Skip to main content
SpringerLink
Log in

Bifurcations underlying sigh and eupnea rhythmic transition in a pre-Bötzinger complex model

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Neuronal networks control motor output through multi-rhythmic electrical activities with different frequencies and amplitudes of different neurons. For example, the pre-Bötzinger complex related to respiratory function exhibits sigh (slow frequency and large amplitude) and eupnea (fast frequency and small amplitude) rhythms. In the present paper, rhythm transitions modulated by several physiological factors are simulated in a coupling model composed of sigh and eupnea compartments, and the roles of ionic currents and the underlying bifurcation mechanism of the rhythm transitions are acquired. The transition from sigh- and eupnea-rhythm to the eupnea rhythm induced by the blockage of calcium or hyperpolarization-activated channels is related to supercritical Hopf bifurcation of the sigh compartment, and to the sigh rhythm caused by the blockage of persistent sodium channel or change of extracellular potassium concentration is associated with subcritical Hopf/fold limit cycle bifurcation of the eupnea compartment. The parameter regions of ionic currents and dynamical mechanism of rhythm transitions in the pre-Bötzinger complex are helpful for the modulation to the respiratory rhythms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. A. Shaffer, R. Follmann, A.L. Harris, S. Postnova, H. Braun, E.R. Jr, Eur Phys J Spec Top. 226, 1939 (2017). https://doi.org/10.1140/epjst/e2017-70024-6

  2. Y. Li, B. Jia, X. Zhang, Y. Yang, Eur Phys J Spec Top. 227, 821 (2018). https://doi.org/10.1140/epjst/e2018-800006-2

    Article  Google Scholar 

  3. Y. Zhang, Y. Xu, Z. Yao, J. Ma, Nonlinear Dyn. 102, 1849 (2020). https://doi.org/10.1007/s11071-020-05991-y

    Article  Google Scholar 

  4. H. Hua, B. Lu, H. Gu, Acta Phys Sin. 69, 090502 (2020). https://doi.org/10.7498/aps.69.20191709

    Article  Google Scholar 

  5. P. Meyrand, J. Simmers, M. Moulins, Nature. 351, 60 (1991). https://doi.org/10.1038/351060a0

    Article  ADS  Google Scholar 

  6. P. Dickinson, C. Mecsas, E. Marder, Nature. 344, 155 (1990). https://doi.org/10.1038/344155a0

    Article  ADS  Google Scholar 

  7. W. Stein, J Comp Physiol A. 195, 989 (2009). https://doi.org/10.1007/s00359-009-0483-y

    Article  Google Scholar 

  8. P. Li, W. Janczewski, K. Yackle, K. Kam, S. Pagliardini, M.A. Krasnow, Nature. 530, 293 (2016). https://doi.org/10.1038/nature16964

    Article  ADS  Google Scholar 

  9. M. Chevalier, N. Toporikova, J. Simmers, M. Thoby-Brisson, eLife. 5, e16125 (2016) doi: https://doi.org/10.7554/eLife.16125

  10. B.J. Bacak, T. Kim, J.C. Smith, J.E. Rubin, I.A. Rybak, eLife. 5, e13403 (2016) doi: https://doi.org/10.7554/eLife.13403

  11. H. Koizumi, J.C. Smith, J Neurosci. 28, 1773 (2008). https://doi.org/10.1523/jneurosci.3916-07.2008

    Article  Google Scholar 

  12. R.W. Pace, D.D. Mackay, J.L. Feldman, C.A.D. Negro, J Physiol. 580, 485 (2007). https://doi.org/10.1113/jphysiol.2006.124602

    Article  Google Scholar 

  13. R.W. Pace, D.D. Mackay, J.L. Feldman, C.A.D. Negro, J Physiol. 582, 113 (2007). https://doi.org/10.1113/jphysiol.2007.133660

    Article  Google Scholar 

  14. C.A.D. Nnegro, C. Morgado-Valle, J.A. Hayes, D.D. Mackay, R.W. Pace, E.A. Crowder, J.L. Feldman, J Neurosci. 25, 446 (2005). https://doi.org/10.1523/jneurosci.2237-04.2005

    Article  Google Scholar 

  15. L. Beltran-Parrazal, J. Fernandez-Ruiz, R. Toledo, J. Manzo, C. Morgado-Valle, Neuroscience. 224, 116 (2012). https://doi.org/10.1016/j.neuroscience.2012.08.016

    Article  Google Scholar 

  16. N. Toporikova, M. Chevalier, M. Thoby-Brisson, eNeuro. 2, 2 (2015) doi: https://doi.org/10.1523/eneuro.0074-14.2015

  17. L. Duan, J. Liu, X. Chen, P. Xiao, Y. Zhao, Cogn Neurodyn. 11, 91 (2017). https://doi.org/10.1007/s11571-016-9411-3

    Article  Google Scholar 

  18. Y.X. Yang, Y.Y. Li, H.G. Gu, Acta Phys Sin. 69, 040501 (2020). https://doi.org/10.7498/aps.69.20191509

    Article  Google Scholar 

  19. N. Toporikova, R.J. Butera, J Comput Neurosci. 30, 515 (2011). https://doi.org/10.1007/s10827-010-0274-z

    Article  MathSciNet  Google Scholar 

  20. B. Jia, H. Gu, Int J Bifurcat Chaos 27, 1750113 (2017). https://doi.org/10.1142/S0218127417501139

    Article  Google Scholar 

  21. H. Gu, B. Pan, G. Chen, L. Duan, Nonlinear Dyn. 78, 391 (2014). https://doi.org/10.1007/s11071-014-1447-5

    Article  Google Scholar 

  22. Y. Yang, Y. Cui, K. Sang, Y. Dong, Z. Ni, S. Ma, H. Hu, Nature. 554, 317 (2018). https://doi.org/10.1038/nature25509

    Article  ADS  Google Scholar 

  23. Z. Faghani, S. Jafari, C.Y. Chen, F. Nazarimehr, Eur Phys J B. 93, 216 (2020). https://doi.org/10.1140/epjb/e2020-10477-6

    Article  ADS  Google Scholar 

  24. K. Rajagopal, F. Nazarimehr, A. Karthikeyan, A. Alsaedi, T. Hayat, V.T. Pham, Frontiers Inf Technol Electronic Eng. 20, 584 (2019). https://doi.org/10.1631/fitee.1800389

    Article  Google Scholar 

  25. N. Zandi-Mehran, S. Jafari, S.M. Golpayegani, F. Nazarimehr, M. Perc, Nonlinear Dyn. 100, 11s (2020). https://doi.org/10.1007/s11071-020-05576-9

    Article  Google Scholar 

  26. H. Hua, H. Gu, Y. Jia, B. Lu, Commun Nonlinear Sci. 110, 106370 (2022). https://doi.org/10.1016/j.cnsns.2022.106370

    Article  Google Scholar 

  27. B. Ermentrout, Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students (SIAM, Philadelphia, 2002)

    Book  MATH  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11872276 and 12072236).

Author information

Authors and Affiliations

  1. School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang, 453003, China

    Hongtao Hua

  2. School of Aerospace and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Huaguang Gu

Authors
  1. Hongtao Hua
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huaguang Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Huaguang Gu made contributions to the acquisition and supervision of funds and participated in investigation and writing and review. Hongtao Hua simulated the model, analyzed the bifurcations, and wrote the first draft.

Corresponding author

Correspondence to Huaguang Gu.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hua, H., Gu, H. Bifurcations underlying sigh and eupnea rhythmic transition in a pre-Bötzinger complex model. Eur. Phys. J. Spec. Top. 231, 4109–4116 (2022). https://doi.org/10.1140/epjs/s11734-022-00631-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-022-00631-5

Search

Navigation