Symmetry in the Transcriptome and Genome Sequences of Siberian Larch (Larix sibirica Ledeb.)

We studied the structuredness and order in draft assemblies of the Siberian larch (Larix sibirica Ledeb.) transcriptome and genome. Assembled contigs were converted into the triplet frequency dictionaries followed by their cluster analysis. The transformation maps the contigs into a metric space. We used K-means clusterization to analyze the transcriptome and genome structures, which were visualized with the elastic map technique. The observed clusters demonstrated several interesting symmetries, also including those in the statistical and combinatorial properties. For instance, clustering in two classes yields stable classification with a good separability of clusters. We have checked the pattern of the second Chargaff’s parity rule implementation for pairs of palindromic triplets within the first and the second classes and between them. It was found that the transcriptome sequences had significantly less discrepancy between the classes compared to genome sequences. Probably, it was due to the presence of contigs in the transcriptome assembly representing RNA sequences transcribed from opposite strands. Unlike the transcriptome, genome contigs demonstrated an inverse pattern of discrepancies regarding the second Chargaff’s parity rule. The hypothesis was confirmed by BLAST. In addition, an unexpected octahedral structure exhibiting rotational symmetry was discovered in triplet frequency dictionary ensembles.