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A Uniqueness Theorem of Molecular Recognition

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Abstract

Phrased in terms of electron density deformations due to molecular interactions, an optimality condition, and the fundamental holographic properties of molecular electron densities, it is shown that molecular recognition is necessarily unique. A simple proof is given and the connections of this result with the Duality Principle of Molecular Recognition and related Selectivity Measures for molecular recognition are discussed.

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References

  1. W. Kabsch and C. Sander, Dictionary of protein secondary structure: pattern recognition of hydrogenbonded and geometrical features, Biopolymers 22 (1983) 2577–2637.

    PubMed  Google Scholar 

  2. W. Kabsch and C. Sander, On the use of sequence homologies to predict protein structure: identical pentapeptides can have completely different conformations, Proc. Nat. Acad. Sci. U.S.A. 81 (1984) 1075–1078.

    Google Scholar 

  3. P.G. Mezey, Potential Energy Hypersurfaces (Elsevier, Amsterdam, 1987).

    Google Scholar 

  4. P.G. Mezey, Group theory of electrostatic potentials: a tool for quantum chemical drug design, Internat. J. Quantum Chem., Quant. Biol. Symp. 12 (1986) 113–122.

    Google Scholar 

  5. P.G. Mezey, Tying knots around chiral centres: chirality polynomials and conformational invariants for molecules, J. Amer. Chem. Soc. 108 (l986) 3976–3984.

    Google Scholar 

  6. P.G.Mezey, The shape of molecular charge distributions: group theory without symmetry, J. Comput. Chem. 8 (1987) 462–469.

    Google Scholar 

  7. P.G.Mezey, Group theory of shapes of asymmetric biomolecules, Internat. J. Quantum Chem., Quant. Biol. Symp. 14 (1987) 127–132.

    Google Scholar 

  8. P.G.Mezey, Shape group studies of molecular similarity: shape groups and shape graphs of molecular contour surfaces, J. Math. Chem. 2 (1988) 299–323.

    Google Scholar 

  9. P.G. Mezey, Global and local relative convexity and oriented relative convexity; Application to molecular shapes in external fields, J. Math. Chem. 2 (1988) 325–346.

    Google Scholar 

  10. P.G. Mezey, The degree of similarity of three-dimensional bodies; Applications to molecular shapes, J. Math. Chem. 7 (1991) 39–49.

    Google Scholar 

  11. P.G. Mezey, Similarity analysis in two and three dimensions using lattice animals and polycubes, J. Math. Chem. 11 (1992) 27–45.

    Google Scholar 

  12. F. Harary and P.G.Mezey, Graphical shapes: seeing graphs of chemical curves and molecular surfaces, J. Math. Chem. 2 (1988) 377–389.

    Google Scholar 

  13. F. Harary and P.G. Mezey, Similarity and complexity of the shapes of square-cell configurations, Theor. Chim. Acta 79 (1991) 379–387.

    Google Scholar 

  14. F. Harary and P.G. Mezey, Chiral and achiral square-cell configurations and the degree of chirality, in: New Developments in Molecular Chirality, ed. P.G. Mezey (Kluwer Academic, Dordrecht, 1991) pp. 241–256.

    Google Scholar 

  15. P.G. Mezey, A global approach to molecular chirality, in: New Developments in Molecular Chirality, ed. P.G. Mezey (Kluwer Academic, Dordrecht, 1991) pp. 257–289.

    Google Scholar 

  16. 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.

    Google Scholar 

  17. P.G. Mezey, Molecular surfaces, in: Reviews in Computational Chemistry, eds. K.B. Lipkowitz and D.B. Boyd (VCH, New York, l990) chapter 7, pp. 265–294.

    Google Scholar 

  18. P.G. Mezey, Topological shape analysis of chain molecules: an application of the GSTE principle, J. Math. Chem. 12 (1993) 365–373.

    Google Scholar 

  19. P.G. Mezey, Dynamic shape analysis of molecules in restricted domains of a configuration space, J. Math. Chem. 13 (1993) 59–70.

    Google Scholar 

  20. [20] P.G. Mezey, Dynamic shape analysis of biomolecules using topological shape codes, in: The Role of Computational Models and Theories in Biotechnology, ed. J. Bertran (Kluwer Academic, Dordrecht, 1992) pp. 83–104.

    Google Scholar 

  21. P.G. Mezey, Shape in Chemistry: an Introduction toMolecular Shape and Topology (VCH, New York, 1993).

    Google Scholar 

  22. P.D. Walker and P.G. Mezey, Molecular electron density lego approach to molecule building, J. Amer. Chem. Soc. 115 (1993) 12423–12430.

    Google Scholar 

  23. P.D. Walker and P.G. Mezey, Ab initio quality electron densities for proteins: a MEDLA approach, J. Amer. Chem. Soc. 116 (1994) 12022–12032.

    Google Scholar 

  24. P.D. Walker and P.G. Mezey, Realistic, detailed images of proteins and tertiary structure elements: ab initio quality electron density calculations for Bovine insulin, Canad. J. Chem. 72 (1994) 2531–2536.

    Google Scholar 

  25. P.D. Walker and P.G. Mezey, A new computational microscope for molecules: high resolution MEDLA images of taxol and HIV-1 protease, using additive electron density fragmentation principles and fuzzy set methods, J. Math. Chem. 17 (1995) 203–234.

    Google Scholar 

  26. P.G. Mezey, Macromolecular density matrices and electron densities with adjustable nuclear geometries, J. Math. Chem. 18 (1995) 141–168.

    Google Scholar 

  27. P.G. Mezey, Quantum similarity measures and Löwdin's transform for approximate density matrices and macromolecular forces, Internat. J. Quantum Chem. 63 (1997) 39–48.

    Google Scholar 

  28. P.G. Mezey, Quantum chemical shape: new density domain relations for the topology of molecular bodies, functional groups, and chemical bonding, Canad. J. Chem. 72 (1994) 928–935 (special issue dedicated to Prof. J.C. Polanyi).

    Google Scholar 

  29. P.G. Mezey, Iterated similarity sequences and shape ID numbers for molecules, J. Chem. Inf. Comput. Sci. 34 (1994) 244–247.

    Google Scholar 

  30. P.G. Mezey, Shape analysis of macromolecular electron densities, Structural Chem. 6 (1995) 261–270.

    Google Scholar 

  31. P.G. Mezey, Molecular similarity measures for assessing reactivity, in: Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches, ed. R. Carbó (Kluwer Academic, Dordrecht, The Netherlands,l995) pp. 57–76.

    Google Scholar 

  32. P.G. Mezey, Methods of molecular shape-similarity analysis and topological shape design, in: Molecular Similarity in Drug Design, ed. P.M. Dean (Chapman & Hall/Blackie, Glasgow, UK, l995) pp. 241–268.

    Google Scholar 

  33. P.G. Mezey, Density domain bonding topology and molecular similarity measures, in: Topics in Current Chemistry, Vol. 173, Molecular Similarity, ed. K. Sen (Springer, Heidelberg, l995) pp. 63–83.

    Google Scholar 

  34. P.D. Walker, P.G. Mezey, G.M. Maggiora, M.A. Johnson and J.D. Petke, Application of the shape group method to conformational processes: shape and conjugation changes in the conformers of 2-phenyl pyrimidine, J. Comput. Chem. 16 (1995) 1474–1482.

    Google Scholar 

  35. P.D. Walker, G.M. Maggiora, M.A. Johnson, J.D. Petke and P.G. Mezey, Shape group analysis of molecular similarity: shape similarity of six-membered aromatic ring systems, J. Chem. Inf. Comput. Sci. 35 (1995) 568–578.

    Google Scholar 

  36. P.G. Mezey, Local shape analysis ofmacromolecular electron densities, in: Computational Chemistry: Reviews and Current Trends, Vol. 1, ed. J. Leszczynski (World Scientific, Singapore, 1996) pp. 109–137.

    Google Scholar 

  37. P.G. Mezey, Molecular similarity measures of conformational changes and electron density deformations, Advances in Molecular Similarity 1 (1996) 89–120.

    Google Scholar 

  38. Z. Zimpel and P.G.Mezey, A topological analysis of molecular shape and structure, Internat. J. Quantum Chem. 59 (1996) 379–390.

    Google Scholar 

  39. P.G. Mezey, Functional groups in quantum chemistry, Advances in Quantum Chemistry 27 (1996) 163–222.

    Google Scholar 

  40. P.G. Mezey, Descriptors of molecular shape in 3D, in: From Chemical Topology to Three-Dimensional Geometry, ed. A.T. Balaban (Plenum, New York, 1997) pp. 25–42.

    Google Scholar 

  41. P.G. Mezey, Fuzzy measures of molecular shape and size, in: Fuzzy Logic in Chemistry, ed. D.H. Rouvray (Academic Press, San Diego, 1997) pp. 139–223.

    Google Scholar 

  42. P.G. Mezey, Quantum chemistry of macromolecular shape, Internat. Rev. Phys. Chem. 16 (1997) 361–388.

    Google Scholar 

  43. P.G. Mezey, Shape in quantum chemistry, in: Conceptual Trends in Quantum Chemistry, Vol. 3, eds. J.-L. Calais and E.S. Kryachko (Kluwer Academic, Dordrecht, The Netherlands, 1997) pp. 519–550.

    Google Scholar 

  44. P.G. Mezey, Shape analysis, in: Encyclopedia of Computational Chemistry, Vol. 4, eds. P.V.R. Schleyer, N.L. Allinger, T. Clark, J. Gasteiger, P.A. Kollman, H.F. Schaefer III and P.R. Schreiner (Wiley, Chichester, UK, 1998) pp. 2582–2589.

    Google Scholar 

  45. P.G. Mezey, Combinatorial aspects of biomolecular shape analysis, Bolyai Soc. Math. Stud. 7 (1999) 323–332.

    Google Scholar 

  46. P.G. Mezey, K. Fukui, S. Arimoto and K. Taylor, Polyhedral shapes of functional group distributions in biomolecules and related similarity measures, Internat. J. Quantum Chem. 66 (1998) 99–105.

    Google Scholar 

  47. P.G. Mezey, Molecular similarity and host-guest interactions, Theor. Comput. Chem. 6 (1999) 593–612, in: Pauling's Legacy: Modern Modelling of the Chemical Bond, eds. Z. Maksic and W.J. Orville-Thomas (Elsevier Science, Amsterdam, The Netherlands, 1999) chapter 23, pp. 593–612.

    Google Scholar 

  48. P.G. Mezey, Topological methods of molecular shape analysis: continuum models and discretization, in: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 51 (2000) pp. 267–278.

    Google Scholar 

  49. M. Levy, Elementary concepts in density functional theory, in: Recent Developments and Applications of Modern Density Functional Theory, Theoretical and Computational Chemistry, Vol. 4, ed. J.M. Seminario (Elsevier Science, Amsterdam, 1996) pp. 3–24.

    Google Scholar 

  50. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964) B864-B865.

    Google Scholar 

  51. J. Riess and W. Münch, The theorem of Hohenberg and Kohn for subdomains of a quantum system, Theor. Chim. Acta 58 (1981) 295–300.

    Google Scholar 

  52. P.G. Mezey, Generalized chirality and symmetry deficiency, J. Math. Chem. 23 (1998) 65–84.

    Google Scholar 

  53. P.G. Mezey, The holographic electron density theorem and quantum similarity measures, Mol. Phys. 96 (1999) 169–178.

    Google Scholar 

  54. P.G. Mezey, Holographic electron density shape theorem and its role in drug design and toxicological risk assessment, J. Chem. Inf. Comp. Sci. 39 (1999) 224–230.

    Google Scholar 

  55. P.G. Mezey, The holographic principle for latent molecular properties, J. Math. Chem. 30 (2001) 299–303.

    Google Scholar 

  56. P.G. Mezey, The holographic electron density theorem and some of its consequences, in: Computational Chemistry Approaches to Molecular Similarity, ed. R. Carbó-Dorca (Kluwer Academic/ Plenum, New York) in press (accepted May 29, 2000).

    Google Scholar 

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Mezey, P.G. A Uniqueness Theorem of Molecular Recognition. Journal of Mathematical Chemistry 30, 305–313 (2001). https://doi.org/10.1023/A:1015175727727

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