About this Journal Submit a Manuscript Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 193761, 14 pages
http://dx.doi.org/10.1155/2012/193761
Research Article

Entropy and Multifractality for the Myeloma Multiple TET 2 Gene

1DipMat, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy
2System Biology, PhD School, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy
3SSFO, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 27 June 2011; Accepted 8 September 2011

Academic Editor: Shengyong Chen

Copyright © 2012 Carlo Cattani et al. 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, “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 · View at Zentralblatt MATH · View at Scopus
  2. C. Cattani, “Wavelet algorithms for DNA analysis,” in Computational Molecular Biology: Techniques, Approaches and Applications, M. Elloumi and A. Y. Zomaya, Eds., Wiley Series in Bioinformatics, chapter 35, John Wiley & Sons, New York, NY, USA, 2010.
  3. C. Cattani and G. Pierro, “Complexity on acute myeloid leukemia mRNA transcript variant,” Mathematical Problems in Engineering, vol. 2011, Article ID 379873, 16 pages, 2011. View at Publisher · View at Google Scholar
  4. 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
  5. R. F. Voss, “Long-Range Fractal Correlations in DNA introns and exons,” Fractals, vol. 2, pp. 1–6, 1992.
  6. S. V. Buldyrev, A. L. Goldberger, S. Havlin et al., “Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis,” Physical Review E, vol. 51, no. 5, pp. 5084–5091, 1995. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Metze, “Fractal dimension of chromatin and cancer prognosis,” Epigenomics, vol. 2, no. 5, pp. 601–604, 2010. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  8. 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 Scopus
  9. 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 PubMed · View at Scopus
  10. 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 PubMed · View at Scopus
  11. 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 PubMed · View at Scopus
  12. 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.
  13. 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, vol. 10, article 260, 2010. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  14. 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 PubMed · View at Scopus
  15. 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 PubMed · View at Scopus
  16. 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 Publisher · View at Google Scholar · View at Scopus
  17. A. Delides, I. Panayiotides, A. Alegakis et al., “Fractal dimension as a prognostic factor for laryngeal carcinoma,” Anticancer Research, vol. 25, no. 3, pp. 2141–2144, 2005. View at Scopus
  18. 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 Scopus
  19. J. M. Adams, A. W. Harris, and C. A. Pinkert, “The c-myc oncogene driven by immunoglobulin enhancers induces lymphoid malignancy in transgenic mice,” Nature, vol. 318, no. 6046, pp. 533–538, 1985.
  20. L. Pontrjagin and L. Schnirelmann, “Sur une propriété métrique de la dimension,” Annals of Mathematics, vol. 33, pp. 156–162, 1932. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. N. Kolmogorov and V. M. Tihomiroff, “ε> -Entropy and ε -capacity of sets in functional spaces,” Uspekhi Mat. Nauk, vol. 14, no. 2, pp. 3–86, 1949.
  22. J. Patrick 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 Publisher · View at Google Scholar
  23. H. Gee, “A journey into the genome: what’s there,” Nature, 2001.
  24. 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 Zentralblatt MATH
  25. 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 Publisher · View at Google Scholar
  26. 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 Publisher · View at Google Scholar
  27. 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 Publisher · View at Google Scholar
  28. 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 PubMed
  29. 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
  30. 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 PubMed
  31. 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, 2001. View at Publisher · View at Google Scholar
  32. 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 Zentralblatt MATH
  33. 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 Publisher · View at Google Scholar
  34. W. Li and J. Bentley, “The complexity of DNA: the measure of compositional heterogenity in DNA sequence and measures of complexity,” Complexity, vol. 3, pp. 33–37, 1997.
  35. S. Karlin and V. Brendel, “Patchiness and correlations in DNA sequences,” Science, vol. 259, no. 5095, pp. 677–680, 1993. View at Publisher · View at Google Scholar
  36. 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.
  37. E. Schrödinger, What is Life? Physical Aspects of Living Cell, Cambridge University Press, Cambridge, UK, 1948.
  38. National Center for Biotechnology Information, http://www.ncbi.nlm.nih.gov/genbank/.
  39. Universal Protein Resource, http://www.uniprot.org/help/about.
  40. Gene Location, Weizmann Institute of Science, http://genecards.weizmann.ac.il/geneloc/.
  41. e!Ensemble, Ensembl project, EMBL-EBI & Wellcome Trust Sanger Institute, http://www.ensemble.org.
  42. H. Avet-Loiseau, T. Facon, A. Daviet et al., “14q32 translocations and monosomy 13 observed in monoclonal gammopathy of undetermined significance delineate a multistep process for the oncogenesis of multiple myeloma,” Cancer Research, vol. 59, no. 18, pp. 4546–4550, 1999.
  43. J. Drach, J. Schuster, H. Nowotny et al., “Multiple myeloma: high incidence of chromosomal aneuploidy as detected by interphase fluorescence in situ hybridization,” Cancer Research, vol. 55, no. 17, pp. 3854–3859, 1995.
  44. M. Flactif, M. Zandecki, J. L. Laï et al., “Interphase fluorescence in situ hybridization (FISH) as a powerful tool for the detection of aneuploidy in multiple myeloma,” Leukemia, vol. 9, no. 12, pp. 2109–2114, 1995.
  45. R. Fonseca, G. J. Ahmann, S. M. Jalal et al., “Chromosomal abnormalities in systemic amyloidosis,” British Journal of Haematology, vol. 103, no. 3, pp. 704–710, 1998. View at Publisher · View at Google Scholar
  46. M. Zandecki, J.-L. Laï, F. Geneviève et al., “Several cytogenetic subclones may be identified within plasma cells from patients with monoclonal gammopathy of undetermined significance, both at diagnosis and during the indolent course of this condition,” Blood, vol. 90, no. 9, pp. 3682–3690, 1997.
  47. G. W. Dewald, R. A. Kyle, G. A. Hicks, and P. R. Greipp, “The clinical significance of cytogenetic studies in 100 patients with multiple myeloma, plasma cell leukemia, or amyloidosis,” Blood, vol. 66, no. 2, pp. 380–390, 1985.
  48. B. Barlogie, J. Epstein, P. Selvanayagam, and R. Alexanian, “Plasma cell myeloma—New biological insights and advances in therapy,” Blood, vol. 73, no. 4, pp. 865–879, 1989.
  49. W. Liang, J. E. Hopper, and J. D. Rowley, “Karyotypic abnormalities and clinical aspects of patients with multiple myeloma and related paraproteinemic disorders,” Cancer, vol. 44, no. 2, pp. 630–644, 1979.
  50. G. Gahrton, L. Zech, and K. Nillsson, “2 Translocations, t(11;14) and t(1;6), in a patient with plasma cell leukaemia and 2 populations of plasma cells,” Scandinavian Journal of Haematology, vol. 24, no. 1, pp. 42–46, 1980.
  51. G. J. Morgan, F. E. Davies, and M. Linet, “Myeloma aetiology and epidemiology,” Biomedicine and Pharmacotherapy, vol. 56, no. 5, pp. 223–234, 2002. View at Publisher · View at Google Scholar
  52. H. Avet-Loiseau, M. Attal, P. Moreau et al., “Genetic abnormalities and survival in multiple myeloma: the experience of the Intergroupe Francophone du Myélome,” Blood, vol. 109, no. 8, pp. 3489–3495, 2007. View at Publisher · View at Google Scholar · View at PubMed
  53. J. R. Sawyer, J. A. Waldron, S. Jagannath, and B. Barlogie, “Cytogenetic findings in 200 patients with multiple myeloma,” Cancer Genetics and Cytogenetics, vol. 82, no. 1, pp. 41–49, 1995. View at Publisher · View at Google Scholar
  54. O. Landgren, R. A. Kyle, R. M. Pfeiffer et al., “Monoclonal gammopathy of undetermined significance (MGUS) consistently precedes multiple myeloma: a prospective study,” Blood, vol. 113, no. 22, pp. 5412–5417, 2009. View at Publisher · View at Google Scholar · View at PubMed
  55. S. M. C. Langemeijer, R. P. Kuiper, M. Berends et al., “Acquired mutations in TET2 are common in myelodysplastic syndromes,” Nature Genetics, vol. 41, no. 7, pp. 838–842, 2009. View at Publisher · View at Google Scholar · View at PubMed
  56. M. Ko, Y. Huang, A. M. Jankowska et al., “Impaired hydroxylation of 5-methylcytosine in myeloid cancers with mutant TET2,” Nature, vol. 468, no. 7325, pp. 839–843, 2010. View at Publisher · View at Google Scholar · View at PubMed
  57. R. B. Lorsback, J. Moore, S. Mathew, S. C. Raimondi, S. T. Mukatira, and J. R. Downing, “TET1, a member of a novel protein family, is fused to MLL in acute myeloid leukemia containing the t(10;11)(q22;23) [3],” Leukemia, vol. 17, no. 3, pp. 637–641, 2003. View at Publisher · View at Google Scholar · View at PubMed
  58. S. Y. Chen and Q. Guan, “Parametric shape representation by a deformable NURBS model for cardiac functional measurements,” IEEE Transactions on Biomedical Engineering, vol. 58, no. 3, part 1, pp. 480–487, 2011. View at Publisher · View at Google Scholar · View at PubMed
  59. S. Chen, J. Zhang, H. Zhang et al., “Myocardial motion analysis for determination of tei-index of human heart,” Sensors, vol. 10, no. 12, pp. 11428–11439, 2010. View at Publisher · View at Google Scholar