Attractor dynamics in local neuronal networks

A hallmark feature of cortical networks is the presence of synaptic motifs, defined as ensembles of neurons whose synaptic pattern follows a particular configuration [1]. Simulated networks of neurons whose excitatory synapses follow a three-node "relay" motif (Figure 1A)-the most frequent motif in primate visual cortex- exhibit synchronization with zero time lag [2], a form of activity reported in a spectrum of experiments [3]. Here, using simulations of leaky integrate-and-fire networks (LIF) as well as mean-field stability analyses, we show that this relay motif promotes the emergence of a limit cycle whose period is determined by intrinsic properties of the model (Figure 1B). While cortical recordings show evidence of limit-cycle oscillations [4], this behavior is typically transient in non-pathological states. The question thus arises, of how to generate transient yet precise synchronization under different forms of motif connectivity. To address this question, we introduce a mechanism of selective gain inhibition by which cortical circuits may disengage from a strict limit cycle behavior. This mechanism works by tuning the gain inhibition [5] of a selective population of neurons in the model. In a first series of simulations, we show that applying selective gain inhibition to one population of a network (Figure 1A, shown in black) disengages the network from a limit cycle behaviour (Figure 1C). Next, we examine the effect of selective gain inhibition on a network's response to an incoming stimulus and show that transient synchronization arises in response to a time-delimited input current (Figure 1D). Selective gain inhibition enables stimulus-induced synchronization under strong stimulation and suppresses zero-lag synchrony under weak stimulation (Figure 1E). Transient synchronization would not be possible without selective gain inhibition, given that a network configured with a "relay" motif follows a limit cycle attractor (Figure 1B). We conclude that a "relay' motif of connectivity imposes strict constraints on the types of dynamics produced by a network under both spontaneous and evoked states. Going further, results of simulations suggest that a mechanism of selective gain inhibition breaks the rigid constraints imposed by synaptic connectivity, providing flexible and transient responses to incoming stimuli.

Figure 1

Transient synchronization in LIF networks. A. Three groups of neurons with arrows showing the presence of between-group synapses (1,000 neurons/group; gain inhibition set to 1.5 nS). B. Spike raster of spontaneous activity for network in A. C. Raster with gain inhibition of neuron group in black set to 2.25 nS). D. Same as C, with all excitatory neurons injected with a constant current. E. Cross-correlations averaged over all neurons, with constant current (each simulation lasting 10 sec).