From networks to optimal higher-order models of complex systems

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Rich data is revealing that complex dependencies between the nodes of a network may escape models based on pairwise interactions. Higher-order network models go beyond these limitations, offering new perspectives for understanding complex systems.

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Structure and function of the feed-forward loop network motif.

S Mangan, U Alon (2011)

Engineered systems are often built of recurring circuit modules that carry out key functions. Transcription networks that regulate the responses of living cells were recently found to obey similar principles: they contain several biochemical wiring patterns, termed network motifs, which recur throughout the network. One of these motifs is the feed-forward loop (FFL). The FFL, a three-gene pattern, is composed of two input transcription factors, one of which regulates the other, both jointly regulating a target gene. The FFL has eight possible structural types, because each of the three interactions in the FFL can be activating or repressing. Here, we theoretically analyze the functions of these eight structural types. We find that four of the FFL types, termed incoherent FFLs, act as sign-sensitive accelerators: they speed up the response time of the target gene expression following stimulus steps in one direction (e.g., off to on) but not in the other direction (on to off). The other four types, coherent FFLs, act as sign-sensitive delays. We find that some FFL types appear in transcription network databases much more frequently than others. In some cases, the rare FFL types have reduced functionality (responding to only one of their two input stimuli), which may partially explain why they are selected against. Additional features, such as pulse generation and cooperativity, are discussed. This study defines the function of one of the most significant recurring circuit elements in transcription networks.

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Multilayer networks

M. Kivelä, A. Arenas, M. Barthelemy … (2014)

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Finding community structure in networks using the eigenvectors of matrices.

Amy E M Newman (2006)

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.

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Journal

Journal ID (nlm-journal-id): 101235387

Journal ID (pubmed-jr-id): 34285

Journal ID (nlm-ta): Nat Phys

Journal ID (iso-abbrev): Nat Phys

Title: Nature physics

ISSN (Print): 1745-2473

Publication date Nihms-submitted: 26 February 2019

Publication date (Electronic): 25 March 2019

Publication date (Print): April 2019

Publication date PMC-release: 25 September 2019

Volume: 15

Issue: 4

Pages: 313-320

Affiliations

[† ]University of Oxford, United Kingdom

[* ]Integrated Science Lab, Department of Physics, Umeå University, Sweden

[‡ ]Data Analytics Group, Department of Informatics (IfI), University of Zurich, Switzerland

Article

Manuscript ID: EMS81685

DOI: 10.1038/s41567-019-0459-y

PMC ID: 6445364

PubMed ID: 30956684

SO-VID: 04a6cf45-32cd-4f17-88cd-28da25f96b16

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Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use: http://www.nature.com/authors/editorial_policies/license.html#terms

From networks to optimal higher-order models of complex systems

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Most cited references 55

Structure and function of the feed-forward loop network motif.

Multilayer networks

Finding community structure in networks using the eigenvectors of matrices.

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