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Modelling periodic oscillation of biological systems with multiple timescale networks

Modelling periodic oscillation of biological systems with multiple timescale networks

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In this paper, we aim to develop a new methodology to model and design periodic oscillators of biological networks, in particular gene regulatory networks with multiple genes, proteins and time delays, by using multiple timescale networks (MTN). Fast reactions constitute a positive feedback-loop network (PFN), while slow reactions consist of a cyclic feedback-loop network (CFN), in MTN. Multiple timescales are exploited to simplify models according to singular perturbation theory. We show that a MTN has no stable equilibrium but stable periodic orbits when certain conditions are satisfied. Specifically, we first prove the basic properties of MTNs with only one PFN, and then generalise the result to MTNs with multiple PFNs. Finally, we design a biologically plausible gene regulatory network by the cI and Lac genes, to demonstrate the theoretical results. Since there is less restriction on the network structure of a MTN, it can be expected to apply to a wide variety of areas on the modelling, analysing and designing of biological systems.

Inspec keywords: proteins; feedback; system theory; biocontrol; periodic control; genetics; physiological models; delays; perturbation theory; time-varying networks; molecular biophysics

Other keywords: multiple timescale networks; singular perturbation theory; cyclic feedback-loop network; time delays; positive feedback-loop network; stable periodic orbits; periodic oscillation modelling; proteins; biological systems; gene regulatory networks; cl genes; Lac genes

Subjects: Time-varying control systems; Optimal control; General, theoretical, and mathematical biophysics; Distributed parameter control systems; Systems theory applications in biology and medicine

References

    1. 1)
      • J. Mallet-Paret , G.R. Sell . The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay. J. Differ. Equ. , 441 - 489
    2. 2)
      • L. Chen , R. Wang , T. Kobayashi , K. Aihara . Dynamics of gene regulatory networks with cell division cycle. Physical Review E Stat. Nonlinear Soft Matter Phys.
    3. 3)
      • B.C. Goodwin . Oscillatory behavior in enzymatic control process. Adv. Enzyme Reg. , 425 - 438
    4. 4)
      • L. Chen , K. Aihara . Stability of genetic regulatory networks with time delay. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. , 602 - 608
    5. 5)
      • D. McMillen , N. Kopell , J. Hasty , J.J. Collins . Synchronizing genetic relaxation oscillators by intercell signaling. Proc. Natl. Acad. Sci. USA , 679 - 684
    6. 6)
      • L. Chen , K. Aihara . A model of periodic oscillation for genetic regulatory systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. , 1429 - 1436
    7. 7)
      • E.M. Ozbudak , M. Thattai , H.N. Lim , B. Shraiman , A.V. Oudenaardeb . Multi-stability in the lactose utilization network of Escherichia Coli. Nature , 737 - 740
    8. 8)
      • R. Wang , Z. Jing , L. Chen . Periodic oscillators in genetic networks with negative feedback loops. WSEAS Trans. Math. , 150 - 156
    9. 9)
      • N. Barbai , S. Leibler . Biological rhythms: circadian clocks limited by noise. Nature
    10. 10)
      • A. Hunding . Limit cycles in enzyme systems with nonlinear negtive feedback. Biophys. Struct. Mech. , 47 - 54
    11. 11)
      • S.A. Campbell , S. Ruan , J. Wei . Qualitative analysis of a neural network model with multiple time delays. Int. J. Bifurcation Chaos Appl. Sci. Eng. , 1585 - 1595
    12. 12)
      • A. Becskei , B. Seraphin , L. Serrano . Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion. EMBO J. , 2528 - 2535
    13. 13)
      • P.S. Swain , M.B. Elowitz , E.D. Siggia . Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl. Acad. Sci. USA , 12795 - 12800
    14. 14)
      • A. Becskei , L. Serrano . Engineering Stability in Gene Networks by Autoregulation. Nature , 590 - 593
    15. 15)
      • J. Hasty , F. Isaacs , M. Dolnik , D. Mcmillen , J.J. Collins . Designer gene networks: Towards fundamental cellular control. Chaos , 207 - 220
    16. 16)
      • J. Mallet-Paret , G.R. Sell . Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions. J. Diff. Equ. , 385 - 440
    17. 17)
      • M.B. Elowitz , S. Leibler . A synthetic oscillatory network of transcriptional regulators. Nature , 335 - 338
    18. 18)
      • T. Kobayashi , L. Chen , K. Aihara . Design of genetic switches with only positive feedback loops. Proc. IEEE Computer Society Conf. on Bioinformatics , 151 - 162
    19. 19)
      • M. Elowitz , A. Levine , E. Siggia , P. Swain . Stochastic gene expression in a single cell. Science , 1183 - 1186
    20. 20)
      • L. Glass , S.A. Kauffman . The logical analysis of continuous, non-linear biochemical control networks. J. Theor. Biol. , 103 - 129
    21. 21)
      • J.C. Dunlap . Molecular bases for circadian clocks. Cell , 271 - 290
    22. 22)
      • T.S. Gardner , C.R. Cantor , J.J. Collins . Construction of a genetic toggle dwitch in Escherichia coli. Nature , 339 - 342
    23. 23)
      • R. Wang , Z. Jing , L. Chen . Modelling periodic oscillation of gene regulatory networks with cycle feedback systems.
    24. 24)
      • H. Smith . Periodic tridiagonal competitive and cooperative systems of differential equations. SIAM J. Math. Anal. , 1102 - 1109
    25. 25)
      • D. Gonze , J-C. Leloup , A. Goldbeter . Theoretical models for circadian rhythms in Neurospora and Drosophila. C. R. Hebd. Acad. Sci. (Paris) III , 57 - 67
    26. 26)
      • T. Kobayashi , L. Chen , K. Aihara . Modelling Genetic Switches with Positive Feedback Loops. J. Theor. Biol. , 379 - 399
    27. 27)
      • J. Hasty , M. Dolnik , V. Rottschäfer , J.J. Collins . Synthetic gene network for entraining and amplifying cellular oscillations. Phys. Rev. Lett. , 1 - 4
    28. 28)
      • H. Smith . (1995) Monotone Dynamical Systems: An introduction to the Theory of Competitive and Cooperative Systems.
    29. 29)
      • J. Wu , X. Zou . Patterns of sustained oscillations in neural networks with delayed interactions. Appl. Math. Comput. , 55 - 75
    30. 30)
      • V.I. Zubov . (1999) Theory of Oscillations.
    31. 31)
      • T. Zhou , L. Chen , K. Aihara . Intercellular communications induced by random fluctuations.
    32. 32)
      • J. Belair , S.A. Campbell , P. Driessche . Frustration, stability, and delay-induced oscillations in a neural network model. SIAM J. Appl. Math. , 245 - 255
    33. 33)
      • H.O. Walther . The 2-dimensional attractor of x(t)=−μx(t)+ f(x(t−1)). Mem. Amer. Math. Soc.
    34. 34)
      • A. Goldbeter . A model for circadian oscillations in the Drosophila period protein (PER). Proc. R. Soc. Lond. B , 319 - 324
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