Name
Title | ||
|---|---|---|
Residual Dipolar Coupling, Protein Backbone Conformation and Semidefinite Programming. |
Abstract | ||
|---|---|---|
We investigate the classical problem of protein structure determination in NMR spectroscopy from geometrical restraints using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a semidefinite program (SDP). However, in practice there are often too few distance restraints for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between bond directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires good initializations. In this paper, we model the protein backbone as an articulated structure composed of rigid units. We estimate the rotation of each rigid unit using SDP relaxation that incorporates quaternion algebra. The two SDP based methods we propose - RDC-SDP and RDC-NOE-SDP have polynomial time complexity in the number of amino-acids, with average running time being 25 seconds and 3 minutes respectively for calculating protein fragments of typical size on a personal laptop. We further introduce the Cramer-Rao bound (CRB) to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy RDC measurements. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise, for realistic noise magnitude our SDP attains the CRB. Finally, we apply our proposed method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental distance restraints and RDC measurements obtained in two alignment medium. Comparing to the X-ray structure, the ubiquitin fragments considered are determined to 0.6 AA resolution and the full protein structure formed from the fragments has 1 AA error. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Computational Engineering, Finance, and Science | Pairwise comparison,Mathematical optimization,Quaternion algebra,Residual dipolar coupling,Gaussian noise,Convex optimization,Optimization problem,Mathematics,Semidefinite programming,Protein structure |
DocType | Volume | Citations |
Journal | abs/1604.01504 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuehaw Khoo | 1 | 32 | 6.04 |
| Amit Singer | 2 | 18 | 2.49 |
| David Cowburn | 3 | 0 | 0.34 |