Topologically invariant macroscopic statistics
in balanced networks of conductance-based
integrate-and-fire neurons.
Pierre Yger, Sami El Boustani, Alain Destexhe and Yves
Frégnac
Journal of Computational Neuroscience 31: 229-245, 2011.
Abstract
The relationship between the dynamics of neural networks and
their patterns of connectivity is far from clear, despite its
importance for understanding functional properties. Here, we have
studied sparsely-connected networks of conductance-based
integrate-and-fire (IF) neurons with balanced excitatory and
inhibitory connections and with finite axonal propagation speed.
We focused on the genesis of states with highly irregular spiking
activity and synchronous firing patterns at low rates, called slow
Synchronous Irregular (SI) states. In such balanced networks, we
examined the ``macroscopic'' properties of the spiking activity,
such as ensemble correlations and mean firing rates, for different
intracortical connectivity profiles ranging from randomly
connected networks to networks with Gaussian-distributed local
connectivity. We systematically computed the distance-dependent
correlations at the extracellular (spiking) and intracellular
(membrane potential) levels between randomly assigned pairs of
neurons. The main finding is that such properties, when they are
averaged at a macroscopic scale, are invariant with respect to the
different connectivity patterns, provided the excitatory-inhibitory
balance is the same. In particular, the same correlation structure
holds for different connectivity profiles. In addition, we examined
the response of such networks to external input, and found that the
correlation landscape can be modulated by the mean level of
synchrony imposed by the external drive. This modulation was
found again to be independent of the external connectivity profile.
We conclude that first and second-order ``mean-field'' statistics of
such networks do not depend on the details of the connectivity at a
microscopic scale. This study is an encouraging step toward a
mean-field description of topological neuronal networks.
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