Anthony Bak

Computational Topology Projects

1. DHFR Inhibitor and cancer therapies . In a current collaboration with Michael Lerner (NIH) we are using persistent homology and bottleneck distance to construct the moduli space of DHFR-type inhibitors and identify those regions of the space corresponding to molecules useful for use in cancer therapies. Preliminary results are encouraging and validate the promise of these topological techniques. The known inhibitors appear to cluster in the moduli space of all DHFR inhibitors, and we hope to identify some new candidates for potential cancer drugs. The database used is available as part of a open competition run by McMaster University, and our preliminary results look significantly better then previous attempts.

2. Moduli Space of Protein Topologies. Proteins are the molecular machinery that drive life, and a deep understanding of their mechanisms and interactions is key to developing insights into both basic biology and bioengineering applications such as drug design. At a fundamental level protein interactions are driven by the shapes of the involved molecules, and our goal is to use modern, sophisticated techniques from the rapidly-developing field of computational topology to construct a moduli space, parameterizing all protein topologies.

   Whereas efforts such as SCOP and CATH are limited to the ability classify and group protein topologies, our techniques do this and give a natural metric between proteins. This allows us to consider local questions (What are ``nearby'' proteins like?) in a more sophisticated manner than has been possible. Perhaps more importantly, we can for the first time ask global questions (Are there holes or gaps in the moduli space of proteins? What does the space of proteins with property X look like? What new biochemical interactions can we predict?) in a mathematically rigorous way. We hope that answers to these questions will revolutionize our understanding of proteins.