Using a state-space model with hidden variables to infer transcription factor activities

Flexible modeling of regulatory networks improves transcription factor activity estimation

Transcriptional regulation plays a crucial role in determining cell fate and disease, yet inferring the key regulators from gene expression data remains a significant challenge. Existing methods for estimating transcription factor (TF) activity often rely on static TF-gene interaction databases and cannot adapt to changes in regulatory mechanisms across different cell types and disease conditions. Here, we present a new algorithm - Transcriptional Inference using Gene Expression and Regulatory data (TIGER) - that overcomes these limitations by flexibly modeling activation and inhibition events, up-weighting essential edges, shrinking irrelevant edges towards zero through a sparse Bayesian prior, and simultaneously estimating both TF activity levels and changes in the underlying regulatory network. When applied to yeast and cancer TF knock-out datasets, TIGER outperforms comparable methods in terms of prediction accuracy. Moreover, our application of TIGER to tissue- and cell-type-specific RNA-seq data demonstrates its ability to uncover differences in regulatory mechanisms. Collectively, our findings highlight the utility of modeling context-specific regulation when inferring transcription factor activities.

Hierarchical graphical model reveals HFR1 bridging circadian rhythm and flower development in Arabidopsis thaliana

To study systems-level properties of the cell, it is necessary to go beyond individual regulators and target genes to study the regulatory network among transcription factors (TFs). However, it is difficult to directly dissect the TFs mediated genome-wide gene regulatory network (GRN) by experiment. Here, we proposed a hierarchical graphical model to estimate TF activity from mRNA expression by building TF complexes with protein cofactors and inferring TF's downstream regulatory network simultaneously. Then we applied our model on flower development and circadian rhythm processes in Arabidopsis thaliana. The computational results show that the sequence specific bHLH family TF HFR1 recruits the chromatin regulator HAC1 to flower development master regulator TF AG and further activates AG's expression by histone acetylation. Both independent data and experimental results supported this discovery. We also found a flower tissue specific H3K27ac ChIP-seq peak at AG gene body and a HFR1 motif in the center of this H3K27ac peak. Furthermore, we verified that HFR1 physically interacts with HAC1 by yeast two-hybrid experiment. This HFR1-HAC1-AG triplet relationship may imply that flower development and circadian rhythm are bridged by epigenetic regulation and enrich the classical ABC model in flower development. In addition, our TF activity network can serve as a general method to elucidate molecular mechanisms on other complex biological regulatory processes.

Reverse Engineering of Genome-wide Gene Regulatory Networks from Gene Expression Data

Transcriptional regulation plays vital roles in many fundamental biological processes. Reverse engineering of genome-wide regulatory networks from high-throughput transcriptomic data provides a promising way to characterize the global scenario of regulatory relationships between regulators and their targets. In this review, we summarize and categorize the main frameworks and methods currently available for inferring transcriptional regulatory networks from microarray gene expression profiling data. We overview each of strategies and introduce representative methods respectively. Their assumptions, advantages, shortcomings, and possible improvements and extensions are also clarified and commented.

Influenza A immunomics and public health omics: the dynamic pathway interplay in host response to H1N1 infection

Towards unraveling the influenza A (H1N1) immunome, this work aims at constructing the murine host response pathway interactome. To accomplish that, an ensemble of dynamic and time-varying Gene Regulatory Network Inference methodologies was recruited to set a confident interactome based on mouse time series transcriptome data (day 1-day 60). The proposed H1N1 interactome demonstrated significant transformations among activated and suppressed pathways in time. Enhanced interplay was observed at day 1, while the maximal network complexity was reached at day 8 (correlated with viral clearance and iBALT tissue formation) and one interaction was present at day 40. Next, we searched for common interactivity features between the murine-adapted PR8 strain and other influenza A subtypes/strains. For this, two other interactomes, describing the murine host response against H5N1 and H1N1pdm, were constructed, which in turn validated many of the observed interactions (in the period day 1-day 7). The H1N1 interactome revealed the role of cell cycle both in innate and adaptive immunity (day 1-day 14). Also, pathogen sensory pathways (e.g., RIG-I) displayed long-lasting association with cytokine/chemokine signaling (until day 8). Interestingly, the above observations were also supported by the H5N1 and H1N1pdm models. It also elucidated the enhanced coupling of the activated innate pathways with the suppressed PPAR signaling to keep low inflammation until viral clearance (until day 14). Further, it showed that interactions reflecting phagocytosis processes continued long after the viral clearance and the establishment of adaptive immunity (day 8-day 40). Additionally, interactions involving B cell receptor pathway were evident since day 1. These results collectively inform the emerging field of public health omics and future clinical studies aimed at deciphering dynamic host responses to infectious agents.

Network component analysis provides quantitative insights on an Arabidopsis transcription factor-gene regulatory network

Background

Gene regulatory networks (GRNs) are models of molecule-gene interactions instrumental in the coordination of gene expression. Transcription factor (TF)-GRNs are an important subset of GRNs that characterize gene expression as the effect of TFs acting on their target genes. Although such networks can qualitatively summarize TF-gene interactions, it is highly desirable to quantitatively determine the strengths of the interactions in a TF-GRN as well as the magnitudes of TF activities. To our knowledge, such analysis is rare in plant biology. A computational methodology developed for this purpose is network component analysis (NCA), which has been used for studying large-scale microbial TF-GRNs to obtain nontrivial, mechanistic insights. In this work, we employed NCA to quantitatively analyze a plant TF-GRN important in floral development using available regulatory information from AGRIS, by processing previously reported gene expression data from four shoot apical meristem cell types.

Results

The NCA model satisfactorily accounted for gene expression measurements in a TF-GRN of seven TFs (LFY, AG, SEPALLATA3 [SEP3], AP2, AGL15, HY5 and AP3/PI) and 55 genes. NCA found strong interactions between certain TF-gene pairs including LFY → MYB17, AG → CRC, AP2 → RD20, AGL15 → RAV2 and HY5 → HLH1, and the direction of the interaction (activation or repression) for some AGL15 targets for which this information was not previously available. The activity trends of four TFs - LFY, AG, HY5 and AP3/PI as deduced by NCA correlated well with the changes in expression levels of the genes encoding these TFs across all four cell types; such a correlation was not observed for SEP3, AP2 and AGL15.

Conclusions

For the first time, we have reported the use of NCA to quantitatively analyze a plant TF-GRN important in floral development for obtaining nontrivial information about connectivity strengths between TFs and their target genes as well as TF activity. However, since NCA relies on documented connectivity information about the underlying TF-GRN, it is currently limited in its application to larger plant networks because of the lack of documented connectivities. In the future, the identification of interactions between plant TFs and their target genes on a genome scale would allow the use of NCA to provide quantitative regulatory information about plant TF-GRNs, leading to improved insights on cellular regulatory programs.

Differential reconstructed gene interaction networks for deriving toxicity threshold in chemical risk assessment

Background

Pathway alterations reflected as changes in gene expression regulation and gene interaction can result from cellular exposure to toxicants. Such information is often used to elucidate toxicological modes of action. From a risk assessment perspective, alterations in biological pathways are a rich resource for setting toxicant thresholds, which may be more sensitive and mechanism-informed than traditional toxicity endpoints. Here we developed a novel differential networks (DNs) approach to connect pathway perturbation with toxicity threshold setting.

Methods

Our DNs approach consists of 6 steps: time-series gene expression data collection, identification of altered genes, gene interaction network reconstruction, differential edge inference, mapping of genes with differential edges to pathways, and establishment of causal relationships between chemical concentration and perturbed pathways. A one-sample Gaussian process model and a linear regression model were used to identify genes that exhibited significant profile changes across an entire time course and between treatments, respectively. Interaction networks of differentially expressed (DE) genes were reconstructed for different treatments using a state space model and then compared to infer differential edges/interactions. DE genes possessing differential edges were mapped to biological pathways in databases such as KEGG pathways.

Results

Using the DNs approach, we analyzed a time-series Escherichia coli live cell gene expression dataset consisting of 4 treatments (control, 10, 100, 1000 mg/L naphthenic acids, NAs) and 18 time points. Through comparison of reconstructed networks and construction of differential networks, 80 genes were identified as DE genes with a significant number of differential edges, and 22 KEGG pathways were altered in a concentration-dependent manner. Some of these pathways were perturbed to a degree as high as 70% even at the lowest exposure concentration, implying a high sensitivity of our DNs approach.

Conclusions

Findings from this proof-of-concept study suggest that our approach has a great potential in providing a novel and sensitive tool for threshold setting in chemical risk assessment. In future work, we plan to analyze more time-series datasets with a full spectrum of concentrations and sufficient replications per treatment. The pathway alteration-derived thresholds will also be compared with those derived from apical endpoints such as cell growth rate.

Large-scale dynamic gene regulatory network inference combining differential equation models with local dynamic Bayesian network analysis

MOTIVATION

Reverse engineering gene regulatory networks, especially large size networks from time series gene expression data, remain a challenge to the systems biology community. In this article, a new hybrid algorithm integrating ordinary differential equation models with dynamic Bayesian network analysis, called Differential Equation-based Local Dynamic Bayesian Network (DELDBN), was proposed and implemented for gene regulatory network inference.

RESULTS

The performance of DELDBN was benchmarked with an in vivo dataset from yeast. DELDBN significantly improved the accuracy and sensitivity of network inference compared with other approaches. The local causal discovery algorithm implemented in DELDBN also reduced the complexity of the network inference algorithm and improved its scalability to infer larger networks. We have demonstrated the applicability of the approach to a network containing thousands of genes with a dataset from human HeLa cell time series experiments. The local network around BRCA1 was particularly investigated and validated with independent published studies. BRAC1 network was significantly enriched with the known BRCA1-relevant interactions, indicating that DELDBN can effectively infer large size gene regulatory network from time series data.

AVAILABILITY

The R scripts are provided in File 3 in Supplementary Material.

CONTACT

zheng.li@monsanto.com; jingdong.liu@monsanto.com

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Reconstructing genome-wide regulatory network of E. coli using transcriptome data and predicted transcription factor activities

Background

Gene regulatory networks play essential roles in living organisms to control growth, keep internal metabolism running and respond to external environmental changes. Understanding the connections and the activity levels of regulators is important for the research of gene regulatory networks. While relevance score based algorithms that reconstruct gene regulatory networks from transcriptome data can infer genome-wide gene regulatory networks, they are unfortunately prone to false positive results. Transcription factor activities (TFAs) quantitatively reflect the ability of the transcription factor to regulate target genes. However, classic relevance score based gene regulatory network reconstruction algorithms use models do not include the TFA layer, thus missing a key regulatory element.

Results

This work integrates TFA prediction algorithms with relevance score based network reconstruction algorithms to reconstruct gene regulatory networks with improved accuracy over classic relevance score based algorithms. This method is called Gene expression and Transcription factor activity based Relevance Network (GTRNetwork). Different combinations of TFA prediction algorithms and relevance score functions have been applied to find the most efficient combination. When the integrated GTRNetwork method was applied to E. coli data, the reconstructed genome-wide gene regulatory network predicted 381 new regulatory links. This reconstructed gene regulatory network including the predicted new regulatory links show promising biological significances. Many of the new links are verified by known TF binding site information, and many other links can be verified from the literature and databases such as EcoCyc. The reconstructed gene regulatory network is applied to a recent transcriptome analysis of E. coli during isobutanol stress. In addition to the 16 significantly changed TFAs detected in the original paper, another 7 significantly changed TFAs have been detected by using our reconstructed network.

Conclusions

The GTRNetwork algorithm introduces the hidden layer TFA into classic relevance score-based gene regulatory network reconstruction processes. Integrating the TFA biological information with regulatory network reconstruction algorithms significantly improves both detection of new links and reduces that rate of false positives. The application of GTRNetwork on E. coli gene transcriptome data gives a set of potential regulatory links with promising biological significance for isobutanol stress and other conditions.

Sparse Regulatory Networks

In many organisms the expression levels of each gene are controlled by the activation levels of known "Transcription Factors" (TF). A problem of considerable interest is that of estimating the "Transcription Regulation Networks" (TRN) relating the TFs and genes. While the expression levels of genes can be observed, the activation levels of the corresponding TFs are usually unknown, greatly increasing the difficulty of the problem. Based on previous experimental work, it is often the case that partial information about the TRN is available. For example, certain TFs may be known to regulate a given gene or in other cases a connection may be predicted with a certain probability. In general, the biology of the problem indicates there will be very few connections between TFs and genes. Several methods have been proposed for estimating TRNs. However, they all suffer from problems such as unrealistic assumptions about prior knowledge of the network structure or computational limitations. We propose a new approach that can directly utilize prior information about the network structure in conjunction with observed gene expression data to estimate the TRN. Our approach uses L(1) penalties on the network to ensure a sparse structure. This has the advantage of being computationally efficient as well as making many fewer assumptions about the network structure. We use our methodology to construct the TRN for E. coli and show that the estimate is biologically sensible and compares favorably with previous estimates.

Mathematical modeling: bridging the gap between concept and realization in synthetic biology

Mathematical modeling plays an important and often indispensable role in synthetic biology because it serves as a crucial link between the concept and realization of a biological circuit. We review mathematical modeling concepts and methodologies as relevant to synthetic biology, including assumptions that underlie a model, types of modeling frameworks (deterministic and stochastic), and the importance of parameter estimation and optimization in modeling. Additionally we expound mathematical techniques used to analyze a model such as sensitivity analysis and bifurcation analysis, which enable the identification of the conditions that cause a synthetic circuit to behave in a desired manner. We also discuss the role of modeling in phenotype analysis such as metabolic and transcription network analysis and point out some available modeling standards and software. Following this, we present three case studies—a metabolic oscillator, a synthetic counter, and a bottom-up gene regulatory network—which have incorporated mathematical modeling as a central component of synthetic circuit design.

Reconstructing transcriptional regulatory networks through genomics data

One central problem in biology is to understand how gene expression is regulated under different conditions. Microarray gene expression data and other high throughput data have made it possible to dissect transcriptional regulatory networks at the genomics level. Owing to the very large number of genes that need to be studied, the relatively small number of data sets available, the noise in the data and the different natures of the distinct data types, network inference presents great challenges. In this article, we review statistical and computational methods that have been developed in the last decade in response to genomics data for inferring transcriptional regulatory networks.

Using a state-space model and location analysis to infer time-delayed regulatory networks

Computational gene regulation models provide a means for scientists to draw biological inferences from time-course gene expression data. Based on the state-space approach, we developed a new modeling tool for inferring gene regulatory networks, called time-delayed Gene Regulatory Networks (tdGRNs). tdGRN takes time-delayed regulatory relationships into consideration when developing the model. In addition, a priori biological knowledge from genome-wide location analysis is incorporated into the structure of the gene regulatory network. tdGRN is evaluated on both an artificial dataset and a published gene expression data set. It not only determines regulatory relationships that are known to exist but also uncovers potential new ones. The results indicate that the proposed tool is effective in inferring gene regulatory relationships with time delay. tdGRN is complementary to existing methods for inferring gene regulatory networks. The novel part of the proposed tool is that it is able to infer time-delayed regulatory relationships.

Modelling and analysis of gene regulatory networks

Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, the cell cycle and signal transduction. By understanding the dynamics of these networks we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated. Accurate prediction of the behaviour of regulatory networks will also speed up biotechnological projects, as such predictions are quicker and cheaper than lab experiments. Computational methods, both for supporting the development of network models and for the analysis of their functionality, have already proved to be a valuable research tool.

Statistical inference of transcriptional module-based gene networks from time course gene expression profiles by using state space models

MOTIVATION

Statistical inference of gene networks by using time-course microarray gene expression profiles is an essential step towards understanding the temporal structure of gene regulatory mechanisms. Unfortunately, most of the current studies have been limited to analysing a small number of genes because the length of time-course gene expression profiles is fairly short. One promising approach to overcome such a limitation is to infer gene networks by exploring the potential transcriptional modules which are sets of genes sharing a common function or involved in the same pathway.

RESULTS

In this article, we present a novel approach based on the state space model to identify the transcriptional modules and module-based gene networks simultaneously. The state space model has the potential to infer large-scale gene networks, e.g. of order 10(3), from time-course gene expression profiles. Particularly, we succeeded in the identification of a cell cycle system by using the gene expression profiles of Saccharomyces cerevisiae in which the length of the time-course and number of genes were 24 and 4382, respectively. However, when analysing shorter time-course data, e.g. of length 10 or less, the parameter estimations of the state space model often fail due to overfitting. To extend the applicability of the state space model, we provide an approach to use the technical replicates of gene expression profiles, which are often measured in duplicate or triplicate. The use of technical replicates is important for achieving highly-efficient inferences of gene networks with short time-course data. The potential of the proposed method has been demonstrated through the time-course analysis of the gene expression profiles of human umbilical vein endothelial cells (HUVECs) undergoing growth factor deprivation-induced apoptosis.

AVAILABILITY

Supplementary Information and the software (TRANS-MNET) are available at http://daweb.ism.ac.jp/~yoshidar/software/ssm/.

Dynamical pathway analysis

Background

Although a great deal is known about one gene or protein and its functions under different environmental conditions, little information is available about the complex behaviour of biological networks subject to different environmental perturbations. Observing differential expressions of one or more genes between normal and abnormal cells has been a mainstream method of discovering pertinent genes in diseases and therefore valuable drug targets. However, to date, no such method exists for elucidating and quantifying the differential dynamical behaviour of genetic regulatory networks, which can have greater impact on phenotypes than individual genes.

Results

We propose to redress the deficiency by formulating the functional study of biological networks as a control problem of dynamical systems. We developed mathematical methods to study the stability, the controllability, and the steady-state behaviour, as well as the transient responses of biological networks under different environmental perturbations. We applied our framework to three real-world datasets: the SOS DNA repair network in E. coli under different dosages of radiation, the GSH redox cycle in mice lung exposed to either poisonous air or normal air, and the MAPK pathway in mammalian cell lines exposed to three types of HIV type I Vpr, a wild type and two mutant types; and we found that the three genetic networks exhibited fundamentally different dynamical properties in normal and abnormal cells.

Conclusion

Difference in stability, relative stability, degrees of controllability, and transient responses between normal and abnormal cells means considerable difference in dynamical behaviours and different functioning of cells. Therefore differential dynamical properties can be a valuable tool in biomedical research.

A systematic approach to detecting transcription factors in response to environmental stresses

Background

Eukaryotic cells have developed mechanisms to respond to external environmental or physiological changes (stresses). In order to increase the activities of stress-protection functions in response to an environmental change, the internal cell mechanisms need to induce certain specific gene expression patterns and pathways by changing the expression levels of specific transcription factors (TFs). The conventional methods to find these specific TFs and their interactivities are slow and laborious. In this study, a novel efficient method is proposed to detect the TFs and their interactivities that regulate yeast genes that respond to any specific environment change.

Results

For each gene expressed in a specific environmental condition, a dynamic regulatory model is constructed in which the coefficients of the model represent the transcriptional activities and interactivities of the corresponding TFs. The proposed method requires only microarray data and information of all TFs that bind to the gene but it has superior resolution than the current methods. Our method not only can find stress-specific TFs but also can predict their regulatory strengths and interactivities. Moreover, TFs can be ranked, so that we can identify the major TFs to a stress. Similarly, it can rank the interactions between TFs and identify the major cooperative TF pairs. In addition, the cross-talks and interactivities among different stress-induced pathways are specified by the proposed scheme to gain much insight into protective mechanisms of yeast under different environmental stresses.

Conclusion

In this study, we find significant stress-specific and cell cycle-controlled TFs via constructing a transcriptional dynamic model to regulate the expression profiles of genes under different environmental conditions through microarray data. We have applied this TF activity and interactivity detection method to many stress conditions, including hyper- and hypo- osmotic shock, heat shock, hydrogen peroxide and cell cycle, because the available expression time profiles for these conditions are long enough. Especially, we find significant TFs and cooperative TFs responding to environmental changes. Our method may also be applicable to other stresses if the gene expression profiles have been examined for a sufficiently long time.

Biological network mapping and source signal deduction

MOTIVATION

Many biological networks, including transcriptional regulation, metabolism, and the absorbance spectra of metabolite mixtures, can be represented in a bipartite fashion. Key to understanding these bipartite networks are the network architecture and governing source signals. Such information is often implicitly imbedded in the data. Here we develop a technique, network component mapping (NCM), to deduce bipartite network connectivity and regulatory signals from data without any need for prior information.

RESULTS

We demonstrate the utility of our approach by analyzing UV-vis spectra from mixtures of metabolites and gene expression data from Saccharomyces cerevisiae. From UV-vis spectra, hidden mixing networks and pure component spectra (sources) were deduced to a higher degree of resolution with our method than other current bipartite techniques. Analysis of S. cerevisiae gene expression from two separate environmental conditions (zinc and DTT treatment) yielded transcription networks consistent with ChIP-chip derived network connectivity. Due to the high degree of noise in gene expression data, the transcription network for many genes could not be inferred. However, with relatively clean expression data, our technique was able to deduce hidden transcription networks and instances of combinatorial regulation. These results suggest that NCM can deduce correct network connectivity from relatively accurate data. For noisy data, NCM yields the sparsest network capable of explaining the data. In addition, partial knowledge of the network topology can be incorporated into NCM as constraints.

AVAILABILITY

Algorithm available on request from the authors. Soon to be posted on the web, http://www.seas.ucla.edu/~liaoj/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Bayesian model-based inference of transcription factor activity

Background

In many approaches to the inference and modeling of regulatory interactions using microarray data, the expression of the gene coding for the transcription factor is considered to be an accurate surrogate for the true activity of the protein it produces. There are many instances where this is inaccurate due to post-translational modifications of the transcription factor protein. Inference of the activity of the transcription factor from the expression of its targets has predominantly involved linear models that do not reflect the nonlinear nature of transcription. We extend a recent approach to inferring the transcription factor activity based on nonlinear Michaelis-Menten kinetics of transcription from maximum likelihood to fully Bayesian inference and give an example of how the model can be further developed.

Results

We present results on synthetic and real microarray data. Additionally, we illustrate how gene and replicate specific delays can be incorporated into the model.

Conclusion

We demonstrate that full Bayesian inference is appropriate in this application and has several benefits over the maximum likelihood approach, especially when the volume of data is limited. We also show the benefits of using a non-linear model over a linear model, particularly in the case of repression.

A new framework for identifying combinatorial regulation of transcription factors: a case study of the yeast cell cycle

By integrating heterogeneous functional genomic datasets, we have developed a new framework for detecting combinatorial control of gene expression, which includes estimating transcription factor activities using a singular value decomposition method and reducing high-dimensional input gene space by considering genomic properties of gene clusters. The prediction of cooperative gene regulation is accomplished by either Gaussian Graphical Models or Pairwise Mixed Graphical Models. The proposed framework was tested on yeast cell cycle datasets: (1) 54 known yeast cell cycle genes with 9 cell cycle regulators and (2) 676 putative yeast cell cycle genes with 9 cell cycle regulators. The new framework gave promising results on inferring TF-TF and TF-gene interactions. It also revealed several interesting mechanisms such as negatively correlated protein-protein interactions and low affinity protein-DNA interactions that may be important during the yeast cell cycle. The new framework may easily be extended to study other higher eukaryotes.