Perturbation analysis analyzed—mathematical modeling of intact and perturbed gene regulatory circuits for animal development

Gene regulatory networks for animal development are the underlying mechanisms controlling cell fate specification and differentiation. The architecture of gene regulatory circuits determines their information processing properties and their developmental function. It is a major task to derive realistic network models from exceedingly advanced high throughput experimental data. Here we use mathematical modeling to study the dynamics of gene regulatory circuits to advance the ability to infer regulatory connections and logic function from experimental data. This study is guided by experimental methodologies that are commonly used to study gene regulatory networks that control cell fate specification. We study the effect of a perturbation of an input on the level of its downstream genes and compare between the cis-regulatory execution of OR and AND logics. Circuits that initiate gene activation and circuits that lock on the expression of genes are analyzed. The model improves our ability to analyze experimental data and construct from it the network topology. The model also illuminates information processing properties of gene regulatory circuits for animal development.     

Network modelling of gene regulation

Gene regulatory network (GRN) modelling has gained increasing attention in the past decade. Many computational modelling techniques have been proposed to facilitate the inference and analysis of GRN. However, there is often confusion about the aim of GRN modelling, and how a gene network model can be fully utilised as a tool for systems biology. The aim of the present article is to provide an overview of this rapidly expanding subject. In particular, we review some fundamental concepts of systems biology and discuss the role of network modelling in understanding complex biological systems. Several commonly used network modelling paradigms are surveyed with emphasis on their practical use in systems biology research.     

Towards precise reconstruction of gene regulatory networks by data integration

Background: More and more high-throughput datasets are available from multiple levels of measuring gene regulations. The reverse engineering of gene regulatory networks from these data offers a valuable research paradigm to decipher regulatory mechanisms. So far, numerous methods have been developed for reconstructing gene regulatory networks. Results: In this paper, we provide a review of bioinformatics methods for inferring gene regulatory network from omics data. To achieve the precision reconstruction of gene regulatory networks, an intuitive alternative is to integrate these available resources in a rational framework. We also provide computational perspectives in the endeavors of inferring gene regulatory networks from heterogeneous data. We highlight the importance of multi-omics data integration with prior knowledge in gene regulatory network inferences. Conclusions: We provide computational perspectives of inferring gene regulatory networks from multiple omics data and present theoretical analyses of existing challenges and possible solutions. We emphasize on prior knowledge and data integration in network inferences owing to their abilities of identifying regulatory causality.     

Gene network inference using continuous time Bayesian networks: a comparative study and application to Th17 cell differentiation

Background

Dynamic aspects of gene regulatory networks are typically investigated by measuring system variables at multiple time points. Current state-of-the-art computational approaches for reconstructing gene networks directly build on such data, making a strong assumption that the system evolves in a synchronous fashion at fixed points in time. However, nowadays omics data are being generated with increasing time course granularity. Thus, modellers now have the possibility to represent the system as evolving in continuous time and to improve the models’ expressiveness.

Results

Continuous time Bayesian networks are proposed as a new approach for gene network reconstruction from time course expression data. Their performance was compared to two state-of-the-art methods: dynamic Bayesian networks and Granger causality analysis. On simulated data, the methods comparison was carried out for networks of increasing size, for measurements taken at different time granularity densities and for measurements unevenly spaced over time. Continuous time Bayesian networks outperformed the other methods in terms of the accuracy of regulatory interactions learnt from data for all network sizes. Furthermore, their performance degraded smoothly as the size of the network increased. Continuous time Bayesian networks were significantly better than dynamic Bayesian networks for all time granularities tested and better than Granger causality for dense time series. Both continuous time Bayesian networks and Granger causality performed robustly for unevenly spaced time series, with no significant loss of performance compared to the evenly spaced case, while the same did not hold true for dynamic Bayesian networks. The comparison included the IRMA experimental datasets which confirmed the effectiveness of the proposed method. Continuous time Bayesian networks were then applied to elucidate the regulatory mechanisms controlling murine T helper 17 (Th17) cell differentiation and were found to be effective in discovering well-known regulatory mechanisms, as well as new plausible biological insights.

Conclusions

Continuous time Bayesian networks were effective on networks of both small and large size and were particularly feasible when the measurements were not evenly distributed over time. Reconstruction of the murine Th17 cell differentiation network using continuous time Bayesian networks revealed several autocrine loops, suggesting that Th17 cells may be auto regulating their own differentiation process.     

Gene network inference and visualization tools for biologists: application to new human transcriptome datasets

Gene regulatory networks inferred from RNA abundance data have generated significant interest, but despite this, gene network approaches are used infrequently and often require input from bioinformaticians. We have assembled a suite of tools for analysing regulatory networks, and we illustrate their use with microarray datasets generated in human endothelial cells. We infer a range of regulatory networks, and based on this analysis discuss the strengths and limitations of network inference from RNA abundance data. We welcome contact from researchers interested in using our inference and visualization tools to answer biological questions.     

Inference of the Xenopus tropicalis embryonic regulatory network and spatial gene expression patterns

Background

During embryogenesis, signaling molecules produced by one cell population direct gene regulatory changes in neighboring cells and influence their developmental fates and spatial organization. One of the earliest events in the development of the vertebrate embryo is the establishment of three germ layers, consisting of the ectoderm, mesoderm and endoderm. Attempts to measure gene expression in vivo in different germ layers and cell types are typically complicated by the heterogeneity of cell types within biological samples (i.e., embryos), as the responses of individual cell types are intermingled into an aggregate observation of heterogeneous cell types. Here, we propose a novel method to elucidate gene regulatory circuits from these aggregate measurements in embryos of the frog Xenopus tropicalis using gene network inference algorithms and then test the ability of the inferred networks to predict spatial gene expression patterns.

Results

We use two inference models with different underlying assumptions that incorporate existing network information, an ODE model for steady-state data and a Markov model for time series data, and contrast the performance of the two models. We apply our method to both control and knockdown embryos at multiple time points to reconstruct the core mesoderm and endoderm regulatory circuits. Those inferred networks are then used in combination with known dorsal-ventral spatial expression patterns of a subset of genes to predict spatial expression patterns for other genes. Both models are able to predict spatial expression patterns for some of the core mesoderm and endoderm genes, but interestingly of different gene subsets, suggesting that neither model is sufficient to recapitulate all of the spatial patterns, yet they are complementary for the patterns that they do capture.

Conclusion

The presented methodology of gene network inference combined with spatial pattern prediction provides an additional layer of validation to elucidate the regulatory circuits controlling the spatial-temporal dynamics in embryonic development.     

Inferring Regulatory Networks from Expression Data Using Tree-Based Methods

One of the pressing open problems of computational systems biology is the elucidation of the topology of genetic regulatory networks (GRNs) using high throughput genomic data, in particular microarray gene expression data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) challenge aims to evaluate the success of GRN inference algorithms on benchmarks of simulated data. In this article, we present GENIE3, a new algorithm for the inference of GRNs that was best performer in the DREAM4 In Silico Multifactorial challenge. GENIE3 decomposes the prediction of a regulatory network between p genes into p different regression problems. In each of the regression problems, the expression pattern of one of the genes (target gene) is predicted from the expression patterns of all the other genes (input genes), using tree-based ensemble methods Random Forests or Extra-Trees. The importance of an input gene in the prediction of the target gene expression pattern is taken as an indication of a putative regulatory link. Putative regulatory links are then aggregated over all genes to provide a ranking of interactions from which the whole network is reconstructed. In addition to performing well on the DREAM4 In Silico Multifactorial challenge simulated data, we show that GENIE3 compares favorably with existing algorithms to decipher the genetic regulatory network of Escherichia coli. It doesn''t make any assumption about the nature of gene regulation, can deal with combinatorial and non-linear interactions, produces directed GRNs, and is fast and scalable. In conclusion, we propose a new algorithm for GRN inference that performs well on both synthetic and real gene expression data. The algorithm, based on feature selection with tree-based ensemble methods, is simple and generic, making it adaptable to other types of genomic data and interactions.     

Inferring the perturbed microRNA regulatory networks from gene expression data using a network propagation based method

Background

MicroRNAs (miRNAs) are a class of endogenous small regulatory RNAs. Identifications of the dys-regulated or perturbed miRNAs and their key target genes are important for understanding the regulatory networks associated with the studied cellular processes. Several computational methods have been developed to infer the perturbed miRNA regulatory networks by integrating genome-wide gene expression data and sequence-based miRNA-target predictions. However, most of them only use the expression information of the miRNA direct targets, rarely considering the secondary effects of miRNA perturbation on the global gene regulatory networks.

Results

We proposed a network propagation based method to infer the perturbed miRNAs and their key target genes by integrating gene expressions and global gene regulatory network information. The method used random walk with restart in gene regulatory networks to model the network effects of the miRNA perturbation. Then, it evaluated the significance of the correlation between the network effects of the miRNA perturbation and the gene differential expression levels with a forward searching strategy. Results show that our method outperformed several compared methods in rediscovering the experimentally perturbed miRNAs in cancer cell lines. Then, we applied it on a gene expression dataset of colorectal cancer clinical patient samples and inferred the perturbed miRNA regulatory networks of colorectal cancer, including several known oncogenic or tumor-suppressive miRNAs, such as miR-17, miR-26 and miR-145.

Conclusions

Our network propagation based method takes advantage of the network effect of the miRNA perturbation on its target genes. It is a useful approach to infer the perturbed miRNAs and their key target genes associated with the studied biological processes using gene expression data.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-255) contains supplementary material, which is available to authorized users.     

Gene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information

Abstract

The extended Kalman filter (EKF) has been applied to inferring gene regulatory networks. However, it is well known that the EKF becomes less accurate when the system exhibits high nonlinearity. In addition, certain prior information about the gene regulatory network exists in practice, and no systematic approach has been developed to incorporate such prior information into the Kalman-type filter for inferring the structure of the gene regulatory network. In this paper, an inference framework based on point-based Gaussian approximation filters that can exploit the prior information is developed to solve the gene regulatory network inference problem. Different point-based Gaussian approximation filters, including the unscented Kalman filter (UKF), the third-degree cubature Kalman filter (CKF₃), and the fifth-degree cubature Kalman filter (CKF₅) are employed. Several types of network prior information, including the existing network structure information, sparsity assumption, and the range constraint of parameters, are considered, and the corresponding filters incorporating the prior information are developed. Experiments on a synthetic network of eight genes and the yeast protein synthesis network of five genes are carried out to demonstrate the performance of the proposed framework. The results show that the proposed methods provide more accurate inference results than existing methods, such as the EKF and the traditional UKF.

     

Dynamic-module redundancy confers robustness to the gene regulatory network involved in hair patterning of Arabidopsis epidermis

Redundancy among dynamic modules is emerging as a potentially generic trait in gene regulatory networks. Moreover, module redundancy could play an important role in network robustness to perturbations. We explored the effect of dynamic-module redundancy in the networks associated to hair patterning in Arabidopsis root and leaf epidermis. Recent studies have put forward several dynamic modules belonging to these networks. We defined these modules in a discrete dynamical framework that was previously reported. Then, we addressed whether these modules are sufficient or necessary for recovering epidermal cell types and patterning. After defining two quantitative estimates of the system's robustness, we also compared the robustness of each separate module with that of a network coupling all the leaf or root modules. We found that, considering certain assumptions, all the dynamic modules proposed so far are sufficient on their own for pattern formation, but reinforce each other during epidermal development. Furthermore, we found that networks of coupled modules are more robust to perturbations than single modules. These results suggest that dynamic-module redundancy might be an important trait in gene regulatory networks and point at central questions regarding network evolution, module coupling, pattern robustness and the evolution of development.     

Considerations for using integral feedback control to construct a perfectly adapting synthetic gene network

It has long been known to control theorists and engineers that integral feedback control leads to, and is necessary for, “perfect” adaptation to step input perturbations in most systems. Consequently, implementation of this robust control strategy in a synthetic gene network is an attractive prospect. However, the nature of genetic regulatory networks (density-dependent kinetics and molecular signals that easily reach saturation) implies that the design and construction of such a device is not straightforward. In this study, we propose a generic two-promoter genetic regulatory network for the purpose of exhibiting perfect adaptation; our treatment highlights the challenges inherent in the implementation of a genetic integral controller. We also present a numerical case study for a specific realization of this two-promoter network, “constructed” using commonly available parts from the bacterium Escherichia coli. We illustrate the possibility of optimizing this network's transient response via analogy to a linear, free-damped harmonic oscillator. Finally, we discuss extensions of this two-promoter network to a proportional-integral controller and to a three-promoter network capable of perfect adaptation under conditions where first-order protein removal effects would otherwise disrupt the adaptation.