Informational Orthogonality of Two-Dimensional Chromatographic Separations

Abstract

A qualitative informational similarity technique has been used to describe the informational orthogonality of projected two-dimensional (2-D) chromatographic separations of complex mixtures from their one-dimensional 1-D separations. The reversed-phase liquid chromatography (RPLC), supercritical fluid chromatography (SFC), gas-liquid chromatography (GLC), and micellar electrokinetic capillary chromatography (MECC) retention behavior of up to 46 solutes of varying molecular properties was studied by 2-D range-scaled retention time plots and information entropy calculations. One hundred five combinations of technique/stationary phase pairs were used to simulate the 2-D chromatographic analyses. The informational entropy of one and two dimensions, the mutual information, the synentropy or "cross information", and the informational similarity were calculated to describe the informational orthogonality. In addition, pattern descriptors were used to qualitatively describe the 2-D peak distribution. With the solutes tested, informational orthogonality, zero informational similarity, was observed with MECC-SDS/SFC-C1, MECC-SDS/SFC-Carbowax, MECC-TTAB/SFC-Carbowax, HPLC-C18/GLC-DB-5, HPLC-PBD/SFC-phenyl, SFC-Carbowax/GLC-DB5, and HPLC-phenyl/SFC-phenyl 2-D chromatographic systems. Conversely, with the solutes tested, informational nonorthogonal behavior described by range-scaled retention time plots to moderate to severe band overlap and data clustering was observed with 2-D chromatographic systems with high informational similarity and moderate to high degrees of synentropy. These results should prove useful for predicting complementary 2-D techniques as well as for choosing a second separation technique for confirmation of separation or peak purity.

Spot overlapping in two‐dimensional polyacrylamide gel electrophoresis maps: Relevance to proteomics

“…The situation is a consequence of the mixture complexity itself and results in a drop in the quality of analytical information contained in the map; this loss is proportional to the degree of randomness of the map itself [18][19][20]. As a consequence of spot overlapping [18][19][20][21][22][23][24][25][26][27][28][29][30] (i) the number of spots, p, detectable in the map is always lower than the number m of components present in the mixture. The number of spots, p, does not represent the real complexity of the mixture: the loss of analytical information is represented by the separation degree g = p/m and is proportional to the degree of overlapping present in the mixture [18][19] Therefore, the total number of detectable spots, p, is given by:…”

“…Many statistic theories have been developed to describe spot overlapping in 2-D separations [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]: they all have been tested extensively by computer-simulated data [19][20][21][22][23][24]26] as well as by experimental data [25,30]. In the simplest and more general model, spots formed by only 1 SC are randomly distributed on all the separation space [19,20].…”

Comprehensive multi‐dimensional liquid chromatographic separation in biomedical and pharmaceutical analysis: a review

“…In a detailed study, they investigated this approach using 46 substantially hydrophobic solutes and a variety of chromatographic approaches. Synentropy is then the percentage informational entropy of diagonally aligned data over total informational entropy and gives a measure of correlation to confirm orthogonality (Slonecker et al, 1996).…”

Recent Developments in Capillary Electrophoresis–Mass Spectrometry of Proteins and Peptides

“…Ideally, the dimensions should be orthogonal (i.e., independent), and the separation accomplished in the first dimension should be preserved in the next. 138,139 Combining a reversed-phase chromatographic method with an electrophoretic-based one is particularly attractive because of the complementarity of these techniques; the former resolves the analytes according to their hydrophobic interaction with a stationary phase, while the latter does so according to the analytes' charge-to-size ratios; hence, there is little redundancy in mechanisms. 140 CIEF, as the first dimension, has been coupled to LC-MS. Apart from the extremely high resolving power of such combination, inserting an LC step between CIEF and MS has the advantage of enabling ampholyte removal to minimize interference during the MS analysis.…”