Symmetric Protein Structure Determination Using Arrangements of Circular Arcs
Abstract
Nuclear magnetic resonance (NMR) spectroscopy is a primary tool to perform structural studies of proteins in physiologicallyrelevant solution conditions. Restraints on distances between pairs of nuclei in the protein, derived from the nuclear Overhauser effect (NOE), provide information about the structure of the protein in its folded state. NMR studies of symmetric protein homooligomers present a unique challenge. Using Xfiltered NOESY experiments, it is possible to determine whether an NOE restrains a pair of protons across different subunits or within a single subunit, but current experimental techniques are unable to determine in which subunits the restrained protons lie. Consequently, it is difficult to assign NOEs to particular pairs of subunits with certainty, thus hindering the structural analysis of the oligomeric state. Computational approaches are needed to address this subunit ambiguity, but traditional solutions often rely on stochastic search coupled with simulated annealing and simulations of simplified molecular dynamics, which have many tunable parameters that must be chosen carefully and can also fail to report structures consistent with the experimental restraints. In addition, these traditional approaches rarely provide guarantees on running time or solution quality. We reduce the structure determination of homooligomers with cyclic symmetry to computing geometric arrangements of unions of annuli in a plane. Our algorithm, DISCO, runs in expected O(n^2) time, where n is the number of distance restraints, potentially assigned ambiguously. DISCO is guaranteed to report the exact set of oligomer structures consistent with the distance restraints and also with orientational restraints from residual dipolar couplings (RDCs). We demonstrate our method using two symmetric protein complexes: the trimeric E. coli Diacylglycerol Kinase (DAGK), and a dimeric mutant of the immunoglobulinbinding domain B1 of streptococcal protein G (GB1). In both cases, DISCO computes oligomer structures with high precision and also finds distance restraints that are either mutually inconsistent or inconsistent with the RDCs.
References
 Martin J, Yan T, Zhou P, BaileyKellogg C, Donald BR.
A graphical method for analyzing distance restraints using residual dipolar couplings for structure determination of symmetric protein homooligomers.
Protein Science, 20(6):970–985, 2011. [link]  Martin J, Yan T, Zhou P, BaileyKellogg C, Donald BR.
A geometric arrangement algorithm for structure determination of symmetric protein homooligomers from NOEs and RDCs.In: Bafna V, Sahinalp SC, Eds. (2011) Proceedings of the Fifteenth Annual International Conference on Research in Computational Molecular Biology (RECOMB). Springer, Berlin, pp 222–237.  Martin J, Yan T, Zhou P, BaileyKellogg C, Donald BR.
A geometric arrangement algorithm for structure determination of symmetric protein homooligomers from NOEs and RDCs.
Journal of Computational Biology. (in press)  Bruce R. Donald.
Algorithms in Structural Molecular Biology.
MIT Press (2011). [link]
Contact
Jeffrey W. Martin 

Bruce R. Donald 