Compression ratios based on the Universal Similarity Metric still yield protein distances far from CATH distances

Kolmogorov complexity has inspired several alignment-free distance measures, based on the comparison of lengths of compressions, which have been applied successfully in many areas. One of these measures, the so-called Universal Similarity Metric (USM), has been used by Krasnogor and Pelta to compare simple protein contact maps, showing that it yielded good clustering on four small datasets. We report an extensive test of this metric using a much larger and representative protein dataset: the domain dataset used by Sierk and Pearson to evaluate seven protein structure comparison methods and two protein sequence comparison methods. One result is that Krasnogor-Pelta method has less domain discriminant power than any one of the methods considered by Sierk and Pearson when using these simple contact maps. In another test, we found that the USM based distance has low agreement with the CATH tree structure for the same benchmark of Sierk and Pearson. In any case, its agreement is lower than the one of a standard sequential alignment method, SSEARCH. Finally, we manually found lots of small subsets of the database that are better clustered using SSEARCH than USM, to confirm that Krasnogor-Pelta's conclusions were based on datasets that were too small.