Information Science Reference

Table of Contents:

TENTATIVE

Section I: Introduction

Chapter I: Introduction to GRNs

The post-genomic era shifted the main biological focus from ¡¥single-gene¡¦ to ¡¥genome-wide¡¦ approaches. High throughput data available from new technologies allowed to get inside main features of gene expression and its regulation and, at the same time, to discover a more complex level of organization. Analysis of this complexity demonstrated the existence of non-random and well-defined structures that determine a network of interactions. In the first part of the chapter we present a functional introduction to mechanisms involved in genes expression regulation, an overview of network theory and main technologies developed in last years to analyze biological processes are discussed. In the second part, we review genes regulatory networks and their importance in system biology.

Chapter II: What are Gene Regulatory Networks?

Alberto de la Fuente, CRS4 Bioinformatica, Italy

This book deals with algorithms for inferring and analyzing Gene Regulatory Networks using mainly gene expression data. What precisely are the Gene Regulatory Networks that are inferred by such algorithms from this type of data? There is still much confusion in the current literature and it is important to start a book about computational methods for Gene Regulatory Networks with a definition that is as unambiguous as possible. In this chapter I provide a definition and try to clearly explain what Gene Regulatory Networks are in terms of the underlying biochemical processes. To do the latter in a formal way I will use a linear approximation to the in general non-linear kinetics underlying interactions in biochemical systems and show how a biochemical system can be ¡¥condensed¡¦ into a more compact description, i.e. Gene Regulatory Networks. Important differences between the defined Gene Regulatory Networks and other network models for gene regulation, i.e. Transcriptional Regulatory Networks and Co-Expression Networks, will be highlighted.

Section II: Network Inference

Chapter III: Bayesian Networks for Modeling and Inferring Gene Regulatory Networks

Bayesian networks have become a commonly used tool for inferring structure of gene regulatory networks from gene expression data. In this framework, genes are mapped to nodes of a graph, and Bayesian techniques are used to determine a set of edges that best explain the data, i.e., to infer the underlying structure of the network. This chapter begins with an explanation of the mathematical framework of Bayesian networks in the context of reverse engineering of genetic networks. The second part of this review discusses a number of variations upon the basic methodology, including analysis of discrete vs. continuous data or static vs. dynamic Bayesian networks, different methods of exploring the potentially huge search space of network structures, and the use of priors to improve the prediction performance. This review concludes with a discussion of methods for evaluating the performance of network structure inference algorithms.

Chapter IV: Inferring Gene Regulatory Networks from Genetical Genomics Data

In this chapter, we review the current state of Gene Regulatory Network inference based on ¡¥Genetical Genomics¡¦ experiments (Brem & Kruglyak, 2005; Brem, Yvert, Clinton & Kruglyak, 2002; Jansen, 2003; Jansen & Nap, 2001; Schadt et al., 2003) as a special case of causal network inference in ¡¥Systems Genetics¡¦ (Threadgill, 2006). In a Genetical Genomics experiment, a segregating or genetically randomized population is DNA marker genotyped and gene-expression profiled on a genome-wide scale. The genotypes are regarded as natural, multifactorial perturbations resulting in different gene-expression ¡¥phenotypes¡¦, and causal relationships can therefore be established between the measured genotypes and the gene-expression phenotypes. In this chapter, we review different computational approaches to Gene Regulatory Network inference based on the joint analysis of DNA marker and expression data and additionally of DNA sequence information if available. This includes different methods for expression QTL mapping, selection of regulator-target pairs, construction of an encompassing network, which strongly constrains the network search space, and pairwise and multivariate methods for Gene Regulatory Network inference, such as Bayesian Networks and Structural Equation Modeling.

Chapter V: Inferring Genetic Regulatory Interactions with Bayesian Logic-based Model

Svetlana Bulashevska, German Cancer Research Centre (DKFZ), Germany

This chapter describes the model of genetic regulatory interactions. The model has a Boolean logic semantics representing the cooperative influence of regulators (activators and inhibitors) on the expression of a gene. The model is a probabilistic one, hence allowing for the statistical learning to infer the genetic interactions from microarray gene expression data. Bayesian approach to model inference is employed enabling flexible definitions of a priori probability distributions of the model parameters. Markov Chain Monte Carlo (MCMC) simulation technique Gibbs sampling is used to facilitate Bayesian inference. The problem of identifying actual regulators of a gene from a high number of potential regulators is considered as a Bayesian variable selection task. Strategies for the definition of parameters reducing the parameter space and efficient MCMC sampling methods are the matter of the current research.

Chapter VI: A Bayes Regularized Ordinary Differential Equation Model for the Inference of Gene Regulatory Networks

Differential equation models provide a detailed, quantitative description of transcription regulatory networks. However, due to the large number of model parameters, they are usually applicable to small networks only, with at most a few dozen genes. Moreover, they are not well suited to deal with noisy data. In this chapter, we show how to circumvent these limitations by integrating an ordinary differential equation model into a stochastic framework. The resulting model is then embedded into a Bayesian learning approach. We integrate the - biologically motivated - expectation of sparse connectivity in the network into the inference process using a specifically defined prior distribution on model parameters. The approach is evaluated on simulated data and a dataset of the transcriptional network governing the yeast cell cycle.

Section III: Modeling Methods

Chapter VII: Computational Approaches for Modeling Intrinsic Noise and Delays in Genetic Regulatory Networks

This chapter focuses on the interactions and roles between delays and intrinsic noise effects within cellular pathways and regulatory networks. We address these aspects by focusing on genetic regulatory networks that share a common network motif, namely the negative feedback loop, leading to oscillatory gene expression and protein levels. In this context, we discuss computational simulation algorithms for addressing the interplay of delays and noise within the signaling pathways based on biological data. We address implementational issues associated with efficiency and robustness. In a Molecular Biology setting we present two case studies of temporal models for the Hes1 gene (Monk, 2003; Hirata et al., 2002), known to act as a molecular clock, and the Her1/Her7 regulatory system controlling the periodic somite segmentation in vertebrate embryos (Giudicelli and Lewis, 2004; Horikawa et al., 2006).

Chapter VIII: Modeling Gene Regulatory Networks with Delayed Stochastic Dynamics

We present a recently developed modeling strategy of gene regulatory networks (GRN) that uses the delayed stochastic simulation algorithm to drive its dynamics. First, we present experimental evidence that led us to use this strategy. Next, we describe the stochastic simulation algorithm (SSA), and the delayed SSA, able to simulate time-delayed events. We then present a model of single gene expression. From this, we present the general modeling strategy of GRN. Specific applications of the approach are presented, beginning with the model of single gene expression which mimics a recent experimental measurement of gene expression at single-protein level, to validate our modeling strategy. We also model a toggle switch with realistic noise and delays, used in cells as differentiation pathway switches. We show that its dynamics differs from previous modeling strategies predictions. As a final example, we model the P53-Mdm2 feedback loop, whose malfunction is associated to 50% of cancers, and can induce cells apoptosis. In the end, we briefly discuss some issues in modeling the evolution of GRNs, and outline some directions for further research.

Chapter IX: Nonlinear Stochastic Differential Equations Method for Reverse Engineering of Gene Regulatory Network

In this chapter we present a method to infer the structure of the gene regulatory network that takes in account both the kinetic molecular interactions and the randomness of data. The dynamics of the gene expression level are fitted via a nonlinear stochastic differential equation (SDE) model. The drift term of the equation contains the transcription rate related to the architecture of the local regulatory network. The statistical analysis of data combines Maximum Likelihood principle with Akaike Information Criteria (AIC) through a Forward Selection Strategy to yield a set of specific regulators and their contribution. Tested with expression data concerning the cell cycle for S. Cerevisiae and embryogenesis for the D. melanogaster, this method provides a framework for the reverse engineering of various gene regulatory networks.

Chapter X: Modeling Gene Regulatory Networks Using Computational Intelligence Techniques

This chapter presents modelling gene regulatory networks (GRNs) using probabilistic causal model and the guided genetic algorithm. The problem of modelling is explained from both a biological and computational perspective. Further, a comprehensive methodology for developing a GRN model is presented where the application of computation intelligence (CI) techniques can be seen to be significantly important in each phase of modelling. An illustrative example of the causal model for GRN modelling is also included and applied to model the yeast cell cycle dataset. The results obtained are compared for providing biological relevance to the findings which thereby underpins the CI based modelling techniques.

Section IV: Struture and Parameter Learning

Chapter XI: A Synthesis Method of Gene Regulatory Networks based on Gene Expression by Network Learning

Investigating gene regulatory networks is important to understand mechanisms of cellular functions. Recently, the synthesis of gene regulatory networks having desired functions has become of interest to many researchers because it is a complementary approach to understanding gene regulatory networks, and it could be the first step in controlling living cells. In this chapter, we discuss a synthesis problem in gene regulatory networks by network learning. The problem is to determine parameters of a gene regulatory network such that it possesses given gene expression pattern sequences as desired properties. We also discuss a controller synthesis method of gene regulatory networks. Some experiments illustrate the performance of this method.

Chapter XII: Structural Learning of Genetic Regulatory Networks Based on Prior Biological Knowledge and Microarray Gene Expression Measurements

The reconstruction of genetic regulatory networks from microarray gene expression measurements has been a challenging problem in bioinformatics. Various methods have been proposed for this problem including the Bayesian Network (BN) approach. In this chapter we provide a comprehensive survey of the current development of using structure priors derived from high-throughput experimental results such as protein-protein interactions, transcription factor binding location data, evolutionary relationships and literature database in learning regulatory networks.

Chapter XIII: Problems for Structure Learning: Aggregation and Computational Complexity

Machine learning methods to find graphical models of genetic regulatory networks from cDNA microarray data have become increasingly popular in recent years. We provide three reasons to question the reliability of such methods: (1) a major theoretical challenge to any method using conditional independence relations; (2) a simulation study using realistic data that confirms the importance of the theoretical challenge; and (3) an analysis of the computational complexity of algorithms that avoid this theoretical challenge. We have no proof that one cannot possibly learn the structure of a genetic regulatory network from microarray data alone, nor do we think that such a proof is likely. However, the combination of (i) fundamental challenges from theory, (ii) practical evidence that those challenges arise in realistic data, and (iii) the difficulty of avoiding those challenges leads us to conclude that it is unlikely that current microarray technology will ever be successfully applied to this structure learning problem.

Section V: Analysis & Complexity

Chapter XIV: Complexity of the BN and the PBN Models of GRNs and Mappings for Complexity Reduction

Ivan V. Ivanov, Texas A&M University, USA

Constructing computational models of genomic regulation faces several major challenges. While the advances in technology can help in obtaining more and better quality gene expression data, the complexity of the models that can be inferred from data is often high. This high complexity impedes the practical applications of such models, especially when one is interested in developing intervention strategies for disease control, e.g., preventing tumor cells from entering a proliferative state. Thus, estimating the complexity of a model and designing strategies for complexity reduction become crucial in problems such as model selection, construction of tractable sub-network models, and control of the dynamical behavior of the model. In this chapter we discuss these issues in the setting of Boolean networks and probabilistic Boolean networks ¡V two important classes of network models for genomic regulatory networks.

Chapter XV: Abstraction Methods for Analysis of Gene Regulatory Networks

With advances in high throughput methods of data collection for gene regulatory networks, we are now in a position to face the challenge of elucidating how these genes coupled with environmental stimuli orchestrate the regulation of cell-level behaviors. Understanding the behavior of such complex systems is likely impossible to achieve with wet-lab experiments alone due to the amount and complexity of the data being collected. Therefore, it is essential to integrate the experimental work with efficient and accurate computational methods for analysis. Unfortunately, such analysis is complicated not only by the sheer size of the models of interest but also by the fact that gene regulatory networks often involve small molecular counts making discrete and stochastic analysis necessary. To address this problem, this chapter presents a model abstraction methodology which systematically performs various model abstractions to reduce the complexity of computational biochemical models resulting in substantial improvements in analysis time with limited loss in accuracy.

Chapter XVI: Improved Model Checking Techniques for State Space Analysis of Gene Regulatory Networks

A better understanding of the behavior of a cell, as a system, depends on our ability to model and understand the complex regulatory mechanisms that control gene expression. High level, qualitative models, of gene regulatory networks can be used to analyze and characterize the behavior of complex systems, and to provide important insights on the behavior of these systems. In this chapter, we describe a number of additional functionalities that, when supported by a symbolic model checker, make it possible to answer important questions about the nature of the state spaces of gene regulatory networks, such as the nature and size of attractors, and the characteristics of the basins of attraction. We illustrate the type of analysis that can be performed by applying an improved model checker to two well studied gene regulatory models, the network that controls the cell cycle in the yeast S. cerevisiae, and the network that regulates formation of the Dorsal-Ventral boundary in D. melanogaster. The results show that the insights provided by the analysis can be used to understand and improve the models, and to formulate hypotheses that are biologically relevant and that can be confirmed experimentally.

Chapter XVII: Determining the Properties of Gene Regulatory Networks from Expression Data

The expression of genes depends on the physical structure of DNA, how the function of DNA is regulated by the transcription factors expressed by other genes, RNA regulation such as that through RNA interference, and protein signals mediated by protein-protein interaction networks. We illustrate different approaches to determining information about the network of gene regulation from experimental data. First, we show that we can use statistical information of the mRNA expression values to determine the global topological properties of the gene regulatory network. Second, we show that analyzing the changes in expression due to mutations or different environmental conditions can give us information on the relative importance of the different mechanisms involved in gene regulation.

Chapter XVIII: Generalized Boolean Networks: How Spatial and Temporal Choices Influence Their Dynamics

Gene regulatory networks are formed by genes, messenger RNA, and proteins. The interactions between these elements include transcription, translation, and transcriptional regulation (Albert, 2001). The processes are extremely complex and we are just beginning understanding them in detail. However, it is possible, and useful, to abstract many details of the particular kinetic equations in the cell and focus on the system-level properties of the whole network dynamics. This Complex Systems Biology approach, although not strictly applicable to any given particular case, may still provide interesting general insight.

Section VI: Heterogenous Data

Chapter XIX: A Linear Programming Framework for Inferring Gene Regulatory Networks by Integrating Heterogeneous Data

There exist many heterogeneous data sources that are closely related to gene regulatory networks. These data sources provide rich information for depicting complex biological processes at different levels and from different aspects. Here, we introduce a linear programming framework to infer the gene regulatory networks. Within this framework, we extensively integrate the available information derived from multiple time-course expression datasets, ChIP-chip data, regulatory motif-binding patterns, protein-protein interaction data, protein-small molecule interaction data, and documented regulatory relationships in literature and databases. Results on synthetic and real experimental data both demonstrate that the linear programming framework allows us to recover gene regulations in a more robust and reliable manner.

Chapter XX: Integrating Various Data Sources for Improved Quality in Reverse Engineering of Gene Regulatory Networks

In this chapter we outline a methodology to reverse engineer GRNs from various data sources within an ODE framework. The methodology is generally applicable and is suitable to handle the broad error distribution present in microarrays. The main effort of this chapter is the exploration of a fully data driven approach to the integration problem in a ¡¡¡Ósoft evidence¡¨ based way. Integration is here seen as the process of incorporation of uncertain a priori knowledge and is therefore only relied upon if it lowers the prediction error. An efficient implementation is carried out by a Linear Programming formulation. This LP problem is solved repeatedly with small modifications, from which we can benefit by restarting the primal simplex method from nearby solutions, which enables a computational efficient execution. We perform a case study for data from the yeast cell cycle, where all verified genes are putative regulators and the a priori knowledge consists of several types of binding data, text-mining and annotation knowledge.

Section VII: Network Simulation Studies

Chapter XXI: Dynamic Links and Evolutionary History in Simulated Gene Regulatory Networks

In this chapter, we describe the use of evolutionary methods for the in silico generation of artificial gene regulatory networks (GRNs). These usually serve as models for biological networks and can be used for enhancing analysis methods in biology. We clarify our motivation in adopting this strategy by showing the importance of detailed knowledge of all processes, especially the regulatory dynamics of interactions undertaken during gene expression. To illustrate how such a methodology works, two different approaches to the evolution of small-scale GRNs with specified functions, are briefly reviewed and discussed. Thereafter, we present an approach to evolve medium sized GRNs with the ability to produce stable multi-cellular growth. The computational method employed allows for a detailed analysis of the dynamics of the GRNs as well as their evolution. We have observed the emergence of negative feedback during the evolutionary process, and we suggest its implication to the mutational robustness of the regulatory network which is further supported by evidence observed in additional experiments.

Chapter XXII: A Model for a Heterogeneous Genetic Network

In this chapter we propose a new model for Gene Regulatory Networks (GRN). The model incorporates more biological detail than other approaches, and is based on an artificial genome from which several products like genes, mRNA, miRNA, non-coding RNA, and proteins are extracted and connected, giving rise to a heterogeneous directed graph. We study the dynamics of the networks thus obtained, along with their topology (using degree distributions). Some considerations are made about the biological meaning of the outcome of the simulations.

Section VIII: Other Studies

Chapter XXIII: Planning Interventions for Gene Regulatory Networks as Partially Observable Markov Decision Processes

In this chapter a computational formalism for modeling and reasoning about the control of biological processes is explored. It comprises five main sections: a survey of related work, a background on methods (including discussion of the Wnt5a gene regulatory network, the coefficient of determination method for deriving gene regulatory network models, and the partially observable Markov decision process model and its role in modeling intervention planning problems), a main section on the approach taken (including algorithms for solving the intervention planning problems and techniques for representing components of the problems), an empirical evaluation of the intervention planning algorithms on synthetic and the Wnt5a gene regulatory networks, and a conclusion and future directions section. The techniques described present a promising avenue of future research in reasoning algorithms for improved scalability in planning interventions in gene regulatory networks.

Chapter XXIV: Mathematical Modeling of the Switch¡XA Fuzzy Logic Approach

Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the switch.

Chapter XXV: Petri Nets and GRN Models

Ina Koch, 1Beuth University for Technology Berlin, Germany; Max Planck Institute for Molecular Genetics, Germany

In this chapter, modeling of GRNs using Petri net theory is considered. It aims at providing a conceptual understanding of Petri nets to enable the reader to explore GRNs applying Petri net modeling and analysis techniques. Starting with an overview on modeling biochemical networks using Petri nets, the state-of-the-art with focus on GRNs is described. Other modeling techniques, for example, hybrid Petri nets are discussed. Basic concepts of Petri net theory are introduced involving special analysis techniques for modeling biochemical systems, for example, MCT-sets, T-clusters, and Mauritius maps. To illustrate these Petri net concepts, a more complex case study ¡V the gene regulation in Duchenne Muscular Dystrophy ¡V is explained in detail, considering the biological background and the interpretation of analysis results. Considering both, advantages and disadvantages, the chapter demonstrates the usefulness of Petri net modeling, in particular for GRNs.