Protein structural calculation from NMR spectroscopy

Abstract

NMR spectroscopy has been used to determine more than 11000 protein structures in the Protein Data Bank (PDB). By providing geometric constraints between pairs of nuclei in the protein, from NMR spectroscopy the 3D structure of the protein can be obtained. The best established structural calculation methods use distance restraints between pairs of hydrogen atoms provided by nuclear Overhauser effect (NOE). Since the extraction of distance restraints from NOE can be challenging for large protein, the use of the residual dipolar coupling (RDC) has become a popular alternative for protein structuring.

In this thesis, integrated structural calculation approaches using restraints provided by both NOE and RDC are studied. Since the optimization problems arise in structural calculation are non-convex in nature, we devise convex relaxation methods to obtain the global optimum of these problems. This is in contrast to traditional optimization approaches such as simulated annealing that lack the guarantees of global optimality. In the first part of the thesis, we present a divide-and-conquer approach to solve the structural determination problem from distance restraints. In this approach, small fragments of the molecules are first built from distance restraints. Then in Chapter 2, a global registration method is developed to stitch the small fragments into a global structure. Such divide-and-conquer approach can shorten the running-time via parallel computing. However, the divide-and-conquer approach is essentially a distance based procedure in that it only uses distance restraints to build each fragment. Therefore in Chapter 3, we present an integrated approach that directly uses both RDC and NOE to construct the 3D structure of the protein with high accuracy. We apply our method to the protein ubiquitin and obtain structure with 1 Angstrom resolution. In Chapter 4, we describe a method for Saupe tensor estimation from RDC when having multiple protein fragments. In particular, we study the bias arises in Saupe tensor estimation from the structural noise of the protein fragments. We show how Saupe tensor estimation can be used to enhance the global registration method by aligning the small fragments to a principal axis frame.