Topology regulates the distribution pattern of excitations in excitable dynamics on graphs

Müller-Linow, Mark; Marr, Carsten; Hütt, Marc‐Thorsten

doi:10.1103/physreve.74.016112

Cited by 34 publications

(43 citation statements)

References 37 publications

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“…In this range of f the distribution patterns of excitations are dominated by burst regimes (as discussed in [36]. The pattern formation for f >0.1 is strongly influenced by random firing events, while for f <10 −3 the modular boundaries are followed only partly by the dynamics, hinting at another form of correlation between dynamics and topology, which acts on a larger topological scale.…”

Section: Resultsmentioning

confidence: 89%

“…Other variants of three-state excitable dynamics have been used to describe epidemic spreading [31]–[34]. As discussed previously [35],[36], this general model can readily be implemented on arbitrary network architectures. It has been shown that short-cuts inserted into a regular (e.g., ring-like) architecture can mimic the dynamic effect of spontaneous excitations [35].…”

Section: Introductionmentioning

confidence: 99%

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Organization of Excitable Dynamics in Hierarchical Biological Networks

2008

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This study investigates the contributions of network topology features to the dynamic behavior of hierarchically organized excitable networks. Representatives of different types of hierarchical networks as well as two biological neural networks are explored with a three-state model of node activation for systematically varying levels of random background network stimulation. The results demonstrate that two principal topological aspects of hierarchical networks, node centrality and network modularity, correlate with the network activity patterns at different levels of spontaneous network activation. The approach also shows that the dynamic behavior of the cerebral cortical systems network in the cat is dominated by the network's modular organization, while the activation behavior of the cellular neuronal network of Caenorhabditis elegans is strongly influenced by hub nodes. These findings indicate the interaction of multiple topological features and dynamic states in the function of complex biological networks.

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Section: Resultsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Organization of Excitable Dynamics in Hierarchical Biological Networks

2008

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“…The three-state UAR description introduced above is reminiscent of Susceptible–Excited–Refractory (SER) models widely adopted to study network signal propagation (Dodds and Watts, 2004; Müller-Linow et al, 2006; Centola et al, 2007; Müller-Linow et al, 2008; Hütt et al, 2012) except that our definition of p U→A i takes into account the two-hop neighborhood of each astrocytes, i.e., the activation state of neighbors of the cells coupled to each astrocyte. If the status of activation of the two-hop neighborhood is indeed crucial in ICW propagation, then we expect that the essence of ICW dynamics in the astrocyte networks considered so far, will be reproduced if we substitute the ChI astrocyte model by the UAR description.…”

Section: Resultsmentioning

confidence: 99%

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks

Lallouette

Pittà

Ben‐Jacob

et al. 2014

Front. Comput. Neurosci.

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Traditionally, astrocytes have been considered to couple via gap-junctions into a syncytium with only rudimentary spatial organization. However, this view is challenged by growing experimental evidence that astrocytes organize as a proper gap-junction mediated network with more complex region-dependent properties. On the other hand, the propagation range of intercellular calcium waves (ICW) within astrocyte populations is as well highly variable, depending on the brain region considered. This suggests that the variability of the topology of gap-junction couplings could play a role in the variability of the ICW propagation range. Since this hypothesis is very difficult to investigate with current experimental approaches, we explore it here using a biophysically realistic model of three-dimensional astrocyte networks in which we varied the topology of the astrocyte network, while keeping intracellular properties and spatial cell distribution and density constant. Computer simulations of the model suggest that changing the topology of the network is indeed sufficient to reproduce the distinct ranges of ICW propagation reported experimentally. Unexpectedly, our simulations also predict that sparse connectivity and restriction of gap-junction couplings to short distances should favor propagation while long–distance or dense connectivity should impair it. Altogether, our results provide support to recent experimental findings that point toward a significant functional role of the organization of gap-junction couplings into proper astroglial networks. Dynamic control of this topology by neurons and signaling molecules could thus constitute a new type of regulation of neuron-glia and glia-glia interactions.

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“…The mean field approximation (MFA) has been applied to investigate the dynamics and steady state of propagation models, such as the forest fire [31,32,33] and epidemiological models [33,34,35] in complex networks. In this framework, the steady-state equilibrium forest density of the cellular-automata model defined by the above rules (1)- (5) is studied following the approach defined in reference [36] for a similar CA model.…”

Section: Mean-field Approachmentioning

confidence: 99%

Forest-fire model with resistant trees

Camelo-Neto

Coutinho

2011

J. Stat. Mech.

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Abstract. The role of forest heterogeneity in the long-term, large-scale dynamics of forest fires is investigated by means of a cellular automata model and mean field approximation. Heterogeneity was conceived as trees (or acres of forest) with distinct strengths of resistance to burn. The scaling analysis of fire-size and fire-lifetime frequency distributions in the non-interacting fire steady-state limit indicates the breakdown of the power-law behavior whenever the resistance strength parameter R exceeds a certain value. For higher resistant strength, exponential behavior characterizes the frequency distributions, while power-law like behavior was observed for the lower resistant case in the same manner as reported in the literature for a homogeneous counterpart model. For the intermediate resistance strength, however, it may be described either by a stretched exponential or by a power-law plot whenever the fraction of recovering empty cells by susceptible trees not-exceeds or exceeds a certain threshold respectively, also suggesting a dynamical percolation transition with respect to the stationary forest density.

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Topology regulates the distribution pattern of excitations in excitable dynamics on graphs

Cited by 34 publications

References 37 publications

Organization of Excitable Dynamics in Hierarchical Biological Networks

Organization of Excitable Dynamics in Hierarchical Biological Networks

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks

Forest-fire model with resistant trees

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