Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

Fretter, Christoph; Lesne, Annick; Hilgetag, Claus C.; Hütt, Marc‐Thorsten

doi:10.1038/srep42340

Cited by 14 publications

(18 citation statements)

References 51 publications

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“…Both correctly predicts the exchange of stability between the non-trivial fixed point and the value c o E = f corresponding to the extinction of excitation propagation. We have shown in [11] that a sustained activity (corresponding to the non trivial steady state) occurs up to a value κ m that can be roughly estimated from the graph topology as the maximal degree k max of the graph, in agreement with the upper bound 1/ k (larger that 1/k max ) predicted here using mean-field analysis. The observed lower bound c * E can be explained as a fluctuation effect: the actual number of excited neighbors of a node of degree k can be higher than kc * E , which accommodates excitation propagation for relative threshold values higher than κ = c * E .…”

Section: Pair-correlation Equationssupporting

confidence: 86%

Unravelling Topological Determinants of Excitable Dynamics on Graphs Using Analytical Mean-field Approaches

Hütt

Lesne

2020

Discrete and Continuous Models in the Theory of Networks

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We present our use of analytical mean-field approaches in investigating how the interplay between graph topology and excitable dynamics produce spatio-temporal patterns. We first detail the derivation of mean-field equations for a few simple model situations, mainly 3-state discrete-time excitable dynamics with an absolute or a relative excitation threshold. Comparison with direct numerical simulation shows that their solution satisfactorily predicts the steady-state excitation density. In contrast, they often fail to capture more complex dynamical features, however we argue that the analysis of this failure is in itself insightful, by pinpointing the key role of mechanisms neglected in the mean-field approach. Moreover, we show how second-order mean-field approaches, in which a topological object (e.g. a cycle or a hub) is considered as embedded in a mean-field surrounding, allow us to go beyond the spatial homogenization currently associated with plain mean-field calculations. The confrontation between these refined analytical predictions and simulation quantitatively evidences the specific contribution of this topological object to the dynamics.

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Section: Pair-correlation Equationssupporting

confidence: 86%

Unravelling Topological Determinants of Excitable Dynamics on Graphs Using Analytical Mean-field Approaches

Hütt

Lesne

2020

Discrete and Continuous Models in the Theory of Networks

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“…Sensory systems for example have an axis along the hierarchical depth from the input nodes to processing nodes generating ever more abstract representations of the sensory input. 51,52 The same is true for manufacturing systems with their hierarchy of input, production and assembly/output layers. 53 The situation we face in our attempts to epitomize the spatiotemporal constraints imposed on the emergence of gene expression patterns is reminicent of the work by Brockmann and Helbing 54 on the spread of epidemic diseases.…”

Section: Discussionmentioning

confidence: 96%

Chromosomal origin of replication coordinates logically distinct types of bacterial genetic regulation

et al. 2020

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For a long time it has been hypothesized that bacterial gene regulation involves an intricate interplay of the transcriptional regulatory network (TRN) and the spatial organization of genes in the chromosome. Here we explore this hypothesis both on a structural and on a functional level. On the structural level, we study the TRN as a spatially embedded network. On the functional level, we analyze gene expression patterns from a network perspective ("digital control"), as well as from the perspective of the spatial organization of the chromosome ("analog control"). Our structural analysis reveals the outstanding relevance of the symmetry axis defined by the origin (Ori) and terminus (Ter) of replication for the network embedding and, thus, suggests the coevolution of two regulatory infrastructures, namely the transcriptional regulatory network and the spatial arrangement of genes on the chromosome, to optimize the cross-talk between two fundamental biological processes: genomic expression and replication. This observation is confirmed by the functional analysis based on the differential gene expression patterns of more than 4000 pairs of microarray and RNA-Seq datasets for E. coli from the Colombos Database using complex network and machine learning methods. This large-scale analysis supports the notion that two logically distinct types of genetic control are cooperating to regulate gene expression in a complementary manner. Moreover, we find that the position of the gene relative to the Ori is a feature of very high predictive value for gene expression, indicating that the Ori-Ter symmetry axis coordinates the action of distinct genetic control mechanisms.

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“…61) or relative thresholds (a certain percentage of neighbors needs to be active to trigger an excitation; ref. 25) can also be explored. It seems intuitive, for example, that in relative threshold models, the contribution from the degree gradient will be less important.…”

Section: Resultsmentioning

confidence: 99%

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks

Moretti

Hütt

2020

Proc. Natl. Acad. Sci. U.S.A.

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In models of excitable dynamics on graphs, excitations can travel in both directions of an undirected link. However, as a striking interplay of dynamics and network topology, excitations often establish a directional preference. Some of these cases of “link-usage asymmetry” are local in nature and can be mechanistically understood, for instance, from the degree gradient of a link (i.e., the difference in node degrees at both ends of the link). Other contributions to the link-usage asymmetry are instead, as we show, self-organized in nature, and strictly nonlocal. This is the case for excitation waves, where the preferential propagation of excitations along a link depends on its orientation with respect to a hub acting as a source, even if the link in question is several steps away from the hub itself. Here, we identify and quantify the contribution of such self-organized patterns to link-usage asymmetry and show that they extend to ranges significantly longer than those ascribed to local patterns. We introduce a topological characterization, the hub-set-orientation prevalence of a link, which indicates its average orientation with respect to the hubs of a graph. Our numerical results show that the hub-set-orientation prevalence of a link strongly correlates with the preferential usage of the link in the direction of propagation away from the hub core of the graph. Our methodology is embedding-agnostic and allows for the measurement of wave signals and the sizes of the cores from which they originate.

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Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

Cited by 14 publications

References 51 publications

Unravelling Topological Determinants of Excitable Dynamics on Graphs Using Analytical Mean-field Approaches

Unravelling Topological Determinants of Excitable Dynamics on Graphs Using Analytical Mean-field Approaches

Chromosomal origin of replication coordinates logically distinct types of bacterial genetic regulation

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks

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