Email updates

Keep up to date with the latest news and content from BMC Neuroscience and BioMed Central.

This article is part of the supplement: Eighteenth Annual Computational Neuroscience Meeting: CNS*2009

Open Access Poster presentation

Switching to criticality by synchronized input

Anna Levina12*, Theo Geisel12 and J Michael Herrmann123

Author Affiliations

1 Bernstein Center for Computational Neuroscience, 37073 Göttingen, Germany

2 Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany

3 IPAB, School of Informatics, University of Edinburgh, Edinburgh, EH8 9AB, UK

For all author emails, please log on.

BMC Neuroscience 2009, 10(Suppl 1):P155  doi:10.1186/1471-2202-10-S1-P155


The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/10/S1/P155


Published:13 July 2009

© 2009 Levina et al; licensee BioMed Central Ltd.

Poster presentation

The concept of self-organized criticality (SOC) describes a variety of phenomena ranging from plate tectonics, the dynamics of granular media and stick-slip motion to neural avalanches [1]. In all these cases the dynamics is marginally stable and event sizes obey a characteristic power-law distribution.

It was previously shown that an extended critical interval can be obtained in a neural network by incorporation of depressive synapses [2]. In the present study we scrutinize a more realistic dynamics for the synaptic interactions that can be considered as the state-of-the-art in computational modeling of synaptic interaction (Figure 1) [2]. Interestingly, the more complex model does not exclude an analytical treatment and it shows a type of stationary state consisting of self-organized critical phase and a subcritical phase that has not been previously described. The phases are connected by first- or second-order phase transitions in a cusp bifurcation. Switching between phases can be induced by synchronized activity or by activity deprivation (Figure 2). We present exact analytical results supported by extensive numerical simulations.

thumbnailFigure 1. The distribution of avalanche sizes changes in dependence on the interaction parameter α from subcritical (circles, α = 0.52) via critical (stars, α = 0.56) to supercritical (triangles, α = 0.59). The inset shows the hysteresis of the distribution at an exemplary avalanche size (L = 40). The circles result at increasing α, stars at decreasing α.

thumbnailFigure 2. Dynamic transition from a critical (red circles) to a subcritical state (green circles) by short-term activity deprivation. The two stars represent the immediate effect of the deprivation in a particular trial.

By elucidating the relation between the elementary synaptic processes and the network dynamics, our mean-field approach revealed a macroscopic bifurcation pattern, which can be verified experimentally through predicted hysteresis. Furthermore it may be able to explain observations of up and down states in the prefrontal cortex [4] as well as the discrete changes in synaptic potentiation and depression [5] as network effects.

References

  1. Beggs J, Plenz D: Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures.

    J Neurosci 2004, 24:5216-5229. PubMed Abstract | Publisher Full Text OpenURL

  2. Levina A, Herrmann JM, Geisel T: Dynamical synapses causing self-organized criticality in neural networks.

    Nature Physics 2007, 3:857-860. OpenURL

  3. Tsodyks MV, Markram H: The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability.

    PNAS 1997, 94:719-723. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  4. Wilson CJ: The generation of natural firing patterns in neostriatal neurons.

    Prog Brain Res 1993, 99:277-297. PubMed Abstract OpenURL

  5. Petersen CCH, Malenka RC, Nicoll RA, Hopfield JJ: All-or-none potentiation at CA3-CA1 synapses.

    PNAS Neurobiology 1998, 95:4732-4737. OpenURL