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Mathematical Theory to Compute Stochastic Cellular Processes

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Applications + Practical Conceptualization + Mathematics = fruitful Innovation

Part of the book series: Mathematics for Industry ((MFI,volume 11))

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Abstract

A central challenge of gene expression analysis during the last few decades has been the characterization of the expression patterns experimentally and theoretically. Modern techniques on single-cell and -molecule resolution reveal that transcriptions and translations are stochastic in time and that clonal population of cells displays heterogeneity in the abundance of a given RNA and protein per cell. Hence, to take into account a cell-to-cell variability, we consider a stochastic model of transcription and the chemical master equation. Our stochastic analysis and Monte-Carlo simulation show that the limiting distribution of mRNA copy number can be expressed by a Poisson-beta distribution. The distribution represents the four different types of expression patters, which are typically found in various experimental profiles.

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References

  1. Holstege, F.C.P., Jennings, E.G., Wyrick, J.J., Lee, T.I., Hengartner, C.J., Green, M.R., Golub, T.R., Lander, E.S., Young, R.A.: Cell 95, 717–728 (1998)

    Article  Google Scholar 

  2. Takahashi, K., Yamanaka, S.: Cell 126, 663–676 (2006)

    Article  Google Scholar 

  3. Kitano, H.: Science 295, 1662–1664 (2002)

    Article  Google Scholar 

  4. Elowitz, M.B., Levine, A.J., Siggia, E.D., Swain, P.S.: Science 297, 1183–1186 (2002)

    Article  Google Scholar 

  5. Golding, I., Paulsson, J., Zawilski, S.M., Cox, E.C.: Cell 123, 1025–1036 (2005)

    Article  Google Scholar 

  6. Chubb, J.R., Trcek, T., Shenoy, S.M., Singer, R.H.: Curr. Biol. 16, 1018–1025 (2006)

    Article  Google Scholar 

  7. Sanchez, A., Golding, I.: Science 342, 1188–1193 (2013)

    Article  Google Scholar 

  8. Burrage, K., Hegland, M., Macnamara, S., Sidje, R.B.: Markov Anniversary Meeting: an International Conference to Celebrate the 150th Anniversary of the Birth of A.A. Markov, Boson Books, pp. 21–38 (2006)

    Google Scholar 

  9. Selvarajoo, K.: Wiley Interdiscip. Rev. Syst. Biol. Med. 4, 385–399 (2012)

    Google Scholar 

  10. Hegland, M., Burden, C., Santoso, L., MacNamara, S., Booth, H.: J. Comput. Appl. Math. 205, 708–724 (2007)

    Article  MathSciNet  Google Scholar 

  11. Peccoud, J., Ycart, B.: Theor. Popul. Biol. 48, 222–234 (1995)

    Article  Google Scholar 

  12. Golding, I., Cox, E.C.: Curr. Biol. 16, R371–R373 (2006)

    Article  Google Scholar 

  13. Kim, J.K., Marioni, J.C.: Genome Biol. 14, 1–12 (2013)

    Article  Google Scholar 

  14. Monod, J., Jacob, F.: Cold Spring Harb. Symp. Quant. Biol. 26, 389–401 (1961)

    Article  Google Scholar 

  15. Simon, Z.: J. Theor. Biol. 8, 258–263 (1965)

    Article  Google Scholar 

  16. Griffith, J.S.: J. Theor. Biol. 20, 202–208 (1968)

    Article  Google Scholar 

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Acknowledgments

This work was supported by Tohoku University’s Juten Senryaku Program.

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Authors and Affiliations

  1. Tohoku University, 1-1 Seiryo-machi, Aoba-ku, Sendai, Miyagi, 980-8574, Japan

    Keita Iida & Yoshitaka Kimura

Authors
  1. Keita Iida
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  2. Yoshitaka Kimura
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Corresponding author

Correspondence to Yoshitaka Kimura .

Editor information

Editors and Affiliations

  1. CSIRO Computational Informatics, Canberra, Aust Capital Terr, Australia

    Robert S. Anderssen

  2. La Trobe University, Melbourne, Victoria, Australia

    Philip Broadbridge

  3. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Yasuhide Fukumoto

  4. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Kenji Kajiwara

  5. Kyushu University, Fukuoka, Japan

    Tsuyoshi Takagi

  6. Leiden University, Leiden, The Netherlands

    Evgeny Verbitskiy

  7. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Masato Wakayama

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Iida, K., Kimura, Y. (2016). Mathematical Theory to Compute Stochastic Cellular Processes. In: Anderssen, R., et al. Applications + Practical Conceptualization + Mathematics = fruitful Innovation. Mathematics for Industry, vol 11. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55342-7_10

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  • DOI: https://doi.org/10.1007/978-4-431-55342-7_10

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  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-55341-0

  • Online ISBN: 978-4-431-55342-7

  • eBook Packages: EngineeringEngineering (R0)

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