Skip to main content

On characterizing proteomics maps by using weighted Voronoi maps

Journal of Mathematical Chemistry volume 50, pages 2689–2702 (2012)Cite this article

Abstract

In contrast to the standard construction of Voronoi regions, in which the boundaries between different regions are at equal distance from the given points, we consider the construction of modified Voronoi regions obtained by giving greater weights to spots reported to have higher abundance. Specifically we are interested in applying this approach to 2-D proteomics maps and their numerical characterization. As will be seen, the boundaries of the weighted Voronoi regions are sensitive to the relative abundances of the protein spots and thus the abundances of protein spots, the z component of the (x, y, z) triplet, are automatically incorporated in the numerical analysis of the adjacency matrix, rather than used to augment the adjacency matrix as non-zero diagonal matrix elements. The outlined approach is general and it may be of interest for numerical analyses of other maps that are defined by triplets (x, y, z) as input information.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Randić M.: Quantitative Characterization of Proteomics Maps by Matrix Invariants, (ed.). by Conn., P.M. Handbook of Proteomics Methods, pp. 429–450. Humana Press, Inc., Totowa, NJ (2003)

    Chapter  Google Scholar 

  2. Randić M., Zupan J., Balaban A.T., Vikić-Topić D., Plavšić D.: Graphical representation of proteins. Chem. Rev. 111, 790–862 (2011)

    Article  Google Scholar 

  3. González-Díaz H., González-Díaz Y., Santana L., Ubeira F.M., Uriarte E.: Proteomics, networks and connectivity indices. Proteomics 8, 750–778 (2008)

    Article  Google Scholar 

  4. Randić M., Orel R.: On numerical characterization of proteomics maps based on partitioning of 2-D maps into Voronoi regions. J. Math. Chem. 49, 1759–1768 (2011)

    Article  Google Scholar 

  5. Randić M., Kleiner A.F., DeAlba L.M.: Distance/distance matrices. J. Chem. Inf. Comput. Sci. 34, 277–286 (1994)

    Article  Google Scholar 

  6. Randić M.: Novel graph theoretical approach to heteroatom in quantitative structure-activity relationship. Intel. Lab. Syst. 10, 213–227 (1991)

    Article  Google Scholar 

  7. Randić M.: Topological Indices, (ed.) by Schleyer, P.V.R., Allinger, N.L., Clark, T., Gasteiger, J., Kollman, P.A., Schaefer, H.F., Schreiner, P.R. The Encyclopedia of Computational Chemistry, pp. 3018–3032. Wiley, Chichester (1998)

    Google Scholar 

  8. Devillers J., Balaban A.T.: Topological Indices and Related Descriptors in QSAR and QSPR. CRC Press, Boca Raton, FL (2000)

    Google Scholar 

  9. Anderson N.L., Esquer-Blasco R., Richardson F., Foxworthy P., Eacho P.: The effects of peroxisome proliferations on protein abundances in mouse liver. Toxicol. Appl. Pharmacol. 137, 75–89 (1996)

    Article  CAS  Google Scholar 

  10. Randić M., Novič M., Vračko M.: On characterization of dose variations of 2-D proteomics maps by matrix invariants. J. Proteome Res. 1, 217–226 (2002)

    Article  Google Scholar 

  11. Randić M., Estrada E.: Order from chaos: observing hormesis at the proteome level. J. Proteome Res. 4, 2133–2136 (2005)

    Article  Google Scholar 

  12. Randić M.: On graphical and numerical characterization of proteomics maps. J. Chem. Inf. Comput. Sci. 41, 1330–1338 (2001)

    Article  Google Scholar 

  13. Randić M., Zupan J., Novič M.: On 3-D graphical representation of proteomics maps and their numerical characterization. J. Chem. Inf. Comput. Sci. 41, 1339–1344 (2001)

    Article  Google Scholar 

  14. Randić M., Witzmann F., Vračko M., Basak S.C.: On characterization of proteomivcs maps and chemically induced chanes in proteomes using matrix invariants: application to peroxisome proliferators. Med. Chem. Res. 10, 456–479 (2001)

    Google Scholar 

  15. Randić M., Zupan J., Novič M., Gute B.D., Basak S.C.: Novel matrix invariants for characterization of changes of proteoics maps. SAR QSAR Environ. Res. 13, 689–703 (2002)

    Article  Google Scholar 

  16. Randić M., Lerš N., Vukičević D., Plavšić D., Gute B.D., Basak S.C.: Canonical labeling of proteome maps. J. Proteome Res. 4, 1347–1352 (2005)

    Article  Google Scholar 

  17. Randić M.: A graph theoretical characterization of proteomics maps. Int. J. Quantum Chem. 90, 848–858 (2002)

    Article  Google Scholar 

  18. Randić M., Novič M., Vračko M., Plavšić D.: Study of proteome maps using partial ordering. J. Theor. Biol. 266, 21–28 (2010)

    Article  Google Scholar 

  19. Bajzer Ž., Randić M., Plavšić D., Basak S.C.: Novel map descriptors for characterization of toxic effects in proteomics maps. J. Mol. Graph. Model. 22, 1–9 (2003)

    Article  CAS  Google Scholar 

  20. Randić M., Lerš N., Plavšić D., Basak S.C.: Characterization of 2-D proteome maps based on the nearest neighborhoods of spots. Croat. Chem. Acta 77, 345–351 (2004)

    Google Scholar 

  21. Randić M., Novič M., Vračko M.: Novel characterization of proteomics maps by sequential neighborhood of protein spots. J. Chem. Inf. Model. 45, 1205–1213 (2005)

    Article  Google Scholar 

  22. Randić M., Lerš N., Plavšić D., Basak S.C.: On invariants of a 2-D proteome map derived from neighborhood graphs. J. Proteome Res. 3, 778–785 (2004)

    Article  Google Scholar 

  23. Randić M., Orel R.: On numerical characterization of proteomics maps based on partitioning of 2-D maps into Voronoi regions. J. Math. Chem. 49, 1759–1768 (2011)

    Article  Google Scholar 

  24. Voronoi G.: Nouvelles applications des paramètres continus à à la théorie des forms quadratiques. J. Reine Angewandte Math. 133, 97–178 (1907)

    Google Scholar 

  25. Delaunay B: Sur la sphère vide. Izv. Akad. Nauk SSSR, Otdel. Mat. Estest. Nauk 7, 793–800 (1934)

    Google Scholar 

  26. Kowalski B.R., Bender C.F.: Pattern recognition. Powerful approach to interpreting chemical data. J. Am. Cem. Soc. 94, 5632–5639 (1972)

    Article  CAS  Google Scholar 

  27. Ash P.F., Bolker E.D.: Generalized Dirichlet tessellations. Geometrie Dedicata 20, 209–243 (1986)

    Google Scholar 

  28. L. Mu, WVD2009 (Multiplicatively weighted Voronoi diagram, computer program) http://www.ggy.uga.edu/people/faculty/mu/ (2009)

Download references

Author information

Authors and Affiliations

  1. XLAB, Pot za Brdom 100, Ljubljana, Slovenia

    Rok Orel

  2. National Institute of Chemistry, Hajdrihova 19, Ljubljana, Slovenia

    Milan Randić

Authors
  1. Rok Orel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Milan Randić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Milan Randić.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Orel, R., Randić, M. On characterizing proteomics maps by using weighted Voronoi maps. J Math Chem 50, 2689–2702 (2012). https://doi.org/10.1007/s10910-012-0058-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-012-0058-y

Keywords

  • Proteomics maps
  • Voronoi regions
  • LY171833 peroxisome proliferator
  • Weighted Voronoi regions