Principal-oscillation-pattern analysis of gene expression

Principal-oscillation-pattern (POP) analysis is a multivariate and systematic technique for identifying the dynamic characteristics of a system from time-series data. In this study, we demonstrate the first application of POP analysis to genome-wide time-series gene-expression data. We use POP analysis to infer oscillation patterns in gene expression. Typically, a genomic system matrix cannot be directly estimated because the number of genes is usually much larger than the number of time points in a genomic study. Thus, we first identify the POPs of the eigen-genomic system that consists of the first few significant eigengenes obtained by singular value decomposition. By using the linear relationship between eigengenes and genes, we then infer the POPs of the genes. Both simulation data and real-world data are used in this study to demonstrate the applicability of POP analysis to genomic data. We show that POP analysis not only compares favorably with experiments and existing computational methods, but that it also provides complementary information relative to other approaches.     

Inference of scale-free networks from gene expression time series

Quantitative time-series observation of gene expression is becoming possible, for example by cell array technology. However, there are no practical methods with which to infer network structures using only observed time-series data. As most computational models of biological networks for continuous time-series data have a high degree of freedom, it is almost impossible to infer the correct structures. On the other hand, it has been reported that some kinds of biological networks, such as gene networks and metabolic pathways, may have scale-free properties. We hypothesize that the architecture of inferred biological network models can be restricted to scale-free networks. We developed an inference algorithm for biological networks using only time-series data by introducing such a restriction. We adopt the S-system as the network model, and a distributed genetic algorithm to optimize models to fit its simulated results to observed time series data. We have tested our algorithm on a case study (simulated data). We compared optimization under no restriction, which allows for a fully connected network, and under the restriction that the total number of links must equal that expected from a scale free network. The restriction reduced both false positive and false negative estimation of the links and also the differences between model simulation and the given time-series data.     

Combined static and dynamic analysis for determining the quality of time-series expression profiles

Expression profiling of time-series experiments is widely used to study biological systems. However, determining the quality of the resulting profiles remains a fundamental problem. Because of inadequate sampling rates, the effect of arrest-and-release methods and loss of synchronization, the measurements obtained from a series of time points may not accurately represent the underlying expression profiles. To solve this, we propose an approach that combines time-series and static (average) expression data analysis--for each gene, we determine whether its temporal expression profile can be reconciled with its static expression levels. We show that by combining synchronized and unsynchronized human cell cycle data, we can identify many cycling genes that are missed when using only time-series data. The algorithm also correctly distinguishes cycling genes from genes that specifically react to an environmental stimulus even if they share similar temporal expression profiles. Experimental validation of these results shows the utility of this analytical approach for determining the accuracy of gene expression patterns.     

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.     

PAGE: phase-shifted analysis of gene expression

Grouping of gene expression patterns across biological experiments, treatments and time-series data is performed in q-intervals of measurements using phase-shifted analysis of gene expression (PAGE); a Java-based tool to find clusters of genes that share trends of expression profiles within the dataset. The patterns and genes within q-Clusters are visualized in trend plots and compared to determine biological relevance from the gene annotations.     

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.     

In search of functional association from time-series microarray data based on the change trend and level of gene expression

Background  

The increasing availability of time-series expression data opens up new possibilities to study functional linkages of genes. Present methods used to infer functional linkages between genes from expression data are mainly based on a point-to-point comparison. Change trends between consecutive time points in time-series data have been so far not well explored.     

Searching the principal genes for neural differentiation of mouse ES cells by factorizing eigengenes of clusters

A time-series microarray experiment is useful to study the changes in the expression of a large number of genes over time. Many methods for clustering genes using gene expression profiles have been suggested, but it is not easy to interpret the biological significance of the results or utilize these methods for understanding the dynamics of gene regulatory systems. In this study, we introduce an algorithm for readjusting the boundaries of clusters by adopting the advantages of both k-means and singular value decomposition (SVD). In addition, we suggest a methodology for searching the principal genes that can be the most crucial genes in regulation of clusters. We found 34 principal genes from 171 clusters having strong concentratedness in their expression patterns and distinct ranges of oscillatory phases, by using a time-series microarray dataset of mouse embryonic stem (ES) cells after induction of dopaminergic neural differentiation. The biological significance of the principal genes examined in the literature supports the feasibility of our algorithms in that the hierarchy of clusters may lead the manifestation of the phenotypes, e.g., the development of the nervous system.     

Function approximation approach to the inference of reduced NGnet models of genetic networks

Background  

The inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks.     

Assessing Homeostasis Through Circadian Patterns

An organism is thought to be in a dynamic state of homeostasis when each physiological and behavioral system reaches a delicate balance within the framework of other regulatory processes. Many biological systems target specific set-point variables and generate circadian patterns. In this article, we focus on specific measurements representative of two systems, namely deep-body temperature and activity counts. We examine data collected every 30 minutes in mice, assume there are underlying circadian patterns, and extend the approach presented in Brumback and Rice (1998, Journal of the American Statistical Association 93, 961-976) in order to obtain estimates in the presence of correlated data. We then assess homeostasis using these estimates and their statistical properties.     

An intelligent two-stage evolutionary algorithm for dynamic pathway identification from gene expression profiles

From gene expression profiles, it is desirable to rebuild cellular dynamic regulation networks to discover more delicate and substantial functions in molecular biology, biochemistry, bioengineering and pharmaceutics. S-system model is suitable to characterize biochemical network systems and capable to analyze the regulatory system dynamics. However, inference of an S-system model of N-gene genetic networks has 2N(N+1) parameters in a set of non-linear differential equations to be optimized. This paper proposes an intelligent two-stage evolutionary algorithm (iTEA) to efficiently infer the S-system models of genetic networks from time-series data of gene expression. To cope with curse of dimensionality, the proposed algorithm consists of two stages where each uses a divide-and-conquer strategy. The optimization problem is first decomposed into N subproblems having 2(N+1) parameters each. At the first stage, each subproblem is solved using a novel intelligent genetic algorithm (IGA) with intelligent crossover based on orthogonal experimental design (OED). At the second stage, the obtained N solutions to the N subproblems are combined and refined using an OED-based simulated annealing algorithm for handling noisy gene expression profiles. The effectiveness of iTEA is evaluated using simulated expression patterns with and without noise running on a single-processor PC. It is shown that 1) IGA is efficient enough to solve subproblems; 2) IGA is significantly superior to the existing method SPXGA; and 3) iTEA performs well in inferring S-system models for dynamic pathway identification.     

Seasonal plankton dynamics along a cross-shelf gradient

Much interest has recently been devoted to reconstructing the dynamic structure of ecological systems on the basis of time-series data. Using 10 years of monthly data on phyto- and zooplankton abundance from the Bay of Biscay (coastal to shelf-break sites), we demonstrate that the interaction between these two plankton components is approximately linear, whereas the effects of environmental factors (nutrients, temperature, upwelling and photoperiod) on these two plankton population growth rates are nonlinear. With the inclusion of the environmental factors, the main observed seasonal and inter-annual dynamic patterns within the studied plankton assemblage also indicate the prevalence of bottom-up regulatory control.     

Analyzing time series gene expression data

MOTIVATION: Time series expression experiments are an increasingly popular method for studying a wide range of biological systems. However, when analyzing these experiments researchers face many new computational challenges. Algorithms that are specifically designed for time series experiments are required so that we can take advantage of their unique features (such as the ability to infer causality from the temporal response pattern) and address the unique problems they raise (e.g. handling the different non-uniform sampling rates). RESULTS: We present a comprehensive review of the current research in time series expression data analysis. We divide the computational challenges into four analysis levels: experimental design, data analysis, pattern recognition and networks. For each of these levels, we discuss computational and biological problems at that level and point out some of the methods that have been proposed to deal with these issues. Many open problems in all these levels are discussed. This review is intended to serve as both, a point of reference for experimental biologists looking for practical solutions for analyzing their data, and a starting point for computer scientists interested in working on the computational problems related to time series expression analysis.     

Detecting causality from short time-series data based on prediction of topologically equivalent attractors

Background

Detecting causality for short time-series data such as gene regulation data is quite important but it is usually very difficult. This can be used in many fields especially in biological systems. Recently, several powerful methods have been set up to solve this problem. However, it usually needs very long time-series data or much more samples for the existing methods to detect causality among the given or observed data. In our real applications, such as for biological systems, the obtained data or samples are short or small. Since the data or samples are highly depended on experiment or limited resource.

Results

In order to overcome these limitations, here we propose a new method called topologically equivalent position method which can detect causality for very short time-series data or small samples. This method is mainly based on attractor embedding theory in nonlinear dynamical systems. By comparing with inner composition alignment, we use theoretical models and real gene expression data to show the effectiveness of our method.

Conclusions

As a result, it shows our method can be effectively used in biological systems. We hope our method can be useful in many other fields in near future such as complex networks, ecological systems and so on.