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Fuzzy polynucleotide spaces and metrics

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Abstract

The study of genetic sequences is of great importance in biology and medicine. Mathematics is playing an important role in the study of genetic sequences and, generally, in bioinformatics. In this paper, we extend the work concerning the Fuzzy Polynuclotide Space (FPS) introduced in Torres, A., Nieto, J.J., 2003. The fuzzy polynuclotide Space: Basic properties. Bioinformatics 19(5); 587–592 and Nieto, J.J., Torres, A., Vazquez-Trasande, M.M. 2003. A metric space to study differences between polynucleotides. Appl. Math. Lett. 27:1289–1294: by studying distances between nucleotides and some complete genomes using several metrics. We also present new results concerning the notions of similarity, difference and equality between polynucleotides. The results are encouraging since they demonstrate how the notions of distance and similarity between polynucleotides in the FPS can be employed in the analysis of genetic material.

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References

  • DasGupta, B., Jiang, T., Kannan, S., Sweedyk, E., 1998. On the complexity and approximation of syntenic distance. Discrete Appl. Math. 88, 59–82.

    Article  MATH  MathSciNet  Google Scholar 

  • Engelking, R., 1977. General Topology. Warszawa.

  • Foster, M., Heath, A., Afzal, M., 1999. Application of distance geometry to 3D visualization of sequence relation ships. Bionformatics 15, 89–90.

    Article  Google Scholar 

  • Gusev, V.D., Nemytikova, L.A., Chuzhanova, N.A., 1999. On the complexity measures of genetic sequences. Bioinformatics 15, 994–999.

    Article  PubMed  Google Scholar 

  • He, M.X., Petoukhov, S.V., Ricci, P.E., 2004. Genetic code, hamming distance and stochastic matrices. Bull. Math. Biol. 66, 1405–1421.

    Article  PubMed  MathSciNet  Google Scholar 

  • Hegalson, C.M., Jobe, T.H., 1998. The fuzzy cube and causal efficacy: Representation of concomitant mechanisms in stroke. Neural Networks 11, 549–555.

    Article  PubMed  Google Scholar 

  • Jamshidi, N., Edwards, J.S., Fahland, T., Church, G.M., Palsson, B.O., 2001. Dynamic simulation of the human red blood cell matabolic network. Bioinformatics 17, 286–287.

    Article  PubMed  Google Scholar 

  • Jiang, T., Lin, G., Ma, B., Zhang, K., 2002. A general edit distance between RNA structures. J. Comput. Biol. 9, 371–388.

    Article  PubMed  Google Scholar 

  • Kosko, B., 1992. Neural Networks and Fuzzy Systems. Prentice-Hall, Englewood Cliffs, NJ.

    MATH  Google Scholar 

  • Li, M., Badger, J.H., Chen, X., Kwong, S., Kearney, P., Zhang, H., 2001. An information-based sequence distance and its application to whole mitochondrian phylogeny. Bioinformatics 17, 149–154.

    Article  PubMed  Google Scholar 

  • Liben-Nowell, D., 2001. On the structure of syntenic distance. J. Comput. Biol. 8, 53–67.

    Article  PubMed  Google Scholar 

  • Lin, C.T., 1997. Adaptive subsethood for radial basis fuzzy systems. In: Kosko, B. (Ed.), Fuzzy Engineering. Prentice-Hall, Upper Saddle River, NJ, pp. 429–464.

  • Morgenstern, B., 2002. A simple and space-efficient fragment-chaining algorithm for alignment of DNA and protein sequences. Appl. Math. Lett. 151, 11–16.

    Article  MATH  MathSciNet  Google Scholar 

  • Nieto, J.J., Torres, A., 2003. Midpoints for fuzzy sets and their application in medicine. Artif. Intell. Med. 17, 81–101.

    Article  Google Scholar 

  • Nieto, J.J., Torres, A., Vazquez-Trasande, M.M., 2003. A metric space to study differences between polynucleotides. Appl. Math. Lett. 27, 1289–1294.

    Article  MathSciNet  Google Scholar 

  • Paun, Gh., Rozenberg, G., Saloma, A., 1998. DNA Computing: New Computing Paradigms. Springer, Berlin.

    MATH  Google Scholar 

  • Percus, J., 2002. Mathematics of Genome Analysis. Cambridge University Press, Cambridge.

    Google Scholar 

  • Sadegh-Zadeh, K., 1999. Fundamentals of clinical methodology: Vol 3. Nosology. Artif. Intell. Med. 17, 87–108.

    Article  Google Scholar 

  • Sadegh-Zadeh, K., 2000. Fuzzy genomes. Artif. Intell. Med. 18, 1–28.

    Article  PubMed  Google Scholar 

  • Tang, B., 2000. Evaluation of some DNA cloning strategies. Comput. Math. Appl. 3911, 43–48.

    Article  MATH  MathSciNet  Google Scholar 

  • Torres, A., Nieto, J.J., 2003. The fuzzy polynucleotide space: Basic properties. Bioinformatics 195, 587–592.

    Article  PubMed  Google Scholar 

  • Zaus, M., 1999. Crisp and Soft Computing with Hypercubical Calculus. Physica-Verlag, Heideberg.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela,  , 15782, Spain

    Juan J. Nieto

  2. Departamento de Psiquiatría Radiología y Salud Pública, Facultad de Medicina, Universidad de Santiago de Compostela,  , 15782, Spain

    A. Torres

  3. Department of Mathematics, University of Patras, 265 00, Patras, Greece

    D. N. Georgiou

  4. Department of Civil Engineering, University of Thessaly, 383 34, Volos, Greece

    T. E. Karakasidis

Authors
  1. Juan J. Nieto
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  2. A. Torres
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  3. D. N. Georgiou
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  4. T. E. Karakasidis
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Correspondence to Juan J. Nieto.

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Nieto, J.J., Torres, A., Georgiou, D.N. et al. Fuzzy polynucleotide spaces and metrics. Bull. Math. Biol. 68, 703–725 (2006). https://doi.org/10.1007/s11538-005-9020-5

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  • DOI: https://doi.org/10.1007/s11538-005-9020-5

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