Topological Measurement of Protein Compressibility via Persistence Diagrams

We exploit recent advances in computational topology to study the compressibility of various proteins found in the Protein Data Bank (PDB). Our fundamental tool is the persistence diagram, a topological invariant which captures the sizes and robustness of geometric features such as tunnels and cavities in protein molecules. Based on certain physical and chemical properties conjectured to impact protein compressibility, we propose a topological measurement CP for each protein molecule P . CP can be efficiently computed from the PDB data of P . Our main result establishes a clear linear correlation between CP and the experimentally measured compressibility of most proteins for which both PDB information and experimental compressibility data are available.