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Modeling a synthetic biological chaotic system: relaxation oscillators coupled by quorum sensing

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Abstract

Chaos exists in biological systems. Through investigating synthetic genetic relaxation oscillators coupled by quorum sensing, this paper reports a chaotic system. The detailed dynamical behaviors of this chaotic biological system are investigated, including Lyapunov exponents spectrum, bifurcation, and Poincaré mapping.

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References

  1. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Leloup, J.C., Goldbeter, A.: A model for circadian rhythms in drosophila incorporating the formation of a complex between the PER and TIM proteins. J. Biol. Rhythms 13, 70–87 (1998)

    Article  Google Scholar 

  3. Leloup, J.C., Goldbeter, A.: Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in drosophila. J. Theor. Biol. 198, 445–459 (1999)

    Article  Google Scholar 

  4. Leloup, J.C., Goldbeter, A.: Limit cycle models for circadian rhythms based on transcriptional regulation in drosophila and neurospora. J. Biol. Rhythms 14, 433–448 (1999)

    Article  Google Scholar 

  5. Glossop, N.R., Lyons, L.C., Hardin, P.E.: Interlocked feedback loops within the drosophila circadian oscillator. Science 286, 766–768 (1999)

    Article  Google Scholar 

  6. Tyson, J.J., Hong, C.I., Thron, C.D., Novak, B.: A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM. Biophys. J. 77, 2411–2417 (1999)

    Article  Google Scholar 

  7. Ullner, E., Zaikin, A., Volkov, E., Kantz, H., Garcia-Ojalvo, J.: Multistability and clustering in a population of synthetic genetic oscillators with repressive cell-to-cell communication. Phys. Rev. Lett. 99, 148103 (2007)

    Article  Google Scholar 

  8. Ullner, E., Koseska, A., Kurths, J., Volkov, E., Kantz, H., Garcia-Ojalvo, J.: Multistability of synthetic genetic networks with repressive cell-to-cell communication. Phys. Rev. E 78, 031904 (2008)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Hall, N.: Exploring Chaos: A Guide to the New Science of Disorder. Norton, New York (1994)

    Google Scholar 

  11. Guevara, M., Glass, L., Shrier, A.: Phase-locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science 214, 1350–1353 (1981)

    Article  Google Scholar 

  12. Guevara, M.R., Shrier, A., Glass, L.: Chaotic and complex cardiac rhythms. In: Zipes, D., Jalife, J. (eds.) Cardiac Electrophysiology: From Cell to Bedside, pp. 192–201. Saunders, Philadelphia (1990)

    Google Scholar 

  13. Glass, L., Mackey, M.: From Clocks to Chaos: The Rhythms of Life. Princeton University Press, Princeton (1988)

    MATH  Google Scholar 

  14. Chialvo, D.R., Gilmour, J., Jalife, J.: Low dimensional chaos in cardiac tissue. Nature 343, 653–657 (1990)

    Article  Google Scholar 

  15. Courtemanche, M., Glass, L., Rosengarten, M.D., Goldberger, A.L.: Beyond pure parasystole: promises and problems in modeling complex arrhythmias. Am. J. Physiol. 257, H693–H706 (1989)

    Google Scholar 

  16. Segundo, J.P., Altshuler, E., Stiber, M., Garfinkel, A.: Periodic inhibition of living pacemaker neurons. I. Locked, intermittent, messy, and hopping behaviors. Int. J. Bifurc. Chaos 1, 549–581 (1991)

    Article  MATH  Google Scholar 

  17. Hayashi, H., Ishizuka, S.: Chaos in molluscan neuron. In: Degn, H. (ed.) Chaos in Biological Systems, pp. 157–166. Plenum, New York (1988)

    Google Scholar 

  18. Yip, K.P., Holstein-Rathlou, N.H., Marsh, D.J.: Chaos in blood flow control in genetic and renovascular hypertensive rats. Am. J. Physiol. 26l, F400–F408 (1991)

    Google Scholar 

  19. Olsen, L.F., Schaffer, W.M.: Chaos versus noisy periodicity: alternative hypotheses for childhood epidemics. Science 249, 499–504 (1990)

    Article  Google Scholar 

  20. Monod, F., Jacob, J.: Genetic regulatory mechanisms in the synthesis of proteins. J. Mol. Biol. 3, 318–356 (1961)

    Article  Google Scholar 

  21. Dickson, R., Abelson, J., Barnes, W., Reznikoff, W.: Genetic regulation: the Lac control region. Science 187, 27–35 (1975)

    Article  Google Scholar 

  22. Elowitz, M.B., Leibler, S.: A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000)

    Article  Google Scholar 

  23. McMillen, D., Kopell, N., Hasty, J., Collins, J.J.: Synchronizing genetic relaxation oscillators by intercell signaling. Proc. Natl. Acad. Sci. USA 99, 679–684 (2002)

    Article  Google Scholar 

  24. Zhang, J.J., Yuan, Z.J., Zhou, T.S.: Synchronization and clustering of synthetic genetic networks: a role for cis-regulatory nodules. Phys. Rev. E 79, 041903 (2009)

    Article  Google Scholar 

  25. Weiss, R., Knight, T.F.: Engineered communications for microbial robotics. In: DNA6: Sixth International Meeting on DNA Based Computers, 13–17 June, Leiden, The Netherlands (2000)

  26. Gardner, T.S., Cantor, C.R., Collins, J.J.: Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000)

    Article  Google Scholar 

  27. Becskei, A., Serrano, L.: Engineering stability in gene networks by autoregulation. Nature 405, 590–593 (2000)

    Article  Google Scholar 

  28. Guido, N.J., Wang, X., Adalsteinsson, D., McMillen, D., Hasty, J., Cantor, C.R., Elston, T.C., Collins, J.J.: A bottom-up approach to gene regulation. Nature 439, 856–860 (2006)

    Article  Google Scholar 

  29. Ellis, T., Wang, X., Collins, J.J.: Diversity-based, model-guided construction of synthetic gene networks with predicted functions. Nat. Biotechnol. 27, 465–471 (2009)

    Article  Google Scholar 

  30. Friedland, A.E., Lu, T.K., Wang, X., Shi, D., Church, G., Collins, J.J.: Synthetic gene networks that count. Science 324, 1199–1202 (2009)

    Article  Google Scholar 

  31. Ausubel, F.: Current Protocols in Molecular Biology. Greene & Wiley, New York (1987)

    Google Scholar 

  32. Sambrook, J., Russell, D.: Molecular Cloning: A Laboratory Manual. Cold Spring Harbor Lab. Press, Plainview (2001)

    Google Scholar 

  33. Tyson, J.J., Othmer, H.G.: The dynamics of feedback control circuits in biochemical pathways. Prog. Theor. Biol. 5, 1–62 (1978)

    Google Scholar 

  34. Keller, A.D.: Model genetic circuits encoding autoregulatory transcription factors. J. Theor. Biol. 172, 169–185 (1995)

    Article  Google Scholar 

  35. Wolf, D.M., Eeckman, F.H.: On the relationship between genomic regulatory element organization and gene regulatory dynamics. J. Theor. Biol. 195, 167–186 (1998)

    Article  Google Scholar 

  36. Cherry, J.L., Adler, F.R.: How to make a biological switch. J. Theor. Biol. 203, 117–133 (2000)

    Article  Google Scholar 

  37. Bialek, W.: Advances in Neural Information Processing Systems, vol. 13. MIT Press, Cambridge (2001)

    Google Scholar 

  38. Thomas, R., Thieffry, D., Kaufman, M.: Dynamical behaviour of biological regulatory networks. Bull. Math. Biol. 57, 247–276 (1995)

    MATH  Google Scholar 

  39. Mestl, T., Lemay, C., Glass, L.: Chaos in high-dimensional neural and gene networks. Physica D 98, 33–52 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  40. Smolen, P., Baxter, D.A., Byrne, J.H.: Frequency selectivity, multistability and oscillations emerge from models of genetic regulatory systems. Am. J. Physiol. 43, C531–C542 (1998)

    Google Scholar 

  41. Smolen, P., Baxter, D., Byrne, J.: Effects of macromolecular transport and stochastic fluctuations on dynamics of genetic regulatory systems. Am. J. Physiol. 277, C777–C790 (1999)

    Google Scholar 

  42. Barkai, N., Leibler, S.: Circadian clocks limited by noise. Nature 403, 267–268 (2000)

    Google Scholar 

  43. Savageau, M.A.: Comparison of classical and autogenous systems of regulation in inducible operons. Nature 252, 546–549 (1974)

    Article  Google Scholar 

  44. Hasty, J., Isaacs, F., Dolnik, M., McMillen, D., Collins, J.J.: Designer gene networks: towards fundamental cellular control. Chaos 11, 207–220 (2001)

    Article  MATH  Google Scholar 

  45. Fuqua, C., Winans, S., Greenberg, E.P.: Census and consensus in bacterial ecosystems: the LuxR-LuxI family of quorum-sensing transcriptional regulators. Annu. Rev. Microbiol. 50, 727–751 (1996)

    Article  Google Scholar 

  46. Bassler, B.L.: How bacteria talk to each other: regulation of gene expression by quorum sensing. Curr. Opin. Microbiol. 2, 582–587 (1999)

    Article  Google Scholar 

  47. Stricker, J., Cookson, S., Bennett, M.R., Mather, W.H., Tsimring, L.S., Hasty, J.: A fast, robust and tunable synthetic gene oscillator. Nature 456, 516–519 (2008)

    Article  Google Scholar 

  48. Tal Danino, T., Octavio Mondragón-Palomino, O., Tsimring, L., Hasty, J.: A synchronized quorum of genetic clocks. Nature 463, 326–330 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics, Henan University, Kaifeng, 475004, China

    Aimin Chen

  2. School of Mathematics and Information Science, Henan University, Kaifeng, 475004, China

    Aimin Chen

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  1. Aimin Chen
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Correspondence to Aimin Chen.

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Chen, A. Modeling a synthetic biological chaotic system: relaxation oscillators coupled by quorum sensing. Nonlinear Dyn 63, 711–718 (2011). https://doi.org/10.1007/s11071-010-9832-1

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  • DOI: https://doi.org/10.1007/s11071-010-9832-1

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