulation and theory

The probability Pr(sLC×LC) that all peaks are separated by a resolution of 1.5 or more in selective comprehensive two-dimensional liquid chromatography (sLC × LC) is computed for simple model systems of 5 to 60 peaks and first-dimension (¹D) gradient times of 100 to 2000 s. The computations include mimics of a commercial instrument, whose fixed second-dimension (²D) gradient time and use of one cycle time for initialization reduces Pr(sLC×LC) relative to an earlier report. For serial sLC × LC, in which a single device collects and transfers ¹D multiplets to the second dimension, Pr(sLC×LC) under practical conditions is predicted to be only slightly larger than the probability of total resolution in LC × LC for separations of the same duration in each case. To increase Pr(sLC×LC), two model systems are proposed based on parallel processing, in which one device collects multiplets from the first separation while a second device simultaneously transfers fractions from previously collected multiplets to the second dimension for further separation. A sum of probabilities guideline is proposed by which optimal fixed ²D gradient times, ranging from 9.5 to 12 s, are found for both serial and parallel models. The increases of Pr(sLC×LC) based on parallel processing are modest; the largest is only 0.062 for one system and 0.106 for the other, relative to the serial model. A theory is derived that rationalizes the modesty of the increase, which was unexpected. It shows that Pr(sLC×LC) equals the probability of total resolution in the first dimension, plus the product of the probability that all ¹D multiplets are transferred to the second dimension and the probability that all multiplets are separated in the second dimension. The theory shows that, although parallel processing is better than serial processing for multiplet transfer, the ability to leverage this gain is offset by the limited probability that all multiplets are then actually separated in the second dimension, which is only about 0.55 for conditions where the change from serial to parallel processing is most beneficial. With these findings in hand, two scenarios are examined for future consideration: one in which the ²D peak capacity is doubled, and another in which multiplets are always transferred to the second dimension. The latter shows considerable promise for increasing Pr(sLC×LC) substantially beyond its counterpart in LC × LC. For example, a 50% probability of separating all peaks in a 15-component mixture can be reached in 1150 s using LC × LC. The same probability can be reached in the same time for a sample with nearly twice as many components (27) in the case of sLC × LC, assuming transfer of all multiplets to the second dimension. These findings will be useful to those considering systematic approaches to developing 2D-LC methods for moderately complex mixtures, and to those interested in instrument development for 2D-LC.

Characterization of therapeutic antibodies and related products by two-dimensional liquid chromatography coupled with UV absorbance and mass spectrometric detection

The development of analytical tools for the characterization of large biomolecules is an emerging and rapidly evolving area. This development activity is motivated largely by the current trend involving the increase in development and use of large biomolecules for therapeutic uses. Given the inherent complexity of these biomolecules, which arises from their sheer size and possibilities for chemical modification as well as changes over time (e.g., through modification in solution, aggregation), two-dimensional liquid chromatography (2D-LC) has attracted considerable interest as an analytical tool to address the challenges faced in characterizing these materials. The immediate potential benefits of 2D-LC over conventional one-dimensional liquid chromatography in this context include: (1) higher overall resolving power; (2) complementary information gained from two dimensions of separation in a single analysis; and (3) enabling indirect coupling of separation modes that are inherently incompatible with mass spectrometric (MS) detection (e.g., ion-exchange, because of high-salt eluents) to MS through a more compatible second dimension separation such as reversed-phase LC. In this review we summarize the work in this area, most of which has occurred in the past five years. Although the future is bright for further development in this area, some challenges have already been addressed through new 2D-LC methods. These include: (1) deep characterization of monoclonal antibodies to understand charge heterogeneity, glycosylation patterns, and other modifications; (2) characterization of antibody-drug conjugates to understand the extent and localization of small molecule conjugation; (3) detailed study of excipients in protein drug formulations; and (4) detection of host-cell proteins on biotherapeutic molecule preparations. We fully expect that in the near future we will see this list expanded, and that continued development will lead to methods with further improved performance metrics.

Recent advances in 2D-LC for bioanalysis

This article summarizes the most important developments in the use of 2D-LC for bioanalysis in the last 5 years. While several interesting and powerful applications have been developed recently, this work has been supported by continued, significant development of theoretical concepts, instrument development and practical aspects of method development. Some of the most exciting applications have been focused on the use of 2D-LC and characterize proteins both as biotherapeutic drug substances, and in formulations. These materials are inherently complex, difficult to resolve chromatographically and present problems that are essentially unknown (e.g., aggregation) in the small molecule world, thus 2D-LC can be leveraged very effectively to address these challenges.