Genomic regulatory networks and animal development

The synthesis of gene expression data and cis-regulatory analysis permits the elucidation of genomic regulatory networks. These networks provide a direct visualization of the functional interconnections among the regulatory genes and signaling components leading to cell-specific patterns of gene activity. Complex developmental processes are thereby illuminated in ways not revealed by the conventional analysis of individual genes. In this review, we describe emerging networks in several different model systems, and compare them with the gene regulatory network that controls dorsoventral patterning of the Drosophila embryo.     

Perturbation analysis analyzed—mathematical modeling of intact and perturbed gene regulatory circuits for animal development

Gene regulatory networks for animal development are the underlying mechanisms controlling cell fate specification and differentiation. The architecture of gene regulatory circuits determines their information processing properties and their developmental function. It is a major task to derive realistic network models from exceedingly advanced high throughput experimental data. Here we use mathematical modeling to study the dynamics of gene regulatory circuits to advance the ability to infer regulatory connections and logic function from experimental data. This study is guided by experimental methodologies that are commonly used to study gene regulatory networks that control cell fate specification. We study the effect of a perturbation of an input on the level of its downstream genes and compare between the cis-regulatory execution of OR and AND logics. Circuits that initiate gene activation and circuits that lock on the expression of genes are analyzed. The model improves our ability to analyze experimental data and construct from it the network topology. The model also illuminates information processing properties of gene regulatory circuits for animal development.     

Gene and epigene networks: Two levels in organizing the hereditary system

Intracellular governing gene networks consisting of genes and regulatory bonds among them are considered as the first level in organizing the hereditary system. We give examples of both prokaryotic gene network that controls the development of the λ-phage and eukaryotic gene network that controls the early Drosophila ontogenesis. Using the method of generalized threshold models kinetic curves are shown for some gene products of these networks. Gene networks that govern ontogenetic processes can be envisioned as epigene networks, the networks of the subsequent level in organizing the hereditary systems. Based on the mathematical model our computer experiments show that even the simplest hypothetical two-epigene network is capable of ensuring divergent determination, conservation of determinate states and reproduction of the initial “zygotic” functional state. In addition, the experimental results are given on construction an artificial epigene.     

Genes under weaker stabilizing selection increase network evolvability and rapid regulatory adaptation to an environmental shift

Regulatory networks play a central role in the modulation of gene expression, the control of cellular differentiation, and the emergence of complex phenotypes. Regulatory networks could constrain or facilitate evolutionary adaptation in gene expression levels. Here, we model the adaptation of regulatory networks and gene expression levels to a shift in the environment that alters the optimal expression level of a single gene. Our analyses show signatures of natural selection on regulatory networks that both constrain and facilitate rapid evolution of gene expression level towards new optima. The analyses are interpreted from the standpoint of neutral expectations and illustrate the challenge to making inferences about network adaptation. Furthermore, we examine the consequence of variable stabilizing selection across genes on the strength and direction of interactions in regulatory networks and in their subsequent adaptation. We observe that directional selection on a highly constrained gene previously under strong stabilizing selection was more efficient when the gene was embedded within a network of partners under relaxed stabilizing selection pressure. The observation leads to the expectation that evolutionarily resilient regulatory networks will contain optimal ratios of genes whose expression is under weak and strong stabilizing selection. Altogether, our results suggest that the variable strengths of stabilizing selection across genes within regulatory networks might itself contribute to the long‐term adaptation of complex phenotypes.     

A comprehensive gene regulatory network for the diauxic shift in Saccharomyces cerevisiae

Existing machine-readable resources for large-scale gene regulatory networks usually do not provide context information characterizing the activating conditions for a regulation and how targeted genes are affected. Although this information is essentially required for data interpretation, available networks are often restricted to not condition-dependent, non-quantitative, plain binary interactions as derived from high-throughput screens. In this article, we present a comprehensive Petri net based regulatory network that controls the diauxic shift in Saccharomyces cerevisiae. For 100 specific enzymatic genes, we collected regulations from public databases as well as identified and manually curated >400 relevant scientific articles. The resulting network consists of >300 multi-input regulatory interactions providing (i) activating conditions for the regulators; (ii) semi-quantitative effects on their targets; and (iii) classification of the experimental evidence. The diauxic shift network compiles widespread distributed regulatory information and is available in an easy-to-use machine-readable form. Additionally, we developed a browsable system organizing the network into pathway maps, which allows to inspect and trace the evidence for each annotated regulation in the model.     

Tuning genetic clocks employing DNA binding sites

Periodic oscillations play a key role in cell physiology from the cell cycle to circadian clocks. The interplay of positive and negative feedback loops among genes and proteins is ubiquitous in these networks. Often, delays in a negative feedback loop and/or degradation rates are a crucial mechanism to obtain sustained oscillations. How does nature control delays and kinetic rates in feedback networks? Known mechanisms include proper selection of the number of steps composing a feedback loop and alteration of protease activity, respectively. Here, we show that a remarkably simple means to control both delays and effective kinetic rates is the employment of DNA binding sites. We illustrate this design principle on a widely studied activator-repressor clock motif, which is ubiquitous in natural systems. By suitably employing DNA target sites for the activator and/or the repressor, one can switch the clock “on” and “off” and precisely tune its period to a desired value. Our study reveals a design principle to engineer dynamic behavior in biomolecular networks, which may be largely exploited by natural systems and employed for the rational design of synthetic circuits.     

On construction of stochastic genetic networks based on gene expression sequences

Reconstruction of genetic regulatory networks from time series data of gene expression patterns is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been proposed as an effective model for gene regulatory networks. PBNs are able to cope with uncertainty, corporate rule-based dependencies between genes and discover the sensitivity of genes in their interactions with other genes. However, PBNs are unlikely to use directly in practice because of huge amount of computational cost for obtaining predictors and their corresponding probabilities. In this paper, we propose a multivariate Markov model for approximating PBNs and describing the dynamics of a genetic network for gene expression sequences. The main contribution of the new model is to preserve the strength of PBNs and reduce the complexity of the networks. The number of parameters of our proposed model is O(n2) where n is the number of genes involved. We also develop efficient estimation methods for solving the model parameters. Numerical examples on synthetic data sets and practical yeast data sequences are given to demonstrate the effectiveness of the proposed model.     

Reverse-engineering of gene networks for regulating early blood development from single-cell measurements

Background

Recent advances in omics technologies have raised great opportunities to study large-scale regulatory networks inside the cell. In addition, single-cell experiments have measured the gene and protein activities in a large number of cells under the same experimental conditions. However, a significant challenge in computational biology and bioinformatics is how to derive quantitative information from the single-cell observations and how to develop sophisticated mathematical models to describe the dynamic properties of regulatory networks using the derived quantitative information.

Methods

This work designs an integrated approach to reverse-engineer gene networks for regulating early blood development based on singel-cell experimental observations. The wanderlust algorithm is initially used to develop the pseudo-trajectory for the activities of a number of genes. Since the gene expression data in the developed pseudo-trajectory show large fluctuations, we then use Gaussian process regression methods to smooth the gene express data in order to obtain pseudo-trajectories with much less fluctuations. The proposed integrated framework consists of both bioinformatics algorithms to reconstruct the regulatory network and mathematical models using differential equations to describe the dynamics of gene expression.

Results

The developed approach is applied to study the network regulating early blood cell development. A graphic model is constructed for a regulatory network with forty genes and a dynamic model using differential equations is developed for a network of nine genes. Numerical results suggests that the proposed model is able to match experimental data very well. We also examine the networks with more regulatory relations and numerical results show that more regulations may exist. We test the possibility of auto-regulation but numerical simulations do not support the positive auto-regulation. In addition, robustness is used as an importantly additional criterion to select candidate networks.

Conclusion

The research results in this work shows that the developed approach is an efficient and effective method to reverse-engineer gene networks using single-cell experimental observations.

     

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.     

Improved Reconstruction of In Silico Gene Regulatory Networks by Integrating Knockout and Perturbation Data

We performed computational reconstruction of the in silico gene regulatory networks in the DREAM3 Challenges. Our task was to learn the networks from two types of data, namely gene expression profiles in deletion strains (the ‘deletion data’) and time series trajectories of gene expression after some initial perturbation (the ‘perturbation data’). In the course of developing the prediction method, we observed that the two types of data contained different and complementary information about the underlying network. In particular, deletion data allow for the detection of direct regulatory activities with strong responses upon the deletion of the regulator while perturbation data provide richer information for the identification of weaker and more complex types of regulation. We applied different techniques to learn the regulation from the two types of data. For deletion data, we learned a noise model to distinguish real signals from random fluctuations using an iterative method. For perturbation data, we used differential equations to model the change of expression levels of a gene along the trajectories due to the regulation of other genes. We tried different models, and combined their predictions. The final predictions were obtained by merging the results from the two types of data. A comparison with the actual regulatory networks suggests that our approach is effective for networks with a range of different sizes. The success of the approach demonstrates the importance of integrating heterogeneous data in network reconstruction.     

Learning Gene Networks under SNP Perturbations Using eQTL Datasets

The standard approach for identifying gene networks is based on experimental perturbations of gene regulatory systems such as gene knock-out experiments, followed by a genome-wide profiling of differential gene expressions. However, this approach is significantly limited in that it is not possible to perturb more than one or two genes simultaneously to discover complex gene interactions or to distinguish between direct and indirect downstream regulations of the differentially-expressed genes. As an alternative, genetical genomics study has been proposed to treat naturally-occurring genetic variants as potential perturbants of gene regulatory system and to recover gene networks via analysis of population gene-expression and genotype data. Despite many advantages of genetical genomics data analysis, the computational challenge that the effects of multifactorial genetic perturbations should be decoded simultaneously from data has prevented a widespread application of genetical genomics analysis. In this article, we propose a statistical framework for learning gene networks that overcomes the limitations of experimental perturbation methods and addresses the challenges of genetical genomics analysis. We introduce a new statistical model, called a sparse conditional Gaussian graphical model, and describe an efficient learning algorithm that simultaneously decodes the perturbations of gene regulatory system by a large number of SNPs to identify a gene network along with expression quantitative trait loci (eQTLs) that perturb this network. While our statistical model captures direct genetic perturbations of gene network, by performing inference on the probabilistic graphical model, we obtain detailed characterizations of how the direct SNP perturbation effects propagate through the gene network to perturb other genes indirectly. We demonstrate our statistical method using HapMap-simulated and yeast eQTL datasets. In particular, the yeast gene network identified computationally by our method under SNP perturbations is well supported by the results from experimental perturbation studies related to DNA replication stress response.     

A computational model of a class of gene networks with positive and negative controls

This article proposes a computational framework for modelling the logical behavior of a class of gene networks. We characterize the basic behavior of genes in terms of a state-and-transition structure, and model the individual genes as language-generating automata. We consider positive and negative controls as the interaction mechanisms among the genes, and treat such controls as constraints (also expressed in automata) imposed on the behavior of the gene network. By computing the intersection of the languages generated by the gene models and the constraints, we obtain the complete set of pathways in a gene network. Implications and possible improvement of this work are discussed.     

Optimization of a stochastically simulated gene network model via simulated annealing

By rearranging naturally occurring genetic components, gene networks can be created that display novel functions. When designing these networks, the kinetic parameters describing DNA/protein binding are of great importance, as these parameters strongly influence the behavior of the resulting gene network. This article presents an optimization method based on simulated annealing to locate combinations of kinetic parameters that produce a desired behavior in a genetic network. Since gene expression is an inherently stochastic process, the simulation component of simulated annealing optimization is conducted using an accurate multiscale simulation algorithm to calculate an ensemble of network trajectories at each iteration of the simulated annealing algorithm. Using the three-gene repressilator of Elowitz and Leibler as an example, we show that gene network optimizations can be conducted using a mechanistically realistic model integrated stochastically. The repressilator is optimized to give oscillations of an arbitrary specified period. These optimized designs may then provide a starting-point for the selection of genetic components needed to realize an in vivo system.