The relevance of network micro-structure for neural dynamics

Abstract

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.

A small-world-based population encoding model of the primary visual cortex

“…There are also many researchers dedicating to exploring the influence of network structure on the population dynamics of neurons. Pernice et al (2013) and Trousdale et al (2013) have respectively established numerical models and revealed Fig. 7 The performance comparison among models is based on networks with different levels of small-worldness.…”

“…A small-world network constitutes a compromise between random and nearest neighbor regimes, resulting in a short average path length despite the predominance of local connections (Kaiser 2008), which reflects the high efficiency of the network in transmitting and processing information (Achard and Bullmore 2007). Several simulated models have also been established to prove the important role of topological structure in representing the encoding dynamics of neural populations (Pernice et al 2013(Pernice et al , 2011Trousdale et al 2012). However, most of those models are based on a large quantity of neurons (even more than 10,000), which exceeds the recording capability of MEA.…”

Synaptic Plasticity Shapes Brain Connectivity: Implications for Network Topology

“…Addressing the relationship between synaptic plasticity and brain network organization is particularly difficult due to multiple reciprocal influences between brain network structure and function. Indeed, network architecture strongly influences neuronal activity [57][58][59][60][61][62][63][64], and patterns of neuronal activity may differently shape synaptic connections.…”

Three-dimensional mapping of microcircuit correlation structure

“…Theoretical work has shown that the precise structure of correlated neuronal variability, so called noise correlations, can significantly enhance or diminish the information capacity of neural ensembles (Zohary et al, 1994; Abbott and Dayan, 1999; Sompolinsky et al, 2001; Wilke and Eurich, 2002; Averbeck and Lee, 2004; Shamir and Sompolinsky, 2004; Ecker et al, 2011). However, these studies typically rely on extrapolating the population correlation structure from data recorded with pairs of neurons, but the assumptions behind this extrapolation can dramatically change the results (Shamir and Sompolinsky, 2006; Ecker et al, 2011; Pernice et al, 2013). Therefore, it is important to decode real populations to validate these theoretical studies and ultimately determine the impact of correlations on population coding (Graf et al, 2011; Berens et al, 2012).…”