Transitions between asynchronous and synchronous states
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Transitions between asynchronous and synchronous states : a theory of correlations in small neural circuits. / Fasoli, Diego; Cattani, Anna; Panzeri, Stefano.
in: J COMPUT NEUROSCI, Jahrgang 44, Nr. 1, 02.2018, S. 25-43.Publikationen: SCORING: Beitrag in Fachzeitschrift/Zeitung › SCORING: Zeitschriftenaufsatz › Forschung › Begutachtung
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TY - JOUR
T1 - Transitions between asynchronous and synchronous states
T2 - a theory of correlations in small neural circuits
AU - Fasoli, Diego
AU - Cattani, Anna
AU - Panzeri, Stefano
PY - 2018/2
Y1 - 2018/2
N2 - The study of correlations in neural circuits of different size, from the small size of cortical microcolumns to the large-scale organization of distributed networks studied with functional imaging, is a topic of central importance to systems neuroscience. However, a theory that explains how the parameters of mesoscopic networks composed of a few tens of neurons affect the underlying correlation structure is still missing. Here we consider a theory that can be applied to networks of arbitrary size with multiple populations of homogeneous fully-connected neurons, and we focus its analysis to a case of two populations of small size. We combine the analysis of local bifurcations of the dynamics of these networks with the analytical calculation of their cross-correlations. We study the correlation structure in different regimes, showing that a variation of the external stimuli causes the network to switch from asynchronous states, characterized by weak correlation and low variability, to synchronous states characterized by strong correlations and wide temporal fluctuations. We show that asynchronous states are generated by strong stimuli, while synchronous states occur through critical slowing down when the stimulus moves the network close to a local bifurcation. In particular, strongly positive correlations occur at the saddle-node and Andronov-Hopf bifurcations of the network, while strongly negative correlations occur when the network undergoes a spontaneous symmetry-breaking at the branching-point bifurcations. These results show how the correlation structure of firing-rate network models is strongly modulated by the external stimuli, even keeping the anatomical connections fixed. These results also suggest an effective mechanism through which biological networks may dynamically modulate the encoding and integration of sensory information.
AB - The study of correlations in neural circuits of different size, from the small size of cortical microcolumns to the large-scale organization of distributed networks studied with functional imaging, is a topic of central importance to systems neuroscience. However, a theory that explains how the parameters of mesoscopic networks composed of a few tens of neurons affect the underlying correlation structure is still missing. Here we consider a theory that can be applied to networks of arbitrary size with multiple populations of homogeneous fully-connected neurons, and we focus its analysis to a case of two populations of small size. We combine the analysis of local bifurcations of the dynamics of these networks with the analytical calculation of their cross-correlations. We study the correlation structure in different regimes, showing that a variation of the external stimuli causes the network to switch from asynchronous states, characterized by weak correlation and low variability, to synchronous states characterized by strong correlations and wide temporal fluctuations. We show that asynchronous states are generated by strong stimuli, while synchronous states occur through critical slowing down when the stimulus moves the network close to a local bifurcation. In particular, strongly positive correlations occur at the saddle-node and Andronov-Hopf bifurcations of the network, while strongly negative correlations occur when the network undergoes a spontaneous symmetry-breaking at the branching-point bifurcations. These results show how the correlation structure of firing-rate network models is strongly modulated by the external stimuli, even keeping the anatomical connections fixed. These results also suggest an effective mechanism through which biological networks may dynamically modulate the encoding and integration of sensory information.
KW - Action Potentials/physiology
KW - Correlation of Data
KW - Humans
KW - Models, Neurological
KW - Nerve Net/physiology
KW - Neural Networks, Computer
KW - Neurons/physiology
KW - Stochastic Processes
KW - Synapses/physiology
KW - Time Factors
U2 - 10.1007/s10827-017-0667-3
DO - 10.1007/s10827-017-0667-3
M3 - SCORING: Journal article
C2 - 29124505
VL - 44
SP - 25
EP - 43
JO - J COMPUT NEUROSCI
JF - J COMPUT NEUROSCI
SN - 0929-5313
IS - 1
ER -