Nuclear magnetic resonance (NMR) spectroscopy is the most-used technique for protein structure determination besides X-ray crystallography. In this talk, the computational problem of protein structuring from residual dipolar coupling (RDC) will be discussed.

Typically the 3D structure of a protein is obtained through finding the coordinates of atoms subject to pairwise distance constraints. RDC measurements provide additional geometric information on the angles between bond directions and the principal-axis-frame. The optimization problem involving RDC is non-convex and we present a novel convex programming relaxation to it by incorporating quaternion algebra. In simulations we attain the Cramer-Rao lower bound with relatively efficient running time. From real data, we obtain the protein backbone structure for ubiquitin with 1 Angstrom resolution.

This is joint work with Jose Frederico Ferreira, Amit Singer and David Cowburn.

Yuehaw Khoo is a post-doctoral scholar at Stanford University, working with Lexing Ying. Previously, he did his Ph.D. study at Princeton with Amit Singer. He is interested in the application of optimization and machine learning techniques in biological and physical applications.