From the statistics of connectivity to the statistics of spike times in neuronal networks

Ocker, Gabriel Koch; Hu, Yu; Buice, Michael A.; Doiron, Brent; Josić, Krešimir; Rosenbaum, Robert; Shea‐Brown, Eric

doi:10.1016/j.conb.2017.07.011

Cited by 62 publications

(63 citation statements)

References 99 publications

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“…To understand the emergence of such non-random connectivity, a growing body of theoretical and computa-24 tional work has been developed to link connectivity architecture to the coordinated spiking activity of neurons, 25 especially in recurrent networks [28][29][30][31][32][33][34][35][36][37][38][39][40][41]. These studies can be divided into two classes: those that examine the 26 influence of externally structured input on activity-dependent refinement [42][43][44][45], and those that investigate the 27 autonomous emergence of non-random connectivity in the absence of patterned external input, purely driven by 28 emergent network interactions [5,6,46].…”

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Autonomous emergence of connectivity assemblies via spike triplet interactions

Montangie

Gjorgjieva

2019

Preprint

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AbstractNon-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP) which depends on the interactions of three precisely-timed spikes and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We describe synaptic changes arising from emergent higher-order correlations, and investigate their influence on different connectivity motifs in the network. Our motif expansion framework reveals novel motif structures under the triplet STDP rule, which support the formation of bidirectional connections and loops in contrast to the classical pair-based STDP rule. Therefore, triplet STDP drives the spontaneous emergence of self-connected groups of neurons, or assemblies, proposed to represent functional units in neural circuits. Assembly formation has often been associated with plasticity driven by firing rates or external stimuli. We propose that assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule commonly assumed in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of triplet STDP or the synaptic transmission function differentially promote connectivity motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures.

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confidence: 99%

“…We write the pairwise covariance as a sum of the internal correlation and a novel term that conveys the 370 external structured activity as common input [40]:…”

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confidence: 99%

Autonomous emergence of connectivity assemblies via spike triplet interactions

Montangie

Gjorgjieva

2019

Preprint

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“…390 The necessity of higher-order patterns for stable activity has strong implications for 391 neural coding. Previous work has already demonstrated that correlations enhance 392 coding, with triplet correlations having an advantage over pairwise 393 [5,16,18,[21][22][23][52][53][54]. The neural code must rest upon a foundation of stable 394 propagation of spikes, which we have shown in turn rests on higher-order motifs and 395 coordinated integration.…”

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confidence: 77%

Cyclic transitions between higher order motifs underlie sustained activity in asynchronous sparse recurrent networks

Bojanek

Zhu

MacLean

2019

Preprint

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Many studies have demonstrated the prominence of higher-order patterns in excitatory synaptic connectivity as well as activity in neocortex. Surveyed as a whole, these results suggest that there may be an essential role for higher-order patterns in neocortical function. In order to stably propagate signal within and between regions of neocortex, the most basic -yet nontrivial -function which neocortical circuitry must satisfy is the ability to maintain stable spiking activity over time. Here we algorithmically construct spiking neural network models comprised of 5000 neurons using topological statistics from neocortex and a set of objective functions that identify networks which produce naturalistic low-rate, asynchronous, and critical activity. We find that the same network topology can exhibit either sustained activity under one set of initial membrane voltages or truncated activity under a different set. Yet these two outcomes are not readily differentiated by rate or criticality. By summarizing the statistical dependencies in the pairwise activity of neurons as directed weighted functional networks, we examined the transient manifestations of higher-order motifs in the functional networks across time. We find that stereotyped low variance cyclic transitions between three isomorphic triangle motifs, quantified as a Markov process, are required for sustained activity. If the network fails to engage the dynamical regime characterized by a recurring stable pattern of motif dominance, spiking activity ceased. Motif cycling generalized across manipulations of synaptic weights and across topologies, demonstrating the robustness of this dynamical regime for sustained spiking in critical asynchronous network activity. Our results point to the necessity of higher-order patterns amongst excitatory connections for sustaining activity in sparse recurrent networks. They also provide a possible explanation as to why such excitatory synaptic connectivity and activity patterns have been prominently reported in neocortex. Author summaryHere we address two questions. First, it remains unclear how activity propagates stably through a network since neurons are leaky and connectivity is sparse and weak. Second, higher order patterns abound in neocortex, hinting at potential functional relevance for their presence. Several lines of evidence suggest that higher-order network interactions September 16, 2019 1/23 may be instrumental for spike propagation. For example, excitatory synaptic connectivity shows a prevalence of local neuronal cliques and patterns, and propagating activity in vivo displays elevated clustering dominated by specific triplet motifs. In this study we demonstrate a mechanistic link between activity propagation and higher-order motifs at the level of individual neurons and across networks. We algorithmically build spiking neural network (SNN) models to mirror the topological and dynamical statistics of neocortex. Using a combination of graph theory, information theory, and probabilistic tools, we show that higher ...

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“…Several related studies have focused on a theoretical link between network structure and correlated spiking activity recorded from a large number of neurons, without attempting to explicitly estimate synaptic connections (see [88][89][90][91][92][93][94] and [95] for review). Of major relevance in this regard is the extent to which effective interactions among observed neurons are reshaped by coupling to unobserved neurons [83,96].…”

Section: Estimation Of Synaptic Couplingmentioning

confidence: 99%

Inferring and validating mechanistic models of neural microcircuits based on spike-train data

Ladenbauer

McKenzie

English

et al. 2018

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The interpretation of neuronal spike-train recordings often relies on abstract statistical models that allow for principled parameter estimation and model-selection but provide only limited insights into underlying microcircuits. On the other hand, mechanistic neuronal models are useful to interpret microcircuit dynamics, but are rarely quantitatively matched to experimental data due to methodological challenges. We present analytical methods to efficiently fit spiking circuit models to single-trial spike trains. Using the maximallikelihood approach, we statistically infer the mean and variance of hidden inputs, neuronal adaptation properties and connectivity for coupled integrate-and-fire neurons. Parameter estimation is found to be very accurate, even for highly sub-sampled networks. We apply our methods to recordings from cortical neurons of awake ferrets to reveal properties of the hidden synaptic inputs, in particular underlying population-level equalization between excitatory and inhibitory inputs. The methods introduced here open the door to a quantitative, mechanistic interpretation of recorded neuronal population activity.

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From the statistics of connectivity to the statistics of spike times in neuronal networks

Cited by 62 publications

References 99 publications

Autonomous emergence of connectivity assemblies via spike triplet interactions

Autonomous emergence of connectivity assemblies via spike triplet interactions

Cyclic transitions between higher order motifs underlie sustained activity in asynchronous sparse recurrent networks

Inferring and validating mechanistic models of neural microcircuits based on spike-train data

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