Topologically invariant macroscopic statistics in balanced networks of conductance-based integrate-and-fire neurons

Yger, Pierre; Boustani, Sami El; Destexhe, Alain; Frégnac, Yves

doi:10.1007/s10827-010-0310-z

Cited by 51 publications

(91 citation statements)

References 52 publications

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“…This insensitivity to fine-tuning is due to the homogeneity of the connectivity of individual neurons in this type of networks. The effect has also been observed in a very recent study, where large-scale simulations were performed [42]. In networks with more complex structural elements, like hubs or patches, however, we find that also average correlations depend on details of the connectivity pattern.…”

Section: Introductionsupporting

confidence: 85%

How Structure Determines Correlations in Neuronal Networks

et al. 2011

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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.

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Section: Introductionsupporting

confidence: 85%

How Structure Determines Correlations in Neuronal Networks

et al. 2011

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“…Indeed, most studies simply ignore w or, at best, they assume that w and b are the same. More recent studies looked into the effect of shared inputs on the network dynamics (which contribute to b ) and found that the membrane potential fluctuations induced by shared inputs are very efficiently canceled by the recurrent network feedback (Renart et al, 2010;Yger et al, 2011;Tetzlaff et al, 2012). However, when we separate the input correlations into within-and between-correlations, it becomes apparent that the single neuron membrane fluctuations are mostly determined by the within-correlations.…”

Section: Discussionmentioning

confidence: 99%

Role of Input Correlations in Shaping the Variability and Noise Correlations of Evoked Activity in the Neocortex

2015

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Recent analysis of evoked activity recorded across different brain regions and tasks revealed a marked decrease in noise correlations and trial-by-trial variability. Given the importance of correlations and variability for information processing within the rate coding paradigm, several mechanisms have been proposed to explain the reduction in these quantities despite an increase in firing rates. These models suggest that anatomical clusters and/or tightly balanced excitation-inhibition can generate intrinsic network dynamics that may exhibit a reduction in noise correlations and trial-by-trial variability when perturbed by an external input. Such mechanisms based on the recurrent feedback crucially ignore the contribution of feedforward input to the statistics of the evoked activity. Therefore, we investigated how statistical properties of the feedforward input shape the statistics of the evoked activity. Specifically, we focused on the effect of input correlation structure on the noise correlations and trial-by-trial variability. We show that the ability of neurons to transfer the input firing rate, correlation, and variability to the output depends on the correlations within the presynaptic pool of a neuron, and that an input with even weak within-correlations can be sufficient to reduce noise correlations and trial-by-trial variability, without requiring any specific recurrent connectivity structure. In general, depending on the ongoing activity state, feedforward input could either increase or decrease noise correlation and trial-by-trial variability. Thus, we propose that evoked activity statistics are jointly determined by the feedforward and feedback inputs.

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“…The network is topographically arranged in one dimension, with length L, and wrapped onto the circle, to avoid boundary effects. As in previous work4565, the network has local connections defined by a Gaussian spatial profile:…”

Section: Methodsmentioning

confidence: 99%

The stimulus-evoked population response in visual cortex of awake monkey is a propagating wave

et al. 2014

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Propagating waves occur in many excitable media and were recently found in neural systems from retina to neocortex. While propagating waves are clearly present under anaesthesia, whether they also appear during awake and conscious states remains unclear. One possibility is that these waves are systematically missed in trial-averaged data, due to variability. Here we present a method for detecting propagating waves in noisy multichannel recordings. Applying this method to single-trial voltage-sensitive dye imaging data, we show that the stimulus-evoked population response in primary visual cortex of the awake monkey propagates as a travelling wave, with consistent dynamics across trials. A network model suggests that this reliability is the hallmark of the horizontal fibre network of superficial cortical layers. Propagating waves with similar properties occur independently in secondary visual cortex, but maintain precise phase relations with the waves in primary visual cortex. These results show that, in response to a visual stimulus, propagating waves are systematically evoked in several visual areas, generating a consistent spatiotemporal frame for further neuronal interactions.

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Topologically invariant macroscopic statistics in balanced networks of conductance-based integrate-and-fire neurons

Cited by 51 publications

References 52 publications

How Structure Determines Correlations in Neuronal Networks

How Structure Determines Correlations in Neuronal Networks

Role of Input Correlations in Shaping the Variability and Noise Correlations of Evoked Activity in the Neocortex

The stimulus-evoked population response in visual cortex of awake monkey is a propagating wave

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