A Quantitative and Dynamic Model of the Arabidopsis Flowering Time Gene Regulatory Network

Various environmental signals integrate into a network of floral regulatory genes leading to the final decision on when to flower. Although a wealth of qualitative knowledge is available on how flowering time genes regulate each other, only a few studies incorporated this knowledge into predictive models. Such models are invaluable as they enable to investigate how various types of inputs are combined to give a quantitative readout. To investigate the effect of gene expression disturbances on flowering time, we developed a dynamic model for the regulation of flowering time in Arabidopsis thaliana. Model parameters were estimated based on expression time-courses for relevant genes, and a consistent set of flowering times for plants of various genetic backgrounds. Validation was performed by predicting changes in expression level in mutant backgrounds and comparing these predictions with independent expression data, and by comparison of predicted and experimental flowering times for several double mutants. Remarkably, the model predicts that a disturbance in a particular gene has not necessarily the largest impact on directly connected genes. For example, the model predicts that SUPPRESSOR OF OVEREXPRESSION OF CONSTANS (SOC1) mutation has a larger impact on APETALA1 (AP1), which is not directly regulated by SOC1, compared to its effect on LEAFY (LFY) which is under direct control of SOC1. This was confirmed by expression data. Another model prediction involves the importance of cooperativity in the regulation of APETALA1 (AP1) by LFY, a prediction supported by experimental evidence. Concluding, our model for flowering time gene regulation enables to address how different quantitative inputs are combined into one quantitative output, flowering time.     

Stochasticity Versus Determinism: Consequences for Realistic Gene Regulatory Network Modelling and Evolution

Gene regulation is one important mechanism in producing observed phenotypes and heterogeneity. Consequently, the study of gene regulatory network (GRN) architecture, function and evolution now forms a major part of modern biology. However, it is impossible to experimentally observe the evolution of GRNs on the timescales on which living species evolve. In silico evolution provides an approach to studying the long-term evolution of GRNs, but many models have either considered network architecture from non-adaptive evolution, or evolution to non-biological objectives. Here, we address a number of important modelling and biological questions about the evolution of GRNs to the realistic goal of biomass production. Can different commonly used simulation paradigms, in particular deterministic and stochastic Boolean networks, with and without basal gene expression, be used to compare adaptive with non-adaptive evolution of GRNs? Are these paradigms together with this goal sufficient to generate a range of solutions? Will the interaction between a biological goal and evolutionary dynamics produce trade-offs between growth and mutational robustness? We show that stochastic basal gene expression forces shrinkage of genomes due to energetic constraints and is a prerequisite for some solutions. In systems that are able to evolve rates of basal expression, two optima, one with and one without basal expression, are observed. Simulation paradigms without basal expression generate bloated networks with non-functional elements. Further, a range of functional solutions was observed under identical conditions only in stochastic networks. Moreover, there are trade-offs between efficiency and yield, indicating an inherent intertwining of fitness and evolutionary dynamics.     

Special Issue on Gene Regulatory Network

The journal Genomics Proteomics & Bioinformatics(GPB) is now inviting submissions for a special issue(to be published around April 2013) on the topic of Gene Regulatory Network.     

Special Issue on “Gene Regulatory Network”

The journal Genomics Proteomics & Bioinformatics (GPB) is now inviting submissions for a special issue (to be published around Dec 2012) on the topic of Gene Regulatory Network. The Gene Regulatory Network (GRN) is a collection of DNA sequences which interact with each other and other cellular components, thereby governing the rates at which genes in the network are transcribed to change the genomic activity. GRNs are evolutionally-conserved and play critical roles in various biological processes and attract more and more research interest.     

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.     

Gene Regulatory Network Reconstruction Using Conditional Mutual Information

The inference of gene regulatory network from expression data is an important area of research that provides insight to the inner workings of a biological system. The relevance-network-based approaches provide a simple and easily-scalable solution to the understanding of interaction between genes. Up until now, most works based on relevance network focus on the discovery of direct regulation using correlation coefficient or mutual information. However, some of the more complicated interactions such as interactive regulation and coregulation are not easily detected. In this work, we propose a relevance network model for gene regulatory network inference which employs both mutual information and conditional mutual information to determine the interactions between genes. For this purpose, we propose a conditional mutual information estimator based on adaptive partitioning which allows us to condition on both discrete and continuous random variables. We provide experimental results that demonstrate that the proposed regulatory network inference algorithm can provide better performance when the target network contains coregulated and interactively regulated genes.     

Gene Regulatory Network Interactions in Sea Urchin Endomesoderm Induction

A major goal of contemporary studies of embryonic development is to understand large sets of regulatory changes that accompany the phenomenon of embryonic induction. The highly resolved sea urchin pregastrular endomesoderm–gene regulatory network (EM-GRN) provides a unique framework to study the global regulatory interactions underlying endomesoderm induction. Vegetal micromeres of the sea urchin embryo constitute a classic endomesoderm signaling center, whose potential to induce archenteron formation from presumptive ectoderm was demonstrated almost a century ago. In this work, we ectopically activate the primary mesenchyme cell–GRN (PMC-GRN) that operates in micromere progeny by misexpressing the micromere determinant Pmar1 and identify the responding EM-GRN that is induced in animal blastomeres. Using localized loss-of -function analyses in conjunction with expression of endo16, the molecular definition of micromere-dependent endomesoderm specification, we show that the TGFβ cytokine, ActivinB, is an essential component of this induction in blastomeres that emit this signal, as well as in cells that respond to it. We report that normal pregastrular endomesoderm specification requires activation of the Pmar1-inducible subset of the EM-GRN by the same cytokine, strongly suggesting that early micromere-mediated endomesoderm specification, which regulates timely gastrulation in the sea urchin embryo, is also ActivinB dependent. This study unexpectedly uncovers the existence of an additional uncharacterized micromere signal to endomesoderm progenitors, significantly revising existing models. In one of the first network-level characterizations of an intercellular inductive phenomenon, we describe an important in vivo model of the requirement of ActivinB signaling in the earliest steps of embryonic endomesoderm progenitor specification.     

面向异步多时延基因调控网络建模的高阶动态贝叶斯网络模型及其结构 学习算法

目的：由基因芯片数据精确学习建模具有异步多时延表达调控关系的基因调控网络。方法：提出了一种高阶动态贝叶斯网 络模型,并给出了网络结构学习算法,该模型假定基因的调控过程为多阶马尔科夫过程,从而能够建模基因调控网络中的异步多 时延特性。结果：由酵母基因调控网络一个子网络人工生成了加入10%含噪声的表达数据用于调控网络结构学习。在75%的后验 概率下,本文提出的高阶动态贝叶斯网络模型能够正确建模实际网络中全部的异步多时延调控关系,而经典动态贝叶斯网络仅 能够正确建模实际网络中1/3的调控关系;ROC曲线对比表明在各个后验概率水平上高阶动态贝叶斯网络模型的效果均优于经 典动态贝叶斯网络。结论：本文提出的高阶动态贝叶斯网络模型能够精确学习建模具有异步多时延表达调控关系的基因调控网 络。     

Gene Regulatory Network Inferences Using a Maximum-Relevance and Maximum-Significance Strategy

Recovering gene regulatory networks from expression data is a challenging problem in systems biology that provides valuable information on the regulatory mechanisms of cells. A number of algorithms based on computational models are currently used to recover network topology. However, most of these algorithms have limitations. For example, many models tend to be complicated because of the “large p, small n” problem. In this paper, we propose a novel regulatory network inference method called the maximum-relevance and maximum-significance network (MRMSn) method, which converts the problem of recovering networks into a problem of how to select the regulator genes for each gene. To solve the latter problem, we present an algorithm that is based on information theory and selects the regulator genes for a specific gene by maximizing the relevance and significance. A first-order incremental search algorithm is used to search for regulator genes. Eventually, a strict constraint is adopted to adjust all of the regulatory relationships according to the obtained regulator genes and thus obtain the complete network structure. We performed our method on five different datasets and compared our method to five state-of-the-art methods for network inference based on information theory. The results confirm the effectiveness of our method.     

The Impact of Gene Expression Variation on the Robustness and Evolvability of a Developmental Gene Regulatory Network

Regulatory interactions buffer development against genetic and environmental perturbations, but adaptation requires phenotypes to change. We investigated the relationship between robustness and evolvability within the gene regulatory network underlying development of the larval skeleton in the sea urchin Strongylocentrotus purpuratus. We find extensive variation in gene expression in this network throughout development in a natural population, some of which has a heritable genetic basis. Switch-like regulatory interactions predominate during early development, buffer expression variation, and may promote the accumulation of cryptic genetic variation affecting early stages. Regulatory interactions during later development are typically more sensitive (linear), allowing variation in expression to affect downstream target genes. Variation in skeletal morphology is associated primarily with expression variation of a few, primarily structural, genes at terminal positions within the network. These results indicate that the position and properties of gene interactions within a network can have important evolutionary consequences independent of their immediate regulatory role.     

Chromatin Accessibility-Based Characterization of the Gene Regulatory Network Underlying Plasmodium falciparum Blood-Stage Development

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A Boolean Model of the Gene Regulatory Network Underlying Mammalian Cortical Area Development

The cerebral cortex is divided into many functionally distinct areas. The emergence of these areas during neural development is dependent on the expression patterns of several genes. Along the anterior-posterior axis, gradients of Fgf8, Emx2, Pax6, Coup-tfi, and Sp8 play a particularly strong role in specifying areal identity. However, our understanding of the regulatory interactions between these genes that lead to their confinement to particular spatial patterns is currently qualitative and incomplete. We therefore used a computational model of the interactions between these five genes to determine which interactions, and combinations of interactions, occur in networks that reproduce the anterior-posterior expression patterns observed experimentally. The model treats expression levels as Boolean, reflecting the qualitative nature of the expression data currently available. We simulated gene expression patterns created by all possible networks containing the five genes of interest. We found that only of these networks were able to reproduce the experimentally observed expression patterns. These networks all lacked certain interactions and combinations of interactions including auto-regulation and inductive loops. Many higher order combinations of interactions also never appeared in networks that satisfied our criteria for good performance. While there was remarkable diversity in the structure of the networks that perform well, an analysis of the probability of each interaction gave an indication of which interactions are most likely to be present in the gene network regulating cortical area development. We found that in general, repressive interactions are much more likely than inductive ones, but that mutually repressive loops are not critical for correct network functioning. Overall, our model illuminates the design principles of the gene network regulating cortical area development, and makes novel predictions that can be tested experimentally.