Interplay between gene expression noise and regulatory network architecture

Complex regulatory networks orchestrate most cellular processes in biological systems. Genes in such networks are subject to expression noise, resulting in isogenic cell populations exhibiting cell-to-cell variation in protein levels. Increasing evidence suggests that cells have evolved regulatory strategies to limit, tolerate or amplify expression noise. In this context, fundamental questions arise: how can the architecture of gene regulatory networks generate, make use of or be constrained by expression noise? Here, we discuss the interplay between expression noise and gene regulatory network at different levels of organization, ranging from a single regulatory interaction to entire regulatory networks. We then consider how this interplay impacts a variety of phenomena, such as pathogenicity, disease, adaptation to changing environments, differential cell-fate outcome and incomplete or partial penetrance effects. Finally, we highlight recent technological developments that permit measurements at the single-cell level, and discuss directions for future research.     

An integer optimization algorithm for robust identification of non-linear gene regulatory networks

ABSTRACT: BACKGROUND: Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. RESULTS: We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in-silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data. CONCLUSIONS: Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.     

Inferring gene regulatory relationships by combining target-target pattern recognition and regulator-specific motif examination

Although microarray data have been successfully used for gene clustering and classification, the use of time series microarray data for constructing gene regulatory networks remains a particularly difficult task. The challenge lies in reliably inferring regulatory relationships from datasets that normally possess a large number of genes and a limited number of time points. In addition to the numerical challenge, the enormous complexity and dynamic properties of gene expression regulation also impede the progress of inferring gene regulatory relationships. Based on the accepted model of the relationship between regulator and target genes, we developed a new approach for inferring gene regulatory relationships by combining target-target pattern recognition and examination of regulator-specific binding sites in the promoter regions of putative target genes. Pattern recognition was accomplished in two steps: A first algorithm was used to search for the genes that share expression profile similarities with known target genes (KTGs) of each investigated regulator. The selected genes were further filtered by examining for the presence of regulator-specific binding sites in their promoter regions. As we implemented our approach to 18 yeast regulator genes and their known target genes, we discovered 267 new regulatory relationships, among which 15% are rediscovered, experimentally validated ones. Of the discovered target genes, 36.1% have the same or similar functions to a KTG of the regulator. An even larger number of inferred genes fall in the biological context and regulatory scope of their regulators. Since the regulatory relationships are inferred from pattern recognition between target-target genes, the method we present is especially suitable for inferring gene regulatory relationships in which there is a time delay between the expression of regulating and target genes.     

Integrating heterogeneous gene expression data for gene regulatory network modelling

Gene regulatory networks (GRNs) are complex biological systems that have a large impact on protein levels, so that discovering network interactions is a major objective of systems biology. Quantitative GRN models have been inferred, to date, from time series measurements of gene expression, but at small scale, and with limited application to real data. Time series experiments are typically short (number of time points of the order of ten), whereas regulatory networks can be very large (containing hundreds of genes). This creates an under-determination problem, which negatively influences the results of any inferential algorithm. Presented here is an integrative approach to model inference, which has not been previously discussed to the authors' knowledge. Multiple heterogeneous expression time series are used to infer the same model, and results are shown to be more robust to noise and parameter perturbation. Additionally, a wavelet analysis shows that these models display limited noise over-fitting within the individual datasets.     

ATTED-II updates: condition-specific gene coexpression to extend coexpression analyses and applications to a broad range of flowering plants

ATTED-II (http://atted.jp) is a gene coexpression database for a wide variety of experimental designs, such as prioritizations of genes for functional identification and analyses of the regulatory relationships among genes. Here, we report updates of ATTED-II focusing on two new features: condition-specific coexpression and homologous coexpression with rice. To analyze a broad range of biological phenomena, it is important to collect data under many diverse experimental conditions, but the meaning of coexpression can become ambiguous under these conditions. One approach to overcome this difficulty is to calculate the coexpression for each set of conditions with a clear biological meaning. With this viewpoint, we prepared five sets of experimental conditions (tissue, abiotic stress, biotic stress, hormones and light conditions), and users can evaluate the coexpression by employing comparative gene lists and switchable gene networks. We also developed an interactive visualization system, using the Cytoscape web system, to improve the network representation. As the second update, rice coexpression is now available. The previous version of ATTED-II was specifically developed for Arabidopsis, and thus coexpression analyses for other useful plants have been difficult. To solve this problem, we extended ATTED-II by including comparison tables between Arabidopsis and rice. This representation will make it possible to analyze the conservation of coexpression among flowering plants. With the ability to investigate condition-specific coexpression and species conservation, ATTED-II can help researchers to clarify the functional and regulatory networks of genes in a broad array of plant species.     

Comprehensive analysis of gene-environmental interactions with temporal gene expression profiles in Pseudomonas aeruginosa

To explore gene-environment interactions, based on temporal gene expression information, we analyzed gene and treatment information intensively and inferred interaction networks accordingly. The main idea is that gene expression reflects the response of genes to environmental factors, assuming that variations of gene expression occur under different conditions. Then we classified experimental conditions into several subgroups based on the similarity of temporal gene expression profiles. This procedure is useful because it allows us to combine diverse gene expression data as they become available, and, especially, allowing us to lay the regulatory relationships on a concrete biological basis. By estimating the activation points, we can visualize the gene behavior, and obtain a consensus gene activation order, and hence describe conditional regulatory relationships. The estimation of activation points and building of synthetic genetic networks may result in important new insights in the ongoing endeavor to understand the complex network of gene regulation.     

Modeling stochasticity and variability in gene regulatory networks

Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This article contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability. We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.     

Gene expression network reconstruction by convex feature selection when incorporating genetic perturbations

Cellular gene expression measurements contain regulatory information that can be used to discover novel network relationships. Here, we present a new algorithm for network reconstruction powered by the adaptive lasso, a theoretically and empirically well-behaved method for selecting the regulatory features of a network. Any algorithms designed for network discovery that make use of directed probabilistic graphs require perturbations, produced by either experiments or naturally occurring genetic variation, to successfully infer unique regulatory relationships from gene expression data. Our approach makes use of appropriately selected cis-expression Quantitative Trait Loci (cis-eQTL), which provide a sufficient set of independent perturbations for maximum network resolution. We compare the performance of our network reconstruction algorithm to four other approaches: the PC-algorithm, QTLnet, the QDG algorithm, and the NEO algorithm, all of which have been used to reconstruct directed networks among phenotypes leveraging QTL. We show that the adaptive lasso can outperform these algorithms for networks of ten genes and ten cis-eQTL, and is competitive with the QDG algorithm for networks with thirty genes and thirty cis-eQTL, with rich topologies and hundreds of samples. Using this novel approach, we identify unique sets of directed relationships in Saccharomyces cerevisiae when analyzing genome-wide gene expression data for an intercross between a wild strain and a lab strain. We recover novel putative network relationships between a tyrosine biosynthesis gene (TYR1), and genes involved in endocytosis (RCY1), the spindle checkpoint (BUB2), sulfonate catabolism (JLP1), and cell-cell communication (PRM7). Our algorithm provides a synthesis of feature selection methods and graphical model theory that has the potential to reveal new directed regulatory relationships from the analysis of population level genetic and gene expression data.     

Modeling and simulation of biological systems with stochasticity

Mathematical modeling is a powerful approach for understanding the complexity of biological systems. Recently, several successful attempts have been made for simulating complex biological processes like metabolic pathways, gene regulatory networks and cell signaling pathways. The pathway models have not only generated experimentally verifiable hypothesis but have also provided valuable insights into the behavior of complex biological systems. Many recent studies have confirmed the phenotypic variability of organisms to an inherent stochasticity that operates at a basal level of gene expression. Due to this reason, development of novel mathematical representations and simulations algorithms are critical for successful modeling efforts in biological systems. The key is to find a biologically relevant representation for each representation. Although mathematically rigorous and physically consistent, stochastic algorithms are computationally expensive, they have been successfully used to model probabilistic events in the cell. This paper offers an overview of various mathematical and computational approaches for modeling stochastic phenomena in cellular systems.     

Computable visually observed phenotype ontological framework for plants

Background

Gene regulatory networks have an essential role in every process of life. In this regard, the amount of genome-wide time series data is becoming increasingly available, providing the opportunity to discover the time-delayed gene regulatory networks that govern the majority of these molecular processes.

Results

This paper aims at reconstructing gene regulatory networks from multiple genome-wide microarray time series datasets. In this sense, a new model-free algorithm called GRNCOP2 (Gene Regulatory Network inference by Combinatorial OPtimization 2), which is a significant evolution of the GRNCOP algorithm, was developed using combinatorial optimization of gene profile classifiers. The method is capable of inferring potential time-delay relationships with any span of time between genes from various time series datasets given as input. The proposed algorithm was applied to time series data composed of twenty yeast genes that are highly relevant for the cell-cycle study, and the results were compared against several related approaches. The outcomes have shown that GRNCOP2 outperforms the contrasted methods in terms of the proposed metrics, and that the results are consistent with previous biological knowledge. Additionally, a genome-wide study on multiple publicly available time series data was performed. In this case, the experimentation has exhibited the soundness and scalability of the new method which inferred highly-related statistically-significant gene associations.

Conclusions

A novel method for inferring time-delayed gene regulatory networks from genome-wide time series datasets is proposed in this paper. The method was carefully validated with several publicly available data sets. The results have demonstrated that the algorithm constitutes a usable model-free approach capable of predicting meaningful relationships between genes, revealing the time-trends of gene regulation.     

Systematic intervention of transcription for identifying network response to disease and cellular phenotypes

MOTIVATION: A major challenge in post-genomic research has been to understand how physiological and pathological phenotypes arise from the networks of expressed genes. Here, we addressed this issue by developing an algorithm to mimic the behavior of regulatory networks in silico and to identify the dynamic response to disease and changing cellular conditions. RESULTS: With regulatory pathway and gene expression data as input, the algorithm provides quantitative assessments of a wide range of responses, including susceptibility to disease, potential usefulness of a given drug, or consequences to such external stimuli as pharmacological interventions or caloric restriction. The algorithm is particularly amenable to the analysis of systems that are difficult to recapitulate in vitro, yet they may have important clinical value. The hypotheses derived from the algorithm were biologically relevant and were successfully validated via independent experiments, as illustrated here in the analysis of the leukemia-associated BCR-ABL pathway and the insulin/IGF pathway related to longevity. The algorithm correctly identified the leukemia drug target and genes important for longevity, and also provided new insights into our understanding of these two processes. AVAILABILITY: The software package is available upon request to the authors.     

Gene regulatory network modeling via global optimization of high-order dynamic Bayesian network

ABSTRACT: BACKGROUND: Dynamic Bayesian network (DBN) is among the mainstream approaches for modeling various biological networks, including the gene regulatory network (GRN). Most current methods for learning DBN employ either local search such as hill-climbing, or a meta stochastic global optimization framework such as genetic algorithm or simulated annealing, which are only able to locate sub-optimal solutions. Further, current DBN applications have essentially been limited to small sized networks. RESULTS: To overcome the above difficulties, we introduce here a deterministic global optimization based DBN approach for reverse engineering genetic networks from time course gene expression data. For such DBN models that consist only of inter time slice arcs, we show that there exists a polynomial time algorithm for learning the globally optimal network structure. The proposed approach, named GlobalMIT+, employs the recently proposed information theoretic scoring metric named mutual information test (MIT). GlobalMIT+ is able to learn high-order time delayed genetic interactions, which are common to most biological systems. Evaluation of the approach using both synthetic and real data sets, including a 733 cyanobacterial gene expression data set, shows significantly improved performance over other techniques. CONCLUSIONS: Our studies demonstrate that deterministic global optimization approaches can infer large scale genetic networks.