Most studies on the dynamics of recurrent cortical networks are either based on purely random wiring or local couplings [1,2]. Neuronal wiring in the cortex, however, shows a complex spatial pattern composed of local and long-range patchy connections, i.e., spatially clustered synapses [3,4]. We analyze to what extent such geometric traits influence the dynamics of cortical network models. Assuming an enlarged spatial scale we assume the following network architectures: random (RD) and local (LO) wiring, local combined with random remote (RM) or patchy (PB) projections (Figure 1). Then, by computing several characteristic measures describing spiking neuronal networks (e.g., firing rate, correlation coefficient, regularity measure), we explore and compare the dynamical phase spaces and the activity patterns of different network models.
Figure 1. Considered networks. Red symbols indicate post-synaptic projection targets of an excitatory cell, cyan symbols those of an inhibitory cell.
Network dynamics are simulated using NEST/PyNN . They are based on 50.000 neurons, randomly distributed in 5 squared millimeters with a global connectivity c ~0.0125. We consider conductance-based integrate-and-fire neurons with regular spiking excitatory and fast spiking inhibitory cells. Varying the poissonian input rates and the numeric relation between excitatory and inhibitory synaptic strength, we explore the phase spaces of different networks. In addition, we apply spatially restricted activity injections, i.e., a group of neighboring neurons receives additional input.
Results and discussion
Similar to previous studies we observe synchronous regular firing for high input rates combined with low inhibition, while small rates and high inhibition results in asynchronous irregular firing. The amount of local connections influences the boundaries at which the network switches between states, and the interesting input parameter range changes accordingly. Non-random networks provide significantly higher firing rates, as well as sharper transitions. These networks exhibit "new" activity patterns that indicate the spatio-temporal spread of activity that random networks cannot account for.
This work is based on the PhD project  and supported by EU Grant 15879 (FACETS).