Observations on "orthogonality" in comprehensive two-dimensional separations

The concept and definition of orthogonality in the context of comprehensive two-dimensional (2D) separations are interesting topics of active discussion. Over the years, several approaches have been taken to quantify the degree of orthogonality, primarily to serve as a metric to optimize (and compare) comprehensive 2D separations. Recently, a mathematical function was reported that is qualitatively instructive for the purpose of providing such a metric. However, the mathematical function has some quantitative shortcomings. Herein, we both explore and partially correct this function. The orthogonality metric, referred to previously and herein as the orthogonality, O, was mathematically related to the fraction of the 2D separation space occupied by compounds (i.e., fractional coverage) and the peak capacity, P, for one dimension of the 2D separation. The fractional coverage, f, is simply related to the percentage coverage, which is equal to 100%(f). Our main finding was that the values for O as a function of P for a given percentage coverage achieve a constant value at large P but deviate severely to lower O values at small P. For comprehensive 2D separations operated such that the second dimension is at small P, the findings we report have consequences for those who consider applying the O metric. Finally, it is discussed that the percentage coverage may be a better metric to gauge the extent to which the compounds in a given sample mixture have been disseminated in the 2D separation space.     

Effect of first-dimension undersampling on effective peak capacity in comprehensive two-dimensional separations

The objective of this work is to establish a means of correcting the theoretical maximum peak capacity of comprehensive two-dimensional (2D) separations to account for the deleterious effect of undersampling first-dimension peaks. Simulations of comprehensive 2D separations of hundreds of randomly distributed sample constituents were carried out, and 2D statistical overlap theory was used to calculate an effective first-dimension peak width based on the number of observed peaks in the simulated separations. The distinguishing feature of this work is the determination of the effective first-dimension peak width using the number of observed peaks in the entire 2D separation as the defining metric of performance. We find that the ratio of the average effective first-dimension peak width after sampling to its width prior to sampling (defined as ) is a simple function of the ratio of the first-dimension sampling time (t(s)) to the first-dimension peak standard deviation prior to sampling (1sigma): = square root1+0.21(t /(s)(1) sigma(2) This is valid for 2D separations of constituents having either randomly distributed or weakly correlated retention times, over the range of 0.2 on t(s)/1 sigma from this expression is in qualitative agreement with previous work based on the effect of undersampling on the effective width of a single first-dimension peak, but predicts up to 35% more broadening of first-dimension peaks than is predicted by previous models. This simple expression and accurate estimation of the effect of undersampling first-dimension peaks should be very useful in making realistic corrections to theoretical 2D peak capacities, and in guiding the optimization of 2D separations.     

Dependence of effective peak capacity in comprehensive two-dimensional separations on the distribution of peak capacity between the two dimensions

One of the basic tenets of comprehensive two-dimensional chromatography is that the total peak capacity is simply the product of the first- and second-dimension peak capacities. As formulated, the total peak capacity does not depend on the relative values of the individual dimensions but only on the product of the two. This concept is tested here for the experimentally realistic situation wherein the first-dimension separation is undersampled. We first propose that a relationship exists between the number of observed peaks in a two-dimensional separation and the effective peak capacity. We then show here for a range of reasonable total peak capacities (500-4000) and various contributions of peak capacity in each dimension (10-150) that the number of observed peaks is only slightly dependent on the relative contributions over a reasonable and realistic range in sampling times (equal to the first-dimension peak standard deviation, multiplied by 0.2-16). Most of this work was carried out under the assumption of totally uncorrelated retention times. For uncorrelated separations, the small deviations from the product rule are due to the "edge effect" of statistical overlap theory and a recently introduced factor that corrects for the broadening of first-dimension peaks by undersampling them. They predict that relatively more peaks will be observed when the ratio of the first- to the second-dimension peak capacity is much less than unity. Additional complications are observed when first- and second-dimension retention times show some correlation, but again the effects are small. In both cases, deviations from the product rule are measured by the relative standard deviations of the number of observed peaks, which are typically 10 or less. Thus, although the basic tenet of two-dimensional chromatography is not exact when the first dimension is undersampled, the deviations from the product rule are sufficiently small as to be unimportant in practical work. Our results show that practitioners have a high degree of flexibility in designing and optimizing experimental comprehensive two-dimensional separations.     

Objective data alignment and chemometric analysis of comprehensive two-dimensional separations with run-to-run peak shifting on both dimensions.

Data from comprehensive two-dimensional (2-D) separation techniques, such as comprehensive 2-D gas chromatography (GC x GC), liquid chromatography/liquid chromatography (LC x LC) and liquid chromatography/ capillary electrophoresis (LC x CE) can be readily analyzed by various chemometric methods to increase chemical analysis capabilities. A retention time alignment, preprocessing method is presented that objectively corrects for run-to-run retention time variations on both separation dimensions of comprehensive 2-D separations prior to application of chemometric data analysis algorithms. The 2-D alignment method corrects for run-to-run shifting of a sample data matrix relative to a standard data matrix on both separation time axes in an independent, stepwise fashion. After 2-D alignment, the generalized rank annihilation method (GRAM) is successfully applied, substantiating the performance of the alignment method. The alignment method should have important implications, because most 2-D separation techniques exhibit, in the context of chemometric data analysis, considerable run-to-run retention time shifting on both dimensions. Even when there are only three to four points/peak, that is, with three to four separations on the second dimension (column 2) per peak width from the first dimension (column 1), the 2-D alignment coupled with GRAM provides dependable analyte peak identification capabilities and adequate quantitative precision for unresolved analyte peaks. Thus, the 2-D alignment algorithm is applicable to lower data density conditions, which broadens the scope of chemometric analysis to high-speed 2-D separations.     

Orthogonality of two-dimensional separations based on conditional entropy

A new approach to assess the orthogonality of two-dimensional (2-D) separation systems based on conditional entropy is developed. It considers the quantitative distribution of peaks in the entire separation space such that the orthogonality obtained is independent of the number of peaks observed for each separation technique. Therefore, it can be used to compare the orthogonality of different 2-D separation protocols for a given sample. Herein, the developed method has been employed to estimate the orthogonality of peptide separation by off-gel electrophoresis (OGE) hyphenated to capillary zone electrophoresis (CZE).     

Quantification in comprehensive two-dimensional liquid chromatography

Although the use of comprehensive two-dimensional liquid chromatography (LCxLC) as a powerful separation technique is continuously increasing, its employment in quantification experiments is rather limited. The present research is focused on the quantification of a series of standards, as well as real-world sample compounds, by using dedicated laboratory-constructed LCxLC software, developed through a novel approach. Moreover, the difficulties encountered during software operation, in various elution conditions, are described and discussed. The results attained were compared with those observed in conventional LC, and no statistically significant differences were observed in the determination of aurapten in grapefruit oil. However, a loss in sensitivity was observed when using LCxLC (limit of detection = 0.10 ppm) compared to conventional LC (limit of detection = 0.05 ppm) as a consequence of the sample dilution in comprehensive two-dimensional liquid chromatography.     

High-efficiency, two-dimensional separations of protein digests on microfluidic devices

High-efficiency, two-dimensional separations of tryptic digests were achieved using glass microfluidic devices. Following micellar electrokinetic chromatography (MEKC) separations in a 19.6-cm-long serpentine channel, the peptides were rapidly sampled into a 1.3-cm-long second-dimension channel, where they were separated by capillary electrophoresis (CE). The turns in the serpentine channel were asymmetrically tapered to minimize geometrical contributions to band broadening and to provide ample channel length for high-efficiency chromatographic separations. Analysis of rhodamine B injections routinely produced plate numbers of 230000 and 40000 in the first (MEKC) and second (CE) dimensions, respectively, corresponding to plate heights of 0.9 and 0.3 microm. The electric field strengths were 200 V/cm for MEKC and 2400 V/cm for CE. In analysis times less than 15 min, two-dimensional separation of bovine serum albumin tryptic digest produced a peak capacity of 4200 (110 in the first dimension and 38 in the second dimension). The system was used to identify a peptide from a tryptic digest of ovalbumin using standard addition and to distinguish between tryptic digests of human and bovine hemoglobin.     

Method for an automatic search of two-dimensional peaks in neutron diffraction spectra

This paper describes a method for the search of two-dimensional peaks in the diffraction spectra obtained from the pulsed neutron source by a position-sensitive detector. The method involves the following steps: (1) smoothing the spectrum by filters of the spline type, (2) search of the peak tops by a specific identifier — quasicurvature, and (3) sorting the found peaks by an algorithm of the cluster analysis. The method is implemented in a FORTRAN program, called FIND2, oriented to the interaction with the program DOMUS [1].     

A comprehensive two-dimensional retention time alignment algorithm to enhance chemometric analysis of comprehensive two-dimensional separation data

A comprehensive two-dimensional (2D) retention time alignment algorithm was developed using a novel indexing scheme. The algorithm is termed comprehensive because it functions to correct the entire chromatogram in both dimensions and it preserves the separation information in both dimensions. Although the algorithm is demonstrated by correcting comprehensive two-dimensional gas chromatography (GC x GC) data, the algorithm is designed to correct shifting in all forms of 2D separations, such as LC x LC, LC x CE, CE x CE, and LC x GC. This 2D alignment algorithm was applied to three different data sets composed of replicate GC x GC separations of (1) three 22-component control mixtures, (2) three gasoline samples, and (3) three diesel samples. The three data sets were collected using slightly different temperature or pressure programs to engender significant retention time shifting in the raw data and then demonstrate subsequent corrections of that shifting upon comprehensive 2D alignment of the data sets. Thirty 12-min GC x GC separations from three 22-component control mixtures were used to evaluate the 2D alignment performance (10 runs/mixture). The average standard deviation of first column retention time improved 5-fold from 0.020 min (before alignment) to 0.004 min (after alignment). Concurrently, the average standard deviation of second column retention time improved 4-fold from 3.5 ms (before alignment) to 0.8 ms (after alignment). Alignment of the 30 control mixture chromatograms took 20 min. The quantitative integrity of the GC x GC data following 2D alignment was also investigated. The mean integrated signal was determined for all components in the three 22-component mixtures for all 30 replicates. The average percent difference in the integrated signal for each component before and after alignment was 2.6%. Singular value decomposition (SVD) was applied to the 22-component control mixture data before and after alignment to show the restoration of trilinearity to the data, since trilinearity benefits chemometric analysis. By applying comprehensive 2D retention time alignment to all three data sets (control mixtures, gasoline samples, and diesel samples), classification by principal component analysis (PCA) substantially improved, resulting in 100% accurate scores clustering.     

Modulation ratio in comprehensive two-dimensional gas chromatography

Comprehensive two-dimensional chromatography employs a serially coupled two-column arrangement where effluent from the first column is collected or sampled and then introduced to the second column according to a chosen modulation period. This is effected by use of a modulator at or near the column junction. One of the considerations in applying the technique is the period of the modulator, which determines the sampling duration of the first column effluent. Here, we propose that the sampling rate can be most effectively described by a new term, called the modulation ratio (MR). This is defined as the ratio of 4 times the first column peak standard deviation (4sigma) divided by the modulation period (PM) or 1.6985 times the half-height width of the peak (wh): MR = 4sigma/PM = wb/PM = (wh x 1.6985)/PM. The 4sigma value is more commonly recognized as the peak base width (wb). The use of 4sigma as the numerator is preferred to simply sigma because when the PM value used for an experiment is equal to sigma, then the MR value is calculated to be 4, implying that the primary peak will be modulated approximately 4 times as is normally recommended for a comprehensive multidimensional separation. The less well-defined term of modulation number (NM) has been previously used and proposed as the number of modulations per peak and, therefore, is intended to convey the manner in which the primary column peak is sampled; this is a subjective and not well-characterized value. The use of MR should provide users with a meaningful and strictly defined value when reporting experimental conditions. The utility of MR is demonstrated through a mathematical model of the modulation process for both Gaussian and tailing peaks, supported by an experimental study of the modulation ratio. It is shown that for the analysis of trace compounds where precise quantitative measurements are being made, the experiment should be conducted with an MR of at least 3. Conversely, for semiquantitative methods or the analysis of major components, an MR of approximately 1.5 should suffice.     

Separation orthogonality in temperature-programmed comprehensive two-dimensional gas chromatography

In a comprehensive two-dimensional gas chromatograph, a thermal modulator serially couples two columns containing dissimilar stationary phases. The secondary column generates a series of high-speed secondary chromatograms from the sample stream formed by the chromatogram eluting from the primary column. This series of secondary chromatograms forms a two-dimensional gas chromatogram with peaks dispersed over a retention plane rather than along a line. The method is comprehensive because the entire primary column chromatogram is transmitted through the secondary column with fidelity. One might expect that a two-dimensional separation in which both dimensions are basically the same technique, gas chromatography, would be inefficient because the two dimensions would behave similarly, generating peaks whose retentions correlate across dimensions. Applying a temperature program to the two columns, however, can tune the separation to eliminate this inefficiency. The temperature program reduces the retentive power of the secondary column as a function of progress of the primary chromatogram such that the retention mechanism of the primary column is eliminated from the second dimension. Retention of a substance in the second dimension is then determined by the difference in its interaction with the two stationary phases. Retention times in the second dimension then fall within a fixed range, and the whole retention plane is accessible. In a properly tuned comprehensive two-dimensional chromatogram, retention times in the two dimensions are independent of each other, and the two-dimensional chromatogram is orthogonal. Orthogonality is important for two reasons. First, an orthogonal separation efficiently uses the separation space and so has either greater speed or peak capacity than nonorthogonal separations. Second, retention in the two dimensions of an orthogonal chromatogram is determined by two different and independent mechanisms and so provides two independent measures of molecular properties.     

Considerations on orthogonality duality in comprehensive two-dimensional gas chromatography

The term "orthogonal" in comprehensive two-dimensional gas chromatography (GC × GC) has a double sided meaning as it stands for a separation resulting from the combination of two independent retention mechanisms (Giddings, J. C. J. High Resolut. Chromatogr. 1987, 10, 319) but also for a 2D separation where the components are evenly distributed over the entire 2D space. It is shown in the present study that a nonorthogonal GC × GC system associating a polar stationary phase in the first dimension (poly(ethylene glycol)) to a nonpolar one in the second dimension (poly(dimethyl siloxane)) leads to a structured chromatogram, a high peak capacity, and a great 2D space occupation. This idea is demonstrated through the characterization of oxygenated compounds in a coal-derived middle distillate. Results show a clear separation between oxygenated species and hydrocarbons which are classified into linear alkanes, cyclic alkanes, and aromatics. A breakthrough configuration combining a polar poly(ethylene glycol) first dimension and a trifluoropropyl methyl stationary phase in the second dimension enabled a unique identification and quantification of linear, cyclic, and aromatic alcohols. This configuration which could be considered as nonorthogonal still involves two different retention mechanisms: polarity and boiling point in the first dimension and electronic interactions in the second dimension. It is selective toward electronegative poles of alcohols and phenols. The contributions of these two configurations compared to a conventional orthogonal system as well as their roles for oxygenated compounds speciation are highlighted. This contribution is measured through three 2D space occupation factors. It appears through these two examples that orthogonality is intimately linked to analyte properties, and a general concept of dimensionality must be considered.     

Limits of detection and quantification in comprehensive multidimensional separations. 1. A theoretical look

Comprehensive multidimensional separations (e.g., GC×GC, LC×LC, etc.) are increasingly popular tools for the analysis of complex samples, due to their many advantages, such as vastly increased peak capacity, and improvements in sensitivity. The most well-established of these techniques, GC×GC, has revolutionized analytical separations in fields as diverse as petroleum, environmental research, food and flavors, and metabolic profiling. Using multidimensional approaches, analytes can be quantified at levels substantially lower than those possible by one-dimensional techniques. However, it has also been shown that the modulation process introduces a new source of error to the measurement. In this work, we present the results of a study into the limits of quantification and detection (LOQ and LOD) in comprehensive multidimensional separations using GC×GC and the more popular "two-step" integration algorithm as an example. Simulation of chromatographic data permits precise control of relevant parameters of peak geometry and modulation phase. Results are expressed in terms of the dimensionless parameter of signal-to-noise ratio of the base peak (S/N(BP)) making them transportable to any result where quantification is performed using a two-step algorithm. Based on these results, the LOD is found to depend upon the modulation ratio used for the experiment and vary between a S/N(BP) of 10-17, while the LOQ depends on both the modulation ratio and the phase of the modulation for the peak and ranges from a S/N(BP) of 10 to 50, depending on the circumstances.     

Application of two-dimensional correlation spectroscopy to chemometrics: self-modeling curve resolution analysis of spectral data sets

This paper demonstrates the use of two-dimensional (2D) correlation spectroscopy in conjunction with alternating least squares (ALS) based self-modeling curve resolution (SMCR) analysis of spectral data sets. This iterative regression technique utilizes the non-negativity constraints for spectral intensity and concentration. ALS-based SMCR analysis assisted with 2D correlation was applied to Fourier transform infrared (FT-IR) spectra of a polystyrene/methyl ethyl ketone/deuterated toluene (PS/MEK/d-toluene) solution mixture during the solvent evaporation process to obtain the pure component spectra and then the time-dependent concentration profiles of these three components during the evaporation process. We focus the use of asynchronous 2D correlation peaks for the identification of pure variables needed for the initial estimates of the ALS process. Choosing the most distinct bands via the positions of asynchronous 2D peaks is a viable starting point for ALS iteration. Once the pure variables are selected, ALS regression can be used to obtain the concentration profiles and pure component spectra. The obtained pure component spectra of MEK, d-toluene, and PS matched well with known spectra. The concentration profiles for components looked reasonable.     

Optimization of two-dimensional off-line LC/MS separations to improve resolution of complex proteomic samples

In off-line 2D-HPLC a continuous salt gradient is applied in the first separation dimension. This increases the number of identified proteins from complex samples significantly due to higher chromatographic resolution compared to stepwise elution. Achievement of optimal resolution requires the optimization of the two separation dimensions. The influence of LC elution gradients in the first and second dimensions, of analysis time, of stationary-phase material, and of column dimensions was systematically investigated in order to obtain information on the overall peak capacity of the separation system. Provided data indicate that for complex samples such as an E. coli cell extract, a shallow LC SCX gradient with a high number of collected fractions significantly increases the overall peak capacity while for lower complexity samples short gradients with few fractions were sufficient to obtain a maximum of identified peptides. In addition, column dimensions and materials exhibited a strong effect on the overall efficiency of the 2D HPLC separation. The outcome of these experiments could hence serve as a guideline for investigators to adapt their method for the separation of their specific proteome sample to achieve a maximum of peptide sequence information by 2D LC MS/MS analysis.     

Experimental study of the quantitative precision for valve-based comprehensive two-dimensional gas chromatography

For complex sample analysis, there is a need for multidimensional chromatographic instrumentation to be able to separate more compounds, often in shorter time frames. This has led to the development of comprehensive two-dimensional chromatographic instrumentation, such as comprehensive two-dimensional gas chromatography (GC × GC). Lately, much of the focus in this field has been on decreasing peak widths and, therefore, increasing peak capacity and peak capacity production. All of these advancements make it possible to analyze more compounds in a shorter amount of time, but the data still need to remain quantitative to address the needs of most applications. In this report, the relationship among the modulation ratio (M(R)), peak sampling phase (φ), retention time variation (Δt(R)), and how these parameters relate to quantitative analysis precision via the relative standard deviation (RSD) was studied experimentally using a valve-based GC × GC instrument. A wide range of the number of modulations across the first dimension peak width, that is, a M(R) range from ~1 to 10, was examined through maintaining an average first dimension peak width at the base, (1)w(b) of ~3 s and varying the second dimension separation run time from 300 to 2900 ms. An average RSD of 2.1% was experimentally observed at an average M(R) of 2, with a corresponding peak capacity production of ~1200 peaks/min possible. Below this M(R) the RSD quickly increased. In a long-term study of the quantitative precision at a M(R) of 2.5, using 126 replicate injections of a test mixture spanning ~35 h, the RSD averaged 3.0%. The findings have significant implications for optimizing peak capacity production by allowing the use of the longest second dimension run time, while maintaining quantitative precision.     

Pyrolysis comprehensive two-dimensional gas chromatography study of petroleum source rock

Detailed compositional analyses of sedimentary organic matter can provide information on its biotic input, environment of deposition, and level of thermal maturation. Pyrolysis-gas chromatography (py-GC), often coupled with a mass spectrometer (py-GC/MS), is one technique used to provide this information. New developments in comprehensive two-dimensional gas chromatography (GC x GC or 2D-GC), coupled with pyrolysis (py-GC x GC), offer the prospect of providing more complete and quantitative compositional information of complex organic solids, such as kerogen and coals. This study will describe applications of pyrolysis-GC x GC to the characterization of petroleum source rocks using flame ionization detector (FID) and sulfur chemiluminescence detector (SCD). In the hydrocarbon analysis by FID, paraffins, naphthenes, and aromatics form distinct two-dimensional separated groups. In the analysis with SCD, sulfur-containing compounds can be distinguished as different classes, such as mercaptans, sulfides, thiophenes, benzothiophenes, and dibenzothiophenes. Single components or summed bands of homologous components can be analyzed qualitatively and quantitatively. With these detailed molecular fingerprints, the relations between kerogen composition and its biotic input, environment of deposition, and thermal maturation may be better understood.     

Automated instrumentation for comprehensive two-dimensional high-performance liquid chromatography of proteins

A comprehensive two-dimensional (2-D) liquid chromatographic separation system is presented. The system uses a microbore cation exchange column, operated under gradient conditions, as the first dimension separation. Effluent from this first column alternately fills one of two loops on a computer-controlled eight-port valve. A second pump then forces loop material onto a second column, a size exclusion column. UV detection is used, and the system is applied to the separation of protein standards and serum proteins. The 2-D system has a higher resolving power and peak capacity than either of the two columns used alone. The entire first column effluent is analyzed on the second column in virtually the same time it takes to complete the first column separation, without the use of stopped flow methods. The entire system is automated and operated under computer control. Three-dimensional (3-D) data representation provides a means of viewing peak profiles in either separation dimension and contour mapping of the 3-D data provides a more reliable means of peak identification from run to run than that provided by single-column elution times.     

Increasing durability of lightweight concrete through FRP wrap

The purpose of this study was to investigate the effects of Fiber Reinforced Polymer (FRP) wraps on reducing chloride ingress and increasing the durability of lightweight concrete. Several prior studies have dealt with FRP application on normal weight concrete. However, the literature on externally bonded FRP application on lightweight concrete is sparse. This study involved an accelerated testing to determine concrete degradation and decrease in chloride ingress and associated increased durability that FRP wrapping can provide to lightweight concrete. Forty two cylinders were subjected to electricity induced accelerated testing in a saline solution for 50 days. Samples were removed from the immersion tank after specific failures and analyzed for chloride content and failure modes. Both lightweight and normal weight concrete greatly benefited from FRP wrapping in terms of increased time to failure and reduced concrete chloride. Lightweight concrete generally performed better with Carbon FRP (CFRP), and normal weight concrete with Glass FRP (GFRP). CFRP wraps produced the best overall protection. Multiple wraps were more effective at reducing chloride ingress than single wraps. Lightweight concrete had greater chloride permeability reductions, whereas normal weight concrete benefited more from FRP confinement effects. The majority of sample failures were caused by cracking in the concrete substrate.