Topological Surveillance of Recurrent Mutations in SARS-CoV-2

Topological Data Analysis of the ongoing convergent evolution of the coronavirus

© 2022 Michael Bleher, Lukas Hahn, Maximilian Neumann, Andreas Ott
Karlsruhe Institute of Technology and Heidelberg University, Germany


CoVtRec report as of 2022-08-22
CoVtRec report as of 2022-07-21
CoVtRec report as of 2022-06-17
CoVtRec report as of 2022-05-17
CoVtRec report as of 2022-04-28
CoVtRec report as of 2022-03-15


CoVtRec is a custom Python pipeline for the computation of the topological recurrence index (tRI) for mutations in the evolution of the genome of the coronavirus SARS-CoV-2 in the current COVID-19 pandemic. The topological recurrence index is a measure for the ongoing convergent evolution. It provides a lower bound for the number of independent occurrences of a given mutation in the phylogeny. Its computation relies on persistent homology, one of the main tools in the mathematical field of Topological Data Analysis (TDA). CoVtRec systematically detects convergent events in viral evolution merely by their topological footprint, overcoming limitations of current phylogenetic inference techniques. Due to highly optimized algorithms it easily scales to hundreds of thousands of distinct genomes. We provide regular reports about potentially adpative mutations based on current SARS-CoV-2 genome data.

CoVtRec uses hammingdist for the computation of genetic distance matrices and Ripser for the computation of persistent homology. It implements a new approach based on Vietoris-Rips transformations in multipersistent homology. This leverages the stratification by time of genomic data for efficient tRI time series analyses on a daily basis.


Michael Bleher, Lukas Hahn, Juan Ángel Patiño-Galindo, Mathieu Carrière, Ulrich Bauer, Raúl Rabadán, and Andreas Ott: “Topological data analysis identifies emerging adaptive mutations in SARS-CoV-2”, arXiv:2106.07292

Maximilian Neumann, Michael Bleher, Lukas Hahn, Samuel Braun, Holger Obermaier, Mehmet Soysal, René Caspart, and Andreas Ott: “MuRiT: Efficient Computation of Pathwise Persistence Barcodes in Multi-Filtered Flag Complexes via Vietoris-Rips Transformations”, arXiv:2207.03394


We acknowledge the use of de.NBI Cloud within the German Network for Bioinformatics Infrastructure (de.NBI) and the support by the High Performance and Cloud Computing Group at the Zentrum für Datenverarbeitung of the University of Tübingen and the German Federal Ministry of Education and Research (BMBF) through grant no 031 A535A. We acknowledge support from the Steinbuch Centre for Computing (SCC) at Karlsruhe Institute of Technology.