Topology and geometry based classification of tauopathies

Neurodegenerative diseases, like Alzheimer's, are associated with the presence of neurofibrillary lesions formed by tau protein filaments. While it is known that different morphologies of tau filaments characterize different neurodegenerative diseases, there are few metrics of global and local structure complexity that enable to quantify their structural diversity rigorously. By using cryo-electron microscopy structures of tau filaments that are available in the Protein Data Bank, we employ for the first time mathematical topology and geometry to classify neurodegenerative diseases and also to identify specific sites of interest such as the PHF6 motifs and the 301 mutation site, and other aspects of their filament structure relevant to experiments. Our results reveal a hierarchy of classification from global to local topology and geometry characteristics. In particular, we find that tauopathies can be classified with respect to the handedness of their global conformations and the handedness of the relative orientations of their repeats. Progressive supranuclear palsy is identified as an outlier with an observable knotoid structure. This topological characteristic can be attributed to a pattern of the beginning of the R3 domain that is present in all tauopathies but at different extent. Our results also reveal that topology and geometry of structures alone can predict site-specific mutations that are experimentally shown to lead to protein aggregation and disease.