Application of multiresolution analyses to electron density maps of small molecules: Critical point representations for molecular superposition

Journal of Mathematical Chemistry

Volumn 29, Issue 1, 2001, Pages 47-83

  Leherte, Laurence ^a  

^a UNIVERSITY OF NAMUR   (Belgium)

Author keywords

Ab initio and ASA density functions; Critical points; Electron density; Molecular similarity; Multiresolution; Wavelets

Indexed keywords

EID: 0035533579     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011075018107     Document Type: Article

References (72)

1. J.M. Troyer and F.E. Cohen, Simplified models for understanding and predicting protein structure, in: Reviews in Computational Chemistry, Vol. 2, eds. K.B. Lipkowitz and D.B. Boyd (VCH Publishers, New York, 1990) pp. 57-80.
2. J. Cherfils, S. Duquerroy and J. Janin, Protein-protein recognition analyzed by docking simulation, Proteins 11 (1991) 271-280.
3. M.J.E. Sternberg, H.A. Gabb and R.M. Jackson, Predictive docking of protein-protein and protein-DNA complexes, Curr. Opin. Struct. Biol. 8 (1998) 250-256.
4. I.A. Vakser, O.G. Matar and C.F. Lam, A systematic study of low-resolution recognition in protein-protein complexes, Proc. Natl. Acad. Sci. USA 96 (1999) 8477-8482.
5. E. Katchalski-Katzir, I. Shariv, M. Eisenstein, A.A. Friesem, C. Aflalo and I.A. Vakser, Molecular surface recognition: Determination of geometric fit between proteins and their ligands by correlation techniques, Proc. Natl. Acad. Sci. USA 89 (1992) 2195-2199.
6. M. Carson, Wavelets and molecular structure, J. Comp.-Aided Mol. Des. 10 (1996) 273-283.
7. D.W. Ritchie and G.J.L. Kemp, Fast computation, rotation and comparison of low resolution spherical harmonic molecular surfaces, J. Comput. Chem. 20 (1999) 383-395.
8. B.S. Duncan and A.J. Olson, Shape analysis of molecular surfaces, Biopolymers 33 (1993) 231-238.
9. M. Butzlaff, W. Dahmen, S. Diekmann, A. Dress, E. Schmitt and E. von Kitzing, A hierarchical approach to force field calculations through spline approximations, J. Math. Chem. 15 (1994) 77-92.
10. E. von Kitzing and E. Schmitt, Configurational space of biological macromolecules as seen by semi-empirical force fields: Inherent problems for molecular design and strategies to solve them by means of hierarchical force fields, J. Mol. Struct. (Theochem) 336 (1995) 245-259.
11. W.K. Olson, Simulating DNA at low resolution, Curr. Opin. Struct. Biol. 6 (1996) 242-256.
12. Y. Takahashi, M. Sukekawa and S.-I. Sasaki, Automatic identification of molecular similarity using reduced-graph representation of chemical structure, J. Chem. Inf. Comput. Sci. 32 (1992) 639-643.
13. T.S. Baker and J.E. Johnson, Low resolution meets high: Towards a resolution continuum from cells to atoms, Curr. Opin. Struct. Biol. 6 (1996) 585-594.
14. J.-L. Stark, F. Murtagh and A. Bijaoui, Image Processing and Data Analysis - The Multiscale Approach (Cambridge University Press, Cambridge, UK, 1997).
15. M. Pilard and Y. Epelboin, Multiresolution analysis for the restoration of noisy X-ray topographs, J. Appl. Cryst. 31 (1998) 36-46.
16. J.I. Glasgow, S. Fortier and F.H. Allen, Molecular scene analysis: crystal and molecular structure determination through imagery, in: Artificial Intelligence and Molecular Biology, ed. L. Hunter (AAAI Press, Menlo Park, CA, 1993) pp. 433-458.
17. K. Baxter, E. Steeg, R. Lathrop, J. Glasgow and S. Fortier, From electron density and sequence to structure: Integrating protein image analysis and threading for structure determination, in: Proc. 4th International Conference on Intelligent Systems for Molecular Biology, eds. D.J. States, P. Agarwal, T. Gaasterland, L. Hunter and R.F. Smith (AAAI Press, Menlo Park, CA, 1996) pp. 25-33.
18. L. Leherte, J. Glasgow, K. Baxter, E. Steeg and S. Fortier, Analysis of three-dimensional protein images, J. Artificial Intelligence Research 7 (1997) 125-159.
19. K. Edgecombe, A. Ableson, K. Baxter, A. Chiverton, J. Glasgow and S. Fortier, Protein model determination from crystallographic data, in: Proceedings of the Pacific Symposium on Biocomputing'98, eds. R. Altman, A.K. Dunker, L. Hunter and T.E. Klein (1998).
20. A. Ableson and J.I. Glasgow, Crystallographic threading, in: Proc. 7th International Conference on Intelligent Systems for Molecular Biology, eds. T. Lengauer, R. Schneider, P. Bork, D. Brutlag, J. Glasgow, H.-W. Mewes and R. Zimmer (AAAI Press, Menlo Park, CA, 1999) pp. 2-9.
21. J. Mestres, D.C. Rohrer and G.M. Maggiora, MIMIC: A molecular-field matching program. Exploiting applicability of molecular similarity approaches, J. Comput. Chem. 18 (1997) 934-954.
22. R. Carbó, B. Calabuig, L. Vera and E. Besalú, Molecular quantum similarity: Theoretical framework, ordering principles, and visualization techniques, Adv. Quantum Chem. 25 (1994) 253-313.
23. P.G. Mezey, Three-dimensional topological aspects of molecular similarity, in: Concepts and Applications of Molecular Similarity, eds. M.A. Johnson and G.M. Maggiora (Wiley, New York, 1990) pp. 321-368.
24. P.G. Mezey, The shape of molecular charge distribution: group theory without symmetry, J. Comput. Chem. 8 (1987) 462-469.
25. G.A. Arteca and P.G. Mezey, Shape group studies of molecular similarity and regioselectivity in chemical reactions, J. Comput. Chem. 9 (1988) 608-619.
26. R.W. Bader, Atoms in Molecules - A Quantum Theory, 2nd ed. (Clarendon Press, Oxford, 1995).
27. P.L.A. Popelier, Quantum molecular similarity. 1. BCP space, J. Phys. Chem. A 103 (1999) 2883-2890.
28. C.K. Johnson, ORCRIT. The Oak Ridge critical point network program, Technical report, Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, TN (1977).
29. R.N. Shirsat, S.V. Bapat and S.R. Gadre, Molecular electrostatics. A comprehensive topographical approach, Chem. Phys. Lett. 200 (1992), 373-378.
30. S.R. Gadre and S.S. Pundlik, Topographical analysis of electron density and molecular electrostatic potential for cyclopropa- and cyclobutabenzenes, J. Am. Chem. Soc. 117 (1995) 9559-9563.
31. D.J. Wild and P. Willett, Similarity searching in files of three-dimensional chemical structures: Alignment of molecular electrostatic potential fields with a genetic algorithm, J. Chem. Inf. Comput. Sci. 36 (1996) 159-167.
32. D.A. Thorner, D.J. Wild, P. Willett and P.M. Wright, Similarity searching in files of three-dimensional chemical structures: Flexible field-based searching of molecular electrostatic potentials, J. Chem. Inf. Comput. Sci. 36 (1996) 900-908.
33. M. Leboeuf, A.M. Köster, K. Jug and D.R. Salahub, Topological analysis of the molecular electrostatic potential, J. Chem. Phys. 111 (1999) 4893-4905.
34. L. Leherte and F.H. Allen, Shape information from a critical point analysis of calculated electron density maps: Application to DNA-drug systems, J. Comput.-Aided Mol. Des. 8 (1994) 257-272.
35. L. Leherte, S. Fortier, J. Glasgow and F.H. Allen, Molecular scene analysis: application of a topological approach to the automated interpretation of protein electron density maps, Acta Cryst. Sec. D 50 (1994) 155-166.
36. L. Leherte and D.P. Vercauteren, Critical point analysis of calculated electron density maps at medium resolution: Application to shape analysis of zeolite-like systems, J. Molec. Model. 3 (1997) 156-171.
37. XTAL 3.0 User's Manual, eds. S.R. Hall and J.M. Stewart (Universities of Western Australia and Maryland, 1990).
38. L. Leherte, N. Meurice and D.P. Vercauteren, Critical point representation of electron density maps for the comparison of benzodiazepine-type ligands, J. Chem. Inf. Comput. Sci. 40 (2000) 816-832.
39. L. Leherte, Th. Latour and D.P. Vercauteren, Topological analysis of electron density maps of chiral cyclodextrin-guest complexes: A steric interaction evaluation, Supramolecular Sci. 2 (1995) 209-217.
40. L. Leherte, N. Meurice and D.P. Vercauteren, Application of multiresolution analyses to electron density maps: A critical point analysis approach for the comparison of molecules, in: Mathematics and Computers in Modern Science - Acoustics and Music, Biology and Chemistry, Business and Economics, ed. N. Mastorakis (World Scientific Engineering Society, 2000) pp. 158-164.
41. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle and J.A. Pople, Gaussian 94, Revision A.7 (Gaussian Inc., Pittsburgh, PA, 1994).
42. L. Amat and R. Carbó-Dorca, Quantum similarity measures under atomic shell approximation: First order density fitting using elementary Jacobi rotations, J. Comput. Chem. 19 (1997) 2023-2039.
43. J. Kostrowicki, L. Piela, B.J. Cherayil and H.A. Scheraga, Performance of the diffusion equation method in searches for optimum structures of clusters of Lennard-Jones atoms, J. Phys. Chem. 95 (1991) 4113-4119.
44. A.K.-M. Leung, F.-T. Chau and J.-B. Gao, A review on applications of wavelet transform techniques in chemical analysis: 1989-1997, Chemometrics and Intelligent Laboratory Systems 43 (1998) 165-184.
45. P. Fischer and M. Defranceschi, The wavelet transform: a new mathematical tool for quantum chemistry, in: Conceptual Trends in Quantum Chemistry, eds. E.S. Kryachko and J.-L. Calais (Kluwer Academic, Dordrecht, 1994) pp. 227-247.
46. J.-L. Calais, Wavelets - something for quantum chemistry?, Int. J. Quant. Chem. 58 (1996) 541-548.
47. T.A. Arias, Multiresolution analysis of electronic structure: Semicardinal and wavelet bases, Rev. Mod. Phys. 71 (1999) 267-311.
48. C.K. Chui, Wavelet Analysis and its Applications, Vol. 1, An Introduction to Wavelets (Academic Press, San Diego, CA, USA, 1992).
49. G. Strang and T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, MA, USA, 1997).
50. I. Daubechies, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math. 41 (1988) 909-996.
51. S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Machine Intell. 11 (1989) 674-693.
52. M. Bourges-Sévenier, WaveLib 1.1 - a C and Matlab library of wavelet functions, Réalisation d'une bibliothèque C de fonctions ondelettes, Publication interne no. 864, IRISA, Rennes, France (1994).
53. B. Jawerth and W. Sweldens, An overview of wavelet based multiresolution analyses, Technical Report, University of South Carolina, USA (1993), ftp://maxwell.math.scarolina.edu:/pub/ wavelet/papers/varia/sirev-36-3.tex.
54. O.M. Nielsen, Wavelets in scientific computing, Ph.D. thesis, Technical University of Denmark, Lyngby (1998), http://www.imm.dtu.dk/~omni/thesis.ps.gz.
55. E.J. Stollnitz, T.D. DeRose and D.H. Salesin, Wavelets for computer graphics: a primer, part 1, IEEE Computer Graphics and Applications 15 (1995) 76-84.
56. WWW site http://iqc.udg.es/cat/similarity/ASA/funcset.html.
57. X. Gironés, L. Amat and R. Carbó-Dorca, A comparative study of isodensity surfaces using ab initio and ASA density functions, J. Mol. Graphics Model. 16 (1998) 190-196.
58. J.W.M. Nissink, M.L. Verdonk, J. Kroon, T. Mietzner and G. Klebe, Superposition of molecules: Electron density fitting by application of Fourier transforms, J. Comput. Chem. 18 (1997) 638-645.
59. H. Brandstetter, D. Turk, H.W. Hoeffken, D. Grosse, J. Stürzebecher, P.D. Martin, B.F.P. Edwards and W. Bode, Refined 2.3 angstroms X-ray crystal structure of bovine thrombin complexes formed with the benzamidine and arginine-based thrombin inhibitors NAPAP, 4-TAPAP and MQPA: A starting point for improving antithrombotics, J. Mol. Biol. 226 (1992) 1085-1099.
60. F.C. Berstein, T.F. Koetzle, G.J. Williams, E.E. Meyer, Jr., M.D. Brice, J.R. Rodgers, O. Kennard, T. Shimanovishi and M. Tasumi, The Protein Data Bank: a computer-based archival file for macromolecular structures, J. Mol. Biol. 112 (1977) 535.
61. H.M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T.N. Bhat, H. Weissig, I.N. Shindyalov and P.E. Bourne, The Protein Data Bank, Nucleic Acids Research 28 (2000) 235-242, http://www.rcsb.org/pdb/.
62. Insight II, Version 4.0.0 (MSI, San Diego, 1998).
63. IBM Visualization Data Explorer (IBM Corporation, 1996).
64. M. Hô, H. Schmider, K.E. Edgecombe and V.H. Smith, Jr., Topological analysis of valence electron charge distributions from semiempirical and ab initio methods, Int. J. Quant. Chem. Quant. Chem. Symp. 28 (1994) 215-226.
65. E. Steiner, The Chemistry Maths Book (Oxford Science Publications, Oxford, 1998).
66. S. Mallat and S. Zhong, Wavelet maxima representation, in: Wavelet and Applications, ed. Y. Meyer (Masson, Paris, 1991) pp. 207-284.
67. S. Mallat and W.L. Hwang, Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory 38 (1992) 617-643.
68. M.J. Shensa, The discrete wavelet transform: Wedding the A Trous and Mallat algorithms, IEEE Trans. Signal Process. 40 (1992) 2464-2482.
69. The molecular graphics program XMol, Version 1.3.1 (Minnesota Supercomputer Center, Minneapolis, MN, 1993), ftp://ftp.msc.edu/pub/xmol.
70. F. Buyck, Analyse topologique de cartes de densité électronique de ligands pour les récepteurs benzodiazépiniques centraux, M.Sc. thesis, Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium (1994).
71. N. Meurice, Développement d'un algorithme génétique original pour l'alignement de graphes moléculaires issus de la densité électronique. Application à l'étude comparative de composés d'intérêt pharmacologique, Ph.D. thesis, Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium (2000).
72. D.J. Heisterberg, Technical report, Ohio Supercomputer Center, Columbus, OH; translation from FORTRAN to C and Input/Output by J. Labanowski, Ohio Supercomputer Center, Columbus, OH (1990).