Inferring gene networks from time series microarray data using dynamic Bayesian networks

Dynamic Bayesian networks (DBNs) are considered as a promising model for inferring gene networks from time series microarray data. DBNs have overtaken Bayesian networks (BNs) as DBNs can construct cyclic regulations using time delay information. In this paper, a general framework for DBN modelling is outlined. Both discrete and continuous DBN models are constructed systematically and criteria for learning network structures are introduced from a Bayesian statistical viewpoint. This paper reviews the applications of DBNs over the past years. Real data applications for Saccharomyces cerevisiae time series gene expression data are also shown.     

Automatic reconstruction of molecular and genetic networks from discrete time series data

We apply a mathematical algorithm which processes discrete time series data to generate a complete list of Petri net structures containing the minimal number of nodes required to reproduce the data set. The completeness of the list as guaranteed by a mathematical proof allows to define a minimal set of experiments required to discriminate between alternative network structures. This in principle allows to prove all possible minimal network structures by disproving all alternative candidate structures. The dynamic behaviour of the networks in terms of a switching rule for the transitions of the Petri net is part of the result. In addition to network reconstruction, the algorithm can be used to determine how many yet undetected components at least must be involved in a certain process. The algorithm also reveals all alternative structural modifications of a network that are required to generate a predefined behaviour.     

Reconstructing biochemical pathways from time course data

Time series data on biochemical reactions reveal transient behavior, away from chemical equilibrium, and contain information on the dynamic interactions among reacting components. However, this information can be difficult to extract using conventional analysis techniques. We present a new method to infer biochemical pathway mechanisms from time course data using a global nonlinear modeling technique to identify the elementary reaction steps which constitute the pathway. The method involves the generation of a complete dictionary of polynomial basis functions based on the law of mass action. Using these basis functions, there are two approaches to model construction, namely the general to specific and the specific to general approach. We demonstrate that our new methodology reconstructs the chemical reaction steps and connectivity of the glycolytic pathway of Lactococcus lactis from time course experimental data.     

Boolean dynamics of genetic regulatory networks inferred from microarray time series data

MOTIVATION: Methods available for the inference of genetic regulatory networks strive to produce a single network, usually by optimizing some quantity to fit the experimental observations. In this article we investigate the possibility that multiple networks can be inferred, all resulting in similar dynamics. This idea is motivated by theoretical work which suggests that biological networks are robust and adaptable to change, and that the overall behavior of a genetic regulatory network might be captured in terms of dynamical basins of attraction. RESULTS: We have developed and implemented a method for inferring genetic regulatory networks for time series microarray data. Our method first clusters and discretizes the gene expression data using k-means and support vector regression. We then enumerate Boolean activation-inhibition networks to match the discretized data. Finally, the dynamics of the Boolean networks are examined. We have tested our method on two immunology microarray datasets: an IL-2-stimulated T cell response dataset and a LPS-stimulated macrophage response dataset. In both cases, we discovered that many networks matched the data, and that most of these networks had similar dynamics. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

An effective data mining technique for reconstructing gene regulatory networks from time series expression data

Recent development in DNA microarray technologies has made the reconstruction of gene regulatory networks (GRNs) feasible. To infer the overall structure of a GRN, there is a need to find out how the expression of each gene can be affected by the others. Many existing approaches to reconstructing GRNs are developed to generate hypotheses about the presence or absence of interactions between genes so that laboratory experiments can be performed afterwards for verification. Since, they are not intended to be used to predict if a gene in an unseen sample has any interactions with other genes, statistical verification of the reliability of the discovered interactions can be difficult. Furthermore, since the temporal ordering of the data is not taken into consideration, the directionality of regulation cannot be established using these existing techniques. To tackle these problems, we propose a data mining technique here. This technique makes use of a probabilistic inference approach to uncover interesting dependency relationships in noisy, high-dimensional time series expression data. It is not only able to determine if a gene is dependent on another but also whether or not it is activated or inhibited. In addition, it can predict how a gene would be affected by other genes even in unseen samples. For performance evaluation, the proposed technique has been tested with real expression data. Experimental results show that it can be very effective. The discovered dependency relationships can reveal gene regulatory relationships that could be used to infer the structures of GRNs.     

Duality between time series and networks

Studying the interaction between a system's components and the temporal evolution of the system are two common ways to uncover and characterize its internal workings. Recently, several maps from a time series to a network have been proposed with the intent of using network metrics to characterize time series. Although these maps demonstrate that different time series result in networks with distinct topological properties, it remains unclear how these topological properties relate to the original time series. Here, we propose a map from a time series to a network with an approximate inverse operation, making it possible to use network statistics to characterize time series and time series statistics to characterize networks. As a proof of concept, we generate an ensemble of time series ranging from periodic to random and confirm that application of the proposed map retains much of the information encoded in the original time series (or networks) after application of the map (or its inverse). Our results suggest that network analysis can be used to distinguish different dynamic regimes in time series and, perhaps more importantly, time series analysis can provide a powerful set of tools that augment the traditional network analysis toolkit to quantify networks in new and useful ways.     

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.     

Inferring dynamic architecture of cellular networks using time series of gene expression, protein and metabolite data

MOTIVATION: High-throughput technologies have facilitated the acquisition of large genomics and proteomics datasets. However, these data provide snapshots of cellular behavior, rather than help us reveal causal relations. Here, we propose how these technologies can be utilized to infer the topology and strengths of connections among genes, proteins and metabolites by monitoring time-dependent responses of cellular networks to experimental interventions. RESULTS: We demonstrate that all connections leading to a given network node, e.g. to a particular gene, can be deduced from responses to perturbations none of which directly influences that node, e.g. using strains with knock-outs to other genes. To infer all interactions from stationary data, each node should be perturbed separately or in combination with other nodes. Monitoring time series provides richer information and does not require perturbations to all nodes. Overall, the methods we propose are capable of deducing and quantifying functional interactions within and across cellular gene, signaling and metabolic networks. SUPPLEMENTARY INFORMATION: Supplementary material is available at http://www.dbi.tju.edu/bioinformatics2004.pdf     

Dynamic Bayesian network and nonparametric regression for nonlinear modeling of gene networks from time series gene expression data

We propose a dynamic Bayesian network and nonparametric regression model for constructing a gene network from time series microarray gene expression data. The proposed method can overcome a shortcoming of the Bayesian network model in the sense of the construction of cyclic regulations. The proposed method can analyze the microarray data as a continuous data and can capture even nonlinear relations among genes. It can be expected that this model will give a deeper insight into complicated biological systems. We also derive a new criterion for evaluating an estimated network from Bayes approach. We conduct Monte Carlo experiments to examine the effectiveness of the proposed method. We also demonstrate the proposed method through the analysis of the Saccharomyces cerevisiae gene expression data.     

Characterising neurological time series data using biologically motivated networks of coupled discrete maps

Artificial biochemical networks (ABNs) are a class of computational dynamical system whose architectures are motivated by the organisation of genetic and metabolic networks in biological cells. Using evolutionary algorithms to search for networks with diagnostic potential, we demonstrate how ABNs can be used to carry out classification when stimulated with time series data collected from human subjects with and without Parkinson's disease. Artificial metabolic networks, composed of coupled discrete maps, offer the best recognition of Parkinsonian behaviour, achieving accuracies in the region of 90%. This is comparable to the diagnostic accuracies found in clinical diagnosis, and is significantly higher than those found in primary and non-expert secondary care. We also illustrate how an evolved classifier is able to recognise diverse features of Parkinsonian behaviour and, using perturbation analysis, show that the evolved classifiers have interesting computational behaviours.     

Learning genetic regulatory network connectivity from time series data

Recent experimental advances facilitate the collection of time series data that indicate which genes in a cell are expressed. This information can be used to understand the genetic regulatory network that generates the data. Typically, Bayesian analysis approaches are applied which neglect the time series nature of the experimental data, have difficulty in determining the direction of causality, and do not perform well on networks with tight feedback. To address these problems, this paper presents a method to learn genetic network connectivity which exploits the time series nature of experimental data to achieve better causal predictions. This method first breaks up the data into bins. Next, it determines an initial set of potential influence vectors for each gene based upon the probability of the gene's expression increasing in the next time step. These vectors are then combined to form new vectors with better scores. Finally, these influence vectors are competed against each other to determine the final influence vector for each gene. The result is a directed graph representation of the genetic network's repression and activation connections. Results are reported for several synthetic networks with tight feedback showing significant improvements in recall and runtime over Yu's dynamic Bayesian approach. Promising preliminary results are also reported for an analysis of experimental data for genes involved in the yeast cell cycle.     

Calculation of rate spectra from noisy time series data

As the resolution of experiments to measure folding kinetics continues to improve, it has become imperative to avoid bias that may come with fitting data to a predetermined mechanistic model. Toward this end, we present a rate spectrum approach to analyze timescales present in kinetic data. Computing rate spectra of noisy time series data via numerical discrete inverse Laplace transform is an ill‐conditioned inverse problem, so a regularization procedure must be used to perform the calculation. Here, we show the results of different regularization procedures applied to noisy multiexponential and stretched exponential time series, as well as data from time‐resolved folding kinetics experiments. In each case, the rate spectrum method recapitulates the relevant distribution of timescales present in the data, with different priors on the rate amplitudes naturally corresponding to common biases toward simple phenomenological models. These results suggest an attractive alternative to the “Occam's razor” philosophy of simply choosing models with the fewest number of relaxation rates. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

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.