Revisiting the variation of clustering coefficient of biological networks suggests new modular structure

NJGCG: A node-based joint Gaussian copula graphical model for gene networks inference across multiple states

Inferring the interactions between genes is essential for understanding the mechanisms underlying biological processes. Gene networks will change along with the change of environment and state. The accumulation of gene expression data from multiple states makes it possible to estimate the gene networks in various states based on computational methods. However, most existing gene network inference methods focus on estimating a gene network from a single state, ignoring the similarities between networks in different but related states. Moreover, in addition to individual edges, similarities and differences between different networks may also be driven by hub genes. But existing network inference methods rarely consider hub genes, which affects the accuracy of network estimation. In this paper, we propose a novel node-based joint Gaussian copula graphical (NJGCG) model to infer multiple gene networks from gene expression data containing heterogeneous samples jointly. Our model can handle various gene expression data with missing values. Furthermore, a tree-structured group lasso penalty is designed to identify the common and specific hub genes in different gene networks. Simulation studies show that our proposed method outperforms other compared methods in all cases. We also apply NJGCG to infer the gene networks for different stages of differentiation in mouse embryonic stem cells and different subtypes of breast cancer, and explore changes in gene networks across different stages of differentiation or different subtypes of breast cancer. The common and specific hub genes in the estimated gene networks are closely related to stem cell differentiation processes and heterogeneity within breast cancers.

Node features of chromosome structure networks and their connections to genome annotation

The 3D conformations of chromosomes can encode biological significance, and the implications of such structures have been increasingly appreciated recently. Certain chromosome structural features, such as A/B compartmentalization, are frequently extracted from Hi-C pairwise genome contact information (physical association between different regions of the genome) and compared with linear annotations of the genome, such as histone modifications and lamina association. We investigate how additional properties of chromosome structure can be deduced using an abstract graph representation of the contact heatmap, and describe specific network properties that can have a strong connection with some of these biological annotations. We constructed chromosome structure networks (CSNs) from bulk Hi-C data and calculated a set of site-resolved (node-based) network properties. These properties are useful for characterizing certain aspects of chromosomal structure. We examined the ability of network properties to differentiate several scenarios, such as haploid vs diploid cells, partially inverted nuclei vs conventional architecture, depletion of chromosome architectural proteins, and structural changes during cell development. We also examined the connection between network properties and a series of other linear annotations, such as histone modifications and chromatin states including poised promoter and enhancer labels. We found that semi-local network properties exhibit greater capability in characterizing genome annotations compared to diffusive or ultra-local node features. For example, the local square clustering coefficient can be a strong classifier of lamina-associated domains. We demonstrated that network properties can be useful for highlighting large-scale chromosome structure differences that emerge in different biological situations.

Identifying Tumor-Associated Genes from Bilayer Networks of DNA Methylation Sites and RNAs

Network theory has attracted much attention from the biological community because of its high efficacy in identifying tumor-associated genes. However, most researchers have focused on single networks of single omics, which have less predictive power. With the available multiomics data, multilayer networks can now be used in molecular research. In this study, we achieved this with the construction of a bilayer network of DNA methylation sites and RNAs. We applied the network model to five types of tumor data to identify key genes associated with tumors. Compared with the single network, the proposed bilayer network resulted in more tumor-associated DNA methylation sites and genes, which we verified with prognostic and KEGG enrichment analyses.

Self-Organization and Information Processing: From Basic Enzymatic Activities to Complex Adaptive Cellular Behavior

One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation.

Structural and functional analyses of microbial metabolic networks reveal novel insights into genome-scale metabolic fluxes

We present here an integrated analysis of structures and functions of genome-scale metabolic networks of 17 microorganisms. Our structural analyses of these networks revealed that the node degree of each network, represented as a (simplified) reaction network, follows a power-law distribution, and the clustering coefficient of each network has a positive correlation with the corresponding node degree. Together, these properties imply that each network has exactly one large and densely connected subnetwork or core. Further analyses revealed that each network consists of three functionally distinct subnetworks: (i) a core, consisting of a large number of directed reaction cycles of enzymes for interconversions among intermediate metabolites; (ii) a catabolic module, with a largely layered structure consisting of mostly catabolic enzymes; (iii) an anabolic module with a similar structure consisting of virtually all anabolic genes; and (iv) the three subnetworks cover on average ∼56, ∼31 and ∼13% of a network's nodes across the 17 networks, respectively. Functional analyses suggest: (1) cellular metabolic fluxes generally go from the catabolic module to the core for substantial interconversions, then the flux directions to anabolic module appear to be determined by input nutrient levels as well as a set of precursors needed for macromolecule syntheses; and (2) enzymes in each subnetwork have characteristic ranges of kinetic parameters, suggesting optimized metabolic and regulatory relationships among the three subnetworks.

Inferring gene expression networks with hubs using a degree weighted Lasso approach

MOTIVATION

Genome-scale gene networks contain regulatory genes called hubs that have many interaction partners. These genes usually play an essential role in gene regulation and cellular processes. Despite recent advancements in high-throughput technology, inferring gene networks with hub genes from high-dimensional data still remains a challenging problem. Novel statistical network inference methods are needed for efficient and accurate reconstruction of hub networks from high-dimensional data.

RESULTS

To address this challenge we propose DW-Lasso, a degree weighted Lasso (least absolute shrinkage and selection operator) method which infers gene networks with hubs efficiently under the low sample size setting. Our network reconstruction approach is formulated as a two stage procedure: first, the degree of networks is estimated iteratively, and second, the gene regulatory network is reconstructed using degree information. A useful property of the proposed method is that it naturally favors the accumulation of neighbors around hub genes and thereby helps in accurate modeling of the high-throughput data under the assumption that the underlying network exhibits hub structure. In a simulation study, we demonstrate good predictive performance of the proposed method in comparison to traditional Lasso type methods in inferring hub and scale-free graphs. We show the effectiveness of our method in an application to microarray data of Escherichia coli and RNA sequencing data of Kidney Clear Cell Carcinoma from The Cancer Genome Atlas datasets.

AVAILABILITY AND IMPLEMENTATION

Under the GNU General Public Licence at https://cran.r-project.org/package=DWLasso.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Handling Noise in Protein Interaction Networks

Protein-protein interactions (PPIs) can be conveniently represented as networks, allowing the use of graph theory for their study. Network topology studies may reveal patterns associated with specific organisms. Here, we propose a new methodology to denoise PPI networks and predict missing links solely based on the network topology, the organization measurement (OM) method. The OM methodology was applied in the denoising of the PPI networks of two Saccharomyces cerevisiae datasets (Yeast and CS2007) and one Homo sapiens dataset (Human). To evaluate the denoising capabilities of the OM methodology, two strategies were applied. The first strategy compared its application in random networks and in the reference set networks, while the second strategy perturbed the networks with the gradual random addition and removal of edges. The application of the OM methodology to the Yeast and Human reference sets achieved an AUC of 0.95 and 0.87, in Yeast and Human networks, respectively. The random removal of 80% of the Yeast and Human reference set interactions resulted in an AUC of 0.71 and 0.62, whereas the random addition of 80% interactions resulted in an AUC of 0.75 and 0.72, respectively. Applying the OM methodology to the CS2007 dataset yields an AUC of 0.99. We also perturbed the network of the CS2007 dataset by randomly inserting and removing edges in the same proportions previously described. The false positives identified and removed from the network varied from 97%, when inserting 20% more edges, to 89%, when 80% more edges were inserted. The true positives identified and inserted in the network varied from 95%, when removing 20% of the edges, to 40%, after the random deletion of 80% edges. The OM methodology is sensitive to the topological structure of the biological networks. The obtained results suggest that the present approach can efficiently be used to denoise PPI networks.

High-dimensional causal discovery under non-Gaussianity

We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable-specific error term and the other observed variables $Y_u$ with $\sigma(u) < \sigma (v)$. The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has previously been shown that when the variable-specific error terms are non-Gaussian, the exact causal graph, as opposed to a Markov equivalence class, can be consistently estimated from observational data. We propose an algorithm that yields consistent estimates of the graph also in high-dimensional settings in which the number of variables may grow at a faster rate than the number of observations, but in which the underlying causal structure features suitable sparsity; specifically, the maximum in-degree of the graph is controlled. Our theoretical analysis is couched in the setting of log-concave error distributions.

Centrality and the shortest path approach in the human interactome

Many notions and concepts for network analysis, including the shortest path approach, came to systems biology from the theory of graphs - the field of mathematics that studies graphs. We studied the relationship between the shortest paths and a biologically meaningful molecular path between vertices in human molecular interaction networks. We analyzed the sets of the shortest paths in the human interactome derived from HPRD and HIPPIE databases between all possible combinations of start and end proteins in eight signaling pathways in the KEGG database - NF-kappa B, MAPK, Jak-STAT, mTOR, ErbB, Wnt, TGF-beta, and the signaling part of the apoptotic process. We investigated whether the shortest paths match the canonical paths. We studied whether centrality of vertices and paths in the subnetworks induced by the shortest paths can highlight vertices and paths that are part of meaningful molecular paths. We found that the shortest paths match canonical counterparts only for canonical paths of length 2 or 3 interactions. The shortest paths match longer canonical counterparts with shortcuts or substitutions by protein complex members. We found that high centrality vertices are part of the canonical paths for up to 80% of the canonical paths depending on the database and the length.

Randomization algorithms for large sparse networks

In many domains it is necessary to generate surrogate networks, e.g., for hypothesis testing of different properties of a network. Generating surrogate networks typically requires that different properties of the network are preserved, e.g., edges may not be added or deleted and edge weights may be restricted to certain intervals. In this paper we present an efficient property-preserving Markov chain Monte Carlo method termed CycleSampler for generating surrogate networks in which (1) edge weights are constrained to intervals and vertex strengths are preserved exactly, and (2) edge and vertex strengths are both constrained to intervals. These two types of constraints cover a wide variety of practical use cases. The method is applicable to both undirected and directed graphs. We empirically demonstrate the efficiency of the CycleSampler method on real-world data sets. We provide an implementation of CycleSampler in R, with parts implemented in C.

Mining Featured Biomarkers Linked with Epithelial Ovarian CancerBased on Bioinformatics

Epithelial ovarian cancer (EOC) is the18th most common cancer worldwide and the 8th most common in women. The aim of this study was to diagnose the potential importance of, as well as novel genes linked with, EOC and to provide valid biological information for further research. The gene expression profiles of E-MTAB-3706 which contained four high-grade ovarian epithelial cancer samples, four normal fallopian tube samples and four normal ovarian epithelium samples were downloaded from the ArrayExpress database. Pathway enrichment and Gene Ontology (GO) enrichment analysis of differentially expressed genes (DEGs) were performed, and protein-protein interaction (PPI) network, microRNA-target gene regulatory network and TFs (transcription factors) -target gene regulatory network for up- and down-regulated were analyzed using Cytoscape. In total, 552 DEGs were found, including 276 up-regulated and 276 down-regulated DEGs. Pathway enrichment analysis demonstrated that most DEGs were significantly enriched in chemical carcinogenesis, urea cycle, cell adhesion molecules and creatine biosynthesis. GO enrichment analysis showed that most DEGs were significantly enriched in translation, nucleosome, extracellular matrix organization and extracellular matrix. From protein-protein interaction network (PPI) analysis, modules, microRNA-target gene regulatory network and TFs-target gene regulatory network for up- and down-regulated, and the top hub genes such as E2F4, SRPK2, A2M, CDH1, MAP1LC3A, UCHL1, HLA-C (major histocompatibility complex, class I, C), VAT1, ECM1 and SNRPN (small nuclear ribonucleoprotein polypeptide N) were associated in pathogenesis of EOC. The high expression levels of the hub genes such as CEBPD (CCAAT enhancer binding protein delta) and MID2 in stages 3 and 4 were validated in the TCGA (The Cancer Genome Atlas) database. CEBPD andMID2 were associated with the worst overall survival rates in EOC. In conclusion, the current study diagnosed DEGs between normal and EOC samples, which could improve our understanding of the molecular mechanisms in the progression of EOC. These new key biomarkers might be used as therapeutic targets for EOC.

Two-State Co-Expression Network Analysis to Identify Genes Related to Salt Tolerance in Thai rice

Khao Dawk Mali 105 (KDML105) rice is one of the most important crops of Thailand. It is a challenging task to identify the genes responding to salinity in KDML105 rice. The analysis of the gene co-expression network has been widely performed to prioritize significant genes, in order to select the key genes in a specific condition. In this work, we analyzed the two-state co-expression networks of KDML105 rice under salt-stress and normal grown conditions. The clustering coefficient was applied to both networks and exhibited significantly different structures between the salt-stress state network and the original (normal-grown) network. With higher clustering coefficients, the genes that responded to the salt stress formed a dense cluster. To prioritize and select the genes responding to the salinity, we investigated genes with small partners under normal conditions that were highly expressed and were co-working with many more partners under salt-stress conditions. The results showed that the genes responding to the abiotic stimulus and relating to the generation of the precursor metabolites and energy were the great candidates, as salt tolerant marker genes. In conclusion, in the case of the complexity of the environmental conditions, gaining more information in order to deal with the co-expression network provides better candidates for further analysis.

A novel topological centrality measure capturing biologically important proteins

Topological centrality in protein interaction networks and its biological implications have widely been investigated in the past. In the present study, a novel metric of centrality-weighted sum of loads eigenvector centrality (WSL-EC)-based on graph spectra is defined and its performance in identifying topologically and biologically important nodes is comparatively investigated with common metrics of centrality in a human protein-protein interaction network. The metric can capture nodes from peripherals of the network differently from conventional eigenvector centrality. Different metrics were found to selectively identify hub sets that are significantly associated with different biological processes. The widely accepted metrics degree centrality, betweenness centrality, subgraph centrality and eigenvector centrality are subject to a bias towards super-hubs, whereas WSL-EC is not affected by the presence of super-hubs. WSL-EC outperforms other metrics of centrality in detecting biologically central nodes such as pathogen-interacting, cancer, ageing, HIV-1 or disease-related proteins and proteins involved in immune system processes and autoimmune diseases in the human interactome.

Elements of the cellular metabolic structure

A large number of studies have demonstrated the existence of metabolic covalent modifications in different molecular structures, which are able to store biochemical information that is not encoded by DNA. Some of these covalent mark patterns can be transmitted across generations (epigenetic changes). Recently, the emergence of Hopfield-like attractor dynamics has been observed in self-organized enzymatic networks, which have the capacity to store functional catalytic patterns that can be correctly recovered by specific input stimuli. Hopfield-like metabolic dynamics are stable and can be maintained as a long-term biochemical memory. In addition, specific molecular information can be transferred from the functional dynamics of the metabolic networks to the enzymatic activity involved in covalent post-translational modulation, so that determined functional memory can be embedded in multiple stable molecular marks. The metabolic dynamics governed by Hopfield-type attractors (functional processes), as well as the enzymatic covalent modifications of specific molecules (structural dynamic processes) seem to represent the two stages of the dynamical memory of cellular metabolism (metabolic memory). Epigenetic processes appear to be the structural manifestation of this cellular metabolic memory. Here, a new framework for molecular information storage in the cell is presented, which is characterized by two functionally and molecularly interrelated systems: a dynamic, flexible and adaptive system (metabolic memory) and an essentially conservative system (genetic memory). The molecular information of both systems seems to coordinate the physiological development of the whole cell.

Learning Graphical Models With Hubs

We consider the problem of learning a high-dimensional graphical model in which there are a few hub nodes that are densely-connected to many other nodes. Many authors have studied the use of an ℓ₁ penalty in order to learn a sparse graph in the high-dimensional setting. However, the ℓ₁ penalty implicitly assumes that each edge is equally likely and independent of all other edges. We propose a general framework to accommodate more realistic networks with hub nodes, using a convex formulation that involves a row-column overlap norm penalty. We apply this general framework to three widely-used probabilistic graphical models: the Gaussian graphical model, the covariance graph model, and the binary Ising model. An alternating direction method of multipliers algorithm is used to solve the corresponding convex optimization problems. On synthetic data, we demonstrate that our proposed framework outperforms competitors that do not explicitly model hub nodes. We illustrate our proposal on a webpage data set and a gene expression data set.

Spatiotemporal positioning of multipotent modules in diverse biological networks

A biological network exhibits a modular organization. The modular structure dependent on functional module is of great significance in understanding the organization and dynamics of network functions. A huge variety of module identification methods as well as approaches to analyze modularity and dynamics of the inter- and intra-module interactions have emerged recently, but they are facing unexpected challenges in further practical applications. Here, we discuss recent progress in understanding how such a modular network can be deconstructed spatiotemporally. We focus particularly on elucidating how various deciphering mechanisms operate to ensure precise module identification and assembly. In this case, a system-level understanding of the entire mechanism of module construction is within reach, with important implications for reasonable perspectives in both constructing a modular analysis framework and deconstructing different modular hierarchical structures.

On functional module detection in metabolic networks

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models.