[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content

Advertisement

Springer Nature Link
Log in

Bifurcations and enhancement of neuronal firing induced by negative feedback

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Bifurcations and enhancement of neuronal firing induced by negative feedback from an inhibitory autapse are investigated. A slow inhibitory autapse model that can exhibit dynamics similar to the inhibitory autapse of a rat interneuron is considered. Compared with a Morris–Lecar (ML) model without an autapse, enlargement of the parameter region of firing activities in the ML model with a slow inhibitory autapse can be identified with 1-parameter and 2-parameter bifurcations and is induced by a shift of an inverse Hopf bifurcation point. The right shift of the inverse Hopf bifurcation point from firing to resting state with a high membrane potential level causes the resting state in the ML model without an autapse to change to firing in the ML model with an autapse. This shows that the autapse can enhance neuronal firing and can be well interpreted by the dynamic responses of the resting state to inhibitory impulse current. In addition, many complex dynamics such as coexisting behaviors and codimension-2 bifurcations are also induced, and the relationship between the inverse Hopf bifurcation point and a physiological concept, depolarization block, a phenomenon in which a neuron enters from firing to resting state when it receives excessive excitatory or depolarizing current, is discussed. The results provide a novel viewpoint that the inhibitory autapse enhances rather than suppresses neuronal firing near the inverse Hopf bifurcation point, which is an important example showing that negative feedback can play a positive role in nonlinear dynamics.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Izhikevich, E.M.: Neural excitability, spiking and bursting. Int. J. Bifurc. Chaos 10, 1171–1266 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Izhikevich, E.M.: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. MIT Press, Cambridge (2007)

    Google Scholar 

  3. Gu, H.G., Pan, B.B., Chen, G.R., Duan, L.X.: Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models. Nonlinear Dyn. 78, 391–407 (2014)

    Article  MathSciNet  Google Scholar 

  4. Gu, H.G.: Different bifurcation scenarios of neural firing patterns observed in the biological experiment on identical pacemakers. Int. J. Bifurc. Chaos 23, 1350195 (2013)

    Article  MathSciNet  Google Scholar 

  5. Gu, H.G.: Experimental observation of transition from chaotic bursting to chaotic spiking in a neural pacemaker. Chaos 23, 023126 (2013)

    Article  Google Scholar 

  6. Gu, H.G., Pan, B.B.: A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model. Nonlinear Dyn. 81, 2107–2126 (2015)

    Article  MathSciNet  Google Scholar 

  7. Gu, H.G.: Biological experimental observations of an unnoticed chaos as simulated by the Hindmarsh–Rose model. PLoS One 8, e81759 (2013)

    Article  Google Scholar 

  8. Gu, H.G., Pan, B.B.: Identification of neural firing patterns, frequency and temporal coding mechanisms in individual aortic baroreceptors. Front. Comput. Neurosci. 9, 108 (2015)

    Article  Google Scholar 

  9. Finke, C., Freund, J.A., Rosa Jr., E., Braun, H.A., Feudel, U.: On the role of subthreshold currents in the Huber–Braun cold receptor model. Chaos 20, 045107 (2010)

    Article  Google Scholar 

  10. Vreeswijk, C.V., Abbott, L.F., Ermentrout, G.B.: When inhibition not excitation synchronizes neural firing. J. Comput. Neurosci. 1, 313–321 (1994)

    Article  Google Scholar 

  11. Pfeuty, B., Mato, G., Golomb, D., Hansel, D.: Electrical synapses and synchrony: the role of intrinsic currents. J. Neurosci. 23, 6280–6294 (2003)

    MATH  Google Scholar 

  12. Pfeuty, B., Mato, G., Golomb, D., Hansel, D.: The combined effects of inhibitory and electrical synapses in synchrony. Neural Comput. 17, 633–670 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hansel, D., Mato, G., Meunier, C.: Synchrony in excitatory neural networks. Neural Comput. 7, 307–337 (1995)

    Article  Google Scholar 

  14. Ernst, U., Pawelzik, K., Geisel, T.: Synchronization induced by temporal delays in pulse-coupled oscillators. Phys. Rev. Lett. 74, 1570–1573 (1995)

    Article  Google Scholar 

  15. Wang, X.J., Buzsáki, G.: Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci. 16, 6402–6413 (1996)

    Google Scholar 

  16. Bartos, M., Vida, I., Frotscher, M., Meyer, A., Monyer, H., Geiger, J.R.P., Jonas, P.: Fast synaptic inhibition promotes synchronized gamma oscillations in hippocampal interneuron networks. Proc. Natl. Acad. Sci. USA 99, 13222–13227 (2002)

    Article  Google Scholar 

  17. Yilmaz, E., Baysal, V., Perc, M., Ozer, M.: Enhancement of pacemaker induced stochastic resonance by an autapse in a scale-free neuronal network. Sci. China Technol. Sci. 59, 364–370 (2016)

    Article  Google Scholar 

  18. Song, X.L., Wang, C.N., Ma, J., Tang, J.: Transition of electric activity of neurons induced by chemical and electric autapses. Sci. China Technol. Sci. 58, 1007–1014 (2015)

    Article  Google Scholar 

  19. Qin, H.X., Ma, J., Wang, C.N., Wu, Y.: Autapse-induced spiral wave in network of neurons under noise. PLoS One 9, e100849 (2014)

    Article  Google Scholar 

  20. Connelly, W.M.: Autaptic connections and synaptic depression constrain and promote gamma oscillations. PLoS One 9, e89995 (2014)

    Article  Google Scholar 

  21. Wu, Y.N., Gong, Y.B., Wang, Q.: Autaptic activity-induced synchronization transitions in Newman–Watts network of Hodgkin–Huxley neurons. Chaos 25, 043113 (2015)

    Article  MathSciNet  Google Scholar 

  22. Wang, X.J., Rinzel, J.: Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Comput. 4, 84–97 (1992)

    Article  Google Scholar 

  23. Zhao, Z.G., Gu, H.G.: The influence of single neuron dynamics and network topology on time delay-induced multiple synchronous behaviors in inhibitory coupled network. Chaos Solitons Fractals 80, 96–108 (2015)

    Article  MathSciNet  Google Scholar 

  24. Gu, H.G., Zhao, Z.G.: Dynamics of time delay-induced multiple synchronous behaviors in inhibitory coupled neurons. PLoS One 10, 0138593 (2015)

    Google Scholar 

  25. Loos, H.V.D., Glaser, E.M.: Autapses in neocortex cerebri: synapses between a pyramidal cells axon and its own dendrites. Brain Res. 48, 355–360 (1972)

    Article  Google Scholar 

  26. Wang, H.T., Ma, J., Chen, Y.L., Chen, Y.: Effect of an autapse on the firing pattern transition in a bursting neuron. Commun. Nonlinear Sci. Numer. Simul. 19, 3242–3254 (2014)

    Article  MathSciNet  Google Scholar 

  27. Wang, H.T., Wang, L.F., Chen, Y.L., Chen, Y.: Effect of autaptic activity on the response of a Hodgkin–Huxley neuron. Chaos 24, 033122 (2014)

    Article  MathSciNet  Google Scholar 

  28. Hashemi, M., Valizadeh, A., Azizi, Y.: Effect of duration of synaptic activity on spike rate of a Hodgkin-Huxley neuron with delayed feedback. Phys. Rev. E 85, 021917 (2012)

    Article  Google Scholar 

  29. Wang, L., Zeng, Y.J.: Control of bursting behavior in neurons by autaptic modulation. Neurol. Sci. 34, 1977–1984 (2013)

    Article  Google Scholar 

  30. Yilmaz, E., Baysal, V., Ozer, M., Perc, M.: Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks. Physica A 444, 538–546 (2016)

    Article  MathSciNet  Google Scholar 

  31. Saada, R., Miller, N., Hurwitz, I., Susswein, A.J.: Autaptic excitation elicits persistent activity and a plateau potential in a neuron of known behavioral function. Curr. Biol. 19, 479–684 (2009)

    Article  Google Scholar 

  32. Bacci, A., Huguenard, J.R., Prince, D.A.: Functional autaptic neurotransmission in fast-spiking interneurons: a novel form of feedback inhibition in the neocortex. J. Neurosci. 23, 859–866 (2003)

    Google Scholar 

  33. Bacci, A., Huguenard, J.R.: Enhancement of spike-timing precision by autaptic transmission in neocortical inhibitory interneurons. Neuron 49, 119–130 (2006)

    Article  Google Scholar 

  34. Bacci, A., Huguenard, J.R., Prince, D.A.: Modulation of neocortical interneurons: extrinsic influences and exercises in self-control. Trends Neurosci. 28, 602–610 (2005)

    Article  Google Scholar 

  35. Cobb, S.R., Halasy, K., Vida, I., NyiRi, G., Tamás, G., Buhl, E.H., Somogyi, P.: Synaptic effects of identified interneurons innervating both interneurons and pyramidal cells in the rat hippocampus. Neuroscience 79, 629–648 (1997)

    Article  Google Scholar 

  36. Tamás, G., Buhl, E.H., Somogyi, P.: Massive autaptic self-innervation of GABAergic neurons in cat visual cortex. J. Neurosci. 17, 6352–6364 (1997)

    Google Scholar 

  37. Pouzat, C., Marty, A.: Autaptic inhibitory currents recorded from interneurons in rat cerebellar slices. J. Physiol. 509, 777–783 (1998)

    Article  Google Scholar 

  38. Tateno, T., Pakdaman, K.: Random dynamics of the Morris–Lecar neural model. Chaos 14, 511–530 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  39. Jalil, S., Belykh, I., Shilnikov, A.: Spikes matter for phase-locked bursting in inhibitory neurons. Phys. Rev. E 85, 036214 (2012)

    Article  Google Scholar 

  40. Somers, D., Kopell, N.: Rapid synchronization through fast threshold modulation. Biol. Cybern. 68, 393–407 (1993)

    Article  Google Scholar 

  41. Cymbalyuk, G.S., Gaudry, Q., Masino, M.A., Calabrese, R.L.: Bursting in leech heart interneurons: cell-autonomous and network-based mechanisms. J. Neurosci. 22, 10580–10592 (2002)

    Google Scholar 

  42. Ermentrout, B.: Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM, Philadelphia (2002)

    Book  MATH  Google Scholar 

  43. Dhooge, A., Govaerts, W., Kuznetsov, Y.A.: MATCONT: a MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Softw. 29, 141–164 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  44. Heyward, P., Ennis, M., Keller, A., Shipley, M.T.: Membrane bistability in olfactory bulb mitral cells. J. Neurosci. 21, 5311–5320 (2001)

    Google Scholar 

  45. Anderson, J., Lampl, I., Reichova, I., Carandini, M., Ferster, D.: Stimulus dependence of two-state fluctuations of membrane potential in cat visual cortex. Nat. Neurosci. 3, 617–621 (2000)

    Article  Google Scholar 

  46. Marder, E., Abbott, L.F., Turrigiano, G.G., Liu, Z., Golowasch, J.: Memory from the dynamics of intrinsic membrane currents. Proc. Natl. Acad. Sci. USA 93, 13481–13486 (1996)

    Article  Google Scholar 

  47. Wang, W., Nakadate, K., Masugi-Tokita, M., Shutoh, F., Aziz, W., Tarusawa, E., Lorincz, A., Molnár, E., Kesaf, S., Li, Y.Q.: Distinct cerebellar engrams in short-term and long-term motor learning. Proc. Natl. Acad. Sci. USA 111, E188–E193 (2014)

    Article  Google Scholar 

  48. Dovzhenok, A., Kuznetsov, A.S.: Exploring neuronal bistability at the depolarization block. PLoS One 7, e42811 (2012)

    Article  Google Scholar 

  49. Hubel, N., Scholl, E., Dahlem, M.A.: Bistable dynamics underlying excitability of ion homeostasis in neuron models. PLoS Comput. Biol. 10, e1003551 (2014)

    Article  Google Scholar 

  50. Le, T., Verley, D.R., Goaillard, J.M., Messinger, D.I., Christie, A.E., Birmingham, J.T.: Bistable behavior originating in the axon of a crustacean motor neuron. J. Neurophysiol. 95, 1356–1368 (2006)

    Article  Google Scholar 

  51. Lee, R.H., Heckman, C.J.: Influence of voltage-sensitive dendritic conductances on bistable firing and effective synaptic current in cat spinal motoneurons in vivo. J. Neurophysiol. 76, 2107–2110 (1996)

    Google Scholar 

  52. Grace, A.A., Bunney, B.S., Moore, H., Todd, C.L.: Dopamine-cell depolarization block as a model for the therapeutic actions of antipsychotic drugs. Trends Neurosci. 20, 31–37 (1997)

    Article  Google Scholar 

  53. Valenti, O., Cifelli, P., Gill, K.M., Grace, A.A.: Antipsychotic drugs rapidly induce dopamine neuron depolarization block in a developmental rat model of schizophrenia. J. Neurosci. 31, 12330–12338 (2011)

    Article  Google Scholar 

  54. Pietrobon, D., Moskowitz, M.A.: Chaos and commotion in the wake of cortical spreading depression and spreading depolarizations. Nat. Rev. Neurosci. 15, 379–393 (2014)

    Article  Google Scholar 

  55. Houssaini, K.E.I., Ivanov, A.I., Bernard, C., Jirsa, V.K.: Seizures, refractory status epilepticus, and depolarization block as endogenous brain activities. Phys. Rev. E. 91, 010701 (2015)

    Article  Google Scholar 

  56. Bianchi, D., Marasco, A., Limongiello, A., Marchetti, C., Marie, H., Tirozzi, B., Migliore, M.: On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. J. Comput. Neurosci. 33, 207–225 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Zhiguo Zhao & Huaguang Gu

  2. School of Life Sciences, Fudan University, Shanghai, 200433, China

    Bing Jia

Authors
  1. Zhiguo Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bing Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huaguang Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huaguang Gu.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11572225, 11402055, and 11372224.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Z., Jia, B. & Gu, H. Bifurcations and enhancement of neuronal firing induced by negative feedback. Nonlinear Dyn 86, 1549–1560 (2016). https://doi.org/10.1007/s11071-016-2976-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2976-x

Keywords

Search

Navigation