Topology and geometry-based methods for quantifying the complexity of protein structures

New topological and geometrical methods in knot theory provide a way to rigorously measure the entanglement of open curves in 3-space for the first time. These methods enable the topological analysis of physical systems of filaments, such as those formed by proteins. In this dissertation we employ tools from knot theory in combination with available experimental data and molecular simulations to analyze the topological complexity of tau proteins. These proteins are involved in a class of neurodegenerative diseases, called tauopathies. The methods developed in this dissertation are general and applicable to other proteins as well as any physical systems of filaments. By using topological measures (Linking Number, Writhe and second Vassiliev measure) to quantify three-dimensional structures of tau filaments in the Protein Data Bank, this research provides a new classification of tauopathies based on the global and local structures of different tau filaments. This novel classification reveals more subtle differences in the structures of diseases with different pathologies that were previously unknown. Moreover, these tools also predict important sites in tau filaments such as the PGGG motifs that stabilize those filaments, as well as the 301 mutation site known experimentally to promote aggregation. The novelty and importance of these results is that they are based solely on static structures of proteins, yet they seemingly predict aspects of protein folding and aggregation. This points to these methods as tools to predict novel structure- and site-specific therapeutics. Indeed, tau antibody analysis shows the mathematical topology of an antibody can predict antigen binding sites. By employing coarse grained molecular dynamics simulations of full-length tau proteins in solution, we find that co-factors such as RNA and stress can affect the topology/geometry of unfolded tau proteins. Moreover, it is shown that local conformations of tau proteins with these co-factors are more favorable than those of tau filaments alone, which may imply that they could stabilize the proteins. The data also demonstrate that knotting of a tau protein in the unfolded ensemble is a possible but rare event.

Grantor dc:publisher

University of Tennessee at Chattanooga

Year dc:date.available

2025

Author dc:creator

• Sugiyama, Masumi

Contributors dc:contributor

• Panagiotou, Eleni
• Skjellum, Anthony; Cox, Christopher L. (Christopher Lee); Wang, Jin
• College of Engineering and Computer Science

• Knot theory
• Proteins--Conformation
• Proteins--Structure
• Nervous system--Degeneration

Licence

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/956

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-2135