We consider the problem of identifying common three-dimensional substructures between proteins. Our method is based on comparing the shape of the #-carbon backbone structures of the proteins in order to find 3D rigid motions that bring portions of the geometric structures into correspondence. We propose a geometric representation of protein backbone chains that is compact yet allows for similarity measures that are robust against noise and outliers. We represent the structure of the backbone as a sequence of unit vectors, defined by each adjacent pair of #-carbons; we then define a measure of the similarity of two protein structures based on the RMS (root mean squared) distance between corresponding orientation vectors of the two proteins.

The rational approach to pharmaceutical drug design begins with an investigation of the relationship between chemical structure and biological activity. Information gained from this analysis is used to aid the design of new, or improved, drugs. Primary considerations during this investigation are the geometric and chemical characteristics of the molecules.

And then the man steps right up to the microphone And says at last as the time bell rings ``Thank you good night now it's time to go home'' and he makes it fast with one more thing ``We are the Sultans of Swing''

structure alignment

In this paper we present a new technique for partial surface and volume matching of images in three dimensions. In this problem, we are given two objects in 3-space, each represented as a set of points, scattered uniformly along its boundary or inside its volume. The goal is to find a rigid motion of one object which makes a sufficiently large portion of its boundary lying sufficiently close to a corresponding portion of the boundary of the second object. This is an important problem in pattern recognition and in computer vision, with many industrial, medical, and chemical applications. Our algorithm is based on assigning a directed footprint to every point of the two sets, and locating all the pairs of points (one of each set) whose undirected components of the footprints are sufficiently similar. The algorithm then computes for each such pair of points all the rigid transformations that map the first point to the second, while making the respective direction components of ...

Identifying the common 3-D substructure between two drug or protein molecules is an important problem in synthetic drug design and molecular biology. This problem can be represented as the following geometric pattern matching problem: given two point sets A and B in three-dimensions, and a real number ffl? 0, find the maximum cardinality subset S ` A for which there is an isometry I, such that each point of I(S) is within ffl distance of a distinct point of B. Since it is difficult to solve this problem exactly, in this paper we have proposed several approximation algorithms with guaranteed approximation ratio. Our algorithms can be classified into two groups. In the first we extend the notion of partial decision algorithms for ffl-congruence of point sets in 2-D in order to approximate the size of S. All the algorithms in this class exactly satisfy the constraint imposed by ffl. In the second class of algorithms this constraint is satisfied only approximately. In the latter case, we improve the known approximation ratio for this class of algorithms, while keeping the time complexity unchanged. For the existing approximation ratio, we propose algorithms with substantially better running times. We also suggest several improvements of our basic algorithms, all of which have a running time of O(n

this paper is to

Determining structural similarities between proteins is an important problem since it can help identify functional and evolutionary relationships. In this paper, an algorithm is proposed to align two protein structures. Given the protein backbones, the algorithm nds a rigid motion of one backbone onto the other such that large substructures are matched. The algorithm uses a representation of the backbone that is independent of their relative orientations in space and applies dynamic programming to this representation to compute an initial alignment, which is then re ned iteratively. Experiments indicate that the algorithm is competitive with two well-known algorithms, namely DALI [12] and LOCK [19].

FlexProt is a novel technique for the alignment of � exible proteins. Unlike all previous algorithms designed to solve the problem of structural comparisons allowing hinge-bending motions, FlexProt does not require an a priori knowledge of the location of the hinge(s). Flex-Prot carries out the � exible alignment, superimposing the matching rigid subpart pairs, and detects the � exible hinge regions simultaneously. A large number of methods are available to handle rigid structural alignment. However, proteins are � exible molecules, which may appear in different conformations. Hence, protein structural analysis requires algorithms that can deal with molecular � exibility. Here, we present a method addressing speci � cally a � exible protein alignment task. First, the method ef � ciently detects maximal congruent rigid fragments in both molecules. Transforming the task into a graph theoretic problem, our method proceeds to calculate the optimal arrangement of previously detected maximal congruent rigid fragments. The fragment arrangement does not violate the protein sequence order. A clustering procedure is performed on fragment-pairs which have the same 3-D rigid transformation regardless of insertions and deletions (such as loops and turns) which separate

In this paper we describe the Geometric Hashing paradigm for matching of a set of geometric features against a database of such feature sets. Specific examples are model based object recognition in computer vision for which this technique was originally developed, matching of volumetric data obtained from CT or MRI images of different persons, matching of an individual fingerprint versus a database, matching the molecular surface of a receptor molecule against a data base of drugs and so on. The features considered can be points, segments, infinite lines, corners and any other geometric entities. The matching is performed under any non-elastic geometric transformation such as the rigid, similarity, affine and projective transformations in any dimension. Moreover, the problem addressed is the much more difficult partial matching problem, where one tries to detect (previously unknown) large subsets of the feature set which are compatible with subsets of the database feature sets...