The relevance of network micro-structure for neural dynamics

The activity of cortical neurons is determined by the input they receive from presynaptic neurons. Many previous studies have investigated how specific aspects of the statistics of the input affect the spike trains of single neurons and neurons in recurrent networks. However, typically very simple random network models are considered in such studies. Here we use a recently developed algorithm to construct networks based on a quasi-fractal probability measure which are much more variable than commonly used network models, and which therefore promise to sample the space of recurrent networks in a more exhaustive fashion than previously possible. We use the generated graphs as the underlying network topology in simulations of networks of integrate-and-fire neurons in an asynchronous and irregular state. Based on an extensive dataset of networks and neuronal simulations we assess statistical relations between features of the network structure and the spiking activity. Our results highlight the strong influence that some details of the network structure have on the activity dynamics of both single neurons and populations, even if some global network parameters are kept fixed. We observe specific and consistent relations between activity characteristics like spike-train irregularity or correlations and network properties, for example the distributions of the numbers of in- and outgoing connections or clustering. Exploiting these relations, we demonstrate that it is possible to estimate structural characteristics of the network from activity data. We also assess higher order correlations of spiking activity in the various networks considered here, and find that their occurrence strongly depends on the network structure. These results provide directions for further theoretical studies on recurrent networks, as well as new ways to interpret spike train recordings from neural circuits.