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.