Finn P.W., Kavraki L.E., Latombe J.-C. et al. (1998). RAPID: Randomized Pharmacophore Identification. Comp. Geom.: Theory & Appl. 10(4), 263--272  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a facility location problem can also be regarded as a clustering problem. These facility location (or clustering) problems arise in many areas, including operations research, shape analysis [247, 208, 142] data compression and vector quantization [197] information retrieval [81, 80] drug design [119], and data mining [28, 48, 251] A useful extension of the facility location problem, which has been widely studied, is the capacitated facility location problem, in which we have an additional constraint that the size of each cluster should be at most c for some parameter c n=p. If p is ....

P. Finn, L. Kavraki, J.-C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao, Rapid: randomized pharmacophore identification for drug design, Proc. 13th Annu. ACM Sympos. Comput. Geom., 1997, pp. 324--333.

.... can be achieved for low degree of freedom problems (low dimensional C space) motion planning algorithms typically run slowly when faced with many degrees of freedom [9] Motion planning has applications in a variety of fields such as assembly planning, virtual prototyping [3] drug design [4], and computer graphics simulations [8, 10] However, despite the applicability of motion planning techniques to computer graphics simulations, the problem has not been addressed much in the computer graphics community [2] As stressed by Latombe [12] non robotics applications (e.g. graphics ....

Finn, P. W., Kavraki, L. E., Latombe, J. C., Motwani, R., Shelton, C., Venkatasubramania, S., Yao, A., "Rapid: Randomized Pharmacophore Identification for Drug Design", Proceedings of 13 th ACM Symposium on Computational Geometry (SoCG'97), 1997.

....in this eld, in the form of genetic algorithms [4] and simulated annealing [5] this paper, to the best of our knowledge, represents the rst work where it has been used in such a stark way. The randomized approach that we present, derives its motivation from a technique used by Finn et al. [6] to solve a Chemical Engineering Journal 72 (1999) 209216 Corresponding author. E mail: pallab che.iitb.ernet.in 1 This work was carried out when the author was at the Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur. samarjit tik.ee.ethz.ch ....

....to be existing at #T min #26#C. However, in our procedure, several lower cost networks are seen to exist at #T min without taking into account the restrictions imposed by the pinch design [21] To use this method independently, it might be useful to use concepts similar to those presented in [6] for molecular conformational search. After each network is randomly generated, an efcient minimizer [22,23] can be used to transform it to a local minimum nearest to it. This way, by generating networks uniformly over the underlying space, the chances of nding the optimal network can be expected ....

P.W. Finn, L.E. Kavraki, J.C. Latombe, R. Motwani, C. Shelton,S. Venkatasubramanian, A. Yao, RAPID: Randomized PharmacophoreIdentification for Drug Design, Proceedings of the 13th Annual ACM Symposium on Computational Geometry, 1997, pp. 324333.

....the portions that do not match dominate the RMS value, thereby rendering the measure ine#ective. Of late, a new measure called the bottleneck matching metric has been studied in a number of papers for the purpose of identifying structural similarities between two drug or protein molecules [1, 7, 10]. Given two equal cardinality point sets, the bottleneck matching metric seeks a perfect bipartite matching between the two sets such that the maximum distance between any two matched points is minimized, and it returns this distance [9] In the context of our problem, given two point sets A and B ....

....results in a running time of O(n 3.5 log n) If the resulting algorithm outputs # then there exists a subset S # A of size # min( A , B ) which is 8# congruent to some subset of B. 8 4. 2 Improvements using random sampling We finally show that by using standard random sampling techniques [3, 10, 16] the complexity of the algorithms can be further reduced, at the cost of a small failure probability. Instead of computing the transformations corresponding to all possible pairs of amino acids, we randomly sample a subset A # of amino acids from A and compute only those transformations ....

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P. W. Finn, L. E. Kavraki, J. C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. RAPID: Randomized pharmacophore identification for drug design. In Proc. 13th Annual ACM Symp. on Computational Geometry, pages 324--333, 1997.

....a facility location problem can also be regarded as a clustering problem. These facility location (or clustering) problems arise in many areas, including operations research, shape analysis [96, 146, 173] data compression and vector quantization [137] information retrieval [58, 59] drug design [81], and data mining [16, 33, 176] If p is considered as part of the input, most facility location problems are NP Hard, even in the plane or even when only an approximate solution is being sought (provided that is a sufficiently small constant) 80, 93, 126, 136, 149, 150] Although many of ....

P. Finn, L. E. Kavraki, J.-C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao, Rapid: randomized pharmacophore identification for drug design, Proc. 13th Annu. ACM Sympos. Comput. Geom., 1997, pp. 324--333.

....the largest common substructure between two drug or protein molecules has important implications in synthetic drug design, and in studying biomolecular recognition and interaction of proteins. Of late, there has been considerable effort to develop computational tools to expedite this process ([7, 9, 15] and the references therein) Towards this, a molecule is modelled as a set of points in 3 D space, each point representing the centre of an atom. Given two such point sets, the problem is to find a rigid transformation of one point set relative to the This work was carried out when the author ....

.... is called the largest common point set problem, or, LCP [4] However, since it is unreasonable to expect an exact match between two atom positions, two points are considered to be superimposed if the distance between them is less than a predefined constant ffl, called the point location error [9]. Hence the abstract version of the problem is that of finding the LCP of two 3 D point sets with exact congruence replaced by ffl congruence. Closely related problems, involving both exact and also ffl congruence have been extensively studied in computational geometry, references to which can be ....

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P. W. Finn, L. E. Kavraki, J-C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. RAPID: Randomized pharmacophore identification for drug design. In Proc. 13th. Annual ACM Symp. on Computational Geometry, pages 324--333, Centre Universitaire M'editerran'een, Nice, France, 1997.

....(over low dimensional Euclidean spaces) is a commonly used metric over geometric objects. Geometric point set matching in two and three dimensions is a well studied family of problems with application to areas such as computer vision [22] pattern recognition [6, 13] and computational chemistry [11, 12, 23]. Thus the problem of computing (exactly or approximately) the Hausdorff distance between two point sets P and Q in two and three dimensions has been studied extensively [1, 5, 6, 13, 24] with the interesting problems being those where one set can be rotated or translated and one seeks the ....

....one seeks the transform which minimizes the Hausdorff distance. Unfortunately, no efficient algorithms have been designed for the case when we want to match P with many Q s and find the closest one. This problem is of crucial importance in many applications; in particular, computational chemistry [11, 12, 23] and pattern recognition [6, 13] require matching a pattern against a huge database of molecules or images, respectively. Our results. Here we sketch out the flavor of the results, highlighting the main contributions. Our first result is an algorithm for approximate nearest neighbor searching in ....

P. Finn, L. E. Kavraki, J. C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification for drug design. In Proceedings of the Thirteenth Annual ACM Symposium on Computational Geometry, 1997.

....distinct conformations have also been tried. Recent arti cles, which attempt to compare different methods, emphasize the superior quality of the results obtained with randomized methods [43] The random sampling method for exploring the conformation space of small molecules de scribed in [36, 37] works as follows. Initially a large number of conformations are generated at random. A random conformation is obtained by selecting each degree of freedom from its allowed range according to a user specified distribution. This distribution is frequently the uni 13 File BuildSEdit View Compute ....

....atoms of ci and cj, after ci is transformed to cj. This transformation is computed using a basis of three predefined atoms al, a2, and a3. The clustering performed minimizes the maximum inter cluster distance [49] Figure 5 shows two of the clusters obtained with the randomized approach of [36, 37] for CDP. At the end of the clustering step, a representative per cluster can be retained. The method de scribed above borrows ideas from randomized techniques for path planning in high dimensional configuration spaces [66] Experimental observations show that it is very effective in discovering ....

[Article contains additional citation context not shown here]

P. W. Finn, L. E. Kavraki, J.-C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification. In Proceedings of the International Symposium on Computational Geometry, pages 324-333, Nice, France, 1997.

....of previous and related work on robust floating point geometric algorithms can be found in [17] 18] 22] 27] 32] and [33] Our motivating application is geometric modeling of molecules. Our software package is part of a toolbox aimed to support the chemist in the drug design process [12] [13]. The basic geometric model of a molecule that we use is the so called hard sphere model where every atom is represented by a sphere at some fixed position relative to the other atom spheres in the molecule. Since the hard sphere model is an approximate model to begin with, we have the freedom to ....

P. Finn, L. Kavraki, J.-C. Latombe, R. Motwani, C. Shelton, S. Venkatsubramanian, and F. Yao. Rapid: randomized pharmacophore identification for drug design. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 324--333, 1997.

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P. Finn, L. E. Kavraki, J. C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification for drug design. In Proceedings of the Thirteenth Annual ACM Symposium on Computational Geometry, 1997.

....polylines of M and F the associated safe region. A best match is computed between the line segments in P and those in p, yielding an euclidean transform aligning P with p. Our algorithm is similar to a previous algorithm used to discover and align substructures shared by 3 D molecular structures [21]. It samples pairs of line segments from p at random. For each pair (u 1 ; u 2 ) it finds a pair of segments (v 1 ; v 2 ) in P with the same angle. The correspondence u 1 v 1 ; u 2 v 2 yields a transform T (x; y; obtained by solving least square equations. a) b) Figure 6: a) Unaligned ....

Finn, P.W., L.E. Kavraki, J.C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao (1998). RAPID: Randomized Pharmacophore Identification for Drug Design. J. of Comp. Geometry: Theory and Applic. , 10:263-272.

No context found.

P. Finn, L. E. Kavraki, J. C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification for drug design. In Proceedings of the Thirteenth Annual ACM Symposium on Computational Geometry, 1997.

....of previous and related work on robust floating point geometric algorithms can be found in [17] 18] 22] 27] 32] and [33] Our motivating application is geometric modeling of molecules. Our software package is part of a toolbox aimed to support the chemist in the drug design process [12] [13]. The basic geometric model of a molecule that we use is the so called hard sphere model where every atom is represented by a sphere at some fixed position relative to the other atom spheres in the molecule. Since the hard sphere model is an approximate model to begin with, we have the freedom to ....

P.W. Finn, L. Kavraki, J.-C. Latombe, R. Motwani, C. Shelton, S. Venkatsubramanian, and F. Yao. Rapid: randomized pharmacophore identification for drug design. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 324--333, 1997.

No context found.

P. Finn, L. E. Kavraki, J. C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification for drug design. In Proceedings of the Thirteenth Annual ACM Symposium on Computational Geometry, 1997.

....Motivation and Applications. Our motivating application is the design of data structures and algorithms for the maintainence of kinematic structures, as described by Halperin, Latombe, and Motwani [10] Such structures are used to maintain conformations of molecules in computational biology [6, 10, 7], motion planning in robotics [4, 8, 19] and computer animation [12] Consider a collection of rigid bodies moving in 3 dimensional space and hinged together in a kinematic structure. We model these objects as a graph (typically, a path or a tree) whose vertices are the rigid bodies and edges are ....

P. FINN, L.E. KAVRAKI, J-C. LATOMBE, R. MOTWANI, C. SHELTON, S. VENKATASUBRAMANIAN AND A. YAO. RAPID: Randomized Pharmacophore Identification in Drug Design. to appear in Proceedings of 13th Annual ACM Symposium on Computational Geometry, 1997.

....The planner is also part of the software package sold by Accuray, Inc. Regarding deformable structures, the PI and co workers have developed software to reason about the possible motions of flexible ligands (small molecules) to determine if they are likely to bind at targeted receptor sites [28, 29, 54, 81]. Initiated with Pfizer Pharmaceuticals, this work is now being pursued with Prof. D. Brutlag in the Biochemistry Department at Stanford. Recently, the PI has started investigating the modeling of small blood vessels [84] with Dr. M. Stephanides (Functional Restoration Department) and Dr. K. ....

P.W. Finn, L.E. Kavraki, J.C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. RAPID: Randomized Pharmacophore Identification for Drug Design. Proc. 13th ACM Symp. on Computational Geometry (SoCG'97), pp. 324-333, 1997.

....B. COOK L. E. KAVRAKI R. MOTWANI y During the process of pharmaceutical drug design, computational chemists often compute different lowenergy conformations of small drug molecules (ligands) Such conformations are used in solving docking problems [5] and in pharmacophore identification [3]. Most methods that identify different low energy conformations of ligands employ clustering to partition the generated conformations (typically tens of thousands) into sets that capture geometric similarity. Since the generation and clustering of conformations is a time consuming operation [2] ....

P. Finn, L. Kavraki, J.-C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification. In Proceedings of the International Symposium on Computational Geometry, pages 324--333, Nice, France, 1997.

No context found.

Finn P.W., Kavraki L.E., Latombe J.-C. et al. (1998). RAPID: Randomized Pharmacophore Identification. Comp. Geom.: Theory & Appl. 10(4), 263--272

No context found.

P. W. Finn, L. E. Kavraki, J. Latombe, R. Motwani, C. R. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification for drug design. Symposium on Computational Geometry, pages 324--333, 1997.

No context found.

P. W. Finn, L. E. Kavraki, J. Latombe, R. Motwani, C. R. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification for drug design. Symposium on Computational Geometry, pages 324--333, 1997.

No context found.

P. Finn, L. E. Kavraki, J. C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: Randomized pharmacophore identification for drug design. In Proceedings of the Thirteenth Annual ACM Symposium on Computational Geometry, 1997.

No context found.

P. W. Finn, L. E. Kavraki, J. Latombe. R. Motwani, C. R. Shelton, S. Venkatasubramanian and A. Yao, "RAPID: Randomized Pharmacophore Identification for Drug Design", Symposium on Computational Geometry, 324-333 (1997)

No context found.

P. W. Finn, L. E. Kavraki, J-C. Latombe, R. Motwani, C. Shelton, S. Venktasubramanian, A. Yao. RAPID: Randomized Pharmacophore Identification for Drug Design. Proc. 13'th ACM Symp. Comp. Geom., 324333, 1997.

No context found.

P. W. Finn, L. E. Kavraki, J. C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. RAPID: Randomized pharmacophore identification for drug design. In Proc. 13th. Annual ACM Symp. on Computational Geometry [ACM97], pages 324--333.

No context found.

P. Finn, L. Kavraki, J.-C. Latombe, R. Motwani, C. Shelton, S. Venkatasubramanian, and A. Yao. Rapid: randomized pharmacophore identification for drug design. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 324--333, 1997.

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