How scale-free are biological networks

SGCP: a spectral self-learning method for clustering genes in co-expression networks

BACKGROUND

A widely used approach for extracting information from gene expression data employs the construction of a gene co-expression network and the subsequent computational detection of gene clusters, called modules. WGCNA and related methods are the de facto standard for module detection. The purpose of this work is to investigate the applicability of more sophisticated algorithms toward the design of an alternative method with enhanced potential for extracting biologically meaningful modules.

RESULTS

We present self-learning gene clustering pipeline (SGCP), a spectral method for detecting modules in gene co-expression networks. SGCP incorporates multiple features that differentiate it from previous work, including a novel step that leverages gene ontology (GO) information in a self-leaning step. Compared with widely used existing frameworks on 12 real gene expression datasets, we show that SGCP yields modules with higher GO enrichment. Moreover, SGCP assigns highest statistical importance to GO terms that are mostly different from those reported by the baselines.

CONCLUSION

Existing frameworks for discovering clusters of genes in gene co-expression networks are based on relatively simple algorithmic components. SGCP relies on newer algorithmic techniques that enable the computation of highly enriched modules with distinctive characteristics, thus contributing a novel alternative tool for gene co-expression analysis.

Reassessing the modularity of gene co-expression networks using the Stochastic Block Model

Finding communities in gene co-expression networks is a common first step toward extracting biological insight from these complex datasets. Most community detection algorithms expect genes to be organized into assortative modules, that is, groups of genes that are more associated with each other than with genes in other groups. While it is reasonable to expect that these modules exist, using methods that assume they exist a priori is risky, as it guarantees that alternative organizations of gene interactions will be ignored. Here, we ask: can we find meaningful communities without imposing a modular organization on gene co-expression networks, and how modular are these communities? For this, we use a recently developed community detection method, the weighted degree corrected stochastic block model (SBM), that does not assume that assortative modules exist. Instead, the SBM attempts to efficiently use all information contained in the co-expression network to separate the genes into hierarchically organized blocks of genes. Using RNAseq gene expression data measured in two tissues derived from an outbred population of Drosophila melanogaster, we show that (a) the SBM is able to find ten times as many groups as competing methods, that (b) several of those gene groups are not modular, and that (c) the functional enrichment for non-modular groups is as strong as for modular communities. These results show that the transcriptome is structured in more complex ways than traditionally thought and that we should revisit the long-standing assumption that modularity is the main driver of the structuring of gene co-expression networks.

A modeling framework for detecting and leveraging node-level information in Bayesian network inference

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

Reassessing the modularity of gene co-expression networks using the Stochastic Block Model

Finding communities in gene co-expression networks is a common first step toward extracting biological insight from these complex datasets. Most community detection algorithms expect genes to be organized into assortative modules, that is, groups of genes that are more associated with each other than with genes in other groups. While it is reasonable to expect that these modules exist, using methods that assume they exist a priori is risky, as it guarantees that alternative organizations of gene interactions will be ignored. Here, we ask: can we find meaningful communities without imposing a modular organization on gene co-expression networks, and how modular are these communities? For this, we use a recently developed community detection method, the weighted degree corrected stochastic block model (SBM), that does not assume that assortative modules exist. Instead, the SBM attempts to efficiently use all information contained in the co-expression network to separate the genes into hierarchically organized blocks of genes. Using RNA-seq gene expression data measured in two tissues derived from an outbred population of Drosophila melanogaster, we show that (a) the SBM is able to find ten times as many groups as competing methods, that (b) several of those gene groups are not modular, and that (c) the functional enrichment for non-modular groups is as strong as for modular communities. These results show that the transcriptome is structured in more complex ways than traditionally thought and that we should revisit the long-standing assumption that modularity is the main driver of the structuring of gene co-expression networks.

The Enrichment of miRNA-Targeted mRNAs in Translationally Less Active over More Active Polysomes

miRNAs moderately inhibit the translation and enhance the degradation of their target mRNAs via cognate binding sites located predominantly in the 3'-untranslated regions (UTR). Paradoxically, miRNA targets are also polysome-associated. We studied the polysome association by the comparative translationally less-active light- and more-active heavy-polysome profiling of a wild type (WT) human cell line and its isogenic mutant (MT) with a disrupted DICER1 gene and, thus, mature miRNA production. As expected, the open reading frame (ORF) length is a major determinant of light- to heavy-polysome mRNA abundance ratios, but is rendered less powerful in WT than in MT cells by miRNA-regulatory activities. We also observed that miRNAs tend to target mRNAs with longer ORFs, and that adjusting the mRNA abundance ratio with the ORF length improves its correlation with the 3'-UTR miRNA-binding-site count. In WT cells, miRNA-targeted mRNAs exhibit higher abundance in light relative to heavy polysomes, i.e., light-polysome enrichment. In MT cells, the DICER1 disruption not only significantly abrogated the light-polysome enrichment, but also narrowed the mRNA abundance ratio value range. Additionally, the abrogation of the enrichment due to the DICER1 gene disruption, i.e., the decreases of the ORF-length-adjusted mRNA abundance ratio from WT to MT cells, exhibits a nearly perfect linear correlation with the 3'-UTR binding-site count. Transcription factors and protein kinases are the top two most enriched mRNA groups. Taken together, the results provide evidence for the light-polysome enrichment of miRNA-targeted mRNAs to reconcile polysome association and moderate translation inhibition, and that ORF length is an important, though currently under-appreciated, transcriptome regulation parameter.

Decision tree classifier based on topological characteristics of subgraph for the mining of protein complexes from large scale PPI networks

The growing accessibility of large-scale protein interaction data demands extensive research to understand cell organization and its functioning at the network level. Bioinformatics and data mining researchers have extensively studied network clustering to examine the structural and operational features of protein protein interaction (PPI) networks. Clustering PPI networks has proven useful in numerous research over the past two decades for identifying functional modules, understanding the roles of previously unknown proteins, and other purposes. Protein complexes represent one of the essential cellular components for creating biological activities. Inferring protein complexes has been made more accessible by experimental approaches. We offer a novel method that integrates the classification model with local topological data, making it more reliable and efficient. This article describes a decision tree classifier based on topological characteristics of the subgraph for mining protein complexes. The proposed graph-based algorithm is an effective and efficient way to identify protein complexes from large-scale PPI networks. The performance of the proposed algorithm is observed in protein-protein interaction networks of yeast and human in the Database of Interacting Proteins (DIP) and the Biological General Repository for Interaction Datasets (BioGRID) using widely accepted benchmark protein complexes from the comprehensive resource of mammalian protein complexes (CORUM) and the comprehensive catalogue of yeast protein complexes (CYC2008). The outcomes demonstrate that our method can outperform the best-performing supervised, semi-supervised, and unsupervised approaches to detecting protein complexes.

The cluster D-trace loss for differential network analysis

A growing literature suggests that gene expression can be greatly altered in disease conditions, and identifying those changes will improve the understanding of complex diseases such as cancers or diabetes. A prevailing direction in the analysis of gene expression studies the changes in gene pathways which include sets of related genes. Therefore, introducing structured exploration to differential analysis of gene expression networks may lead to meaningful discoveries. The topic of this paper is differential network analysis, which focuses on capturing the differences between two or more precision matrices. We discuss the connection between the thresholding method and the D-trace loss method on differential network analysis in the case that the precision matrices share the common connected components. Based on this connection, we further propose the cluster D-trace loss method which directly estimates the differential network and achieves model selection consistency. Simulation studies demonstrate its improved performance and computational efficiency. Finally, the usefulness of our proposed estimator is demonstrated by a real-data analysis on non-small cell lung cancer.

Network and functional analyses of differentially expressed genes in gastric cancer provide new biomarkers associated with disease pathogenesis

BACKGROUND

Gastric cancer is a dominant source of cancer-related death around the globe and a serious threat to human health. However, there are very few practical diagnostic approaches and biomarkers for the treatment of this complex disease.

METHODS

This study aimed to evaluate the association between differentially expressed genes (DEGs), which may function as potential biomarkers, and the diagnosis and treatment of gastric cancer (GC). We constructed a protein-protein interaction network from DEGs followed by network clustering. Members of the two most extensive modules went under the enrichment analysis. We introduced a number of hub genes and gene families playing essential roles in oncogenic pathways and the pathogenesis of gastric cancer. Enriched terms for Biological Process were obtained from the "GO" repository.

RESULTS

A total of 307 DEGs were identified between GC and their corresponding normal adjacent tissue samples in GSE63089 datasets, including 261 upregulated and 261 downregulated genes. The top five hub genes in the PPI network were CDK1, CCNB1, CCNA2, CDC20, and PBK. They are involved in focal adhesion formation, extracellular matrix remodeling, cell migration, survival signals, and cell proliferation. No significant survival result was found for these hub genes.

CONCLUSIONS

Using comprehensive analysis and bioinformatics methods, important key pathways and pivotal genes related to GC progression were identified, potentially informing further studies and new therapeutic targets for GC treatment.

Co-expression network of heat-response transcripts: A glimpse into how splicing factors impact rice basal thermotolerance

To identify novel solutions to improve rice yield under rising temperatures, molecular components of thermotolerance must be better understood. Alternative splicing (AS) is a major post-transcriptional mechanism impacting plant tolerance against stresses, including heat stress (HS). AS is largely regulated by splicing factors (SFs) and recent studies have shown their involvement in temperature response. However, little is known about the splicing networks between SFs and AS transcripts in the HS response. To expand this knowledge, we constructed a co-expression network based on a publicly available RNA-seq dataset that explored rice basal thermotolerance over a time-course. Our analyses suggest that the HS-dependent control of the abundance of specific transcripts coding for SFs might explain the widespread, coordinated, complex, and delicate AS regulation of critical genes during a plant's inherent response to extreme temperatures. AS changes in these critical genes might affect many aspects of plant biology, from organellar functions to cell death, providing relevant regulatory candidates for future functional studies of basal thermotolerance.

Investigating the Complexity of Gene Co-expression Estimation for Single-cell Data

With the rapid advance of single-cell RNA sequencing (scRNA-seq) technology, understanding biological processes at a more refined single-cell level is becoming possible. Gene co-expression estimation is an essential step in this direction. It can annotate functionalities of unknown genes or construct the basis of gene regulatory network inference. This study thoroughly tests the existing gene co-expression estimation methods on simulation datasets with known ground truth co-expression networks. We generate these novel datasets using two simulation processes that use the parameters learned from the experimental data. We demonstrate that these simulations better capture the underlying properties of the real-world single-cell datasets than previously tested simulations for the task. Our performance results on tens of simulated and eight experimental datasets show that all methods produce estimations with a high false discovery rate potentially caused by high-sparsity levels in the data. Finally, we find that commonly used pre-processing approaches, such as normalization and imputation, do not improve the co-expression estimation. Overall, our benchmark setup contributes to the co-expression estimator development, and our study provides valuable insights for the community of single-cell data analyses.

The pathophysiology of major depressive disorder through the lens of systems biology: Network analysis of the psycho-immune-neuroendocrine physiome

BACKGROUND/AIMS

The psycho-immune-neuroendocrine (PINE) network is a predominantly physiological (metabolomic) model constructed from the literature, inter-linking multiple biological processes associated with major depressive disorder (MDD), thereby integrating putative mechanistic pathways for MDD into a single network.

MATERIAL AND METHODS

Previously published metabolomic pathways for the PINE network based on literature searches conducted in 1991-2021 were used to construct an edge table summarizing all physiological pathways in pairs of origin nodes and target nodes. The Gephi software program was used to calculate network metrics from the edge table, including total degree and centrality measures, to ascertain key network nodes and construct a directed network graph.

RESULTS

An edge table and directional network graph of physiological relationships in the PINE network is presented. The network has properties consistent with complex biological systems, with analysis yielding key network nodes comprising pro-inflammatory cytokines (TNF- α, IL6 and IL1), glucocorticoids and corticotropin releasing hormone (CRH). These may represent central structural and regulatory elements in the context of MDD.

CONCLUSION

The identified hubs have a high degree of connection and are known to play roles in the progression from health to MDD. These nodes represent strategic targets for therapeutic intervention or prevention. Future work is required to build a weighted and dynamic simulation of the network PINE.

WINNER: A network biology tool for biomolecular characterization and prioritization

Background and contribution

In network biology, molecular functions can be characterized by network-based inference, or “guilt-by-associations.” PageRank-like tools have been applied in the study of biomolecular interaction networks to obtain further the relative significance of all molecules in the network. However, there is a great deal of inherent noise in widely accessible data sets for gene-to-gene associations or protein-protein interactions. How to develop robust tests to expand, filter, and rank molecular entities in disease-specific networks remains an ad hoc data analysis process.

Results

We describe a new biomolecular characterization and prioritization tool called Weighted In-Network Node Expansion and Ranking (WINNER). It takes the input of any molecular interaction network data and generates an optionally expanded network with all the nodes ranked according to their relevance to one another in the network. To help users assess the robustness of results, WINNER provides two different types of statistics. The first type is a node-expansion p-value, which helps evaluate the statistical significance of adding “non-seed” molecules to the original biomolecular interaction network consisting of “seed” molecules and molecular interactions. The second type is a node-ranking p-value, which helps evaluate the relative statistical significance of the contribution of each node to the overall network architecture. We validated the robustness of WINNER in ranking top molecules by spiking noises in several network permutation experiments. We have found that node degree–preservation randomization of the gene network produced normally distributed ranking scores, which outperform those made with other gene network randomization techniques. Furthermore, we validated that a more significant proportion of the WINNER-ranked genes was associated with disease biology than existing methods such as PageRank. We demonstrated the performance of WINNER with a few case studies, including Alzheimer's disease, breast cancer, myocardial infarctions, and Triple negative breast cancer (TNBC). In all these case studies, the expanded and top-ranked genes identified by WINNER reveal disease biology more significantly than those identified by other gene prioritizing software tools, including Ingenuity Pathway Analysis (IPA) and DiAMOND.

Conclusion

WINNER ranking strongly correlates to other ranking methods when the network covers sufficient node and edge information, indicating a high network quality. WINNER users can use this new tool to robustly evaluate a list of candidate genes, proteins, or metabolites produced from high-throughput biology experiments, as long as there is available gene/protein/metabolic network information.

The Analysis of the Power Law Feature in Complex Networks

Consensus about the universality of the power law feature in complex networks is experiencing widespread challenges. In this paper, we propose a generic theoretical framework in order to examine the power law property. First, we study a class of birth-and-death networks that are more common than BA networks in the real world, and then we calculate their degree distributions; the results show that the tails of their degree distributions exhibit a distinct power law feature. Second, we suggest that in the real world two important factors-network size and node disappearance probability-will affect the analysis of power law characteristics in observation networks. Finally, we suggest that an effective way of detecting the power law property is to observe the asymptotic (limiting) behavior of the degree distribution within its effective intervals.

Complex Prediction in Large PPI Networks Using Expansion and Stripe of Core Cliques

The widespread availability and importance of large-scale protein-protein interaction (PPI) data demand a flurry of research efforts to understand the organisation of a cell and its functionality by analysing these data at the network level. In the bioinformatics and data mining fields, network clustering acquired a lot of attraction to examine a PPI network's topological and functional aspects. The clustering of PPI networks has been proven to be an excellent method for discovering functional modules, disclosing functions of unknown proteins, and other tasks in numerous research over the last decade. This research proposes a unique graph mining approach to detect protein complexes using dense neighbourhoods (highly connected regions) in an interaction graph. Our technique first finds size-3 cliques associated with each edge (protein interaction), and then these core cliques are expanded to form high-density subgraphs. Loosely connected proteins are stripped out from these subgraphs to produce a potential protein complex. Finally, the redundancy is removed based on the Jaccard coefficient. Computational results are presented on the yeast and human protein interaction dataset to highlight our proposed technique's efficiency. Predicted protein complexes of the proposed approach have a significantly higher score of similarity to those used as gold standards in the CYC-2008 and CORUM benchmark databases than other existing approaches.

Benchmarking imputation methods for network inference using a novel method of synthetic scRNA-seq data generation

Background

Single cell RNA-sequencing (scRNA-seq) has very rapidly become the new workhorse of modern biology providing an unprecedented global view on cellular diversity and heterogeneity. In particular, the structure of gene-gene expression correlation contains information on the underlying gene regulatory networks. However, interpretation of scRNA-seq data is challenging due to specific experimental error and biases that are unique to this kind of data including drop-out (or technical zeros).

Methods

To deal with this problem several methods for imputation of zeros for scRNA-seq have been developed. However, it is not clear how these processing steps affect inference of genetic networks from single cell data. Here, we introduce Biomodelling.jl, a tool for generation of synthetic scRNA-seq data using multiscale modelling of stochastic gene regulatory networks in growing and dividing cells.

Results

Our tool produces realistic transcription data with a known ground truth network topology that can be used to benchmark different approaches for gene regulatory network inference. Using this tool we investigate the impact of different imputation methods on the performance of several network inference algorithms.

Conclusions

Biomodelling.jl provides a versatile and useful tool for future development and benchmarking of network inference approaches using scRNA-seq data.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04778-9

Identifying candidate genes and drug targets for Alzheimer's disease by an integrative network approach using genetic and brain region-specific proteomic data

Genome-wide association studies (GWAS) have identified more than 75 genetic variants associated with Alzheimer's disease (ad). However, how these variants function and impact protein expression in brain regions remain elusive. Large-scale proteomic datasets of ad postmortem brain tissues have become available recently. In this study, we used these datasets to investigate brain region-specific molecular pathways underlying ad pathogenesis and explore their potential drug targets. We applied our new network-based tool, Edge-Weighted Dense Module Search of GWAS (EW_dmGWAS), to integrate ad GWAS statistics of 472 868 individuals with proteomic profiles from two brain regions from two large-scale ad cohorts [parahippocampal gyrus (PHG), sample size n = 190; dorsolateral prefrontal cortex (DLPFC), n = 192]. The resulting network modules were evaluated using a scale-free network index, followed by a cross-region consistency evaluation. Our EW_dmGWAS analyses prioritized 52 top module genes (TMGs) specific in PHG and 58 TMGs in DLPFC, of which four genes (CLU, PICALM, PRRC2A and NDUFS3) overlapped. Those four genes were significantly associated with ad (GWAS gene-level false discovery rate < 0.05). To explore the impact of these genetic components on TMGs, we further examined their differentially co-expressed genes at the proteomic level and compared them with investigational drug targets. We pinpointed three potential drug target genes, APP, SNCA and VCAM1, specifically in PHG. Gene set enrichment analyses of TMGs in PHG and DLPFC revealed region-specific biological processes, tissue-cell type signatures and enriched drug signatures, suggesting potential region-specific drug repurposing targets for ad.

GURFAP: A Platform for Gene Function Analysis in Glycyrrhiza Uralensis

Glycyrrhiza uralensis (Licorice), which belongs to Leguminosae, is famous for the function of pharmacologic action and natural sweetener with its dried roots and rhizomes. In recent years, the whole-genome sequence of G. uralensis has been completed, which will help to lay the foundation for the study of gene function. Here, we integrated the available genomic and transcriptomic data of G. uralensis and constructed the G. uralensis gene co-expression network. We then annotated gene functions of G. uralensis via aligning with public databases. Furthermore, gene families of G. uralensis were predicted by tools including iTAK (Plant Transcription factor and Protein kinase Identifier and Classifier), HMMER (hidden Markov models), InParanoid, and PfamScan. Finally, we constructed a platform for gene function analysis in G. uralensis (GURFAP, www.gzybioinfoormatics.cn/GURFAP). For analyzed and predicted gene function, we introduced various tools including BLAST (Basic local alignment search tool), GSEA (Gene set enrichment analysis), Motif, Heatmap, and JBrowse. Our analysis based on this platform indicated that the biosynthesis of glycyrrhizin might be regulated by MYB and bHLH. We also took CYP88D6, CYP72A154, and bAS gene in the synthesis pathway of glycyrrhizin as examples to demonstrate the reliability and availability of our platform. Our platform GURFAP will provide convenience for researchers to mine the gene function of G. uralensis and thus discover more key genes involved in the biosynthetic pathway of active ingredients.

Curation, inference, and assessment of a globally reconstructed gene regulatory network for Streptomyces coelicolor

Streptomyces coelicolor A3(2) is a model microorganism for the study of Streptomycetes, antibiotic production, and secondary metabolism in general. Even though S. coelicolor has an outstanding variety of regulators among bacteria, little effort to globally study its transcription has been made. We manually curated 29 years of literature and databases to assemble a meta-curated experimentally-validated gene regulatory network (GRN) with 5386 genes and 9707 regulatory interactions (~ 41% of the total expected interactions). This provides the most extensive and up-to-date reconstruction available for the regulatory circuitry of this organism. Only ~ 6% (534/9707) are supported by experiments confirming the binding of the transcription factor to the upstream region of the target gene, the so-called “strong” evidence. While for the remaining interactions there is no confirmation of direct binding. To tackle network incompleteness, we performed network inference using several methods (including two proposed here) for motif identification in DNA sequences and GRN inference from transcriptomics. Further, we contrasted the structural properties and functional architecture of the networks to assess the reliability of the predictions, finding the inference from DNA sequence data to be the most trustworthy approach. Finally, we show two applications of the inferred and the curated networks. The inference allowed us to propose novel transcription factors for the key Streptomyces antibiotic regulatory proteins (SARPs). The curated network allowed us to study the conservation of the system-level components between S. coelicolor and Corynebacterium glutamicum. There we identified the basal machinery as the common signature between the two organisms. The curated networks were deposited in Abasy Atlas (https://abasy.ccg.unam.mx/) while the inferences are available as Supplementary Material.

Three topological features of regulatory networks control life-essential and specialized subsystems

Gene regulatory networks (GRNs) play key roles in development, phenotype plasticity, and evolution. Although graph theory has been used to explore GRNs, associations amongst topological features, transcription factors (TFs), and systems essentiality are poorly understood. Here we sought the relationship amongst the main GRN topological features that influence the control of essential and specific subsystems. We found that the K_nn, page rank, and degree are the most relevant GRN features: the ones are conserved along the evolution and are also relevant in pluripotent cells. Interestingly, life-essential subsystems are governed mainly by TFs with intermediary K_nn and high page rank or degree, whereas specialized subsystems are mainly regulated by TFs with low K_nn. Hence, we suggest that the high probability of TFs be toured by a random signal, and the high probability of the signal propagation to target genes ensures the life-essential subsystems' robustness. Gene/genome duplication is the main evolutionary process to rise K_nn as the most relevant feature. Herein, we shed light on unexplored topological GRN features to assess how they are related to subsystems and how the duplications shaped the regulatory systems along the evolution. The classification model generated can be found here: https://github.com/ivanrwolf/NoC/ .

Emergency of Tsallis statistics in fractal networks

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.

LjaFGD: Lonicera japonica functional genomics database

Lonicera japonica Thunb., a traditional Chinese herb, has been used for treating human diseases for thousands of years. Recently, the genome of L. japonica has been decoded, providing valuable information for research into gene function. However, no comprehensive database for gene functional analysis and mining is available for L. japonica. We therefore constructed LjaFGD (www.gzybioinformatics.cn/LjaFGD and bioinformatics.cau.edu.cn/LjaFGD), a database for analyzing and comparing gene function in L. japonica. We constructed a gene co-expression network based on 77 RNA-seq samples, and then annotated genes of L. japonica by alignment against protein sequences from public databases. We also introduced several tools for gene functional analysis, including Blast, motif analysis, gene set enrichment analysis, heatmap analysis, and JBrowse. Our co-expression network revealed that MYB and WRKY transcription factor family genes were co-expressed with genes encoding key enzymes in the biosynthesis of chlorogenic acid and luteolin in L. japonica. We used flavonol synthase 1 (LjFLS1) as an example to show the reliability and applicability of our database. LjaFGD and its various associated tools will provide researchers with an accessible platform for retrieving functional information on L. japonica genes to further biological discovery.

Unveiling the Pathogenesis of Psychiatric Disorders Using Network Models

Psychiatric disorders are complex brain disorders with a high degree of genetic heterogeneity, affecting millions of people worldwide. Despite advances in psychiatric genetics, the underlying pathogenic mechanisms of psychiatric disorders are still largely elusive, which impedes the development of novel rational therapies. There has been accumulating evidence suggesting that the genetics of complex disorders can be viewed through an omnigenic lens, which involves contextualizing genes in highly interconnected networks. Thus, applying network-based multi-omics integration methods could cast new light on the pathophysiology of psychiatric disorders. In this review, we first provide an overview of the recent advances in psychiatric genetics and highlight gaps in translating molecular associations into mechanistic insights. We then present an overview of network methodologies and review previous applications of network methods in the study of psychiatric disorders. Lastly, we describe the potential of such methodologies within a multi-tissue, multi-omics approach, and summarize the future directions in adopting diverse network approaches.

SeqNet: An R Package for Generating Gene-Gene Networks and Simulating RNA-Seq Data

Gene expression data provide an abundant resource for inferring connections in gene regulatory networks. While methodologies developed for this task have shown success, a challenge remains in comparing the performance among methods. Gold-standard datasets are scarce and limited in use. And while tools for simulating expression data are available, they are not designed to resemble the data obtained from RNA-seq experiments. SeqNet is an R package that provides tools for generating a rich variety of gene network structures and simulating RNA-seq data from them. This produces in silico RNA-seq data for benchmarking and assessing gene network inference methods. The package is available on CRAN and on GitHub at https://github.com/tgrimes/SeqNet.

Systems Biomedicine of Primary and Metastatic Colorectal Cancer Reveals Potential Therapeutic Targets

Colorectal cancer (CRC) is one of the major causes of cancer deaths across the world. Patients' survival at time of diagnosis depends mainly on stage of the tumor. Therefore, understanding the molecular mechanisms from low-grade to high-grade stages of cancer that lead to cellular migration from one tissue/organ to another tissue/organ is essential for implementing therapeutic approaches. To this end, we performed a unique meta-analysis flowchart by identifying differentially expressed genes (DEGs) between normal, primary (primary sites), and metastatic samples (Colorectal metastatic lesions in liver and lung) in some Test datasets. DEGs were employed to construct a protein-protein interaction (PPI) network. A smaller network containing 39 DEGs was then extracted from the PPI network whose nodes expression induction or suppression alone or in combination with each other would inhibit tumor progression or metastasis. These DEGs were then verified by gene expression profiling, survival analysis, and multiple Validation datasets. We suggested for the first time that downregulation of mitochondrial genes, including ETHE1, SQOR, TST, and GPX3, would help colorectal cancer cells to produce more energy under hypoxic conditions through mechanisms that are different from "Warburg Effect". Augmentation of given antioxidants and repression of P4HA1 and COL1A2 genes could be a choice of CRC treatment. Moreover, promoting active GSK-3β together with expression control of EIF2B would prevent EMT. We also proposed that OAS1 expression enhancement can induce the anti-cancer effects of interferon-gamma, while suppression of CTSH hinders formation of focal adhesions. ATF5 expression suppression sensitizes cancer cells to anchorage-dependent death signals, while LGALS4 induction recovers cell-cell junctions. These inhibitions and inductions would be another combinatory mechanism that inhibits EMT and cell migration. Furthermore, expression inhibition of TMPO, TOP2A, RFC3, GINS1, and CKS2 genes could prevent tumor growth. Besides, TRIB3 suppression would be a promising target for anti-angiogenic therapy. SORD is a poorly studied enzyme in cancer, found to be upregulated in CRC. Finally, TMEM131 and DARS genes were identified in this study whose roles have never been interrogated in any kind of cancer, neither as a biomarker nor curative target. All the mentioned mechanisms must be further validated by experimental wet-lab techniques.

Discovery of network motifs based on induced subgraphs using a dynamic expansion tree

Biological networks are powerful representations of topological features in biological systems. Finding network motifs in biological networks is a computationally hard problem due to their huge size and abrupt increase of search space with the increase of motif size. Motivated by the computational challenges of network motif discovery and considering the importance of this topic, an efficient and scalable network motif discovery algorithm based on induced subgraphs in a dynamic expansion tree is proposed. This algorithm uses a pruning strategy to overcome the space limitation of the static expansion tree. The proposed algorithm can identify large network motifs up to size 15 by significantly reducing the computationally expensive subgraph isomorphism checks. Further, the present work avoids the unnecessary growth of patterns that do not have any statistical significance. The runtime performance of the proposed algorithm outperforms most of the existing algorithms for large network motifs.

Revisiting Parameter Estimation in Biological Networks: Influence of Symmetries

Graph models often give us a deeper understanding of real-world networks. In the case of biological networks they help in predicting the evolution and history of biomolecule interactions, provided we map properly real networks into the corresponding graph models. In this paper, we show that for biological graph models many of the existing parameter estimation techniques overlook the critical property of graph symmetry (also known formally as graph automorphisms), thus the estimated parameters give statistically insignificant results concerning the observed network. To demonstrate it and to develop accurate estimation procedures, we focus on the biologically inspired duplication-divergence model, and the up-to-date data of protein-protein interactions of seven species including human and yeast. Using exact recurrence relations of some prominent graph statistics, we devise a parameter estimation technique that provides the right order of symmetries and uses phylogenetically old proteins as the choice of seed graph nodes. We also find that our results are consistent with the ones obtained from maximum likelihood estimation (MLE). However, the MLE approach is significantly slower than our methods in practice.

New Cross-Talks between Pathways Involved in Grapevine Infection with 'Candidatus Phytoplasma solani' Revealed by Temporal Network Modelling

Understanding temporal biological phenomena is a challenging task that can be approached using network analysis. Here, we explored whether network reconstruction can be used to better understand the temporal dynamics of bois noir, which is associated with 'Candidatus Phytoplasma solani', and is one of the most widespread phytoplasma diseases of grapevine in Europe. We proposed a methodology that explores the temporal network dynamics at the community level, i.e., densely connected subnetworks. The methodology offers both insights into the functional dynamics via enrichment analysis at the community level, and analyses of the community dissipation, as a measure that accounts for community degradation. We validated this methodology with cases on experimental temporal expression data of uninfected grapevines and grapevines infected with 'Ca. P. solani'. These data confirm some known gene communities involved in this infection. They also reveal several new gene communities and their potential regulatory networks that have not been linked to 'Ca. P. solani' to date. To confirm the capabilities of the proposed method, selected predictions were empirically evaluated.

Scarcity of scale-free topology is universal across biochemical networks

Biochemical reactions underlie the functioning of all life. Like many examples of biology or technology, the complex set of interactions among molecules within cells and ecosystems poses a challenge for quantification within simple mathematical objects. A large body of research has indicated many real-world biological and technological systems, including biochemistry, can be described by power-law relationships between the numbers of nodes and edges, often described as "scale-free". Recently, new statistical analyses have revealed true scale-free networks are rare. We provide a first application of these methods to data sampled from across two distinct levels of biological organization: individuals and ecosystems. We analyze a large ensemble of biochemical networks including networks generated from data of 785 metagenomes and 1082 genomes (sampled from the three domains of life). The results confirm no more than a few biochemical networks are any more than super-weakly scale-free. Additionally, we test the distinguishability of individual and ecosystem-level biochemical networks and show there is no sharp transition in the structure of biochemical networks across these levels of organization moving from individuals to ecosystems. This result holds across different network projections. Our results indicate that while biochemical networks are not scale-free, they nonetheless exhibit common structure across different levels of organization, independent of the projection chosen, suggestive of shared organizing principles across all biochemical networks.

An Early Stage Researcher's Primer on Systems Medicine Terminology

Background: Systems Medicine is a novel approach to medicine, that is, an interdisciplinary field that considers the human body as a system, composed of multiple parts and of complex relationships at multiple levels, and further integrated into an environment. Exploring Systems Medicine implies understanding and combining concepts coming from diametral different fields, including medicine, biology, statistics, modeling and simulation, and data science. Such heterogeneity leads to semantic issues, which may slow down implementation and fruitful interaction between these highly diverse fields. Methods: In this review, we collect and explain more than100 terms related to Systems Medicine. These include both modeling and data science terms and basic systems medicine terms, along with some synthetic definitions, examples of applications, and lists of relevant references. Results: This glossary aims at being a first aid kit for the Systems Medicine researcher facing an unfamiliar term, where he/she can get a first understanding of them, and, more importantly, examples and references for digging into the topic.

Complexity and critical thresholds in the dynamics of visceral leishmaniasis

We study a general multi-host model of visceral leishmaniasis including both humans and animals, and where host and vector characteristics are captured via host competence along with vector biting preference. Additionally, the model accounts for spatial heterogeneity in human population and heterogeneity in biting behaviour of sandflies. We then use parameters for visceral leishmaniasis in the Indian subcontinent as an example and demonstrate that the model exhibits backward bifurcation, i.e. it has a human infection and a sandfly population threshold, characterized by a bi-stable region. These thresholds shift as a function of host competence, host population size, vector feeding preference, spatial heterogeneity, biting heterogeneity and control efforts. In particular, if control is applied through human treatment a new and lower human infection threshold is created, making elimination difficult to achieve, before eventually the human infection threshold no longer exists, making it impossible to control the disease by only reducing the infection levels below a certain threshold. A better strategy would be to reduce the human infection below a certain threshold potentially by early diagnosis, control animal population levels and keep the vector population under check. Spatial heterogeneity in human populations lowers the overall thresholds as a result of weak migration between patches.

How rare are power-law networks really?

The putative scale-free nature of real-world networks has generated a lot of interest in the past 20 years: if networks from many different fields share a common structure, then perhaps this suggests some underlying ‘network law’. Testing the degree distribution of networks for power-law tails has been a topic of considerable discussion. Ad hoc statistical methodology has been used both to discredit power-laws as well as to support them. This paper proposes a statistical testing procedure that considers the complex issues in testing degree distributions in networks that result from observing a finite network, having dependent degree sequences and suffering from insufficient power. We focus on testing whether the tail of the empirical degrees behaves like the tail of a de Solla Price model, a two-parameter power-law distribution. We modify the well-known Kolmogorov–Smirnov test to achieve even sensitivity along the tail, considering the dependence between the empirical degrees under the null distribution, while guaranteeing sufficient power of the test. We apply the method to many empirical degree distributions. Our results show that power-law network degree distributions are not rare, classifying almost 65% of the tested networks as having a power-law tail with at least 80% power.

Herding or wisdom of the crowd? Controlling efficiency in a partially rational financial market

Herding has often been blamed as one of the possible causes of market instabilities, ultimately yielding to bubbles and crushes. On the other hand, researchers hypothesized that financial systems may benefit from the so-called wisdom of the crowd. To solve this apparent dichotomy, we leverage a novel financial market model, where the agents form their expectations by combining their individual return estimation with the expectations of their neighbors. By establishing a link between herding, sociality, and market instabilities, we point out that the emergence of collective decisions in the market is not necessarily detrimental. Indeed, when all the agents tend to conform their expectations to those of one or few leaders, herding might dramatically reduce market efficiency. However, when each agent accounts for a plurality of opinions, thus following the wisdom of the crowd, market dynamics become efficient. Following these observations, we propose two alternative control strategies to reduce market instability and enhance its efficiency.

A biochemical network modeling of a whole-cell

All cellular processes can be ultimately understood in terms of respective fundamental biochemical interactions between molecules, which can be modeled as networks. Very often, these molecules are shared by more than one process, therefore interconnecting them. Despite this effect, cellular processes are usually described by separate networks with heterogeneous levels of detail, such as metabolic, protein-protein interaction, and transcription regulation networks. Aiming at obtaining a unified representation of cellular processes, we describe in this work an integrative framework that draws concepts from rule-based modeling. In order to probe the capabilities of the framework, we used an organism-specific database and genomic information to model the whole-cell biochemical network of the Mycoplasma genitalium organism. This modeling accounted for 15 cellular processes and resulted in a single component network, indicating that all processes are somehow interconnected. The topological analysis of the network showed structural consistency with biological networks in the literature. In order to validate the network, we estimated gene essentiality by simulating gene deletions and compared the results with experimental data available in the literature. We could classify 212 genes as essential, being 95% of them consistent with experimental results. Although we adopted a relatively simple organism as a case study, we suggest that the presented framework has the potential for paving the way to more integrated studies of whole organisms leading to a systemic analysis of cells on a broader scale. The modeling of other organisms using this framework could provide useful large-scale models for different fields of research such as bioengineering, network biology, and synthetic biology, and also provide novel tools for medical and industrial applications.

Assessment of the SRC Inhibition Role in the Efficacy of Breast Cancer Radiotherapy

Introduction: Radiotherapy (RT) is an effective therapeutic method for preventing the recurrence of breast cancer after surgery. The development and improvement of RT are of interest to scientists. Possible improvement of RT via study of dysregulated proteins of breast cancer cell line MDA-MB-231 which is exposed to 10 Gray (Gy) radiation is aim of this study. Methods: Using protein-protein interaction (PPI) network analysis by means of running Cytoscape software via the STRING database, the up-regulated proteins of MDA-MB-231 breast cancer cells irradiated by a single and fractioned 10 Gy 137Cs γ-radiation were analyzed. The network was analyzed by using the Network analyzer to characterize the central genes. The action map was mapped for the queried genes and the added neighbors via CluePedia-STRING ACTIONS-v10.5- 20.11.2017. Results: The 14 differentially expressed proteins (DEPs) plus 10 neighbors interacted to construct a network. Among the 14 queried DEPs, FN1, CSPG4, LRP1, GSN, RTN4, and CTSD were highlighted as a complex set in the analysis. The analysis revealed that SRC as an added neighbor was activated by the critical DEPs. The activation of other oncogenes like AKT1 was also determined. Conclusion: The results indicate that the inhibition of SRC activity or the inhibition of its activators is a useful function of breast cancer RT.

Are RNA networks scale-free?

A network is scale-free if its connectivity density function is proportional to a power-law distribution. It has been suggested that scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the presence of a few highly connected hub nodes and a large number of small-degree nodes may provide alternate paths between any two nodes on average—such robustness has been suggested in studies of metabolic networks, gene interaction networks and protein folding. A theoretical justification for why many networks appear to be scale-free has been provided by Barabási and Albert, who argue that expanding networks, in which new nodes are preferentially attached to highly connected nodes, tend to be scale-free. In this paper, we provide the first efficient algorithm to compute the connectivity density function for the ensemble of all homopolymer secondary structures of a user-specified length—a highly nontrivial result, since the exponential size of such networks precludes their enumeration. Since existent power-law fitting software, such as powerlaw, cannot be used to determine a power-law fit for our exponentially large RNA connectivity data, we also implement efficient code to compute the maximum likelihood estimate for the power-law scaling factor and associated Kolmogorov–Smirnov p value. Hypothesis tests strongly indicate that homopolymer RNA secondary structure networks are not scale-free; moreover, this appears to be the case for real (non-homopolymer) RNA networks.

MTGO-SC, A Tool to Explore Gene Modules in Single-Cell RNA Sequencing Data

The identification of functional modules in gene interaction networks is a key step in understanding biological processes. Network interpretation is essential for unveiling biological mechanisms, candidate biomarkers, or potential targets for drug discovery/repositioning. Plenty of biological module identification algorithms are available, although none is explicitly designed to perform the task on single-cell RNA sequencing (scRNA-seq) data. Here, we introduce MTGO-SC, an adaptation for scRNA-seq of our biological network module detection algorithm MTGO. MTGO-SC isolates gene functional modules by leveraging on both the network topological structure and the annotations characterizing the nodes (genes). These annotations are provided by an external source, such as databases and literature repositories (e.g., the Gene Ontology, Reactome). Thanks to the depth of single-cell data, it is possible to define one network for each cell cluster (typically, cell type or state) composing each sample, as opposed to traditional bulk RNA-seq, where the emerging gene network is averaged over the whole sample. MTGO-SC provides two complexity levels for interpretation: the gene-gene interaction and the intermodule interaction networks. MTGO-SC is versatile in letting the users define the rules to extract the gene network and integrated with the Seurat scRNA-seq analysis pipeline. MTGO-SC is available at https://github.com/ne1s0n/MTGOsc.

From Discrete to Continuous Modeling of Lymphocyte Development and Plasticity in Chronic Diseases

The molecular events leading to differentiation, development, and plasticity of lymphoid cells have been subject of intense research due to their key roles in multiple pathologies, such as lymphoproliferative disorders, tumor growth maintenance and chronic diseases. The emergent roles of lymphoid cells and the use of high-throughput technologies have led to an extensive accumulation of experimental data allowing the reconstruction of gene regulatory networks (GRN) by integrating biochemical signals provided by the microenvironment with transcriptional modules of lineage-specific genes. Computational modeling of GRN has been useful for the identification of molecular switches involved in lymphoid specification, prediction of microenvironment-dependent cell plasticity, and analyses of signaling events occurring downstream the activation of antigen recognition receptors. Among most common modeling strategies to analyze the dynamical behavior of GRN, discrete dynamic models are widely used for their capacity to capture molecular interactions when a limited knowledge of kinetic parameters is present. However, they are less powerful when modeling complex systems sensitive to biochemical gradients. To compensate it, discrete models may be transformed into regulatory networks that includes state variables and parameters varying within a continuous range. This approach is based on a system of differential equations dynamics with regulatory interactions described by fuzzy logic propositions. Here, we discuss the applicability of this method on modeling of development and plasticity processes of adaptive lymphocytes, and its potential implications in the study of pathological landscapes associated to chronic diseases.

BASiNET-BiologicAl Sequences NETwork: a case study on coding and non-coding RNAs identification

With the emergence of Next Generation Sequencing (NGS) technologies, a large volume of sequence data in particular de novo sequencing was rapidly produced at relatively low costs. In this context, computational tools are increasingly important to assist in the identification of relevant information to understand the functioning of organisms. This work introduces BASiNET, an alignment-free tool for classifying biological sequences based on the feature extraction from complex network measurements. The method initially transform the sequences and represents them as complex networks. Then it extracts topological measures and constructs a feature vector that is used to classify the sequences. The method was evaluated in the classification of coding and non-coding RNAs of 13 species and compared to the CNCI, PLEK and CPC2 methods. BASiNET outperformed all compared methods in all adopted organisms and datasets. BASiNET have classified sequences in all organisms with high accuracy and low standard deviation, showing that the method is robust and non-biased by the organism. The proposed methodology is implemented in open source in R language and freely available for download at https://cran.r-project.org/package=BASiNET.

FunCoup 4: new species, data, and visualization

This release of the FunCoup database (http://funcoup.sbc.su.se) is the fourth generation of one of the most comprehensive databases for genome-wide functional association networks. These functional associations are inferred via integrating various data types using a naive Bayesian algorithm and orthology based information transfer across different species. This approach provides high coverage of the included genomes as well as high quality of inferred interactions. In this update of FunCoup we introduce four new eukaryotic species: Schizosaccharomyces pombe, Plasmodium falciparum, Bos taurus, Oryza sativa and open the database to the prokaryotic domain by including networks for Escherichia coli and Bacillus subtilis. The latter allows us to also introduce a new class of functional association between genes - co-occurrence in the same operon. We also supplemented the existing classes of functional association: metabolic, signaling, complex and physical protein interaction with up-to-date information. In this release we switched to InParanoid v8 as the source of orthology and base for calculation of phylogenetic profiles. While populating all other evidence types with new data we introduce a new evidence type based on quantitative mass spectrometry data. Finally, the new JavaScript based network viewer provides the user an intuitive and responsive platform to further evaluate the results.

Testing Statistical Laws in Complex Systems

The availability of large datasets requires an improved view on statistical laws in complex systems, such as Zipf's law of word frequencies, the Gutenberg-Richter law of earthquake magnitudes, or scale-free degree distribution in networks. In this Letter, we discuss how the statistical analysis of these laws are affected by correlations present in the observations, the typical scenario for data from complex systems. We first show how standard maximum-likelihood recipes lead to false rejections of statistical laws in the presence of correlations. We then propose a conservative method (based on shuffling and undersampling the data) to test statistical laws and find that accounting for correlations leads to smaller rejection rates and larger confidence intervals on estimated parameters.

Scale-free networks are rare

Real-world networks are often claimed to be scale free, meaning that the fraction of nodes with degree k follows a power law k-α, a pattern with broad implications for the structure and dynamics of complex systems. However, the universality of scale-free networks remains controversial. Here, we organize different definitions of scale-free networks and construct a severe test of their empirical prevalence using state-of-the-art statistical tools applied to nearly 1000 social, biological, technological, transportation, and information networks. Across these networks, we find robust evidence that strongly scale-free structure is empirically rare, while for most networks, log-normal distributions fit the data as well or better than power laws. Furthermore, social networks are at best weakly scale free, while a handful of technological and biological networks appear strongly scale free. These findings highlight the structural diversity of real-world networks and the need for new theoretical explanations of these non-scale-free patterns.

An intersection network based on combining SNP coassociation and RNA coexpression networks for feed utilization traits in Japanese Black cattle

Genome-wide association studies (GWAS) of quantitative traits have detected numerous genetic associations, but they encounter difficulties in pinpointing prominent candidate genes and inferring gene networks. The present study used a systems genetics approach integrating GWAS results with external RNA-expression data to detect candidate gene networks in feed utilization and growth traits of Japanese Black cattle, which are matters of concern. A SNP coassociation network was derived from significant correlations between SNPs with effects estimated by GWAS across 7 phenotypic traits. The resulting network genes contained significant numbers of annotations related to the traits. Using bovine transcriptome data from a public database, an RNA coexpression network was inferred based on the similarity of expression patterns across different tissues. An intersection network was then generated by superimposing the SNP and RNA networks and extracting shared interactions. This intersection network contained 4 tissue-specific modules: nervous system, reproductive system, muscular system, and glands. To characterize the structure (topographical properties) of the 3 networks, their scale-free properties were evaluated, which revealed that the intersection network was the most scale-free. In the subnetwork containing the most connected transcription factors (URI1, ROCK2, and ETV6), most genes were widely expressed across tissues, and genes previously shown to be involved in the traits were found. Results indicated that the current approach might be used to construct a gene network that better reflects biological information, providing encouragement for the genetic dissection of economically important quantitative traits.

From hairballs to hypotheses-biological insights from microbial networks

Microbial networks are an increasingly popular tool to investigate microbial community structure, as they integrate multiple types of information and may represent systems-level behaviour. Interpreting these networks is not straightforward, and the biological implications of network properties are unclear. Analysis of microbial networks allows researchers to predict hub species and species interactions. Additionally, such analyses can help identify alternative community states and niches. Here, we review factors that can result in spurious predictions and address emergent properties that may be meaningful in the context of the microbiome. We also give an overview of studies that analyse microbial networks to identify new hypotheses. Moreover, we show in a simulation how network properties are affected by tool choice and environmental factors. For example, hub species are not consistent across tools, and environmental heterogeneity induces modularity. We highlight the need for robust microbial network inference and suggest strategies to infer networks more reliably.

A Bipartite Network and Resource Transfer-Based Approach to Infer lncRNA-Environmental Factor Associations

Phenotypes and diseases are often determined by the complex interactions between genetic factors and environmental factors (EFs). However, compared with protein-coding genes and microRNAs, there is a paucity of computational methods for understanding the associations between long non-coding RNAs (lncRNAs) and EFs. In this study, we focused on the associations between lncRNA and EFs. By using the common miRNA partners of any pair of lncRNA and EF, based on the competing endogenous RNA (ceRNA) hypothesis and the technique of resources transfer within the experimentally-supported lncRNA-miRNA and miRNA-EF association bipartite networks, we propose an algorithm for predicting new lncRNA-EF associations. Results show that, compared with another recently-proposed method, our approach is capable of predicting more credible lncRNA-EF associations. These results support the validity of our approach to predict biologically significant associations, which could lead to a better understanding of the molecular processes.

Pathways of topological rank analysis (PoTRA): a novel method to detect pathways involved in hepatocellular carcinoma

Complex diseases such as cancer are usually the result of a combination of environmental factors and one or several biological pathways consisting of sets of genes. Each biological pathway exerts its function by delivering signaling through the gene network. Theoretically, a pathway is supposed to have a robust topological structure under normal physiological conditions. However, the pathway's topological structure could be altered under some pathological condition. It is well known that a normal biological network includes a small number of well-connected hub nodes and a large number of nodes that are non-hubs. In addition, it is reported that the loss of connectivity is a common topological trait of cancer networks, which is an assumption of our method. Hence, from normal to cancer, the process of the network losing connectivity might be the process of disrupting the structure of the network, namely, the number of hub genes might be altered in cancer compared to that in normal or the distribution of topological ranks of genes might be altered. Based on this, we propose a new PageRank-based method called Pathways of Topological Rank Analysis (PoTRA) to detect pathways involved in cancer. We use PageRank to measure the relative topological ranks of genes in each biological pathway, then select hub genes for each pathway, and use Fisher's exact test to test if the number of hub genes in each pathway is altered from normal to cancer. Alternatively, if the distribution of topological ranks of gene in a pathway is altered between normal and cancer, this pathway might also be involved in cancer. Hence, we use the Kolmogorov-Smirnov test to detect pathways that have an altered distribution of topological ranks of genes between two phenotypes. We apply PoTRA to study hepatocellular carcinoma (HCC) and several subtypes of HCC. Very interestingly, we discover that all significant pathways in HCC are cancer-associated generally, while several significant pathways in subtypes of HCC are HCC subtype-associated specifically. In conclusion, PoTRA is a new approach to explore and discover pathways involved in cancer. PoTRA can be used as a complement to other existing methods to broaden our understanding of the biological mechanisms behind cancer at the system-level.