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The ability to analyze large molecular structures by NMR techniques requires efficient methods for structure calculation. Currently, there are several widely available methods for tackling these problems, which, in general, rely on the optimization of penalty-type target functions to satisfy the conformational restraints. Typically, these methods combine simulated annealing protocols with molecular dynamics and local minimization, either in distance or torsional angle space. In this work, both a novel formulation and algorithmic procedure for the solution of the NMR structure prediction problem is outlined. First, the unconstrained, penalty-type structure prediction problem is reformulated using nonlinear constraints, which can be individually enumerated for all, or subsets, of the distance restraints. In this way, the violation can be controlled as a constraint, in contrast to the usual penalty-type restraints. In addition, the customary simplified objective function is replaced by a full atom force field in the torsional angle space. This guarantees a better description of atomic interactions, which dictate the native structure of the molecule along with the distance restraints. The second novel portion of this work involves the solution method. Rather than pursue the typical simulated annealing procedure, this work relies on a deterministic method, which theoretically guarantees that the global solution can be located. This branch and bound technique, based on the aBB algorithm, has already been successfully applied to the identification of global minimum energy structures of peptides modeled by full atom force Correspondence to: C. A. Floudas; e-mail: floudas@titan. princeton.edu Contractrgrant sponsor: the National Science Foundation, Air Force Office of Scientific Research, and the National InstiŽ . tutes of Health; contractrgrant number: NIH R01 GM52032 ( ) Journal of Computational Chemistry, Vol. 20, No. 13, 1354]137

Predicting peptide structures using NMR data and deterministic global optimization