Unveiling the terra cognita of sequence spaces using Cartesian projection of asymmetric distances

Visualizing relationships within massive biological datasets remains a significant challenge, particularly as sequence length and volume increase. We introduce CAPASYDIS (Cartesian Projections of Asymmetric Distances), a scalable approach designed to map the explored regions of a given sequence space. Unlike traditional dimensionality reduction methods, CAPASYDIS calculates asymmetric distances which account for both the position and type of sequence differences. It projects sequences into a fixed, low-dimensional coordinate system, termed a "seqverse," where each sequence occupies a permanent and unique location. This design allows for the instant mapping of new sequences without the need to recalculate the global coordinate system, enabling the exploration of the diversity space on a standardized map. We applied this method to a large rRNA sequence dataset spanning the three domains of life. Our results demonstrate that the sequences of Bacteria, Archaea, and Eukaryota occupy spatially distinct regions characterized by fundamentally different shapes and patterns of variation. Furthermore, the resulting seqverses retain high amount of taxonomic information, when analyzed from broad domain levels to single-base differences. Overall, CAPASYDIS provides a reproducible, scalable framework for defining the boundaries and topography of biological sequence universes.