Comparison of orthogonality estimation methods for the two-dimensional separations of peptides

In two-dimensional chromatography, the orthogonality of separation is important for achieving high peak capacity. In this paper, a number of different metrics are compared as measures of orthogonality. Six peptide elution data sets acquired on different stationary phases are plotted against reversed phase retention data and examined as two-dimensional chromatographic pairs. The data, including six in silico prepared data pairs, are utilized to challenge and compare selected orthogonality metrics. The metrics include correlation coefficients, mutual information, box-counting dimensionality, and surface fractional coverage with different hulls. Although correlation coefficients were found to be less suited for the intended purpose, other methods can provide a suitable measure of orthogonality. The presented results are discussed in terms of method utility, simplicity, and applicability for statistically small sets of chromatographic data. Two of the methods, box counting dimensionality and fractional coverage, were found to be mathematically related.