Dataset Information

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition.

ABSTRACT: Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics.

SUBMITTER: Ritchie M

PROVIDER: S-EPMC4698307 | biostudies-literature | 2016 Jan

REPOSITORIES: biostudies-literature

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Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition.

Ritchie Martin M Berthouze Luc L Kiss Istvan Z IZ

Journal of mathematical biology 20150417 1-2

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive ...[more]

PMID: 25893260

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Project description:BackgroundRepresenting the complex interplay between different types of biomolecules across different omics layers in multi-omics networks bears great potential to gain a deep mechanistic understanding of gene regulation and disease. However, multi-omics networks easily grow into giant hairball structures that hamper biological interpretation. Module detection methods can decompose these networks into smaller interpretable modules. However, these methods are not adapted to deal with multi-omics data nor consider topological features. When deriving very large modules or ignoring the broader network context, interpretability remains limited. To address these issues, we developed a SUbgraph BAsed mulTi-OMIcs Clustering framework (SUBATOMIC), which infers small and interpretable modules with a specific topology while keeping track of connections to other modules and regulators.ResultsSUBATOMIC groups specific molecular interactions in composite network subgraphs of two and three nodes and clusters them into topological modules. These are functionally annotated, visualized and overlaid with expression profiles to go from static to dynamic modules. To preserve the larger network context, SUBATOMIC investigates statistically the connections in between modules as well as between modules and regulators such as miRNAs and transcription factors. We applied SUBATOMIC to analyze a composite Homo sapiens network containing transcription factor-target gene, miRNA-target gene, protein-protein, homologous and co-functional interactions from different databases. We derived and annotated 5586 modules with diverse topological, functional and regulatory properties. We created novel functional hypotheses for unannotated genes. Furthermore, we integrated modules with condition specific expression data to study the influence of hypoxia in three cancer cell lines. We developed two prioritization strategies to identify the most relevant modules in specific biological contexts: one considering GO term enrichments and one calculating an activity score reflecting the degree of differential expression. Both strategies yielded modules specifically reacting to low oxygen levels.ConclusionsWe developed the SUBATOMIC framework that generates interpretable modules from integrated multi-omics networks and applied it to hypoxia in cancer. SUBATOMIC can infer and contextualize modules, explore condition or disease specific modules, identify regulators and functionally related modules, and derive novel gene functions for uncharacterized genes. The software is available at https://github.com/CBIGR/SUBATOMIC .

Project description:Advances in functional magnetic resonance spectroscopy (fMRS) have enabled the quantification of activity-dependent changes in neurotransmitter concentrations in vivo. However, the physiological basis of the large changes in GABA and glutamate observed by fMRS (>10%) over short time scales of less than a minute remain unclear as such changes cannot be accounted for by known synthesis or degradation metabolic pathways. Instead, it has been hypothesized that fMRS detects shifts in neurotransmitter concentrations as they cycle from presynaptic vesicles, where they are largely invisible, to extracellular and cytosolic pools, where they are detectable. The present paper uses a computational modelling approach to demonstrate the viability of this hypothesis. A new mean-field model of the neural mechanisms generating the fMRS signal in a cortical voxel is derived. The proposed macroscopic mean-field model is based on a microscopic description of the neurotransmitter dynamics at the level of the synapse. Specifically, GABA and glutamate are assumed to cycle between three metabolic pools: packaged in the vesicles; active in the synaptic cleft; and undergoing recycling and repackaging in the astrocytic or neuronal cytosol. Computational simulations from the model are used to generate predicted changes in GABA and glutamate concentrations in response to different types of stimuli including pain, vision, and electric current stimulation. The predicted changes in the extracellular and cytosolic pools corresponded to those reported in empirical fMRS data. Furthermore, the model predicts a selective control mechanism of the GABA/glutamate relationship, whereby inhibitory stimulation reduces both neurotransmitters, whereas excitatory stimulation increases glutamate and decreases GABA. The proposed model bridges between neural dynamics and fMRS and provides a mechanistic account for the activity-dependent changes in the glutamate and GABA fMRS signals. Lastly, these results indicate that echo-time may be an important timing parameter that can be leveraged to maximise fMRS experimental outcomes.

Dataset Information

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition.

Publications

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition.

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