Automated multiple structure alignment and detection of a common substructural motif.

While a number of approaches have been geared toward multiple sequence alignments, to date there have been very few approaches to multiple structure alignment and detection of a recurring substructural motif. Among these, none performs both multiple structure comparison and motif detection simultaneously. Further, none considers all structures at the same time, rather than initiating from pairwise molecular comparisons. We present such a multiple structural alignment algorithm. Given an ensemble of protein structures, the algorithm automatically finds the largest common substructure (core) of C(alpha) atoms that appears in all the molecules in the ensemble. The detection of the core and the structural alignment are done simultaneously. Additional structural alignments also are obtained and are ranked by the sizes of the substructural motifs, which are present in the entire ensemble. The method is based on the geometric hashing paradigm. As in our previous structural comparison algorithms, it compares the structures in an amino acid sequence order-independent way, and hence the resulting alignment is unaffected by insertions, deletions and protein chain directionality. As such, it can be applied to protein surfaces, protein-protein interfaces and protein cores to find the optimally, and suboptimally spatially recurring substructural motifs. There is no predefinition of the motif. We describe the algorithm, demonstrating its efficiency. In particular, we present a range of results for several protein ensembles, with different folds and belonging to the same, or to different, families. Since the algorithm treats molecules as collections of points in three-dimensional space, it can also be applied to other molecules, such as RNA, or drugs.

Alignment of flexible protein structures.

We present two algorithms which align flexible protein structures. Both apply efficient structural pattern detection and graph theoretic techniques. The FlexProt algorithm simultaneously detects the hinge regions and aligns the rigid subparts of the molecules. It does it by efficiently detecting maximal congruent rigid fragments in both molecules and calculating their optimal arrangement which does not violate the protein sequence order. The FlexMol algorithm is sequence order independent, yet requires as input the hypothesized hinge positions. Due its sequence order independence it can also be applied to protein-protein interface matching and drug molecule alignment. It aligns the rigid parts of the molecule using the Geometric Hashing method and calculates optimal connectivity among these parts by graph-theoretic techniques. Both algorithms are highly efficient even compared with rigid structure alignment algorithms. Typical running times on a standard desktop PC (400 MHz) are about 7 seconds for FlexProt and about 1 minute for FlexMol.

Multiple structural alignment and core detection by geometric hashing.

A Multiple Structural Alignment algorithm is presented. The algorithm accepts an ensemble of protein structures and finds the largest substructure (core) of C alpha atoms whose geometric configuration appear in all the molecules of the ensemble (core). Both the detection of this core and the resulting structural alignment are done simultaneously. Other large enough multistructural superimpositions are detected as well. Our method is based on the Geometric Hashing paradigm and a superimposition clustering technique which represents superimpositions by sets of matching atoms. The algorithm proved to be efficient on real data in a series of experiments. The same method can be applied to any ensemble of molecules (not necessarily proteins) since our basic technique is sequence order independent.