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Handbook of research on computational methodologies in gene regulatory
networks / Sanjoy Das ... [et al.], editors.
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Summary: "This book focuses on methods widely used in modeling gene networks
including structure discovery, learning, and optimization"--Provided by
publisher.
ISBN 978-1-60566-685-3 (hardcover) -- ISBN 978-1-60566-686-0 (ebook) 1.
Genetic regulation--Mathematical models--Handbooks, manuals, etc. I. Das,
Sanjoy, 1968-
QH450.H36 2010
572.8'65--dc22
2009017383
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- 5. Handbook of research on computational methodologies in gene regulatory networks 1st Edition Sanjoy Das Digital Instant Download Author(s): Sanjoy Das, Doina Caragea, Stephen M. Welch, WilliamH. Hsu, Sanjoy Das, Doina Caragea, Stephen M. Welch, WilliamH. Hsu ISBN(s): 9781605666853, 1605666858 Edition: 1 File Details: PDF, 9.74 MB Year: 2009 Language: english
- 7. Handbook of Research on Computational Methodologies in Gene Regulatory Networks Sanjoy Das Kansas State University, USA Doina Caragea Kansas State University, USA Stephen M. Welch Michigan State University, USA William H. Hsu Kansas State University, USA Hershey • New York Medical inforMation science reference
- 8. Director of Editorial Content: Kristin Klinger Senior Managing Editor: Jamie Snavely Assistant Managing Editor: Michael Brehm Publishing Assistant: Sean Woznicki Typesetter: Michael Brehm, Kurt Smith Cover Design: Lisa Tosheff Printed at: Yurchak Printing Inc. Published in the United States of America by Medical Information Science Reference (an imprint of IGI Global) 701 E. Chocolate Avenue Hershey PA 17033 Tel: 717-533-8845 Fax: 717-533-8661 E-mail: cust@igi-global.com Web site: http://www.igi-global.com/reference Copyright © 2010 by IGI Global. All rights reserved. No part of this publication may be reproduced, stored or distributed in any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress Cataloging-in-Publication Data Handbook of research on computational methodologies in gene regulatory networks / Sanjoy Das ... [et al.], editors. p. cm. Includes bibliographical references and index. Summary: "This book focuses on methods widely used in modeling gene networks including structure discovery, learning, and optimization"--Provided by publisher. ISBN 978-1-60566-685-3 (hardcover) -- ISBN 978-1-60566-686-0 (ebook) 1. Genetic regulation--Mathematical models--Handbooks, manuals, etc. I. Das, Sanjoy, 1968- QH450.H36 2010 572.8'65--dc22 2009017383 British Cataloguing in Publication Data A Cataloguing in Publication record for this book is available from the British Library. All work contributed to this book is new, previously-unpublished material. The views expressed in this book are those of the authors, but not necessarily of the publisher.
- 9. List of Reviewers Manuel Barrio, University of Valladolid, Spain Sebastian Bauer, Charité Universitätsmedizin Berlin, Germany Daniel Bryce, Utah State University, USA Kevin Burrage, University of Queensland, Australia Doina Caragea, Kansas State University, USA Adriana Climescu-Haulica, Université Joseph Fourier, France Yang Dai, University of Illinois at Chicago David Danks, Carnegie Mellon University, USA Christian Darabos, Université de Lausanne, Switzerland Alberto de la Fuente, CRS4 Bioinformatica, Italy Chris Glymour, Carnegie Mellon University, USA Angela Gon¸calves, Darwin College, UK Mika Gustafsson, Linköpings universitet, Sweden Ina Hoeschele, Virginia Polytechnic Institute and State University, USA Jack Horner, USA William H. Hsu, Kansas State University, USA Lars Kaderali, University of Heidelberg, Germany Ivan V. Ivanov, Texas A&M University, USA Seungchan Kim, Arizona State University, USA Ina Koch, Max Planck Institute for Molecular Genetics, Germany Hiroyuki Kuwahara, University of Trento Centre for Computational and Systems Biology, Italy Larry Liebovitch, Florida Atlantic University, USA Bing Liu, Monsanto Co., USA Michael Margaliot, Tel Aviv University, Israel Yosihiro Mori, Kyoto Institute of Technology, Japan Chris J. Myers, University of Utah, USA Masahiro Okamoto, Kyushu University, Japan Arlindo L. Oliveira, Cadence Research Laboratories, USA Nicole Radde, University of Leipzig, Germany Ramesh Ram, Monash University, Australia Andre S. Ribeiro, Tampere University of Technology, Finland David Sankoff, University of Ottawa, Canada Till Steiner, Honda Research Institute Europe GmbH, Germany Ala Ugo, University of Turin, Turin, Italy Yong Wang, Chinese Academy of Sciences, China Stephen M. Welch, Kansas State University, USA
- 10. List of Contributors Ala, Ugo / Università di Torino, Italy................................................................................................... 28 Almasri, Eyad / University of Illinois at Chicago, USA.................................................................... 289 Barrio, Manuel / University of Valladolid, Spain.............................................................................. 169 Bauer, Sebastian / Charité Universitätsmedizin Berlin, Germany...................................................... 57 Bryce, Daniel / Utah State University, USA....................................................................................... 546 Bulashevska, Svetlana / German Cancer Research Centre (DKFZ), Germany ............................... 108 Burrage, Kevin / The University of Oxford, UK ............................................................................... 169 Burrage, Pamela / The University of Queensland, Australia............................................................ 169 Chen, Guanrao / University of Illinois at Chicago, USA.................................................................. 289 Chen, Luonan / Osaka Sangyo University, Japan............................................................................. 450 Chetty, Madhu / Monash University, Australia ................................................................................ 244 Chu, Tianjiao / University of Pittsburgh, USA.................................................................................. 310 Climescu-Haulica, Adriana / Université Joseph Fourier, France.................................................... 219 Costa, Ernesto J. F. / Pólo II- Pinhal de Marrocos, Portugal .......................................................... 523 Dai, Yang / University of Illinois at Chicago, USA............................................................................ 289 Damasco, Christian / Università di Torino, Italy................................................................................ 28 Danks, David / Carnegie Mellon University and Institute for Human & Machine Cognition, USA .............................................................................................................................. 310 Darabos, Christian / University of Lausanne, Switzerland; University of Turin, Italy .................... 429 de la Fuente, Alberto / CRS4 Bioinformatica, Italy........................................................................ 1, 79 Freitas, Ana T. / INESC-ID/IST, Portugal......................................................................................... 386 Giacobini, Mario / University of Torino, Italy .................................................................................. 429 Glymour, Clark / Carnegie Mellon University and Institute for Human & Machine Cognition, USA .............................................................................................................................. 310 Gonçalves, Ângela T. F. / Darwin College, UK ................................................................................ 523 Grefenstette, John J. / George Mason University, USA.................................................................... 198 Gustafsson, Mika / Linköping University, Sweden............................................................................ 476 Hoeschele, Ina / Virginia Polytechnic Institute and State University, USA......................................... 79 Hörnquist, Michael / Linköping University, Sweden ........................................................................ 476 Hütt, Marc-Thorsten / Jacobs University, Germany........................................................................ 405 Ivanov, Ivan V. / Texas A&M University, USA .................................................................................. 334 Jin, Y. / Honda Research Institute Europe GmbH, Germany............................................................. 498 Jirsa, Viktor K. / Florida Atlantic University, USA .......................................................................... 405
- 11. Joshi, Trupti / University of Missouri, USA ...................................................................................... 450 Kaderali, Lars / University of Heidelberg, Germany........................................................................ 139 Kauffman, Stuart A. / University of Calgary, Canada..................................................................... 198 Kim, Seungchan / Arizona State University, USA............................................................................. 546 Koch, Ina / Beuth University for Technology Berlin, Germany; Max Planck Institute for Molecular Genetics, Germany ................................................................................................. 604 Kuroe, Yasuaki / Kyoto Institute of Technology, Japan..................................................................... 266 Kuwahara, Hiroyuki / Carnegie Mellon University, USA; Microsoft Research - University of Trento CoSBi, Italy................................................................................................... 352 Larsen, Peter / University of Illinois at Chicago, USA ..................................................................... 289 Laschov, Dmitriy / Tel Aviv University, Israel................................................................................... 573 Leier, André / ETH Zurich, Switzerland............................................................................................ 169 Liebovitch, Larry S. / Florida Atlantic University, USA .................................................................. 405 Liu, Bing / Monsanto Co., USA ........................................................................................................... 79 Margaliot, Michael / Tel Aviv University, Israel ............................................................................... 573 Márquez Lago, Tatiana / ETH Zurich, Switzerland ......................................................................... 169 Marr, Carsten / Helmholtz Zentrum München, Germany ................................................................. 405 McMillan, Kenneth L. / Cadence Research Laboratories,USA ....................................................... 386 Mori, Yoshihiro / Kyoto Institute of Technology, Japan.................................................................... 266 Myers, Chris J. / University of Utah, USA........................................................................................ 352 Oliveira, Arlindo L. / Cadence Research Laboratories, USA and INESC-ID/IST, Portugal............ 386 Pais, Hélio C. / Cadence Research Laboratories, USA and INESC-ID/IST, Portugal ...................... 386 Quirk, Michelle / Los Alamos National Laboratory, USA ................................................................ 219 Radde, Nicole / University of Leipzig, Germany ............................................................................... 139 Ram, Ramesh / Monash University, Australia .................................................................................. 244 Ribeiro, Andre S. / Tampere University of Technology, Finland....................................................... 198 Robinson, Peter / Charité Universitätsmedizin Berlin, Germany....................................................... 57 Schramm, L. / Technische Universitaet Darmstadt, Germany.......................................................... 498 Sendhoff, B. / Honda Research Institute Europe GmbH, Germany................................................... 498 Sentovich, Ellen M. / Cadence Research Laboratories,USA ............................................................ 386 Shehadeh, Lina A. / University of Miami, USA ................................................................................ 405 Steiner, T. / Honda Research Institute Europe GmbH, Germany ...................................................... 498 Tomassini, Marco / University of Lausanne, Switzerland................................................................. 429 Wang, Rui-Sheng / Renmin University, China.................................................................................. 450 Wang, Yong / Academy of Mathematics and Systems Science, China............................................... 450 Wimberly, Frank / Carnegie Mellon University (retired), USA ....................................................... 310 Xia, Yu / Boston University, USA....................................................................................................... 450 Xu, Dong / University of Missouri, USA............................................................................................ 450 Zhang, Xiang-Sun / Academy of Mathematics and Systems Science, China.................................... 450
- 12. Preface ...............................................................................................................................................xxii Acknowledgment..............................................................................................................................xxix Section 1 Introduction Chapter 1 What are Gene Regulatory Networks? ................................................................................................... 1 Alberto de la Fuente, CRS4 Bioinformatica, Italy Chapter 2 Introduction to GRNs............................................................................................................................ 28 Ugo Ala, Università di Torino, Italy Christian Damasco, Università di Torino, Italy Section 2 Network Inference Chapter 3 Bayesian Networks for Modeling and Inferring Gene Regulatory Networks ...................................... 57 Sebastian Bauer, Charité Universitätsmedizin Berlin, Germany Peter Robinson, Charité Universitätsmedizin Berlin, Germany Chapter 4 Inferring Gene Regulatory Networks from Genetical Genomics Data................................................. 79 Bing Liu, Monsanto Co., USA Ina Hoeschele, Virginia Polytechnic Institute and State University, USA Alberto de la Fuente, CRS4 Bioinformatica, Italy Table of Contents
- 13. Chapter 5 Inferring Genetic Regulatory Interactions with Bayesian Logic-Based Model.................................. 108 Svetlana Bulashevska, German Cancer Research Centre (DKFZ), Germany Chapter 6 A Bayes Regularized Ordinary Differential Equation Model for the Inference of Gene Regulatory Networks ............................................................................................................ 139 Nicole Radde, University of Leipzig, Germany Lars Kaderali, University of Heidelberg, Germany Section 3 Modeling Methods Chapter 7 Computational Approaches for Modeling Intrinsic Noise and Delays in Genetic Regulatory Networks......................................................................................................... 169 Manuel Barrio, University of Valladolid, Spain Kevin Burrage, The University of Oxford, UK Pamela Burrage, The University of Queensland, Australia André Leier, ETH Zurich, Switzerland Tatiana Márquez Lago, ETH Zurich, Switzerland Chapter 8 Modeling Gene Regulatory Networks with Delayed Stochastic Dynamics....................................... 198 Andre S. Ribeiro, Tampere University of Technology, Finland John J. Grefenstette, George Mason University, USA Stuart A. Kauffman, University of Calgary, Canada Chapter 9 Nonlinear Stochastic Differential Equations Method for Reverse Engineering of Gene Regulatory Network.............................................................................................................. 219 Adriana Climescu-Haulica, Université Joseph Fourier, France Michelle Quirk, Los Alamos National Laboratory, USA Chapter 10 Modelling Gene Regulatory Networks Using Computational Intelligence Techniques..................... 244 Ramesh Ram, Monash University, Australia Madhu Chetty, Monash University, Australia
- 14. Section 4 Structure and Parameter Learning Chapter 11 A Synthesis Method of Gene Regulatory Networks based on Gene Expression by Network Learning.......................................................................................................................... 266 Yoshihiro Mori, Kyoto Institute of Technology, Japan Yasuaki Kuroe, Kyoto Institute of Technology, Japan Chapter 12 Structural Learning of Genetic Regulatory Networks Based on Prior Biological Knowledge and Microarray Gene Expression Measurements ............................................................................... 289 Yang Dai, University of Illinois at Chicago, USA Eyad Almasri, University of Illinois at Chicago, USA Peter Larsen, University of Illinois at Chicago, USA Guanrao Chen, University of Illinois at Chicago, USA Chapter 13 Problems for Structure Learning: Aggregation and Computational Complexity ............................... 310 Frank Wimberly, Carnegie Mellon University (retired), USA David Danks, Carnegie Mellon University and Institute for Human & Machine Cognition, USA Clark Glymour, Carnegie Mellon University and Institute for Human & Machine Cognition, USA Tianjiao Chu, University of Pittsburgh, USA Section 5 Analysis & Complexity Chapter 14 Complexity of the BN and the PBN Models of GRNs and Mappings for Complexity Reduction................................................................................................................... 334 Ivan V. Ivanov, Texas A&M University, USA Chapter 15 Abstraction Methods for Analysis of Gene Regulatory Networks ..................................................... 352 Hiroyuki Kuwahara, Carnegie Mellon University, USA; Microsoft Research - University of Trento CoSBi, Italy Chris J. Myers, University of Utah, USA
- 15. Chapter 16 Improved Model Checking Techniques for State Space Analysis of Gene Regulatory Networks ............................................................................................................ 386 Hélio C. Pais, Cadence Research Laboratories, USA and INESC-ID/IST, Portugal Kenneth L. McMillan, Cadence Research Laboratories,USA Ellen M. Sentovich, Cadence Research Laboratories,USA Ana T. Freitas, INESC-ID/IST, Portugal Arlindo L. Oliveira, Cadence Research Laboratories, USA and INESC-ID/IST, Portugal Chapter 17 Determining the Properties of Gene Regulatory Networks from Expression Data............................ 405 Larry S. Liebovitch, Florida Atlantic University, USA Lina A. Shehadeh, University of Miami, USA Viktor K. Jirsa, Florida Atlantic University, USA Marc-Thorsten Hütt, Jacobs University, Germany Carsten Marr, Helmholtz Zentrum München, Germany Chapter 18 Generalized Boolean Networks: How Spatial and Temporal Choices Influence Their Dynamics................................................................................................................... 429 Christian Darabos, University of Lausanne, Switzerland; University of Turin, Italy Mario Giacobini, University of Torino, Italy Marco Tomassini, University of Lausanne, Switzerland Section 6 Heterogenous Data Chapter 19 A Linear Programming Framework for Inferring Gene Regulatory Networks by Integrating Heterogeneous Data .................................................................................................... 450 Yong Wang, Academy of Mathematics and Systems Science, China Rui-Sheng Wang, Renmin University, China Trupti Joshi, University of Missouri, USA Dong Xu, University of Missouri, USA Xiang-Sun Zhang, Academy of Mathematics and Systems Science, China Luonan Chen, Osaka Sangyo University, Japan Yu Xia, Boston University, USA Chapter 20 Integrating Various Data Sources for Improved Quality in Reverse Engineering of Gene Regulatory Networks ............................................................................................................ 476 Mika Gustafsson, Linköping University, Sweden Michael Hörnquist, Linköping University, Sweden
- 16. Section 7 Network Simulation Studies Chapter 21 Dynamic Links and Evolutionary History in Simulated Gene Regulatory Networks........................ 498 T. Steiner, Honda Research Institute Europe GmbH, Germany Y. Jin, Honda Research Institute Europe GmbH, Germany L. Schramm, Technische Universitaet Darmstadt, Germany B. Sendhoff, Honda Research Institute Europe GmbH, Germany Chapter 22 A Model for a Heterogeneous Genetic Network................................................................................. 523 Ângela T. F. Gonçalves, Darwin College, UK Ernesto J. F. Costa, Pólo II- Pinhal de Marrocos, Portugal Section 8 Other Studies Chapter 23 Planning Interventions for Gene Regulatory Networks as Partially Observable Markov Decision Processes................................................................................................................ 546 Daniel Bryce, Utah State University, USA Seungchan Kim, Arizona State University, USA Chapter 24 Mathematical Modeling of the λ Switch: A Fuzzy Logic Approach................................................... 573 Dmitriy Laschov, Tel Aviv University, Israel Michael Margaliot, Tel Aviv University, Israel Chapter 25 Petri Nets and GRN Models ............................................................................................................... 604 Ina Koch, Beuth University for Technology Berlin, Germany; Max Planck Institute for Molecular Genetics, Germany Compilation of References ............................................................................................................... 638 About the Contributors.................................................................................................................... 688 Index................................................................................................................................................... 703
- 17. Preface ...............................................................................................................................................xxii Acknowledgment..............................................................................................................................xxix Section 1 Introduction Chapter 1 What are Gene Regulatory Networks? ................................................................................................... 1 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 algo- rithms 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 de- scription, that is Gene Regulatory Networks. Important differences between the defined Gene Regulatory Networks and other network models for gene regulation, that is Transcriptional Regulatory Networks and Co-Expression Networks, will be highlighted. Chapter 2 Introduction to GRNs............................................................................................................................ 28 Ugo Ala, Università di Torino, Italy Christian Damasco, Università di Torino, Italy 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 nonrandom and well-defined structures that Detailed Table of Contents
- 18. determine a network of interactions. In the first part of the chapter, we present a functional introduc- tion 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. Section 2 Network Inference Chapter 3 Bayesian Networks for Modeling and Inferring Gene Regulatory Networks ...................................... 57 Sebastian Bauer, Charité Universitätsmedizin Berlin, Germany Peter Robinson, Charité Universitätsmedizin Berlin, Germany 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, that is 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 4 Inferring Gene Regulatory Networks from Genetical Genomics Data................................................. 79 Bing Liu, Monsanto Co., USA Ina Hoeschele, Virginia Polytechnic Institute and State University, USA Alberto de la Fuente, CRS4 Bioinformatica, Italy In this chapter, we address techniques that can be applied to establish causality between the various nodes in a GRN. These techniques are based on the joint analysis of DNA marker and expression as well as DNA sequence information. In addition to Bayesian networks, another modeling approach, statistical equation modeling, is discussed. Chapter 5 Inferring Genetic Regulatory Interactions with Bayesian Logic-Based Model.................................. 108 Svetlana Bulashevska, German Cancer Research Centre (DKFZ), Germany This chapter describes the model of genetic regulatory interactions. The model has a Boolean logic se- mantics 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
- 19. 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 6 A Bayes Regularized Ordinary Differential Equation Model for the Inference of Gene Regulatory Networks ............................................................................................................ 139 Nicole Radde, University of Leipzig, Germany Lars Kaderali, University of Heidelberg, Germany 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 differen- tial 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 3 Modeling Methods Chapter 7 Computational Approaches for Modeling Intrinsic Noise and Delays in Genetic Regulatory Networks......................................................................................................... 169 Manuel Barrio, University of Valladolid, Spain Kevin Burrage, The University of Oxford, UK Pamela Burrage, The University of Queensland, Australia André Leier, ETH Zurich, Switzerland Tatiana Márquez Lago, ETH Zurich, Switzerland As noise and delays are intrinsic to biochemical processes, they must be accounted for when dealing with the most detailed differential equation models of GRNs. The issue is addressed in this chapter. A basic Monte Carlo simulation technique to simulate noisy biochemical reactions, as well as a general- ization to include delays, is described in this chapter. The chapter follows this with a study into ‘coarse grain’ approaches, which reduce computational costs when dealing with larger biochemical systems. The methodology is demonstrated with a few case studies.
- 20. Chapter 8 Modeling Gene Regulatory Networks with Delayed Stochastic Dynamics....................................... 198 Andre S. Ribeiro, Tampere University of Technology, Finland John J. Grefenstette, George Mason University, USA Stuart A. Kauffman, University of Calgary, Canada 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 9 Nonlinear Stochastic Differential Equations Method for Reverse Engineering of Gene Regulatory Network.............................................................................................................. 219 Adriana Climescu-Haulica, Université Joseph Fourier, France Michelle Quirk, Los Alamos National Laboratory, USA 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 withAkaike 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 10 Modelling Gene Regulatory Networks Using Computational Intelligence Techniques..................... 244 Ramesh Ram, Monash University, Australia Madhu Chetty, Monash University, Australia 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
- 21. 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 4 Structure and Parameter Learning Chapter 11 A Synthesis Method of Gene Regulatory Networks based on Gene Expression by Network Learning.......................................................................................................................... 266 Yoshihiro Mori, Kyoto Institute of Technology, Japan Yasuaki Kuroe, Kyoto Institute of Technology, Japan 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 12 Structural Learning of Genetic Regulatory Networks Based on Prior Biological Knowledge and Microarray Gene Expression Measurements ............................................................................... 289 Yang Dai, University of Illinois at Chicago, USA Eyad Almasri, University of Illinois at Chicago, USA Peter Larsen, University of Illinois at Chicago, USA Guanrao Chen, University of Illinois at Chicago, USA 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 13 Problems for Structure Learning: Aggregation and Computational Complexity ............................... 310 Frank Wimberly, Carnegie Mellon University (retired), USA David Danks, Carnegie Mellon University and Institute for Human & Machine Cognition, USA Clark Glymour, Carnegie Mellon University and Institute for Human & Machine Cognition, USA Tianjiao Chu, University of Pittsburgh, USA
- 22. Machine learning methods to find graphical models of genetic regulatory networks from cDNAmicroar- ray 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 indepen- dence 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 5 Analysis & Complexity Chapter 14 Complexity of the BN and the PBN Models of GRNs and Mappings for Complexity Reduction................................................................................................................... 334 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 com- plexity 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, for example, 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 subnetwork 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–two important classes of network models for genomic regulatory networks. Chapter 15 Abstraction Methods for Analysis of Gene Regulatory Networks ..................................................... 352 Hiroyuki Kuwahara, Carnegie Mellon University, USA; Microsoft Research - University of Trento CoSBi, Italy Chris J. Myers, University of Utah, USA 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 ac- curate 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
- 23. 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 16 Improved Model Checking Techniques for State Space Analysis of Gene Regulatory Networks ............................................................................................................ 386 Hélio C. Pais, Cadence Research Laboratories, USA and INESC-ID/IST, Portugal Kenneth L. McMillan, Cadence Research Laboratories,USA Ellen M. Sentovich, Cadence Research Laboratories,USA Ana T. Freitas, INESC-ID/IST, Portugal Arlindo L. Oliveira, Cadence Research Laboratories, USA and INESC-ID/IST, Portugal A better understanding of the behavior of a cell, as a system, depends on our ability to model and under- stand 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 num- ber 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 17 Determining the Properties of Gene Regulatory Networks from Expression Data............................ 405 Larry S. Liebovitch, Florida Atlantic University, USA Lina A. Shehadeh, University of Miami, USA Viktor K. Jirsa, Florida Atlantic University, USA Marc-Thorsten Hütt, Jacobs University, Germany Carsten Marr, Helmholtz Zentrum München, Germany The expression of genes depends on the physical structure of DNA, how the function of DNA is regu- lated 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.
- 24. Chapter 18 Generalized Boolean Networks: How Spatial and Temporal Choices Influence Their Dynamics................................................................................................................... 429 Christian Darabos, University of Lausanne, Switzerland; University of Turin, Italy Mario Giacobini, University of Torino, Italy Marco Tomassini, University of Lausanne, Switzerland This chapter relaxes the requirements in random Boolean network models, that genes operate in synchrony and that their connectivity remain fixed. These modifications, it is argued, enable Boolean networks to better capture some characteristics present in gene expression, such as activation sequences in genes and periodic attractors. Section 6 Heterogenous Data Chapter 19 A Linear Programming Framework for Inferring Gene Regulatory Networks by Integrating Heterogeneous Data .................................................................................................... 450 Yong Wang, Academy of Mathematics and Systems Science, China Rui-Sheng Wang, Renmin University, China Trupti Joshi, University of Missouri, USA Dong Xu, University of Missouri, USA Xiang-Sun Zhang, Academy of Mathematics and Systems Science, China Luonan Chen, Osaka Sangyo University, Japan Yu Xia, Boston University, USA 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 mul- tiple 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 20 Integrating Various Data Sources for Improved Quality in Reverse Engineering of Gene Regulatory Networks ............................................................................................................ 476 Mika Gustafsson, Linköping University, Sweden Michael Hörnquist, Linköping University, Sweden 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
- 25. 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 “soft 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 regula- tors and the a priori knowledge consists of several types of binding data, text-mining, and annotation knowledge. Section 7 Network Simulation Studies Chapter 21 Dynamic Links and Evolutionary History in Simulated Gene Regulatory Networks........................ 498 T. Steiner, Honda Research Institute Europe GmbH, Germany Y. Jin, Honda Research Institute Europe GmbH, Germany L. Schramm, Technische Universitaet Darmstadt, Germany B. Sendhoff, Honda Research Institute Europe GmbH, Germany 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 dif- ferent 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 multicellular 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 22 A Model for a Heterogeneous Genetic Network................................................................................. 523 Ângela T. F. Gonçalves, Darwin College, UK Ernesto J. F. Costa, Pólo II- Pinhal de Marrocos, Portugal 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, noncoding 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.
- 26. Section 8 Other Studies Chapter 23 Planning Interventions for Gene Regulatory Networks as Partially Observable Markov Decision Processes................................................................................................................ 546 Daniel Bryce, Utah State University, USA Seungchan Kim, Arizona State University, USA 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 de- scribed present a promising avenue of future research in reasoning algorithms for improved scalability in planning interventions in gene regulatory networks. Chapter 24 Mathematical Modeling of the λ Switch: A Fuzzy Logic Approach................................................... 573 Dmitriy Laschov, Tel Aviv University, Israel Michael Margaliot, Tel Aviv University, Israel Gene regulation plays a central role in the development and functioning of living organisms. Develop- ing 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 25 Petri Nets and GRN Models ............................................................................................................... 604 Ina Koch, Beuth 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
- 27. 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–the gene regulation in Duchenne Muscular Dystrophy– 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. Compilation of References ............................................................................................................... 638 About the Contributors.................................................................................................................... 688 Index................................................................................................................................................... 703
- 28. xxii For decades, molecular geneticists have been intensively studying the individual genes of various organisms and how these genes influence their phenotypic behavior. Unfortunately, it is usually very difficult, if not impossible, to isolate specific genetic signals for any arbitrary behavioral aspect or trait. The problem is analogous to that of finding a grass skirt in a very large haystack. Even if one locates a plausible-looking bit of grass, until its connections are laboriously traced out, one cannot know if it is part of the skirt or, as is much more likely, just an unrelated piece of straw. As an example, there are over 100 genes that are known to affect flowering time in the model plant Arabidopsis thaliana. Together, the interactionsofthesegenescompriseacomplexsignalprocessingnetworkthatintegratesmultipleinternal and external cues to make one of the most critical decisions in a plant’s life cycle–when to reproduce. Yet, all together, these genes comprise only 0.4% of the species’ complete gene network. Recent advances in molecular genetic technologies are beginning to shed light on the complex in- terplay between genes that elicit phenotypic behavior characteristic of any given organism. Even so, unraveling the specific details about how these genetic pathways interact to regulate development, shape life histories, and respond to environmental cues remains a very daunting task. A wide variety of models depicting gene-gene interactions, which are commonly referred to as gene regulatory networks (GRNs), have been proposed in recent literature. While a GRN must be able to mimic experimentally observed behavior, reproducing complex behaviors accurately may entail com- putationally prohibitive costs. Under these circumstances, model simplicity is an important trade-off for functional fidelity. Consequently, modeling approaches taken are wide and disparate. Machine learning based GRN models are specifically meant for simplicity and/or algorithmic tractability.They rely heavily on computational learning theory, and usually are used to simulate qualitatively, phenotypic behavior of GRNs. We refer to these as high level models. At the other end are more detailed models that take into account the underlying biochemical processes. These models are capable of reproducing realistic gene expressions with great fidelity. This book is a collection of articles on the various computational tools that are available to decode, model, and analyze GRNs. It is conveniently organized into separate sections, beginning with an in- troductory section. Each section contains a handful of chapters written by researchers in the field that focus on a specific computational approach. Section 1: introduction The first section contains two introductory chapters on GRNs. Chapter 1 (“What are Gene Regulatory Networks”) provides a conceptual framework for GRNs. It shows how the complex nonlinear biochemi- cal processes can be linearized and portrayed as simple graphical models. The nodes of such a network Preface
- 29. xxiii are either individual genes or groups of functionally related ones. The network can have both directed as well as undirected edges. The chapter also highlights the differences between such networks and two other similar structures, transcriptional regulatory networks and co-expression networks. The next chapter in this section (Chapter 2) is entitled “Introduction to Gene Regulatory Networks” and has a slightly different focus. While introducing the GRN as a graph, it also details further biologi- cal insights into the various underlying biochemical processes within GRNs. The chapter also surveys recent advances in array-based technologies that are available to study such processes. Only minimum background in advanced mathematics is assumed here, making the chapter very useful to biologists interested in this subject. Section 2: network inference While the previous section introduces GRNs as graphical structures, the chapters in this section focus on systems identification; they shed light on how GRNs can be reverse engineered from experimental data. While simply arranging genes into various functional units may be accomplished easily through simple statistical means, depicting causality between these units is more challenging. To varying degrees, all four chapters in this section deal with Bayesian network approach. Bayes- ian networks, a marriage between graph theory and probability theory, are a high level abstraction of GRNs. An introductory, yet thorough mathematical description of Bayesian networks in provided in Chapter 3 (“Bayesian Networks for Modeling and Inferring Gene Regulatory Networks”). This chapter considers both discrete probabilities as well as continuous probability distributions. Dynamic Bayesian networks are taken up briefly to show how cyclic graphs can be modeled. The latter half of the chapter casts the tasks of discovering the structure of the Bayesian network and estimating the parameters of its probability distribution(s) as two aspects of learning. Lastly, it addresses issues relating to assessing the performance of inferred networks. Chapter4(“InferringGeneRegulatoryNetworksfromGeneticalGenomicsData”)addressestechniques that can be applied to establish causality between the various nodes in a GRN. These techniques are based on the joint analysis of DNA marker and expression as well as DNA sequence information. In addition to Bayesian networks, another modeling approach, statistical equation modeling, is discussed. Boolean networks are a GRN modeling approach where each gene is associated with a simple logical function. Chapter 5 (“Inferring Genetic Regulatory Interactions with Bayesian Logic-Based Model”) combines this modeling approach with Bayesian networks. Using simple Boolean semantics to depict underlying interactions among gene products allows for the analysis of larger networks, while the Bayes- ian framework helps penalize overly complex models. As examples, results of applying this method to data from S. cerevisiae and to Plasmodium falciparum are provided. Depicting the dynamic interactions of genes within a network as a set of ordinary differential equa- tions helps preserve biochemical fidelity. Unfortunately, this detailed approach is too complex to be extended beyond a few genes. Chapter 6 (“A Bayes Regularized Ordinary Differential Equation Model for the Inference of Gene Regulatory Networks”), makes use of the stochastic nature of GRNs to inte- grate the differential equation models within a probabilistic network. Bayesian learning is applied to determine the parameters of the differential equation model. The effectiveness of this overall approach is demonstrated by applying it to the yeast cell.
- 30. xxiv Section 3: Modeling MethodS As noise and delays are intrinsic to biochemical processes, they must be accounted for when dealing with the most detailed differential equation models of GRNs. This issue is addressed in Chapter 7 (“ComputationalApproachesforModelingIntrinsicNoiseandDelaysinGeneticRegulatoryNetworks”) and in the following one, Chapter 8 (“Modeling Gene Regulatory Networks with Delayed Stochastic Dynamics”). A basic Monte Carlo simulation technique to simulate noisy biochemical reactions, as well as a generalization to include delays, are described in both chapters, although to different ends. Chapter 7 follows this with a study into ‘coarse grain’ approaches, which reduce computational costs when deal- ing with larger biochemical systems. The methodology is demonstrated with a few case studies. In contrast, Chapter 8 discusses simulation studies with single genes as well as simple networks of genes. It concludes with a genetic algorithm1 based simulation to investigate how simple GRNs evolve. Chapter 9 (“Nonlinear Stochastic Differential Equations Method for Reverse Engineering of Gene Regulatory Networks”) is a study on how structures of GRNs can be obtained from expression data. It uses stochastic differential equation models, where noise is depicted as a Brownian process. The authors show how regulators for genes are selected using heuristics based on statistical and information theoretic principles, and demonstrate this concept with a few case studies. The last chapter in this section, Chapter 10 (“Modelling Gene Regulatory Networks with Computa- tional Intelligence Techniques”) introduces computational intelligence techniques in GRNs with a focus on genetic algorithms. The authors propose the guided genetic algorithm as an optimization method for causal modeling of GRNs. Case studies involving both simulated data as well as real yeast data are described to show how their approach works. Section 4: Structure and ParaMeter learning This section contains a set of chapters that are most directly related to algorithmic approaches for learning structures and parameters of GRNs. It begins with Chapter 11 (“A Synthesis Method of Gene Regulatory Networks based on Gene Expression by Networking Learning”), which addresses how GRNs can be modeled to produce oscillatory behavior. This is an important problem as oscillations such as circadian rhythm are routinely observed in gene expression patterns. The chapter proposes a recurrent neural network modeling approach to derive networks of low complexity that can produce desired oscillatory sequences. Chapter 12 (“Structural Learning of Genetic Regulatory Networks Based on Prior Biological Knowl- edge and Microarray Gene Expression Measurements”) is a survey of current methods on Bayesian network models of GRNs. It focuses on structure priors derived from experimental results such as protein-protein interactions, transcription factor binding locations, evolutionary relationships as well as existing literature. Thefollowingchapter,Chapter13(“ProblemsforStructureLearning:AggregationandComputational Complexity”) offers a critique on current approaches to inferring model structure using standard machine learning techniques. The authors identify three specific factors in support of their argument: that the methods reported in the literature make use of synthetic as opposed to real data, that they claim success when the actual gene network structure is not known, and that only isolated successes are published.
- 31. xxv Section 5: analySiS and coMPlexity Large, heterogeneous datasets arising from a variety of experiments, intricacies involved at various stages of the modeling process, as well as the intrinsically complex nature of the genetic interactions within the organisms themselves–shaped through millenia of evolution–all contribute to models that are often difficult to analyze and comprehend. A collection of articles that address this issue is included in this section. Chapter 14 (“Complexity of the BN and the PBN Models of GRNs and Mappings for Complexity Reduction”) is intended to provide a generic framework for model complexity reduction in Boolean and probabilistic Boolean networks. Statistical and information theoretic views of complexity are described. Approaches to map larger GRNs into smaller, more tractable ones, while preserving the overall dynami- cal behavior, are considered within this scheme. Chapter 15 (“Abstraction Methods for Analysis of Gene Regulatory Networks”) also addresses the issue of reducing the complexity in GRNs. It details steps that can be taken to merge similar reactions and eliminate insignificant ones from large-scale models of biochemical reactions. Using these simpli- fications, models based on chemical kinetics can be abstracted into higher level ones called finite state systems. Chapter 16 (“Improved Model Checking Techniques for State Space Analysis of Gene Regulatory Networks”) describes a software tool that applies model checking–a technique used to analyze computer programs–to discrete GRN models. Using this technique, steady state characteristics of the models can be examined. Two case studies, the gene network for cell cycle of yeast, as well as that for wing forma- tion in D. melanogaster, illustrate the effectiveness of this technique. Chapter 17 (“Determining the Properties of Gene Regulatory Networks from Expression Data”) shows how topological properties of GRNs can be applied to the practical analysis of experimental gene expression data. Using examples that apply this approach, the authors argue that there is much more to regulation between genes than just transcription factors. Chapter 18 (“Generalized Boolean Networks: How Spatial and Temporal Choices Influence Their Dynamics”)relaxestherequirementsinrandomBooleannetworkmodels,thatgenesoperateinsynchrony and that their connectivity remain fixed. These modifications, it is argued, enable Boolean networks to better capture some characteristics present in gene expression, such as activation sequences in genes and periodic attractors. Section 6: heterogeneouS data Linear programming–a simple technique for the constrained optimization of linear functions–can be used to synthesize GRNs from multiple data sources, as the next two chapters show. In Chapter 19 (“A Linear Programming Framework for Inferring Gene Regulatory Network by In- tegrating Heterogeneous Data”), the authors use linear differential equation models of GRNs to which matrix decomposition methods and linear programming are applied. Data from heterogeneous sources, such as documented literature, protein-protein interaction data, and so forth are added as constraints. Using this formulation, the authors attempt to obtain robust GRN models that are consistent with mul- tiple datasets. Chapter 20 (“Integrating Various Data Sources for Improved Quality in Reverse Engineering of Gene Regulatory Networks”) shows how to reverse engineer large-scale GRNs by integrating various data sources, such as information gleaned by text mining of published research. Using this prior knowledge as
- 32. xxvi soft evidence, a methodology is proposed to obtain GRN models that can account for large error distribu- tions in microarrays. Simulations with yeast cell data corroborate the effectiveness of this method. Section 7: network SiMulation StudieS Chapter 21 (“Dynamic Links and Evolutionary History in Simulated Gene Regulatory Networks”) de- scribes computational studies on the evolution of GRNs. Using evolutionary strategies, an algorithmic approach similar to genetic algorithms, the authors are able to simulate the evolution of GRNs that produce stable multicellular growth. They observe that the evolutionary process favors the appearance of negative feedback in the evolved networks. They hypothesize that this is because negative feedback imparts the network with robustness to potentially deleterious mutations. A new GRN model that incorporates greater biological detail than traditional methods is outlined in the other simulation study in this section (Chapter 22 “A Model for a Heterogeneous Genetic Network”). The authors report computer experiments to generate GRNs using this biologically-motivated approach. They examine the topological features and dynamic behaviors of models obtained in this manner, and provide arguments that such models possess features that correlate well with biological observations. Section 8: other StudieS One of the purposes of GRNs is to model cellular dynamics, which are usually characterized by stable attractors. In this context, planned external interventions to redirect these networks from abnormal states (as in with the onset of cancer) to more regular ones is important for many applications, such as prescribing effective drugs. In Chapter 23 (“Planning Interventions for Gene Regulatory Networks as Partially Observable Markov Decision Processes”), this intervention problem is modeled as a Markov decision process. Two well known algorithms borrowed for artificial intelligence are proposed to solve the problem. There are two modes of propagation of a bacterial virus known as the λ phage: direct replication and integration with the host bacterium. The decision concerning which mode to adopt is controlled by a simple GRN called the λ switch. Chapter 24 “Mathematical Modeling of the λ Switch: A Fuzzy Logic Approach” uses fuzzy logic to model the switch, making it tractable to mathematical treatment. Using this approach, the chapter suggests explanations for certain behavioral aspects of the λ switch, particularly how the bacterium switches to the direct replication mode of transmission when DNA dam- age occurs in the host. Chapter 25, “Petri Nets and GRN Models,” introduces Petri nets, a graphical modeling approach for modeling GRNs. An introduction to Petri nets as well as related techniques useful in modeling bio- chemical processes is provided. The application of this approach for the gene regulation in Duchenne muscular dystrophy (DMD) is taken up. An analysis of the results sheds lights on the advantages and disadvantages of the method. concluSion This book provides a bird’s eye view of the vast range of computational methods used to model GRNs. It contains introductory material and surveys, as well as articles describing in-depth research in various
- 33. xxvii aspects of GRN modeling. The editors expect it to be useful to researchers in a variety of ways. It can provide a comprehensive overview of artificial intelligence approaches for learning and optimization and their use in gene networks to biologists involved in genetic research. It can assist computer science and artificial intelligence theorists in understanding how their methodologies can be applied to GRN model- ing. Although not intended to be a textbook, the book can be of immense use as a reference for students and classroom instructors. As the book would bridge the gap between computer science and genomic research communities, it will be very useful to graduate students considering research in this direction. Finally, this book would be useful to industrial researchers involved in gene regulatory modeling. Sanjoy Das Doina Caragea Stephen M. Welch William H. Hsu additional reading Bansal, M., Gatta, G. D., di Bernardo, D. (2006). Inference of gene regulatory networks and compound mode of action from time course gene expression profiles. Bioinformatics, 22(7), 815–822. Bolouri, H. (2008). Computational modeling of gene regulatory networks: A primer. World Scientific. Davidich, M., & Bornholdt, S. (2008). The transition from differential equations to Boolean networks: A case study in simplifying a regulatory network model. Journal of Theoretical Biology, 255(3), 269–277. Davidson, E. H. (2006). The regulatory genome: Gene regulatory networks in development and evolu- tion. Elsevier. de Jong, H. (2008). Search for steady states of piecewise-linear differential equation models of genetic regulatory networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 5(2), 208–222. Grzegorczyk, M., Husmeier, D., Edwards, K. D., Ghazal, P., & Millar, A. J. (2008). Modelling nonsta- tionary gene regulatory processes with a nonhomogeneous Bayesian network and the allocation sampler. Bioinformatics, 24(18), 2071–2078. Kærn, M., Blake, W. J., & Collins, J. J. (2003). The engineering of gene regulatory networks. Annual Review of Biomedical Engineering, 5, 179–206. Karlebach,G.,&Shamir,R.(2008).Modellingandanalysisofgeneregulatorynetworks.NatureReviews Molecular Cell Biology, 9, 770–780. Koduru, P., Dong, Z., Das, S., Welch, S. M., Roe, J., & Charbit, E. (2008). Multi-objective evolutionary- simplex hybrid approach for the optimization of differential equation models of gene networks. IEEE Transactions on Evolutionary Computation, 12(5), 572–590. Lähdesmäki, H., Hautaniemi, S., Shmulevich, I., &Yli-Harja, O. (2006). Relationships between probabi- listic Boolean networks and dynamic Bayesian networks as models of gene regulatory networks. Signal Processing, 86(4), 814–834.
- 34. xxviii Schlitt T., & Brazma, A. (2007). Current approaches to gene regulatory network modeling. BMC Bio- informatics, 8(Suppl 6), S9. Welch, S. M., Dong, Z., Roe, J. L., & Das, S. (2005). Flowering time control: Gene network modeling and the link to quantitative genetics. Australian Journal of Agricultural Research, 56, 919–936. Wilczek, A. M., Roe, J., Knapp, M. C., Cooper, M. D., Lopez-Gallego, C., Martin, L. J., Muir, C. D., Sim, S., Walker, A., Anderson, J., Egan, J. F., Moyers, B. T., Petipas, R., Giakountis, A., Charbit, E., Coupland, G., Welch, S. M., & Schmitt, J. (2009). Effects of genetic perturbation on seasonal life history plasticity. Science, 323(5916), 930–934. endnote 1 Genetic algorithms are a class of approaches borrowed from computational intelligence for sto- chastic optimization. The usage of the word “genetic” does not imply a direct relationship with GRNs, but stems from the fact that these algorithms loosely mimic biological evolution.
- 35. xxix Acknowledgment The editors would like to thank Nancy Williams and Jayme Brown for their kind help and support during the painstaking process of editing this book. They would also like to thank Amity Wilczek for her sug- gestions on the preface and everyone who participated in the review process. The editors are appreciative of all their insightful comments. Finally, the editors would like to express their gratitude to the authors of the 25 chapters in this book, each of whose contributions has made this book a success. This work has been supported in part by the U.S. National Science Foundation through Grant No. NSF FIBR 0425759. Sanjoy Das Doina Caragea Stephen M. Welch William H. Hsu
- 37. 1 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 1 What are Gene Regulatory Networks? Alberto de la Fuente CRS4 Bioinformatica, Italy introduction Several terms have been used to indicate models of regulatory processes and functional relations between genes, such as Gene Regulatory Networks, Gene Networks, Gene Expression Networks, Co-Expression Networks, Genetic Regulatory Networks, Transcriptional Regulatory Networks and Genetic Interaction Networks. While often used as such in the literature, not all of the above terms are actually synonyms. I therefore will provide a precise definition of the ‘Gene Regulatory Network’ and point out the essen- abStract 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 algo- rithms 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 the more compact description of Gene Regulatory Networks. Important differences between the defined Gene Regulatory Networks and other network models for gene regulation, such as Transcriptional Regulatory Networks and Co-Expression Networks, will be highlighted. DOI: 10.4018/978-1-60566-685-3.ch001
- 38. 2 What are Gene Regulatory Networks? tial differences with two other network models frequently used for gene regulation, i.e. Transcriptional Regulatory Networks and Co-Expression Networks. Before a clear definition of Gene Regulatory Networks can be given, we first need to consider the abstract definition of a ‘network’, also formally called ‘graph’. The mathematical theory of graphs is called graph theory (Bollobas, 1998; Erdös & Renyi, 1959), but recent advances in Complex Network Sciencegobeyondgraphtheoryaloneandincorporateideasfromphysics,sociologyandbiology(Barabasi & Oltvai, 2004; Dorogovtsev & Mendes, 2003; Newman, 2003; Pieroni et al., 2008; Watts & Strogatz, 1998). Three main types of graphs are essential in the context of Gene Regulatory Networks: An undirected graph G is an ordered pair G: = (V, U) that is subject to the following conditions: V is a set, whose elements are called vertices or nodes (the later will be used in the remainder of the chapter) and U is a set of unordered pairs of distinct vertices, called undirected edges, links or lines (‘un- directed edges’will be used in the remainder of the chapter). For each edge uij = {vi, vj} the nodes vi and vj are said to be connected, linked or adjacent to each other. Undirected graphs can be effectively used to represent the existence of associations or functional relationships (edges) between entities (nodes). A directed graph or digraph G is an ordered pair G: = (V, D) with V being a set of nodes and D a set of ordered pairs of vertices, called directed edges, arcs, or arrows (‘directed edges’ will be used in the remainder of the chapter). A directed edge dij = {vi, vj} is considered to be directed from node vi to vj; vj is called the head or target and vi is called the tail or source; vj is said to be a direct successor, or child, of vi, and vi is said to be a direct predecessor, or parent, of vj. If a directed path leads from vi to vj, then vi is said to be an ancestor of vj. Directed graphs can be effectively used to represent causal influences or communication between the nodes. A mixed graph G is a graph in which some edges may be directed and some may be undirected. It is written as an ordered triple G:= (V, U, D) with V, U, and D defined as above. Directed and undirected graphs are special cases of such mixed graphs. These graphs can thus represent associations as well as causal influences between the nodes. As we will see, Gene Regulatory Networks can most completely be represented as mixed graphs. gene regulatory networkS I start out by giving a possible formal definition for Gene Regulatory Networks. The remainder of the chapter is entirely dedicated to provide a detailed explanation of this definition. Definition – Gene Regulatory Network (GRN): a Gene Regulatory Network is a mixed graph G:= (V, U, D) over a set V of nodes, corresponding to gene-activities, with unordered pairs U, the undirected edges, and ordered pairs D, the directed edges. A directed edge dij from vi to vj is present iff a causal effect runs from node vi to vj and there exist no nodes or subsets of nodes in V that are intermediating the causal influence (it may be mediated by hidden variables, i.e. variables not in V).An undirected edge uij between nodes vi and vj is present iff gene-activities vi and vj are associated by other means than a direct causal influence, and there exist no nodes or subsets of nodes in V that explain that association (it is caused by a variable hidden to V). What do the nodes in GRNs precisely represent? The nodes in GRNs are often said to correspond to ‘genes’. More precisely, they rather correspond to ‘gene-activities’ (‘gene expression levels’ or ‘RNA concentrations’) as these are the dynamical and quantitative variables that are related by the algorithms discussed in this book. Of course ‘gene-activity’could be included in the definition of ‘gene’. Therefore, there will be no need to adapt the name ‘Gene-activity Regulatory Networks’.
- 39. 3 What are Gene Regulatory Networks? What do the edges in GRNs precisely represent? The directed edges in GRNs correspond to causal influences between gene-activities. These could include regulation of transcription by transcription fac- tors, but also less intuitive causal effects between genes involving signal-transduction or metabolism (Figure 2). It is of uttermost importance to realize that when inferring GRNs from gene-expression data alone, the metabolites and proteins act as hidden variables. These variables mediate communication between genes, but since they are not included explicitly in the GRNs, only their effects appear as edges between the observed variables, i.e. the gene-activities. Only cause-effect relations between observed quantities can be established. No matter of how many hidden intermediate causal steps are involved between them, the effects appear to be direct with respect to the set of observed variables. GRNs thus describe communication between genes implicitly including all regulatory processes inside living cells and therefore give a complete description of cellular regulation projected on the gene activities. GRNs are phenomenological, since the mechanisms underlying the edges are generally unknown (yet) and could correspond to complicated paths through proteins and metabolites. However, GRNs are based on a dynamic view of gene regulation: the presence of communication is important, while the precise mechanism of communication is of secondary importance. Figure 1. Abstract depiction of cellular physiology. Reprinted with permission from Elsevier from Bra- zhnik, P., de la Fuente, A., & Mendes, P. (2002). Gene Networks: How to Put the Function in Genomics. In Trends in Biotechnology, 20(11), 6.
- 40. 4 What are Gene Regulatory Networks? Figure 1 shows a simplified depiction of the biochemistry of living cells conceptually decomposed in three ‘spaces’ (also referred to as ‘levels’ in this chapter). Influences between gene-activities, with- out explicitly taking account for the proteins and metabolites, result from a projection of all regulatory processes on the ‘gene space’ (Brazhnik, de la Fuente & Mendes, 2002). Figure 2 shows the GRN resulting from the projection. The influence of gene-activity 1 on gene- activity2couldhaveastraightforwardinterpretation:gene1codesforaTranscriptionfactorthatregulates gene 2. But an alternative explanation is also possible: protein 1 could modify the rate of gene 1’s RNA degradation. The GRN representation doesn’t distinguish between the mechanisms as it only accounts for the causal effects: inhibiting a gene’s activity could occur through inhibition of transcription or ac- tivation of RNA degradation. The effects of gene-activities 3 and 4 are more complicated: their protein products form a complex and then regulate gene 2. The effect gene 2 on gene 4 involves all three levels. Note that the edge from gene-activity 2 to gene-activity 4 will never be present in a Transcriptional Regulatory Network (discussed below), because the protein product of gene 2 does not physically bind to the promoter region of gene 4 to establish its effect. Nevertheless, as we consider only the causal re- lations between gene-activities, by all means, this effect is considered direct, as the underlying cascade of causality is hidden with respect to the observed quantities. The undirected edges in GRNs represent ‘associations’ (for example ‘correlations’) between gene- activities, due to effects of confounding hidden variables (such as metabolites and proteins). The undi- rected edges should not be confused with reciprocal effects, i.e. two nodes that are connected by directed edges in both directions. In many studies of complex networks, for example in sociological networks (in which nodes are human individuals and edges represent human interactions such as ‘friendships’), the undirected edges are interpreted as such. When two human individuals are friends, information flows in both directions between them (at least it is supposed to be that way!) and in this sense such networks are thus actually directed networks with reciprocal directed edges between each connected pair. Then Figure 2. The GRN corresponding to the system depicted in figure 1. Reprinted with permission from Elsevier from Brazhnik, P., de la Fuente, A., & Mendes, P. (2002). Gene Networks: How to Put the Function in Genomics. In Trends in Biotechnology, 20(11), 6.
- 41. 5 What are Gene Regulatory Networks? simply out of convenience they are represented as undirected networks. The undirected edges in GRNs can not be interpreted this way: these edges represent associations between pairs of gene-activities that do not correspond to causal influences between the pair. In Genetic Interaction Networks as defined in (Tong et al., 2004) two genes are linked whenever they result in a lethal phenotype when knock-out together, while individual knockouts are viable. The undirected edges in these networks thus reflect a functional similarity between the nodes with respect to a certain phenotype, in contrast to undirected edges in GRNs, which reflect a dynamic association between gene-activities. As an example, figure 3 shows a partial GRN recently inferred for the yeast S. cerevisiae (Mancosu et al., 2008). The network consists of 4239 nodes and 14,723 directed edges. It is partial in the sense that it lacks the undirected edges that form part of the GRN: only directed edges are presented. The layout is performed according to the networks ‘bow tie’ structure. Similar structure has been found in metabolic networks of many organisms (Ma & Zeng, 2003) as well as in the World Wide Web (Broder et al., 2000). In the middle of the network there appears a Giant Strongly Connected Component (GSCC) of 339 genes and 1643 edges. In this component all nodes are connected by cycles. A directed cycle is defined by a directed path starting at a certain node and ending at that same node. The nodes in the IN component (74 nodes and 78 edges) can reach the GSCC through directed paths, but not vice versa. The nodes in the OUT component (3268 nodes and 1559 edges) can be reached from the GSCC but not vice versa. ‘Tubes’ contain nodes connecting IN to OUT without going through the GSCC. Nodes which are reached from the IN and reach the OUT but which do not belong to any of the aforementioned components are called ‘tendrils’(530 nodes and 197 edges). Many edges interface the components: between IN and GSCC 113 edges, GSCC and OUT 9630 edges and between IN and OUT 769 edges. It is not possible to identify causality from all types of experimental data. In certain cases the algo- rithms will only be able to produce an undirected network as a final result in which the undirected edges Figure 3. The bow-tie structure of the yeast GRN. The picture was obtained by combining several layout algorithms implemented in Pajek (Batagelj & Mrvar, 2003). Arrows indicate the direction of the flow of information (taken from (Mancosu et al., 2008)).
- 42. 6 What are Gene Regulatory Networks? could correspond to direct causal influences. Such networks are not GRNs, but rather Co-Expression Networks (CENs). co-expression networks (cens) Similar to GRNs, CENs are inferred from gene expression data. In CENs two genes are connected by an undirected edge if their activities have significant association over a series of gene expression measurements, usually quantified by Pearson correlation (Butte, Tamayo, Slonim, Golub & Kohane, 2000; D’Haeseleer, Liang & Somogyi, 2000), Spearman correlation (D’Haeseleer, Liang & Somogyi, 2000) or Mutual Information (Butte & Kohane, 2000; Steuer, Kurths, Daub, Weise & Selbig, 2002). Again, it is also important to emphasize the difference between GRNs and CENs, since the latter has also been mistakenly called GRNs in the literature by several authors. Gene activities can be correlated due to different causal relationships 1) direct effects 2) indirect effects (correlation is transitive) and 3) confounding. Several algorithms have been proposed to eliminate edges corresponding to 2 and 3 (if the confounding variables are measured), thus resulting in a network which is the undirected version of the GRN (de la Fuente, Bing, Hoeschele & Mendes, 2004; Schäfer & Strimmer, 2005a, 2005b; Veiga, Vicente, Grivet, de la Fuente & Vasconcelos, 2007; Wille & Buhlmann, 2006; Wille et al., 2004). Still, a correlation does not imply causation and many of the undirected edges may be due to hidden confounding factors. In a later section I will explicitly demonstrate how such edges arise. Only gene expression data obtained through a strategy of ‘gene perturbations’, or other targeted disturbances to the system, allow for inferring causal relationships.While it has been shown that under certain assumptions it ispossibletoinfercausalitywithoutmakingexperimentalinterventions(Pearl,2000;Spirtes,Glymour& Scheines,1993),suchassumptionsareunfortunatelynotjustifiedinthiscontext.Thestrongestassumption is that there are no hidden variables with confounding effects on the observed variables (Spirtes, Glymour & Scheines, 1993). Given the fact that gene-activities are generally the only observed quantities in the data used to infer CENs or GRNs, and that all variables mediating the causal effects between them, i.e. the proteins and metabolites are hidden, such assumption can not be justified under any circumstance. Gene perturbations are thus necessary to infer causality and thus GRNs. Such perturbations could be experimentally created by knocking-out or over-expressing genes (de la Fuente, Brazhnik & Mendes, 2001, 2002; Gardner, di Bernardo, Lorenz & Collins, 2003; Hughes et al., 2000; Mnaimneh et al., 2004; Wagner, 2001), or as will be discussed in other chapters in this book, also natural occurring genetic polymorphisms could be used to infer causal relationships between gene-activities (Bing & Hoeschele, 2005; Liu, de la Fuente & Hoeschele, 2008; Zhu et al., 2004) (see also Liu et al. – this book). transcriptional regulatory networks (trns) As the name already implies, Transcriptional Regulatory Networks (Guelzim, Bottani, Bourgine & Kepes, 2002; Lee et al., 2002; Luscombe et al., 2004; Shen-Orr, Milo, Mangan & Alon, 2002) only include gene-regulation through transcription, which as we saw is only a small fraction of mechanisms by which the communication between gene-activities occurs. TRNs have directed edges between source and target genes only if it has been experimentally established that the protein product of the source gene physically binds to the promoter region of the target gene and thus potentially regulates transcription, using experimental techniques such as the ChIP-Chip (Buck & Lieb, 2004; Iyer et al., 2001; Lee et al., 2002; Lieb, Liu, Botstein & Brown, 2001; Ren et al., 2000).All edges in TRNs are directed and the only
- 43. 7 What are Gene Regulatory Networks? source nodes are genes coding for Transcription Factors (TFs). TRNs are a mechanistic description of gene regulation with a clear molecular interpretation, straightforwardly connecting to the paradigm of ‘molecular biology’, while the concept of GRNs considered throughout this book requires one to take the point of view of ‘systems biology’, i.e. taking a more abstract, but integrated system-wide approach, rather than collecting sets of molecular relationships. Given that GRNs summarize the whole of cellular regulation, to gain insight into the global functional and dynamical organization of gene regulation, GRNs rather than TRNs should be studied. Can we expect large overlap between experimentally identified GRNs and TRNs of a particular or- ganism? While intuitively one would think so, I claim this is not necessarily the case for the following reasons: 1. Noise: First of all, in general there may be mistakes in both networks. GRNs are predominantly based on gene expression data (Brazhnik, de la Fuente & Mendes, 2002; D’Haeseleer, Liang & Somogyi,2000).TRNsarebasedonpredominantlyChIP-Chipdata(Harbisonetal.,2004;Leeetal., 2002). Both gene expression data and ChIP-Chip data are plagued by inaccuracies. Gene expression data have several sources of error and ChIP-Chip measurements suffer from a-specific binding. A recent paper showed that TFs bind many sites in the genome; many of which are not believed to be near coding sequences at all (Li et al., 2008). It was also shown that many genes whose promoters were bound were not transcribed in response to the binding event (Li et al., 2008). Furthermore, there is a Multiple Hypothesis Testing (MHT) problem (Storey & Tibshirani, 2003). While many algorithms for GRN inference employ (or at least try to do so) a formal procedure to deal with MHT, most TRNs were obtained using arbitrary p-value thresholds (c.f.Storey & Tibshirani, 2003). Better statistical approaches to obtain TRNs from ChIP-Chip data are in development (Margolin, Palomero, Ferrando, Califano & Stolovitzky, 2007). 2. Physiologically active regulatory processes: Edges in TRNs that are not present in GRNs could be explained as follows: to formulate TRNs, the ChIP-Chip experiments are often performed in- vitro after cells have been subjected to many different experimental conditions (Harbison et al., 2004). Thus, the TRN could be expected to nearly completely account for all possible transcrip- tional regulatory events by the TFs. However, as was shown for the yeast TRN, in each particular physiological state only subsets of these regulatory events are dynamically active (Luscombe et al., 2004). Also, in a recent study, the E. coli TRN was compared to a network obtained through gene expression data measured in many different conditions (Faith et al., 2007). Still, only 10% of the ‘known’ E. coli transcription regulatory interactions were recovered (Faith et al., 2007), in ac- cordance with the observation that only small parts of TRNs are dynamically active or too weakly active to detect from expression data. It was shown for the yeast TRN that only relatively small parts are active in specific physiological states and that the active sub-networks in those states show widely different topological properties (Luscombe et al., 2004), suggesting that topological analysis of TRNs as a whole is rather meaningless. GRNs inferred in a particular physiologically setting will be entirely active since it is constructed from dynamic information on gene-activities. Therefore, it is justified to explore the whole GRNs for topological features, rather than of sub- graphs. It must be stressed that the structure of GRNs are context dependent as well: in different experimental settings (different culture media, temperatures, pH etc.) different causal influences between gene-activities will be physiologically active, leading to a different structure of the inferred GRNs. I expect that the structures of the GRNs obtained for different cell types of a multi-cellular organism can be quite different, both in quantitative as well as in qualitative sense.
- 44. 8 What are Gene Regulatory Networks? 3. Regulation beyond Transcription Factors: The edges in the GRNs not present in the TRN have a straightforward explanation: the GRN contains much regulation beyond simply transcription factors. Certain processes regulate gene expression independently of transcription, for example regulation through RNA degradation and the small interfering RNAs, which were discovered to play a mayor role in regulation of gene-expression levels (Shimoni et al., 2007). Other processes do involve transcription, but the source nodes are not TFs. For example, genes that code for kinases that activate/inactivate TFs upon phosphorylation will have directed edges to the targets of the TFs. Genes coding for enzymes producing metabolites that in turn activate/inactivate TFs by binding to them, will have directed edges to the targets of the TFs. comment on cyclicity Cyclic network patterns have been found only rarely in TRNs (Lee et al., 2002; Shen-Orr, Milo, Mangan &Alon, 2002). In the TRN of E. coli from RegulonDB (Gama-Castro et al., 2008; Huerta, Salgado, Thi- effry & Collado-Vides, 1998; Salgado et al., 2004; Salgado et al., 2006a; Salgado et al., 2000; Salgado et al., 2001; Salgado et al., 2006b; Salgado et al., 1999) there were no cyclic dependencies at all (Shen- Orr, Milo, Mangan & Alon, 2002). This observation was made in 2002 and since then RegulonDB was subjected to several updates. Still, in current updates of RegulonDB only very few cyclic dependencies are listed. In the TRN studied in (Luscombe et al., 2004) there is a cyclic component involving only 25 nodes. The fact that between genes coding for TFs not much feedback seems to be present does not imply that GRNs are largely acyclic as well. Since GRNs result from a projection of all regulatory pro- cesses onto gene space, many cycles can be expected. Indeed the cyclic component of the yeast GRN presented in figure 1 shows a large component of 339 nodes. This component will be responsible for most of the dynamical properties of the whole network. Cyclic dependencies are associated with many (if not all!) fundamental properties of living systems, such as homeostasis, robustness, excitability, multi- stationarity and biological rhythms (e.g. cell cycle, circadian rhythm) (Kauffman, 1969; Noble, 2006; Thieffry & Thomas, 1998; Thomas, 1973; Tyson, Chen & Novak, 2003; von Bertalanffy, 1968; Weiner, 1948; Westerhoff & van Dam, 1987). Again, this emphasizes that TRNs are only representing a part of the global regulatory system, lacking the regulation on the Proteome and Metabolome levels. GRNs, on the other hand, represent the entire global regulatory system, but in a more phenomenological way. Physiological State dependent ‘rewiring’ The structures of GRNs may quantitatively as well as qualitatively depend on the physiological state of the cell. Each of the cell types of a multi-cellular organism can be expected to have GRNs with different structures. Yeast grown in presence of oxygen may have a physiologically active GRN that is different from the physiologically active GRN in anaerobic conditions, etc. How does this ‘rewiring’ happen? One explanation comes from the fact that gene-expression rates are dependent on the activator/inhibitor concentrations in a non-linear (usually hyperbolic or sigmoidal) fashion. Consider the ‘dose-response curve’ given in Figure 4. This example displays the sigmoidal dependence of one gene’s activity on the activity of an activating gene. There are three qualitatively distinct regions in the curve, indicated by the dashed lines. Only in the middle part will the activity of gene i appreciably change upon (small) fluctuations in gene j. In the left and right part the effects are very small, for example, increasing gene- activity j from value 3 to 4 hardly result in any change in gene-activity i. At physiological values of
- 45. 9 What are Gene Regulatory Networks? gene-activity below 0.5 or above 2, gene-activity i will not ‘feel’ changes in gene-activity j, effectively thus not receiving input from gene-activity j. In each specific physiological state gene-activity j will have different values determined by its inputs in turn. In each physiological state, fluctuations in gene-activity j will ‘sample’ different parts of this curve, resulting in different strengths of causal influences. This results in quantitative changes in the network structure. If very small effects are ignored (since they are too small of significance to the behavior of the system, or at least can not be determined experimentally) this would translate into qualitative changes in the GRN: edges that appear in one physiological state may not appear in other physiological states. Several authors (Kauffman, 1969; Thieffry & Thomas, 1998; Thomas, 1973; Wagner, 2001; Yeung, Tegner & Collins, 2002) have argued that GRNs are sparsely connected. However, there are simple arguments that suggest the opposite for GRNs of which I will list a few here. All transcription steps dependent on metabolic energy. Consequently, genes that code for enzymes that have control on the cellular energy level may causally affect all gene-activities. The rates of transcription depend on the concentrations of nucleotides as these are the building blocks of nucleic acids; so all genes coding for enzymes involved in nucleotide synthesis may be inputs of all other genes. Any other genes that affect transcription or RNA degradation, in some general way, will be inputs to all genes. For instance, genes that code for transporters that are responsible for transport of regulating metabolites or proteins into the nucleus. There are many other examples of causal influences that could arise from the complex interplay between the unobserved Proteome and Metabolome and the observed Transcriptome. Since the rate of production of each of the gene-activities competes for the same energy, building blocks, polymerases and transcriptional machinery, an increase in the formation rate of one gene-activity may cause a decrease in all others, implying that GRNs are essentially ‘complete graphs’, i.e. networks with edges between all pairs of nodes. Whether these numerous potential interactions have a significant magnitude or not is an Figure 4. Sigmoidal dependence of the value of gene-activity i on the value of gene-activity j. The dashed lines separate regions where gene-activity i is (almost) insensitive to the value of gene-activity j (left and right regions) from the region where gene-activity i is sensitive to the value of gene-activity j (middle region).
- 46. 10 What are Gene Regulatory Networks? open question. Certainly, almost all of these interactions will have small magnitude, as for example in many physiological situations there are plenty of nucleotides such that transcription rates are saturated with them, reducing the related effects to negligible strengths. This situation corresponds to the part of the curve in the third region in figure 4. ‘condenSing’ biocheMiStry into grnS directed edges Here I will show how to ‘condense’ biochemical systems into GRNs in order to clearly demonstrate what the directed edges in GRNs mean in terms of the underlying biochemical processes (de la Fuente & Mendes, 2002). I use the word ‘condense’, because the GRN is a compact representation of the whole biochemical system; a condensed description of the whole. To this effort is useful to represent a bio- chemical system as a dynamical system. For each concentration xi in a biochemical system (metabolites, proteins, gene-activities) a non-linear differential equation can be written to relate its rate of change to a set of parameters k and the set of concentrations x in the system: dx dt f i i = ( ) k x , (1) For simplicity, I will consider a linearization of the model, but the following reasoning should in principle hold for non-linear systems as well. The linearization describes deviations from a reference state: D D D dx dt a x u i ij j n j i æ è ç ç ç ç ö ø ÷ ÷ ÷ ÷ ÷ = + å (2) The a-coefficients are non-zero iff xj directly affects the rate of change of xi and zero otherwise. These coefficients are elements of a matrix A that represents the wiring structure of the biochemical system. MatrixAis square with dimension n×n, with n the number of variables (e.g. metabolites, proteins and gene-activities) in the biochemical system. An element in row i and column j, i.e. aij, provides the strength by which xj affects xi. If aij is positive, xj activates xi and if negative xj inhibits xi. Matrix A is a so-called weight matrix and corresponds to the Jacobian matrix of the linearized system with ele- ments ¶( ) ¶ dx dt x i j , the partial derivatives of rates of changes with respect to the variables. Another matrix representation of networks is the adjacency matrix, which contains simply the number 1 on non-zero positions of A and 0 otherwise. It therefore is a qualitative version of matrix A. Dxj are the deviations of xj out of the reference state. Dui are deviations from the values in the reference state of a rate-parameter that specifically affects dx dt i . These deviations can be either seen as experimentally created, i.e. experimental perturbations (interventions), or as spontaneously occurring fluctuations due to ‘biological variability’: the fact that no repeated observations on the same (or similar) system are identical (even when experimental noise is ignored). While the study of dynamics in time of GRNs is certainly relevant, especially in studies of organ- ismal development (Bolouri & Davidson, 2003), I will here consider systems in a stable steady state
- 47. 11 What are Gene Regulatory Networks? for the relative simplicity of the following discussion. Note that the main train of thought applies to time-dynamics as well. In a steady state of the biochemical system all activities are constant in time (the time-derivatives are zero) and we can express a relationship between rate-parameter perturbations (fluctuations) and interactions between gene-activities: 0 = + åa x u ij j n j i D D or 0 = + åa x u ij j n j i D D (3) These relations can be written in matrix format AX U = - (4) HereA(n×n)istheweight-matrix,U(n×k)isamatrixcontainingratefluctuations Duik ,withelements the deviation of the rate specific to xi in observation k, and X (n×k) is a matrix containing responses (deviations from the reference state) resulting from the fluctuations in U. k is the number of observa- tions made to the system. Eq. 4 can be written explicitly in terms of the three functional levels of organization of cells, i.e. the Transcriptome, Proteome and Metabolome. One could argue that a ‘functional’ distinction should not be made, since all bio-molecules, big or small, are ‘metabolized’ through production and degradation reactions and thus all could be seen as one Metabolome (Cornish-Bowden, Cardenas, Letelier & Soto- Andrade, 2007). Nevertheless, from the point of view of the experimental accessibility of the three levels, it is certainly a useful ‘conceptual’ distinction. Matrix A can be written in blocks corresponding to the interactions within (diagonal blocks) and between the levels (off-diagonal blocks). Matrices X and U are partitioned accordingly in three separate blocks of rows: A A A A A A A A A X X X TT TP TM PT PP PM MT TP MM T P M é ë ê ê ê ê ê ù û ú ú ú ú ú é ë ê ê ê ê ê ù û ú ú úú ú ú = - é ë ê ê ê ê ê ù û ú ú ú ú ú U U U T P M (5) The subscript T refers ‘Transcripts’or ‘Transcriptome’(gene-activities), P to ‘Proteins’or ‘Proteome’ and M to ‘Metabolites’ or ‘Metabolome’. Lets take nt as the number of transcripts in the system, np the number of proteins and nm the number of metabolites. The elements of ATT (dimensions nt×nt) represent the effects of the transcript concentrations on the rates of change of transcript concentrations. These effects are mainly due to the degradation rates, since each transcript increases its own degrada- tion rate, transcripts usually do not interfere with the synthesis or degradation of other transcripts (again making the assumption that energy, building bocks and polymerases are not limiting) and transcription is an irreversible process. In the simplest case ATT is merely a lower diagonal matrix with negative numbers: the self-effect due to the enhancement of the degradation rate. Regulation of gene expression by microRNAs will lead to a more complicated form of ATT. The elements ofATP(nt×np) represent the effects of the protein concentrations on the rates of change oftranscriptconcentrations.RNA-polymerases,TranscriptionFactorsandRNases,forexample,aresome of the proteins involved in these effects. Also the proteins that make up the spliceosome and proteins that transport mRNA from the nucleus to the cytoplasm will appear in this sub matrix.
- 48. 12 What are Gene Regulatory Networks? ATM (nt×nm) describes the effect of the metabolites on the rate of change of transcript concentra- tions. Certain metabolites interfere with the transcription of genes by changing the binding affinities of regulating proteins, leading to a change in transcript formation rate. A famous example is tryptophan synthesis in E. coli, in which the trp-operon is inhibited by the concentration of L-tryptophan, the product metabolite of the pathway (Morse, Mosteller & Yanofsky, 1969; Santillan & Mackey, 2001). APT (np×nt) describes the effects of the transcriptome on the proteome. Since the rate of translation depends on the number of available mRNA molecules each gene-activity positively influences the con- centration of the protein it codes for. The columns referring to rRNAs will have positive values in almost every row, since they are part of the ribosomes and thus stimulate the formation rate of all proteins.Also the regulation of translation by microRNAs will give non-zero elements in this sub-matrix. APP (np×np) contains information of many different types of interaction between proteins. The col- umns of proteases will have many negative elements; ribosomal proteins will have positive entries in almost all rows. The effects of phosphatases and kinases, and other components of signaling cascades appear in this sub matrix, as well as any other form of protein-protein interaction. APM (np×nm) shows the effects of metabolites on rate changes in the proteome. Some metabolites interfere with the synthesis or degradation of proteins. For example, protein synthesis and many post- translation modification reactions depend on ATP, GTP and other metabolite concentrations. AMT (nm×nt) would represent the rare cases of ribozymes catalyzing metabolic reactions, and most entries can be expected to be zero. AMP (nm×np) mainly contains the effects of metabolic enzymes on the rates of change of substrates and products of the reactions it catalyses. Also contained are the effects of transporters that pump me- tabolites in and out the cell. AMM (nm×nm) describes the effects that metabolites have on the rate of change of metabolite con- centrations. These are the effects of substrates, products and metabolic modifiers on metabolic reaction rates. XT (nt×k), XP (np×k), XM (nm×k), UT (nt×k), UP (np×k) and UM (nm×k), with k the total number of measurements made to the system. Experimentally the elements in UTcould be accessed by knocking- out genes or over-expressing them (de la Fuente, Brazhnik & Mendes, 2002; Gardner, di Bernardo, Lorenz & Collins, 2003). Experimental perturbations in UPrequire inhibition/stimulation of for example translation and perturbations in UM could be created by adding inhibitors of metabolic rates. In the following, the inverse of A is assumed to exist. This is equivalent to assume that the system is present in a structurally stable steady state and that none of the variables can be written as a linear com- bination of other variables (Heinrich & Schuster, 1996). The responses of the state variables (deviations of the xs from the reference state) towards the perturbations can be written as follows. X X X A A A A A A A A A T P M TT TP TM PT PP PM MT MP MM é ë ê ê ê ê ê ù û ú ú ú ú ú = é ë ê ê ê ê ê ù û ú úú ú ú ú é ë ê ê ê ê ê ù û ú ú ú ú ú -1 U U U T P M (6) This equation clearly shows how the network of the biochemical system, represented as a weighted matrix, through its inverse transforms the rate-deviations into responses of the concentration of the system variables.
- 49. 13 What are Gene Regulatory Networks? Using the relationship for the inverse of block matrices (Gantmacher, 1960), the inverse of a matrix can be expressed in terms of its blocks (assuming that matrices P and S are non-singular, again related to the structural stability of the sub-systems): X Y Z U P Q R S I 0 0 I X Y Z U é ë ê ê ê ù û ú ú ú é ë ê ê ê ù û ú ú ú = é ë ê ê ê ù û ú ú ú Þ é ë ê ê ê ù û ú ú ú = = - ( ) - - ( ) - - ( ) - ( ) é ë - - - - - - - - - - P QS R P Q S RP Q S R P QS R S RP Q 1 1 1 1 1 1 1 1 1 1 êê ê ê ê ù û ú ú ú ú In the present context we are only interested in the top left block, because that is the block that trans- forms the rate-fluctuations (perturbations) originating in each gene UT into gene-activity responses XT. For the sake of clarity of the following explanation it is assumed that no fluctuations arise or perturba- tions are made in the Proteome and Metabolome, i.e. UP = 0 and UM = 0. In a later section I will show the implication of fluctuations in those levels separately. Applying the above rule we obtain: X A A A A A A A A A T TT TP TM PP PM MP MM PT MT = -( ) æ è ç ç ç ç ç ö ø ÷ ÷ ÷ ÷ ÷ æ è ç ç ç ç ç ö ø -1 ÷ ÷ ÷ ÷ ÷ ÷ æ è ç ç ç ç ç ç ö ø ÷ ÷ ÷ ÷ ÷ ÷ ÷ -1 UT (7) The block rule is applied again on the inverse matrix on the inside and by taking B A A A A B A A A A PP PP PM MM MP MM MM MP PP PM = - ( ) = - ( ) - - 1 1 we can write XT as: X A U A A B A A A A B A A T GRN T TT TP PP PT TP PP PM MM MT T = ( ) = - ( ) - ( ) ( ) + - - - - 1 1 1 1 M M MM MT TM MM MP PP PT B A A A A A ( ) - ( ) ( ) æ è ç ç ç ç ç ç ç ç ç ç ç ç ç ç ç ç ç ç ç ö - - - 1 1 1 ’ ø ø ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ -1 UT (8) Now we have an expression of AGRN, the weight matrix describing the directed part of the GRN structure: non-zero elements in AGRN correspond to directed edges in the GRN.
- 50. 14 What are Gene Regulatory Networks? A A A B A A A A B A A B A GRN TT TP PP PT TP PP PM MM MT TM MM = - ( ) - ( ) ( ) + ( ) - - - - 1 1 1 1 M MT TM MM MP PP PT - ( ) ( ) - - A A A A 1 1 ’ (9) Thewaythisequationispresentedshowsclearlyhowthecommunicationbetweengenes,givenbytheweight- matrix AGRN iscomposedofseveralcontributionsthatrunthroughtheentiresystem. AGRN isthena‘condensed’ representation of the whole system. First of all, there is a ‘local’effect on the gene-activities, i.e. ATT . Then, influences mediated separately by the Proteome, A B A TP PP PT ( ) -1 , and Metabolome, A B A TM MM MT ( ) -1 as well as influences through the Proteome and Metabolome, A A A A TM MM MP PP PT ( ) ( ) - - 1 1 ’ and Metabolome and Proteome, A A A B A TP PP PM MM MT ( ) ( ) - - 1 1 . Note that even though I mention that A B A TP PP PT ( ) -1 and A B A TM MM MT ( ) -1 are effects that separately run thorugh the Proteome and Metabolome, the presence of the B matrices in these expressions show that the strengths of the influ- ences depend on cyclic communication between the two levels. Toclearlydemonstratethemeaningoftheratherabstractderivationof AGRN aboveIwillhereconsider an example. The example is chosen to be as simple as possible: it concerns two gene-activities commu- nicating through a metabolite (figure 5). Note that synthesis and degradation rates are explicitly included in the depiction, in order to emphasize that the communication occurs through modifying rates. The whole matrix A for this system reads: A A A A A A A A A A A 0 A A A 0 TT TM PT PP = é ë ê ê ê ê ê ù û ú ú ú ú ú = TT TP TM PT PP PM MT MP MM 0 0 A A MP MM é ë ê ê ê ê ê ù û ú ú ú ú ú = a a a a a a TT T M T T T M PT P P 1 1 1 2 2 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 2 a a a a a PT P P MP MP MM é ë ê ê ê ê ê ê ê ê ê ù û ú ú ú ú ú ú ú ú ú (10) The diagonal elements (‘self-effects’) appear due to the fact that the degradation rates of each variable depend on their concentrations. Self-effects will always be negative, except if there is an auto-catalytic effect (e.g. a protein that stimulates its own translation) that exceeds the degradation effects in magnitude. When considering the effects between the gene-activities inATT we see that each gene-activity only affects itself: without the other system-levels there is no communication between the genes. By using the expression for AGRN above, the GRN structure corresponding to the system in figure 5 can be derived. Because A 0 PM = (a matrix full with zeros) note that B A B A PP PP MM MM = =
- 51. Another Random Scribd Document with Unrelated Content
- 55. The Project Gutenberg eBook of The Ballad of Ensign Joy
- 56. This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title: The Ballad of Ensign Joy Author: E. W. Hornung Release date: July 11, 2016 [eBook #52559] Most recently updated: October 23, 2024 Language: English Credits: Produced by David Widger from page images generously provided by the Internet Archive *** START OF THE PROJECT GUTENBERG EBOOK THE BALLAD OF ENSIGN JOY ***
- 57. THE BALLAD of ENSIGN JOY
- 58. By E.W. Hornung E. P. Dutton & Company 1917
- 59. THE BALLAD of ENSIGN JOY
- 60. IT is the story of Ensign Joy And the obsolete rank withal That I love for each gentle English boy Who jumped to his country's call. By their fire and fun, and the
- 61. I I deeds they've done, I would gazette them Second to none Who faces a gun in Gaul!) T is also the story of Ermyntrude A less appropriate name For the dearest prig and the prettiest prude! But under it, all the same, The usual consanguineous squad Had made her an honest child of God— And left her to play the game. T was just when the grind of the Special Reserves, Employed upon Coast Defence, Was getting on every Ensign's nerves— Sick-keen to be drafted hence— That they met and played tennis and danced and sang, The lad with the laugh and the schoolboy slang, The girl with the eyes intense.
- 62. Y H ET it wasn't for him that she languished and sighed, But for all of our dear deemed youth; And it wasn't for her, but her sex, that he cried, If he could but have probed the truth ! Did she? She would none of his hot young heart; As khaki escort he's tall and smart, As lover a shade uncouth. E went with his draft. She returned to her craft. He wrote in his merry vein: She read him aloud, and the Studio laughed! Ermyntrude bore the strain. He was full of gay bloodshed and Old Man Fritz: His flippancy sent her friends into fits. Ermyntrude frowned with pain.
- 63. H Y IS tales of the Sergeant who swore so hard Left Ermyntrude cold and prim; The tactless truth of the picture jarred, And some of his jokes were grim. Yet, let him but skate upon tender ice, And he had to write to her twice or thrice Before she would answer him. ET once she sent him a fairy's box, And her pocket felt the brunt Of tinned contraptions and books and socks— Which he hailed as "a sporting stunt!" She slaved at his muffler none the less, And still took pleasure in mur- muring, "Yes! For a friend of mine at the Front.")
- 64. O I H NE fine morning his name appears— Looking so pretty in print! "Wounded!" she warbles in tragedy tears— And pictures the reddening lint, The drawn damp face and the draggled hair . . . But she found him blooming in Grosvenor Square, With a punctured shin in a splint. T wasn't a haunt of Ermyn- trude's, That grandiose urban pile; Like starlight in arctic altitudes Was the stately Sister's smile. It was just the reverse with Ensign Joy— In his golden greeting no least alloy— In his shining eyes no guile! E showed her the bullet that
- 65. S I did the trick— He showed her the trick, x-ray'd; He showed her a table timed to a tick, And a map that an airman made. He spoke of a shell that caused grievous loss— But he never mentioned a certain cross For his part in the escapade! HE saw it herself in a list next day, And it brought her back to his bed, With a number of beautiful things to say, Which were mostly over his head. Turned pink as his own pyjamas' stripe, To her mind he ceased to em- body a type— Sank into her heart instead. WONDER that all of you didn't retire!"
- 66. H T "My blighters were not that kind." "But it says you 'advanced un- der murderous fire, Machine-gun and shell com- bined—'" "Oh, that's the regular War Office wheeze!" "'Advanced'—with that leg!— 'on his hands and knees'!" "I couldn't leave it behind." E was soon trick-driving an invalid chair, and dancing about on a crutch; The haute noblesse of Grosvenor Square Felt bound to oblige as such; They sent him for many a motor- whirl— With the wistful, willowy wisp of a girl Who never again lost touch. HEIR people were most of them dead and gone. They had only themselves to His pay was enough to marry
- 67. T A upon, As every Ensign sees. They would muddle along (as in fact they did) With vast supplies of the tertium quid You bracket with bread-and- cheese. please. HEY gave him some leave after Grosvenor Square— And bang went a month on banns; For Ermyntrude had a natural flair For the least unusual plans. Her heaviest uncle came down well, And entertained, at a fair hotel, The dregs of the coupled clans. CERTAIN number of cheques accrued To keep the wolf from the door: The economical Ermyntrude Had charge of the dwindling
- 68. H F store, When a Board reported her bridegroom fit As—some expression she didn't permit . . . And he left for the Front once more. IS crowd had been climbing the jaws of hell: He found them in death's dog- teeth, With little to show but a good deal to tell In their fissure of smoking heath. There were changes—of course —but the change in him Was the ribbon that showed on his tunic trim And the tumult hidden be- neath! OR all he had suffered and seen before Seemed nought to a husband's care; And the Chinese puzzle of mod-
- 69. Y B ern war For subtlety couldn't compare With the delicate springs of the complex life To be led with a highly sensitised wife In a slightly rarefied air! ET it's good to be back with the old platoon— "A man in a world of men"! Each cheery dog is a henchman boon— Especially Sergeant Wren! Ermyntrude couldn't endure his name— Considered bad language no lien on fame, Yet it's good to—hear it again! ETTER to feel the Ser- geant's grip, Though your fingers ache to the bone! Better to take the Sergeant's tip Than to make up your mind alone.
- 70. B H They can do things together, can Wren and Joy— The bristly bear and the beard- less boy— That neither could do on his own. UT there's never a word about Old Man Wren In the screeds he scribbles to-day— Though he praises his N.C.O.'s and men In rather a pointed way. And he rubs it in (with a knitted brow) That the war's as good as a pic- nic now, And better than any play! IS booby-hutch is "as safe as the Throne," And he fares "like the C.-in- Chief," But has purchased "a top-hole gramophone By way of comic relief." (And he sighs as he hears the
- 71. H H men applaud, While the Woodbine spices are wafted abroad With the odour of bully-beef.) E may touch on the latest type of bomb, But Ermyntrude needn't blench, For he never says where you hurl it from, And it might be from your trench. He never might lead a stealthy band, Or toe the horrors of No Man's Land, Or swim at the sickly stench. . . . ER letters came up by ration-cart As the men stood-to before dawn: He followed the chart of her soaring heart With face transfigured yet drawn: It filled him with pride, touched
- 72. T A with chivalrous shame. But—it spoilt the war, as a first- class game, For this particular pawn. HE Sergeant sees it, and damns the cause In a truly terrible flow; But turns and trounces, without a pause, A junior N. C. O. For the crime of agreeing that Ensign Joy Isn't altogether the officer boy That he was four months ago! T length he's dumfounded (the month being May) By a sample of Ermyntrude's fun! "You will kindly get leave over Christmas Day, Or make haste and finish the But Christmas means presents, she bids him beware: "So what do you say to a son and heir? I'm thinking of giving you
- 73. W T H Hun!" HAT, indeed, does the Ensign say? What does he sit and write? What do his heart-strings drone all day? What do they throb all night? What does he add to his piteous prayers?— "Not for my own sake, Lord, but —theirs, See me safe through ..." HEY talk—and he writhes —"of our spirit out here, Our valour and all the rest! There's my poor, lonely, delicate dear, As brave as the very best! We stand or fall in a cheery crowd, And yet how often we grouse aloud! She faces that with a jest!" E has had no sleep for a day and a night;
- 74. H I He has written her half a ream; He has Iain him down to wait for the light, And at last come sleep—and a dream. He's hopping on sticks up the studio stair: A telegraph-boy is waiting there, And—that is his darling's scream! E picks her up in a tender storm— But how does it come to pass That he cannot see his reflected form With hers in the studio glass? "What's wrong with that mir- ror?"' he cries. But only the Sergeant's voice replies: "Wake up, Sir! The Gas— the Gas!" S it a part of the dream of dread? What are the men about?
- 75. T E Each one sticking a haunted head Into a spectral clout! Funny, the dearth of gibe and joke, When each one looks like a pig in a poke, Not omitting the snout! HERE'S your mask, Sir! No time to lose!" Ugh, what a gallows shape! Partly white cap, and partly noose! Somebody ties the tape. Goggles of sorts, it seems, inset: Cock them over the parapet, Study the battlescape. NSIGN JOY'S in the second line— And more than a bit cut off; A furlong or so down a green incline The fire-trench curls in the trough. Joy cannot see it—it's in the bed Of a river of poison that brims
- 76. N T instead. He can only hear—a cough! OTHING to do for the Companies there— Nothing but waiting now, While the Gas rolls up on the balmy air, And a small bird cheeps on a bough. All of a sudden the sky seems full Of trusses of lighted cotton-wool And the enemy's big bow- wow! HE firmament cracks with his airy mines, And an interlacing hail Threshes the clover between our lines, As a vile invisible flail. And the trench has become a mighty vice That holds us, in skins of molten ice, For the vapors that fringe the veil.
- 77. I W N T'S coming—in billowy swirls —as smoke From the roof a world on fire. It—comes! And a lad with a heart of oak Knows only that heart's de- sire! His masked lips whimper but one dear name— And so is he lost to inward shame That he thrills at the word: "Re-tire!" HOSE is the order, thrice renewed? Ensign Joy cannot tell : Only, that way lies Ermyntrude, And the other way this hell! Three men leap from the pois- oned fosse, Three men plunge from the para- dos, And—their—officer—as well! OW, as he flies at their fly- ing heels,
- 78. H N He awakes to his deep dis- grace, But the yawning pit of his shame reveals A way of saving his face: He twirls his stick to a shep- herd's crook, To trip and bring one of them back to book, As though he'd been giving chase! E got back gasping— "They'd too much start!" "I'd've shot 'em instead!" said Wren. "That was your job, Sir, if you'd the 'eart— But it wouldn't 've been you, then. I pray my Lord I may live to see A firing-party in front o' them three!" (That's what he said to the men.) OW, Joy and Wren, of Company B,
- 79. N D Are a favourite firm of mine; And the way they reinforced A, C, and D Was, perhaps, not unduly fine; But it meant a good deal both to Wren and Joy— That grim, gaunt man, but that desperate boy!— And it didn't weaken the Line. OT a bad effort of yours, my lad," The Major deigned to declare. "My Sergeant's plan, Sir"— "And that's not bad— But you've lost that ribbon you wear?" "It—must have been eaten away by the Gas!" "Well—ribbons are ribbons— but don't be an ass! It's better to do than dare." ARE! He has dared to de- sert his post— But he daren't acknowledge his sin! He has dared to face Wren with
- 80. D B a lying boast— But Wren is not taken in. None sings his praises so long and loud— With look so loving and loyal and proud! But the boy sees under his skin. AILY and gaily he wrote to his wife, Who had dropped the beati- fied droll And was writing to him on the Meaning of Life And the Bonds between Body and Soul. Her courage was high—though she mentioned its height; She was putting upon her the Armour of Light— Including her aureole! UT never a helm had the lad we know, As he went on his nightly raids With a brace of his Blighters, an N. G O.
- 81. H M And a bagful of hand-grenades And the way he rattled and harried the Hun— The deeds he did dare, and the risks he would run— Were the gossip of the Bri- gades. OW he'd stand stockstill as the trunk of a tree, With his face tucked down out of sight, When a flare went up and the other three Fell prone in the frightening light. How the German sandbags, that made them quake, Were the only cover he cared to take, But he'd eavesdrop there all night. ACHINE-GUNS, tapping a phrase in Morse, Grew hot on a random quest, And swarms of bullets buzzed down the course
- 82. H B Like wasps from a trampled nest. Yet, that last night! They had just set off When he pitched on his face with a smothered cough, And a row of holes in his chest. E left a letter. It saved the lives Of the three who ran from the Gas; A small enclosure alone survives, In Middlesex, under glass: Only the ribbon that left his breast On the day he turned and ran with the rest, And lied with a lip of brass! UT the letters they wrote about the boy, From the Brigadier to the men! They would never forget dear Mr. Joy, Not look on his like again. Ermyntrude read them with dry,
- 83. T A proud eye. There was only one letter that made her cry. It was from Sergeant Wren: HERE never was such a fear- less man, Or one so beloved as he. He was always up to some daring plan, Or some treat for his men and me. There wasn't his match when he went away; But since he got back, there has not been a day But what he has earned a V. C CYNICAL story? That's not my view. The years since he fell are twain. What were his chances of coming through? Which of his friends remain? But Ermyntrude's training a splendid boy
- 84. A Y Twenty years younger than En- sign Joy. On balance, a British gain! ND Ermyntrude, did she lose her all Or find it, two years ago? O young girl-wives of the boys who fall, With your youth and your babes to show! No heart but bleeds for your widowhood. Yet Life is with you, and Life is good. No bone of your bone lies low! OUR blessedness came—as it went—in a day. Deep dread but heightened your mirth. Your idols' feet never turned to clay— Never lit upon common earth. Love is the Game but is not the Goal: You played it together, body and soul,
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