Dynamics of networks of excitatory and inhibitory neuronsin response to time-dependent inputs

• Main Authors: Erwan eLedoux, Nicolas eBrunel
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2011-05-01
• Series: Frontiers in Computational Neuroscience
• Subjects: feedback inhibition; Synaptic connectivity; Dynamics of neural networks; feed-forward inhibition; leaky integrate and fire neuron; Sinusoidal inputs
• Online Access: http://journal.frontiersin.org/Journal/10.3389/fncom.2011.00025/full

We investigate the dynamics of recurrent networks of excitatory (E) and inhibitory(I) neurons in the presence of time-dependent inputs. The dynamics is characterizedby the network dynamical transfer function, i.e. how the population firing rate ismodulated by sinusoidal inputs at arbitrary frequencies. Two types of networks arestudied and compared: (i) a Wilson-Cowan type firing rate model; and (ii) a fullyconnected network of leaky integrate-and-fire neurons, in a strong noise regime. Wefirst characterize the region of stability of the ‘asynchronous state’ (a state in whichpopulation activity is constant in time when external inputs are constant) in the spaceof parameters characterizing the connectivity of the network. We then systematicallycharacterize the qualitative behaviors of the dynamical transfer function, as a functionof the connectivity. We find that the transfer function can be either low-pass, or witha single or double resonance, depending on the connection strengths and synaptic timeconstants. Resonances appear when the system is close to Hopf bifurcations, that canbe induced by two separate mechanisms: the I-I connectivity and the E-I connectivity.Double resonances can appear when excitatory delays are larger than inhibitory delays,due to the fact that two distinct instabilities exist with a finite gap between thecorresponding frequencies. In networks of LIF neurons, changes in external inputs andexternal noise are shown to be able to change qualitatively the network transfer function.Firing rate models are shown to exhibit the same diversity of transfer functions asthe LIF network, provided delays are present. They can also exhibit input-dependentchanges of the transfer function, provided a suitable static nonlinearity is incorporated.