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PubMed2005

Inferring gene regulatory networks with time delays using a genetic algorithm.

Recently a state-space model with time delays for inferring gene regulatory networks was proposed. It was assumed that each regulation between two internal state variables had multiple time delays. This assumption caused underestimation of the model with many current gene expression datasets. In biological reality, one regulatory relationship may have just a single time delay, and not multiple time delays. This study employs Boolean variables to capture the existence of the time-delayed regulatory relationships in gene regulatory networks in terms of the state-space model. As the solution space of time delayed relationships is too large for an exhaustive search, a genetic algorithm (GA) is proposed to determine the optimal Boolean variables (the optimal time-delayed regulatory relationships). Coupled with the proposed GA, Bayesian information criterion (BIC) and probabilistic principle component analysis (PPCA) are employed to infer gene regulatory networks with time delays. Computational experiments are performed on two real gene expression datasets. The results show that the GA is effective at finding time-delayed regulatory relationships. Moreover, the inferred gene regulatory networks with time delays from the datasets improve the prediction accuracy and possess more of the expected properties of a real network, compared to a gene regulatory network without time delays.

Algorithms↗
PubMed2005

A stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae.

MOTIVATION: The explosion of microarray studies has promised to shed light on the temporal expression patterns of thousands of genes simultaneously. However, available methods are far from adequate in efficiently extracting useful information to aid in a greater understanding of transcriptional regulatory network. Biological systems have been modeled as dynamic systems for a long history, such as genetic networks and cell regulatory network. This study evaluated if the stochastic differential equation (SDE), which is prominent for modeling dynamic diffusion process originating from the irregular Brownian motion, can be applied in modeling the transcriptional regulatory network in Saccharomyces cerevisiae. RESULTS: To model the time-continuous gene-expression datasets, a model of SDE is applied to depict irregular patterns. Our goal is to fit a generalized linear model by combining putative regulators to estimate the transcriptional pattern of a target gene. Goodness-of-fit is evaluated by log-likelihood and Akaike Information Criterion. Moreover, estimations of the contribution of regulators and inference of transcriptional pattern are implemented by statistical approaches. Our SDE model is basic but the test results agree well with the observed dynamic expression patterns. It implies that advanced SDE model might be perfectly suited to portray transcriptional regulatory networks. AVAILABILITY: The R code is available on request. CONTACT: cykao@csie.ntu.edu.tw SUPPLEMENTARY INFORMATION: http://www.csie.ntu.edu.tw/~b89x035/yeast/

Gene Expression Regulation↗
PubMed2026

gMISpy: integration of complex regulatory networks and genome scale metabolic models.

MOTIVATION: Genome-scale metabolic models lack explicit regulatory mechanisms, limiting their predictive accuracy for genetic interventions. Current methods for computing genetic Minimal Cut Sets either ignore regulatory networks entirely or use simplified acyclic representations that cannot capture regulatory feedback loops, ubiquitous features critical in cellular modeling. RESULTS: We developed gMISpy, a Python package that that enables efficient computation of genetic Minimal Intervention Sets (gMISs) in integrated genome-scale metabolic and regulatory networks. gMISpy incorporates cyclic regulatory logic into our previous computational framework using layered Boolean networks and BoNesis framework, resulting in a more accurate modeling of how regulatory interactions affect metabolic genes. Benchmarking across four different regulatory networks with Human-GEM showed consistent improvements in prediction accuracy, with Matthews correlation coefficient gains ranging from 2.50% to 14.42%. Validation against cancer data from DepMap and Project Score confirmed that cyclic integration reduces false positives and better captures biological vulnerabilities compared to acyclic approaches. AVAILABILITY AND IMPLEMENTATION: https://github.com/PlanesLab/cyclic-gMISpy.

Software↗
PubMed2004

Hierarchical structure and modules in the Escherichia coli transcriptional regulatory network revealed by a new top-down approach.

BACKGROUND: Cellular functions are coordinately carried out by groups of genes forming functional modules. Identifying such modules in the transcriptional regulatory network (TRN) of organisms is important for understanding the structure and function of these fundamental cellular networks and essential for the emerging modular biology. So far, the global connectivity structure of TRN has not been well studied and consequently not applied for the identification of functional modules. Moreover, network motifs such as feed forward loop are recently proposed to be basic building blocks of TRN. However, their relationship to functional modules is not clear. RESULTS: In this work we proposed a top-down approach to identify modules in the TRN of E. coli. By studying the global connectivity structure of the regulatory network, we first revealed a five-layer hierarchical structure in which all the regulatory relationships are downward. Based on this regulatory hierarchy, we developed a new method to decompose the regulatory network into functional modules and to identify global regulators governing multiple modules. As a result, 10 global regulators and 39 modules were identified and shown to have well defined functions. We then investigated the distribution and composition of the two basic network motifs (feed forward loop and bi-fan motif) in the hierarchical structure of TRN. We found that most of these network motifs include global regulators, indicating that these motifs are not basic building blocks of modules since modules should not contain global regulators. CONCLUSION: The transcriptional regulatory network of E. coli possesses a multi-layer hierarchical modular structure without feedback regulation at transcription level. This hierarchical structure builds the basis for a new and simple decomposition method which is suitable for the identification of functional modules and global regulators in the transcriptional regulatory network of E. coli. Analysis of the distribution of feed forward loops and bi-fan motifs in the hierarchical structure suggests that these network motifs are not elementary building blocks of functional modules in the transcriptional regulatory network of E. coli.

Amino Acid Motifs↗
PubMed2006

Iterative reconstruction of transcriptional regulatory networks: an algorithmic approach.

The number of complete, publicly available genome sequences is now greater than 200, and this number is expected to rapidly grow in the near future as metagenomic and environmental sequencing efforts escalate and the cost of sequencing drops. In order to make use of this data for understanding particular organisms and for discerning general principles about how organisms function, it will be necessary to reconstruct their various biochemical reaction networks. Principal among these will be transcriptional regulatory networks. Given the physical and logical complexity of these networks, the various sources of (often noisy) data that can be utilized for their elucidation, the monetary costs involved, and the huge number of potential experiments approximately 10(12)) that can be performed, experiment design algorithms will be necessary for synthesizing the various computational and experimental data to maximize the efficiency of regulatory network reconstruction. This paper presents an algorithm for experimental design to systematically and efficiently reconstruct transcriptional regulatory networks. It is meant to be applied iteratively in conjunction with an experimental laboratory component. The algorithm is presented here in the context of reconstructing transcriptional regulation for metabolism in Escherichia coli, and, through a retrospective analysis with previously performed experiments, we show that the produced experiment designs conform to how a human would design experiments. The algorithm is able to utilize probability estimates based on a wide range of computational and experimental sources to suggest experiments with the highest potential of discovering the greatest amount of new regulatory knowledge.

Algorithms↗
PubMed2006

Global genetic regulatory networks controlling hematopoietic cell fates.

PURPOSE OF REVIEW: The gene expression profile of a cell is a consequence of transcription factor activities, which, in turn, are controlled by extra-cellular signals. The relationships between all these regulators constitute a genetic regulatory network, which can be used to predict the behavior of the cell in changing environments. We outline the progress being made to identify Genetic Regulatory Networks for hematopoiesis, using gene-by-gene approaches or emerging genomic technologies. RECENT FINDINGS: The construction of genetic regulatory networks for single and multicellular organisms has inspired the building of genetic regulatory networks for erythropoiesis and B-cell differentiation. genetic regulatory networks are 'scale-free', whereby some genes have many connections while others have very few. The well connected genes, or hubs, correspond to master regulators of the networks, acting to integrate signals and control the sequential passage of the cells through the differentiation process. Lineage decisions are governed by cross-antagonism between two hubs. Large datasets from genome-wide analyses support the concept of multilineage priming and will increasingly refine the network topologies. SUMMARY: As the underlying genetic regulatory networks for hematopoiesis continue to emerge, the program for lineage choice and differentiation will be revealed. More large-scale datasets identifying network components are needed alongside continued gene-by-gene analyses.

Animals↗
PubMed2002

Combining location and expression data for principled discovery of genetic regulatory network models.

We develop principled methods for the automatic induction (discovery) of genetic regulatory network models from multiple data sources and data modalities. Models of regulatory networks are represented as Bayesian networks, allowing the models to compactly and robustly capture probabilistic multivariate statistical dependencies between the various cellular factors in these networks. We build on previous Bayesian network validation results by extending the validation framework to the context of model induction, leveraging heuristic simulated annealing search algorithms and posterior model averaging. Using expression data in isolation yields results inconsistent with location data so we incorporate genomic location data to guide the model induction process. We combine these two data modalities by allowing location data to influence the model prior and expression data to influence the model likelihood. We demonstrate the utility of this approach by discovering genetic regulatory models of thirty-three variables involved in S. cerevisiae pheromone response. The models we automatically generate are consistent with the current understanding regarding this regulatory network, but also suggest new directions for future experimental investigation.

Bayes Theorem↗
PubMed2006

A method for the generation of standardized qualitative dynamical systems of regulatory networks.

BACKGROUND: Modeling of molecular networks is necessary to understand their dynamical properties. While a wealth of information on molecular connectivity is available, there are still relatively few data regarding the precise stoichiometry and kinetics of the biochemical reactions underlying most molecular networks. This imbalance has limited the development of dynamical models of biological networks to a small number of well-characterized systems. To overcome this problem, we wanted to develop a methodology that would systematically create dynamical models of regulatory networks where the flow of information is known but the biochemical reactions are not. There are already diverse methodologies for modeling regulatory networks, but we aimed to create a method that could be completely standardized, i.e. independent of the network under study, so as to use it systematically. RESULTS: We developed a set of equations that can be used to translate the graph of any regulatory network into a continuous dynamical system. Furthermore, it is also possible to locate its stable steady states. The method is based on the construction of two dynamical systems for a given network, one discrete and one continuous. The stable steady states of the discrete system can be found analytically, so they are used to locate the stable steady states of the continuous system numerically. To provide an example of the applicability of the method, we used it to model the regulatory network controlling T helper cell differentiation. CONCLUSION: The proposed equations have a form that permit any regulatory network to be translated into a continuous dynamical system, and also find its steady stable states. We showed that by applying the method to the T helper regulatory network it is possible to find its known states of activation, which correspond the molecular profiles observed in the precursor and effector cell types.

Cell Differentiation↗
PubMed2006

Discrete time piecewise affine models of genetic regulatory networks.

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. These models reduce to boolean networks in one limiting case of a parameter, and their asymptotic dynamics approaches that of a differential equation in another limiting case of this parameter. For intermediate values, the model present an original phenomenology which is argued to be due to delay effects. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle - with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with non-negligible delay effects.

Algorithms↗
PubMed2006

Integrated biclustering of heterogeneous genome-wide datasets for the inference of global regulatory networks.

BACKGROUND: The learning of global genetic regulatory networks from expression data is a severely under-constrained problem that is aided by reducing the dimensionality of the search space by means of clustering genes into putatively co-regulated groups, as opposed to those that are simply co-expressed. Be cause genes may be co-regulated only across a subset of all observed experimental conditions, biclustering (clustering of genes and conditions) is more appropriate than standard clustering. Co-regulated genes are also often functionally (physically, spatially, genetically, and/or evolutionarily) associated, and such a priori known or pre-computed associations can provide support for appropriately grouping genes. One important association is the presence of one or more common cis-regulatory motifs. In organisms where these motifs are not known, their de novo detection, integrated into the clustering algorithm, can help to guide the process towards more biologically parsimonious solutions. RESULTS: We have developed an algorithm, cMonkey, that detects putative co-regulated gene groupings by integrating the biclustering of gene expression data and various functional associations with the de novo detection of sequence motifs. CONCLUSION: We have applied this procedure to the archaeon Halobacterium NRC-1, as part of our efforts to decipher its regulatory network. In addition, we used cMonkey on public data for three organisms in the other two domains of life: Helicobacter pylori, Saccharomyces cerevisiae, and Escherichia coli. The biclusters detected by cMonkey both recapitulated known biology and enabled novel predictions (some for Halobacterium were subsequently confirmed in the laboratory). For example, it identified the bacteriorhodopsin regulon, assigned additional genes to this regulon with apparently unrelated function, and detected its known promoter motif. We have performed a thorough comparison of cMonkey results against other clustering methods, and find that cMonkey biclusters are more parsimonious with all available evidence for co-regulation.

Algorithms↗
PubMed2005

Xenopus as a model system to study transcriptional regulatory networks.

Development is controlled by a complex series of events requiring sequential gene activation. Understanding the logic of gene networks during development is necessary for a complete understanding of how genes contribute to phenotype. Pioneering work initiated in the sea urchin and Drosophila has demonstrated that reasonable transcriptional regulatory network diagrams representing early development in multicellular animals can be generated through use of appropriate genomic, genetic, and biochemical tools. Establishment of similar regulatory network diagrams for vertebrate development is a necessary step. The amphibian Xenopus has long been used as a model for vertebrate early development and has contributed greatly to the elucidation of gene regulation. Because the best and most extensively studied transcriptional regulatory network in Xenopus is that underlying the formation and function of Spemann's organizer, we describe the current status of our understanding of this gene regulatory network and its relationship to mesodermal patterning. Seventy-four transcription factors currently known to be expressed in the mesoendoderm of Xenopus gastrula were characterized according to their modes of action, DNA binding consensus sequences, and target genes. Among them, nineteen transcription factors were characterized sufficiently in detail, allowing us to generate a gene regulatory network diagram. Additionally, we discuss recent amphibian work using a combined DNA microarray and bioinformatics approach that promises to accelerate regulatory network studies.

Animals↗
PubMed2000

Hybrid Petri net representation of gene regulatory network.

It is important to provide a representation method of gene regulatory networks which realizes the intuitions of biologists while keeping the universality in its computational ability. In this paper, we propose a method to exploit hybrid Petri net (HPN) for representing gene regulatory networks. The HPN is an extension of Petri nets which have been used to represent many kinds of systems including stochastic ones in the field of computer sciences and engineerings. Since the HPN has continuous and discrete elements, it can easily handle biological factors such as protein and mRNA concentrations. We demonstrate that, by using HPNs, it is possible to translate biological facts into HPNs in a natural manner. It should be also emphasized that a hierarchical approach is taken for our construction of the genetic switch mechanism of lambda phage which is realized by using HPNs. This hierarchical approach with HPNs makes easier the arrangement of the components in the gene regulatory network based on the biological facts and provides us a prospective view of the network. We also show some computational results of the protein dynamics of the lambda phage mechanism that is simulated and observed by implementing the HPN on a currently available tool.

Bacteriophage lambda↗
PubMed2002

Probabilistic Boolean Networks: a rule-based uncertainty model for gene regulatory networks.

MOTIVATION: Our goal is to construct a model for genetic regulatory networks such that the model class: (i) incorporates rule-based dependencies between genes; (ii) allows the systematic study of global network dynamics; (iii) is able to cope with uncertainty, both in the data and the model selection; and (iv) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes. RESULTS: We introduce Probabilistic Boolean Networks (PBN) that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty. We show how the dynamics of these networks can be studied in the probabilistic context of Markov chains, with standard Boolean networks being special cases. Then, we discuss the relationship between PBNs and Bayesian networks--a family of graphical models that explicitly represent probabilistic relationships between variables. We show how probabilistic dependencies between a gene and its parent genes, constituting the basic building blocks of Bayesian networks, can be obtained from PBNs. Finally, we present methods for quantifying the influence of genes on other genes, within the context of PBNs. Examples illustrating the above concepts are presented throughout the paper.

Cell Cycle↗
PubMed2006

CoryneRegNet: an ontology-based data warehouse of corynebacterial transcription factors and regulatory networks.

BACKGROUND: The application of DNA microarray technology in post-genomic analysis of bacterial genome sequences has allowed the generation of huge amounts of data related to regulatory networks. This data along with literature-derived knowledge on regulation of gene expression has opened the way for genome-wide reconstruction of transcriptional regulatory networks. These large-scale reconstructions can be converted into in silico models of bacterial cells that allow a systematic analysis of network behavior in response to changing environmental conditions. DESCRIPTION: CoryneRegNet was designed to facilitate the genome-wide reconstruction of transcriptional regulatory networks of corynebacteria relevant in biotechnology and human medicine. During the import and integration process of data derived from experimental studies or literature knowledge CoryneRegNet generates links to genome annotations, to identified transcription factors and to the corresponding cis-regulatory elements. CoryneRegNet is based on a multi-layered, hierarchical and modular concept of transcriptional regulation and was implemented by using the relational database management system MySQL and an ontology-based data structure. Reconstructed regulatory networks can be visualized by using the yFiles JAVA graph library. As an application example of CoryneRegNet, we have reconstructed the global transcriptional regulation of a cellular module involved in SOS and stress response of corynebacteria. CONCLUSION: CoryneRegNet is an ontology-based data warehouse that allows a pertinent data management of regulatory interactions along with the genome-scale reconstruction of transcriptional regulatory networks. These models can further be combined with metabolic networks to build integrated models of cellular function including both metabolism and its transcriptional regulation.

Computer Graphics↗
PubMed2006

Unraveling condition specific gene transcriptional regulatory networks in Saccharomyces cerevisiae.

BACKGROUND: Gene expression and transcription factor (TF) binding data have been used to reveal gene transcriptional regulatory networks. Existing knowledge of gene regulation can be presented using gene connectivity networks. However, these composite connectivity networks do not specify the range of biological conditions of the activity of each link in the network. RESULTS: We present a novel method that utilizes the expression and binding patterns of the neighboring nodes of each link in existing experimentally-based, literature-derived gene transcriptional regulatory networks and extend them in silico using TF-gene binding motifs and a compendium of large expression data from Saccharomyces cerevisiae. Using this method, we predict several hundreds of new transcriptional regulatory TF-gene links, along with experimental conditions in which known and predicted links become active. This approach unravels new links in the yeast gene transcriptional regulatory network by utilizing the known transcriptional regulatory interactions, and is particularly useful for breaking down the composite transcriptional regulatory network to condition specific networks. CONCLUSION: Our methods can facilitate future binding experiments, as they can considerably help focus on the TFs that must be surveyed to understand gene regulation.(Supplemental material and the latest version of the MATLAB implementation of the United Signature Algorithm is available online at 1 or [see Additional files 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]).

Algorithms↗
PubMed2026

GRNContext: an interactive web platform for contextualized gene regulatory networks visualization across human cancers.

SUMMARY: While current Gene Regulatory Network (GRN) databases provide comprehensive reference maps of potential interactions between transcription factors and target genes, they do not specify which regulatory interactions are active within specific biological contexts. This limitation is particularly critical in cancer, where transcriptional programs are inherently tissue-specific. To address this gap, we developed GRNContext, an interactive web platform designed for the visualization, exploration, and comparative analysis of gene regulatory networks contextualized across 33 cancer types from The Cancer Genome Atlas (TCGA). Our approach uses the TFLink human reference GRN as a starting point and integrates TCGA transcriptomic profiles to infer cancer-specific regulatory activity. Regulatory relevance was assessed using complementary machine learning and statistical methods, which were unified into a consensus score to prioritize and filter the most relevant candidate regulators for each target gene. By providing both curated context-specific GRNs and a user-friendly platform, GRNContext constitutes a comprehensive and accessible resource that supports mechanistic investigations, hypothesis generation, and translational research focused on transcriptional regulation in cancer. AVAILABILITY AND IMPLEMENTATION: GRNContext is supported by all major browsers and freely available on the web at https://apps.cienciavida.org/grncontext. It is implemented as a client-server web application featuring a FastAPI backend and a React frontend utilizing Cytoscape.js for interactive network visualization, all containerized via Docker for cross-platform compatibility.

Humans↗
PubMed2005

A statistical method for constructing transcriptional regulatory networks using gene expression and sequence data.

Transcriptional regulation is one of the most important means of gene regulation. Uncovering transcriptional regulatory networks helps us to understand the complex cellular process. In this paper, we describe a statistical approach for constructing transcriptional regulatory networks using data of gene expression, promoter sequence, and transcription factor binding sites. Our simulation studies show that the overall and false positive error rates in the estimated transcriptional regulatory networks are expected to be small if the systematic noise in the constructed feature matrix is small. Our analysis based on 658 microarray experiments on yeast gene expression programs and 46 transcription factors suggests that the method is capable of identifying significant transcriptional regulatory interactions and uncovering the corresponding regulatory network structures.

Computational Biology↗
PubMed1995

A mathematical framework for describing and analysing gene regulatory networks.

This paper presents a mathematical framework for describing and analysing gene regulatory networks by autonomous differential equations. It represents an improvement on existing frameworks in that it may handle a wider range of gene regulatory mechanisms. Gene regulatory networks are frequently threshold-dominated, i.e. genes are activated only when the concentration of certain gene products lie between definite thresholds. Here, the concept of regulatory domain is introduced to describe these regions in the phase space. To each regulatory domain is associated an indicator function whose value is 1 inside and 0 outside the domain. The indicator functions thus reflect the logical structure of the network. The sharp borders between the regulatory domains may be smoothed by replacing the logical step functions by continuous sigmoids or so-called logoid functions. A logoid function coincides with the step function outside a narrow interval around the threshold, and rises continuously from 0 to 1 inside it. Using logoids, the task of finding steady states is considerably simplified. A list of regions in phase space comprising all steady states lying close to a threshold is obtained by examining a certain type of matrix called the Logoid-Jacobian. In addition, this matrix leads to the conditions necessary for stability of the steady states. External signals may be conveniently incorporated in the form of Boolean variables. Thus the framework is well suited for studying gene regulatory networks both in single cells and multicellular systems.

Animals↗