Modularity in complex multilayer networks with multiple aspects: a static perspective

Gene communities in co-expression networks across different tissues

With the recent availability of tissue-specific gene expression data, e.g., provided by the GTEx Consortium, there is interest in comparing gene co-expression patterns across tissues. One promising approach to this problem is to use a multilayer network analysis framework and perform multilayer community detection. Communities in gene co-expression networks reveal groups of genes similarly expressed across individuals, potentially involved in related biological processes responding to specific environmental stimuli or sharing common regulatory variations. We construct a multilayer network in which each of the four layers is an exocrine gland tissue-specific gene co-expression network. We develop methods for multilayer community detection with correlation matrix input and an appropriate null model. Our correlation matrix input method identifies five groups of genes that are similarly co-expressed in multiple tissues (a community that spans multiple layers, which we call a generalist community) and two groups of genes that are co-expressed in just one tissue (a community that lies primarily within just one layer, which we call a specialist community). We further found gene co-expression communities where the genes physically cluster across the genome significantly more than expected by chance (on chromosomes 1 and 11). This clustering hints at underlying regulatory elements determining similar expression patterns across individuals and cell types. We suggest that KRTAP3-1, KRTAP3-3, and KRTAP3-5 share regulatory elements in skin and pancreas. Furthermore, we find that CELA3A and CELA3B share associated expression quantitative trait loci in the pancreas. The results indicate that our multilayer community detection method for correlation matrix input extracts biologically interesting communities of genes.

Efficient community detection in multilayer networks using boolean compositions

Networks (or graphs) are used to model the dyadic relations between entities in complex systems. Analyzing the properties of the networks reveal important characteristics of the underlying system. However, in many disciplines, including social sciences, bioinformatics, and technological systems, multiple relations exist between entities. In such cases, a simple graph is not sufficient to model these multiple relations, and a multilayer network is a more appropriate model. In this paper, we explore community detection in multilayer networks. Specifically, we propose a novel network decoupling strategy for efficiently combining the communities in the different layers using the Boolean primitives AND, OR, and NOT. Our proposed method, network decoupling, is based on analyzing the communities in each network layer individually and then aggregating the analysis results. We (i) describe our network decoupling algorithms for finding communities, (ii) present how network decoupling can be used to express different types of communities in multilayer networks, and (iii) demonstrate the effectiveness of using network decoupling for detecting communities in real-world and synthetic data sets. Compared to other algorithms for detecting communities in multilayer networks, our proposed network decoupling method requires significantly lower computation time while producing results of high accuracy. Based on these results, we anticipate that our proposed network decoupling technique will enable a more detailed analysis of multilayer networks in an efficient manner.

Functional characterization of nutraceuticals using spectral clustering: Centrality of caveolae-mediated endocytosis for management of nitric oxide and vitamin D deficiencies and atherosclerosis

It is well recognized that redox imbalance, nitric oxide (NO), and vitamin D deficiencies increase risk of cardiovascular, metabolic, and infectious diseases. However, clinical studies assessing efficacy of NO and vitamin D supplementation have failed to produce unambiguous efficacy outcomes suggesting that the understanding of the pharmacologies involved is incomplete. This raises the need for using systems pharmacology tools to better understand cause-effect relationships at biological systems levels. We describe the use of spectral clustering methodology to analyze protein network interactions affected by a complex nutraceutical, Cardio Miracle (CM), that contains arginine, citrulline, vitamin D, and antioxidants. This examination revealed that interactions between protein networks affected by these substances modulate functions of a network of protein complexes regulating caveolae-mediated endocytosis (CME), TGF beta activity, vitamin D efficacy and host defense systems. Identification of this regulatory scheme and the working of embedded reciprocal feedback loops has significant implications for treatment of vitamin D deficiencies, atherosclerosis, metabolic and infectious diseases such as COVID-19.

Unspoken Assumptions in Multi-layer Modularity maximization

A principled approach to recover communities in social networks is to find a clustering of the network nodes into modules (i.e groups of nodes) for which the modularity over the network is maximal. This guarantees partitioning the network nodes into sparsely connected groups of densely connected nodes. A popular extension of modularity has been proposed in the literature so it applies to multi-layer networks, that is, networks that model different types/aspects of interactions among a set of actors. In this extension, a new parameter, the coupling strength ω, has been introduced to couple different copies (i.e nodes) of the same actor with specific weights across different layers. This allows two nodes that refer to the same actor to reward the modularity score with an amount proportional to ω when they appear in the same community. While this extension seems to provide an effective tool to detect communities in multi-layer networks, it is not always clear what kind of communities maximising the generalised modularity can identify in multi-layer networks and whether these communities are inclusive to all possible community structures possible to exist in multi-layer networks. In addition, it has not been thoroughly investigated yet how to interpret ω in real-world scenarios, and whether a proper tuning of ω, if exists, is enough to guarantee an accurate recoverability for different types of multi-layer community structures. In this article, we report the different ways used in the literature to tune ω. We analyse different community structures that can be recovered by maximising the generalised modularity in relation to ω. We propose different models for multi-layer communities in multiplex and time-dependent networks and test if they are recoverable by modularity-maximization community detection methods under any assignment of ω. Our main finding is that only few simple models of multi-layer communities in multiplex and time-dependent networks are recoverable by modularity maximisation methods while more complex models are not accurately recoverable under any assignment of ω.