Effects of limited input distance constraints upon the distance geometry algorithm

In this paper we examine the distance geometry (DG) algorithm in the form used to determine the structure of proteins. We focus on three aspects of the algorithm: bound smoothing with the triangle inequality, the random selection of distances within the bounds, and the number of distances needed to specify a structure. Computational experiments are performed using simulated and real data for basic pancreatic trypsin inhibitor (BPTI) from nmr and crystallographic measurements. We find that the upper bounds determined by bound smoothing to be a linear function of the true crystal distance. A simple model that describes the results obtained with randomly selected trial distances is proposed. Using this representation of the trial distances, we show that BPTI DG structures are more compact than the true crystal structure. We also show that the DG-generated structures no longer resemble test structures when the number of these interresidue distance constraints is less than the number of degrees of freedom of the protein backbone. While the actual model will be sensitive the way distances are chosen, our conclusions are likely to apply to other versions of the DG algorithm.