How Structure Determines Correlations in Neuronal Networks

Abstract

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.

Multiple Tests Based on a Gaussian Approximation of the Unitary Events Method with Delayed Coincidence Count

“…However, we think that pure testing procedures do not give fully satisfying answers and that it would be legitimate to provide an estimation of the dependence notably, through the Hawkes model (Krumin et al, 2010). It is already known that this model can easily deal with more than two neurons (Daley & Vere-Jones, 2003;Pernice et al, 2011Pernice et al, , 2012Chornoboy et al, 1988). However, it is only in a recent work that we have proposed theoretical statistical methods to deal with several neurons and large delays of interaction through Lasso methods (Hansen et al, 2012).…”

“…They constitute a particular case of more general counting processes, called the Hawkes processes, which can be simulated by thinning algorithms (Daley & Vere-Jones, 2003;Ogata, 1981;Reimer et al, 2012). After a brief apparition in (Chornoboy et al, 1988), they have recently been used again to model spike trains in (Krumin et al, 2010;Pernice et al, 2011Pernice et al, , 2012. A bivariate Hawkes process (N 1 , N 2 ) is described by its respective conditional intensities with respect to the past, (λ 1 (.…”

Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations

“…Previous studies show that intrinsic neuronal dynamics (de la Rocha et al 2007;Litwin-Kumar et al 2011;Barreiro et al 2010;Hong et al 2012), reciprocal feedback inhibition (Ly et al 2012;Middleton et al 2012;Litwin-Kumar et al 2012;Tetzlaff et al 2012) and recurrent network dynamics (Hertz 2010;Renart et al 2010;Pernice et al 2011;Pernice et al 2012;Trousdale et al 2012) also act as decorrelating mechanisms. It is not immediately clear, however, how short-term synaptic depression and stochastic vesicle dynamics interact with recurrent network dynamics to determine correlations.…”

“…Due to the difficulty of obtaining accurate estimates of spiking correlations in vivo (Ecker et al 2010;Cohen and Kohn 2011) and the obscurity of the sources of correlations measured in complicated networks, computational modeling plays an important role in understanding how correlations arise in networks and how they are affected by various neural mechanisms. Computational studies have been successful at identifying a number of mechanisms that impact the amplitude and structure of correlations in neuronal networks (Binder and Powers 2001;Parga 2006, 2009;de la Rocha et al 2007;Renart et al 2010;Rosenbaum et al 2010;Tchumatchenko et al 2010;Litwin-Kumar et al 2011;Macke et al 2011;Pernice et al 2011;Ly et al 2012;Tetzlaff et al 2012;Trousdale et al 2012), but the impact of short-term synaptic depression on neuronal correlations has not been systematically addressed in the literature.…”

Concentration inequalities, counting processes and adaptive statistics

“…The multivariate version can model dependency between action potentials of different neurons in neuroscience [13,39]. It can also be used on genomic data, where this framework was introduced in [21] to model occurrences of events such as positions of genes, promoter sites or words on the DNA sequence.…”