Abstract
Recent studies of tau proteins point to specific sites or motifs along the protein related to its misfolding and aggregation propensity, which is associated with neurodegenerative diseases of structure-dependent pathology. In this manuscript we employ topology and geometry to analyze the local structure of tau proteins obtained from the Protein Data Bank. Our results show that mathematical topology/geometry of cryo-EM structures alone identify the PGGG motifs, and the PHF6(*) motifs as sites of interest and reveal a geometrical hierarchy of the PGGG motifs that differs for 3R+4R and 4R tauopathies. By employing the Local Topological Free Energy (LTE), we find that progressive supranuclear palsy (PSP) and globular glial tauopathy (GGT) have the highest LTE values around residues 302-305, which are inside the jR2R3 peptide and in the vicinity of the 301 site, experimentally associated with aggregation. By extending the LTE definition to estimate a global topological free energy, we find that the jR2R3 peptide of PSP and GGT, has in fact the lowest global topological free energy among other tauopathies. These results point to a possible correlation between the global topological free energy of parts of the protein and the LTE of specific sites.