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We describe new methods for predicting protein tertiary structures to low resolution given the specification of secondary structure and a limited set of long-range NMR distance constraints. The NMR data sets are derived from a realistic protocol involving completely deuterated ¹⁵N and ¹³C-labeled samples. A global optimization method, based upon a modification of the αBB (branch and bound) algorithm of Floudas and co-workers, is employed to minimize an objective function combining the NMR distance restraints with a residue-based protein folding potential containing hydrophobicity, excluded volume, and van der Waals interactions. To assess the efficacy of the new methodology, results are compared with benchmark calculations performed via the X-PLOR program of Brünger and co-workers using standard distance geometry/molecular dynamics (DGMD) calculations. Seven mixed α/β proteins are examined …