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Mathematical Problems in Engineering
Volume 2011, Article ID 379873, 16 pages
http://dx.doi.org/10.1155/2011/379873
Research Article

Complexity on Acute Myeloid Leukemia mRNA Transcript Variant

Dipartimento di Matematica, Università di Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy

Received 10 January 2011; Accepted 18 February 2011

Academic Editor: Cristian Toma

Copyright © 2011 Carlo Cattani and Gaetano Pierro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Cattani, “Wavelet algorithms for DNA analysis,” in Algorithms in Computational Molecular Biology: Techniques, Approaches and Applications, M. Elloumi and A. Y. Zomaya, Eds., Wiley Series in Bioinformatics, chapter 35, pp. 799–842, John Wiley & Sons, New York, NY, USA, 2010. View at Google Scholar
  2. K. Metze, “Fractal dimension of chromatin and cancer prognosis,” Epigenomics, vol. 2, no. 5, pp. 601–604, 2010. View at Google Scholar
  3. R. L. Adam, R. C. Silva, F. G. Pereira, N. J. Leite, I. Lorand-Metze, and K. Metze, “The fractal dimension of nuclear chromatin as a prognostic factor in acute precursor B lymphoblastic leukemia,” Cellular Oncology, vol. 28, no. 1-2, pp. 55–59, 2006. View at Google Scholar · View at Scopus
  4. K. Metze, I. Lorand-Metze, N. J. Leite, and R. L. Adam, “Goodness-of-fit of the fractal dimension as a prognostic factor,” Cellular Oncology, vol. 31, no. 6, pp. 503–504, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. D. V. Lebedev, M. V. Filatov, A. I. Kuklin et al., “Fractal nature of chromatin organization in interphase chicken erythrocyte nuclei: DNA structure exhibits biphasic fractal properties,” FEBS Letters, vol. 579, no. 6, pp. 1465–1468, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. J. G. McNally and D. Mazza, “Fractal geometry in the nucleus,” The EMBO Journal, vol. 29, no. 1, pp. 2–3, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Takahashi, “A fractal model of chromosomes and chromosomal DNA replication,” Journal of Theoretical Biology, vol. 141, no. 1, pp. 117–136, 1989. View at Google Scholar · View at Scopus
  8. A. Delides, I. Panayiotides, A. Alegakis et al., “Fractal dimension as a prognostic factor for laryngeal carcinoma,” Anticancer Research, vol. 25, no. 3 B, pp. 2141–2144, 2005. View at Google Scholar · View at Scopus
  9. R. C. Ferreira, P. S. De Matos, R. L. Adam, N. J. Leite, and K. Metze, “Application of the Minkowski-Bouligand fractal dimension for the differential diagnosis of thyroid follicular neoplasias,” Cellular Oncology, vol. 28, no. 5-6, pp. 331–333, 2006. View at Google Scholar · View at Scopus
  10. M. R. B. Mello, K. Metze, R. L. Adam et al., “Phenotypic subtypes of acute lymphoblastic leukemia associated with different nuclear chromatin texture,” Analytical and Quantitative Cytology and Histology, vol. 30, no. 2, pp. 92–98, 2008. View at Google Scholar · View at Scopus
  11. L. Goutzanis, N. Papadogeorgakis, P. M. Pavlopoulos et al., “Nuclear fractal dimension as a prognostic factor in oral squamous cell carcinoma,” Oral Oncology, vol. 44, no. 4, pp. 345–353, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. A. Mashiah, O. Wolach, J. Sandbank, O. Uziel, P. Raanani, and M. Lahav, “Lymphoma and leukemia cells possess fractal dimensions that correlate with their biological features,” Acta Haematologica, vol. 119, no. 3, pp. 142–150, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. K. Metze, D. P. Ferro, M. A. Falconi et al., “Fractal characteristics of nuclear chromatin in routinely stained cytology are independent prognostic factors in patients with multiple myeloma,” Virchows Archiv, vol. 445, supplement 1, pp. 7–21, 2009. View at Google Scholar
  14. V. Bedin, R. L. Adam, B. C. S. de Sá, G. Landman, and K. Metze, “Fractal dimension of chromatin is an independent prognostic factor for survival in melanoma,” BMC Cancer, pp. 260–265, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. L. Pontrjagin and L. Schnirelmann, “Sur une propriété métrique de la dimension,” Annals of Mathematics, vol. 33, pp. 156–162, 1932. View at Google Scholar
  16. A. N. Kolmogorov and V. M. Tihomiroff, “ε-entropy and ε-capacity of sets in functional spaces,” Uspehi Matematicheskih Nauk, vol. 14, no. 2, pp. 3–86, 1961. View at Google Scholar
  17. J. P. Fitch and B. Sokhansanj, “Genomic engineering: moving beyond DNA sequence to function,” Proceedings of the IEEE, vol. 88, no. 12, pp. 1949–1971, 2000. View at Google Scholar · View at Scopus
  18. H. Gee, “A journey into the genome: what's there,” Nature, 2001. View at Publisher · View at Google Scholar
  19. P. D. Cristea, “Large scale features in DNA genomic signals,” Signal Processing, vol. 83, no. 4, pp. 871–888, 2003. View at Publisher · View at Google Scholar · View at Scopus
  20. K. B. Murray, D. Gorse, and J. M. Thornton, “Wavelet transforms for the characterization and detection of repeating motifs,” Journal of Molecular Biology, vol. 316, no. 2, pp. 341–363, 2002. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Arneodo, Y. D'Aubenton-Carafa, E. Bacry, P. V. Graves, J. F. Muzy, and C. Thermes, “Wavelet based fractal analysis of DNA sequences,” Physica D, vol. 96, no. 1–4, pp. 291–320, 1996. View at Google Scholar · View at Scopus
  22. B. Borstnik, D. Pumpernik, and D. Lukman, “Analysis of apparent spectrum in DNA sequences,” Europhysics Letters, vol. 23, pp. 389–394, 1993. View at Google Scholar
  23. C. K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, “Mosaic organization of DNA nucleotides,” Physical Review E, vol. 49, no. 2, pp. 1685–1689, 1994. View at Publisher · View at Google Scholar · View at Scopus
  24. S. Karlin and V. Brendel, “Patchiness and correlations in DNA sequences,” Science, vol. 259, no. 5095, pp. 677–680, 1993. View at Google Scholar · View at Scopus
  25. E. Schrödinger, What is Life? Physical Aspects of Living Cell, Cambridge University Press, Cambridge, UK, 1948.
  26. C. Cattani, “Fractals and hidden symmetries in DNA,” Mathematical Problems in Engineering, vol. 2010, Article ID 507056, 31 pages, 2010. View at Publisher · View at Google Scholar
  27. R. F. Voss, “Evolution of long-range fractal correlations and 1/f noise in DNA base sequences,” Physical Review Letters, vol. 68, no. 25, pp. 3805–3808, 1992. View at Publisher · View at Google Scholar · View at Scopus
  28. R. F. Voss, “Long-range fractal correlations in DNA introns and exons,” Fractals, vol. 2, pp. 1–6, 1992. View at Google Scholar
  29. M. Zhang, “Exploratory analysis of long genomic DNA sequences using the wavelet transform: examples using polyomavirus genomes,” in Genome Sequencing and Analysis Conference VI, pp. 72–85, Hilton Head, NC, USA, 1995.
  30. A. Arneodo, E. Bacry, P. V. Graves, and J. F. Muzy, “Characterizing long-range correlations in DNA sequences from wavelet analysis,” Physical Review Letters, vol. 74, no. 16, pp. 3293–3296, 1995. View at Publisher · View at Google Scholar · View at Scopus
  31. B. Audit, C. Vaillant, A. Arneodo, Y. D'Aubenton-Carafa, and C. Thermes, “Long-range correlations between DNA bending sites: relation to the structure and dynamics of nucleosomes,” Journal of Molecular Biology, vol. 316, no. 4, pp. 903–918, 2002. View at Publisher · View at Google Scholar · View at Scopus
  32. S. V. Buldyrev, A. L. Goldberger, A. L. Havlin et al., “Long-range fractal correlations in DNA,” Physical Review E, vol. 51, no. 5, pp. 5084–5091, 1995. View at Google Scholar
  33. H. Herzel, E. N. Trifonov, O. Weiss, and I. Große, “Interpreting correlations in biosequences,” Physica A, vol. 249, no. 1–4, pp. 449–459, 1998. View at Google Scholar · View at Scopus
  34. W. Li, “The study of correlation structures of DNA sequences: a critical review,” Computers and Chemistry, vol. 21, no. 4, pp. 257–271, 1997. View at Google Scholar · View at Scopus
  35. W. Li and K. Kaneko, “Long-range correlations and partial spectrum in a noncoding DNA sequence,” Europhysics Letters, vol. 17, pp. 655–660, 1992. View at Google Scholar
  36. C. K. Peng, S. V. Buldyrev, A. L. Goldberger et al., “Long-range correlations in nucleotide sequences,” Nature, vol. 356, no. 6365, pp. 168–170, 1992. View at Publisher · View at Google Scholar · View at Scopus
  37. O. Weiss and H. Herzel, “Correlations in protein sequences and property codes,” Journal of Theoretical Biology, vol. 190, no. 4, pp. 341–353, 1998. View at Publisher · View at Google Scholar · View at Scopus
  38. Z. G. Yu, V. V. Anh, and B. Wang, “Correlation property of length sequences based on global structure of the complete genome,” Physical Review E, vol. 63, no. 1, Article ID 011903, 8 pages, 2001. View at Publisher · View at Google Scholar · View at Scopus
  39. P. P. Vaidyanathan and B. J. Yoon, “The role of signal-processing concepts in genomics and proteomics,” Journal of the Franklin Institute, vol. 341, no. 1-2, pp. 111–135, 2004. View at Publisher · View at Google Scholar · View at Scopus
  40. P. Bernaola-Galván, R. Román-Roldán, and J. L. Oliver, “Compositional segmentation and long-range fractal correlations in DNA sequences,” Physical Review E, vol. 53, no. 5, pp. 5181–5189, 1996. View at Google Scholar · View at Scopus
  41. W. Li, “The complexity of DNA: the measure of compositional heterogenity in DNA sequence and measures of complexity,” Complexity, vol. 3, pp. 33–37, 1997. View at Google Scholar
  42. J. M. Bennett, M. L. Young, J. W. Andersen et al., “Long-term survival in acute myeloid leukemia: the Eastern Cooperative Oncology Group experience,” Cancer, vol. 80, no. 11, pp. 2205–2209, 1997. View at Google Scholar · View at Scopus
  43. D. Grimwade, H. Walker, F. Oliver et al., “The importance of diagnostic cytogenetics on outcome in AML: analysis of 1,612 patients entered into the MRC AML 10 trial,” Blood, vol. 92, no. 7, pp. 2322–2333, 1998. View at Google Scholar
  44. M. L. Slovak, K. J. Kopecky, P. A. Cassileth et al., “Karyotypic analysis predicts outcome of preremission and postremission therapy in adult acute myeloid leukemia: a Southwest oncology group/Eastern cooperative oncology group study,” Blood, vol. 96, no. 13, pp. 4075–4083, 2000. View at Google Scholar · View at Scopus
  45. National Center for Biotechnology Information, http://www.ncbi.nlm.nih.gov/.
  46. “Gene Location,” Weizmann Institute of Science, http://genecards.weizmann.ac.il/geneloc/index.shtml.
  47. “e!Ensemble, Ensembl project,” EMBL-EBI & Wellcome Trust Sanger Institute, http://www.ensemble.org/.