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Spatial Effects of Delay-Induced Stochastic Oscillations in a Multi-scale Cellular System

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Proceedings of ECCS 2014

Part of the book series: Springer Proceedings in Complexity ((SPCOM))

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Abstract

The combined spatial effect of time delay and intrinsic noise on gene regulation is studied numerically. It is based on the multi-scale chemo-mechanical model of the epithelium. The protein fluctuations in each cell are described by a single-gene auto-repressor model with constant delay. It is found that time delay, noise and spatial signaling can result in the protein pattern formation even when deterministic description exhibits no patterns.

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References

  1. Kepler, T.B., Elston, C.: Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys. J. 81, 3116–3136 (2001)

    Article  ADS  Google Scholar 

  2. Hasty, J., Collins, J.J.: Translating the noise. Nat. Gen. 31, 13–14 (2002)

    Article  Google Scholar 

  3. Rosenfeld, N., Young, J.W., Alon, U., Swain, P.S., Elowitz, M.B.: Gene regulation at the single-cell level. Science 307, 1962–1965 (2005)

    Article  ADS  Google Scholar 

  4. Tsimring, L.S.: Noise in biology. Rep. Prog. Phys. 77, 026601 (2014)

    Article  ADS  Google Scholar 

  5. Bratsun, D., Volfson, D., Hasty, J., Tsimring, L.S.: Delay-induced stochastic oscillations in gene regulation. Proc. Natl. Acad. Sci. U.S.A. 102, 14593–14598 (2005)

    Article  ADS  Google Scholar 

  6. Bratsun, D., Volfson, D., Hasty, J., Tsimring, L.: Non-Marcovian processes in Gene Regulation. In: Kish, L.B., Lindenberg, K., Gingl, Z. (eds.) Noise in Complex Systems and Stochastic Dynamics III. Proceedings of the SPIE, vol. 5845, pp. 210–219 (2005)

    Google Scholar 

  7. Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977)

    Article  Google Scholar 

  8. Lemerle, C., Di Ventura, B., Serrano, L.: Space as the final frontier in stochastic simulations of biological systems. FEBS Lett. 579, 1789–1794 (2005)

    Article  Google Scholar 

  9. Li, C.-W., Chen, B.-S.: Stochastic spatio-temporal dynamic model for gene/protein interaction network in early drosophila development. Gene Regul. Syst. Biol. 3, 191–210 (2009)

    Google Scholar 

  10. Burrage, K., Burrage, P.M., Leier, A., Marquez-Lago, T., Nicolau, D.V.: Stochastic simulation for spatial modelling of dynamic processes in a living cell. In: Koeppl, H., Densmore, D., Setti, G., Di Bernardo, M. (eds.) Design and Analysis of Biomolecular Circuits: Engineering Approaches to Systems and Synthetic Biology, pp. 43–62. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Tranquillo, R.T., Murray, J.D.: Continuum model of fibroblast driven wound contraction: inflammation—mediation. J. Theor. Biol. 158, 135–172 (1992)

    Article  Google Scholar 

  12. Poujade, M., Grasland-Mongrain, E., Hertzog, A., Jouanneau, J., Chavrier, P., Ladoux, B., Buguin, A., Silberzan, P.: Collective migration of an epithelial monolayer in response to a model wound. Proc. Natl. Acad. Sci. U.S.A. 104, 15988–15993 (2007)

    Article  ADS  Google Scholar 

  13. Deisboeck, T.S., Stamatakos, G.S.: Multiscale Cancer Modeling. Chapman and Hall/CRC, Boca Raton (2011)

    MATH  Google Scholar 

  14. Salm, M., Pismen, L.M.: Chemical and mechanical signaling in epithelial spreading. Phys. Biol. 9, 026009–026023 (2012)

    Article  ADS  Google Scholar 

  15. Bratsun, D.A., Merkuriev, D.V., Zakharov, A.P., Pismen, L.M.: Multiscale modeling of tumour growth induced by circadian rhythm disruption in epithelial tissue. J. Biol. Phys. 42, 107–132 (2016)

    Google Scholar 

  16. Farhadifar, R., Röper, J.C., Aigouy, B., Eaton, S., Jülicher, F.: The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Curr. Biol. 17, 2095–2104 (2007)

    Article  Google Scholar 

  17. Koseska, A., Ullner, E., Volkov, E., Kurths, J., Garcia-Ojalvo, J.: Cooperative differentiation through clustering in multicellular populations. J. Theor. Biol. 263, 189–202 (2010)

    Google Scholar 

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Acknowledgments

The research has been supported by the Ministry of Education and Science of Perm Region (grant C-26/004.4) and grant of Russian Fund for Basic Research (14-01-96022r_ural_a).

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Authors and Affiliations

  1. Theoretical Physics Department, Perm State Pedagogical University, Perm, Russia

    Dmitry Bratsun & Andrey Zakharov

Authors
  1. Dmitry Bratsun
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  2. Andrey Zakharov
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Correspondence to Dmitry Bratsun .

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Editors and Affiliations

  1. RAF, University of Zürich, Zürich, Switzerland

    Stefano Battiston

  2. CREATE-NET, Trento, Italy

    Francesco De Pellegrini

  3. IMT Lucca, Lucca, Italy

    Guido Caldarelli

  4. School of Science and Technology, University of Camerino, Camerino, Italy

    Emanuela Merelli

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Bratsun, D., Zakharov, A. (2016). Spatial Effects of Delay-Induced Stochastic Oscillations in a Multi-scale Cellular System. In: Battiston, S., De Pellegrini, F., Caldarelli, G., Merelli, E. (eds) Proceedings of ECCS 2014. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-29228-1_9

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