Protein Structure Prediction Using Residual Dipolar Couplings
NMR is important for the determination of protein structures, but the usual NOE distance constraints cannot capture large structures. However, RDC experiments offer global orientation constraints for the H–N backbone vectors. Our first application validates local structure from 3 RDC values, by solving an elliptical equation. Second, we model the protein backbone by drawing upon robot kinematics, and compute the relative orientation of consecutive pairs of peptide planes; we obtain a unique orientation by considering also NOE distances. Third, we present a novel algebraic method for determining the relative orientation of secondary structures, a crucial question in fold classification. The orientation of the magnetic vector relative to the secondary structures is determined using two media, leading to a rotation matrix mapping one molecular frame to the other. A unique solution is obtained from RDC data, with no NOE constraints. Our algorithms use robust algebraic operations and are implemented in MAPLE.
KeywordsInverse kinematics MAPLE implementation polynomial equations protein fold protein kinematics RDC data Saupe tensor secondary structure
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