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What is special of “five” in biological regulatory networks?

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Abstract

Understanding the potential mechanism to achieve dual biological properties is a fundamental challenge in systems biology, which is related to small network modules constructed by nonlinear dynamics. The previous work of adaptation mainly focused on biological regulatory networks whose number of nodes \(n\le 4\), without consideration in the oscillatory process. In this paper, we extend the study to multi-node (\(n\le 9\)) networks, propose the adaptation concept under oscillation cases and compare a class of regulatory networks on oscillation and adaptation performance based on enzymatic dynamics. Through computational studies, a specific strongly symmetric and coupled five-node network topology is found, which is proved to be the minimal structure with excellent performance on both oscillation and adaptation. It indicates regulatory networks with this topological structure are promising candidates to achieve these dual dynamic properties. We present a thorough analysis on this topology which shows significant advantages, including essentiality, parameter variation, frequency adjustment and perfect adaptation. Notably, this specific topology is exactly the same as the yin–yang five-element network in traditional Chinese medicine, and our approach might reveal its characteristics in systems science.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Karin, O., Raz, M., Tendler, A., et al.: A new model for the HPA axis explains dysregulation of stress hormones on the timescale of weeks. Mol. Syst. Biol. 16(7), e9510 (2020)

    Google Scholar 

  2. Tendler, A., Bar, A., Mendelsohn-Cohen, N., et al.: Hormone seasonality in medical records suggests circannual endocrine circuits. Proc. Natl. Acad. Sci. 118(7), e2003926118 (2021)

    Google Scholar 

  3. Verma, V., Ravindran, P., Kumar, P.: Plant hormone-mediated regulation of stress responses. BMC Plant Biol. 16(1), 1–10 (2016)

    Google Scholar 

  4. Li, F., Long, T., Lu, Y., et al.: The yeast cell-cycle network is robustly designed. Proc. Natl. Acad. Sci. 101(14), 4781–4786 (2004)

    Google Scholar 

  5. Zhang, Z., Wang, Q., Ke, Y., et al.: Design of tunable oscillatory dynamics in a synthetic NF-\(\kappa \)B signaling circuit. Cell Syst. 5(5), 460–470 (2017)

    Google Scholar 

  6. Modi, S., Dey, S., Singh, A.: Noise suppression in stochastic genetic circuits using PID controllers. PLoS Comput. Biol. 17(7), e1009249 (2021)

    Google Scholar 

  7. Qiao, L., Zhao, W., Tang, C., et al.: Network topologies that can achieve dual function of adaptation and noise attenuation. Cell Syst. 9(3), 271–285 (2019)

    Google Scholar 

  8. Zhang, M., Tang, C.: Bi-functional biochemical networks. Phys. Biol. 16(1), 016001 (2018)

    Google Scholar 

  9. Ma, W., Trusina, A., El-Samad, H., et al.: Defining network topologies that can achieve biochemical adaptation. Cell 138(4), 760–773 (2009)

    Google Scholar 

  10. Tsai, T., Choi, Y., Ma, W., et al.: Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science 321(5885), 126–129 (2008)

    Google Scholar 

  11. Babaei, M., Evers, T.M.J., Shokri, F., et al.: Biochemical reaction network topology defines dose-dependent Drug–Drug interactions. Comput. Biol. Med. 155, 106584 (2023)

    Google Scholar 

  12. Mangan, S., Alon, U.: Structure and function of the feed-forward loop network motif. Proc. Natl. Acad. Sci. 100(21), 11980–11985 (2003)

    Google Scholar 

  13. Alon, U.: Network motifs: theory and experimental approaches. Nat. Rev. Genet. 8(6), 450–461 (2007)

    Google Scholar 

  14. Nie, Q., Qiao, L., Qiu, Y., et al.: Noise control and utility: from regulatory network to spatial patterning. Sci. China Math. 63, 425–440 (2020)

    MathSciNet  Google Scholar 

  15. Alon, U.: An Introduction to Systems Biology: Design Principles of Biological Circuits. Chapman and Hall/CRC, Boca Raton (2006)

    Google Scholar 

  16. Shen-Orr, S., Milo, R., Mangan, S., et al.: Network motifs in the transcriptional regulation network of Escherichia coli. Nat. Genet. 31(1), 64–68 (2002)

    Google Scholar 

  17. Yi, T., Huang, Y., Simon, M., et al.: Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proc. Natl. Acad. Sci. 97(9), 4649–4653 (2000)

    Google Scholar 

  18. Novák, B., Tyson, J.: Design principles of biochemical oscillators. Nat. Rev. Mol. Cell Biol. 9(12), 981–991 (2008)

    Google Scholar 

  19. Ferrell, J., Tsai, T., Yang, Q.: Modeling the cell cycle: why do certain circuits oscillate? Cell 144(6), 874–885 (2011)

    Google Scholar 

  20. West, B.: Fractal physiology and chaos in medicine. World Scientific, (2012)

  21. Van Ravenswaaij-Arts, C., Kollee, L., Hopman, J., et al.: Heart rate variability. Ann. Intern. Med. 118(6), 436–447 (1993)

    Google Scholar 

  22. Segerstrom, S., Nes, L.: Heart rate variability reflects self-regulatory strength, effort, and fatigue. Psychol. Sci. 18(3), 275–281 (2007)

    Google Scholar 

  23. Strüven, A., Holzapfel, C., Stremmel, C., et al.: Obesity, nutrition and heart rate variability. Int. J. Mol. Sci. 22(8), 4215 (2021)

    Google Scholar 

  24. Lipsitz, L.: Dynamics of stability: the physiologic basis of functional health and frailty. J. Gerontol. A Biol. Sci. Med. Sci. 57(3), B115–B125 (2002)

    Google Scholar 

  25. Hardstone, R., Poil, S., Schiavone, G., et al.: Detrended fluctuation analysis: a scale-free view on neuronal oscillations. Front. Physiol. 3, 450 (2012)

    Google Scholar 

  26. Stanley, H., Buldyrev, S., Goldberger, A., et al.: Statistical mechanics in biology: how ubiquitous are long-range correlations? Physica A 205(1–3), 214–253 (1994)

    Google Scholar 

  27. Hausdorff, J., Purdon, P., Peng, C., et al.: Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. J. Appl. Physiol. 80(5), 1448–1457 (1996)

    Google Scholar 

  28. Goldberger, A., Peng, C., Lipsitz, L.: What is physiologic complexity and how does it change with aging and disease? Neurobiol. Aging 23(1), 23–26 (2002)

    Google Scholar 

  29. El-Samad, H., Goff, J., Khammash, M.: Calcium homeostasis and parturient hypocalcemia: an integral feedback perspective. J. Theor. Biol. 214(1), 17–29 (2002)

    MathSciNet  Google Scholar 

  30. Khammash, M.H.: Perfect adaptation in biology. Cell Systems 12(6), 509–521 (2021)

    Google Scholar 

  31. Li, Z., Bianco, S., Zhang, Z., et al.: Generic properties of random gene regulatory networks. Quantitative biology 1(4), 253–260 (2013)

    Google Scholar 

  32. Burda, Z., Krzywicki, A., Martin, O., et al.: Motifs emerge from function in model gene regulatory networks. Proc. Natl. Acad. Sci. 108(42), 17263–17268 (2011)

    Google Scholar 

  33. Farjami, S., Camargo, K., Dawes, J., et al.: Novel generic models for differentiating stem cells reveal oscillatory mechanisms. J. R. Soc. Interface 18(183), 20210442 (2021)

    Google Scholar 

  34. Li, Z., Liu, S., Yang, Q.: Incoherent inputs enhance the robustness of biological oscillators. Cell Syst. 5(1), 72–81 (2017)

    Google Scholar 

  35. Jr, Ferrell: Feedback loops and reciprocal regulation: recurring motifs in the systems biology of the cell cycle. Current opinion in cell biology 25(6), 676–686 (2013)

  36. Niederholtmeyer, H., Sun, Z., Hori, Y., et al.: A cell-free framework for biological systems engineering. bioRxiv, 018317, 2015 https://doi.org/10.1101/018317

  37. Lin, H., Shi, W., Han, J.: Analysis of Enzymatic Regulatory Five-Element Model. 40th Chinese Control Conference (CCC). IEEE, 6410-6415, (2021)

  38. Lin, H., Shi, W., Han, J.: Comparison of enzymatic regulatory network topologies. In: 41st Chinese Control Conference (CCC). IEEE, pp. 5735–5740 (2022)

  39. Lin, H., Han, J.: Comparison of multi-node networks on biological properties. In: 42nd Chinese Control Conference (CCC). IEEE, pp. 6823–6828 (2023)

  40. Kolomeisky, A.: Michaelis–Menten relations for complex enzymatic networks. J. Chem. Phys. 134(15), 155101 (2011)

    Google Scholar 

  41. Savageau, M.: Michaelis–Menten mechanism reconsidered: implications of fractal kinetics. J. Theor. Biol. 176(1), 115–124 (1995)

    MathSciNet  Google Scholar 

  42. Voit, E., Martens, H., Omholt, S.: 150 years of the mass action law. PLoS Comput. Biol. 11(1), e1004012 (2015)

    Google Scholar 

  43. Iman, R., Davenport, J., Zeigler, D.: Latin hypercube sampling (program user’s guide) [LHC, in FORTRAN]. Sandia Labs., Albuquerque (1980)

    Google Scholar 

  44. Benoit, K.: Linear Regression Models with Logarithmic Transformations. London School of Economics, London (2011)

    Google Scholar 

  45. Kuznetsov, Y.: Andronov-hopf bifurcation. Scholarpedia 1(10), 1858 (2006)

    Google Scholar 

  46. Strogatz, S.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press, Boca Raton (2018)

    Google Scholar 

  47. Ren, H., Li, Y., Han, C., et al.: Pancreatic \(\alpha \) and \(\beta \) cells are globally phase-locked. Nat. Commun. 13(1), 1–16 (2022)

    Google Scholar 

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Acknowledgements

This work was supported by Science and technology innovation special region project.

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Authors and Affiliations

  1. LSC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Haipeng Lin & Jing Han

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Haipeng Lin & Jing Han

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  1. Haipeng Lin
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  2. Jing Han
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Correspondence to Jing Han.

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Lin, H., Han, J. What is special of “five” in biological regulatory networks?. Nonlinear Dyn 112, 7477–7498 (2024). https://doi.org/10.1007/s11071-024-09374-5

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