**UFBA**

# Fundamentals of Systems Biology (2014) (marked)

(Parte **1** de 5)

ALS o f S

Covert

“Author has excellent command of both aspects of systems biology.” —Joel Bader, Johns Hopkins University, Baltimore, Maryland, USA

“… an excellent introduction to systems thinking and modeling in the context of complex biological problems. … uses concrete biological examples to develop systems concepts and models step by step, thus enabling the reader to understand the power of systems biology in the study of complex biological phenomena. … This intuition is then translated into concrete systems modeling approaches enabling readers to apply the systems approach to their own problems.”

—Prof Werner Dubitzky, University of Ulster

For decades biology has focused on decoding cellular processes one gene at a time, but many of the most pressing biological questions, as well as diseases such as cancer and heart disease, are related to complex systems involving the interaction of hundreds, or even thousands, of gene products and other factors. How do we begin to understand this complexity?

Fundamentals of Systems Biology: From Synthetic Circuits to Whole-cell Models introduces students to methods they can use to tackle complex systems head-on, carefully walking them through studies that comprise the foundation and frontier of systems biology. The first section of the book focuses on bringing students quickly up to speed with a variety of modeling methods in the context of a synthetic biological circuit. This innovative approach builds intuition about the strengths and weaknesses of each method and becomes critical in the book’s second half, where much more complicated network models are addressed—including transcriptional, signaling, metabolic, and even integrated multi-network models.

The approach makes the work much more accessible to novices (undergraduates, medical students, and biologists new to mathematical modeling) while still having much to offer experienced modelers—whether their interests are microbes, organs, whole organisms, diseases, synthetic biology, or just about any field that investigates living systems.

ISBN: 978-1-4200-8410-8

Bioengineering

FUNDAMENTALS of

From Synthetic Circuits to Whole-cell Models

FUNDAMENTALS of

From Synthetic Circuits to Whole-cell Models

Markus W. Covert Stanford University

Boca Raton London New York

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Contents

Preface, xi Acknowledgments, xvii About the Author, xix

chapter 1 ◾ | Variations on a Theme of Control 3 |

Section i Building Intuition LEARNING OBJECTIVES 3 VARIATIONS 3 AUTOREGULATION 4

OUR THEME: A TYPICAL NEGATIVE AUTOREGULATORY CIRCUIT 8

CHAPTER SUMMARY 1 RECOMMENDED READING 1

chapter 2 ◾ | Variation: Boolean Representations 13 |

LEARNING OBJECTIVES 13 BOOLEAN LOGIC AND RULES 13 STATE MATRICES 17 STATE TRANSITIONS 18 DYNAMICS 19 TIMESCALES 24

ADVANTAGES AND DISADVANTAGES OF BOOLEAN ANALYSIS 26 vi ◾ Contents

CHAPTER SUMMARY 26 RECOMMENDED READING 27 PROBLEMS 27

chapter 3 ◾ | Variation: Analytical Solutions of Ordinary |

Differential Equations 35

LEARNING OBJECTIVES 35 SYNTHETIC BIOLOGICAL CIRCUITS 36 FROM COMPARTMENT MODELS TO ODES 37

SPECIFYING AND SIMPLIFYING ODES WITH ASSUMPTIONS 41

THE STEADY-STATE ASSUMPTION 43

SOLVING THE SYSTEM WITHOUT FEEDBACK: REMOVAL OF ACTIVATOR 4

KEY PROPERTIES OF THE SYSTEM DYNAMICS 46

SOLVING THE SYSTEM WITHOUT FEEDBACK: ADDITION OF ACTIVATOR 47

COMPARISON OF MODELING TO EXPERIMENTAL MEASUREMENTS 49

ADDITION OF AUTOREGULATORY FEEDBACK 50

COMPARISON OF THE REGULATED AND UNREGULATED SYSTEMS 53

CHAPTER SUMMARY 57 RECOMMENDED READING 58 PROBLEMS 59

chapter 4 ◾ | Variation: Graphical Analysis 65 |

LEARNING OBJECTIVES 65 REVISITING THE PROTEIN SYNTHESIS ODES 6 PLOTTING X VERSUS DX/DT 67 FIXED POINTS AND VECTOR FIELDS 68 FROM VECTOR FIELDS TO TIME-COURSE PLOTS 70 NONLINEARITY 70 BIFURCATION ANALYSIS 73

Contents ◾ vii

ADDING FEEDBACK 75 TWO-EQUATION SYSTEMS 7 CHAPTER SUMMARY 81 RECOMMENDED READING 82 PROBLEMS 83

chapter 5 ◾ | Variation: Numerical Integration 91 |

LEARNING OBJECTIVES 91 THE EULER METHOD 92 ACCURACY AND ERROR 94 THE MIDPOINT METHOD 9 THE RUNGE–KUTTA METHOD 103 CHAPTER SUMMARY 106 RECOMMENDED READING 106 PROBLEMS 107

chapter 6 ◾ | Variation: Stochastic Simulation 1 |

LEARNING OBJECTIVES 1 SINGLE CELLS AND LOW MOLECULE NUMBERS 1 STOCHASTIC SIMULATIONS 113

THE PROBABILITY THAT TWO MOLECULES INTERACT AND REACT IN A GIVEN TIME INTERVAL 116

THE PROBABILITY OF A GIVEN MOLECULAR REACTION OCCURRING OVER TIME 118

THE RELATIONSHIP BETWEEN KINETIC AND STOCHASTIC CONSTANTS 119

GILLESPIE’S STOCHASTIC SIMULATION ALGORITHM 120

STOCHASTIC SIMULATION OF UNREGULATED GENE EXPRESSION 124

STOCHASTIC SIMULATIONS VERSUS OTHER MODELING APPROACHES 131

CHAPTER SUMMARY 132 RECOMMENDED READING 132 PROBLEMS 133 viii ◾ Contents

chapter 7 ◾ | Transcriptional Regulation 143 |

Section i From Circuits to Networks LEARNING OBJECTIVES 143 TRANSCRIPTIONAL REGULATION AND COMPLEXITY 144 MORE COMPLEX TRANSCRIPTIONAL CIRCUITS 145

THE TRANSCRIPTIONAL REGULATORY FEED-FORWARD MOTIF 147

BOOLEAN ANALYSIS OF THE MOST COMMON INTERNALLY CONSISTENT FEED-FORWARD MOTIF IDENTIFIED IN E. COLI 149

AN ODE-BASED APPROACH TO ANALYZING THE COHERENT FEED-FORWARD LOOP 152

ROBUSTNESS OF THE COHERENT FEED-FORWARD LOOP 155

EXPERIMENTAL INTERROGATION OF THE COHERENT FEED-FORWARD LOOP 155

CHANGING THE INTERACTION FROM AN AND TO AN OR RELATIONSHIP 156

THE SINGLE-INPUT MODULE 160 JUST-IN-TIME GENE EXPRESSION 162 GENERALIZATION OF THE FEED-FORWARD LOOP 164

AN EXAMPLE OF A MULTIGENE FEED-FORWARD LOOP: FLAGELLAR BIOSYNTHESIS IN E. COLI 166

OTHER REGULATORY MOTIFS 168 CHAPTER SUMMARY 169 RECOMMENDED READING 170 PROBLEMS 171

chapter 8 ◾ | Signal Transduction 179 |

LEARNING OBJECTIVES 179 RECEPTOR-LIGAND BINDING TO FORM A COMPLEX 179 APPLICATION TO REAL RECEPTOR-LIGAND PAIRS 183 FORMATION OF LARGER COMPLEXES 187 PROTEIN LOCALIZATION 188

Contents ◾ ix

THE NF-κB SIGNALING NETWORK 191 A DETAILED MODEL OF NF-κB ACTIVITY 193 ALTERNATIVE REPRESENTATIONS FOR THE SAME PROCESS 198 SPECIFYING PARAMETER VALUES FROM DATA 200 BOUNDING PARAMETER VALUES 206 MODEL SENSITIVITY TO PARAMETER VALUES 207 REDUCING COMPLEXITY BY ELIMINATING PARAMETERS 210 PARAMETER INTERACTIONS 213 CHAPTER SUMMARY 216 RECOMMENDED READING 217 PROBLEMS 218

chapter 9 ◾ | Metabolism 233 |

LEARNING OBJECTIVES 233 CELLULAR METABOLISM 233 METABOLIC REACTIONS 234

COMPARTMENT MODELS OF METABOLITE CONCENTRATION 237

THE MICHAELIS–MENTEN EQUATION FOR ENZYME KINETICS 237

DETERMINING KINETIC PARAMETERS FOR THE MICHAELIS–MENTEN SYSTEM 245

INCORPORATING ENZYME INHIBITORY EFFECTS 247 FLUX BALANCE ANALYSIS 252 STEADY-STATE ASSUMPTION AND EXCHANGE FLUXES 255 SOLUTION SPACES 258 THE OBJECTIVE FUNCTION 259 DEFINING THE OPTIMIZATION PROBLEM 262 SOLVING FBA PROBLEMS USING MATLAB 263

APPLICATIONS OF FBA TO LARGE-SCALE METABOLIC MODELS 271

USING FBA FOR METABOLIC ENGINEERING 274 CHAPTER SUMMARY 279 x ◾ Contents

RECOMMENDED READING 281 PROBLEMS 282

chapter 10 ◾ | Integrated Models 295 |

LEARNING OBJECTIVES 295

DYNAMIC FBA: EXTERNAL VERSUS INTERNAL CONCENTRATIONS 296

ENVIRONMENTAL CONSTRAINTS 298 INTEGRATION OF FBA SIMULATIONS OVER TIME 300 COMPARING DYNAMIC FBA TO EXPERIMENTAL DATA 303 FBA AND TRANSCRIPTIONAL REGULATION 304 TRANSCRIPTIONAL REGULATORY CONSTRAINTS 305 REGULATORY FBA: METHOD 306 REGULATORY FBA: APPLICATION 308 TOWARD WHOLE-CELL MODELING 310 CHAPTER SUMMARY 315 RECOMMENDED READING 316 PROBLEMS 317

GLOSSARY, 323

Preface

Let’s begin our journey into systems biology by comparing complex diseases to a firing squad. While working as a postdoc at the California Institute of Technology, I had the opportunity to know a talented biologist and a well-read Russian who convinced me to read Tolstoy’s War and Peace. One thrilling highlight of that masterpiece finds the protagonist, Pierre, in front of a firing squad in Moscow. Tolstoy describes the wild thoughts ringing in Pierre’s mind as he faces the guns, wondering how he had come to this point. “Who was it that had really sentenced him to death?” As Pierre looks into the nervous eyes of the young soldiers, he realizes that they are not to blame, for “not one of them had wished to or, evidently, could have done it.”

So, who was responsible? In all the chaos of the scene and his imminent death, Pierre has a moment of clarity. He realizes that it was no one. Rather (and I have added italics for emphasis), “It was a system—a concurrence of circumstances. A system of some sort was killing him—Pierre—depriving him of life, of everything, annihilating him.”

As I read this passage, I could not help but think about the many patients with complex and untreatable diseases that feel virtually the same way as Pierre. What is it that has really sentenced them to death? When they read the newspapers or watch television, they see headline after headline about “the cancer gene” or “the Alzheimer gene,” but if these genes truly exist, then why have cures to these diseases eluded us?

I take my answer from Pierre: Such diseases do not depend on any one gene, but on a “concurrence of circumstances”—a system. A Science commentary on complex diseases emphasizes this point:

The most common diseases are the toughest to crack. Heart disease, cancer, diabetes, psychiatric illness: all of these are “complex” or xii ◾ Preface

“multifactorial” diseases, meaning that they cannot be ascribed to mutations in a single gene or to a single environmental factor. Rather, they arise from the combined action of many genes, environmental factors, and risk-conferring behaviors. One of the greatest challenges facing biomedical researchers today is to sort out how these contributing factors interact in a way that translates into effective strategies for disease diagnosis, prevention, and therapy. (From Kiberstis, P. and Roberts, L. Science. 2002, 296(5568): 685. Reprinted with permission from AAAS.)

Put simply, our ability to tackle complex diseases is limited by our ability to understand biological systems. We need ways to explain organismal behaviors in terms of cellular components and their interactions. Even a small number of components can interact in nonintuitive ways; thus, systems-level research requires mathematical and computational strategies.

We are at the cusp of a revolution in understanding the systems-level mechanisms that underlie human disease. However, before the revolution can achieve its full potential, we first must grasp the systems-level behavior of molecules, pathways, and single cells. Vast progress has been made toward this goal in the past 30 years, but much exciting research remains to be completed before the power of these systems-level investigations can be turned to the elucidation and eradication of human disease.

This book seeks to empower you, the student, by aiding you to develop the tools, techniques, and mindset to directly engage in primary research yourself. Whether you are interested in microbes, organs, whole organisms, diseases, synthetic biology, or just about any field that investigates living systems, the intuition that you will develop through the examples and problems in this book will critically contribute to your success at asking and answering important scientific questions.

This book focuses on the use of computational approaches to model, simulate, and thereby better understand complex molecular and cellular systems, research that is often called “systems biology.” This field has grown rapidly: There is now an Institute for Systems Biology in Seattle, a new Department of Systems Biology in various institutions (notably Harvard Medical School and Stanford University), a Nature/EMBO (European Molecular Biology Organization) journal, Molecular Systems Biology, and an International Conference on Systems Biology that draws over 1,0 people each year. The field has drawn together researchers from nearly every scientific domain. For example, students from biology, bioengineering,

Preface ◾ xiii computer science, chemistry, biomedical informatics, chemical and systems biology, aeronautical engineering, chemical engineering, biophysics, electrical engineering, and physics have all participated in the systems biology class that I teach at Stanford University.

I teach the material in this book to advanced undergraduate and beginning graduate students over 10 weeks, with two 90-minute lecture sessions per week. Both my class and this textbook are divided in half. The first half, “Building Intuition,” focuses on learning the computational tools that underlie systems biology using a simple autoregulatory feedback element as the subject of study. Without grasping these fundamental concepts, you will have great difficulty in forming intuition about the systems-level behavior of molecules and cells, intuition that will strongly contribute to the effectiveness of your systems biology research. The concept of biological feedback and the circuit itself are introduced in Chapter 1, which is followed by five chapters that describe various methods to model this circuit’s behavior. Chapter 2 concerns Boolean logic models, Chapters 3–5 focus on ordinary differential equation-based solutions (using analytical, graphical, and numerical methods, respectively), and Chapter 6 describes how to perform stochastic simulations.

The second half of the text, “From Circuits to Networks,” applies the tool kit developed in Section 1 to study and model three of the most important and interesting biological processes: transcriptional regulation (Chapter 7), signal transduction (Chapter 8), and metabolism (Chapter 9). Finally, Chapter 10 describes the methods for integrating these diverse modeling approaches into integrated hybrid models using the same techniques that recently led to the creation in my lab of a whole-cell model, the first of its kind.

(Parte **1** de 5)