Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Structural alignment of large—size proteins via lagrangian relaxation
Proceedings of the sixth annual international conference on Computational biology
Proceedings of the 5th International Conference on Intelligent Systems for Molecular Biology
Proceedings of the Fourth International Conference on Intelligent Systems for Molecular Biology
Algorithmic Aspects of Protein Structure Similarity
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Rapid protein side-chain packing via tree decomposition
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Graph algorithms for biological systems analysis
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An Efficient Lagrangian Relaxation for the Contact Map Overlap Problem
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Finding compact structural motifs
Theoretical Computer Science
Finding compact structural motifs
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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This paper proposes a parameterized algorithm for aligning two protein structures, in the case where one protein structure is represented by a contact map graph and the other by a contact map graph or a distance matrix. If the sequential order of alignment is not required, the time complexity is polynomial in the protein size and exponential with respect to two parameters $\frac{D_u}{D_l}$ and $\frac{D_c}{D_l}$, which usually can be treated as constants. In particular, Du is the distance threshold determining if two residues are in contact or not, Dc is the maximally allowed distance between two matched residues after two proteins are superimposed, and Dl is the minimum inter-residue distance in a typical protein. This result indicates that if both $\frac{D_u}{D_l}$ and $\frac{D_c}{D_l}$ are small enough, then there is a polynomial-time approximation scheme for the non-sequential protein structure alignment problem. Empirically, both $\frac{D_u}{D_l}$ and $\frac{D_c}{D_l}$ are very small and can be treated as constants. This result clearly demonstrates that the hardness of the contact-map based protein structure alignment problem is related not to protein size but to several parameters, which depend on how the protein structure alignment problem is modeled. The result is achieved by decomposing the protein structure using tree decomposition and discretizing the rigid-body transformation space. We have implemented our algorithm and preliminary experimental results indicate that on a Linux PC, it takes from ten minutes to one hour to align two proteins with approximately 100 residues.