Searching confbrmational space with the spectral distance geometry algorithm

Improved convergence and speed for the distance geometry program APA to determine protein structure

The alternating projections algorithm (APA) is a program that is based on alternating projections and is designed to determine the three dimensional structure of proteins using distance geometry. The sampling and convergence properties of APA, as tested on bovine pancreatic trypsin inhibitor (BPTI) were previously reported in this journal. The results confirmed the program's earlier success with poly-L-alanine. However, the asymptotic convergence of the alternating projections was slow. We show that after good convergence is first obtained via alternating projections, that a weighted quadratic penalty function then produces the final conformation with better convergence in half the time required by the asymptotic convergence of alternating projections.

Distance geometry based comparative modelling

A distance geometry based protein modelling algorithm is presented which relies on the projection of simple model chain coordinates into Euclidean spaces with gradually decreasing dimensionality. Fast embedding was achieved by performing separate distance matrix projections on subsets of the model points. Structural equivalences between the unknown target and related proteins with known structures were deduced either from a mixed sequence/structure multiple alignment or from the output of various fold recognition (threading) approaches. These equivalences were mapped onto the model as structure-specific conserved C alpha atom distances and secondary structure assignments. Additional nonspecific distance restraints derived from general stereochemical properties of folded protein chains were used to guide the modelling process. The method quickly constructed a large number of low-resolution models which could then serve as starting conformations for full-atom refinement. Structure predictions for some targets in the 'Asilomar Challenge' (CASP2) are presented to illustrate potential applications of the approach.