MuxViz: A Tool for Multilayer Analysis and Visualization of Networks

Multilayer relationships among entities and information about entities must be accompanied by the means to analyze, visualize, and obtain insights from such data. We present open-source software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an important way to represent a large variety of complex systems throughout science and engineering. We demonstrate the ability of muxViz to analyze and interactively visualize multilayer data using empirical genetic, neuronal, and transportation networks. Our software is available at https://github.com/manlius/muxViz.Comment: 18 pages, 10 figures (text of the accepted manuscript

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

We investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities. © Copyright © 2019 Pournaki, Merfort, Ruiz, Kouvaris, Hövel and Hizanidis

The Multilayer Connectome of Caenorhabditis elegans.

Connectomics has focused primarily on the mapping of synaptic links in the brain; yet it is well established that extrasynaptic volume transmission, especially via monoamines and neuropeptides, is also critical to brain function and occurs primarily outside the synaptic connectome. We have mapped the putative monoamine connections, as well as a subset of neuropeptide connections, in C. elegans based on new and published gene expression data. The monoamine and neuropeptide networks exhibit distinct topological properties, with the monoamine network displaying a highly disassortative star-like structure with a rich-club of interconnected broadcasting hubs, and the neuropeptide network showing a more recurrent, highly clustered topology. Despite the low degree of overlap between the extrasynaptic (or wireless) and synaptic (or wired) connectomes, we find highly significant multilink motifs of interaction, pinpointing locations in the network where aminergic and neuropeptide signalling modulate synaptic activity. Thus, the C. elegans connectome can be mapped as a multiplex network with synaptic, gap junction, and neuromodulator layers representing alternative modes of interaction between neurons. This provides a new topological plan for understanding how aminergic and peptidergic modulation of behaviour is achieved by specific motifs and loci of integration between hard-wired synaptic or junctional circuits and extrasynaptic signals wirelessly broadcast from a small number of modulatory neurons

Connectomics of extrasynaptic signalling: applications to the nervous system of Caenorhabditis elegans

Connectomics – the study of neural connectivity – is primarily concerned with the mapping and characterisation of wired synaptic links; however, it is well established that long-distance chemical signalling via extrasynaptic volume transmission is also critical to brain function. As these interactions are not visible in the physical structure of the nervous system, current approaches to connectomics are unable to capture them. This work addresses the problem of missing extrasynaptic interactions by demonstrating for the first time that whole-animal volume transmission networks can be mapped from gene expression and ligand-receptor interaction data, and analysed as part of the connectome. Complete networks are presented for the monoamine systems of Caenorhabditis elegans, along with a representative sample of selected neuropeptide systems. A network analysis of the synaptic (wired) and extrasynaptic (wireless) connectomes is presented which reveals complex topological properties, including extrasynaptic rich-club organisation with interconnected hubs distinct from those in the synaptic and gap junction networks, and highly significant multilink motifs pinpointing locations in the network where aminergic and neuropeptide signalling is likely to modulate synaptic activity. Thus, the neuronal connectome can be modelled as a multiplex network with synaptic, gap junction, and neuromodulatory layers representing inter-neuronal interactions with different dynamics and polarity. This represents a prototype for understanding how extrasynaptic signalling can be integrated into connectomics research, and provides a novel dataset for the development of multilayer network algorithms.This work was supported by the Medical Research Council (MRC)