Handbook of Statistical Systems Biology E-Book

Michael Stumpf

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 1158

Veröffentlichungsjahr: 2011

Beschreibung

Systems Biology is now entering a mature phase in which the key issues are characterising uncertainty and stochastic effects in mathematical models of biological systems. The area is moving towards a full statistical analysis and probabilistic reasoning over the inferences that can be made from mathematical models. This handbook presents a comprehensive guide to the discipline for practitioners and educators, in providing a full and detailed treatment of these important and emerging subjects. Leading experts in systems biology and statistics have come together to provide insight in to the major ideas in the field, and in particular methods of specifying and fitting models, and estimating the unknown parameters.

This book:

• Provides a comprehensive account of inference techniques in systems biology.
• Introduces classical and Bayesian statistical methods for complex systems.
• Explores networks and graphical modeling as well as a wide range of statistical models for dynamical systems.
• Discusses various applications for statistical systems biology, such as gene regulation and signal transduction.
• Features statistical data analysis on numerous technologies, including metabolic and transcriptomic technologies.
• Presents an in-depth presentation of reverse engineering approaches.
• Provides colour illustrations to explain key concepts.

This handbook will be a key resource for researchers practising systems biology, and those requiring a comprehensive overview of this important field.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface

Contributors

Part A: Methodological Chapters

Chapter 1: Two Challenges of Systems Biology

1.1 Introduction

1.2 Cell Signaling Systems

1.3 The Challenge of Many Moving Parts

1.4 The Challenge of Parts with Parts

1.5 Closing Remarks

References

Chapter 2: Introduction to Statistical Methods for Complex Systems

2.1 Introduction

2.2 Class Comparison

2.3 Class Prediction

2.4 Class Discovery

References

Chapter 3: Bayesian Inference and Computation

3.1 Introduction

3.2 The Bayesian Argument

3.3 Testing Hypotheses

3.4 Extensions

3.5 Computational Issues

Acknowledgements

References

Chapter 4: Data Integration: Towards Understanding Biological Complexity

4.1 Storing Knowledge: Experimental data, Knowledge Databases, Ontologies and Annotation

4.2 Data Integration in Biological Studies

4.3 Concluding Remarks

References

Chapter 5: Control Engineering Approaches to Reverse Engineering Biomolecular Networks

5.1 Dynamical models for network inference

5.2 Reconstruction methods based on linear models

5.3 Reconstruction methods based on nonlinear models

References

Chapter 6: Algebraic Statistics and Methods in Systems Biology

6.1 Introduction

6.2 Overview of chapter

6.3 Computational algebra

6.4 Algebraic statistical models

6.5 Parameter inference

6.6 Model invariants

6.7 Log-linear models

6.8 Reverse engineering of networks

6.9 Concluding remarks

References

Part B: Technology-Based Chapters

Chapter 7: Transcriptomic Technologies and Statistical Data Analysis

7.1 Biological background

7.2 Technologies for genome-wide profiling of transcription

7.3 Evaluating the significance of individual genes

7.4 Grouping genes to find biological patterns

7.5 Prediction of a biological response

References

Chapter 8: Statistical Data Analysis in Metabolomics

8.1 Introduction

8.2 Analytical technologies and data characteristics

8.3 Statistical analysis

8.4 Conclusions

Acknowledgements

References

Chapter 9: Imaging and Single-Cell Measurement Technologies

9.1 Introduction

9.2 Measurement Techniques

9.3 Analysis of Signal Cell Measurement Data

9.4 Summary

Acknowledgements

References

Chapter 10: Protein Interaction Networks and Their Statistical Analysis

10.1 Introduction

10.2 Proteins and Their Interactions

10.3 Network Analysis

10.4 Comparison of Protein Interaction Networks

10.5 Evolution and the Protein Interaction Network

10.6 Community Detection in PPI Networks

10.7 Predicting Function Using PPI Networks

10.8 Predicting Interactions Using PPI Networks

10.9 Current Trends and Future Directions

References

Part C: Networks and Graphical Models

Chapter 11: Introduction to Graphical Modelling

11.1 Graphical Structures and Random Variables

11.2 Learning Graphical Models

11.3 Inference on Graphical Models

11.4 Application of Graphical Models in Systems Biology

References

Chapter 12: Recovering Genetic Network from Continuous Data with Dynamic Bayesian Networks

12.1 Introduction

12.2 Reverse Engineering Time-homogeneous DBNs

12.3 Go Forward: How to Recover the Structure Changes with Time

12.4 Discussion and Conclusion

References

Chapter 13: Advanced Applications of Bayesian Networks in Systems Biology

13.1 Introduction

13.2 Inclusion of biological prior knowledge

13.3 Heterogeneous DBNs

13.4 Discussion

Acknowledgements

References

Chapter 14: Random Graph Models and Their Application to Protein–Protein Interaction Networks

14.1 Background and motivation

14.2 What do we want from a PPI network?

14.3 PPI network models

14.4 Range-dependent graphs

14.5 Summary

References

Chapter 15: Modelling Biological Networks via Tailored Random Graphs

15.1 Introduction

15.2 Quantitative Characterization of Network Topologies

15.3 Network Families and Random Graphs

15.4 Information-Theoretic Deliverables of Tailored Random Graphs

15.5 Applications to PPINs

15.6 Numerical Generation of Tailored Random Graphs

15.7 Discussion

References

Part D: Dynamical Systems

Chapter 16: Nonlinear Dynamics: A Brief Introduction

16.1 Introduction

16.2 Sensitivity to Initial Conditions and the Lyapunov Exponent

16.3 The Natural Measure

16.4 The Kolmogorov–Sinai Entropy

16.5 Symbolic Dynamics

16.6 Chaos in Biology

References

Chapter 17: Qualitative Inference in Dynamical Systems

17.1 Introduction

17.2 Basic Solution Types

17.3 Qualitative Behaviour

17.4 Stability and Bifurcations

17.5 Ergodicity

17.6 Timescales

17.7 Time Series Analysis

References

Chapter 18: Stochastic Dynamical Systems

18.1 Introduction

18.2 Origins of Stochasticity

18.3 Stochastic Chemical Kinetics

18.4 Inference for Markov Process Models

18.5 Conclusions

Acknowledgements

References

Chapter 19: Gaussian Process Inference for Differential Equation Models of Transcriptional Regulation

19.1 Introduction

19.2 Generalized linear model

19.3 Model based target ranking

19.4 Multiple transcription factors

19.5 Conclusion

References

Chapter 20: Model Identification by Utilizing Likelihood-Based Methods

20.1 ODE Models for Reaction Networks

20.2 Parameter Estimation

20.3 Identifiability

20.4 The Profile Likelihood Approach

20.5 Summary

Acknowledgements

References

Part E: Application Areas

Chapter 21: Inference of Signalling Pathway Models

21.1 Introduction

21.2 Overview of Inference Techniques

21.3 Parameter Inference and Model Selection for Dynamical Systems

21.4 Approximate Bayesian Computation

21.5 Application: Akt Signalling Pathway

21.6 Conclusion

References

Chapter 22: Modelling Transcription Factor Activity

22.1 Integrating an ODE with a Differential Operator

22.2 Computation of the Entries of the Differential Operator

22.3 Applications

22.4 Estimating Intermediate Points

Acknowledgements

References

Chapter 23: Host–Pathogen Systems Biology

23.1 Introduction

23.2 Pathogen genomics

23.3 Metabolic models

23.4 Protein–protein interactions

23.5 Response to environment

23.6 Immune system interactions

23.7 Manipulation of other host systems

23.8 Evolution of the host–pathogen system

23.9 Towards systems medicine for infectious diseases

23.10 Concluding remarks

Acknowledgements

References

Chapter 24: Bayesian Approaches for Mass Spectrometry-Based Metabolomics

24.1 Introduction

24.2 The Challenge of Metabolite Identification

24.3 Bayesian Analysis of Metabolite Mass Spectra

24.4 Incorporating Additional Information

24.5 Probabilistic Peak Detection

24.6 Statistical Inference

24.7 Software Development for Metabolomics

24.8 Conclusion

24.9 References

Chapter 25: Systems Biology of microRNAs

25.1 Introduction

25.2 Current approaches in microRNA Systems Biology

25.3 Experimental findings and data that guide the developments of computational tools

25.4 Approaches to microRNA target predictions

25.5 Analysis of mRNA and microRNA expression data

25.6 Network approach for studying microRNA-mediated regulation

25.7 Kinetic modeling of microRNA regulation

25.8 Discussion

References

Index

This edition first published 2011

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Library of Congress Cataloging-in-Publication Data

Stumpf, M. P. H. (Michael P. H.)

Handbook of statistical systems biology / Michael P.H. Stumpf, David J.

Balding, Mark Girolami.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-71086-9 (cloth)

1. Systems biology–Statistical methods–Handbooks, manuals, etc. 2.

Biological systems–Mathematical models–Handbooks, manuals, etc. 3.

Uncertainty–Mathematical models–Handbooks, manuals, etc. 4. Stochastic

analysis–Mathematical models–Handbooks, manuals, etc. I. Balding, D. J. II.

Girolami, Mark, 1963- III. Title.

QH324.2.S79 2011

570.1'5195–dc23

2011018218

A catalogue record for this book is available from the British Library.

Print ISBN: 978-0-470-71086-9

ePDF ISBN: 978-1-119-97061-3

obook ISBN: 978-1-119-97060-6

ePub ISBN: 978-1-119-95204-6

Mobi ISBN: 978-1-119-95205-3

Preface

Systems biology is data-rich. Technological advances over the past 50 years have allowed us to probe, map and interfere with biological organisms in a number of ways. Most notable are perhaps the sequencing efforts that are continuing to catalogue the genetic diversity of life, including our own species. A whole host of other techniques from biochemistry, molecular, cell and structural biology have been used to study the function of the protein products and other biomolecules that are encoded by these sequences. So we live in a time with ready access to sophisticated techniques that allow us to study how biological systems – ranging from single molecules to whole organisms – function and work.

But systems biology is also hypothesis-rich. By this we mean that there are an overwhelmingly large number of potential mechanisms that could explain many, if not all, biological systems. And each of these models has associated unknown parameters, most of which cannot be measured directly using experimental approaches.

Systems biology is also one of the most fertile fields for modern statistics. The richness in both data and hypotheses pose serious challenges to classical statistical theory. Fisher, Neyman and Pearson and their successors typically dealt with problems where there are only a small number of hypotheses that are evaluated in light of adequate data derived from well designed experiments. The situation in systems biology could hardly be more different: in humans we have some 24 000 genes (and probably several hundred thousand protein products), but only a small number of measurements for each of these genes. A priori each of these genes (or worse, each combination of these genes) could be involved in any biological process or phenotype of interest; the number of hypotheses is vastly larger than the amount of available data. But the resulting so-called ‘large p small n problem’ and the multiple testing problem is only a small part of the problem.

The lack of suitable models weighs much more heavily. Mechanistic models, framed in suitable mathematical language, allow us to summarize our knowledge about biological systems and make testable predictions, which probe our understanding. Iteration between modelling and experimental analysis will thus be required, and in the long run is believed to yield better understanding of biological systems in both health and disease. But where do these models come from?

In a recent polemic, Sydney Brenner has put down the challenge, stating essentially that solving the so-called inverse problem in systems biology is doomed to fail. Given the central role that learning or inferring the structure and dynamics of biological systems has for systems biology this would amount to the long-term failure of the whole enterprise (also of synthetic biology, which cannot do without the mechanistic insights and models provided by systems biology). Rather than inferring models from data, Delbrück proposes to use maps, i.e. mathematical models that connect the different molecular entities inside cells, tissues, organs or whole organisms, to put the wealth of information collected by traditional reductionist molecular and cell biology research into context. Where these maps are coming from or how they are constructed is not clear, however.

In the chapters in this handbook we hope to provide a more optimistic but also nuanced perspective on the inverse problem in systems biology. The different chapters in this handbook provide accessible accounts of basic statistical methodologies and their application in a systems biology setting. There is ample need for such a unified account.

First of all, the field is progressing rapidly and technological advances have allowed researchers to gather data at a phenomenal rate. Not all data are good data, however, from a statistical or reverse-engineering perspective. The type of data collected and the manner in which they are collected can make or break any statistical analysis. Thus some familiarity with statistical methodologies, but also the potential pitfalls will be essential for the design of better experiments and technologies.

Secondly, once a model is given, mathematical analysis and exploration is relatively straightforward. But specifying the model and inferring its parameters are fraught with statistical challenges. The curse of dimensionality is encountered almost everywhere, data are noisy, incomplete and exhibit high levels of dependence and colinearity. Learning anything from such data is challenging. But the fact that biological systems change constantly with time and in response to environmental, physiological and developmental cues means that the window we have for observing a well specified system may be very small indeed.

Thirdly, frequently we are dealing with mathematical models that are much more complex and challenging than those typically considered in statistics. Many nice properties of classical probability models are absent from the contingent, complex and complicated models considered in e.g. the context of metabolic networks or signal transduction networks. Moreover, a host of recent results has led us to re-evaluate our perspective on inference of parameters for dynamical systems. Being able to infer parameters is intimately related to properties of the dynamical system that include stability (of equilibrium solutions) and identifiability. These in turn, however, change with the parameters. In other words, the same dynamical systems may in effect be identifiable in some regions of parameter space but not others. To make any progress in this arena requires us to be aware of both statistics and dynamical systems theory.

This brings us to the fourth point: systems biology is a highly interdisciplinary research area. None of the present practitioners has received any formal training in systems biology; instead they come from a diverse set of backgrounds ranging from mathematics, computer science, physics and the engineering sciences to biology and medicine. The different modelling and experimental approaches must be melded together in order to make progress. Since data take a central part in this dialogue, statistics must also play an essential role at this interface between traditional disciplines.

This handbook aims to introduce researchers, practitioners and students to the statistical approaches that are making an impact on cutting edge systems biology research. It is born out of the editors' belief that the inferential perspective is essential to the whole enterprise of systems biology, and that there is a lack of suitable resources for researchers in the field. We are therefore grateful to Wiley for providing us with the opportunity to develop this handbook. This would, of course, not have been possible without the cooperation of the many contributing authors. Producing comprehensive reviews and overviews over methodologies in such a rapidly moving field is challenging and may often be considered as a distraction from the work we would really like to be getting on with. We are therefore delighted and hugely grateful for the warm response that we have had from our contributors. Each chapter provides insights into some of the areas that we believe are essential for tackling inference problems in systems biology (and biomedical research more generally). Overlap between different chapters is unavoidable but rather than having resulted in redundancy or repetitiveness, these areas of overlap really serve to highlight the different perspectives and validity of alternative approaches.

We are also hugely grateful to Kathryn Sharples, who helped to get this project off the ground and provided invaluable assistance in the early stages. We thank Richard Davies for his unwavering support, diligence and help in bringing the work on the handbook to fruition. He together with Heather Kay and Prachi Sinha-Sahay also delivered the most challenging aspect of the book by editing and proofing chapters and making a consistent whole out of the many individual contributions. Wiley and especially Kathryn, Richard, Heather and Prachi have been wonderful to work with and have accommodated the editors' wishes and concerns with great patience and grace.

M. Stumpf, D. Balding and M. Girolami

Contributors

Waqar Ali, Department of Statistics, University of Oxford, UK.

Alessia Annibale, Department of Mathematics, King's College London, The Strand, London, UK.

Fatihcan M. Atay, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.

Martino Barenco, Institute of Child Health, University College London, UK.

Michael Barrett, Institute of Infection, Immunity and Inflammation, College of Medical, Veterinary and Life Sciences, University of Glasgow, UK.

Declan G. Bates, College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK.

Doron Betel, Institute of Computational Biomedicine, Weill Cornell Medical College, New York, USA.

Rainer Breitling, Institute of Molecular, Cell and Systems Biology, College of Medical, Veterinary and Life Sciences, University of Glasgow, UK.

Daniel Brewer, Institute of Cancer Research, Sutton, UK.

David Gomez-Cabrero, Unit of Computational Medicine, Department of Medicine, Karolinska Institutet, Stockholm, Sweden.

Robin Callard, Institute of Child Health, University College London, UK.

Anthony C. C. Coolen, Department of Mathematics, King's College London, The Strand, London, and Randall Division of Cell and Molecular Biophysics, King's College London, New Hunt's House, London, UK.

Carlo Cosentino, School of Computer and Biomedical Engineering, Università degli Studi Magna Græcia di Catanzaro, Catanzaro, Italy.

Charlotte Deane, Department of Statistics, University of Oxford, UK.

Timothy M. D. Ebbels, Biomolecular Medicine, Department of Surgery and Cancer, Imperial College, London, UK.

Luis Fernandes, Randall Division of Cell and Molecular Biophysics, King's College London, New Hunt's House, London, UK.

Franca Fraternali, Randall Division of Cell and Molecular Biophysics, King's College London, New Hunt's House, London, UK.

Celso Grebogi, Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King's College, University of Aberdeen, UK.

Marco Grzegorczyk, Department of Statistics, TU Dortmund University, Dortmund, Germany.

Desmond J. Higham, Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK.

William S. Hlavacek, Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA.

Antti Honkela, Helsinki Institute for Information Technology, University of Helsinki, Finland.

Tristan Mary-Huard, AgroParisTech and INRA, Paris, France.

Michael Hubank, Institute of Child Health, University College London, UK.

Dirk Husmeier, Biomathematics and Statistics Scotland (BioSS) JCMB, Edinburgh, UK.

Maria De Iorio, Department of Epidemiology and Biostatistics, Imperial College, St Mary's Campus, Norfolk Place, London, UK.

Jürgen Jost, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, and Santa Fe Institute for the Sciences of Complexity, USA.

Raya Khanin, Bioinformatics Core, Memorial Sloan-Kettering Cancer Center, New York, USA.

Jens Kleinjung, Divison of Mathematical Biology, MRC National Institute for Medical Research, London, UK.

Shinya Kuroda, Department of Biophysics and Biochemistry, Graduate School of Science, University of Tokyo, and CREST, Japan Science and Technology Agency, University of Tokyo, Japan.

Neil Lawrence, Department of Computer Science and Sheffield Institute for Translational Neuroscience, University of Sheffield, UK.

Gaëlle Lelandais, DSIMB, INSERM, University of Paris Diderot and INTS, Paris, France.

Juliane Liepe, Division of Molecular Biosciences, Imperial College London, UK.

Sophie Lèbre, LSIIT, University of Strasbourg, France.

Jean-Michel Marin, Institut de Mathematiques et Modelisation de Montpellier, Université de Montpellier 2, France.

Francesco Montefusco, College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK and School of Computer and Biomedical Engineering, Università degli Studi Magna Græcia di Catanzaro, Catanzaro, Italy.

Alessandro Moura, Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King's College, University of Aberdeen, UK.

Sach Mukherjee, Department of Statistics, University of Warwick, Coventry, UK.

Yu-ichi Ozaki, Laboratory for Cell Signaling Dynamics, RIKEN Quantitative Biology Center, Kobe, Japan.

John W. Pinney, Centre for Bioinformatics, Division of Molecular Biosciences, Imperial College London, UK.

Nataša Pržulj, Department of Computing, Imperial College London, UK.

Elizabeth Purdom, Department of Statistics, University of California at Berkeley, USA.

Magnus Rattray, Department of Computer Science and Sheffield Institute for Translational Neuroscience, University of Sheffield, UK.

Andreas Raue, Institute of Physics and Freiburg Institute for Advanced Studies (FRIAS) and Centre for Biological Systems Analysis (ZBSA), University of Freiburg, Germany.

Gesine Reinert, Department of Statistics, University of Oxford, UK.

Christian P. Robert, Université Paris-Dauphine, CEREMADE, France, and CREST and ENSAE, Malakoff, France.

Stéphane Robin, AgroParisTech and INRA, Paris, France.

Simon Rogers, School of Computing Science, University of Glasgow, UK.

Judith Rousseau, Université Paris-Dauphine, CEREMADE, France, and CREST and ENSAE, Malakoff, France.

Richard A. Scheltema, Proteomics and Signal Transduction, Max Planck Institute for Biochemistry, Martinsried, Germany.

Marco Scutari, UCL Genetics Institute (UGI), University College London, UK.

Korbinian Strimmer, Institute for Medical Informatics, Statistics and Epidemiology (IMISE), University of Leipzig, Germany.

Michael P. H. Stumpf, Division of Molecular Biosciences, Imperial College London, UK.

Jesper Tegner, Unit of Computational Medicine, Department of Medicine, Karolinska Institutet, Stockholm, Sweden.

Jens Timmer, Institute of Physics and Freiburg Institute for Advanced Studies (FRIAS) and Centre for Biological Systems Analysis (ZBSA), University of Freiburg, Germany.

Michalis Titsias, School of Computer Science, University of Manchester, UK.

Tina Toni, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, USA.

Adriano V. Werhli, Centro de Ciências Computacionais, Universidade Federal do Rio Grande (FURG), Rio Grande, RS, Brazil.

Darren J. Wilkinson, School of Mathematics and Statistics, Newcastle University, Newcastle-upon-Tyne, UK.

Carsten Wiuf, Bioinformatics Research Centre, Aarhus University, Denmark.

Part A

Methodological Chapters

Chapter 1

Two Challenges of Systems Biology

William S.Hlavacek

Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA

1.1 Introduction

Articulating the challenges faced by a field, or rather the problems that seem worthy of pursuit, can be a useful exercise. A famous example is Hilbert's problems (Hilbert 1902), which profoundly influenced mathematics. This entire handbook can be viewed as an attempt to define challenges faced by systems biologists, especially challenges requiring a statistical approach, and to provide tools for addressing these challenges. This particular chapter provides a personal perspective. If the editors had invited someone else to write it, I am sure it would have materialized in a very different form, as there are many challenges worthy of pursuit in this field.

Much has been written about systems biology, and excellent overviews of the field are available (Kitano 2002). For many years, I believe one of the challenges faced by systems biology has been community building. In recent years, thanks in part to events such as the International Conference on Systems Biology (Kitano 2001) and the q-bio Summer School and Conference (Edwards et al. 2007), a community of systems biology researchers has established itself. This community identifies with the term ‘systems biology’ and broadly agrees upon its loose definition and the general goals of the field. If one is looking for a definition of systems biology, the work presented at the meetings mentioned above serves the purpose well.

A characteristic of systems biology is the systems approach, which is aided by modeling. In systems biology, there has been special interest in the study and modeling of cellular regulatory systems, such as genetic circuits (Alon 2006). This chapter will be focused on a discussion of challenges faced by modelers. Of course, modeling would be aided by technology development, the generation of new quantitative data and in other ways, but I will be concerned mainly with the practice of modeling. Moreover, I will focus on modeling of cell signaling systems, although I believe the discussion is relevant for modeling of other types of cellular regulatory systems.

We need models of cellular regulatory systems to accelerate elucidation of the molecular mechanisms of cellular information processing, to understand design principles of cellular regulatory systems (i.e. the relationships between system structures and functions), and ultimately, to engineer cells for useful purposes. Cell engineering encompasses a number of application areas, including, manipulation of cellular metabolism for production of desirable metabolic products (Keasling 2010), such as biofuels; identification of drug targets for effective treatment or prevention of diseases (Klipp et al. 2010), such as cancer; and creation of cells with entirely new functions and properties through synthetic biology approaches (Khalil and Collins 2010). In each of these areas, predictive models can be used to guide the manipulation of cellular phenotypes through interventions at the molecular level (e.g. genetic modifications or pharmacological perturbations). In traditional engineering fields, predictive models play a central role, and I believe predictive modeling will be just as central to cell engineering efforts in the future. Another more immediate reason to seek models of cellular regulatory systems is that model-guided studies of the molecular mechanisms of cellular information processing can accelerate the pace at which these mechanisms and their design principles are elucidated (Wall et al. 2004; Alon 2006; Novék and Tyson 2008; Rafelski and Marshall 2008; Mukherji and van Oudenaarden 2009). A model of a cellular regulatory system essentially represents a hypothesis about how the system operates and such a model can be used to interpret experimental observations, to design experiments, and generally to extend the reach of human intuition and reasoning. A model can be constructed in a systematic step-by-step fashion and the logical consequences of a model, no matter how complicated, can usually be determined. Although models are useful because they make predictions, models are also useful for other reasons, which are sometimes overlooked, as recently discussed by (Lander 2010).