Inferring the time-invariant topology of a nonlinear sparse gene regulatory network using fully Bayesian spline autoregression

We propose a semiparametric Bayesian model, based on penalized splines, for the recovery of the time-invariant topology of a causal interaction network from longitudinal data. Our motivation is inference of gene regulatory networks from low-resolution microarray time series, where existence of nonlinear interactions is well known. Parenthood relations are mapped by augmenting the model with kinship indicators and providing these with either an overall or gene-wise hierarchical structure. Appropriate specification of the prior is crucial to control the flexibility of the splines, especially under circumstances of scarce data; thus, we provide an informative, proper prior. Substantive improvement in network inference over a linear model is demonstrated using synthetic data drawn from ordinary differential equation models and gene expression from an experimental data set of the Arabidopsis thaliana circadian rhythm.     

Stochastic Models and Numerical Algorithms for a Class of Regulatory Gene Networks

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856–860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.     

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.     

Gene regulatory network reconstruction using Bayesian networks, the Dantzig Selector, the Lasso and their meta-analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth "Dialogue for Reverse Engineering Assessments and Methods" (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on "Systems Genetics" proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the 16 teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics.     

Identification and interpretation of longitudinal gene expression changes in trauma

Rationale

The relationship between leukocyte gene expression and recovery of respiratory function after injury may provide information on the etiology of multiple organ dysfunction.

Objectives

To find a list of genes for which expression after injury predicts respiratory recovery, and to identify which networks and pathways characterize these genes.

Methods

Blood was sampled at 12 hours and at 1, 4, 7, 21 and 28 days from 147 patients who had been admitted to the hospital after blunt trauma. Leukocyte gene expression was measured using Affymetrix oligonucleotide arrays. A linear model, fit to each probe-set expression value, was used to impute the gene expression trajectory over the entire follow-up period. The proportional hazards model score test was used to calculate the statistical significance of each probe-set trajectory in predicting respiratory recovery. A list of genes was determined such that the expected proportion of false positive results was less than 10%. These genes were compared to the Gene Ontology for ‘response to stimulus’ and, using Ingenuity software, were mapped into networks and pathways.

Measurements and Main Results

The median time to respiratory recovery was 6 days. There were 170 probe-sets representing 135 genes that were found to be related to respiratory recovery. These genes could be mapped to nine networks. Two known pathways that were activated were antigen processing and presentation and JAK- signaling.

Conclusions

The examination of the relationship of gene expression over time with a patient''s clinical course can provide information which may be useful in determining the mechanism of recovery or lack of recovery after severe injury.     

Integrating multiple protein-protein interaction networks to prioritize disease genes: a Bayesian regression approach

Background

The identification of genes responsible for human inherited diseases is one of the most challenging tasks in human genetics. Recent studies based on phenotype similarity and gene proximity have demonstrated great success in prioritizing candidate genes for human diseases. However, most of these methods rely on a single protein-protein interaction (PPI) network to calculate similarities between genes, and thus greatly restrict the scope of application of such methods. Meanwhile, independently constructed and maintained PPI networks are usually quite diverse in coverage and quality, making the selection of a suitable PPI network inevitable but difficult.

Methods

We adopt a linear model to explain similarities between disease phenotypes using gene proximities that are quantified by diffusion kernels of one or more PPI networks. We solve this model via a Bayesian approach, and we derive an analytic form for Bayes factor that naturally measures the strength of association between a query disease and a candidate gene and thus can be used as a score to prioritize candidate genes. This method is intrinsically capable of integrating multiple PPI networks.

Results

We show that gene proximities calculated from PPI networks imply phenotype similarities. We demonstrate the effectiveness of the Bayesian regression approach on five PPI networks via large scale leave-one-out cross-validation experiments and summarize the results in terms of the mean rank ratio of known disease genes and the area under the receiver operating characteristic curve (AUC). We further show the capability of our approach in integrating multiple PPI networks.

Conclusions

The Bayesian regression approach can achieve much higher performance than the existing CIPHER approach and the ordinary linear regression method. The integration of multiple PPI networks can greatly improve the scope of application of the proposed method in the inference of disease genes.

     

Integrating external biological knowledge in the construction of regulatory networks from time-series expression data

ABSTRACT: BACKGROUND: Inference about regulatory networks from high-throughput genomics data is of great interest in systems biology. We present a Bayesian approach to infer gene regulatory networks from time series expression data by integrating various types of biological knowledge. RESULTS: We formulate network construction as a series of variable selection problems and use linear regression to model the data. Our method summarizes additional data sources with an informative prior probability distribution over candidate regression models. We extend the Bayesian model averaging (BMA) variable selection method to select regulators in the regression framework. We summarize the external biological knowledge by an informative prior probability distribution over the candidate regression models. CONCLUSIONS: We demonstrate our method on simulated data and a set of time-series microarray experiments measuring the effect of a drug perturbation on gene expression levels, and show that it outperforms leading regression-based methods in the literature.     

Use of gene networks for identifying and validating drug targets

We propose a new method for identifying and validating drug targets by using gene networks, which are estimated from cDNA microarray gene expression profile data. We created novel gene disruption and drug response microarray gene expression profile data libraries for the purpose of drug target elucidation. We use two types of microarray gene expression profile data for estimating gene networks and then identifying drug targets. The estimated gene networks play an essential role in understanding drug response data and this information is unattainable from clustering methods, which are the standard for gene expression analysis. In the construction of gene networks, we use the Bayesian network model. We use an actual example from analysis of the Saccharomyces cerevisiae gene expression profile data to express a concrete strategy for the application of gene network information to drug discovery.     

Formulas for intrinsic noise evaluation in oscillatory genetic networks

The linear noise approximation is a useful method for stochastic noise evaluations in genetic regulatory networks, where the covariance equation described as a Lyapunov equation plays a central role. We discuss the linear noise approximation method for evaluations of an intrinsic noise in autonomously oscillatory genetic networks; in such oscillatory networks, the covariance equation becomes a periodic differential equation that provides generally an unbounded covariance matrix, so that the standard method of noise evaluation based on the covariance matrix cannot be adopted directly. In this paper, we develop a new method of noise evaluation in oscillatory genetic networks; first, we investigate structural properties, e.g., orbital stability and periodicity, of the solutions to the covariance equation given as a periodic Lyapunov differential equation by using the Floquet-Lyapunov theory, and propose a global measure for evaluating stochastic amplitude fluctuations on the periodic trajectory; we also derive an evaluation formula for the period fluctuation. Finally, we apply our method to a model of circadian oscillations based on negative auto-regulation of gene expression, and show validity of our method by comparing the evaluation results with stochastic simulations.     

Genetic network inference: from co-expression clustering to reverse engineering

MOTIVATION: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using high-throughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.     

Adjusting phenotypes by noise control

Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. However, systematic methods for noise control are lacking mainly due to the intractable mathematical structure of noise propagation through reaction networks. Here, we provide a numerical analysis method by quantifying the parametric sensitivity of noise characteristics at the level of the linear noise approximation. Our analysis is readily applicable to various types of noise control and to different types of system; for example, we can orthogonally control the mean and noise levels and can control system dynamics such as noisy oscillations. As an illustration we applied our method to HIV and yeast gene expression systems and metabolic networks. The oscillatory signal control was applied to p53 oscillations from DNA damage. Furthermore, we showed that the efficiency of orthogonal control can be enhanced by applying extrinsic noise and feedback. Our noise control analysis can be applied to any stochastic model belonging to continuous time Markovian systems such as biological and chemical reaction systems, and even computer and social networks. We anticipate the proposed analysis to be a useful tool for designing and controlling synthetic gene networks.     

从酵母表达时间序列估计基因调控网络

基因调控网络是生命功能在基因表达层面上的展现。用组合线性调控模型、调控元件识别和基因聚类等方法 ,从基因组表达谱解读酵母在细胞周期与环境胁迫中的基因调控网络。结果表明 ,细胞在不同环境条件下会调整基因调控网络。在适应的环境下 ,起主要作用的是细胞生长和增殖有关的基因调控网络 ;而在响应环境胁迫时 ,细胞会再规划调控网络 ,抑制细胞生长和增殖相关的基因 ,诱导跟适应性糖类代谢与结构修复相关的基因 ,还可能启动减数分裂产生孢子。分别从细胞周期和环境胁迫响应相关基因中 ,搜索到转录因子Mcm1结合位点TT CC T GGAAA ,和Dal82在尿囊素代谢途径相关基因上的结合位点TGAAAAWTTT。从而 ,从酵母表达时间序列估计基因调控网络是可行的 ,与至今已知的实验观察相当吻合     

Towards precise reconstruction of gene regulatory networks by data integration

Background: More and more high-throughput datasets are available from multiple levels of measuring gene regulations. The reverse engineering of gene regulatory networks from these data offers a valuable research paradigm to decipher regulatory mechanisms. So far, numerous methods have been developed for reconstructing gene regulatory networks. Results: In this paper, we provide a review of bioinformatics methods for inferring gene regulatory network from omics data. To achieve the precision reconstruction of gene regulatory networks, an intuitive alternative is to integrate these available resources in a rational framework. We also provide computational perspectives in the endeavors of inferring gene regulatory networks from heterogeneous data. We highlight the importance of multi-omics data integration with prior knowledge in gene regulatory network inferences. Conclusions: We provide computational perspectives of inferring gene regulatory networks from multiple omics data and present theoretical analyses of existing challenges and possible solutions. We emphasize on prior knowledge and data integration in network inferences owing to their abilities of identifying regulatory causality.     

The selective values of alleles in a molecular network model are context dependent

Classical quantitative genetics has applied linear modeling to the problem of mapping genotypic to phenotypic variation. Much of this theory was developed prior to the availability of molecular biology. The current understanding of the mechanisms of gene expression indicates the importance of nonlinear effects resulting from gene interactions. We provide a bridge between genetics and gene network theories by relating key concepts from quantitative genetics to the parameters, variables, and performance functions of genetic networks. We illustrate this methodology by simulating the genetic switch controlling galactose metabolism in yeast and its response to selection for a population of individuals. Results indicate that genes have heterogeneous contributions to phenotypes and that additive and nonadditive effects are context dependent. Early cycles of selection suggest strong additive effects attributed to some genes. Later cycles suggest the presence of strong context-dependent nonadditive effects that are conditional on the outcomes of earlier selection cycles. A single favorable allele cannot be consistently identified for most loci. These results highlight the complications that can arise with the presence of nonlinear effects associated with genes acting in networks when selection is conducted on a population of individuals segregating for the genes contributing to the network.     

Dynamical properties of model gene networks and implications for the inverse problem

We study the inverse problem, or the "reverse-engineering" problem, for two abstract models of gene expression dynamics, discrete-time Boolean networks and continuous-time switching networks. Formally, the inverse problem is similar for both types of networks. For each gene, its regulators and its Boolean dynamics function must be identified. However, differences in the dynamical properties of these two types of networks affect the amount of data that is necessary for solving the inverse problem. We derive estimates for the average amounts of time series data required to solve the inverse problem for randomly generated Boolean and continuous-time switching networks. We also derive a lower bound on the amount of data needed that holds for both types of networks. We find that the amount of data required is logarithmic in the number of genes for Boolean networks, matching the general lower bound and previous theory, but are superlinear in the number of genes for continuous-time switching networks. We also find that the amount of data needed scales as 2(K), where K is the number of regulators per gene, rather than 2(2K), as previous theory suggests.     

Thermodynamics of Random Reaction Networks

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.