Back to the abstracts page
Back to the NCCD 2015 home page
Dynamics of Balanced Networks with Excess Bidirectional Connectivity
Carl van Vreeswijk, Shrisha Rao and David Hansel
Center of Neurophysics, Physiology and Pathology
Cerebral Dynamics, Learning and Memory Laboratory
CNRS-UMR8119 and Paris Descartes University, Paris, France.

There is increasing evidence for fine-structure in cortical connectivity. Bidirectional connectivity and motifs of 3 or more highly interconnected neurons are more prevalent than expected for an Erdös-Rényi random connectivity [1,2]. What is the effect of these excess motifs on cortical dynamics? To address this question we study the dynamics of networks of neurons randomly connected with a rule such that the probability of bidirectional connections is higher than in the pure chance case. The network consists of NE excitatory ( E ) and NI inhibitory ( I ) neurons connected with probability

Pr ( C ij AB = 1 ) = K / N B , Pr ( C ij AB C ji BA = 1 ) = p AB K / N A N B .

Here C AB are the connection matrices, C ij AB = 1 if there is a connection from neuron j in population B to neuron i in population A and C ij AB = 0 otherwise. We focus on the dynamics of such networks operating in the balanced regime [3].

We investigate networks of binary neurons [4] analytically in the limit where we first take N A and then K , for finite pAB . We show that both excess bidirectional connections between the E cells and excess bidirectional connections between the I cells slow down the fluctuations in the neuronal input. As a result, the autocorrelation of the activity decays more slowly than in the corresponding Erdös-Rényi network. In contrast, bidirectional connections between E and I cells decrease the decorrelation time. Remarkably, bidirectional connections between I cells are more efficacious in slowing down the dynamics than those between E cells. These phenomena are due to the small loops that the bidirectionallity induces in the network architecture. Together with the relatively strong synapses in balanced networks these lead to a non-negligible effective delayed self-coupling.

We also investigate the effect of bidirectional connectivity in a balanced network of conductance-based spiking neurons using numerical simulations. Apart from the connectivity, the network is similar to that in [5]. We show that this network behaves qualitatively similarly to the binary network. Furthermore, bidirectional connections between E cells or between I cells increase the Fano factor of the spike count, while the Fano factor decreases for bidirectional connections between E and I cells. We also investigate the dependence of this effect on the synaptic time constants and study how the spike irregularity is modified by 'sensory' stimulation of the network.

[1] S. Song, P.J. Sjostrom, M. Reigl, S. Nelson, and D.B. Chklovskii . PLoS Biol. 3:e68 (2005).
[2] R. Perin, T.K. Berger and H. Markram, PNAS 108:5419-5424 (2011).
[3] C. van Vreeswijk and H. Sompolinsky, Science 274:1724-1726 (1996).
[4] C. van Vreeswijk and H. Sompolinsky, Neural Comput. 10:1321 - 1371 (1998).
[5] D. Hansel and C. van Vreeswijk, J. Neurosci. 32:4049-4064 (2012).