Protein structures, which enjoy a rich combinatorial geometry, truly serve to regulate and define life as we know it, and the determination and prediction of these structures lies at the heart of contemporary molecular biology.
Ongoing joint work with J. E. Andersen has led to models of protein structures based on techniques from Riemann surface theory. Associated discrete invariants lead to new automatic schemes of classifying protein domains that work rather well.
The continuous parameters underlying these discrete invariants furthermore give profound new tools for studying protein geometric structure.
The discrete and continuous models will be described, and the implementation and experimentation with these new geometric techniques in bio-informatics will be discussed as time permits.