Asynchronous Rate Chaos in Spiking Neuronal Circuits

1. PLoS Comput Biol. 2015 Jul 31;11(7):e1004266. doi:
10.1371/journal.pcbi.1004266. eCollection 2015 Jul.

Asynchronous Rate Chaos in Spiking Neuronal Circuits.

Harish O(1), Hansel D(2).

Author information:
(1)Center for Neurophysics, Physiology and Pathologies, CNRS UMR8119 and
Institute of Neuroscience and Cognition, Université Paris Descartes, Paris,
France.
(2)Center for Neurophysics, Physiology and Pathologies, CNRS UMR8119 and
Institute of Neuroscience and Cognition, Université Paris Descartes, Paris,
France; The Alexander Silberman Institute of Life Sciences, The Hebrew
University of Jerusalem, Jerusalem, Israel.

The brain exhibits temporally complex patterns of activity with features similar
to those of chaotic systems. Theoretical studies over the last twenty years have
described various computational advantages for such regimes in neuronal systems.
Nevertheless, it still remains unclear whether chaos requires specific cellular
properties or network architectures, or whether it is a generic property of
neuronal circuits. We investigate the dynamics of networks of
excitatory-inhibitory (EI) spiking neurons with random sparse connectivity
operating in the regime of balance of excitation and inhibition. Combining
Dynamical Mean-Field Theory with numerical simulations, we show that chaotic,
asynchronous firing rate fluctuations emerge generically for sufficiently strong
synapses. Two different mechanisms can lead to these chaotic fluctuations. One
mechanism relies on slow I-I inhibition which gives rise to slow subthreshold
voltage and rate fluctuations. The decorrelation time of these fluctuations is
proportional to the time constant of the inhibition. The second mechanism relies
on the recurrent E-I-E feedback loop. It requires slow excitation but the
inhibition can be fast. In the corresponding dynamical regime all neurons
exhibit rate fluctuations on the time scale of the excitation. Another feature
of this regime is that the population-averaged firing rate is substantially
smaller in the excitatory population than in the inhibitory population. This is
not necessarily the case in the I-I mechanism. Finally, we discuss the
neurophysiological and computational significance of our results.

DOI: 10.1371/journal.pcbi.1004266
PMCID: PMC4521798
PMID: 26230679 [Indexed for MEDLINE]

Conflict of interest statement: The authors have declared that no competing
interests exist.

Auteurs Bordeaux Neurocampus