Recurrent interactions in spiking networks with arbitrary topology

Pernice, Volker; Staude, Benjamin; Cardanobile, Stefano; Rotter, Stefan

doi:10.1103/physreve.85.031916

Cited by 72 publications

(78 citation statements)

References 29 publications

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“…The topology of connections within a neural circuit molds emergent network dynamics (Buzsaki et al, 2004; Larremore et al, 2011; Ringach, 2009), especially in the absence of external inputs (Galan, 2008). In general, knowledge of network connectivity enables predictions about the correlational structure of the neural responses (Pernice et al, 2012; Trousdale et al, 2012), even though the converse is not true (Kispersky et al, 2011; Sporns, 2012; Trong and Rieke, 2008). Networks that exhibit approximate balance between excitation and inhibition are particularly straightforward in this respect because response correlations are shaped primarily by the first order connections between neurons rather than by higher order, polysynaptic chains of intrinsic connections (Trousdale et al, 2012).…”

Section: Discussionmentioning

confidence: 99%

Natural Grouping of Neural Responses Reveals Spatially Segregated Clusters in Prearcuate Cortex

Kiani

Cueva

Reppas

et al. 2015

Neuron

102

108

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Summary A fundamental challenge in studying the frontal lobe is to parcellate this cortex into ‘natural’ functional modules despite the absence of topographic maps, which are so helpful in primary sensory areas. Here we show that unsupervised clustering algorithms, applied to 96-channel array recordings from prearcuate gyrus, reveal spatially segregated sub-networks that remain stable across behavioral contexts. Looking for natural groupings of neurons based on response similarities, we discovered that the recorded area includes at least two spatially segregated sub-networks that differentially represent behavioral choice and reaction time. Importantly, these sub-networks are detectable during different behavioral states, and surprisingly, are defined better by ‘common noise’ than task-evoked responses. Our parcellation process works well on ‘spontaneous’ neural activity, and thus bears strong resemblance to the identification of ‘resting state’ networks in fMRI datasets. Our results demonstrate a powerful new tool for identifying cortical sub-networks by objective classification of simultaneously recorded electrophysiological activity.

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Section: Discussionmentioning

confidence: 99%

Natural Grouping of Neural Responses Reveals Spatially Segregated Clusters in Prearcuate Cortex

Kiani

Cueva

Reppas

et al. 2015

Neuron

102

108

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“…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.…”

Section: Discussionmentioning

confidence: 99%

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

Rosenbaum

Rubin

Doiron

2013

Journal of Neurophysiology

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Rosenbaum R, Rubin JE, Doiron B. Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations. J Neurophysiol 109: 475-484, 2013. First published October 31, 2012 doi:10.1152/jn.00733.2012.-Correlated neuronal activity is an important feature in many neural codes, a neural correlate of a variety of cognitive states, as well as a signature of several disease states in the nervous system. The cellular and circuit mechanics of neural correlations is a vibrant area of research. Synapses throughout the cortex exhibit a form of short-term depression where increased presynaptic firing rates deplete neurotransmitter vesicles, which transiently reduces synaptic efficacy. The release and recovery of these vesicles are inherently stochastic, and this stochasticity introduces variability into the conductance elicited by depressing synapses. The impact of spiking and subthreshold membrane dynamics on the transfer of neuronal correlations has been studied intensively, but an investigation of the impact of short-term synaptic depression and stochastic vesicle dynamics on correlation transfer is lacking. We find that short-term synaptic depression and stochastic vesicle dynamics can substantially reduce correlations, shape the timescale over which these correlations occur, and alter the dependence of spiking correlations on firing rate. Our results show that short-term depression and stochastic vesicle dynamics need to be taken into account when modeling correlations in neuronal populations. Synaptic neurotransmitter vesicles are released probabilistically in response to a presynaptic spike, and released vesicles are recovered stochastically over a timescale of several hundred milliseconds (Vere-Jones 1966;Wang 1999;Fuhrmann et al. 2002;Goldman 2004;Rosenbaum et al. 2012). The depletion of neurotransmitter vesicles by trains of presynaptic action potentials gives rise to a form of short-term synaptic depression that is pervasive in the cortex (Zucker and Regehr 2002). We find that when two postsynaptic neurons receive correlated input through depressing synapses, the correlation between the synaptic conductances across the neurons' membranes, as well as the neurons' spike trains, are drastically smaller than the correlations predicted by a nondepressing, static synapse model. This reduction in correlation is especially prevalent at higher presynaptic firing rates that more effectively deplete neurotransmitter vesicles. Coupled with the fact that cellular dynamics suppress correlations at low firing rates (de la Rocha et al. 2007), these results show that a population of neurons with depressing synapses exhibit small correlations over a broad range of firing rates, even when their inputs are strongly correlated. Our conclusions reveal an important, yet often ignored, mechanism that promotes asynchronous spiking activity in densely connected neuronal populations. METHODSWe begin by describing the statistical measures used to quantify correlations in this study. We then describe the presyn...

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“…Correlations in feed-forward networks of LIF models are studied in Moreno-Bote and Parga (2006), exact analytical solutions for such network architectures are given in Rosenbaum and Josic (2011) for the case of stochastic random walk models, and threshold crossing neuron models are considered in Tchumatchenko et al (2010) and Burak et al (2009). Covariances in structured networks are investigated for Hawkes processes (Pernice et al, 2011), and in linear approximation for LIF (Pernice et al, 2012) and exponential integrate-and-fire neurons (Trousdale et al, 2012). The latter three works employ an expansion of the propagator (time evolution operator) in terms of the order of interaction.…”

Section: Introductionmentioning

confidence: 99%

A unified view on weakly correlated recurrent networks

Grytskyy

Tetzlaff

Diesmann

et al. 2013

Front. Comput. Neurosci.

131

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The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances in the spiking activity raises the question how these models relate to each other. In particular it is hard to distinguish between generic properties of covariances and peculiarities due to the abstracted model. Here we present a unified view on pairwise covariances in recurrent networks in the irregular regime. We consider the binary neuron model, the leaky integrate-and-fire (LIF) model, and the Hawkes process. We show that linear approximation maps each of these models to either of two classes of linear rate models (LRM), including the Ornstein–Uhlenbeck process (OUP) as a special case. The distinction between both classes is the location of additive noise in the rate dynamics, which is located on the output side for spiking models and on the input side for the binary model. Both classes allow closed form solutions for the covariance. For output noise it separates into an echo term and a term due to correlated input. The unified framework enables us to transfer results between models. For example, we generalize the binary model and the Hawkes process to the situation with synaptic conduction delays and simplify derivations for established results. Our approach is applicable to general network structures and suitable for the calculation of population averages. The derived averages are exact for fixed out-degree network architectures and approximate for fixed in-degree. We demonstrate how taking into account fluctuations in the linearization procedure increases the accuracy of the effective theory and we explain the class dependent differences between covariances in the time and the frequency domain. Finally we show that the oscillatory instability emerging in networks of LIF models with delayed inhibitory feedback is a model-invariant feature: the same structure of poles in the complex frequency plane determines the population power spectra.

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Recurrent interactions in spiking networks with arbitrary topology

Cited by 72 publications

References 29 publications

Natural Grouping of Neural Responses Reveals Spatially Segregated Clusters in Prearcuate Cortex

Natural Grouping of Neural Responses Reveals Spatially Segregated Clusters in Prearcuate Cortex

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

A unified view on weakly correlated recurrent networks

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