Avalanches in simple stochastic spiking network models.
Neuronal avalanches are synchronous aperiodic bursts of spiking activity that generally follow a power law distribution in size. Such avalanches have been observed in a variety of neural networks in vitro and in vivo. It is important to investigate what gives rise to them and why they are such a widespread feature of spontaneously active nervous tissue. We address these questions using Cowan's continuous-time model of spiking networks, the simplest version comprises coupled 2-state Markov processes, each representing a neuron. The networks studied have populations of thousands of neurons, 80% excitatory and 20% inhibitory, with random homogenous connectivity at different levels of sparseness. A comparatively novel feature of our simulation is the use of the Gillespie algorithm at the network level, to provide an exact stochastic simulation of coupled neurons in continuous time.
We find that when the overall ratio of inhibition to excitation (I:E) is too low, the neurons fire as independent Poisson processes. At a threshold in the I:E ratio, a transition to synchronous activity occurs suggestive of a bifurcation. Above this threshold, spikes are organized into avalanches which follow a power law distribution in both size and duration. The degree of synchrony in the network, measured by the coefficient of variation, grows smoothly with the I:E ratio above the threshold, as the mean firing rate falls smoothly. In other words, as the network fires more sparsely, spikes tend more to be grouped temporally into avalanches, as inhibition is increased relative to excitation.
The study indicates that avalanches are a network property, which may arise from very simple elements connected in unstructured ways. Our model produces synchronous dynamics and neuronal avalanches despite lacking many of the features proposed to account for these properties. There is no synaptic depression, nor synaptic plasticity or learning of any kind generating synchrony here. Neither is there any small-world or power law structure in the network connectivity to account for the power law distributions observed in network firing patterns. It appears that a whole region in the network parameter space, sensitive only to the bulk statistics of connectivity and excitability, supports synchronous firing grouped into avalanches. In particular, the avalanches appear above a threshold, rather than only appearing at some critical parameter values ? there is no self-organized criticality here either.
While the observed power law behaviour is qualitatively robust, the value of the power law exponents varies with the I:E ratio as well as with time bin size and other choices made in analyzing the data. For example, there is no unique way to determine the power law exponent of the avalanche size distribution. This variability is also observed in experiments, and poses a challenge for theorists.
Conference:
Computational and systems
neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009.
Presentation Type:
Poster Presentation
Topic:
Poster Presentations
Citation:
(2009). Avalanches in simple stochastic spiking network models..
Front. Syst. Neurosci.
Conference Abstract:
Computational and systems
neuroscience 2009.
doi: 10.3389/conf.neuro.06.2009.03.339
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Received:
04 Feb 2009;
Published Online:
04 Feb 2009.