Two algorithms are introduced that show exceptional promise in finding molecular conformations using distance geometry on nuclear magnetic resonance data. The f i s t algorithm is a gradient version of the majorization algorithm from multidimensional scaling. The main contribution is a large decrease in CPU time. The second algorithm is an iterative algorithm between possible conformations obtained from the f i s t algorithm and permissible data points near the configuration. These ideas are similar to alternating least squares or alternating projections on convex sets. The iterations significantly improve the conformation from the first algorithm when applied to the small peptide E. coZi STh enterotoxin. 0 1993 by John Wiley & Sons, Inc.

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A fundamental problem in molecular biology is the determination of the conformation of macromolecules from NMR data. Several successful distance geometry programs have been developed for this purpose, for example DISGEO. A particularly difficult facet of these programs is the embedding problem, that is the problem of determining those conformations whose distances between atoms are nearest those measured by the NMR techniques. The embedding problem is the distance geometry equivalent of the multiple minima problem, which arises in energy minimization approaches to conformation determination. We show that the distance geometry approach has some nice geometry not associated with other methods that allows one to prove detailed results with regard to the location of local minima. We exploit this geometry to develop some algorithms which are faster and find more minima than the algorithms presently used.