Reconstructing gene regulatory networks: from random to scale-free connectivity

The manipulation of organisms using combinations of gene knockout, RNAi and drug interaction experiments can be used to reveal regulatory interactions between genes. Several algorithms have been proposed that try to reconstruct the underlying regulatory networks from gene expression data sets arising from such experiments. Often these approaches assume that each gene has approximately the same number of interactions within the network, and the methods rely on prior knowledge, or the investigator's best guess, of the average network connectivity. Recent evidence points to scale-free properties in biological networks, however, where network connectivity follows a power-law distribution. For scale-free networks, the average number of regulatory interactions per gene does not satisfactorily characterise the network. With this in mind, a new reverse engineering approach is introduced that does not require prior knowledge of network connectivity and its performance is compared with other published algorithms using simulated gene expression data with biologically relevant network structures. Because this new approach does not make any assumptions about the distribution of network connections, it is suitable for application to scale-free networks.     

Developmental evolution in social insects: regulatory networks from genes to societies

The evolution and development of complex phenotypes in social insect colonies, such as queen-worker dimorphism or division of labor, can, in our opinion, only be fully understood within an expanded mechanistic framework of Developmental Evolution. Conversely, social insects offer a fertile research area in which fundamental questions of Developmental Evolution can be addressed empirically. We review the concept of gene regulatory networks (GRNs) that aims to fully describe the battery of interacting genomic modules that are differentially expressed during the development of individual organisms. We discuss how distinct types of network models have been used to study different levels of biological organization in social insects, from GRNs to social networks. We propose that these hierarchical networks spanning different organizational levels from genes to societies should be integrated and incorporated into full GRN models to elucidate the evolutionary and developmental mechanisms underlying social insect phenotypes. Finally, we discuss prospects and approaches to achieve such an integration.     

Algebraic connectivity may explain the evolution of gene regulatory networks

Gene expression is a result of the interplay between the structure, type, kinetics, and specificity of gene regulatory interactions, whose diversity gives rise to the variety of life forms. As the dynamic behavior of gene regulatory networks depends on their structure, here we attempt to determine structural reasons which, despite the similarities in global network properties, may explain the large differences in organismal complexity. We demonstrate that the algebraic connectivity, the smallest non-trivial eigenvalue of the Laplacian, of the directed gene regulatory networks decreases with the increase of organismal complexity, and may therefore explain the difference between the variety of analyzed regulatory networks. In addition, our results point out that, for the species considered in this study, evolution favours decreasing concentration of strategically positioned feed forward loops, so that the network as a whole can increase the specificity towards changing environments. Moreover, contrary to the existing results, we show that the average degree, the length of the longest cascade, and the average cascade length of gene regulatory networks cannot recover the evolutionary relationships between organisms. Whereas the dynamical properties of special subnetworks are relatively well understood, there is still limited knowledge about the evolutionary reasons for the already identified design principles pertaining to these special subnetworks, underlying the global quantitative features of gene regulatory networks of different organisms. The behavior of the algebraic connectivity, which we show valid on gene regulatory networks extracted from curated databases, can serve as an additional evolutionary principle of organism-specific regulatory networks.     

Learning about gene regulatory networks from gene deletion experiments

Gene regulatory networks are a major focus of interest in molecular biology. A crucial question is how complex regulatory systems are encoded and controlled by the genome. Three recent publications have raised the question of what can be learned about gene regulatory networks from microarray experiments on gene deletion mutants. Using this indirect approach, topological features such as connectivity and modularity have been studied.     

Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks

ABSTRACT: BACKGROUND: Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs). As a logical model, probabilistic Boolean networks (PBNs) consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n) or O(nN2n) for a sparse matrix. RESULTS: This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN). An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n), where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational complexity of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. CONCLUSIONS: Stochastic Boolean networks (SBNs) are proposed as an efficient approach to modelling gene regulatory networks (GRNs). The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.     

Inferring gene regulatory networks using differential evolution with local search heuristics

We present a memetic algorithm for evolving the structure of biomolecular interactions and inferring the effective kinetic parameters from the time series data of gene expression using the decoupled Ssystem formalism. We propose an Information Criteria based fitness evaluation for gene network model selection instead of the conventional Mean Squared Error (MSE) based fitness evaluation. A hill-climbing local-search method has been incorporated in our evolutionary algorithm for efficiently attaining the skeletal architecture which is most frequently observed in biological networks. The suitability of the method is tested in gene circuit reconstruction experiments, varying the network dimension and/or characteristics, the amount of gene expression data used for inference and the noise level present in expression profiles. The reconstruction method inferred the network topology and the regulatory parameters with high accuracy. Nevertheless, the performance is limited to the amount of expression data used and the noise level present in the data. The proposed fitness function has been found more suitable for identifying correct network topology and for estimating the accurate parameter values compared to the existing ones. Finally, we applied the methodology for analyzing the cell-cycle gene expression data of budding yeast and reconstructed the network of some key regulators.     

Synthetic circuits reveal how mechanisms of gene regulatory networks constrain evolution

Phenotypic variation is the raw material of adaptive Darwinian evolution. The phenotypic variation found in organismal development is biased towards certain phenotypes, but the molecular mechanisms behind such biases are still poorly understood. Gene regulatory networks have been proposed as one cause of constrained phenotypic variation. However, most pertinent evidence is theoretical rather than experimental. Here, we study evolutionary biases in two synthetic gene regulatory circuits expressed in Escherichia coli that produce a gene expression stripe—a pivotal pattern in embryonic development. The two parental circuits produce the same phenotype, but create it through different regulatory mechanisms. We show that mutations cause distinct novel phenotypes in the two networks and use a combination of experimental measurements, mathematical modelling and DNA sequencing to understand why mutations bring forth only some but not other novel gene expression phenotypes. Our results reveal that the regulatory mechanisms of networks restrict the possible phenotypic variation upon mutation. Consequently, seemingly equivalent networks can indeed be distinct in how they constrain the outcome of further evolution.     

Inferring gene regulatory networks from multiple microarray datasets

MOTIVATION: Microarray gene expression data has increasingly become the common data source that can provide insights into biological processes at a system-wide level. One of the major problems with microarrays is that a dataset consists of relatively few time points with respect to a large number of genes, which makes the problem of inferring gene regulatory network an ill-posed one. On the other hand, gene expression data generated by different groups worldwide are increasingly accumulated on many species and can be accessed from public databases or individual websites, although each experiment has only a limited number of time-points. RESULTS: This paper proposes a novel method to combine multiple time-course microarray datasets from different conditions for inferring gene regulatory networks. The proposed method is called GNR (Gene Network Reconstruction tool) which is based on linear programming and a decomposition procedure. The method theoretically ensures the derivation of the most consistent network structure with respect to all of the datasets, thereby not only significantly alleviating the problem of data scarcity but also remarkably improving the prediction reliability. We tested GNR using both simulated data and experimental data in yeast and Arabidopsis. The result demonstrates the effectiveness of GNR in terms of predicting new gene regulatory relationship in yeast and Arabidopsis. AVAILABILITY: The software is available from http://zhangorup.aporc.org/bioinfo/grninfer/, http://digbio.missouri.edu/grninfer/ and http://intelligent.eic.osaka-sandai.ac.jp or upon request from the authors.     

From gene regulation to gene function: regulatory networks in bacillus subtilis

Bacillus subtilis is a sporulating Gram-positive bacterium that lives primarily in the soil and associated water sources. The publication of the B. subtilis genome sequence and subsequent systematic functional analysis and gene regulation programmes, together with an extensive understanding of its biochemistry and physiology, makes this micro-organism a prime candidate in which to model regulatory networks in silico. In this paper we discuss combined molecular biological and bioinformatical approaches that are being developed to model this organism's responses to changes in its environment.     

EXAMINE: a computational approach to reconstructing gene regulatory networks

Reverse-engineering of gene networks using linear models often results in an underdetermined system because of excessive unknown parameters. In addition, the practical utility of linear models has remained unclear. We address these problems by developing an improved method, EXpression Array MINing Engine (EXAMINE), to infer gene regulatory networks from time-series gene expression data sets. EXAMINE takes advantage of sparse graph theory to overcome the excessive-parameter problem with an adaptive-connectivity model and fitting algorithm. EXAMINE also guarantees that the most parsimonious network structure will be found with its incremental adaptive fitting process. Compared to previous linear models, where a fully connected model is used, EXAMINE reduces the number of parameters by O(N), thereby increasing the chance of recovering the underlying regulatory network. The fitting algorithm increments the connectivity during the fitting process until a satisfactory fit is obtained. We performed a systematic study to explore the data mining ability of linear models. A guideline for using linear models is provided: If the system is small (3-20 elements), more than 90% of the regulation pathways can be determined correctly. For a large-scale system, either clustering is needed or it is necessary to integrate information in addition to expression profile. Coupled with the clustering method, we applied EXAMINE to rat central nervous system development (CNS) data with 112 genes. We were able to efficiently generate regulatory networks with statistically significant pathways that have been predicted previously.     

Asthma phenotypes: the evolution from clinical to molecular approaches

Although asthma has been considered as a single disease for years, recent studies have increasingly focused on its heterogeneity. The characterization of this heterogeneity has promoted the concept that asthma consists of multiple phenotypes or consistent groupings of characteristics. Asthma phenotypes were initially focused on combinations of clinical characteristics, but they are now evolving to link biology to phenotype, often through a statistically based process. Ongoing studies of large-scale, molecularly and genetically focused and extensively clinically characterized cohorts of asthma should enhance our ability to molecularly understand these phenotypes and lead to more targeted and personalized approaches to asthma therapy.     

Dynamical approaches to modeling developmental gene regulatory networks

The network of interacting regulatory signals within a cell comprises one of the most complex and powerful computational systems in biology. Gene regulatory networks (GRNs) play a key role in transforming the information encoded in a genome into morphological form. To achieve this feat, GRNs must respond to and integrate environmental signals with their internal dynamics in a robust and coordinated fashion. The highly dynamic nature of this process lends itself to interpretation and analysis in the language of dynamical models. Modeling provides a means of systematically untangling the complicated structure of GRNs, a framework within which to simulate the behavior of reconstructed systems and, in some cases, suites of analytic tools for exploring that behavior and its implications. This review provides a general background to the idea of treating a regulatory network as a dynamical system, and describes a variety of different approaches that have been taken to the dynamical modeling of GRNs. Birth Defects Research (Part C) 87:131–142, 2009. © 2009 Wiley‐Liss, Inc.