Data structures and network algorithms
Data structures and network algorithms
Algorithms for the identifications of three-dimensional maximal common substructures
Journal of Chemical Information & Computer Sciences
Triangulating the surface of a molecule
Discrete Applied Mathematics - Special volume on computational molecular biology
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Shock Graphs and Shape Matching
International Journal of Computer Vision
Proceedings of the Fourth International Conference on Intelligent Systems for Molecular Biology
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
A survey on tree edit distance and related problems
Theoretical Computer Science
Graphical Models
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
Modeling macro–molecular interfaces with Intervor
Bioinformatics
Maximum cliques in protein structure comparison
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
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Given a protein complex involving two partners, the receptor and the ligand, this paper addresses the problem of comparing their binding patches, i.e. the sets of atoms accounting for their interaction. This problem has been classically addressed by searching quasi-isometric subsets of atoms within the patches, a task equivalent to a maximum clique problem, a NP-hard problem, so that practical binding patches involving up to 300 atoms cannot be handled. We extend previous work in two directions. First, we present a generic encoding of shapes represented as cell complexes. We partition a shape into concentric shells, based on the shelling order of the cells of the complex. The shelling order yields a shelling tree encoding the geometry and the topology of the shape. Second, for the particular case of cell complexes representing protein binding patches, we present three novel shape comparison algorithms. These algorithms combine a Tree Edit Distance calculation (TED) on shelling trees, together with Edit operations respectively favoring a topological or a geometric comparison of the patches. We show in particular that the geometric TED calculation strikes a balance, in terms of accuracy and running time, between purely geometric and topological comparisons, and we briefly comment on the biological findings reported in a companion paper.