A method for the analytic determination of polypeptide structure using solid state nuclear magnetic resonance: The ‘‘metric method’’

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Abstract
A method, the metric method, is presented for determining the structure of polypeptides using solid state nuclear magnetic resonance (NMR) dipolar interactions. In analogy to the method of distance geometry used for protein structure determination from high resolution NMR spectroscopy, which is based on the general relationships that distances between points must satisfy, a method is developed here which makes use of the general relationships that angles between vectors must satisfy. With this method, analytical expressions are derived for the dihedral angles of the peptide backbone, and a way for minimizing the structural ambiguities associated with solid state NMR data is also presented. Calculations on a model polypeptide structure reveal the dipolar interactions of only the NH and NC1 bonds provide insufficient information for uniquely determining dihedral angles, even when constraints arising from long range interactions are employed, but these calculations yield a manageable number of solutions when the CαH interaction is also considered.