Computing Largest Common Point Sets under Approximate Congruence
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Algorithmic Aspects of Protein Structure Similarity
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Algorithms for optimal protein structure alignment
Bioinformatics
On Protein Structure Alignment under Distance Constraint
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Using dominances for solving the protein family identification problem
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
Optimizing a Widely Used Protein Structure Alignment Measure in Expected Polynomial Time
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Maximum cliques in protein structure comparison
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
SHREC'10 track: protein model classification
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
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We present a mathematical model and exact algorithm for optimally aligning protein structures using the dali scoring model. This scoring model is based on comparing the interresidue distance matrices of proteins and is used in the popular dali software tool, a heuristic method for protein structure alignment. Our model and algorithm extend an integer linear programming approach that has been previously applied for the related, but simpler, contact map overlap problem. To this end, we introduce a novel type of constraint that handles negative score values and relax it in a Lagrangian fashion. The new algorithm, which we call dalix, is applicable to any distance matrix-based scoring scheme. We also review options that allow to consider fewer pairs of interresidue distances explicitly because their large number hinders the optimization process. Using four known data sets of varying structural similarity, we compute many provably score-optimal dali alignments. This allowed, for the first time, to evaluate the dali heuristic in sound mathematical terms. The results indicate that dali usually computes optimal or close to optimal alignments. However, we detect a subset of small proteins for which dali fails to generate any significant alignment, although such alignments do exist.