PMID- 15213422 OWN - NLM STAT- MEDLINE DCOM- 20050131 LR - 20181113 IS - 0925-2738 (Print) IS - 0925-2738 (Linking) VI - 29 IP - 3 DP - 2004 Jul TI - Exact solutions for internuclear vectors and backbone dihedral angles from NH residual dipolar couplings in two media, and their application in a systematic search algorithm for determining protein backbone structure. PG - 223-42 AB - We have derived a quartic equation for computing the direction of an internuclear vector from residual dipolar couplings (RDCs) measured in two aligning media, and two simple trigonometric equations for computing the backbone (phi,psi) angles from two backbone vectors in consecutive peptide planes. These equations make it possible to compute, exactly and in constant time, the backbone (phi,psi) angles for a residue from RDCs in two media on any single backbone vector type. Building upon these exact solutions we have designed a novel algorithm for determining a protein backbone substructure consisting of alpha-helices and beta-sheets. Our algorithm employs a systematic search technique to refine the conformation of both alpha-helices and beta-sheets and to determine their orientations using exclusively the angular restraints from RDCs. The algorithm computes the backbone substructure employing very sparse distance restraints between pairs of alpha-helices and beta-sheets refined by the systematic search. The algorithm has been demonstrated on the protein human ubiquitin using only backbone NH RDCs, plus twelve hydrogen bonds and four NOE distance restraints. Further, our results show that both the global orientations and the conformations of alpha-helices and beta-strands can be determined with high accuracy using only two RDCs per residue. The algorithm requires, as its input, backbone resonance assignments, the identification of alpha-helices and beta-sheets as well as sparse NOE distance and hydrogen bond restraints. FAU - Wang, Lincong AU - Wang L AD - Dartmouth Computer Science Department, Hanover, NH 03755, USA. FAU - Donald, Bruce Randall AU - Donald BR LA - eng GR - R01 GM 65982/GM/NIGMS NIH HHS/United States PT - Journal Article PT - Research Support, Non-U.S. Gov't PT - Research Support, U.S. Gov't, Non-P.H.S. PT - Research Support, U.S. Gov't, P.H.S. PL - Netherlands TA - J Biomol NMR JT - Journal of biomolecular NMR JID - 9110829 RN - 0 (Proteins) RN - 0 (Ubiquitin) SB - IM MH - Algorithms MH - Genomics MH - Humans MH - Kinetics MH - Magnetic Resonance Spectroscopy/*methods MH - Models, Molecular MH - Models, Statistical MH - Protein Conformation MH - Protein Folding MH - Protein Structure, Secondary MH - Proteins/*chemistry MH - Software MH - Ubiquitin/chemistry MH - X-Rays EDAT- 2004/06/24 05:00 MHDA- 2005/02/03 09:00 CRDT- 2004/06/24 05:00 PHST- 2004/06/24 05:00 [pubmed] PHST- 2005/02/03 09:00 [medline] PHST- 2004/06/24 05:00 [entrez] AID - 5270727 [pii] AID - 10.1023/B:JNMR.0000032552.69386.ea [doi] PST - ppublish SO - J Biomol NMR. 2004 Jul;29(3):223-42. doi: 10.1023/B:JNMR.0000032552.69386.ea.