Topological and causal structure of the yeast transcriptional regulatory network

Multi-objective context-guided consensus of a massive array of techniques for the inference of Gene Regulatory Networks

BACKGROUND AND OBJECTIVE

Gene Regulatory Network (GRN) inference is a fundamental task in biology and medicine, as it enables a deeper understanding of the intricate mechanisms of gene expression present in organisms. This bioinformatics problem has been addressed in the literature through multiple computational approaches. Techniques developed for inferring from expression data have employed Bayesian networks, ordinary differential equations (ODEs), machine learning, information theory measures and neural networks, among others. The diversity of implementations and their respective customization have led to the emergence of many tools and multiple specialized domains derived from them, understood as subsets of networks with specific characteristics that are challenging to detect a priori. This specialization has introduced significant uncertainty when choosing the most appropriate technique for a particular dataset. This proposal, named MO-GENECI, builds upon the basic idea of the previous proposal GENECI and optimizes consensus among different inference techniques, through a carefully refined multi-objective evolutionary algorithm guided by various objective functions, linked to the biological context at hand.

METHODS

MO-GENECI has been tested on an extensive and diverse academic benchmark of 106 gene regulatory networks from multiple sources and sizes. The evaluation of MO-GENECI compared its performance to individual techniques using key metrics (AUROC and AUPR) for gene regulatory network inference. Friedman's statistical ranking provided an ordered classification, followed by non-parametric Holm tests to determine statistical significance.

RESULTS

MO-GENECI's Pareto front approximation facilitates easy selection of an appropriate solution based on generic input data characteristics. The best solution consistently emerged as the winner in all statistical tests, and in many cases, the median precision solution showed no statistically significant difference compared to the winner.

CONCLUSIONS

MO-GENECI has not only demonstrated achieving more accurate results than individual techniques, but has also overcome the uncertainty associated with the initial choice due to its flexibility and adaptability. It is shown intelligently to select the most suitable techniques for each case. The source code is hosted in a public repository at GitHub under MIT license: https://github.com/AdrianSeguraOrtiz/MO-GENECI. Moreover, to facilitate its installation and use, the software associated with this implementation has been encapsulated in a Python package available at PyPI: https://pypi.org/project/geneci/.

Adaptation in Unstable Environments and Global Gene Losses: Small but Stable Gene Networks by the May-Wigner Theory

Although gene loss is common in evolution, it remains unclear whether it is an adaptive process. In a survey of seven major mangrove clades that are woody plants in the intertidal zones of daily environmental perturbations, we noticed that they generally evolved reduced gene numbers. We then focused on the largest clade of Rhizophoreae and observed the continual gene set reduction in each of the eight species. A great majority of gene losses are concentrated on environmental interaction processes, presumably to cope with the constant fluctuations in the tidal environments. Genes of the general processes for woody plants are largely retained. In particular, fewer gene losses are found in physiological traits such as viviparous seeds, high salinity, and high tannin content. Given the broad and continual genome reductions, we propose the May-Wigner theory (MWT) of system stability as a possible mechanism. In MWT, the most effective solution for buffering continual perturbations is to reduce the size of the system (or to weaken the total genic interactions). Mangroves are unique as immovable inhabitants of the compound environments in the land-sea interface, where environmental gradients (such as salinity) fluctuate constantly, often drastically. Extending MWT to gene regulatory network (GRN), computer simulations and transcriptome analyses support the stabilizing effects of smaller gene sets in mangroves vis-à-vis inland plants. In summary, we show the adaptive significance of gene losses in mangrove plants, including the specific role of promoting phenotype innovation and a general role in stabilizing GRN in unstable environments as predicted by MWT.

On Low-Rank Directed Acyclic Graphs and Causal Structure Learning

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

A meta-analysis of Boolean network models reveals design principles of gene regulatory networks

Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean networks, which are intuitive, simple to describe, and can yield qualitative results even when data are sparse. We assembled the largest repository of expert-curated Boolean GRN models. A meta-analysis of this diverse set of models reveals several design principles. GRNs exhibit more canalization, redundancy, and stable dynamics than expected. Moreover, they are enriched for certain recurring network motifs. This raises the important question why evolution favors these design mechanisms.

The ensemble of gene regulatory networks at mutation-selection balance

The evolution of diverse phenotypes both involves and is constrained by molecular interaction networks. When these networks influence patterns of expression, we refer to them as gene regulatory networks (GRNs). Here, we develop a model of GRN evolution analogous to work from quasi-species theory, which is itself essentially the mutation-selection balance model from classical population genetics extended to multiple loci. With this GRN model, we prove that-across a broad spectrum of selection pressures-the dynamics converge to a stationary distribution over GRNs. Next, we show from first principles how the frequency of GRNs at equilibrium is related to the topology of the genotype network, in particular, via a specific network centrality measure termed the eigenvector centrality. Finally, we determine the structural characteristics of GRNs that are favoured in response to a range of selective environments and mutational constraints. Our work connects GRN evolution to quasi-species theory-and thus to classical populations genetics-providing a mechanistic explanation for the observed distribution of GRNs evolving in response to various evolutionary forces, and shows how complex fitness landscapes can emerge from simple evolutionary rules.

Patterns of pan-genome occupancy and gene coexpression under water-deficit in Brachypodium distachyon

Natural populations are characterized by abundant genetic diversity driven by a range of different types of mutation. The tractability of sequencing complete genomes has allowed new insights into the variable composition of genomes, summarized as a species pan-genome. These analyses demonstrate that many genes are absent from the first reference genomes, whose analysis dominated the initial years of the genomic era. Our field now turns towards understanding the functional consequence of these highly variable genomes. Here, we analysed weighted gene coexpression networks from leaf transcriptome data for drought response in the purple false brome Brachypodium distachyon and the differential expression of genes putatively involved in adaptation to this stressor. We specifically asked whether genes with variable "occupancy" in the pan-genome - genes which are either present in all studied genotypes or missing in some genotypes - show different distributions among coexpression modules. Coexpression analysis united genes expressed in drought-stressed plants into nine modules covering 72 hub genes (87 hub isoforms), and genes expressed under controlled water conditions into 13 modules, covering 190 hub genes (251 hub isoforms). We find that low occupancy pan-genes are under-represented among several modules, while other modules are over-enriched for low-occupancy pan-genes. We also provide new insight into the regulation of drought response in B. distachyon, specifically identifying one module with an apparent role in primary metabolism that is strongly responsive to drought. Our work shows the power of integrating pan-genomic analysis with transcriptomic data using factorial experiments to understand the functional genomics of environmental response.

Gene Regulatory Network Inference and Gene Module Regulating Virulence in Fusarium oxysporum

In this work, we inferred the gene regulatory network (GRN) of the fungus Fusarium oxysporum by using the regulatory networks of Aspergillus nidulans FGSC A4, Neurospora crassa OR74A, Saccharomyces cerevisiae S288c, and Fusarium graminearum PH-1 as templates for sequence comparisons. Topological properties to infer the role of transcription factors (TFs) and to identify functional modules were calculated in the GRN. From these analyzes, five TFs were identified as hubs, including FOXG_04688 and FOXG_05432, which regulate 2,404 and 1,864 target genes, respectively. In addition, 16 communities were identified in the GRN, where the largest contains 1,923 genes and the smallest contains 227 genes. Finally, the genes associated with virulence were extracted from the GRN and exhaustively analyzed, and we identified a giant module with ten TFs and 273 target genes, where the most highly connected node corresponds to the transcription factor FOXG_05265, homologous to the putative bZip transcription factor CPTF1 of Claviceps purpurea, which is involved in ergotism disease that affects cereal crops and grasses. The results described in this work can be used for the study of gene regulation in this organism and open the possibility to explore putative genes associated with virulence against their host.

Multiplex network disintegration strategy inference based on deep network representation learning

Multiplex networks have attracted more and more attention because they can model the coupling of network nodes between layers more accurately. The interaction of nodes between layers makes the attack effect on multiplex networks not simply a linear superposition of the attack effect on single-layer networks, and the disintegration of multiplex networks has become a research hotspot and difficult. Traditional multiplex network disintegration methods generally adopt approximate and heuristic strategies. However, these two methods have a number of drawbacks and fail to meet our requirements in terms of effectiveness and timeliness. In this paper, we develop a novel deep learning framework, called MINER (Multiplex network disintegration strategy Inference based on deep NEtwork Representation learning), which transforms the disintegration strategy inference of multiplex networks into the encoding and decoding process based on deep network representation learning. In the encoding process, the attention mechanism encodes the coupling relationship of corresponding nodes between layers, and reinforcement learning is adopted to evaluate the disintegration action in the decoding process. Experiments indicate that the trained MINER model can be directly transferred and applied to the disintegration of multiplex networks with different scales. We extend it to scenarios that consider node attack cost constraints and also achieve excellent performance. This framework provides a new way to understand and employ multiplex networks.

Reconstruction of Gene Regulatory Networks Using Multiple Datasets

MOTIVATION

Laboratory gene regulatory data for a species are sporadic. Despite the abundance of gene regulatory network algorithms that employ single data sets, few algorithms can combine the vast but disperse sources of data and extract the potential information. With a motivation to compensate for this shortage, we developed an algorithm called GENEREF that can accumulate information from multiple types of data sets in an iterative manner, with each iteration boosting the performance of the prediction results.

RESULTS

The algorithm is examined extensively on data extracted from the quintuple DREAM4 networks and DREAM5's Escherichia coli and Saccharomyces cerevisiae networks and sub-networks. Many single-dataset and multi-dataset algorithms were compared to test the performance of the algorithm. Results show that GENEREF surpasses non-ensemble state-of-the-art multi-perturbation algorithms on the selected networks and is competitive to present multiple-dataset algorithms. Specifically, it outperforms dynGENIE3 and is on par with iRafNet. Also, we argued that a scoring method solely based on the AUPR criterion would be more trustworthy than the traditional score.

AVAILABILITY

The Python implementation along with the data sets and results can be downloaded from github.com/msaremi/GENEREF.

GPU Accelerated Drug Application on Signaling Pathways Containing Multiple Faults Using Boolean Networks

Cell growth is governed by the flow of information from growth factors to transcription factors. This flow involves protein-protein interactions known as a signaling pathway, which triggers the cell division. The biological network in the presence of malfunctions leads to a rapid cell division without any necessary input conditions. The effect of these malfunctions or faults can be observed if it is simulated explicitly in the Boolean derivative of the biological networks. The consequences thus produced can be nullified to a large extent, with the application of a reduced combination of drugs. This paper provides an insight into the behavior of the signaling pathway in the presence of multiple concurrent malfunctions. First, we simulate the behavior of malfunctions in the Boolean networks. Next, we apply the drug therapy to reduce the effects of malfunctions. In our approach, we introduce a parameter called probabilistic_score, which identifies the reduced drug combinations without prior knowledge of the malfunctions, and it is more beneficial in realistic cancerous conditions. The combinations of different custom drug inhibition points are chosen to produce more efficient results than known drugs. Our approach is significantly faster as GPU acceleration has been carried out during modeling the multiple faults/malfunctions in the Boolean networks.

Additional insights into the organization of transcriptional regulatory modules based on a 3D model of the Saccharomyces cerevisiae genome

Objectives

Transcriptional regulatory modules are usually modelled via a network, in which nodes correspond to genes and edges correspond to regulatory associations between them. In the model yeast Saccharomyces cerevisiae, the topological properties of such a network are well-described (distribution of degrees, hierarchical levels, organization in network motifs, etc.). To go further on this, our aim was to search for additional information resulting from the new combination of classical representations of transcriptional regulatory networks with more realistic models of the spatial organization of S. cerevisiae genome in the nucleus.

Results

Taking advantage of independent studies with high-quality datasets, i.e. lists of target genes for specific transcription factors and chromosome positions in a three dimensional space representing the nucleus, particular spatial co-localizations of genes that shared common regulatory mechanisms were searched. All transcriptional modules of S. cerevisiae, as described in the latest release of the YEASTRACT database were analyzed and significant biases toward co-localization for a few sets of target genes were observed. To help other researchers to reproduce such analysis with any list of genes of their interest, an interactive web tool called 3D-Scere (https://3d-scere.ijm.fr/) is provided.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13104-022-05940-5.

Advanced genomics identifies growth effectors for proteotoxic ER stress recovery in Arabidopsis thaliana

Adverse environmental and pathophysiological situations can overwhelm the biosynthetic capacity of the endoplasmic reticulum (ER), igniting a potentially lethal condition known as ER stress. ER stress hampers growth and triggers a conserved cytoprotective signaling cascade, the unfolded protein response (UPR) for ER homeostasis. As ER stress subsides, growth is resumed. Despite the pivotal role of the UPR in growth restoration, the underlying mechanisms for growth resumption are yet unknown. To discover these, we undertook a genomics approach in the model plant species Arabidopsis thaliana and mined the gene reprogramming roles of the UPR modulators, basic leucine zipper28 (bZIP28) and bZIP60, in ER stress resolution. Through a network modeling and experimental validation, we identified key genes downstream of the UPR bZIP-transcription factors (bZIP-TFs), and demonstrated their functional roles. Our analyses have set up a critical pipeline for functional gene discovery in ER stress resolution with broad applicability across multicellular eukaryotes.

Ko and Brandizzi use Arabidopsis thaliana to investigate the downstream regulators of two major endoplasmic reticulum (ER) stress-related transcription factors, bZIP60 and bZIP28. Their results provide further insight on how two modulators of the unfolded protein response contribute to growth recovery from ER stress.

On the effects of the modularity of gene regulatory networks on phenotypic variability and its association with robustness

Biological adaptations depend on natural selection sorting out those individuals that exhibit characters fit to their environment. Selection, in turn, depends on the phenotypic variation present in a population. Thus, evolutionary outcomes depend, to a certain extent, on the kind of variation that organisms can produce through random genetic perturbation, that is, their phenotypic variability. Moreover, the properties of developmental mechanisms that produce the organisms affect their phenotypic variability. Two of these properties are modularity and robustness. Modularity is the degree to which interactions occur mostly within groups of the system's elements and scarcely between elements in different groups. Robustness is the propensity of a system to endure perturbations while preserving its phenotype. In this paper, we used a model of gene regulatory networks (GRNs) to study the relationship between modularity and robustness in developmental processes and how modularity affects the variation that random genetic mutations produce in the expression patterns of GRNs. Our results show that modularity and robustness are correlated in multifunctional GRNs and that selection for one of these properties affects the other as well. We contend that these observations may help to understand why modularity and robustness are widespread in biological systems. Additionally, we found that modular networks tend to produce new expression patterns with subtle changes localized in the expression of a few groups of genes. This effect in the phenotypic variability of modular GRNs may bear important consequences for adaptive evolution: it may help to adjust the expression of one group of genes at a time, with few alterations on other previously evolved expression patterns.

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/ .

Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.

Testing biological network motif significance with exponential random graph models

Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-021-00434-y.

Computational biology approaches for mapping transcriptional regulatory networks

Transcriptional Regulatory Networks (TRNs) are mainly responsible for the cell-type- or cell-state-specific expression of gene sets from the same DNA sequence. However, so far there are no precise maps of TRNs available for each cell-type or cell-state, and no ideal tool to map those networks clearly and in full from biological samples. In this review, major approaches and tools to map TRNs from high-throughput data are presented, depending on the type of methods or data used to infer them, and their advantages and limitations are discussed. After summarizing the main principles defining the topology and structure–function relationships in TRNs, an overview of the extensive work done to map TRNs from bulk transcriptomic data will be presented by type of methodological approach. Most recent modellings of TRNs using other types of molecular data or integrating different data types, including single-cell RNA-sequencing and chromatin information, will then be discussed, before briefly concluding with improvements expected to come in the field.

Elucidation of dynamic microRNA regulations in cancer progression using integrative machine learning

MOTIVATION

Empowered by advanced genomics discovery tools, recent biomedical research has produced a massive amount of genomic data on (post-)transcriptional regulations related to transcription factors, microRNAs, long non-coding RNAs, epigenetic modifications and genetic variations. Computational modeling, as an essential research method, has generated promising testable quantitative models that represent complex interplay among different gene regulatory mechanisms based on these data in many biological systems. However, given the dynamic changes of interactome in chaotic systems such as cancers, and the dramatic growth of heterogeneous data on this topic, such promise has encountered unprecedented challenges in terms of model complexity and scalability. In this study, we introduce a new integrative machine learning approach that can infer multifaceted gene regulations in cancers with a particular focus on microRNA regulation. In addition to new strategies for data integration and graphical model fusion, a supervised deep learning model was integrated to identify conditional microRNA-mRNA interactions across different cancer stages.

RESULTS

In a case study of human breast cancer, we have identified distinct gene regulatory networks associated with four progressive stages. The subsequent functional analysis focusing on microRNA-mediated dysregulation across stages has revealed significant changes in major cancer hallmarks, as well as novel pathological signaling and metabolic processes, which shed light on microRNAs' regulatory roles in breast cancer progression. We believe this integrative model can be a robust and effective discovery tool to understand key regulatory characteristics in complex biological systems.

AVAILABILITY

http://sbbi-panda.unl.edu/pin/.

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.

Internetwork connectivity of molecular networks across species of life

Molecular interactions are studied as independent networks in systems biology. However, molecular networks do not exist independently of each other. In a network of networks approach (called multiplex), we study the joint organization of transcriptional regulatory network (TRN) and protein-protein interaction (PPI) network. We find that TRN and PPI are non-randomly coupled across five different eukaryotic species. Gene degrees in TRN (number of downstream genes) are positively correlated with protein degrees in PPI (number of interacting protein partners). Gene-gene and protein-protein interactions in TRN and PPI, respectively, also non-randomly overlap. These design principles are conserved across the five eukaryotic species. Robustness of the TRN-PPI multiplex is dependent on this coupling. Functionally important genes and proteins, such as essential, disease-related and those interacting with pathogen proteins, are preferentially situated in important parts of the human multiplex with highly overlapping interactions. We unveil the multiplex architecture of TRN and PPI. Multiplex architecture may thus define a general framework for studying molecular networks. This approach may uncover the building blocks of the hierarchical organization of molecular interactions.

New insights on key genes involved in drought stress response of barley: gene networks reconstruction, hub, and promoter analysis

Background

Barley (Hordeum vulgare L.) is one of the most important cereals worldwide. Although this crop is drought-tolerant, water deficiency negatively affects its growth and production. To detect key genes involved in drought tolerance in barley, a reconstruction of the related gene network and discovery of the hub genes would help. Here, drought-responsive genes in barley were collected through analysis of the available microarray datasets (− 5 ≥ Fold change ≥ 5, adjusted p value ≤ 0.05). Protein-protein interaction (PPI) networks were reconstructed.

Results

The hub genes were identified by Cytoscape software using three Cyto-hubba algorithms (Degree, Closeness, and MNC), leading to the identification of 17 and 16 non-redundant genes at vegetative and reproductive stages, respectively. These genes consist of some transcription factors such as HvVp1, HvERF4, HvFUS3, HvCBF6, DRF1.3, HvNAC6, HvCO5, and HvWRKY42, which belong to AP2, NAC, Zinc-finger, and WRKY families. In addition, the expression pattern of four hub genes was compared between the two studied cultivars, i.e., “Yousef” (drought-tolerant) and “Morocco” (susceptible). The results of real-time PCR revealed that the expression patterns corresponded well with those determined by the microarray. Also, promoter analysis revealed that some TF families, including AP2, NAC, Trihelix, MYB, and one modular (composed of two HD-ZIP TFs), had a binding site in 85% of promoters of the drought-responsive genes and of the hub genes in barley.

Conclusions

The identified hub genes, especially those from AP2 and NAC families, might be among key TFs that regulate drought-stress response in barley and are suggested as promising candidate genes for further functional analysis.

Assessing regulatory features of the current transcriptional network of Saccharomyces cerevisiae

The capacity of living cells to adapt to different environmental, sometimes adverse, conditions is achieved through differential gene expression, which in turn is controlled by a highly complex transcriptional network. We recovered the full network of transcriptional regulatory associations currently known for Saccharomyces cerevisiae, as gathered in the latest release of the YEASTRACT database. We assessed topological features of this network filtered by the kind of supporting evidence and of previously published networks. It appears that in-degree distribution, as well as motif enrichment evolve as the yeast transcriptional network is being completed. Overall, our analyses challenged some results previously published and confirmed others. These analyses further pointed towards the paucity of experimental evidence to support theories and, more generally, towards the partial knowledge of the complete network.

sismonr: simulation of in silico multi-omic networks with adjustable ploidy and post-transcriptional regulation in R

SUMMARY

We present sismonr, an R package for an integral generation and simulation of in silico biological systems. The package generates gene regulatory networks, which include protein-coding and non-coding genes along with different transcriptional and post-transcriptional regulations. The effect of genetic mutations on the system behaviour is accounted for via the simulation of genetically different in silico individuals. The ploidy of the system is not restricted to the usual haploid or diploid situations but can be defined by the user to higher ploidies. A choice of stochastic simulation algorithms allows us to simulate the expression profiles of the genes in the in silico system. We illustrate the use of sismonr by simulating the anthocyanin biosynthesis regulation pathway for three genetically distinct in silico plants.

AVAILABILITY AND IMPLEMENTATION

The sismonr package is implemented in R and Julia and is publicly available on the CRAN repository (https://CRAN.R-project.org/package=sismonr). A detailed tutorial is available from GitHub at https://oliviaab.github.io/sismonr/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Interplay between degree and Boolean rules in the stability of Boolean networks

Empirical evidence has revealed that biological regulatory systems are controlled by high-level coordination between topology and Boolean rules. In this study, we look at the joint effects of degree and Boolean functions on the stability of Boolean networks. To elucidate these effects, we focus on (1) the correlation between the sensitivity of Boolean variables and the degree and (2) the coupling between canalizing inputs and degree. We find that negatively correlated sensitivity with respect to local degree enhances the stability of Boolean networks against external perturbations. We also demonstrate that the effects of canalizing inputs can be amplified when they coordinate with high in-degree nodes. Numerical simulations confirm the accuracy of our analytical predictions at both the node and network levels.

Emergence of informative higher scales in biological systems: a computational toolkit for optimal prediction and control

The biological sciences span many spatial and temporal scales in attempts to understand the function and evolution of complex systems-level processes, such as embryogenesis. It is generally assumed that the most effective description of these processes is in terms of molecular interactions. However, recent developments in information theory and causal analysis now allow for the quantitative resolution of this question. In some cases, macro-scale models can minimize noise and increase the amount of information an experimenter or modeler has about "what does what." This result has numerous implications for evolution, pattern regulation, and biomedical strategies. Here, we provide an introduction to these quantitative techniques, and use them to show how informative macro-scales are common across biology. Our goal is to give biologists the tools to identify the maximally-informative scale at which to model, experiment on, predict, control, and understand complex biological systems.

Scale free topology as an effective feedback system

Biological networks are often heterogeneous in their connectivity pattern, with degree distributions featuring a heavy tail of highly connected hubs. The implications of this heterogeneity on dynamical properties are a topic of much interest. Here we show that interpreting topology as a feedback circuit can provide novel insights on dynamics. Based on the observation that in finite networks a small number of hubs have a disproportionate effect on the entire system, we construct an approximation by lumping these nodes into a single effective hub, which acts as a feedback loop with the rest of the nodes. We use this approximation to study dynamics of networks with scale-free degree distributions, focusing on their probability of convergence to fixed points. We find that the approximation preserves convergence statistics over a wide range of settings. Our mapping provides a parametrization of scale free topology which is predictive at the ensemble level and also retains properties of individual realizations. Specifically, outgoing hubs have an organizing role that can drive the network to convergence, in analogy to suppression of chaos by an external drive. In contrast, incoming hubs have no such property, resulting in a marked difference between the behavior of networks with outgoing vs. incoming scale free degree distribution. Combining feedback analysis with mean field theory predicts a transition between convergent and divergent dynamics which is corroborated by numerical simulations. Furthermore, they highlight the effect of a handful of outlying hubs, rather than of the connectivity distribution law as a whole, on network dynamics.

Nature abounds with complex networks of interacting elements—from the proteins in our cells, through neural networks in our brains, to species interacting in ecosystems. In all of these fields, the relation between network structure and dynamics is an important research question. A recurring feature of natural networks is their heterogeneous structure: individual elements exhibit a huge diversity of connectivity patterns, which complicates the understanding of network dynamics. To address this problem, we devised a simplified approximation for complex structured networks which captures their dynamical properties. Separating out the largest “hubs”—a small number of nodes with disproportionately high connectivity—we represent them by a single node linked to the rest of the network. This enables us to borrow concepts from control theory, where a system’s output is linked back to itself forming a feedback loop. In this analogy, hubs in heterogeneous networks implement a feedback circuit with the rest of the network. The analogy reveals how these hubs can coordinate the network and drive it more easily towards stable states. Our approach enables analyzing dynamical properties of heterogeneous networks, which is difficult to achieve with existing techniques. It is potentially applicable to many fields where heterogeneous networks are important.

Dynamics of genetic variation in transcription factors and its implications for the evolution of regulatory networks in Bacteria

The evolution of regulatory networks in Bacteria has largely been explained at macroevolutionary scales through lateral gene transfer and gene duplication. Transcription factors (TF) have been found to be less conserved across species than their target genes (TG). This would be expected if TFs accumulate mutations faster than TGs. This hypothesis is supported by several lab evolution studies which found TFs, especially global regulators, to be frequently mutated. Despite these studies, the contribution of point mutations in TFs to the evolution of regulatory network is poorly understood. We tested if TFs show greater genetic variation than their TGs using whole-genome sequencing data from a large collection of Escherichia coli isolates. TFs were less diverse than their TGs across natural isolates, with TFs of large regulons being more conserved. In contrast, TFs showed higher mutation frequency in adaptive laboratory evolution experiments. However, over long-term laboratory evolution spanning 60 000 generations, mutation frequency in TFs gradually declined after a rapid initial burst. Extrapolating the dynamics of genetic variation from long-term laboratory evolution to natural populations, we propose that point mutations, conferring large-scale gene expression changes, may drive the early stages of adaptation but gene regulation is subjected to stronger purifying selection post adaptation.

Properties of the Vascular Networks in Malignant Tumors

This work presents an analysis for real and synthetic angiogenic networks using a tomography image that obtains a portrait of a vascular network. After the image conversion into a binary format it is possible to measure various network properties, which includes the average path length, the clustering coefficient, the degree distribution and the fractal dimension. When comparing the observed properties with that produced by the Invasion Percolation algorithm (IPA), we observe that there exist differences between the properties obtained by the real and the synthetic networks produced by the IPA algorithm. Taking into account the former, a new algorithm which models the expansion of an angiogenic network through randomly heuristic rules is proposed. When comparing this new algorithm with the real networks it is observed that now both share some properties. Once creating synthetic networks, we prove the robustness of the network by subjecting the original angiogenic and the synthetic networks to the removal of the most connected nodes, and see to what extent the properties changed. Using this concept of robustness, in a very naive fashion it is possible to launch a hypothetical proposal for a therapeutic treatment based on the robustness of the network.

Critical Nodes Identification in Complex Networks

Critical nodes identification in complex networks is significance for studying the survivability and robustness of networks. The previous studies on structural hole theory uncovered that structural holes are gaps between a group of indirectly connected nodes and intermediaries that fill the holes and serve as brokers for information exchange. In this paper, we leverage the property of structural hole to design a heuristic algorithm based on local information of the network topology to identify node importance in undirected and unweighted network, whose adjacency matrix is symmetric. In the algorithm, a node with a larger degree and greater number of structural holes associated with it, achieves a higher importance ranking. Six real networks are used as test data. The experimental results show that the proposed method not only has low computational complexity, but also outperforms degree centrality, k-shell method, mapping entropy centrality, the collective influence algorithm, DDN algorithm that based on node degree and their neighbors, and random ranking method in identifying node importance for network connectivity in complex networks.

Gene regulatory network stabilized by pervasive weak repressions: microRNA functions revealed by the May-Wigner theory

Food web and gene regulatory networks (GRNs) are large biological networks, both of which can be analyzed using the May-Wigner theory. According to the theory, networks as large as mammalian GRNs would require dedicated gene products for stabilization. We propose that microRNAs (miRNAs) are those products. More than 30% of genes are repressed by miRNAs, but most repressions are too weak to have a phenotypic consequence. The theory shows that (i) weak repressions cumulatively enhance the stability of GRNs, and (ii) broad and weak repressions confer greater stability than a few strong ones. Hence, the diffuse actions of miRNAs in mammalian cells appear to function mainly in stabilizing GRNs. The postulated link between mRNA repression and GRN stability can be seen in a different light in yeast, which do not have miRNAs. Yeast cells rely on non-specific RNA nucleases to strongly degrade mRNAs for GRN stability. The strategy is suited to GRNs of small and rapidly dividing yeast cells, but not the larger mammalian cells. In conclusion, the May-Wigner theory, supplanting the analysis of small motifs, provides a mathematical solution to GRN stability, thus linking miRNAs explicitly to 'developmental canalization'.

Integration of Multiple Data Sources for Gene Network Inference Using Genetic Perturbation Data

The inference of gene networks from large-scale human genomic data is challenging due to the difficulty in identifying correct regulators for each gene in a high-dimensional search space. We present a Bayesian approach integrating external data sources with knockdown data from human cell lines to infer gene regulatory networks. In particular, we assemble multiple data sources, including gene expression data, genome-wide binding data, gene ontology, and known pathways, and use a supervised learning framework to compute prior probabilities of regulatory relationships. We show that our integrated method improves the accuracy of inferred gene networks as well as extends some previous Bayesian frameworks both in theory and applications. We apply our method to two different human cell lines, namely skin melanoma cell line A375 and lung cancer cell line A549, to illustrate the capabilities of our method. Our results show that the improvement in performance could vary from cell line to cell line and that we might need to choose different external data sources serving as prior knowledge if we hope to obtain better accuracy for different cell lines.

Comparative transcriptomic analysis of dermal wound healing reveals de novo skeletal muscle regeneration in Acomys cahirinus

The African spiny mouse, Acomys spp., is capable of scar-free dermal wound healing. Here, we have performed a comprehensive analysis of gene expression throughout wound healing following full-thickness excisional dermal wounds in both Acomys cahirinus and Mus musculus. Additionally, we provide an annotated, de novo transcriptome assembly of A. cahirinus skin and skin wounds. Using a novel computational comparative RNA-Seq approach along with pathway and co-expression analyses, we identify enrichment of regeneration associated genes as well as upregulation of genes directly related to muscle development or function. Our RT-qPCR data reveals induction of the myogenic regulatory factors, as well as upregulation of embryonic myosin, starting between days 14 and 18 post-wounding in A. cahirinus. In contrast, the myogenic regulatory factors remain downregulated, embryonic myosin is only modestly upregulated, and no new muscle fibers of the panniculus carnosus are generated in M. musculus wounds. Additionally, we show that Col6a1, a key component of the satellite cell niche, is upregulated in A. cahirinus compared to M. musculus. Our data also demonstrate that the macrophage profile and inflammatory response is different between species, with A. cahirinus expressing significantly higher levels of Il10. We also demonstrate differential expression of the upstream regulators Wnt7a, Wnt2 and Wnt6 during wound healing. Our analyses demonstrate that A. cahirinus is capable of de novo skeletal muscle regeneration of the panniculus carnosus following removal of the extracellular matrix. We believe this study represents the first detailed analysis of de novo skeletal muscle regeneration observed in an adult mammal.

Gene regulatory networks on transfer entropy (GRNTE): a novel approach to reconstruct gene regulatory interactions applied to a case study for the plant pathogen Phytophthora infestans

Background

The increasing amounts of genomics data have helped in the understanding of the molecular dynamics of complex systems such as plant and animal diseases. However, transcriptional regulation, although playing a central role in the decision-making process of cellular systems, is still poorly understood. In this study, we linked expression data with mathematical models to infer gene regulatory networks (GRN). We present a simple yet effective method to estimate transcription factors’ GRNs from transcriptional data.

Method

We defined interactions between pairs of genes (edges in the GRN) as the partial mutual information between these genes that takes into account time and possible lags in time from one gene in relation to another. We call this method Gene Regulatory Networks on Transfer Entropy (GRNTE) and it corresponds to Granger causality for Gaussian variables in an autoregressive model. To evaluate the reconstruction accuracy of our method, we generated several sub-networks from the GRN of the eukaryotic yeast model, Saccharomyces cerevisae. Then, we applied this method using experimental data of the plant pathogen Phytophthora infestans. We evaluated the transcriptional expression levels of 48 transcription factors of P. infestans during its interaction with one moderately resistant and one susceptible cultivar of yellow potato (Solanum tuberosum group Phureja), using RT-qPCR. With these data, we reconstructed the regulatory network of P. infestans during its interaction with these hosts.

Results

We first evaluated the performance of our method, based on the transfer entropy (GRNTE), on eukaryotic datasets from the GRNs of the yeast S. cerevisae. Results suggest that GRNTE is comparable with the state-of-the-art methods when the parameters for edge detection are properly tuned. In the case of P. infestans, most of the genes considered in this study, showed a significant change in expression from the onset of the interaction (0 h post inoculum - hpi) to the later time-points post inoculation. Hierarchical clustering of the expression data discriminated two distinct periods during the infection: from 12 to 36 hpi and from 48 to 72 hpi for both the moderately resistant and susceptible cultivars. These distinct periods could be associated with two phases of the life cycle of the pathogen when infecting the host plant: the biotrophic and necrotrophic phases.

Conclusions

Here we presented an algorithmic solution to the problem of network reconstruction in time series data. This analytical perspective makes use of the dynamic nature of time series data as it relates to intrinsically dynamic processes such as transcription regulation, were multiple elements of the cell (e.g., transcription factors) act simultaneously and change over time. We applied the algorithm to study the regulatory network of P. infestans during its interaction with two hosts which differ in their level of resistance to the pathogen. Although the gene expression analysis did not show differences between the two hosts, the results of the GRN analyses evidenced rewiring of the genes’ interactions according to the resistance level of the host. This suggests that different regulatory processes are activated in response to different environmental cues. Applications of our methodology showed that it could reliably predict where to place edges in the transcriptional networks and sub-networks. The experimental approach used here can help provide insights on the biological role of these interactions on complex processes such as pathogenicity. The code used is available at https://github.com/jccastrog/GRNTE under GNU general public license 3.0.

Electronic supplementary material

The online version of this article (10.1186/s12976-019-0103-7) contains supplementary material, which is available to authorized users.

Genome-wide analysis of yeast expression data based on a priori generated co-regulation cliques

DNA microarrays are highly sensitive tools to evaluate the gene expression status of organismic samples and standardized array formats exist for many different sample types. Differential expression studies usually utilize the strongest upor downregulated genes to generate networks visualizing the relationships among these genes. To include all yeast genes in one analysis and to get broader information on all cellular responses, we test a priori input of predefined genome-wide expression cliques and subsequent statistical analysis of the expression data. To this end, we generate a set of 72 co-regulation cliques using the information from 3196 microarray experiments. The obtained cliques performed highly significant in gene ontology and transcription factor enrichment analyses. We then tested the clique set on individual microarray experiments reporting on responses to pheromone, glycerol versus glucose based growth and the cellular response to heat. In all cases a highly significant determination of affected expression cliques was possible based on their average expression differences, the positions of their genes within hit rankings (UpRegScore) or the enrichment of the Top200 hits in certain cliques. The 72 cliques were finally used to compare experiments, which reported on the transcriptional response to polyglutamine proteins of different lengths. Using the predefined clique set it is possible to identify with high sensitivity and good significance sample and condition specific changes to gene expression. We thus conclude that an analysis, starting with these 72 preformed expression cliques, can complement traditional microarray analyses by visualizing the entire response on a static genome-wide gene set.

Gene Regulatory Networks: A Primer in Biological Processes and Statistical Modelling

Modelling gene regulatory networks requires not only a thorough understanding of the biological system depicted, but also the ability to accurately represent this system from a mathematical perspective. Throughout this chapter, we aim to familiarize the reader with the biological processes and molecular factors at play in the process of gene expression regulation. We first describe the different interactions controlling each step of the expression process, from transcription to mRNA and protein decay. In the second section, we provide statistical tools to accurately represent this biological complexity in the form of mathematical models. Among other considerations, we discuss the topological properties of biological networks, the application of deterministic and stochastic frameworks, and the quantitative modelling of regulation. We particularly focus on the use of such models for the simulation of expression data that can serve as a benchmark for the testing of network inference algorithms.

On the stability of multilayer Boolean networks under targeted immunization

In this paper, we study targeted immunization in a multilayer Boolean network model for genetic regulatory networks. Given a specific set of nodes immune to perturbations, we find that the stability of a multilayer Boolean network is determined by the largest eigenvalue of the weighted non-backtracking matrix of corresponding aggregated network. Aimed to minimize this largest eigenvalue, we developed the metric of multilayer collective influence (MCI) to quantify the impact of immunizing individual nodes on the stability of the system. Compared with other competing heuristics, immunizing nodes with high MCI scores can stabilize an unstable multilayer network with higher efficiency on both synthetic and real-world networks. Moreover, despite that coupling nodes can exert direct influence across multiple layers, they are found to exhibit less importance as measured by the MCI score. Our work reveals the mechanism of maintaining the stability of multilayer Boolean networks and provides an efficient targeted immunization strategy, which can be potentially applied to the location of pathogenesis of diseases and the development of targeted therapy.

Large scale study of anti-sense regulation by differential network analysis

Background

Systems biology aims to analyse regulation mechanisms into the cell. By mapping interactions observed in different situations, differential network analysis has shown its power to reveal specific cellular responses or specific dysfunctional regulations. In this work, we propose to explore on a large scale the role of natural anti-sense transcription on gene regulation mechanisms, and we focus our study on apple (Malus domestica) in the context of fruit ripening in cold storage.

Results

We present a differential functional analysis of the sense and anti-sense transcriptomic data that reveals functional terms linked to the ripening process. To develop our differential network analysis, we introduce our inference method of an Extended Core Network; this method is inspired by C3NET, but extends the notion of significant interactions. By comparing two extended core networks, one inferred with sense data and the other one inferred with sense and anti-sense data, our differential analysis is first performed on a local view and reveals AS-impacted genes, genes that have important interactions impacted by anti-sense transcription. The motifs surrounding AS-impacted genes gather transcripts with functions mostly consistent with the biological context of the data used and the method allows us to identify new actors involved in ripening and cold acclimation pathways and to decipher their interactions. Then from a more global view, we compute minimal sub-networks that connect the AS-impacted genes using Steiner trees. Those Steiner trees allow us to study the rewiring of the AS-impacted genes in the network with anti-sense actors.

Conclusion

Anti-sense transcription is usually ignored in transcriptomic studies. The large-scale differential analysis of apple data that we propose reveals that anti-sense regulation may have an important impact in several cellular stress response mechanisms. Our data mining process enables to highlight specific interactions that deserve further experimental investigations.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0613-7) contains supplementary material, which is available to authorized users.

Identifying Node Importance in a Complex Network Based on Node Bridging Feature

Identifying node importance in complex networks is of great significance to improve the network damage resistance and robustness. In the era of big data, the size of the network is huge and the network structure tends to change dynamically over time. Due to the high complexity, the algorithm based on the global information of the network is not suitable for the analysis of large-scale networks. Taking into account the bridging feature of nodes in the local network, this paper proposes a simple and efficient ranking algorithm to identify node importance in complex networks. In the algorithm, if there are more numbers of node pairs whose shortest paths pass through the target node and there are less numbers of shortest paths in its neighborhood, the bridging function of the node between its neighborhood nodes is more obvious, and its ranking score is also higher. The algorithm takes only local information of the target nodes, thereby greatly improving the efficiency of the algorithm. Experiments performed on real and synthetic networks show that the proposed algorithm is more effective than benchmark algorithms on the evaluation criteria of the maximum connectivity coefficient and the decline rate of network efficiency, no matter in the static or dynamic attack manner. Especially in the initial stage of attack, the advantage is more obvious, which makes the proposed algorithm applicable in the background of limited network attack cost.

Feedbacks from the metabolic network to the genetic network reveal regulatory modules in E. coli and B. subtilis

The genetic regulatory network (GRN) plays a key role in controlling the response of the cell to changes in the environment. Although the structure of GRNs has been the subject of many studies, their large scale structure in the light of feedbacks from the metabolic network (MN) has received relatively little attention. Here we study the causal structure of the GRNs, namely the chain of influence of one component on the other, taking into account feedback from the MN. First we consider the GRNs of E. coli and B. subtilis without feedback from MN and illustrate their causal structure. Next we augment the GRNs with feedback from their respective MNs by including (a) links from genes coding for enzymes to metabolites produced or consumed in reactions catalyzed by those enzymes and (b) links from metabolites to genes coding for transcription factors whose transcriptional activity the metabolites alter by binding to them. We find that the inclusion of feedback from MN into GRN significantly affects its causal structure, in particular the number of levels and relative positions of nodes in the hierarchy, and the number and size of the strongly connected components (SCCs). We then study the functional significance of the SCCs. For this we identify condition specific feedbacks from the MN into the GRN by retaining only those enzymes that are essential for growth in specific environmental conditions simulated via the technique of flux balance analysis (FBA). We find that the SCCs of the GRN augmented by these feedbacks can be ascribed specific functional roles in the organism. Our algorithmic approach thus reveals relatively autonomous subsystems with specific functionality, or regulatory modules in the organism. This automated approach could be useful in identifying biologically relevant modules in other organisms for which network data is available, but whose biology is less well studied.

Integrating Imaging Genomic Data in the Quest for Biomarkers of Schizophrenia Disease

It's increasingly important but difficult to determine potential biomarkers of schizophrenia (SCZ) disease, owing to the complex pathophysiology of this disease. In this study, a network-fusion based framework was proposed to identify genetic biomarkers of the SCZ disease. A three-step feature selection was applied to single nucleotide polymorphisms (SNPs), DNA methylation, and functional magnetic resonance imaging (fMRI) data to select important features, which were then used to construct two gene networks in different states for the SNPs and DNA methylation data, respectively. Two health networks (one is for SNP data and the other is for DNA methylation data) were combined into one health network from which health minimum spanning trees (MSTs) were extracted. Two disease networks also followed the same procedures. Those genes with significant changes were determined as SCZ biomarkers by comparing MSTs in two different states and they were finally validated from five aspects. The effectiveness of the proposed discovery framework was also demonstrated by comparing with other network-based discovery methods. In summary, our approach provides a general framework for discovering gene biomarkers of the complex diseases by integrating imaging genomic data, which can be applied to the diagnosis of the complex diseases in the future.

Amino acid impact factor

Amino acid mutations in proteins are random and those mutations which are beneficial or neutral survive during the course of evolution. Conservation or co-evolution analyses are performed on the multiple sequence alignment of homologous proteins to understand how important different amino acids or groups of them are. However, these traditional analyses do not explore the directed influence of amino acid mutations, such as compensatory effects. In this work we develop a method to capture the directed evolutionary impact of one amino acid on all other amino acids, and provide a visual network representation for it. The method developed for these directed networks of inter- and intra-protein evolutionary interactions can also be used for noting the differences in amino acid evolution between the control and experimental groups. The analysis is illustrated with a few examples, where the method identifies several directed interactions of functionally critical amino acids. The impact of an amino acid is quantified as the number of amino acids that are influenced as a consequence of its mutation, and it is intended to summarize the compensatory mutations in large evolutionary sequence data sets as well as to rationally identify targets for mutagenesis when their functional significance can not be assessed using structure or conservation.

fastBMA: scalable network inference and transitive reduction

Inferring genetic networks from genome-wide expression data is extremely demanding computationally. We have developed fastBMA, a distributed, parallel, and scalable implementation of Bayesian model averaging (BMA) for this purpose. fastBMA also includes a computationally efficient module for eliminating redundant indirect edges in the network by mapping the transitive reduction to an easily solved shortest-path problem. We evaluated the performance of fastBMA on synthetic data and experimental genome-wide time series yeast and human datasets. When using a single CPU core, fastBMA is up to 100 times faster than the next fastest method, LASSO, with increased accuracy. It is a memory-efficient, parallel, and distributed application that scales to human genome-wide expression data. A 10 000-gene regulation network can be obtained in a matter of hours using a 32-core cloud cluster (2 nodes of 16 cores). fastBMA is a significant improvement over its predecessor ScanBMA. It is more accurate and orders of magnitude faster than other fast network inference methods such as the 1 based on LASSO. The improved scalability allows it to calculate networks from genome scale data in a reasonable time frame. The transitive reduction method can improve accuracy in denser networks. fastBMA is available as code (M.I.T. license) from GitHub (https://github.com/lhhunghimself/fastBMA), as part of the updated networkBMA Bioconductor package (https://www.bioconductor.org/packages/release/bioc/html/networkBMA.html) and as ready-to-deploy Docker images (https://hub.docker.com/r/biodepot/fastbma/).

Dissection of the module network implementation "LemonTree": enhancements towards applications in metagenomics and translation in autoimmune maladies

Under the current deluge of omics, module networks distinctively emerge as methods capable of not only identifying inherently coherent groups (modules), thus reducing dimensionality, but also hypothesizing cause-effect relationships between modules and their regulators. Module networks were first designed in the transcriptomic era and further exploited in the multi-omic context to assess (for example) miRNA regulation of gene expression. Despite a number of available implementations, expansion of module networks to other omics is constrained by a limited characterization of the solutions' (modules plus regulators) accuracy and stability - an immediate need for the better characterization of molecular biology complexity in silico. We hence carefully assessed for LemonTree - a popular and open source module network implementation - the dependency of the software performances (sensitivity, specificity, false discovery rate, solutions' stability) on the input parameters and on the data quality (sample size, expression noise) based on synthetic and real data. In the process, we uncovered and fixed an issue in the code for the regulator assignment procedure. We concluded this evaluation with a table of recommended parameter settings. Finally, we applied these recommended settings to gut-intestinal metagenomic data from rheumatoid arthritis patients, to characterize the evolution of the gut-intestinal microbiome under different pharmaceutical regimens (methotrexate and prednisone) and we inferred innovative clinical recommendations with therapeutic potential, based on the computed module network.

Optimal stabilization of Boolean networks through collective influence

Boolean networks have attracted much attention due to their wide applications in describing dynamics of biological systems. During past decades, much effort has been invested in unveiling how network structure and update rules affect the stability of Boolean networks. In this paper, we aim to identify and control a minimal set of influential nodes that is capable of stabilizing an unstable Boolean network. For locally treelike Boolean networks with biased truth tables, we propose a greedy algorithm to identify influential nodes in Boolean networks by minimizing the largest eigenvalue of a modified nonbacktracking matrix. We test the performance of the proposed collective influence algorithm on four different networks. Results show that the collective influence algorithm can stabilize each network with a smaller set of nodes compared with other heuristic algorithms. Our work provides a new insight into the mechanism that determines the stability of Boolean networks, which may find applications in identifying virulence genes that lead to serious diseases.

Identification of regulatory modules in genome scale transcription regulatory networks

Background

In gene regulatory networks, transcription factors often function as co-regulators to synergistically induce or inhibit expression of their target genes. However, most existing module-finding algorithms can only identify densely connected genes but not co-regulators in regulatory networks.

Methods

We have developed a new computational method, CoReg, to identify transcription co-regulators in large-scale regulatory networks. CoReg calculates gene similarities based on number of common neighbors of any two genes. Using simulated and real networks, we compared the performance of different similarity indices and existing module-finding algorithms and we found CoReg outperforms other published methods in identifying co-regulatory genes. We applied CoReg to a large-scale network of Arabidopsis with more than 2.8 million edges and we analyzed more than 2,300 published gene expression profiles to charaterize co-expression patterns of gene moduled identified by CoReg.

Results

We identified three types of modules in the Arabidopsis network: regulator modules, target modules and intermediate modules. Regulator modules include genes with more than 90% edges as out-going edges; Target modules include genes with more than 90% edges as incoming edges. Other modules are classified as intermediate modules. We found that genes in target modules tend to be highly co-expressed under abiotic stress conditions, suggesting this network struture is robust against perturbation.

Conclusions

Our analysis shows that the CoReg is an accurate method in identifying co-regulatory genes in large-scale networks. We provide CoReg as an R package, which can be applied in finding co-regulators in any organisms with genome-scale regulatory network data.

Electronic supplementary material

The online version of this article (10.1186/s12918-017-0493-2) contains supplementary material, which is available to authorized users.