Algorithm engineering for optimal alignment of protein structure distance matrices

TL;DR

This paper introduces a novel mathematical framework and algorithmic techniques for provably optimal alignment of protein distance matrices, advancing the accuracy and reliability of structural protein comparisons.

Contribution

It presents the first mathematical model and algorithm engineering methods for optimal protein structure alignment based on inter-residue distance matrices.

Findings

First provably optimal alignments using Dali scoring

Unified framework for various scoring functions

Effective handling of large integer linear programs

Abstract

Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring function. We introduce the structural alignment problem formally, which enables us to express a variety of scoring functions used in previous work as special cases in a unified framework. Further, we propose the first mathematical model for computing optimal structural alignments based on dense inter-residue distance matrices. We therefore reformulate the problem as a special graph problem and give a tight integer linear programming model. We then present algorithm engineering techniques to handle the huge integer linear programs of real-life distance matrix alignment problems. Applying these techniques, we can compute provably optimal Dali alignments for the very first time.