Building Blocks of Self-Sustained Activity in a Simple Deterministic Model of Excitable Neural Networks

García, Guadalupe C.; Lesne, Annick; Hütt, Marc‐Thorsten; Hilgetag, Claus C.

doi:10.3389/fncom.2012.00050

Cited by 38 publications

(85 citation statements)

References 69 publications

(106 reference statements)

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“…Similarly to the study at hand, in our earlier work we have found that the amount of network bursts increases with the locality of the network (where also CC is correlated with the locality) [57] in a network of spontaneously active neurons. Our results are backed by [67], where the number of 3-node triangles (comparable to motif 13, see Fig. 1) in the graphs were positively correlated with the mean level of activity in a discrete-state model of neuronal networks.…”

Section: Discussionsupporting

confidence: 70%

“…In such networks, not only the local connectivity but also the connectivity pattern between the clusters would greatly affect the collective dynamics. This aspect is highly relevant when unraveling the function of a vertebrate brain, and ground-laying studies have already been carried out in the context of, e.g., emergence of sustained activity [67], [70]. Promising attempts were also done in [68], where a biologically inspired modular network model of the mammalian pre-Bötzinger complex was studied by computational means.…”

Section: Discussionmentioning

confidence: 99%

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Structure-Dynamics Relationships in Bursting Neuronal Networks Revealed Using a Prediction Framework

et al. 2013

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The question of how the structure of a neuronal network affects its functionality has gained a lot of attention in neuroscience. However, the vast majority of the studies on structure-dynamics relationships consider few types of network structures and assess limited numbers of structural measures. In this in silico study, we employ a wide diversity of network topologies and search among many possibilities the aspects of structure that have the greatest effect on the network excitability. The network activity is simulated using two point-neuron models, where the neurons are activated by noisy fluctuation of the membrane potential and their connections are described by chemical synapse models, and statistics on the number and quality of the emergent network bursts are collected for each network type. We apply a prediction framework to the obtained data in order to find out the most relevant aspects of network structure. In this framework, predictors that use different sets of graph-theoretic measures are trained to estimate the activity properties, such as burst count or burst length, of the networks. The performances of these predictors are compared with each other. We show that the best performance in prediction of activity properties for networks with sharp in-degree distribution is obtained when the prediction is based on clustering coefficient. By contrast, for networks with broad in-degree distribution, the maximum eigenvalue of the connectivity graph gives the most accurate prediction. The results shown for small () networks hold with few exceptions when different neuron models, different choices of neuron population and different average degrees are applied. We confirm our conclusions using larger () networks as well. Our findings reveal the relevance of different aspects of network structure from the viewpoint of network excitability, and our integrative method could serve as a general framework for structure-dynamics studies in biosciences.

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Section: Discussionsupporting

confidence: 70%

Section: Discussionmentioning

confidence: 99%

Structure-Dynamics Relationships in Bursting Neuronal Networks Revealed Using a Prediction Framework

et al. 2013

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“…There is a large body of work on collective activity patterns in neuronal systems [30][31][32][33][34][35]. This activity relates to proactive functions of the brain, e.g., attention and memory [36,37].…”

Section: Introductionmentioning

confidence: 99%

Memory-induced mechanism for self-sustaining activity in networks

Allahverdyan

Steeg²,

Galstyan³

2015

Phys. Rev. E

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We study a mechanism of activity sustaining on networks inspired by a well-known model of neuronal dynamics. Our primary focus is the emergence of self-sustaining collective activity patterns, where no single node can stay active by itself, but the activity provided initially is sustained within the collective of interacting agents. In contrast to existing models of self-sustaining activity that are caused by (long) loops present in the network, here we focus on tree-like structures and examine activation mechanisms that are due to temporal memory of the nodes. This approach is motivated by applications in social media, where long network loops are rare or absent. Our results suggest that under a weak behavioral noise, the nodes robustly split into several clusters, with partial synchronization of nodes within each cluster. We also study the randomly-weighted version of the models where the nodes are allowed to change their connection strength (this can model attention redistribution), and show that it does facilitate the self-sustained activity.

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“…A relative-threshold variant 148 (requiring a certain percentage of a node's neighbors to be active, in order to activate the node) was explored 149 in [46] and [47]. The deterministic limit of the model (p → 1, f → 0) has been analyzed in [48] and in much 150 detail in [6]. 151 In the biological implementation, the topological reinforcement rule was reformulated by using functional 152 connectivity as a surrogate of TO.…”

mentioning

confidence: 99%

Topological Reinforcement as a Principle of Modularity Emergence in Brain Networks

Damicelli

Hilgetag

Hütt

et al. 2018

Preprint

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1Modularity is a ubiquitous topological feature of structural brain networks at various scales. While a variety of 2 potential mechanisms have been proposed, the fundamental principles by which modularity emerges in neural 3 networks remain elusive. We tackle this question with a plasticity model of neural networks derived from a 4 purely topological perspective. Our topological reinforcement model acts enhancing the topological overlap 5 between nodes, iteratively connecting a randomly selected node to a non-neighbor with the highest topological 6 overlap, while pruning another network link at random. This rule reliably evolves synthetic random networks 7 toward a modular architecture. Such final modular structure reflects initial 'proto-modules', thus allowing 8 to predict the modules of the evolved graph. Subsequently, we show that this topological selection principle 9 might be biologically implemented as a Hebbian rule. Concretely, we explore a simple model of excitable 10 dynamics, where the plasticity rule acts based on the functional connectivity between nodes represented by 11 co-activations. Results produced by the activity-based model are consistent with the ones from the purely 12 topological rule, showing a consistent final network configuration. Our findings suggest that the selective 13 reinforcement of topological overlap may be a fundamental mechanism by which brain networks evolve toward 14 modular structure. 15

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Building Blocks of Self-Sustained Activity in a Simple Deterministic Model of Excitable Neural Networks

Cited by 38 publications

References 69 publications

Structure-Dynamics Relationships in Bursting Neuronal Networks Revealed Using a Prediction Framework

Structure-Dynamics Relationships in Bursting Neuronal Networks Revealed Using a Prediction Framework

Memory-induced mechanism for self-sustaining activity in networks

Topological Reinforcement as a Principle of Modularity Emergence in Brain Networks

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