Abstract not found

This article investigate different aspects regarding pairwise and multiple structure comparison, and the problem of automatically discover common patterns in a set of structures. Descriptions and representation of structures and patterns are investigated, as well as scoring and algorithms for comparison and discovery. A framework and nomenclature is developed, and a lot of methods are reviewed and placed into this framework.

We show that calculating contact map overlap (a measure of similarity of protein structures) is NPhard, but can be solved in polynomial time for several interesting and relevant special cases. We identify an important special case of this problem corresponding to self-avoiding walks, and prove a decomposition theorem and a corollary approximation result for this special case. These are the rst approximation algorithms with guaranteed error bounds, and NPcompleteness results in the literature in the area of protein structure alignment/fold recognition for measures of structure similarity of practical interest. A

Structure comparison is a fundamental problem for structural genomics. A variety of structure comparison methods were proposed and several protein structure classification servers e.g., SCOP, DALI, CATH, were designed based on them, and are extensively used in practice. This area of research continues to be very active, being energized bi-annually by the CASP folding competitions, but despite the extraordinary international research effort devoted to it, progress is slow. A fundamental dimension of this bottleneck is the absence of rigorous algorithmic methods. A recent excellent survey on structure comparison by Taylor et.al. [23] records the state of the art of the area: In structure comparison, we do not even have an algorithm that guarantees an optimal answer for pairs of structures ...

Sequence alignment programs such as BLAST and PSI-BLAST are used routinely in pairwise, profile-based, or intermediate-sequencesearch (ISS) methods to detect remote homologies for the purposes of fold assignment and comparative modeling. Yet, the sequence alignment quality of these methods at low sequence identity is not known. We have used the CE structure alignment program (Shindyalov and Bourne, Prot Eng 1998;11: 739) to derive sequence alignments for all superfamily and family-level related proteins in the SCOP domain database. CE aligns structures and their sequences based on distances within each protein, rather than on interprotein distances. We compared BLAST, PSI-BLAST, CLUSTALW, and ISS alignments with the CE structural alignments. We found that global alignments with CLUSTALW were very poor at low sequence identity (<25%), as judged by the CE alignments. We used PSI-BLAST to search the nonredundant sequence database (nr) with every sequence in SCOP using up to four iterations. The resulting matrix was used to search a database of SCOP sequences. PSI-BLAST is only slightly better than BLAST in alignment accuracy on a perresidue basis, but PSI-BLAST matrix alignments are much longer than BLAST's, and so align correctly a larger fraction of the total number of aligned residues in the structure alignments. Any two SCOP sequences in the same superfamily that shared a hit or hits in the nr PSI-BLAST searches were identified as linked by the shared intermediate sequence. We examined the quality of the longest SCOP-query/ SCOP-hit alignment via an intermediate sequence, and found that ISS produced longer alignments than PSI-BLAST searches alone, of nearly comparable per-residue quality. At 10--15% sequence identity, BLAST correctly aligns 28%, PSI-BLAST 40%, and ISS ...

Alignment of protein structures is a fundamental task in computational molecular biology. Good structural alignments can help detect distant evolutionary relationships that are hard or impossible to discern from protein sequences alone. Here, we study the structural alignment problem as a family of optimization problems and develop an approximate polynomial time algorithm to solve them. For a commonly used scoring function, the algorithm runs in O(n ) time, for globular protein of length n, when we wish to detect all scores that are at most # distance away from the optimum. We argue that such approximate solutions are, in fact, of greater interest than exact ones, due to the noisy nature of experimentally determined protein coordinates. The measurement of similarity between a pair of protein structures used by the algorithm involves the Euclidean distance between the structures, after rigidly transforming them. We show that an alternative approach, which relies on internal distance matrices, must incorporate sophisticated geometric ingredients in order to both guarantee optimality and run in polynomial time. We use these observations to visualize the scoring function for several real instances of the problem. Our investigations yield new insights on the computational complexity of protein alignment under various scoring functions. These insights can be used in the design of new scoring functions for which the optimum can be approximated e#ciently, and perhaps in the development of e#cient algorithms for the multiple structural alignment problem.

The predictions made for fold recognition and modeling accuracy at the 1996 Critical Assessment of Structure Prediction meeting (CASP2) were assessed to discover which groups did best. With 32 groups making a total of 369 predictions, it was necessary to use simple criteria for distinguishing between the entries. By focusing on the predictors' ability to use the sequence of the unknown target structure to recognize the target fold from a database of known folds and also on the quality of the model judged by the accuracy of the predicted alignment, it is easy to determine the best predictions for a given target. Assessing overall performance of the predictors on all the targets is much more difficult and use was made of weighted averages of fold recognition and alignment accuracy with and without normalization for target difficulty. By plotting these results in two dimensions the winning groups stand out, allowing readers to focus their attention on the most promising methods. When the ...

Abstract not found

We present a new method for conducting protein structure similarity searches, which improves on the accuracy, robustness, and efficiency of some existing techniques. Our method is grounded in the theory of differential geometry on 3D space curve matching. We generate shape signatures for proteins that are invariant, localized, robust, compact, and biologically meaningful. To improve matching accuracy, we smooth the noisy raw atomic coordinate data with spline fitting. To improve matching efficiency, we adopt a hierarchical coarse-to-fine strategy. We use an efficient hashingbased technique to screen out unlikely candidates and perform detailed pairwise alignments only for a small number of candidates that survive the screening process. Contrary to other hashing based techniques, our technique employs domain specific information (not just geometric information) in constructing the hash key, and hence, is more tuned to the domain of biology. Furthermore, the invariancy, localization, and compactness of the shape signatures allow us to utilize a well-known local sequence alignment algorithm for aligning two protein structures. One measure of the efficacy of the proposed technique is that we were able to discover new, meaningful motifs that were not reported by other structure alignment methods. 1.

Comparing and subsequently classifying protein structures information has received significant attention concurrent with the increase in the number of experimentally derived 3-dimensional structures. Classification schemes have focused on biological function found within protein domains and on structure classification based on topology. Here an alternative view is presented that groups substructures. Substructures are long (50 -- 150 residue) highly repetitive near-contiguous pieces of polypeptide chain that occur frequently in a set of proteins from the PDB defined as structurally nonredundant over the complete polypeptide chain. The substructure classification is based on a previously reported Combinatorial Extension (CE) algorithm that provides a significantly different set of structure alignments than those previously described, having, for example, only a 40% overlap with FSSP. Qualitatively the algorithm provides longer contiguous aligned segments at the price of a slightly highe...