Community detection in graphs using singular value decomposition

Advances in decomposing complex metabolite mixtures using substructure- and network-based computational metabolomics approaches

Covering: up to the end of 2020Recently introduced computational metabolome mining tools have started to positively impact the chemical and biological interpretation of untargeted metabolomics analyses. We believe that these current advances make it possible to start decomposing complex metabolite mixtures into substructure and chemical class information, thereby supporting pivotal tasks in metabolomics analysis including metabolite annotation, the comparison of metabolic profiles, and network analyses. In this review, we highlight and explain key tools and emerging strategies covering 2015 up to the end of 2020. The majority of these tools aim at processing and analyzing liquid chromatography coupled to mass spectrometry fragmentation data. We start with defining what substructures are, how they relate to molecular fingerprints, and how recognizing them helps to decompose complex mixtures. We continue with chemical classes that are based on the presence or absence of particular molecular scaffolds and/or functional groups and are thus intrinsically related to substructures. We discuss novel tools to mine substructures, annotate chemical compound classes, and create mass spectral networks from metabolomics data and demonstrate them using two case studies. We also review and speculate about the opportunities that NMR spectroscopy-based metabolome mining of complex metabolite mixtures offers to discover substructures and chemical classes. Finally, we will describe the main benefits and limitations of the current tools and strategies that rely on them, and our vision on how this exciting field can develop toward repository-scale-sized metabolomics analyses. Complementary sources of structural information from genomics analyses and well-curated taxonomic records are also discussed. Many research fields such as natural products discovery, pharmacokinetic and drug metabolism studies, and environmental metabolomics increasingly rely on untargeted metabolomics to gain biochemical and biological insights. The here described technical advances will benefit all those metabolomics disciplines by transforming spectral data into knowledge that can answer biological questions.

Iterative consensus spectral clustering improves detection of subject and group level brain functional modules

Specialized processing in the brain is performed by multiple groups of brain regions organized as functional modules. Although, in vivo studies of brain functional modules involve multiple functional Magnetic Resonance Imaging (fMRI) scans, the methods used to derive functional modules from functional networks of the brain ignore individual differences in the functional architecture and use incomplete functional connectivity information. To correct this, we propose an Iterative Consensus Spectral Clustering (ICSC) algorithm that detects the most representative modules from individual dense weighted connectivity matrices derived from multiple scans. The ICSC algorithm derives group-level modules from modules of multiple individuals by iteratively minimizing the consensus-cost between the two. We demonstrate that the ICSC algorithm can be used to derive biologically plausible group-level (for multiple subjects) and subject-level (for multiple subject scans) brain modules, using resting-state fMRI scans of 589 subjects from the Human Connectome Project. We employed a multipronged strategy to show the validity of the modularizations obtained from the ICSC algorithm. We show a heterogeneous variability in the modular structure across subjects where modules involved in visual and motor processing were highly stable across subjects. Conversely, we found a lower variability across scans of the same subject. The performance of our algorithm was compared with existing functional brain modularization methods and we show that our method detects group-level modules that are more representative of the modules of multiple individuals. Finally, the experiments on synthetic images quantitatively demonstrate that the ICSC algorithm detects group-level and subject-level modules accurately under varied conditions. Therefore, besides identifying functional modules for a population of subjects, the proposed method can be used for applications in personalized neuroscience. The ICSC implementation is available at https://github.com/SCSE-Biomedical-Computing-Group/ICSC.

Network-based identification of signature genes KLF6 and SPOCK1 associated with oral submucous fibrosis

The molecular mechanism of oral submucous fibrosis (OSF) is yet to be fully elucidated. The identification of reliable signature genes to screen patients with a high risk of OSF and to provide oral cancer surveillance is therefore required. The present study produced a filtering criterion based on network characteristics and principal component analysis, and identified the genes that were involved in OSF prognosis. Two gene expression datasets were analyzed using meta-analysis, the results of which revealed 1,176 biologically significant genes. A co-expression network was subsequently constructed and weighted gene modules were detected. The pathway and functional enrichment analyses of the present study allowed for the identification of modules 1 and 2, and their respective genes, SPARC (osteonectin), cwcv and kazal like domain proteoglycan 1 (SPOCK1) and kruppel like factor 6 (KLF6), which were involved in the occurrence of OSF. The results revealed that both genes had a prominent role in epithelial to mesenchymal transition during OSF progression. The genes identified in the present study require further exploration and validation within clinical settings to determine their roles in OSF.

Evidence for localization and urbanization economies in urban scaling

We study the scaling of (i) numbers of workers and aggregate incomes by occupational categories against city size, and (ii) total incomes against numbers of workers in different occupations, across the functional metropolitan areas of Australia and the USA. The number of workers and aggregate incomes in specific high-income knowledge economy-related occupations and industries show increasing returns to scale by city size, showing that localization economies within particular industries account for superlinear effects. However, when total urban area incomes and/or gross domestic products are regressed using a generalized Cobb-Douglas function against the number of workers in different occupations as labour inputs, constant returns to scale in productivity against city size are observed. This implies that the urbanization economies at the whole city level show linear scaling or constant returns to scale. Furthermore, industrial and occupational organizations, not population size, largely explain the observed productivity variable. The results show that some very specific industries and occupations contribute to the observed overall superlinearity. The findings suggest that it is not just size but also that it is the diversity of specific intra-city organization of economic and social activity and physical infrastructure that should be used to understand urban scaling behaviours.

Study on material base and action mechanism of compound Danshen dripping pills for treatment of atherosclerosis based on modularity analysis

ETHNOPHARMACOLOGICAL RELEVANCE

Traditional Chinese medicine (TCM) has been widely used in China and its surrounding countries in clinical treatments for centuries-long time. However, due to the complexity of TCM constituents, both action mechanism and material base of TCM remain nearly unknown.

AIM OF THE STUDY

The present study was designed to uncover the action mechanism and material base of TCM in a low-cost manner.

MATERIALS AND METHODS

Compound Danshen dripping pills (DSP) is a widely used TCM for treatment of atherosclerosis, and was researched here to demonstrate the effectiveness of our method. We constructed a heterogeneous network for DSP, identified the significant network module, and analyzed the primary pharmacological units by performing GO and pathways enrichment analysis.

RESULTS

Two significant network modules were identified from the heterogeneous network of DSP, and three compounds out of four hub nodes in the network were found to intervene in the process of atherosclerosis. Moreover, 13 out of 20 enriched pathways that were ranked in top 10 corresponding to both the two pharmacological units were found to be involved in the process of atherosclerosis.

CONCLUSIONS

Quercetin, luteolin and apigenin may be the main active compounds which modulate the signaling pathways, such as metabolism of xenobiotics by cytochrome P450, retinol metabolism, etc. The present method helps reveal the action mechanism and material base of DSP for treatment of atherosclerosis.

Spectral-clustering approach to Lagrangian vortex detection

One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.

Eigenvector dynamics under perturbation of modular networks

Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of q communities, the number of eigenvectors corresponding to the q largest eigenvalues form a "community" eigenspace and rotate together, but separately from that of the "bulk" eigenspace spanned by all the other eigenvectors. Using this property, the number of modules or clusters in a network can be estimated in an algorithm-independent way. A general argument and derivation for the theoretical detectability limit for sparse modular networks with q communities is presented, beyond which modularity persists in the system but cannot be detected. It is shown that for detecting the clusters or modules using the adjacency matrix, there is a "band" in which it is hard to detect the clusters even before the theoretical detectability limit is reached, and for which the theoretically predicted detectability limit forms the sufficient upper bound. Analytic estimations of these bounds are presented and empirically demonstrated.

Comprehensive spectral approach for community structure analysis on complex networks

A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a "multipartite" component. These two matrices reveal the structure of the network from different perspectives and can be analyzed at different levels of detail. Their entries, or the entries of their lower-rank approximations, provide measures of the affinity or antagonism between the nodes that highlight the communities and the "gateway" links that connect them together. An algorithm is then proposed to achieve the automatic assignment of the nodes to communities based on the information provided by either matrix. This algorithm naturally generates overlapping communities but can also be tuned to eliminate the overlaps.

Spectral Characterization of Hierarchical Modularity in Product Architectures

Despite the importance of the architectural modularity of products and systems, existing modularity metrics or algorithms do not account for overlapping and hierarchically embedded modules. This paper presents a graph theoretic spectral approach to characterize the degree of modular hierarchical-overlapping organization in the architecture of products and complex engineered systems. It is shown that the eigenvalues of the adjacency matrix of a product architecture graph can reveal layers of hidden modular or hierarchical modular organization that are not immediately visible in the predefined architectural description. We use the approach to analyze and discuss several design, management, and system resilience implications for complex engineered systems.

Spectral characterization of hierarchical network modularity and limits of modularity detection

Many real world networks are reported to have hierarchically modular organization. However, there exists no algorithm-independent metric to characterize hierarchical modularity in a complex system. The main results of the paper are a set of methods to address this problem. First, classical results from random matrix theory are used to derive the spectrum of a typical stochastic block model hierarchical modular network form. Second, it is shown that hierarchical modularity can be fingerprinted using the spectrum of its largest eigenvalues and gaps between clusters of closely spaced eigenvalues that are well separated from the bulk distribution of eigenvalues around the origin. Third, some well-known results on fingerprinting non-hierarchical modularity in networks automatically follow as special cases, threreby unifying these previously fragmented results. Finally, using these spectral results, it is found that the limits of detection of modularity can be empirically established by studying the mean values of the largest eigenvalues and the limits of the bulk distribution of eigenvalues for an ensemble of networks. It is shown that even when modularity and hierarchical modularity are present in a weak form in the network, they are impossible to detect, because some of the leading eigenvalues fall within the bulk distribution. This provides a threshold for the detection of modularity. Eigenvalue distributions of some technological, social, and biological networks are studied, and the implications of detecting hierarchical modularity in real world networks are discussed.