Chaos and synchrony in a model of a hypercolumn in visual cortex

D. Hansel, H. Sompolinsky
Journal of Computational Neuroscience. 1996-03-01; 3(1): 7-34
DOI: 10.1007/bf00158335

1. J Comput Neurosci. 1996 Mar;3(1):7-34. doi: 10.1007/BF00158335.

Chaos and synchrony in a model of a hypercolumn in visual cortex.

Hansel D(1), Sompolinsky H.

Author information:
(1)Centre de Physique Théorique, UPR014-CNRS, Ecole Polytechnique, Palaiseau,
France.

Neurons in cortical slices emit spikes or bursts of spikes regularly in response
to a suprathreshold current injection. This behavior is in marked contrast to
the behavior of cortical neurons in vivo, whose response to electrical or
sensory input displays a strong degree of irregularity. Correlation measurements
show a significant degree of synchrony in the temporal fluctuations of neuronal
activities in cortex. We explore the hypothesis that these phenomena are the
result of the synchronized chaos generated by the deterministic dynamics of
local cortical networks. A model of a « hypercolumn » in the visual cortex is
studied. It consists of two populations of neurons, one inhibitory and one
excitatory. The dynamics of the neurons is based on a Hodgkin-Huxley type model
of excitable voltage-clamped cells with several cellular and synaptic
conductances. A slow potassium current is included in the dynamics of the
excitatory population to reproduce the observed adaptation of the spike trains
emitted by these neurons. The pattern of connectivity has a spatial structure
which is correlated with the internal organization of hypercolumns in
orientation columns. Numerical simulations of the model show that in an
appropriate parameter range, the network settles in a synchronous chaotic state,
characterized by a strong temporal variability of the neural activity which is
correlated across the hypercolumn. Strong inhibitory feedback is essential for
the stabilization of this state. These results show that the cooperative
dynamics of large neuronal networks are capable of generating variability and
synchrony similar to those observed in cortex. Auto-correlation and
cross-correlation functions of neuronal spike trains are computed, and their
temporal and spatial features are analyzed. In other parameter regimes, the
network exhibits two additional states: synchronized oscillations and an
asynchronous state. We use our model to study cortical mechanisms for
orientation selectivity. It is shown that in a suitable parameter regime, when
the input is not oriented, the network has a continuum of states, each
representing an inhomogeneous population activity which is peaked at one of the
orientation columns. As a result, when a weakly oriented input stimulates the
network, it yields a sharp orientation tuning. The properties of the network in
this regime, including the appearance of virtual rotations and broad
stimulus-dependent cross-correlations, are investigated. The results agree with
the predictions of the mean field theory which was previously derived for a
simplified model of stochastic, two-state neurons. The relation between the
results of the model and experiments in visual cortex are discussed.