Abstract
Brain signals such as local field potentials often display gamma-band oscillations (30–70 Hz) in a variety of cognitive tasks. These oscillatory activities possibly reflect synchronization of cell assemblies that are engaged in a cognitive function. A type of pyramidal neurons, i.e., chattering neurons, show fast rhythmic bursting (FRB) in the gamma frequency range, and may play an active role in generating the gamma-band oscillations in the cerebral cortex. Our previous phase response analyses have revealed that the synchronization between the coupled bursting neurons significantly depends on the bursting mode that is defined as the number of spikes in each burst. Namely, a network of neurons bursting through a Ca2+-dependent mechanism exhibited sharp transitions between synchronous and asynchronous firing states when the neurons exchanged the bursting mode between singlet, doublet and so on. However, whether a broad class of bursting neuron models commonly show such a network behavior remains unclear. Here, we analyze the mechanism underlying this network behavior using a mathematically tractable neuron model. Then we extend our results to a multi-compartment version of the NaP current-based neuron model and prove a similar tight relationship between the bursting mode changes and the network state changes in this model. Thus, the synchronization behavior couples tightly to the bursting mode in a wide class of networks of bursting neurons.
Similar content being viewed by others
References
Aoyagi, T., Kang, Y., Terada, N., Kaneko, T., & Fukai, T. (2002). The role of Ca2+-dependent cationic current in generating gamma-frequency rhythmic bursts: Theoretical study. Neuroscience, 115(1), 127–1138.
Aoyagi, T., Takekawa, T., & Fukai, T. (2003). Gamma rhythmic bursts: Coherence control in networks of cortical pyramidal neurons. Neural Computation, 15, 1035–1061.
Booth, V., & Bose, A. (2002). Burst synchrony patterns in hippocampal pyramidal cell model netowkrks. Network: Computation in Neural Systems, 13, 157–177.
Brumberg, J. C., Nowak, L. G., & McCormick, D. A. (2000). Ionic mechanisms underlynig repetitive high-frequency burst firing in supragranular corticalneurons. Journal of Neuroscience, 20, 4829–4843.
Buzsaki, G., & Draguhn, A. (2004). Neuronal oscillations in cortical networks. Science, 304, 1926–1929.
Cardin, J. A., Palmer, L. A., & Contreras, D. (2005). Stimulus-dependent gamma (30–50 Hz) oscillations in simple and complex fast rhythmic bursting cells in primary visual cortex. Journal of Neuroscience, 25, 5339–5350.
Crook, S. M., Ermentrout, G. B., & Bower, J. M. (1998). Dendritic and synaptic effects in systems of coupled cortical oscillators. Journal of Computational Neuroscience, 5, 515–329.
Crook, S. M., Ermentrout, G. B., & Vanier, M. C. (1997). The role of axonal delay in the synchronization of networks of coupled cortical oscillators. Journal of Computational Neuroscience, 4, 161–172.
Cunningham, M. O., Whittington, M. A., Bibbig, A., Roopun, A., LeBeau, F. E. N., Vogt, A., et al. (2004). A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro. Proceedings of the National Academy of Sciences of the United States of America, 101, 7152–7157.
Doiron, B., Laing, C., Longtin, A., & Maler, L. (2002). Ghostbursting: A novel neuronal burst mechanism. Journal of Computational Neuroscience, 12, 5–25.
Dormand, J., & Prince, P. (1980). A family of embedded runge-kutta formulae. Journal of Computational and Applied Mathematics, 6, 19–26.
Ermentrout, G. B. (1996). Type I membranes, phase resetting curves, and synchrony. Neural Computation, 8, 979– 1001.
Ermentrout, G. B., & Kopell, N. (1984). Frequency plateaus in a chain of weakly coupled oscillators. SIAM journal on Mathematical Analysis, 15, 215–237.
Goldberg, J. A., Deister, C. A., & Wilson, C. J. (2007). Response properties and synchronization of rhythmically firing dendritic neurons. Journal of Neurophysiology, 97, 208–219.
Gray, C. M., & McCormick, D. A. (1996). Chattering cells: Superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science, 274, 109–113.
Gray, C. M., & Prisco, G. V. D. (1997). Stimulus-dependent neuronal oscillations and local synchronization in striate cortex of the alert cat. Journal of Neuroscience, 17, 3239– 3253.
Gray, C. M., & Singer, W. (1989). Stimulus-specific neuronal oscillations in orientation columns of cat visua-cortex. Proceedings of the National Academy of Sciences of the United States of America, 86, 1698–1702.
Gutkin, B. S., Ermentrout, G. B., & Reyes, A. D. (2005). Phase-response curves give the responses of neurons to transient inputs. Journal of Neurophysiology, 94, 1623–1635.
Haj-Dahmane, S., & Andrade, R. (1997). Calcium-activated cation nonselective currenct contributes to the fast afterdepolarization in rat prefrontal cortex neurons. Journal of Neurophysiology, 78, 1983–1989.
Hansel, D., Mato, G., & Meunier, C. (1995). Synchrony in excitatory neural network. Neural Computation, 7, 307–337.
Hoppensteadt, F. C., & Izhikevich, E. M. (1997). Weakly connected neural networks. New York: Springer-Verlag.
Izhikevich, E. (2000). Neural excitability, spiking and bursting. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 10, 1171–1266.
Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14, 1569–1572.
Kang, Y., & Kayano, F. (1994). Electrophysiological and morphological characteristics of layer VI pyramidal cells in the cat motor cortex. Journal of Neurophysiology, 72, 578–91.
Kang, Y., Okada, T., & Ohmori, H. (1998) A phenytoin-sensitive cationic current participates in generating afterdepolarization adn burst afterdischarge in rat neocortical pyramidal cells. European Journal of Neuroscience, 10, 1363–1375.
Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Berlin: Springer-Verlag.
Netoff, T. I., Banks, M. I., Dorval, A. D., Acker, C. D., Haas, J. S., Kopell, N., et al. (2005). Synchronization in hybrid neuronal networks of the hippocampal formation. Journal of Neurophysiology, 93, 1197–1208.
Pinsky, P. F., & Rinzel, J. (1994). Intrinsic and network rhythmogenesis in a reduced traub model for CA3 neurons. Journal of Computational Neuroscience, 1, 39–60.
Reyes, A. D., & Fetz, E. E. (1993). Two modes of interspike interval shortening by brief transient depolarizations in cat neocortical neurons. Journal of Neurophysiology, 69, 1661–1672.
Shampine, L. F. (1986). Some practical Runge–Kutta formulas. Mathematics of Computation, 46, 135–150.
Singer, W. (1999). Neuronal synchrony a versatile code for the definition of relations? Neuron, 24, 49–65.
Steriade, M. (2006). Grouping of brain rhythms in corticothalamic systems. Neuroscience, 137, 1087–1106.
Steriade, M., Timofeev, I., Dürmüller, N., & Grenier, F. (1998). Dynamic properties of corticothalamic neurons and local cortical interneurons generation fast rhythmic (30–40 Hz) spike bursts. Journal of Neurophysiology, 79, 483–490.
Takekawa, T., Aoyagi, T., & Fukai, T. (2004). Influences of synaptic location on the synchronization of rhythmic bursting neurons. Network: Computation in Neural Systems, 15, 1–12.
Tallon-Baudry, C., Bertrand, O., Delpuech, C., & Pernier, J. (1997). Oscillatory gamma-band (30–70 Hz) activity induced by a visual search task in humans. Journal of Neuroscience, 17, 722–734.
Traub, R. D., Buhl, E. H., Gloveli, T., & Whittington, M. A. (2003). Fast rhythmic bursting can be induced in layer 2/3 corical neurons by enhancing persisten Na+ conductance or by blocking BK channels. Journal of Neurophysiology, 89, 909–921.
Tsubo, Y., Takada, M., & Fukai, T. (2005). Layer-specific synchronization properties and their cholinergic modulations of rat motor cortex pyramidal neurons. In Abstract of Annual Meeting of the Society for Neuroscience, Washington DC (p 971.13).
van Vreeswijk, C., Abbott, L. F., & Ermentrout, G. B. (1994). When inhibition not excitation synchronizes neuronal firing. Journal of Computational Neuroscience, 1, 313–321.
Wang, X. J. (1999). Fast burst firing and short-term synaptic plasticity: A model of neocortical chattering neurons. Neuroscience, 89, 347–362.
Wilson, G. F., Richardson, F. C., Fisher, T. E., Olivera, B. M., & Kaczmarek, L. K. (1996). Identification and characterization of a Ca2+-sensitive nonspecific cation channel underlying prolonged repetitive firing in aplysia neurons. Journal of Neuroscience, 16, 3661–3671.
Author information
Authors and Affiliations
Corresponding author
Additional information
Action Editor: Xiao-Jing Wang
Rights and permissions
About this article
Cite this article
Takekawa, T., Aoyagi, T. & Fukai, T. Synchronous and asynchronous bursting states: role of intrinsic neural dynamics. J Comput Neurosci 23, 189–200 (2007). https://doi.org/10.1007/s10827-007-0027-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10827-007-0027-9