Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models
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A series of bifurcations from period-1 bursting to period-1 spiking in a complex (or simple) process were observed with increasing extra-cellular potassium concentration during biological experiments on different neural pacemakers. This complex process is composed of three parts: period-adding sequences of burstings, chaotic bursting to chaotic spiking, and an inverse period-doubling bifurcation of spiking patterns. Six cases of bifurcations with complex processes distinguished by period-adding sequences with stochastic or chaotic burstings that can reach different bursting patterns, and three cases of bifurcations with simple processes, without the transition from chaotic bursting to chaotic spiking, were identified. It reveals the structures closely matching those simulated in a two-dimensional parameter space of the Hindmarsh–Rose model, by increasing one parameter \(I\) and fixing another parameter \(r\) at different values. The experimental bifurcations also resembled those simulated in a physiologically based model, the Chay model. The experimental observations not only reveal the nonlinear dynamics of the firing patterns of neural pacemakers but also provide experimental evidence of the existence of bifurcations from bursting to spiking simulated in the theoretical models.
KeywordsBifurcation Neural firing Chaos Bursting Spiking Period-adding bifurcation
This work was supported by the National Natural Science Foundation of China under Grant Nos. 11372224 and 11072135, the Fundamental Research Funds for Central Universities designated to Tongji University under Grant No. 1330219127, and Hong Kong Research Grants Council under the GRF Grant CityU1109/12E.
- 3.Yang, M.H., An, S.C., Gu, H.G., Liu, Z.Q., Ren, W.: Understanding of physiological neural firing patterns through dynamical bifurcation machineries. NeuroReport 17, 995–999 (2006)Google Scholar
- 6.Hansel, D., Sompolinsky, H.: Synchronization and computation in a chaotic neural network. Phys. Rev. Lett. 68, 718–721 (1992)Google Scholar
- 8.Dhamala, M., Jirsa, V.K., Ding, M.: Enhancement of neural synchrony by time delay. Phys. Rev. Lett. 92, 074104 (2004)Google Scholar
- 22.Terman, D.: The transition from bursting to continuous spiking in excitable membrane models. J. Nonlinear Sci. 2, 135–182 (1992)Google Scholar
- 30.Wu, X.B., Mo, J., Yang, M.H., Zheng, Q.H., Gu, H.G., Ren, W.: Two different bifurcation scenarios in neural firing rhythms discovered in biological experiments by adjusting two parameters. Chin. Phys. Lett. 25, 2799–2802 (2008)Google Scholar
- 32.De, L.E., Hasler, M.: Oscillations and oscillatory behavior in small neural circuits. Biol. Cybern. 95(6), 537–554 (2006)Google Scholar
- 45.Holden, A.V., Fan, Y.S.: From simple to simple bursting oscillatory behaviour via chaos in the Hindmarsh–Rose model for neuronal activity. Chaos Solitons Fractals 2, 221–236 (1992)Google Scholar
- 47.González-Miranda, M.: Pacemaker dynamics in the full Morris–Lecar model. Commun. Nonlinear Sci. Numer. Simul. http://dx.doi.org/10.1016/j.cnsns.2014.02.020.
- 55.Moore, K.A., Kohno, T., Karchewski, L.A., Scholz, J., Baba, H., Woolf, C.J.: Partial peripheral nerve injury promotes a selective loss of GABAergic inhibition in the superficial dorsal horn of the spinal cord. J. Neurosci. 22, 6724–6731 (2002)Google Scholar
- 56.Fan, Y.S., Chay, T.R.: Generation of periodic and chaotic bursting in an excitable cell model. Biol. Cybern. 71, 417–431 (1994)Google Scholar
- 60.Djouhri, L., Koutsikou, S., Fang, X., McMullan, S., Lawson, S.N.: Spontaneous pain, both neuropathic and inflammatory, is related to frequency of spontaneous firing in intact C-fiber nociceptors. J. Neurosci. 26, 1281–1292 (2006) Google Scholar
- 61.Yang, J., Duan, Y.B., Xing, J.L., Zhu, J.L., Duan, J.H., Hu, S.J.: Responsiveness of a neural pacemaker near the bifurcation point. Neurosci. Lett. 392, 105–109 (2006)Google Scholar
- 63.Braun, H.A., Voigt, K., Huber, M.T.: Oscillations, resonances and noise: basis of flexible neuronal pattern generation. Biosystems 71, 39–50 (2003)Google Scholar
- 64.Liger-Belair, G., Tufaile, A., Robillard, B., Jeandet, P., Sartorelli, J.C.: Period-adding route in sparkling bubbles. Phys. Rev. E 72, 037204 (2005)Google Scholar