Understanding cancer complexome using networks, spectral graph theory and multilayer framework

Multilayer biological networks to upscale marine research to global change-smart management and sustainable resource use

Human activities are having a massive negative impact on biodiversity and ecological processes worldwide. The rate and magnitude of ecological transformations induced by climate change, habitat destruction, overexploitation and pollution are now so substantial that a sixth mass extinction event is currently underway. The biodiversity crisis of the Anthropocene urges scientists to put forward a transformative vision to promote the conservation of biodiversity, and thus indirectly the preservation of ecosystem functions. Here, we identify pressing issues in global change biology research and propose an integrative framework based on multilayer biological networks as a tool to support conservation actions and marine risk assessments in multi-stressor scenarios. Multilayer networks can integrate different levels of environmental and biotic complexity, enabling us to combine information on molecular, physiological and behaviour responses, species interactions and biotic communities. The ultimate aim of this framework is to link human-induced environmental changes to species physiology, fitness, biogeography and ecosystem impacts across vast seascapes and time frames, to help guide solutions to address biodiversity loss and ecological tipping points. Further, we also define our current ability to adopt a widespread use of multilayer networks within ecology, evolution and conservation by providing examples of case-studies. We also assess which approaches are ready to be transferred and which ones require further development before use. We conclude that multilayer biological networks will be crucial to inform (using reliable multi-levels integrative indicators) stakeholders and support their decision-making concerning the sustainable use of resources and marine conservation.

Measuring cancer driving force of chromosomal aberrations through multi-layer Boolean implication networks

Multi-layer Complex networks are commonly used for modeling and analysing biological entities. This paper presents the advantage of using COMBO (Combining Multi Bio Omics) to suggest a new role of the chromosomal aberration as a cancer driver factor. Exploiting the heterogeneous multi-layer networks, COMBO integrates gene expression and DNA-methylation data in order to identify complex bilateral relationships between transcriptome and epigenome. We evaluated the multi-layer networks generated by COMBO on different TCGA cancer datasets (COAD, BLCA, BRCA, CESC, STAD) focusing on the effect of a specific chromosomal numerical aberration, broad gain in chromosome 20, on different cancer histotypes. In addition, the effect of chromosome 8q amplification was tested in the same TCGA cancer dataset. The results demonstrate the ability of COMBO to identify the chromosome 20 amplification cancer driver force in the different TCGA Pan Cancer project datasets.

NetVA: an R package for network vulnerability and influence analysis

In biological network analysis, identifying key molecules plays a decisive role in the development of potential diagnostic and therapeutic candidates. Among various approaches of network analysis, network vulnerability analysis is quite important, as it assesses significant associations between topological properties and the functional essentiality of a network. Similarly, some node centralities are also used to screen out key molecules. Among these node centralities, escape velocity centrality (EVC), and its extended version (EVC+) outperform others, viz., Degree, Betweenness, and Clustering coefficient. Keeping this in mind, we aimed to develop a first-of-its-kind R package named NetVA, which analyzes networks to identify key molecular players (individual proteins and protein pairs/triplets) through network vulnerability and EVC+-based approaches. To demonstrate the application and relevance of our package in network analysis, previously published and publicly available protein-protein interactions (PPIs) data of human breast cancer were analyzed. This resulted in identifying some most important proteins. These included essential proteins, non-essential proteins, hubs, and bottlenecks, which play vital roles in breast cancer development. Thus, the NetVA package, available at https://github.com/kr-swapnil/NetVA with a detailed tutorial to download and use, assists in predicting potential candidates for therapeutic and diagnostic purposes by exploring various topological features of a disease-specific PPIs network.Communicated by Ramaswamy H. Sarma.

CNVs in 8q24.3 do not influence gene co-expression in breast cancer subtypes

Gene co-expression networks are a useful tool in the study of interactions that have allowed the visualization and quantification of diverse phenomena, including the loss of co-expression over long distances in cancerous samples. This characteristic, which could be considered fundamental to cancer, has been widely reported in various types of tumors. Since copy number variations (CNVs) have previously been identified as causing multiple genetic diseases, and gene expression is linked to them, they have often been mentioned as a probable cause of loss of co-expression in cancerous networks. In order to carry out a comparative study of the validity of this statement, we took 477 protein-coding genes from chromosome 8, and the CNVs of 101 genes, also protein-coding, belonging to the 8q24.3 region, a cytoband that is particularly active in the appearance of breast cancer. We created CNVS-conditioned co-expression networks of each of the 101 genes in the 8q24.3 region using conditional mutual information. The study was carried out using the four molecular subtypes of breast cancer (Luminal A, Luminal B, Her2, and Basal), as well as a case corresponding to healthy samples. We observed that in all cancer cases, the measurement of the Kolmogorov-Smirnov statistic shows that there are no significant differences between one and other values of the CNVs for any case. Furthermore, the co-expression interactions are stronger in all cancer subtypes than in the control networks. However, the control network presents a homogeneously distributed set of co-expression interactions, while for cancer networks, the highest interactions are more confined to specific cytobands, in particular 8q24.3 and 8p21.3. With this approach, we demonstrate that despite copy number alterations in the 8q24 region being a common trait in breast cancer, the loss of long-distance co-expression in breast cancer is not determined by CNVs.

Network topologies for maximal organismal health span and lifespan

The population dynamics of human health and mortality can be jointly captured by complex network models using scale-free network topology. To validate and understand the choice of scale-free networks, we investigate which network topologies maximize either lifespan or health span. Using the Generic Network Model (GNM) of organismal aging, we find that both health span and lifespan are maximized with a "star" motif. Furthermore, these optimized topologies exhibit maximal lifespans that are not far above the maximal observed human lifespan. To approximate the complexity requirements of the underlying physiological function, we then constrain network entropies. Using non-parametric stochastic optimization of network structure, we find that disassortative scale-free networks exhibit the best of both lifespan and health span. Parametric optimization of scale-free networks behaves similarly. We further find that higher maximum connectivity and lower minimum connectivity networks enhance both maximal lifespans and health spans by allowing for more disassortative networks. Our results validate the scale-free network assumption of the GNM and indicate the importance of disassortativity in preserving health and longevity in the face of damage propagation during aging. Our results highlight the advantages provided by disassortative scale-free networks in biological organisms and subsystems.

Nucleotide-based genetic networks: Methods and applications

Genomic variations have been acclaimed as among the key players in understanding the biological mechanisms behind migration, evolution, and adaptation to extreme conditions. Due to stochastic evolutionary forces, the frequency of polymorphisms is affected by changes in the frequency of nearby polymorphisms in the same DNA sample, making them connected in terms of evolution. This article presents all the ingredients to understand the cumulative effects and complex behaviors of genetic variations in the human mitochondrial genome by analyzing co-occurrence networks of nucleotides, and shows key results obtained from such analyses. The article emphasizes recent investigations of these co-occurrence networks, describing the role of interactions between nucleotides in fundamental processes of human migration and viral evolution. The corresponding co-mutation-based genetic networks revealed genetic signatures of human adaptation in extreme environments. This article provides the methods of constructing such networks in detail, along with their graph-theoretical properties, and applications of the genomic networks in understanding the role of nucleotide co-evolution in evolution of the whole genome.

Emerging landscape of molecular interaction networks: Opportunities, challenges and prospects

Network biology finds application in interpreting molecular interaction networks and providing insightful inferences using graph theoretical analysis of biological systems. The integration of computational bio-modelling approaches with different hybrid network-based techniques provides additional information about the behaviour of complex systems. With increasing advances in high-throughput technologies in biological research, attempts have been made to incorporate this information into network structures, which has led to a continuous update of network biology approaches over time. The newly minted centrality measures accommodate the details of omics data and regulatory network structure information. The unification of graph network properties with classical mathematical and computational modelling approaches and technologically advanced approaches like machine-learning- and artificial intelligence-based algorithms leverages the potential application of these techniques. These computational advances prove beneficial and serve various applications such as essential gene prediction, identification of drug–disease interaction and gene prioritization. Hence, in this review, we have provided a comprehensive overview of the emerging landscape of molecular interaction networks using graph theoretical approaches. With the aim to provide information on the wide range of applications of network biology approaches in understanding the interaction and regulation of genes, proteins, enzymes and metabolites at different molecular levels, we have reviewed the methods that utilize network topological properties, emerging hybrid network-based approaches and applications that integrate machine learning techniques to analyse molecular interaction networks. Further, we have discussed the applications of these approaches in biomedical research with a note on future prospects.

Role of mitochondrial genetic interactions in determining adaptation to high altitude human population

Physiological and haplogroup studies performed to understand high-altitude adaptation in humans are limited to individual genes and polymorphic sites. Due to stochastic evolutionary forces, the frequency of a polymorphism is affected by changes in the frequency of a near-by polymorphism on the same DNA sample making them connected in terms of evolution. Here, first, we provide a method to model these mitochondrial polymorphisms as "co-mutation networks" for three high-altitude populations, Tibetan, Ethiopian and Andean. Then, by transforming these co-mutation networks into weighted and undirected gene-gene interaction (GGI) networks, we were able to identify functionally enriched genetic interactions of CYB and CO3 genes in Tibetan and Andean populations, while NADH dehydrogenase genes in the Ethiopian population playing a significant role in high altitude adaptation. These co-mutation based genetic networks provide insights into the role of different set of genes in high-altitude adaptation in human sub-populations.

Classifying diseases by using biological features to identify potential nosological models

Established nosological models have provided physicians an adequate enough classification of diseases so far. Such systems are important to correctly identify diseases and treat them successfully. However, these taxonomies tend to be based on phenotypical observations, lacking a molecular or biological foundation. Therefore, there is an urgent need to modernize them in order to include the heterogeneous information that is produced in the present, as could be genomic, proteomic, transcriptomic and metabolic data, leading this way to more comprehensive and robust structures. For that purpose, we have developed an extensive methodology to analyse the possibilities when it comes to generate new nosological models from biological features. Different datasets of diseases have been considered, and distinct features related to diseases, namely genes, proteins, metabolic pathways and genetical variants, have been represented as binary and numerical vectors. From those vectors, diseases distances have been computed on the basis of several metrics. Clustering algorithms have been implemented to group diseases, generating different models, each of them corresponding to the distinct combinations of the previous parameters. They have been evaluated by means of intrinsic metrics, proving that some of them are highly suitable to cover new nosologies. One of the clustering configurations has been deeply analysed, demonstrating its quality and validity in the research context, and further biological interpretations have been made. Such model was particularly generated by OPTICS clustering algorithm, by studying the distance between diseases based on gene sharedness and following cosine index metric. 729 clusters were formed in this model, which obtained a Silhouette coefficient of 0.43.

The Multiple Dimensions of Networks in Cancer: A Perspective

This perspective article gathers the latest developments in mathematical and computational oncology tools that exploit network approaches for the mathematical modelling, analysis, and simulation of cancer development and therapy design. It instigates the community to explore new paths and synergies under the umbrella of the Special Issue “Networks in Cancer: From Symmetry Breaking to Targeted Therapy”. The focus of the perspective is to demonstrate how networks can model the physics, analyse the interactions, and predict the evolution of the multiple processes behind tumour-host encounters across multiple scales. From agent-based modelling and mechano-biology to machine learning and predictive modelling, the perspective motivates a methodology well suited to mathematical and computational oncology and suggests approaches that mark a viable path towards adoption in the clinic.

Comparative Analyses of Gene Co-expression Networks: Implementations and Applications in the Study of Evolution

Similarities and differences in the associations of biological entities among species can provide us with a better understanding of evolutionary relationships. Often the evolution of new phenotypes results from changes to interactions in pre-existing biological networks and comparing networks across species can identify evidence of conservation or adaptation. Gene co-expression networks (GCNs), constructed from high-throughput gene expression data, can be used to understand evolution and the rise of new phenotypes. The increasing abundance of gene expression data makes GCNs a valuable tool for the study of evolution in non-model organisms. In this paper, we cover motivations for why comparing these networks across species can be valuable for the study of evolution. We also review techniques for comparing GCNs in the context of evolution, including local and global methods of graph alignment. While some protein-protein interaction (PPI) bioinformatic methods can be used to compare co-expression networks, they often disregard highly relevant properties, including the existence of continuous and negative values for edge weights. Also, the lack of comparative datasets in non-model organisms has hindered the study of evolution using PPI networks. We also discuss limitations and challenges associated with cross-species comparison using GCNs, and provide suggestions for utilizing co-expression network alignments as an indispensable tool for evolutionary studies going forward.

Mapping drug-target interactions and synergy in multi-molecular therapeutics for pressure-overload cardiac hypertrophy

Advancements in systems biology have resulted in the development of network pharmacology, leading to a paradigm shift from "one-target, one-drug" to "target-network, multi-component therapeutics". We employ a chimeric approach involving in-vivo assays, gene expression analysis, cheminformatics, and network biology to deduce the regulatory actions of a multi-constituent Ayurvedic concoction, Amalaki Rasayana (AR) in animal models for its effect in pressure-overload cardiac hypertrophy. The proteomics analysis of in-vivo assays for Aorta Constricted and Biologically Aged rat models identify proteins expressed under each condition. Network analysis mapping protein-protein interactions and synergistic actions of AR using multi-component networks reveal drug targets such as ACADM, COX4I1, COX6B1, HBB, MYH14, and SLC25A4, as potential pharmacological co-targets for cardiac hypertrophy. Further, five out of eighteen AR constituents potentially target these proteins. We propose a distinct prospective strategy for the discovery of network pharmacological therapies and repositioning of existing drug molecules for treating pressure-overload cardiac hypertrophy.

The Human Body as a Super Network: Digital Methods to Analyze the Propagation of Aging

Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks-e.g., epigenetic networks, cell-cell networks (such as astroglial networks), and population genetics. Mathematical modeling allows the combination of such networks so that they may be studied in unison, to better understand how the so-called "seven pillars of aging" combine and to generate hypothesis for treating aging as a condition at relatively early biological ages. In this review, we consider how recent progression in mathematical modeling can be utilized to investigate aging, particularly in, but not exclusive to, the context of degenerative neuronal disease. We also consider how the latest techniques for generating biomarker models for disease prediction, such as longitudinal analysis and parenclitic analysis can be applied to as both biomarker platforms for aging, as well as to better understand the inescapable condition. This review is written by a highly diverse and multi-disciplinary team of scientists from across the globe and calls for greater collaboration between diverse fields of research.

Complex Network Characterization Using Graph Theory and Fractal Geometry: The Case Study of Lung Cancer DNA Sequences

This paper discusses an approach developed for exploiting the local elementary movements of evolution to study complex networks in terms of shared common embedding and, consequently, shared fractal properties. This approach can be useful for the analysis of lung cancer DNA sequences and their properties by using the concepts of graph theory and fractal geometry. The proposed method advances a renewed consideration of network complexity both on local and global scales. Several researchers have illustrated the advantages of fractal mathematics, as well as its applicability to lung cancer research. Nevertheless, many researchers and clinicians continue to be unaware of its potential. Therefore, this paper aims to examine the underlying assumptions of fractals and analyze the fractal dimension and related measurements for possible application to complex networks and, especially, to the lung cancer network. The strict relationship between the lung cancer network properties and the fractal dimension is proved. Results show that the fractal dimension decreases in the lung cancer network while the topological properties of the network increase in the lung cancer network. Finally, statistical and topological significance between the complexity of the network and lung cancer network is shown.

Identification of Key Components in Colon Adenocarcinoma Using Transcriptome to Interactome Multilayer Framework

Complexity of cascading interrelations between molecular cell components at different levels from genome to metabolome ordains a massive difficulty in comprehending biological happenings. However, considering these complications in the systematic modelings will result in realistic and reliable outputs. The multilayer networks approach is a relatively innovative concept that could be applied for multiple omics datasets as an integrative methodology to overcome heterogeneity difficulties. Herein, we employed the multilayer framework to rehabilitate colon adenocarcinoma network by observing co-expression correlations, regulatory relations, and physical binding interactions. Hub nodes in this three-layer network were selected using a heterogeneous random walk with random jump procedure. We exploited local composite modules around the hub nodes having high overlay with cancer-specific pathways, and investigated their genes showing a different expressional pattern in the tumor progression. These genes were examined for survival effects on the patient's lifespan, and those with significant impacts were selected as potential candidate biomarkers. Results suggest that identified genes indicate noteworthy importance in the carcinogenesis of the colon.

Characterizing and Comparing Phylogenetic Trait Data from Their Normalized Laplacian Spectrum

The dissection of the mode and tempo of phenotypic evolution is integral to our understanding of global biodiversity. Our ability to infer patterns of phenotypes across phylogenetic clades is essential to how we infer the macroevolutionary processes governing those patterns. Many methods are already available for fitting models of phenotypic evolution to data. However, there is currently no comprehensive nonparametric framework for characterizing and comparing patterns of phenotypic evolution. Here, we build on a recently introduced approach for using the phylogenetic spectral density profile (SDP) to compare and characterize patterns of phylogenetic diversification, in order to provide a framework for nonparametric analysis of phylogenetic trait data. We show how to construct the SDP of trait data on a phylogenetic tree from the normalized graph Laplacian. We demonstrate on simulated data the utility of the SDP to successfully cluster phylogenetic trait data into meaningful groups and to characterize the phenotypic patterning within those groups. We furthermore demonstrate how the SDP is a powerful tool for visualizing phenotypic space across traits and for assessing whether distinct trait evolution models are distinguishable on a given empirical phylogeny. We illustrate the approach in two empirical data sets: a comprehensive data set of traits involved in song, plumage, and resource-use in tanagers, and a high-dimensional data set of endocranial landmarks in New World monkeys. Considering the proliferation of morphometric and molecular data collected across the tree of life, we expect this approach will benefit big data analyses requiring a comprehensive and intuitive framework.

Multilayer network analysis of miRNA and protein expression profiles in breast cancer patients

MiRNAs and proteins play important roles in different stages of breast tumor development and serve as biomarkers for the early diagnosis of breast cancer. A new algorithm that combines machine learning algorithms and multilayer complex network analysis is hereby proposed to explore the potential diagnostic values of miRNAs and proteins. XGBoost and random forest algorithms were employed to screen the most important miRNAs and proteins. Maximal information coefficient was applied to assess intralayer and interlayer connection. A multilayer complex network was constructed to identify miRNAs and proteins that could serve as biomarkers for breast cancer. Proteins and miRNAs that are nodes in the network were subsequently categorized into two network layers considering their distinct functions. The betweenness centrality was used as the first measurement of the importance of the nodes within each single layer. The degree of the nodes was chosen as the second measurement to map their signalling pathways. By combining these two measurements into one score and comparing the difference of the same candidate between normal tissue and cancer tissue, this novel multilayer network analysis could be applied to successfully identify molecules associated with breast cancer.

Network spectra for drug-target identification in complex diseases: new guns against old foes

The fundamental understanding of altered complex molecular interactions in a diseased condition is the key to its cure. The overall functioning of these molecules is kind of jugglers play in the cell orchestra and to anticipate these relationships among the molecules is one of the greatest challenges in modern biology and medicine. Network science turned out to be providing a successful and simple platform to understand complex interactions among healthy and diseased tissues. Furthermore, much information about the structure and dynamics of a network is concealed in the eigenvalues of its adjacency matrix. In this review, we illustrate rapid advancements in the field of network science in combination with spectral graph theory that enables us to uncover the complexities of various diseases. Interpretations laid by network science approach have solicited insights into molecular relationships and have reported novel drug targets and biomarkers in various complex diseases.

Interaction paths promote module integration and network-level robustness of spliceosome to cascading effects

The functionality of distinct types of protein networks depends on the patterns of protein-protein interactions. A problem to solve is understanding the fragility of protein networks to predict system malfunctioning due to mutations and other errors. Spectral graph theory provides tools to understand the structural and dynamical properties of a system based on the mathematical properties of matrices associated with the networks. We combined two of such tools to explore the fragility to cascading effects of the network describing protein interactions within a key macromolecular complex, the spliceosome. Using S. cerevisiae as a model system we show that the spliceosome network has more indirect paths connecting proteins than random networks. Such multiplicity of paths may promote routes to cascading effects to propagate across the network. However, the modular network structure concentrates paths within modules, thus constraining the propagation of such cascading effects, as indicated by analytical results from the spectral graph theory and by numerical simulations of a minimal mathematical model parameterized with the spliceosome network. We hypothesize that the concentration of paths within modules favors robustness of the spliceosome against failure, but may lead to a higher vulnerability of functional subunits, which may affect the temporal assembly of the spliceosome. Our results illustrate the utility of spectral graph theory for identifying fragile spots in biological systems and predicting their implications.

Random Matrix Analysis for Gene Interaction Networks in Cancer Cells

Investigations of topological uniqueness of gene interaction networks in cancer cells are essential for understanding the disease. Although cancer is considered to originate from the topological alteration of a huge molecular interaction network in cellular systems, the theoretical study to investigate such complex networks is still insufficient. It is necessary to predict the behavior of a huge complex interaction network from the behavior of a finite size network. Based on the random matrix theory, we study the distribution of the nearest neighbor level spacings P(s) of interaction matrices of gene networks in human cancer cells. The interaction matrices are computed using the Cancer Network Galaxy (TCNG) database which is a repository of gene interactions inferred by a Bayesian network model. 256 NCBI GEO entries regarding gene expressions in human cancer cells have been used for the inference. We observe the Wigner distribution of P(s) when the gene networks are dense networks that have more than ~38,000 edges. In the opposite case, when the networks have smaller numbers of edges, the distribution P(s) becomes the Poisson distribution. We investigate relevance of P(s) both to the sparseness of the networks and to edge frequency factor which is the reliance (likelihood) of the inferred gene interactions.

Clustering multilayer omics data using MuNCut

BACKGROUND

Omics profiling is now a routine component of biomedical studies. In the analysis of omics data, clustering is an essential step and serves multiple purposes including for example revealing the unknown functionalities of omics units, assisting dimension reduction in outcome model building, and others. In the most recent omics studies, a prominent trend is to conduct multilayer profiling, which collects multiple types of genetic, genomic, epigenetic and other measurements on the same subjects. In the literature, clustering methods tailored to multilayer omics data are still limited. Directly applying the existing clustering methods to multilayer omics data and clustering each layer first and then combing across layers are both "suboptimal" in that they do not accommodate the interconnections within layers and across layers in an informative way.

METHODS

In this study, we develop the MuNCut (Multilayer NCut) clustering approach. It is tailored to multilayer omics data and sufficiently accounts for both across- and within-layer connections. It is based on the novel NCut technique and also takes advantages of regularized sparse estimation. It has an intuitive formulation and is computationally very feasible. To facilitate implementation, we develop the function muncut in the R package NcutYX.

RESULTS

Under a wide spectrum of simulation settings, it outperforms competitors. The analysis of TCGA (The Cancer Genome Atlas) data on breast cancer and cervical cancer shows that MuNCut generates biologically meaningful results which differ from those using the alternatives.

CONCLUSIONS

We propose a more effective clustering analysis of multiple omics data. It provides a new venue for jointly analyzing genetic, genomic, epigenetic and other measurements.

Dysregulated expression of homeobox family genes may influence survival outcomes of patients with epithelial ovarian cancer: analysis of data from The Cancer Genome Atlas

Homeobox (HOX) family genes encode key transcription factors for embryogenesis and may be correlated with carcinogenesis. The aim of this study was to elucidate whether aberrant expression of HOX genes influences outcomes in epithelial ovarian cancer (EOC). Gene expression data and clinicopathologic information from 630 patients with EOC were downloaded from The Cancer Genome Atlas database. We explored correlations between expression levels of HOX gene family members and clinicopathological variables. Higher expression of HOXA1, A4, A5, A7, A10, A11, B13, C13, D1, and D3 was associated with advanced FIGO stage. Suboptimal residual disease after debulking surgery was significantly correlated with higher expression of HOXB9, B13, and C13. Additionally, patients with high expression of HOXC6 and C11 were significantly more likely to have poor performance status. Overall survival was significantly shorter in patients with high, rather than low, expression of two HOX genes (HOXA10 and B3), and significantly longer in patients with high rather than low HOXC5 expression. Dysregulated expression of the HOXA10, B3, and C5 was significantly correlated with overall survival in EOC patients. HOX gene expression levels are potentially useful as a prognostic indicator in EOC, and HOX genes may represent a novel and promising target for anticancer therapeutics.