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This article is part of the supplement: Sixteenth Annual Computational Neuroscience Meeting: CNS*2007

Open Access Poster presentation

Mesoscopic model of balanced neuron networks using a Master equation formalism

Sami El Boustani* and Alain Destexhe

Author Affiliations

UNIC, UPR-2191, CNRS, Gif-sur-Yvette 91198, France

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BMC Neuroscience 2007, 8(Suppl 2):P62  doi:10.1186/1471-2202-8-S2-P62

The electronic version of this article is the complete one and can be found online at:


Published:6 July 2007

© 2007 Boustani and Destexhe; licensee BioMed Central Ltd.

Poster presentation

Cortical activity in awake animals manifests highly complex behaviour [1]. It is during this regime that the main computational tasks are performed and no model is yet able to explain how this complex dynamics is exploited to provide a fast and accurate information processing. However, many efforts have been devoted to the study of how such activity emerges.

Balanced networks have been introduced as a possible model to generate dynamical states similar to the biological ones [2]. The stability of such states was studied for current-based Integrate-And-Fire (IAF) neurons with respect to external input and excitatory-inhibitory synaptic strength ratio [3]. In particular, stable asynchronous irregular (AI) states with a relatively low level of activity have been obtained. Recently, AI states have been observed in balanced networks of conductance-based IAF neurons with self-sustained activity [4].

However, no simple description of the network activity dynamics has been developed yet. First-order mean-field approximation fails to describe these networks because of their inherent dynamics which rely dramatically on activity fluctuations. Moreover, the thermodynamic limit is usually performed for randomly connected networks despite the lack of biological relevance.

We introduce here a new framework in which network dynamics as well as inherent neuron behaviour is taken into account. We aim to obtain a reduced description of mesoscopic balanced networks where finite size effects are not neglected. The model is intended to describe AI states far from critical boundaries where long-term behaviours appear. Furthermore, we set the spatial and temporal scales of the model by using biological data. Using the master equation formalism, we derive a second-order mean-field set of ordinary differential equations.

The transition matrix necessary in the master equation context is computed based on the Fokker-Plank approach. Conductance-based as well as current-based IAF neurons are constructed. The kernel of this formalism lays in the way activity micro-fluctuations are modelled. We discuss different possibilities and considerations in regard to this question.

This model provides at the same time an extracellular and a sub-threshold description of finite size neuron networks. Once the couplings will be adjusted, it will be possible to build a large-scale model of cortical area with specific architectures, where the fundamental unit is the randomly connected network. We further discuss the possibility to compare large-scale behaviour observed in voltage-sensitive dyes experiments with our model.

References

  1. Destexhe A, Contreras D: Neuronal computations with stochastic network states.

    Science 2006, 314:85-90. PubMed Abstract | Publisher Full Text OpenURL

  2. van Vreeswijk C, Sompolinsky H: Chaos in neuronal networks with balanced excitatory and inhibitory activity.

    Science 1996, 274:1724-1726. PubMed Abstract | Publisher Full Text OpenURL

  3. Brunel N: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.

    J Comput Neurosci 2000, 8:183-208. PubMed Abstract | Publisher Full Text OpenURL

  4. Vogels TP, Abbott LF: Signal propagation and logic gating in networks of integrate-and-fire neurons.

    J Neurosci 2005, 25(46):10786-10795. PubMed Abstract | Publisher Full Text OpenURL