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PubMed2006

On the attenuation and amplification of molecular noise in genetic regulatory networks.

BACKGROUND: Noise has many important roles in cellular genetic regulatory functions at the nanomolar scale. At present, no good theory exists for identifying all possible mechanisms of genetic regulatory networks to attenuate the molecular noise to achieve regulatory ability or to amplify the molecular noise to randomize outcomes to the advantage of diversity. Therefore, the noise filtering of genetic regulatory network is an important topic for gene networks under intrinsic fluctuation and extrinsic noise. RESULTS: Based on stochastic dynamic regulation equation, the intrinsic fluctuation in reaction rates is modeled as a state-dependent stochastic process, which will influence the stability of gene regulatory network, especially, with low concentrations of reacting species. Then the mechanisms of genetic regulatory network to attenuate or amplify extrinsic fluctuation are revealed from the nonlinear stochastic filtering point of view. Furthermore, a simple measure of attenuation level or amplification level of extrinsic noise for genetic regulatory networks is also introduced by nonlinear robust filtering method. Based on the global linearization scheme, a convenient method is introduced to measure noise attenuation or amplification for each gene of the nonlinear stochastic regulatory network by solving a set of filtering problems, which correspond to a set of linearized stochastic regulatory networks. Finally, by the proposed methods, several simulation examples of genetic regulatory networks are given to measure their robust stability under intrinsic fluctuations, and to estimate the genes' attenuation and amplification levels under extrinsic noises. CONCLUSION: In this study, a stochastic nonlinear dynamic model is developed for genetic regulatory networks under intrinsic fluctuation and extrinsic noise. By the method we proposed, we could determine the robust stability under intrinsic fluctuations and identify the genes that are significantly affected by extrinsic noises, which we call the weak structure of the network. This method will be potential for robust gene circuit design in future, on which a drug design could be based.

Animals↗
PubMed2004

A method for estimating stochastic noise in large genetic regulatory networks.

MOTIVATION: Genetic regulatory networks are often affected by stochastic noise, due to the low number of molecules taking part in certain reactions. The networks can be simulated using stochastic techniques that model each reaction as a stochastic event. As models become increasingly large and sophisticated, however, the solution time can become excessive; particularly if one wishes to determine the effect on noise of changes to a series of parameters, or the model structure. Methods are therefore required to rapidly estimate stochastic noise. RESULTS: This paper presents an algorithm, based on error growth techniques from non-linear dynamics, to rapidly estimate the noise characteristics of genetic networks of arbitrary size. The method can also be used to determine analytical solutions for simple sub-systems. It is demonstrated on a number of cases, including a prototype model of the galactose regulatory pathway in yeast. AVAILABILITY: A software tool which incorporates the algorithm is available for use as part of the stochastic simulation package Dizzy. It is available for download at http://labs.systemsbiology.net/bolouri/software/Dizzy/ CONTACT: dorrell@systemsbiology.org SUPPLEMENTARY INFORMATION: A conceptual model of the regulatory part of the galactose utilization pathway in yeast, used as an example in the paper, is available at http://labs.systemsbiology.net/bolouri/models/galconcept.dizzy

Algorithms↗
PubMed2004

A proposal for using the ensemble approach to understand genetic regulatory networks.

Understanding the genetic regulatory network comprising genes, RNA, proteins and the network connections and dynamical control rules among them, is a major task of contemporary systems biology. I focus here on the use of the ensemble approach to find one or more well-defined ensembles of model networks whose statistical features match those of real cells and organisms. Such ensembles should help explain and predict features of real cells and organisms. More precisely, an ensemble of model networks is defined by constraints on the "wiring diagram" of regulatory interactions, and the "rules" governing the dynamical behavior of regulated components of the network. The ensemble consists of all networks consistent with those constraints. Here I discuss ensembles of random Boolean networks, scale free Boolean networks, "medusa" Boolean networks, continuous variable networks, and others. For each ensemble, M statistical features, such as the size distribution of avalanches in gene activity changes unleashed by transiently altering the activity of a single gene, the distribution in distances between gene activities on different cell types, and others, are measured. This creates an M-dimensional space, where each ensemble corresponds to a cluster of points or distributions. Using current and future experimental techniques, such as gene arrays, these M properties are to be measured for real cells and organisms, again yielding a cluster of points or distributions in the M-dimensional space. The procedure then finds ensembles close to those of real cells and organisms, and hill climbs to attempt to match the observed M features. Thus obtains one or more ensembles that should predict and explain many features of the regulatory networks in cells and organisms.

Cell Differentiation↗
PubMed2003

Computational discovery of gene modules and regulatory networks.

We describe an algorithm for discovering regulatory networks of gene modules, GRAM (Genetic Regulatory Modules), that combines information from genome-wide location and expression data sets. A gene module is defined as a set of coexpressed genes to which the same set of transcription factors binds. Unlike previous approaches that relied primarily on functional information from expression data, the GRAM algorithm explicitly links genes to the factors that regulate them by incorporating DNA binding data, which provide direct physical evidence of regulatory interactions. We use the GRAM algorithm to describe a genome-wide regulatory network in Saccharomyces cerevisiae using binding information for 106 transcription factors profiled in rich medium conditions data from over 500 expression experiments. We also present a genome-wide location analysis data set for regulators in yeast cells treated with rapamycin, and use the GRAM algorithm to provide biological insights into this regulatory network

Algorithms↗
PubMed2006

Network topology and the evolution of dynamics in an artificial genetic regulatory network model created by whole genome duplication and divergence.

Topological measures of large-scale complex networks are applied to a specific artificial regulatory network model created through a whole genome duplication and divergence mechanism. This class of networks share topological features with natural transcriptional regulatory networks. Specifically, these networks display scale-free and small-world topology and possess subgraph distributions similar to those of natural networks. Thus, the topologies inherent in natural networks may be in part due to their method of creation rather than being exclusively shaped by subsequent evolution under selection. The evolvability of the dynamics of these networks is also examined by evolving networks in simulation to obtain three simple types of output dynamics. The networks obtained from this process show a wide variety of topologies and numbers of genes indicating that it is relatively easy to evolve these classes of dynamics in this model.

Computational Biology↗
PubMed2003

Reconciling gene expression data with known genome-scale regulatory network structures.

The availability of genome-scale gene expression data sets has initiated the development of methods that use this data to infer transcriptional regulatory networks. Alternatively, such regulatory network structures can be reconstructed based on annotated genome information, well-curated databases, and primary research literature. As a first step toward reconciling the two approaches, we examine the consistency between known genome-wide regulatory network structures and extensive gene expression data collections in Escherichia coli and Saccharomyces cerevisiae. By decomposing the regulatory network into a set of basic network elements, we can compute the local consistency of each instance of a particular type of network element. We find that the consistency of network elements is influenced by both structural features of the network such as the number of regulators acting on a target gene and by the functional classes of the genes involved in a particular element. Taken together, the approach presented allows us to define regulatory network subcomponents with a high degree of consistency between the network structure and gene expression data. The results suggest that targeted gene expression profiling data can be used to refine and expand particular subcomponents of known regulatory networks that are sufficiently decoupled from the rest of the network.

Computational Biology↗
PubMed2025

Deep learning-based cell-specific gene regulatory networks inferred from single-cell multiome data.

Gene regulatory networks (GRNs) provide a global representation of how genetic/genomic information is transferred in living systems and are a key component in understanding genome regulation. Single-cell multiome data provide unprecedented opportunities to reconstruct GRNs at fine-grained resolution. However, the inference of GRNs is hindered by insufficient single omic profiles due to the characteristic high loss rate of single-cell sequencing data. In this study, we developed scMultiomeGRN, a deep learning framework to infer transcription factor (TF) regulatory networks via unique integration of single-cell genomic (single-cell RNA sequencing) and epigenomic (single-cell ATAC sequencing) data. We create scMultiomeGRN to elucidate these networks by conceptualizing TF network graph structures. Specifically, we build modality-specific neighbor aggregators and cross-modal attention modules to learn latent representations of TFs from single-cell multi-omics. We demonstrate that scMultiomeGRN outperforms state-of-the-art models on multiple benchmark datasets involved in diseases and health. Via scMultiomeGRN, we identified Alzheimer's disease-relevant regulatory network of SPI1 and RUNX1 for microglia. In summary, scMultiomeGRN offers a deep learning framework to identify cell type-specific gene regulatory network from single-cell multiome data.

Deep Learning↗
PubMed2006

Perturbation avalanches and criticality in gene regulatory networks.

Boolean networks are simplified models of gene regulatory networks. We derive an approximation of the size distribution of perturbation avalanches in Boolean networks based on known results in the theory of branching processes. We show numerically that the approximation works well for different kinds of Boolean networks. It has been suggested that gene regulatory networks may be dynamically critical. To study this, as an application of the presented theory we present a novel method for estimating an order parameter from microarray data. According to the available data and our method, we find that gene regulatory networks appear to be stable and reside near the phase transition between order and chaos.

Animals↗
PubMed2004

External control in Markovian genetic regulatory networks: the imperfect information case.

Probabilistic Boolean Networks, which form a subclass of Markovian Genetic Regulatory Networks, have been recently introduced as a rule-based paradigm for modeling gene regulatory networks. In an earlier paper, we introduced external control into Markovian Genetic Regulatory networks. More precisely, given a Markovian genetic regulatory network whose state transition probabilities depend on an external (control) variable, a Dynamic Programming-based procedure was developed by which one could choose the sequence of control actions that minimized a given performance index over a finite number of steps. The control algorithm of that paper, however, could be implemented only when one had perfect knowledge of the states of the Markov Chain. This paper presents a control strategy that can be implemented in the imperfect information case, and makes use of the available measurements which are assumed to be probabilistically related to the states of the underlying Markov Chain.

Algorithms↗
PubMed2004

Multivariate analysis of noise in genetic regulatory networks.

Stochasticity is an intrinsic property of genetic regulatory networks due to the low copy numbers of the major molecular species, such as, DNA, mRNA, and regulatory proteins. Therefore, investigation of the mechanisms that reduce the stochastic noise is essential in understanding the reproducible behaviors of real organisms and is also a key to design synthetic genetic regulatory networks that can reliably work. We use an analytical and systematic method, the linear noise approximation of the chemical master equation along with the decoupling of a stoichiometric matrix. In the analysis of fluctuations of multiple molecular species, the covariance is an important measure of noise. However, usually the representation of a covariance matrix in the natural coordinate system, i.e. the copy numbers of the molecular species, is intractably complicated because reactions change copy numbers of more than one molecular species simultaneously. Decoupling of a stoichiometric matrix, which is a transformation of variables, significantly simplifies the representation of a covariance matrix and elucidates the mechanisms behind the observed fluctuations in the copy numbers. We apply our method to three types of fundamental genetic regulatory networks, that is, a single-gene autoregulatory network, a two-gene autoregulatory network, and a mutually repressive network. We have found that there are multiple noise components differently originating. Each noise component produces fluctuation in the characteristic direction. The resulting fluctuations in the copy numbers of the molecular species are the sum of these fluctuations. In the examples, the limitation of the negative feedback in noise reduction and the trade-off of fluctuations in multiple molecular species are clearly explained. The analytical representations show the full parameter dependence. Additionally, the validity of our method is tested by stochastic simulations.

Animals↗
PubMed2006

The comprehensive updated regulatory network of Escherichia coli K-12.

BACKGROUND: Escherichia coli is the model organism for which our knowledge of its regulatory network is the most extensive. Over the last few years, our project has been collecting and curating the literature concerning E. coli transcription initiation and operons, providing in both the RegulonDB and EcoCyc databases the largest electronically encoded network available. A paper published recently by Ma et al. (2004) showed several differences in the versions of the network present in these two databases. Discrepancies have been corrected, annotations from this and other groups (Shen-Orr et al., 2002) have been added, making the RegulonDB and EcoCyc databases the largest comprehensive and constantly curated regulatory network of E. coli K-12. RESULTS: Several groups have been using these curated data as part of their bioinformatics and systems biology projects, in combination with external data obtained from other sources, thus enlarging the dataset initially obtained from either RegulonDB or EcoCyc of the E. coli K12 regulatory network. We kindly obtained from the groups of Uri Alon and Hong-Wu Ma the interactions they have added to enrich their public versions of the E. coli regulatory network. These were used to search for original references and curate them with the same standards we use regularly, adding in several cases the original references (instead of reviews or missing references), as well as adding the corresponding experimental evidence codes. We also corrected all discrepancies in the two databases available as explained below. CONCLUSION: One hundred and fifty new interactions have been added to our databases as a result of this specific curation effort, in addition to those added as a result of our continuous curation work. RegulonDB gene names are now based on those of EcoCyc to avoid confusion due to gene names and synonyms, and the public releases of RegulonDB and EcoCyc are henceforth synchronized to avoid confusion due to different versions. Public flat files are available providing direct access to the regulatory network interactions thus avoiding errors due to differences in database modelling and representation. The regulatory network available in RegulonDB and EcoCyc is the most comprehensive and regularly updated electronically-encoded regulatory network of E. coli K-12.

Computer Simulation↗
PubMed1999

The modularity of biological regulatory networks.

A useful approach to complex regulatory networks consists of modeling their elements and interactions by Boolean equations. In this context, feedback circuits (i.e. circular sequences of interactions) have been shown to play key dynamical roles: whereas positive circuits are able to generate multistationarity, negative circuits may generate oscillatory behavior. In this paper, we principally focus on the case of gene networks. These are represented by fully connected Boolean networks where each element interacts with all elements including itself. Flexibility in network design is introduced by the use of Boolean parameters, one associated with each interaction or group of interactions affecting a given element. Within this formalism, a feedback circuit will generate its typical dynamical behavior (i.e. multistationarity or oscillations) only for appropriate values of some of the logical parameters. Whenever it does, we say that the circuit is 'functional'. More interestingly, this formalism allows the computation of the constraints on the logical parameters to have any feedback circuit functional in a network. Using this methodology, we found that the fraction of the total number of consistent combinations of parameter values that make a circuit functional decreases geometrically with the circuit length. From a biological point of view, this suggests that regulatory networks could be decomposed into small and relatively independent feedback circuits or 'regulatory modules'.

Feedback↗
PubMed1999

Population and quantitative genetics of regulatory networks.

I evolved boolean regulatory networks in a computer simulation. I varied mutation, recombination, the size of the network, and the number of connections per node. I measured the performance of networks and the heritability and epistasis of genetic effects. Networks of intermediate connectivity performed best. The distinction between metabolic and quantitative genetic additivity explained some of the variation in performance. Metabolic additivity describes the interaction between changes in a single network, whereas quantitative genetic additivity measures the consistency of phenotypic effect caused by gene substitution in randomly chosen members of the population. I analysed metabolic additivity by the distribution of epistatic effects of pairs of mutations in individual networks. I measured quantitative genetic additivity by heritability. Highly connected networks had greater metabolic additivity for perturbations to individual networks, but had lower additivity when measured by the average effect of a gene substitution (heritability). The lower heritability of highly connected nets appeared to reduce the effectiveness of recombination in searching evolutionary space.

Animals↗
PubMed2002

Modular response analysis of cellular regulatory networks.

The sheer complexity of intracellular regulatory networks, which involve signal transducing, metabolic, and genetic circuits, hampers our ability to carry out a quantitative analysis of their functions. Here, we describe an approach that greatly simplifies this type of analysis by capitalizing on the modular organization of such networks. Steady-state responses of the network as a whole are accounted for in terms of intermodular interactions between the modules alone; processes operating solely within modules need not be considered when analysing signal transfer through the entire network. The intermodular interactions are quantified through (local) response coefficients which populate an interaction map (matrix). This matrix can be derived from a biochemical or molecular biological analysis of (macro) molecular interactions that constitute the regulatory network. The approach is illustrated by two examples: (i) mitogenic signalling through the mitogen-activated protein kinase cascade in the epidermal growth factor receptor network and (ii) regulation of ammonium assimilation in Escherichia coli.

Animals↗
PubMed2005

Estimating gene regulatory networks and protein-protein interactions of Saccharomyces cerevisiae from multiple genome-wide data.

MOTIVATION: Biological processes in cells are properly performed by gene regulations, signal transductions and interactions between proteins. To understand such molecular networks, we propose a statistical method to estimate gene regulatory networks and protein-protein interaction networks simultaneously from DNA microarray data, protein-protein interaction data and other genome-wide data. RESULTS: We unify Bayesian networks and Markov networks for estimating gene regulatory networks and protein-protein interaction networks according to the reliability of each biological information source. Through the simultaneous construction of gene regulatory networks and protein-protein interaction networks of Saccharomyces cerevisiae cell cycle, we predict the role of several genes whose functions are currently unknown. By using our probabilistic model, we can detect false positives of high-throughput data, such as yeast two-hybrid data. In a genome-wide experiment, we find possible gene regulatory relationships and protein-protein interactions between large protein complexes that underlie complex regulatory mechanisms of biological processes.

Algorithms↗
PubMed2006

ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context.

BACKGROUND: Elucidating gene regulatory networks is crucial for understanding normal cell physiology and complex pathologic phenotypes. Existing computational methods for the genome-wide "reverse engineering" of such networks have been successful only for lower eukaryotes with simple genomes. Here we present ARACNE, a novel algorithm, using microarray expression profiles, specifically designed to scale up to the complexity of regulatory networks in mammalian cells, yet general enough to address a wider range of network deconvolution problems. This method uses an information theoretic approach to eliminate the majority of indirect interactions inferred by co-expression methods. RESULTS: We prove that ARACNE reconstructs the network exactly (asymptotically) if the effect of loops in the network topology is negligible, and we show that the algorithm works well in practice, even in the presence of numerous loops and complex topologies. We assess ARACNE's ability to reconstruct transcriptional regulatory networks using both a realistic synthetic dataset and a microarray dataset from human B cells. On synthetic datasets ARACNE achieves very low error rates and outperforms established methods, such as Relevance Networks and Bayesian Networks. Application to the deconvolution of genetic networks in human B cells demonstrates ARACNE's ability to infer validated transcriptional targets of the cMYC proto-oncogene. We also study the effects of misestimation of mutual information on network reconstruction, and show that algorithms based on mutual information ranking are more resilient to estimation errors. CONCLUSION: ARACNE shows promise in identifying direct transcriptional interactions in mammalian cellular networks, a problem that has challenged existing reverse engineering algorithms. This approach should enhance our ability to use microarray data to elucidate functional mechanisms that underlie cellular processes and to identify molecular targets of pharmacological compounds in mammalian cellular networks.

Algorithms↗
PubMed2004

Gene regulatory network growth by duplication.

We are beginning to elucidate transcriptional regulatory networks on a large scale and to understand some of the structural principles of these networks, but the evolutionary mechanisms that form these networks are still mostly unknown. Here we investigate the role of gene duplication in network evolution. Gene duplication is the driving force for creating new genes in genomes: at least 50% of prokaryotic genes and over 90% of eukaryotic genes are products of gene duplication. The transcriptional interactions in regulatory networks consist of multiple components, and duplication processes that generate new interactions would need to be more complex. We define possible duplication scenarios and show that they formed the regulatory networks of the prokaryote Escherichia coli and the eukaryote Saccharomyces cerevisiae. Gene duplication has had a key role in network evolution: more than one-third of known regulatory interactions were inherited from the ancestral transcription factor or target gene after duplication, and roughly one-half of the interactions were gained during divergence after duplication. In addition, we conclude that evolution has been incremental, rather than making entire regulatory circuits or motifs by duplication with inheritance of interactions.

Bacterial Proteins↗
PubMed2004

Reconstruction of microbial transcriptional regulatory networks.

Although metabolic networks can be readily reconstructed through comparative genomics, the reconstruction of regulatory networks has been hindered by the relatively low level of evolutionary conservation of their molecular components. Recent developments in experimental techniques have allowed the generation of vast amounts of data related to regulatory networks. This data together with literature-derived knowledge has opened the way for genome-scale reconstruction of transcriptional regulatory networks. Large-scale regulatory network reconstructions can be converted to in silico models that allow systematic analysis of network behavior in response to changes in environmental conditions. These models can further be combined with genome-scale metabolic models to build integrated models of cellular function including both metabolism and its regulation.

Bacteria↗