Structure Of Gene Regulatory Networks Research Articles

Gene regulatory network structure informs the distribution of perturbation effects.

Gene regulatory networks (GRNs) govern many core developmental and biological processes underlying human complex traits. Even with broad-scale efforts to characterize the effects of molecular perturbations and interpret gene coexpression, it remains challenging to infer the architecture of gene regulation in a precise and efficient manner. Key properties of GRNs, like hierarchical structure, modular organization, and sparsity, provide both challenges and opportunities for this objective. Here, we seek to better understand properties of GRNs using a new approach to simulate their structure and model their function. We produce realistic network structures with a novel generating algorithm based on insights from small-world network theory, and we model gene expression regulation using stochastic differential equations formulated to accommodate modeling molecular perturbations. With these tools, we systematically describe the effects of gene knockouts within and across GRNs, finding a subset of networks that recapitulate features of a recent genome-scale perturbation study. With deeper analysis of these exemplar networks, we consider future avenues to map the architecture of gene expression regulation using data from cells in perturbed and unperturbed states, finding that while perturbation data are critical to discover specific regulatory interactions, data from unperturbed cells may be sufficient to reveal regulatory programs.

Stochastic modeling of a gene regulatory network driving B cell development in germinal centers.

Germinal centers (GCs) are the key histological structures of the adaptive immune system, responsible for the development and selection of B cells producing high-affinity antibodies against antigens. Due to their level of complexity, unexpected malfunctioning may lead to a range of pathologies, including various malignant formations. One promising way to improve the understanding of malignant transformation is to study the underlying gene regulatory networks (GRNs) associated with cell development and differentiation. Evaluation and inference of the GRN structure from gene expression data is a challenging task in systems biology: recent achievements in single-cell (SC) transcriptomics allow the generation of SC gene expression data, which can be used to sharpen the knowledge on GRN structure. In order to understand whether a particular network of three key gene regulators (BCL6, IRF4, BLIMP1), influenced by two external stimuli signals (surface receptors BCR and CD40), is able to describe GC B cell differentiation, we used a stochastic model to fit SC transcriptomic data from a human lymphoid organ dataset. The model is defined mathematically as a piecewise-deterministic Markov process. We showed that after parameter tuning, the model qualitatively recapitulates mRNA distributions corresponding to GC and plasmablast stages of B cell differentiation. Thus, the model can assist in validating the GRN structure and, in the future, could lead to better understanding of the different types of dysfunction of the regulatory mechanisms.

Feasibility of Gene Regulatory Network Inference Under Different Noise Conditions

One of the most difficult and pressing problems in computational cell biology is the inference of gene regulatory network structure from transcriptomic data. Although this topic has been widely studied for more than a decade, it is still unclear how well these methods work and how their performance differs under different conditions. We analyze the feasibility of network inference from mRNA abundance data using simulations of gene regulatory interactions, considering both intrinsic and extrinsic noise in the process of gene expression. We find that under conditions of only intrinsic noise in gene expression, the correlation between mRNA levels of genes in an activation relationship is quite low, suggesting that the task of network inference from transcriptomic data is very difficult under these conditions. By contrast, extrinsic noise affecting the process of gene expression, which could come from an upstream regulator, external stimulus, or change in the cell state, results in higher correlation between mRNA levels of these genes, potentially making the task of network inference from mRNA data more feasible. Lastly, we analyze the problem of false positives between genes that have no direct interaction but share a common upstream regulator, and explore a strategy for distinguishing between these false positives and true interactions based on noise profiles of mRNA expression levels.

Evolution of hierarchy and irreversibility in theoretical cell differentiation model.

The process of cell differentiation in multicellular organisms is characterized by hierarchy and irreversibility in many cases. However, the conditions and selection pressures that give rise to these characteristics remain poorly understood. By using a mathematical model, here we show that the network of differentiation potency (differentiation diagram) becomes necessarily hierarchical and irreversible by increasing the number of terminally differentiated states under certain conditions. The mechanisms generating these characteristics are clarified using geometry in the cell state space. The results demonstrate that the hierarchical organization and irreversibility can manifest independently of direct selection pressures associated with these characteristics, instead they appear to evolve as byproducts of selective forces favoring a diversity of differentiated cell types. The study also provides a new perspective on the structure of gene regulatory networks that produce hierarchical and irreversible differentiation diagrams. These results indicate some constraints on cell differentiation, which are expected to provide a starting point for theoretical discussion of the implicit limits and directions of evolution in multicellular organisms.

Learning massive interpretable gene regulatory networks of the human brain by merging Bayesian networks.

We present the Fast Greedy Equivalence Search (FGES)-Merge, a new method for learning the structure of gene regulatory networks via merging locally learned Bayesian networks, based on the fast greedy equivalent search algorithm. The method is competitive with the state of the art in terms of the Matthews correlation coefficient, which takes into account both precision and recall, while also improving upon it in terms of speed, scaling up to tens of thousands of variables and being able to use empirical knowledge about the topological structure of gene regulatory networks. To showcase the ability of our method to scale to massive networks, we apply it to learning the gene regulatory network for the full human genome using data from samples of different brain structures (from the Allen Human Brain Atlas). Furthermore, this Bayesian network model should predict interactions between genes in a way that is clear to experts, following the current trends in explainable artificial intelligence. To achieve this, we also present a new open-access visualization tool that facilitates the exploration of massive networks and can aid in finding nodes of interest for experimental tests.

Structure-Based Inverse Reinforcement Learning for Quantification of Biological Knowledge.

Gene regulatory networks (GRNs) play crucial roles in various cellular processes, including stress response, DNA repair, and the mechanisms involved in complex diseases such as cancer. Biologists are involved in most biological analyses. Thus, quantifying their policies reflected in available biological data can significantly help us to better understand these complex systems. The primary challenges preventing the utilization of existing machine learning, particularly inverse reinforcement learning techniques, to quantify biologists' knowledge are the limitations and huge amount of uncertainty in biological data. This paper leverages the network-like structure of GRNs to define expert reward functions that contain exponentially fewer parameters than regular reward models. Numerical experiments using mammalian cell cycle and synthetic gene-expression data demonstrate the superior performance of the proposed method in quantifying biologists' policies.

Gene regulation network inference using k-nearest neighbor-based mutual information estimation: revisiting an old DREAM

BackgroundA cell exhibits a variety of responses to internal and external cues. These responses are possible, in part, due to the presence of an elaborate gene regulatory network (GRN) in every single cell. In the past 20 years, many groups worked on reconstructing the topological structure of GRNs from large-scale gene expression data using a variety of inference algorithms. Insights gained about participating players in GRNs may ultimately lead to therapeutic benefits. Mutual information (MI) is a widely used metric within this inference/reconstruction pipeline as it can detect any correlation (linear and non-linear) between any number of variables (n-dimensions). However, the use of MI with continuous data (for example, normalized fluorescence intensity measurement of gene expression levels) is sensitive to data size, correlation strength and underlying distributions, and often requires laborious and, at times, ad hoc optimization.ResultsIn this work, we first show that estimating MI of a bi- and tri-variate Gaussian distribution using k-nearest neighbor (kNN) MI estimation results in significant error reduction as compared to commonly used methods based on fixed binning. Second, we demonstrate that implementing the MI-based kNN Kraskov–Stoögbauer–Grassberger (KSG) algorithm leads to a significant improvement in GRN reconstruction for popular inference algorithms, such as Context Likelihood of Relatedness (CLR). Finally, through extensive in-silico benchmarking we show that a new inference algorithm CMIA (Conditional Mutual Information Augmentation), inspired by CLR, in combination with the KSG-MI estimator, outperforms commonly used methods.ConclusionsUsing three canonical datasets containing 15 synthetic networks, the newly developed method for GRN reconstruction—which combines CMIA, and the KSG-MI estimator—achieves an improvement of 20–35% in precision-recall measures over the current gold standard in the field. This new method will enable researchers to discover new gene interactions or better choose gene candidates for experimental validations.

WpLogicNet: logic gate and structure inference in gene regulatory networks.

The gene regulatory process resembles a logic system in which a target gene is regulated by a logic gate among its regulators. While various computational techniques are developed for a gene regulatory network (GRN) reconstruction, the study of logical relationships has received little attention. Here, we propose a novel tool called wpLogicNet that simultaneously infers both the directed GRN structures and logic gates among genes or transcription factors (TFs) that regulate their target genes, based on continuous steady-state gene expressions. wpLogicNet proposes a framework to infer the logic gates among any number of regulators, with a low time-complexity. This distinguishes wpLogicNet from the existing logic-based models that are limited to inferring the gate between two genes or TFs. Our method applies a Bayesian mixture model to estimate the likelihood of the target gene profile and to infer the logic gate a posteriori. Furthermore, in structure-aware mode, wpLogicNet reconstructs the logic gates in TF-gene or gene-gene interaction networks with known structures. The predicted logic gates are validated on simulated datasets of TF-gene interaction networks from Escherichia coli. For the directed-edge inference, the method is validated on datasets from E.coli and DREAM project. The results show that compared to other well-known methods, wpLogicNet is more precise in reconstructing the network and logical relationships among genes. The datasets and R package of wpLogicNet are available in the github repository, https://github.com/CompBioIPM/wpLogicNet. Supplementary data are available at Bioinformatics online.

Learning complex dependency structure of gene regulatory networks from high dimensional microarray data with Gaussian Bayesian networks

Reconstruction of Gene Regulatory Networks (GRNs) of gene expression data with Probabilistic Network Models (PNMs) is an open problem. Gene expression datasets consist of thousand of genes with relatively small sample sizes (i.e. are large-p-small-n). Moreover, dependencies of various orders coexist in the datasets. On the one hand transcription factor encoding genes act like hubs and regulate target genes, on the other hand target genes show local dependencies. In the field of Undirected Network Models (UNMs)—a subclass of PNMs—the Glasso algorithm has been proposed to deal with high dimensional microarray datasets forcing sparsity. To overcome the problem of the complex structure of interactions, modifications of the default Glasso algorithm have been developed that integrate the expected dependency structure in the UNMs beforehand. In this work we advocate the use of a simple score-based Hill Climbing algorithm (HC) that learns Gaussian Bayesian networks leaning on directed acyclic graphs. We compare HC with Glasso and variants in the UNM framework based on their capability to reconstruct GRNs from microarray data from the benchmarking synthetic dataset from the DREAM5 challenge and from real-world data from the Escherichia coli genome. We conclude that dependencies in complex data are learned best by the HC algorithm, presenting them most accurately and efficiently, simultaneously modelling strong local and weaker but significant global connections coexisting in the gene expression dataset. The HC algorithm adapts intrinsically to the complex dependency structure of the dataset, without forcing a specific structure in advance.

Inferring causal gene regulatory network via GreyNet: From dynamic grey association to causation.

Gene regulatory network (GRN) provides abundant information on gene interactions, which contributes to demonstrating pathology, predicting clinical outcomes, and identifying drug targets. Existing high-throughput experiments provide rich time-series gene expression data to reconstruct the GRN to further gain insights into the mechanism of organisms responding to external stimuli. Numerous machine-learning methods have been proposed to infer gene regulatory networks. Nevertheless, machine learning, especially deep learning, is generally a “black box,” which lacks interpretability. The causality has not been well recognized in GRN inference procedures. In this article, we introduce grey theory integrated with the adaptive sliding window technique to flexibly capture instant gene–gene interactions in the uncertain regulatory system. Then, we incorporate generalized multivariate Granger causality regression methods to transform the dynamic grey association into causation to generate directional regulatory links. We evaluate our model on the DREAM4 in silico benchmark dataset and real-world hepatocellular carcinoma (HCC) time-series data. We achieved competitive results on the DREAM4 compared with other state-of-the-art algorithms and gained meaningful GRN structure on HCC data respectively.

INSISTC: Incorporating network structure information for single-cell type classification

Uncovering gene regulatory mechanisms in individual cells can provide insight into cell heterogeneity and function. Recent accumulated Single-Cell RNA-Seq data have made it possible to analyze gene regulation at single-cell resolution. Understanding cell-type-specific gene regulation can assist in more accurate cell type and state identification. Computational approaches utilizing such relationships are under development. Methods pioneering in integrating gene regulatory mechanism discovery with cell-type classification encounter challenges such as determine gene regulatory relationships and incorporate gene regulatory network structure. To fill this gap, we developed INSISTC, a computational method to incorporate gene regulatory network structure information for single-cell type classification. INSISTC is capable of identifying cell-type-specific gene regulatory mechanisms while performing single-cell type classification. INSISTC demonstrated its accuracy in cell type classification and its potential for providing insight into molecular mechanisms specific to individual cells. In comparison with the alternative methods, INSISTC demonstrated its complementary performance for gene regulation interpretation.

Inference on the structure of gene regulatory networks

In this paper, we conduct theoretical analyses on inferring the structure of gene regulatory networks. Depending on the experimental method and data type, the inference problem is classified into 20 different scenarios. For each scenario, we discuss the problem that with enough data, under what assumptions, what can be inferred about the structure. For scenarios that have been covered in the literature, we provide a brief review. For scenarios that have not been covered in literature, if the structure can be inferred, we propose new mathematical inference methods and evaluate them on simulated data. Otherwise, we prove that the structure cannot be inferred.

Common Themes and Future Challenges in Understanding Gene Regulatory Network Evolution.

A major driving force behind the evolution of species-specific traits and novel structures is alterations in gene regulatory networks (GRNs). Comprehending evolution therefore requires an understanding of the nature of changes in GRN structure and the responsible mechanisms. Here, we review two insect pigmentation GRNs in order to examine common themes in GRN evolution and to reveal some of the challenges associated with investigating changes in GRNs across different evolutionary distances at the molecular level. The pigmentation GRN in Drosophila melanogaster and other drosophilids is a well-defined network for which studies from closely related species illuminate the different ways co-option of regulators can occur. The pigmentation GRN for butterflies of the Heliconius species group is less fully detailed but it is emerging as a useful model for exploring important questions about redundancy and modularity in cis-regulatory systems. Both GRNs serve to highlight the ways in which redeployment of trans-acting factors can lead to GRN rewiring and network co-option. To gain insight into GRN evolution, we discuss the importance of defining GRN architecture at multiple levels both within and between species and of utilizing a range of complementary approaches.

Reconstruction of dynamic regulatory networks reveals signaling-induced topology changes associated with germ layer specification.

SummaryElucidating regulatory relationships between transcription factors (TFs) and target genes is fundamental to understanding how cells control their identity and behavior. Unfortunately, existing computational gene regulatory network (GRN) reconstruction methods are imprecise, computationally burdensome, and fail to reveal dynamic regulatory topologies. Here, we present Epoch, a reconstruction tool that uses single-cell transcriptomics to accurately infer dynamic networks. We apply Epoch to identify the dynamic networks underpinning directed differentiation of mouse embryonic stem cells (ESCs) guided by multiple signaling pathways, and we demonstrate that modulating these pathways drives topological changes that bias cell fate potential. We also find that Peg3 rewires the pluripotency network to favor mesoderm specification. By integrating signaling pathways with GRNs, we trace how Wnt activation and PI3K suppression govern mesoderm and endoderm specification, respectively. Finally, we identify regulatory circuits of patterning and axis formation that distinguish in vitro and in vivo mesoderm specification.

The tolerance to hypoxia is defined by a time-sensitive response of the gene regulatory network in sea urchin embryos.

ABSTRACTDeoxygenation, the reduction of oxygen level in the oceans induced by global warming and anthropogenic disturbances, is a major threat to marine life. This change in oxygen level could be especially harmful to marine embryos that use endogenous hypoxia and redox gradients as morphogens during normal development. Here, we show that the tolerance to hypoxic conditions changes between different developmental stages of the sea urchin embryo, possibly due to the structure of the gene regulatory networks (GRNs). We demonstrate that during normal development, the bone morphogenetic protein (BMP) pathway restricts the activity of the vascular endothelial growth factor (VEGF) pathway to two lateral domains and this restriction controls proper skeletal patterning. Hypoxia applied during early development strongly perturbs the activity of Nodal and BMP pathways that affect the VEGF pathway, dorsal-ventral (DV) and skeletogenic patterning. These pathways are largely unaffected by hypoxia applied after DV-axis formation. We propose that the use of redox and hypoxia as morphogens makes the sea urchin embryo highly sensitive to environmental hypoxia during early development, but the GRN structure provides higher tolerance to hypoxia at later stages.

An order independent algorithm for inferring gene regulatory network using quantile value for conditional independence tests

In recent years, due to the difficulty and inefficiency of experimental methods, numerous computational methods have been introduced for inferring the structure of Gene Regulatory Networks (GRNs). The Path Consistency (PC) algorithm is one of the popular methods to infer the structure of GRNs. However, this group of methods still has limitations and there is a potential for improvements in this field. For example, the PC-based algorithms are still sensitive to the ordering of nodes i.e. different node orders results in different network structures. The second is that the networks inferred by these methods are highly dependent on the threshold used for independence testing. Also, it is still a challenge to select the set of conditional genes in an optimal way, which affects the performance and computation complexity of the PC-based algorithm. We introduce a novel algorithm, namely Order Independent PC-based algorithm using Quantile value (OIPCQ), which improves the accuracy of the learning process of GRNs and solves the order dependency issue. The quantile-based thresholds are considered for different orders of CMI tests. For conditional gene selection, we consider the paths between genes with length equal or greater than 2 while other well-known PC-based methods only consider the paths of length 2. We applied OIPCQ on the various networks of the DREAM3 and DREAM4 in silico challenges. As a real-world case study, we used OIPCQ to reconstruct SOS DNA network obtained from Escherichia coli and GRN for acute myeloid leukemia based on the RNA sequencing data from The Cancer Genome Atlas. The results show that OIPCQ produces the same network structure for all the permutations of the genes and improves the resulted GRN through accurately quantifying the causal regulation strength in comparison with other well-known PC-based methods. According to the GRN constructed by OIPCQ, for acute myeloid leukemia, two regulators BCLAF1 and NRSF reported previously are significantly important. However, the highest degree nodes in this GRN are ZBTB7A and PU1 which play a significant role in cancer, especially in leukemia. OIPCQ is freely accessible at https://github.com/haammim/OIPCQ-and-OIPCQ2.

Network Inference from Gene Expression Data with Distance Correlation and Network Topology Centrality

The reconstruction of gene regulatory networks based on gene expression data can effectively uncover regulatory relationships between genes and provide a deeper understanding of biological control processes. Non-linear dependence is a common problem in the regulatory mechanisms of gene regulatory networks. Various methods based on information theory have been developed to infer networks. However, the methods have introduced many redundant regulatory relationships in the network inference process. A recent measurement method called distance correlation has, in many cases, shown strong and computationally efficient non-linear correlations. In this paper, we propose a novel regulatory network inference method called the distance-correlation and network topology centrality network (DCNTC) method. The method is based on and extends the Local Density Measurement of Network Node Centrality (LDCNET) algorithm, which has the same choice of network centrality ranking as the LDCNET algorithm, but uses a simpler and more efficient distance correlation measure of association between genes. In this work, we integrate distance correlation and network topological centrality into the reasoning about the structure of gene regulatory networks. We will select optimal thresholds based on the characteristics of the distribution of each gene pair in relation to distance correlation. Experiments were carried out on four network datasets and their performance was compared.

Unsupervised Gene Regulatory Network Inference using K-Nearest-Neighbor Based Mutual Information

Biological cells exhibit a variety of responses to internal cues and different external perturbations. This is possible due to elaborate gene regulatory networks (GRNs). The structure of GRN cannot be drawn by reading the genetic code, instead, a series of knockdown experiments on a downstream process or cell state was used to infer the GRN structure. The advancement in large scale gene expression data collection, enables inference of large networks. Basic networks were built by clustering co-expressed genes using a statistical correlation metric, like covariance. Information theory is a widely used correlation metric, as it can detect any correlation (linear and non-linear) between any number of variables (n-dimensional). Using information theory for higher dimensions and continuous data (i.e. normalizes expression data) is sensitive to data size, correlation strength and underlying distributions. To estimate it, few techniques are used: fixed width binning, adaptive partitioning, kernel density estimator and k-nearest neighbor (KNN). Unfortunately, most techniques require user defined parameters and “tweaking” which lead to many different implementations. The era of single cell transcriptome only worsens the problem as data is noisier, and while KNN was shown to be accurate and robust option for any user defined parameter, it was hardly used due to its computational costs. Here, we present a novel GRN inference method that solves two issues in the field: A) Implementation of unsupervised and accurate three-way MI estimator based on KNN, B) Reconstructing the network - we use all two- and three-way MI quantities (total of seven) to generate a digital signature (or “barcode”) to most 3-node network topologies, instead of ranking the interactions according to a single MI quantity with an arbitrary threshold to solve conflicts.

Inferring dynamic gene regulatory networks with low-order conditional independencies – an evaluation of the method

Abstract Over a decade ago, Lèbre (2009) proposed an inference method, G1DBN, to learn the structure of gene regulatory networks (GRNs) from high dimensional, sparse time-series gene expression data. Their approach is based on concept of low-order conditional independence graphs that they extend to dynamic Bayesian networks (DBNs). They present results to demonstrate that their method yields better structural accuracy compared to the related Lasso and Shrinkage methods, particularly where the data is sparse, that is, the number of time measurements n is much smaller than the number of genes p. This paper challenges these claims using a careful experimental analysis, to show that the GRNs reverse engineered from time-series data using the G1DBN approach are less accurate than claimed by Lèbre (2009). We also show that the Lasso method yields higher structural accuracy for graphs learned from the simulated data, compared to the G1DBN method, particularly when the data is sparse ( n < < p $n{< }{< }p$ ). The Lasso method is also better than G1DBN at identifying the transcription factors (TFs) involved in the cell cycle of Saccharomyces cerevisiae.

Differential analysis of gene regulatory networks modeled with structural equation models

A gene regulatory networks (GRN) is composed of a set of genes as well as the regulatory relationships between them. Under different conditions, GRNs with the same gene set usually have similar but not exactly the same structure. The differential analysis of GRNs under different conditions is of great significance to understand gene functions and biological mechanisms. In a naive approach, GRNs under different conditions can be separately inferred via existing GRN inference algorithms, and then the difference between them can be identified by comparing the estimated structures. However, such an approach does not consider the commonality of the pairwise GRNs, which may decrease the predictive accuracy of the differential GRN. In this paper, we model GRNs with the structural equation models (SEMs) to integrate gene expression data and genetic perturbations, and propose a joint differential analysis algorithm named differential sparse SEM (DiffSSEM) to identify the topology structures of GRNs under different conditions as well as the difference between them. The DiffSSEM algorithm simultaneously consider the sparsity of separate GRNs and differential GRN. Simulations were run on synthetic data and the results demonstrated that the DiffSSEM algorithm outperforms the naive approach based on a state-of-the-art sparse SEM inference algorithm. Finally, a real data set of 15 lung genes from 42 tumor tissues and normal tissues was analyzed with the DiffSSEM algorithm to identify the differential GRN.