Algorithms and analytic solutions using sparse residual dipolar couplings for high-resolution automated protein backbone structure determination by NMR

Abstract

Developing robust and automated protein structure determination algorithms using nuclear magnetic resonance (NMR) data is an important goal in computational structural biology. Algorithms based on global orientational restraints from residual dipolar couplings (RDCs) promise to be quicker and more accurate than approaches that use only distance restraints. Recent development of analytic expressions for the roots of RDC equations together with protein kinematics has enabled exact, linear-time algorithms, highly desirable over earlier stochastic methods. In addition to providing guarantees on the number and quality of solutions, exact algorithms require a minimal amount of NMR data, thereby reducing the number of NMR experiments. Implementations of these methods determine the solution structures by explicitly computing the intersections of algebraic curves representing discrete RDC values. However, if additional RDC data can be measured, the algebraic curves no longer generically intersect. We address this situation in the paper and show that globally optimal structures can still be computed analytically as points closest to all of the algebraic curves representing the RDCs. We present new algorithms that expand the types and number of RDCs from which analytic solutions are computed. We evaluate the performance of our algorithms on NMR data for four proteins: human ubiquitin, DNA-damage-inducible protein I (DinI), the Z domain of staphylococcal protein A (SpA), and the third IgG-binding domain of Protein G (GB3). The results show that our algorithms are able to determine high-resolution backbone structures from a limited amount of NMR data. © 2010 Springer-Verlag Berlin Heidelberg.