Learning dynamic systems from time-series data an application to gene regulatory networks

We propose a local search approach for learning dynamic systems from time-series data, using networks of differential equations as the underlying model. We evaluate the performance of our approach for two scenarios: first, by comparing with an l1-regularization approach under the assumption of a uniformly weighted network for identifying systems of masses and springs; and then on the task of learning gene regulatory networks, where we compare it with the best performers in the DREAM4 challenge using the original dataset for that challenge. Our method consistently improves on the performance of the other methods considered in both scenarios.Ivo Timoteo is supported by an FCT Individual Doctoral Fellowship, number SFRH/BD/88466/2012.This is the author accepted manuscript

Bayesian network learning and applications in Bioinformatics

Abstract A Bayesian network (BN) is a compact graphic representation of the probabilistic re- lationships among a set of random variables. The advantages of the BN formalism include its rigorous mathematical basis, the characteristics of locality both in knowl- edge representation and during inference, and the innate way to deal with uncertainty. Over the past decades, BNs have gained increasing interests in many areas, including bioinformatics which studies the mathematical and computing approaches to under- stand biological processes. In this thesis, I develop new methods for BN structure learning with applications to bi- ological network reconstruction and assessment. The first application is to reconstruct the genetic regulatory network (GRN), where each gene is modeled as a node and an edge indicates a regulatory relationship between two genes. In this task, we are given time-series microarray gene expression measurements for tens of thousands of genes, which can be modeled as true gene expressions mixed with noise in data generation, variability of the underlying biological systems etc. We develop a novel BN structure learning algorithm for reconstructing GRNs. The second application is to develop a BN method for protein-protein interaction (PPI) assessment. PPIs are the foundation of most biological mechanisms, and the knowl- edge on PPI provides one of the most valuable resources from which annotations of genes and proteins can be discovered. Experimentally, recently-developed high- throughput technologies have been carried out to reveal protein interactions in many organisms. However, high-throughput interaction data often contain a large number of iv spurious interactions. In this thesis, I develop a novel in silico model for PPI assess- ment. Our model is based on a BN that integrates heterogeneous data sources from different organisms. The main contributions are: 1. A new concept to depict the dynamic dependence relationships among random variables, which widely exist in biological processes, such as the relationships among genes and genes' products in regulatory networks and signaling pathways. This con- cept leads to a novel algorithm for dynamic Bayesian network learning. We apply it to time-series microarray gene expression data, and discover some missing links in a well-known regulatory pathway. Those new causal relationships between genes have been found supportive evidences in literature. 2. Discovery and theoretical proof of an asymptotic property of K2 algorithm ( a well-known efficient BN structure learning approach). This property has been used to identify Markov blankets (MB) in a Bayesian network, and further recover the BN structure. This hybrid algorithm is evaluated on a benchmark regulatory pathway, and obtains better results than some state-of-art Bayesian learning approaches. 3. A Bayesian network based integrative method which incorporates heterogeneous data sources from different organisms to predict protein-protein interactions (PPI) in a target organism. The framework is employed in human PPI prediction and in as- sessment of high-throughput PPI data. Furthermore, our experiments reveal some interesting biological results. 4. We introduce the learning of a TAN (Tree Augmented Naïve Bayes) based net- work, which has the computational simplicity and robustness to high-throughput PPI assessment. The empirical results show that our method outperforms naïve Bayes and a manual constructed Bayesian Network, additionally demonstrate sufficient informa- tion from model organisms can achieve high accuracy in PPI prediction

Dynamic Bayesian networks in molecular plant science: inferring gene regulatory networks from multiple gene expression time series

To understand the processes of growth and biomass production in plants, we ultimately need to elucidate the structure of the underlying regulatory networks at the molecular level. The advent of high-throughput postgenomic technologies has spurred substantial interest in reverse engineering these networks from data, and several techniques from machine learning and multivariate statistics have recently been proposed. The present article discusses the problem of inferring gene regulatory networks from gene expression time series, and we focus our exposition on the methodology of Bayesian networks. We describe dynamic Bayesian networks and explain their advantages over other statistical methods. We introduce a novel information sharing scheme, which allows us to infer gene regulatory networks from multiple sources of gene expression data more accurately. We illustrate and test this method on a set of synthetic data, using three different measures to quantify the network reconstruction accuracy. The main application of our method is related to the problem of circadian regulation in plants, where we aim to reconstruct the regulatory networks of nine circadian genes in Arabidopsis thaliana from four gene expression time series obtained under different experimental conditions

Bayesian regularization of non-homogeneous dynamic Bayesian networks by globally coupling interaction parameters

To relax the homogeneity assumption of classical dynamic Bayesian networks (DBNs), various recent studies have combined DBNs with multiple changepoint processes. The underlying assumption is that the parameters associated with time series segments delimited by multiple changepoints are a priori independent. Under weak regularity conditions, the parameters can be integrated out in the likelihood, leading to a closed-form expression of the marginal likelihood. However, the assumption of prior independence is unrealistic in many real-world applications, where the segment-specific regulatory relationships among the interdependent quantities tend to undergo gradual evolutionary adaptations. We therefore propose a Bayesian coupling scheme to introduce systematic information sharing among the segment-specific interaction parameters. We investigate the effect this model improvement has on the network reconstruction accuracy in a reverse engineering context, where the objective is to learn the structure of a gene regulatory network from temporal gene expression profiles

Stochastic dynamic modeling of short gene expression time-series data

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the expectation maximization (EM) algorithm is applied for modeling the gene regulatory network from gene time-series data. The gene regulatory network is viewed as a stochastic dynamic model, which consists of the noisy gene measurement from microarray and the gene regulation first-order autoregressive (AR) stochastic dynamic process. By using the EM algorithm, both the model parameters and the actual values of the gene expression levels can be identified simultaneously. Moreover, the algorithm can deal with the sparse parameter identification and the noisy data in an efficient way. It is also shown that the EM algorithm can handle the microarray gene expression data with large number of variables but a small number of observations. The gene expression stochastic dynamic models for four real-world gene expression data sets are constructed to demonstrate the advantages of the introduced algorithm. Several indices are proposed to evaluate the models of inferred gene regulatory networks, and the relevant biological properties are discussed

Bioinformatics tools in predictive ecology: Applications to fisheries

This article is made available throught the Brunel Open Access Publishing Fund - Copygith @ 2012 Tucker et al.There has been a huge effort in the advancement of analytical techniques for molecular biological data over the past decade. This has led to many novel algorithms that are specialized to deal with data associated with biological phenomena, such as gene expression and protein interactions. In contrast, ecological data analysis has remained focused to some degree on off-the-shelf statistical techniques though this is starting to change with the adoption of state-of-the-art methods, where few assumptions can be made about the data and a more explorative approach is required, for example, through the use of Bayesian networks. In this paper, some novel bioinformatics tools for microarray data are discussed along with their ‘crossover potential’ with an application to fisheries data. In particular, a focus is made on the development of models that identify functionally equivalent species in different fish communities with the aim of predicting functional collapse

A non-homogeneous dynamic Bayesian network with sequentially coupled interaction parameters for applications in systems and synthetic biology

An important and challenging problem in systems biology is the inference of gene regulatory networks from short non-stationary time series of transcriptional profiles. A popular approach that has been widely applied to this end is based on dynamic Bayesian networks (DBNs), although traditional homogeneous DBNs fail to model the non-stationarity and time-varying nature of the gene regulatory processes. Various authors have therefore recently proposed combining DBNs with multiple changepoint processes to obtain time varying dynamic Bayesian networks (TV-DBNs). However, TV-DBNs are not without problems. Gene expression time series are typically short, which leaves the model over-flexible, leading to over-fitting or inflated inference uncertainty. In the present paper, we introduce a Bayesian regularization scheme that addresses this difficulty. Our approach is based on the rationale that changes in gene regulatory processes appear gradually during an organism's life cycle or in response to a changing environment, and we have integrated this notion in the prior distribution of the TV-DBN parameters. We have extensively tested our regularized TV-DBN model on synthetic data, in which we have simulated short non-homogeneous time series produced from a system subject to gradual change. We have then applied our method to real-world gene expression time series, measured during the life cycle of Drosophila melanogaster, under artificially generated constant light condition in Arabidopsis thaliana, and from a synthetically designed strain of Saccharomyces cerevisiae exposed to a changing environment

An extended Kalman filtering approach to modeling nonlinear dynamic gene regulatory networks via short gene expression time series

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the extended Kalman filter (EKF) algorithm is applied to model the gene regulatory network from gene time series data. The gene regulatory network is considered as a nonlinear dynamic stochastic model that consists of the gene measurement equation and the gene regulation equation. After specifying the model structure, we apply the EKF algorithm for identifying both the model parameters and the actual value of gene expression levels. It is shown that the EKF algorithm is an online estimation algorithm that can identify a large number of parameters (including parameters of nonlinear functions) through iterative procedure by using a small number of observations. Four real-world gene expression data sets are employed to demonstrate the effectiveness of the EKF algorithm, and the obtained models are evaluated from the viewpoint of bioinformatics