Journal of Mathematical Chemistry

, Volume 45, Issue 1, pp 1–6 | Cite as

Some dimension problems in molecular databases

  • Paul G. MezeyEmail author
Original Paper


Molecular databases obtained either by combinatorial chemistry tools or by more traditional methods are usually organized according to a set of molecular properties. A database may be regarded as a multidimensional collection of points within a space spanned by the various molecular properties of interest, the property space. Some properties are likely to be more important than others, those considered important form the essential dimensions of the molecular database. How many properties are essential, this depends on the molecular problem addressed, however, the search in property space is usually limited to a few dimensions. Two types of search strategies are related either to search by property or search by lead compound. The first case corresponds to a lattice model, where the search is based on sets of adjacent blocks, usually hypercubes in property space, whereas lead-based searches in databases can be regarded as search around a center in property space. A natural model for lead-based searches involves a hyperspherical model. In this contribution a theoretical optimum dimension is determined that enhances the effectiveness of lead-based searches in property space of molecular databases.


Molecular databases Lead-based sampling in QSAR  Database dimension Sampling errors in high dimensions QshAR (Quantitative Shape-Activity Relations) 


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  1. 1.
    A. Furka, Notarized notes (1982),
  2. 2.
    A. Furka, F. Sebestyen, M. Asgedom, G. Dibo, in Highlights of Modern Biochemistry. Proceedings of the 14th Internatational Congress of Biochemistry, vol. 5 (VS Publishers, Utrecht, The Nederlands, 1988), p. 47Google Scholar
  3. 3.
    A. Furka, F. Sebestyen, M. Asgedom, G. Dibo, Abstract P. 168, in Abstract, 10th International Symposium on Medicinal Chemistry, (Budapest, 1988), p. 288Google Scholar
  4. 4.
    Furka A., Sebestyen F., Asgedom M., Dibo G. (1991) . Int. J. Pept. Protein Res. 37, 487–492CrossRefGoogle Scholar
  5. 5.
    Mezey P.G., Warburton P., Jako E., Szekeres Z. (2001). Dimension concepts and reduced dimensions in toxicological QShAR databases as tools for data quality assessment. J. Math. Chem. 30, 375–387CrossRefGoogle Scholar
  6. 6.
    Mezey P.G. (2001). Computational aspects of combinatorial quantum chemistry. J. Comput. Meth. Sci. Eng. (JCMSE) 1, 99–106Google Scholar
  7. 7.
    Mezey P.G. (1991). The degree of similarity of three-dimensional bodies; applications to molecular shapes. J. Math. Chem. 7, 39–49CrossRefGoogle Scholar
  8. 8.
    Mezey P.G. (1993). Shape in Chemistry : An introduction to Molecular Shape and Topology. VCH Publishers, New YorkGoogle Scholar
  9. 9.
    Mezey P.G. (1997). Quantum chemistry of macromolecular shape. Int. Rev. Phys. Chem. 16, 361–388CrossRefGoogle Scholar
  10. 10.
    Mezey P.G. (1994). Quantum chemical shape: new density domain relations for the topology of molecular bodies, functional groups, and chemical bonding. Can. J. Chem. 72, 928–935 (Special issue dedicated to Prof. J.C. Polanyi)CrossRefGoogle Scholar
  11. 11.
    Mezey P.G. (1996) Functional groups in quantum chemistry. Adv. Quantum Chem. 27, 163–222CrossRefGoogle Scholar
  12. 12.
    P.G. Mezey, Local electron densities and functional groups in quantum chemistry. in Topics in Current Chemistry, Correlation and Localization, vol. 203, ed. by P.R. Surjan (Springer-Verlag, Berlin, Heidelberg, New York, 1999), pp. 167–186Google Scholar
  13. 13.
    P.G. Mezey, Molecular similarity, quantum topology, and shape. in Computational Medicinal Chemistry and Drug Discovery, ed. by P. Bultinck, J.P. Tollenaere, H. De Winter, W. Langenaeker (Marcel Decker Inc., New York, 2004), pp. 345–364Google Scholar
  14. 14.
    Dubois J.-E., Mezey P.G. (1992). Relations among functional groups within a stoichiometry: a nuclear configuration space approach. Int. J. Quantum Chem. 43, 647–658CrossRefGoogle Scholar
  15. 15.
    Dubois J.-E., Mezey P.G. (1999). A functional group database: a charge density—DARC approach. Mol. Eng. 8, 251–265CrossRefGoogle Scholar
  16. 16.
    Berger M. (1987). Geometry. Springer-Verlag, HeidelbergGoogle Scholar
  17. 17.
    Bourgain J., Milman V.D. (1987). New volume ratio properties of convex symmetric bodies in Rn. Invent. Math. 88, 319–341CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Scientific Modeling and Simulation Laboratory, Department of Chemistry and Department of Physics and Physical OceanographyMemorial University of NewfoundlandSt. John’sCanada
  2. 2.Institute for Advanced StudyCollegium Budapest Szentháromság u. 2BudapestHungary

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