AUTHOR=Roxin Alex 

TITLE=The Role of Degree Distribution in Shaping the Dynamics in Networks of Sparsely Connected Spiking Neurons

JOURNAL=Frontiers in Computational Neuroscience

VOLUME=volume 5 - 2011

YEAR=2011

URL=https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2011.00008

DOI=10.3389/fncom.2011.00008

ISSN=1662-5188

ABSTRACT=Neuronal network models often assume a fixed probability of connection
between neurons.  This  assumption leads to random networks with
binomial in-degree and out-degree distributions which are relatively narrow.  
Here I study the effect of broad
degree distributions  on network dynamics by interpolating between a
binomial and a truncated powerlaw distribution for the in-degree  and
out-degree independently.  This is done both for an inhibitory network
(I network) as well as for the recurrent excitatory connections in a
network of excitatory and inhibitory neurons (EI network).  In both
cases increasing the width of the in-degree distribution affects the
global state of  the network by driving transitions between
asynchronous behavior and oscillations.   This effect is reproduced in
a simplified rate model which includes the heterogeneity in neuronal
input due to the in-degree of cells.  On the other hand, broadening
the out-degree  distribution is shown to increase the fraction of
common inputs to pairs of  neurons.  This leads to increases in the
amplitude of the cross-correlation (CC) of synaptic currents.  In the
case of the I network, despite strong oscillatory CCs in the currents, 
CCs of the membrane potential are low due to filtering and reset effects, 
leading to very weak CCs of the spikecount.  In the asynchronous regime of
the EI network,  broadening the out-degree  increases the amplitude of
CCs in the recurrent excitatory currents, while CC of the total
current is essentially unaffected as are pairwise spiking
correlations.  This is due to  a dynamic balance between excitatory
and inhibitory synaptic currents.  In the oscillatory regime, changes
in the out-degree can have a large effect on spiking correlations and
even on the qualitative  dynamical state of the network.