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Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies

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Abstract

Dynamical behavior of a biological neuronal network depends significantly on the spatial pattern of synaptic connections among neurons. While neuronal network dynamics has extensively been studied with simple wiring patterns, such as all-to-all or random synaptic connections, not much is known about the activity of networks with more complicated wiring topologies. Here, we examined how different wiring topologies may influence the response properties of neuronal networks, paying attention to irregular spike firing, which is known as a characteristic of in vivo cortical neurons, and spike synchronicity. We constructed a recurrent network model of realistic neurons and systematically rewired the recurrent synapses to change the network topology, from a localized regular and a “small-world” network topology to a distributed random network topology. Regular and small-world wiring patterns greatly increased the irregularity or the coefficient of variation (Cv) of output spike trains, whereas such an increase was small in random connectivity patterns. For given strength of recurrent synapses, the firing irregularity exhibited monotonous decreases from the regular to the random network topology. By contrast, the spike coherence between an arbitrary neuron pair exhibited a non-monotonous dependence on the topological wiring pattern. More precisely, the wiring pattern to maximize the spike coherence varied with the strength of recurrent synapses. In a certain range of the synaptic strength, the spike coherence was maximal in the small-world network topology, and the long-range connections introduced in this wiring changed the dependence of spike synchrony on the synaptic strength moderately. However, the effects of this network topology were not really special in other properties of network activity.

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References

  • Achard, S., Salvador, R., Whitcher, B., Suckling, J., & Bullmore, E. (2006). A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. Journal of Neuroscience, 26, 63–72.

    Article  PubMed  CAS  Google Scholar 

  • Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience, 8, 183–208.

    Article  PubMed  CAS  Google Scholar 

  • Buzsaki, G., Geisler, C., Henze, D. A., & Wang, X. J. (2004). Interneuron Diversity series: Circuit complexity and axon wiring economy of cortical interneurons. Trends in Neurosciences, 27, 186–193.

    Article  PubMed  CAS  Google Scholar 

  • Chow, C. C., & White, A. (1996). Spontaneous action potentials due to channel fluctuations. Biophysical Journal, 71, 3013–3021.

    Article  PubMed  CAS  Google Scholar 

  • Destexhe, A., Mainen, Z. F., & Sejnowski, T. J. (1998). Kinetic models of synaptic transmission. In C. Koch, & I. Segev (Eds.), Methods in neural modeling (pp. 1–25). Cambridge, MA: MIT.

    Google Scholar 

  • Destexhe, A., & Paré, D. (1999). Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. Journal of Neurophysiology, 81, 1531–1547.

    PubMed  CAS  Google Scholar 

  • Destexhe, A., Rudolph, M., Fellous, J. M., & Sejnowski, T. J. (2001). Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscientist, 107, 13–24.

    CAS  Google Scholar 

  • Dyhrfjeld-Johnsen, J., Santhakumar, V., Morgan, R. J., Huerta, R., Tsimring, L., Soltesz, I. (2007). Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data. Journal of Neurophysiology, 97, 1566–1587.

    Article  PubMed  Google Scholar 

  • Erisir, A., Lau, D., Rudy, B., & Leonard, C. S. (1999). Function of specific K+ channels in sustained high-frequency firing of fast-spiking neocortical interneurons. Journal of Neurophysiology, 82, 2476–2489.

    PubMed  CAS  Google Scholar 

  • Ermentrout, G. B., & Kopell, N. (1998). Fine structure of neural spiking and synchronization in the presence of conduction delays. Proceedings of the National Academy of Sciences of the United States of America, 95, 1259–1264.

    Article  PubMed  CAS  Google Scholar 

  • Foldy, C., Dyhrfjeld-Johnsen, J., & Soltesz, I. (2005). Structure of cortical microcircuit theory. Journal of Physiology, 562, 47–54.

    Article  PubMed  CAS  Google Scholar 

  • Fukai, T. (2000). Neuronal communication within synchronous gamma oscillations. NeuroReport, 11, 3457–3460.

    Article  PubMed  CAS  Google Scholar 

  • Gupta, A., Wang, Y., & Markram, H. (2000). Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex. Science, 287, 273–278.

    Article  PubMed  CAS  Google Scholar 

  • Holmgren, C., Harkany, T., Svennenfors, B., & Zilberter, Y. (2003). Pyramidal cell communication within local networks in layer 2/3 of rat neocortex. Journal of Physiology, 551, 139–153.

    Article  PubMed  CAS  Google Scholar 

  • Jahr, C. E., & Stevens, C. F. (1990). Voltage dependence of NMDA-activated macroscopic conductances predicted by single-channel kinetics. Journal of Neuroscience, 10, 3178–3182.

    PubMed  CAS  Google Scholar 

  • Kalisman, N., Siberberg, G., & Markram, H. (2005). The neocortical microcircuit as a tabula rasa. Proceedings of the National Academy of Sciences of the United States of America, 102, 880–885.

    Article  PubMed  CAS  Google Scholar 

  • Koch, C. (1999). Biophysics of computation. New York: Oxford University Press.

    Google Scholar 

  • Lago-Fernández, L. F., Huerta, R., Corbacho, F., & Sigüenza, J. A. (2000). Fast response and temporal coherent oscillations in small-world networks. Physical Review Letters, 84, 2758–2761.

    Article  PubMed  Google Scholar 

  • Lewis, T. J., & Rinzel, J. (2003). Dynamics of spiking neurons connected by both inhibitory and electrical coupling. Journal of Computational Neuroscience, 14, 283–309.

    Article  PubMed  Google Scholar 

  • Maass, W., Natschlager, T., & Markram, H. (2002). Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Computation, 14, 2531–2560.

    Article  PubMed  Google Scholar 

  • Mainen, Z. F., & Sejnowski, T. J. (1995). Reliability of spike timing in neocortical neurons. Science, 268, 1503–1506.

    Article  PubMed  CAS  Google Scholar 

  • Netoff, T. I., Clewley, R., Arno, S., Keck, T., & White, J. A. (2004). Epilepsy in small-world networks. Journal of Neuroscience, 24, 8075–8083.

    Article  PubMed  CAS  Google Scholar 

  • Nomura, M., Fukai, T., & Aoyagi, T. (2003). Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses. Neural Computation, 15, 2179–2198.

    Article  PubMed  Google Scholar 

  • Petersen, C. C. H. (2002). Short-term dynamics of synaptic transmission within the excitatory neuronal network of rat layer 4 barrel cortex. Journal of Neurophysiology, 87, 2904–2914.

    PubMed  Google Scholar 

  • Shadlen, M. N., & Newsome, W. T. (1998). The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding. Journal of Neuroscience, 18, 3870–3896.

    PubMed  CAS  Google Scholar 

  • Shinomoto, S., Miyazaki, Y., Tamura, H., & Fujita, I. (2005). Regional and laminar differences in in vivo firing patterns of primate cortical neurons. Journal of Neurophysiology, 94, 567–575.

    Article  PubMed  Google Scholar 

  • Softky, W. R., & Koch, C. (1993). The high irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. Journal of Neuroscience, 13, 334–350.

    PubMed  CAS  Google Scholar 

  • Song, S., Sjöström, P. J., Reigl, M., Nelson, S., & Chklovskii, D. B. (2005). Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biology, 3, e68.

    Article  PubMed  CAS  Google Scholar 

  • Sporns, O., & Zwi, J. D. (2004). The small world of the cerebral cortex. Neuroinformatics, 2, 145–162.

    Article  PubMed  Google Scholar 

  • Stepanyants, A., Tamás, G., & Chklovskii, D. B. (2004). Class-specific features of neuronal wiring. Neuron, 43, 251–259.

    Article  PubMed  CAS  Google Scholar 

  • Stevens, C. F., & Zador, A. M. (1998). Input synchrony and the irregular firing of cortical neurons. Nature Neuroscience, 1, 210–217.

    Article  PubMed  CAS  Google Scholar 

  • Traub, R., Whittington, M., Stanford, M., & Jefferys, J. (1996). A mechanism for generation of long-range synchronous fast oscillations in the cortex. Nature, 383, 621–624.

    Article  PubMed  CAS  Google Scholar 

  • Tsodyks, M., & Markram, H. (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proceedings of the National Academy of Sciences of the United States of America, 94, 710–723.

    Article  Google Scholar 

  • Wang, X. J., & Buzsáki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuron network model. Journal of Neuroscience, 16, 6402–6413.

    PubMed  CAS  Google Scholar 

  • Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442.

    Article  PubMed  CAS  Google Scholar 

  • Wolfart, J., Debay, D., Le Masson, G., Destexhe, A., & Bal, T. (2005). Synaptic background activity controls spike transfer from thalamus to cortex. Nature Neuroscience, 8, 1760–1767.

    Article  PubMed  CAS  Google Scholar 

  • Yoshimura, Y., & Callaway, E. M. (2005). Fine-scale specificity of cortical networks depends on inhibitory cell type and connectivity. Nature Neuroscience, 8, 1552–1559.

    Article  PubMed  CAS  Google Scholar 

  • Yoshimura, Y., Dantzker, J. L. M., & Callaway, E. M. (2005). Excitatory cortical neurons from fine-scale functional networks. Nature, 433, 868–873.

    Article  PubMed  CAS  Google Scholar 

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Acknowledgements

This work was supported by Grant-in-Aid for Scientific Research on Priority Areas “Integrative Brain Research” from the Ministry of Education, Culture, Sports, Science and Technology of Japan (18019036).

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Correspondence to Katsunori Kitano.

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Action Editor: Xiao-Jing Wang

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Kitano, K., Fukai, T. Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies. J Comput Neurosci 23, 237–250 (2007). https://doi.org/10.1007/s10827-007-0030-1

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  • DOI: https://doi.org/10.1007/s10827-007-0030-1

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