Abstract
Self-organized criticality1 is one of the key concepts to describe the emergence of complexity in natural systems. The concept asserts that a system self-organizes into a critical state where system observables are distributed according to a power law. Prominent examples of self-organized critical dynamics include piling of granular media2, plate tectonics3 and stick–slip motion4. Critical behaviour has been shown to bring about optimal computational capabilities5, optimal transmission6, storage of information7 and sensitivity to sensory stimuli8,9,10. In neuronal systems, the existence of critical avalanches was predicted11 and later observed experimentally6,12,13. However, whereas in the experiments generic critical avalanches were found, in the model of ref. 11 they only show up if the set of parameters is fine-tuned externally to a critical transition state. Here, we demonstrate analytically and numerically that by assuming (biologically more realistic) dynamical synapses14 in a spiking neural network, the neuronal avalanches turn from an exceptional phenomenon into a typical and robust self-organized critical behaviour, if the total resources of neurotransmitter are sufficiently large.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
USD 39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987).
Frette, V. et al. Avalanche dynamics in a pile of rice. Nature 397, 49–52 (1996).
Gutenberg, B. & Richter, C. F. Magnitude and energy of earthquakes. Ann. Geofis. 9, 1–15 (1956).
Feder, H. J. S. & Feder, J. Self-organized criticality in a stick-slip process. Phys. Rev. Lett. 66, 2669–2672 (1991).
Legenstein, R. & Maass, W. Edge of chaos and prediction of computational performance for neural circuit models. Neural Networks 20, 323–334 (2007).
Beggs, J. & Plenz, D. Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003).
Haldeman, C. & Beggs, J. Critical branching captures activity in living neural networks and maximizes the number of metastable states. Phys. Rev. Lett. 94, 058101 (2005).
Der, R., Hesse, F. & Martius, G. Rocking stamper and jumping snake from a dynamical system approach to artificial life. Adapt. Behav. 14, 105–115 (2006).
Kinouchi, O. & Copelli, M. Optimal dynamical range of excitable networks at criticality. Nature Phys. 2, 348–352 (2006).
Chialvo, D. Are our senses critical? Nature Phys. 2, 301–302 (2006).
Eurich, C. W., Herrmann, M. & Ernst, U. Finite-size effects of avalanche dynamics. Phys. Rev. E 66, 066137 (2002).
Beggs, J. & Plenz, D. Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216–5229 (2004).
Plenz, D. & Thiagarajan, T. C. The organizing principles of neuronal avalanches: cell assemblies in the cortex? Trends Neurosci. 30, 101–110 (2007).
Markram, H. & Tsodyks, M. Redistribution of synaptic efficacy between pyramidal neurons. Nature 382, 807–810 (1996).
Teramae, J. & Fukai, T. Local cortical circuit model inferred from power-law distributed neuronal avalanches. J. Comput. Neurosci. 22, 301–312 (2007).
Levina, A., Herrmann, J. M. & Geisel, T. in Advances in Neural Information Processing Systems 18 (eds Weiss, Y., Schölkopf, B. & Platt, J.) 771–778 (MIT Press, Cambridge, 2006).
Tsodyks, M., Pawelzik, K. & Markram, H. Neural networks with dynamic synapses. Neural Comput. 10, 821–835 (1998).
Lin, M. & Chen, T.-L. Self-organized criticality in a simple model of neurons based on small-world networks. Phys. Rev. E 71, 016133 (2005).
de Arcangelis, L., Perrone-Capano, C. & Herrmann, H. J. Self-organized criticality model for brain plasticity. Phys. Rev. Lett. 96, 028107 (2006).
Acknowledgements
We thank M. Denker and T. Fukai for useful discussions. This work was partially supported by the BMBF in the framework of the Bernstein Centers for Computational Neuroscience, grant number 01GQ0432. A.L. has received support from DFG Graduiertenkolleg N1023.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Levina, A., Herrmann, J. & Geisel, T. Dynamical synapses causing self-organized criticality in neural networks. Nature Phys 3, 857–860 (2007). https://doi.org/10.1038/nphys758
Received:
Accepted:
Published:
Issue date:
DOI: https://doi.org/10.1038/nphys758
This article is cited by
-
Ising-like model replicating time-averaged spiking behaviour of in vitro neuronal networks
Scientific Reports (2024)
-
The influence of synaptic plasticity on critical coupling estimates for neural populations
Journal of Mathematical Biology (2024)
-
Engineering the structural and electrical interplay of nanostructured Au resistive switching networks by controlling the forming process
Scientific Reports (2023)
-
Fish shoals resemble a stochastic excitable system driven by environmental perturbations
Nature Physics (2023)
-
Scale free avalanches in excitatory-inhibitory populations of spiking neurons with conductance based synaptic currents
Journal of Computational Neuroscience (2023)
