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PART 1 THE FACTS OF LIFE 1

Chapter 1 Why：Biology by the Numbers 3

1.1 BIOLOGICAL CARTOGRAPHY 3

1.2 PHYSICAL BIOLOGY OF THE CELL 4

Model Building Requires a Substrate of Biological Facts and Physical （or Chemical） Principles 5

1.3 THE STUFF OF LIFE 5

Organisms Are Constructed from Four Great Classes of Macromolecules 6

Nucleic Acids and Proteins Are Polymer Languages with Different Alphabets 7

1.4 MODEL BUILDING IN BIOLOGY 9

1.4.1 Models as Idealizations 9

Biological Stuff Can Be Idealized Using Many Different Physical Models 11

1.4.2 Cartoons and Models 16

Biological Cartoons Select Those Features of the Problem Thought to Be Essential 16

Quantitative Models Can Be Built by Mathematicizing the Cartoons 19

1.5 QUANTITATIVE MODELS AND THE POWER OF IDEALIZATION 20

1.5.1 On the Springiness of Stuff 21

1.5.2 The Toolbox of Fundamental Physical Models 22

1.5.3 The Unifying Ideas of Biology 23

1.5.4 Mathematical Toolkit 25

1.5.5 The Role of Estimates 26

1.5.6 On Being Wrong 29

1.5.7 Rules of Thumb：Biology by the Numbers 30

1.6 SUMMARY AND CONCLUSIONS 32

1.7 FURTHER READING 32

1.8 REFERENCES 33

Chapter 2 What and Where：Construction Plans for Cells and Organisms 35

2.1 AN ODE TO E.COLI 35

2.1.1 The Bacterial Standard Ruler 37

The Bacterium E.coli Will Serve as Our Standard Ruler 37

2.1.2 Taking the Molecular Census 38

The Cellular Interior Is Highly Crowded，with Mean Spacings Between Molecules That Are Comparable to Molecular Dimensions 48

2.1.3 Looking Inside Cells 49

2.1.4 Where Does E.coli Fit？ 51

Biological Structures Exist Over a Huge Range of Scales 51

2.2 CELLS AND STRUCTURES WITHIN THEM 52

2.2.1 Cells：A Rogue’s Gallery 52

Cells Come in a Wide Variety of Shapes and Sizes and with a Huge Range of Functions 52

Cells from Humans Have a Huge Diversity of Structure and Function 57

2.2.2 The Cellular Interior：Organelles 59

2.2.3 Macromolecular Assemblies：The Whole is Greater than the Sum of the Parts 63

Macromolecules Come Together to Form Assemblies 63

Helical Motifs Are Seen Repeatedly in Molecular Assemblies 64

Macromolecular Assemblies Are Arranged in Superstructures 65

2.2.4 Viruses as Assemblies 66

2.2.5 The Molecular Architecture of Cells：From Protein Data Bank （PDB） Files to Ribbon Diagrams 69

Macromolecular Structure Is Characterized Fundamentally by Atomic Coordinates 69

Chemical Groups Allow Us to Classify Parts of the Structure of Macromolecules 70

2.3 TELESCOPING UP IN SCALE：CELLS DON’T GO IT ALONE 72

2.3.1 Multicellularity as One of Evolution’s Great Inventions 73

Bacteria Interact to Form Colonies such as Biofilms 73

Teaming Up in a Crisis：Lifestyle of Dictyostelium discoideum 75

Multicellular Organisms Have Many Distinct Communities of Cells 76

2.3.2 Cellular Structures from Tissues to Nerve Networks 77

One Class of Multicellular Structures is the Epithelial Sheets 77

Tissues Are Collections of Cells and Extracellular Matrix 77

Nerve Cells Form Complex，Multicellular Complexes 78

2.3.3 Multicellular Organisms 78

Cells Differentiate During Development Leading to Entire Organisms 78

The Cells of the Nematode Worm，Caenorhabditis Elegans，Have Been Charted，Yielding a Cell-by-Cell Picture of the Organism 80

Higher-Level Structures Exist as Colonies of Organisms 82

2.4 SUMMARY AND CONCLUSIONS 83

2.5 PROBLEMS 83

2.6 FURTHER READING 84

2.7 REFERENCES 85

Chapter 3 When：Stopwatches at Many Scales 87

3.1 THE HIERARCHY OF TEMPORAL SCALES 87

3.1.1 The Pageant of Biological Processes 89

Biological Processes Are Characterized by a Huge Diversity of Time Scales 89

3.1.2 The Evolutionary Stopwatch 95

3.1.3 The Cell Cycle and the Standard Clock 99

The E.coli Cell Cycle Will Serve as Our Standard Stopwatch 99

3.1.4 Three Views of Time in Biology 105

3.2 PROCEDURAL TIME 106

3.2.1 The Machines （or Processes） of the Central Dogma 107

The Central Dogma Describes the Processes Whereby the Genetic Information Is Expressed Chemically 107

The Processes of the Central Dogma Are Carried Out by Sophisticated Molecular Machines 108

3.2.2 Clocks and Oscillators 110

Developing Embryos Divide on a Regular Schedule Dictated by an Internal Clock 111

Diurnal Clocks Allow Cells and Organisms to Be on Time Everyday 111

3.3 RELATIVE TIME 114

3.3.1 Checkpoints and the Cell Cycle 115

The Eukaryotic Cell Cycle Consists of Four Phases Involving Molecular Synthesis and Organization 115

3.3.2 Measuring Relative Time 117

Genetic Networks Are Collections of Genes Whose Expression Is Interrelated 117

The Formation of the Bacterial Flagellum Is Intricately Organized in Space and Time 119

3.3.3 Killing the Cell：The Life Cycles of Viruses 120

Viral Life Cycles Include a Series of Self-Assembly Processes 121

3.3.4 The Process of Development 122

3.4 MANIPULATED TIME 125

3.4.1 Chemical Kinetics and Enzyme Turnover 125

3.4.2 Beating the Diffusive Speed Limit 126

Diffusion Is the Random Motion of Microscopic Particles in Solution 127

Diffusion Times Depend upon the Length Scale 127

Diffusive Transport at the Synaptic Junction Is the Dynamical Mechanism for Neuronal Communication 128

Molecular Motors Move Cargo over Large Distances in a Directed Way 129

Membrane-Bound Proteins Transport Molecules from One Side of a Membrane to the Other 130

3.4.3 Beating the Replication Limit 131

3.4.4 Eggs and Spores：Planning for the Next Generation 132

3.5 SUMMARY AND CONCLUSIONS 133

3.6 PROBLEMS 133

3.7 FURTHER READING 136

3.8 REFERENCES 136

Chapter 4 Who：“Bless the Little Beasties” 137

4.1 CHOOSING A GRAIN OF SAND 137

Modern Genetics Began with the Use of Peas as a Model System 138

4.1.1 Biochemistry and Genetics 138

4.2 HEMOGLOBIN AS A MODEL PROTEIN 143

4.2.1 Hemoglobin，Receptor-Ligand Binding，and the Other Bohr 143

The Binding of Oxygen to Hemoglobin Has Served as a Model System for Ligand-Receptor Interactions More Generally 143

Quantitative Analysis of Hemoglobin Is Based upon Measuring the Fractional Occupancy of the Oxygen-Binding Sites as a Function of Oxygen Pressure 144

4.2.2 Hemoglobin and the Origins of Structural Biology 144

The Study of the Mass of Hemoglobin Was Central in the Development of Centrifugation 145

Structural Biology Has Its Roots in the Determination of the Structure of Hemoglobin 145

4.2.3 Hemoglobin and Molecular Models of Disease 146

4.2.4 The Rise of Allostery and Cooperativity 146

4.3 BACTERIOPHAGES AND MOLECULAR BIOLOGY 147

4.3.1 Bacteriophages and the Origins of Molecular Biology 148

Bacteriophages Have Sometimes Been Called the “Hydrogen Atoms of Biology” 148

Experiments on Phages and Their Bacterial Hosts Demonstrated That Natural Selection Is Operative in Microscopic Organisms 148

The Hershey-Chase Experiment Both Confirmed the Nature of Genetic Material and Elucidated One of the Mechanisms of Viral DNA Entry into Cells 149

Experiments on Phage T4 Demonstrated the Sequence Hypothesis of Collinearity of DNA and Proteins 150

The Triplet Nature of the Genetic Code and DNA Sequencing Were Carried Out on Phage Systems 150

Phages Were Instrumental in Elucidating the Existence of mRNA 151

General Ideas about Gene Regulation Were Learned from the Study of Viruses as a Model System 152

4.3.2 Bacteriophages and Modern Biophysics 153

Many Single- Molecule Studies of Molecular Motors Have Been Performed on Motors from Bacteriophages 154

4.4 A TALE OF TWO CELLS：E.COLI AS A MODEL SYSTEM 154

4.4.1 Bacteria and Molecular Biology 154

4.4.2 E.coli and the Central Dogma 156

The Hypothesis of Conservative Replication Has Falsifiable Consequences 156

Extracts from E.coli Were Used to Perform In Vitro Synthesis of DNA，mRNA，and Proteins 157

4.4.3 The lac Operon as the “Hydrogen Atom” of Genetic Circuits 157

Gene Regulation in E.coli Serves as a Model for Genetic Circuits in General 157

The lac Operon Is a Genetic Network That Controls the Production of the Enzymes Responsible for Digesting the Sugar Lactose 158

4.4.4 Signaling and Motility：The Case of Bacterial Chemotaxis 159

E.coli Has Served as a Model System for the Analysis of Cell Motility 159

4.5 YEAST：FROM BIOCHEMISTRY TO THE CELL CYCLE 161

Yeast Has Served as a Model System Leading to Insights in Contexts Ranging from Vitalism to the Functioning of Enzymes to Eukaryotic Gene Regulation 161

4.5.1 Yeast and the Rise of Biochemistry 162

4.5.2 Dissecting the Cell Cycle 162

4.5.3 Deciding Which Way Is Up：Yeast and Polarity 164

4.5.4 Dissecting Membrane Traffic 166

4.5.5 Genomics and Proteomics 167

4.6 FLIES AND MODERN BIOLOGY 170

4.6.1 Flies and the Rise of Modern Genetics 170

Drosophila melanogaster Has Served as a Model System for Studies Ranging from Genetics to Development to the Functioning of the Brain and Even Behavior 170

4.6.2 How the Fly Got His Stripes 171

4.7 OF MICE AND MEN 173

4.8 THE CASE FOR EXOTICA 174

4.8.1 Specialists and Experts 174

4.8.2 The Squid Giant Axon and Biological Electricity 175

There Is a Steady-State Potential Difference Across the Membrane of Nerve Cells 176

Nerve Cells Propagate Electrical Signals and Use Them to Communicate with Each Other 176

4.8.3 Exotica Toolkit 178

4.9 SUMMARY AND CONCLUSIONS 179

4.10 PROBLEMS 179

4.11 FURTHER READING 181

4.12 REFERENCES 183

PART 2 LIFE AT REST 185

Chapter 5 Mechanical and Chemical Equilibrium in the Living Cell 187

5.1 ENERGY AND THE LIFE OF CELLS 187

5.1.1 The Interplay of Deterministic and Thermal Forces 189

Thermal Jostling of Particles Must Be Accounted for in Biological Systems 189

5.1.2 Constructing the Cell：Managing the Mass and Energy Budget of the Cell 190

5.2 BIOLOGICAL SYSTEMS AS MINIMIZERS 200

5.2.1 Equilibrium Models for Out of Equilibrium Systems 200

Equilibrium Models Can Be Used for Nonequilibrium Problems if Certain Processes Happen Much Faster Than Others 201

5.2.2 Proteins in “Equilibrium” 202

Protein Structures are Free-Energy Minimizers 203

5.2.3 Cells in “Equilibrium” 204

5.2.4 Mechanical Equilibrium from a Minimization Perspective 204

The Mechanical Equilibrium State is Obtained by Minimizing the Potential Energy 204

5.3 THE MATHEMATICS OF SUPERLATIVES 209

5.3.1 The Mathematization of Judgement：Functions and Functionals 209

Functionals Deliver a Number for Every Function They Are Given 210

5.3.2 The Calculus of Superlatives 211

Finding the Maximum and Minimum Values of a Function Requires That We Find Where the Slope of the Function Equals Zero 211

5.4 CONFIGURATIONAL ENERGY 214

In Mechanical Problems，Potential Energy Determines the Equilibrium Structure 214

5.4.1 Hooke’s Law：Actin to Lipids 216

There is a Linear Relation Between Force and Extension of a Beam 216

The Energy to Deform an Elastic Material is a Quadratic Function of the Strain 217

5.5 STRUCTURES AS FREE-ENERGY MINIMIZERS 219

The Entropy is a Measure of the Microscopic Degeneracy of a Macroscopic State 219

5.5.1 Entropy and Hydrophobicity 222

Hydrophobicity Results from Depriving Water Molecules of Some of Their Configurational Entropy 222

Amino Acids Can Be Classified According to Their Hydrophobicity 224

When in Water，Hydrocarbon Tails on Lipids Have an Entropy Cost 225

5.5.2 Gibbs and the Calculus of Equilibrium 225

Thermal and Chemical Equilibrium are Obtained by Maximizing the Entropy 225

5.5.3 Departure from Equilibrium and Fluxes 227

5.5.4 Structure as a Competition 228

Free Energy Minimization Can Be Thought of as an Alternative Formulation of Entropy Maximization 228

5.5.5 An Ode to ΔG 230

The Free Energy Reflects a Competition Between Energy and Entropy 230

5.6 SUMMARY AND CONCLUSIONS 231

5.7 APPENDIX：THE EULER-LAGRANGE EQUATIONS，FINDING THE SUPERLATIVE 232

Finding the Extrema of Functionals Is Carried Out Using the Calculus of Variations 232

The Euler-Lagrange Equations Let Us Minimize Functionals by Solving Differential Equations 232

5.8 PROBLEMS 233

5.9 FURTHER READING 235

5.10 REFERENCES 236

Chapter 6 Entropy Rules！ 237

6.1 THE ANALYTICAL ENGINE OF STATISTICAL MECHANICS 237

The Probability of Different Microstates Is Determined by Their Energy 240

6.1.1 A First Look at Ligand-Receptor Binding 241

6.1.2 The Statistical Mechanics of Gene Expression：RNA Polymerase and the Promoter 244

A Simple Model of Gene Expression Is to Consider the Probability of RNA Polymerase Binding at the Promoter 245

Most Cellular RNA Polymerase Molecules Are Bound to DNA 245

The Binding Probability of RNA Polymerase to Its Promoter Is a Simple Function of the Number of Polymerase Molecules and the Binding Energy 247

6.1.3 Classic Derivation of the Boltzmann Distribution 248

The Boltzmann Distribution Gives the Probability of Microstates for a System in Contact with a Thermal Reservoir 248

6.1.4 Boltzmann Distribution by Counting 250

Different Ways of Partitioning Energy Among Particles Have Different Degeneracies 250

6.1.5 Boltzmann Distribution by Guessing 253

Maximizing the Entropy Corresponds to Making a Best Guess When Faced with Limited Information 253

Entropy Maximization Can Be Used as a Tool for Statistical Inference 255

The Boltzmann Distribution is the Maximum Entropy Distribution in Which the Average Energy is Prescribed as a Constraint 258

6.2 ON BEING IDEAL 259

6.2.1 Average Energy of a Molecule in a Gas 259

The Ideal Gas Entropy Reflects the Freedom to Rearrange Molecular Positions and Velocities 259

6.2.2 Free Energy of Dilute Solutions 262

The Chemical Potential of a Dilute Solution Is a Simple Logarithmic Function of the Concentration 262

6.2.3 Osmotic Pressure as an Entropic Spring 264

Osmotic Pressure Arises from Entropic Effects 264

Viruses，Membrane-Bound Organelles，and Cells Are Subject to Osmotic Pressure 265

Osmotic Forces Have Been Used to Measure the Interstrand Interactions of DNA 266

6.3 THE CALCULUS OF EQUILIBRIUM APPLIED：LAW OF MASS ACTION 267

6.3.1 Law of Mass Action and Equilibrium Constants 267

Equilibrium Constants are Determined by Entropy Maximization 267

6.4 APPLICATIONS OF THE CALCULUS OF EQUILIBRIUM 270

6.4.1 A Second Look at Ligand-Receptor Binding 270

6.4.2 Measuring Ligand-Receptor Binding 272

6.4.3 Beyond Simple Ligand-Receptor Binding：The Hill Function 273

6.4.4 ATP Power 274

The Energy Released in ATP Hydrolysis Depends Upon the Concentrations of Reactants and Products 275

6.5 SUMMARY AND CONCLUSIONS 276

6.6 PROBLEMS 276

6.7 FURTHER READING 278

6.8 REFERENCES 278

Chapter 7 Two-State Systems：From Ion Channels to Cooperative Binding 281

7.1 MACROMOLECULES WITH MULTIPLE STATES 281

7.1.1 The Internal State Variable Idea 281

The State of a Protein or Nucleic Acid Can Be Characterized Mathematically Using a State Variable 282

7.1.2 Ion Channels as an Example of Internal State Variables 286

The Open Probability （σ） of an Ion Channel Can Be Computed Using Statistical Mechanics 287

7.2 STATE VARIABLE DESCRIPTION OF BINDING 289

7.2.1 The Gibbs Distribution：Contact with a Particle Reservoir 289

The Gibbs Distribution Gives the Probability of Microstates for a System in Contact with a Thermal and Particle Reservoir 289

7.2.2 Simple Ligand-Receptor Binding Revisited 291

7.2.3 Phosphorylation as an Example of Two Internal State Variables 292

Phosphorylation Can Change the Energy Balance Between Active and Inactive States 293

Two-Component Systems Exemplify the Use of Phosphorylation in Signal Transduction 295

7.2.4 Hemoglobin as a Case Study in Cooperativity 298

The Binding Affinity of Oxygen for Hemoglobin Depends upon Whether or Not Other Oxygens Are Already Bound 298

A Toy Model of a Dimeric Hemoglobin （Dimoglobin） Illustrate the Idea of Cooperativity 298

The Monod-Wyman-Changeux （MWC） Model Provides a Simple Example of Cooperative Binding 300

Statistical Models of the Occupancy of Hemoglobin Can Be Written Using Occupation Variables 301

There is a Logical Progression of Increasingly Complex Binding Models for Hemoglobin 301

7.3 ION CHANNELS REVISITED：LIGAND-GATED CHANNELS AND THE MWC MODEL 305

7.4 SUMMARY AND CONCLUSIONS 308

7.5 PROBLEMS 308

7.6 FURTHER READING 310

7.7 REFERENCES 310

Chapter 8 Random Walks and the Structure of Macromolecules 311

8.1 WHAT IS A STRUCTURE：PDB OR R G？ 311

8.1.1 Deterministic versus Statistical Descriptions of Structure 312

PDB Files Reflect a Deterministic Description of Macromolecular Structure 312

Statistical Descriptions of Structure Emphasize Average Size and Shape Rather Than Atomic Coordinates 312

8.2 MACROMOLECULES AS RANDOM WALKS 312

Random Walk Models of Macromolecules View Them as Rigid Segments Connected by Hinges 312

8.2.1 A Mathematical Stupor 313

In Random Walk Models of Polymers，EveryMacromolecular Configuration Is Equally Probable 313

The Mean Size of a Random Walk Macromolecule Scales as the Square Root of the Number of Segments，？N 314

The Probability of a Given Macromolecular State Depends Upon Its Microscopic Degeneracy 315

Entropy Determines the Elastic Properties of Polymer Chains 316

The Persistence Length Is a Measure of the Length Scale Over Which a Polymer Remains Roughly Straight 319

8.2.2 How Big Is a Genome？ 321

8.2.3 The Geography of Chromosomes 322

Genetic Maps and Physical Maps of Chromosomes Describe Different Aspects of Chromosome Structure 322

Different Structural Models of Chromatin Are Characterized by the Linear Packing Density of DNA 323

Spatial Organization of Chromosomes Shows Elements of Both Randomness and Order 324

Chromosomes Are Tethered at Different Locations 325

Chromosome Territories Have Been Obsered in Bacterial Cells 327

Chromosome Territories in Vibrio cholerae Can Be Explored Using Models of Polymer Confinement and Tethering 328

8.2.4 DNA Looping：From Chromosomes to Gene Regulation 333

The Lac Repressor Molecule Acts Mechanistically by Forming a Sequestered Loop in DNA 334

Looping of Large DNA Fragments Is Dictated by the Difficulty of Distant Ends Finding Each Other 334

Chromosome Conformation Capture Reveals the Geometry of Packing of Entire Genomes in Cells 336

8.3 THE NEW WORLD OF SINGLE-MOLECULE MECHANICS 337

Single-Molecule Measurement Techniques Lead to Force Spectroscopy 337

8.3.1 Force-Extension Curves：A New Spectroscopy 339

Different Macromolecules Have Different Force Signatures When Subjected to Loading 339

8.3.2 Random Walk Models for Force-Extension Curves 340

The Low-Force Regime in Force-Extension Curves Can Be Understood Using the Random Walk Model 340

8.4 PROTEINS AS RANDOM WALKS 344

8.4.1 Compact Random Walks and the Size of Proteins 345

The Compact Nature of Proteins Leads to an Estimate of Their Size 345

8.4.2 Hydrophobic and Polar Residues：The HP Model 346

The HP Model Divides Amino Acids into Two Classes：Hydrophobic and Polar 346

8.4.3 HP Models of Protein Folding 348

8.5 SUMMARY AND CONCLUSIONS 351

8.6 PROBLEMS 351

8.7 FURTHER READING 353

8.8 REFERENCES 353

Chapter 9 Electrostatics for Salty Solutions 355

9.1 WATER AS LIFE’S AETHER 355

9.2 THE CHEMISTRY OF WATER 358

9.2.1 pH and the Equilibrium Constant 358

Dissociation of Water Molecules Reflects a Competition Between the Energetics of Binding and the Entropy of Charge Liberation 358

9.2.2 The Charge on DNA and Proteins 359

The Charge State of Biopolymers Depends upon the pH of the Solution 359

Different Amino Acids Have Different Charge States 359

9.2.3 Salt and Binding 360

9.3 ELECTROSTATICS FOR SALTY SOLUTIONS 360

9.3.1 An Electrostatics Primer 361

A Charge Distribution Produces an Electric Field Throughout Space 362

The Flux of the Electric Field Measures the Density of Electric Field Lines 363

The Electrostatic Potential Is an Alternative Basis for Describing the Electrical State of a System 364

There Is an Energy Cost Associated With Assembling a Collection of Charges 367

The Energy to Liberate Ions from Molecules Can Be Comparable to the Thermal Energy 368

9.3.2 The Charged Life of a Protein 369

9.3.3 The Notion of Screening：Electrostatics in Salty Solutions 370

Ions in Solution Are Spatially Arranged to Shield Charged Molecules Such as DNA 370

The Size of the Screening Cloud Is Determined by a Balance of Energy and Entropy of the Surrounding Ions 371

9.3.4 The Poisson-Boltzmann Equation 374

The Distribution of Screening Ions Can Be Found by Minimizing the Free Energy 374

The Screening Charge Decays Exponentially Around Macromolecules in Solution 376

9.3.5 Viruses as Charged Spheres 377

9.4 SUMMARY AND CONCLUSION 379

9.5 PROBLEMS 380

9.6 FURTHER READING 382

9.7 REFERENCES 382

Chapter 10 Beam Theory：Architecture for Cells and Skeletons 383

10.1 BEAMS ARE EVERYWHERE：FROM FLAGELLA TO THE CYTOSKELETON 383

One-Dimensional Structural Elements Are the Basis of Much of Macromolecular and Cellular Architecture 383

10.2 GEOMETRY AND ENERGETICS OF BEAM DEFORMATION 385

10.2.1 Stretch，Bend，and Twist 385

Beam Deformations Result in Stretching，Bending，and Twisting 385

A Bent Beam Can Be Analyzed as a Collection of Stretched Beams 385

The Energy Cost to Deform a Beam Is a Quadratic Function of the Strain 387

10.2.2 Beam Theory and the Persistence Length：Stiffness is Relative 389

Thermal Fluctuations Tend to Randomize the Orientation of Biological Polymers 389

The Persistence Length Is the Length Over Which a Polymer Is Roughly Rigid 390

The Persistence Length Characterizes the Correlations in the Tangent Vectors at Different Positions Along the Polymer 390

The Persistence Length Is Obtained by Averaging Over All Configurations of the Polymer 391

10.2.3 Elasticity and Entropy：The Worm-Like Chain 392

The Worm-Like Chain Model Accounts for Both the Elastic Energy and Entropy of Polymer Chains 392

10.3 THE MECHANICS OF TRANSCRIPTIONAL REGULATION：DNA LOOPING REDUX 394

10.3.1 The Iac Operon and Other Looping Systems 394

Transcriptional Regulation Can Be Effected by DNA Looping 395

10.3.2 Energetics of DNA Looping 395

10.3.3 Putting It All Together：The J-Factor 396

10.4 DNA PACKING：FROM VIRUSES TO EUKARYOTES 398

The Packing of DNA in Viruses and Cells Requires Enormous Volume Compaction 398

10.4.1 The Problem of Viral DNA Packing 400

Structural Biologists Have Determined the Structure of Many Parts in the Viral Parts List 400

The Packing of DNA in Viruses Results in a Free-Energy Penalty 402

A Simple Model of DNA Packing in Viruses Uses the Elastic Energy of Circular Hoops 403

DNA Self-Interactions Are also Important in Establishing the Free Energy Associated with DNA Packing in Viruses 404

DNA Packing in Viruses Is a Competition Between Elastic and Interaction Energies 406

10.4.2 Constructing the Nucleosome 407

Nucleosome Formation Involves Both Elastic Deformation and Interactions Between Histones and DNA 408

10.4.3 Equilibrium Accessibility of Nucleosomal DNA 409

The Equilibrium Accessibility of Sites within the Nucleosome Depends upon How Far They Are from the Unwrapped Ends 409

10.5 THE CYTOSKELETON AND BEAM THEORY 413

Eukaryotic Cells Are Threaded by Networks of Filaments 413

10.5.1 The Cellular Interior：A Structural Perspective 414

Prokaryotic Cells Have Proteins Analogous to the Eukaryotic Cytoskeleton 416

10.5.2 Stiffness of Cytoskeletal Filaments 416

The Cytoskeleton Can Be Viewed as a Collection of Elastic Beams 416

10.5.3 Cytoskeletal Buckling 419

A Beam Subject to a Large Enough Force Will Buckle 419

10.5.4 Estimate of the Buckling Force 420

Beam Buckling Occurs at Smaller Forces for Longer Beams 420

10.6 SUMMARY AND CONCLUSIONS 421

10.7 APPENDIX：THE MATHEMATICS OF THE WORM-LIKE CHAIN 421

10.8 PROBLEMS 424

10.9 FURTHER READING 426

10.10 REFERENCES 426

Chapter 11 Biological Membranes：Life in Two Dimensions 427

11.1 THE NATURE OF BIOLOGICAL MEMBRANES 427

11.1.1 Cells and Membranes 427

Cells and Their Organelles Are Bound by Complex Membranes 427

Electron Microscopy Provides a Window on Cellular Membrane Structures 429

11.1.2 The Chemistry and Shape of Lipids 431

Membranes Are Built from a Variety of Molecules That Have an Ambivalent Relationship with Water 431

The Shapes of Lipid Molecules Can Induce Spontaneous Curvature on Membranes 436

11.1.3 The Liveliness of Membranes 436

Membrane Proteins Shuttle Mass Across Membranes 437

Membrane Proteins Communicate Information Across Membranes 439

Specialized Membrane Proteins Generate ATP 439

Membrane Proteins Can Be Reconstituted in Vesicles 439

11.2 ON THE SPRINGINESS OF MEMBRANES 440

11.2.1 An Interlude on Membrane Geometry 440

Membrane Stretching Geometry Can Be Described by a Simple Area Function 441

Membrane Bending Geometry Can Be Described by a Simple Height Function，h（x，y） 441

Membrane Compression Geometry Can Be Described by a Simple Thickness Function，w（x，y） 444

Membrane Shearing Can Be Described by an Angle Variable，θ 444

11.2.2 Free Energy of Membrane Deformation 445

There Is a Free-Energy Penalty Associated with Changing the Area of a Lipid Bilayer 445

There Is a Free-Energy Penalty Associated with Bending a Lipid Bilayer 446

There Is a Free-Energy Penalty for Changing the Thickness of a Lipid Bilayer 446

There Is an Energy Cost Associated with the Gaussian Curvature 447

11.3 STRUCTURE，ENERGETICS，AND FUNCTION OF VESICLES 448

11.3.1 Measuring Membrane Stiffness 448

Membrane Elastic Properties Can Be Measured by Stretching Vesicles 448

11.3.2 Membrane Pulling 450

11.3.3 Vesicles in Cells 453

Vesicles Are Used for a Variety of Cellular Transport Processes 453

There Is a Fixed Free-Energy Cost Associated with Spherical Vesicles of All Sizes 455

Vesicle Formation Is Assisted by Budding Proteins 456

There Is an Energy Cost to Disassemble Coated Vesicles 458

11.4 FUSION AND FISSION 458

11.4.1 Pinching Vesicles：The Story of Dynamin 459

11.5 MEMBRANES AND SHAPE 462

11.5.1 The Shapes of Organelles 462

The Surface Area of Membranes Due to Pleating Is So Large That Organelles Can Have Far More Area than the Plasma Membrane 463

11.5.2 The Shapes of Cells 465

The Equilibrium Shapes of Red Blood Cells Can Be Found by Minimizing the Free Energy 466

11.6 THE ACTIVE MEMBRANE 467

11.6.1 Mechanosensitive Ion Channels and Membrane Elasticity 467

Mechanosensitive Ion Channels Respond to Membrane Tension 467

11.6.2 Elastic Deformations of Membranes Produced by Proteins 468

Proteins Induce Elastic Deformations in the Surrounding Membrane 468

Protein-Induced Membrane Bending Has an Associated Free-Energy Cost 469

11.6.3 One-Dimensional Solution for MscL 470

Membrane Deformations Can Be Obtained by Minimizing the Membrane Free Energy 470

The Membrane Surrounding a Channel Protein Produces a Line Tension 472

11.7 SUMMARY AND CONCLUSIONS 475

11.8 PROBLEMS 476

11.9 FURTHER READING 479

11.10 REFERENCES 479

PART 3 LIFE IN MOTION 481

Chapter 12 The Mathematics of Water 483

12.1 PUTTING WATER IN ITS PLACE 483

12.2 HYDRODYNAMICS OF WATER AND OTHER FLUIDS 484

12.2.1 Water as a Continuum 484

Though Fluids Are Composed of Molecules It Is Possible to Treat Them as a Continuous Medium 484

12.2.2 What Can Newton Tell Us？ 485

Gradients in Fluid Velocity Lead to Shear Forces 485

12.2.3 F= ma for Fluids 486

12.2.4 The Newtonian Fluid and the Navier-Stokes Equations 490

The Velocity of Fluids at Surfaces Is Zero 491

12.3 THE RIVER WITHIN：FLUID DYNAMICS OF BLOOD 491

12.3.1 Boats in the River：Leukocyte Rolling and Adhesion 493

12.4 THE LOW REYNOLDS NUMBER WORLD 495

12.4.1 Stokes Flow：Consider a Spherical Bacterium 495

12.4.2 Stokes Drag in Single-Molecule Experiments 498

Stokes Drag Is Irrelevant for Optical Tweezers Experiments 498

12.4.3 Dissipative Time Scales and the Reynolds Number 499

12.4.4 Fish Gotta Swim，Birds Gotta Fly，and Bacteria Gotta Swim Too 500

Reciprocal Deformation of the Swimmer’s Body Does Not Lead to Net Motion at Low Reynolds Number 502

12.4.5 Centrifugation and Sedimentation：Spin It Down 502

12.5 SUMMARY AND CONCLUSIONS 504

12.6 PROBLEMS 505

12.7 FURTHER READING 507

12.8 REFERENCES 507

Chapter 13 A Statistical View of Biological Dynamics 509

13.1 DIFFUSION IN THE CELL 509

13.1.1 Active versus Passive Transport 510

13.1.2 Biological Distances Measured in Diffusion Times 511

The Time It Takes a Diffusing Molecule to Travel a Distance L Grows as the Square of the Distance 512

Diffusion Is Not Effective Over Large Cellular Distances 512

13.1.3 Random Walk Redux 514

13.2 CONCENTRATION FIELDS AND DIFFUSIVE DYNAMICS 515

Fick’s Law Tells Us How Mass Transport Currents Arise as a Result of Concentration Gradients 517

The Diffusion Equation Results from Fick’s Law and Conservation of Mass 518

13.2.1 Diffusion by Summing Over Microtrajectories 518

13.2.2 Solutions and Properties of the Diffusion Equation 524

Concentration Profiles Broaden Over Time in a Very Precise Way 524

13.2.3 FRAP and FCS 525

13.2.4 Drunks on a Hill：The Smoluchowski Equation 529

13.2.5 The Einstein Relation 530

13.3 DIFFUSION TO CAPTURE 532

13.3.1 Modeling the Cell Signaling Problem 532

Perfect Receptors Result in a Rate of Uptake 4πDcoa 533

A Distribution of Receptors Is Almost as Good as a Perfectly Absorbing Sphere 534

Real Receptors Are Not Always Uniformly Distributed 536

13.3.2 A “Universal” Rate for Diffusion-Limited Chemical Reactions 537

13.4 SUMMARY AND CONCLUSIONS 538

13.5 PROBLEMS 539

13.6 FURTHER READING 540

13.7 REFERENCES 540

Chapter 14 Life in Crowded and Disordered Environments 543

14.1 CROWDING，LINKAGE，AND ENTANGLEMENT 543

14.1.1 The Cell Is Crowded 544

14.1.2 Macromolecular Networks：The Cytoskeleton and Beyond 545

14.1.3 Crowding on Membranes 546

14.1.4 Consequences of Crowding 547

Crowding Alters Biochemical Equilibria 548

Crowding Alters the Kinetics within Cells 548

14.2 EQUILIBRIA IN CROWDED ENVIRONMENTS 550

14.2.1 Crowding and Binding 550

Lattice Models of Solution Provide a Simple Picture of the Role of Crowding in Biochemical Equilibria 550

14.2.2 Osmotic Pressures in Crowded Solutions 552

Osmotic Pressure Reveals Crowding Effects 552

14.2.3 Depletion Forces：Order from Disorder 554

The Close Approach of Large Particles Excludes Smaller Particles Between Them，Resulting in an Entropic Force 554

Depletion Forces Can Induce Entropic Ordering！ 559

14.2.4 Excluded Volume and Polymers 559

Excluded Volume Leads to an Effective Repulsion Between Molecules 559

Self-avoidance Between the Monomers of a Polymer Leads to Polymer Swelling 561

14.2.5 Case Study in Crowding：How to Make a Helix 563

14.2.6 Crowding at Membranes 565

14.3 CROWDED DYNAMICS 566

14.3.1 Crowding and Reaction Rates 566

Enzymatic Reactions in Cells Can Proceed Faster than the Diffusion Limit Using Substrate Channeling 566

Protein Folding Is Facilitated by Chaperones 567

14.3.2 Diffusion in Crowded Environments 567

14.4 SUMMARY AND CONCLUSIONS 569

14.5 PROBLEMS 569

14.6 FURTHER READING 570

14.7 REFERENCES 571

Chapter 15 Rate Equations and Dynamics in the Cell 573

15.1 BIOLOGICAL STATISTICAL DYNAMICS：A FIRST LOOK 573

15.1.1 Cells as Chemical Factories 574

15.1.2 Dynamics of the Cytoskeleton 575

15.2 A CHEMICAL PICTURE OF BIOLOGICAL DYNAMICS 579

15.2.1 The Rate Equation Paradigm 579

Chemical Concentrations Vary in Both Space and Time 580

Rate Equations Describe the Time Evolution of Concentrations 580

15.2.2 All Good Things Must End 581

Macromolecular Decay Can Be Described by a Simple，First-Order Differential Equation 581

15.2.3 A Single-Molecule View of Degradation：Statistical Mechanics Over Trajectories 582

Molecules Fall Apart with a Characteristic Lifetime 582

Decay Processes Can Be Described with Two-State Trajectories 583

Decay of One Species Corresponds to Growth in the Number of a Second Species 585

15.2.4 Bimolecular Reactions 586

Chemical Reactions Can Increase the Concentration of a Given Species 586

Equilibrium Constants Have a Dynamical Interpretation in Terms of Reaction Rates 588

15.2.5 Dynamics of Ion Channels as a Case Study 589

Rate Equations for Ion Channels Characterize the Time Evolution of the Open and Closed Probability 590

15.2.6 Rapid Equilibrium 591

15.2.7 Michaelis-Menten and Enzyme Kinetics 596

15.3 THE CYTOSKELETON IS ALWAYS UNDER CONSTRUCTION 599

15.3.1 The Eukaryotic Cytoskeleton 599

The Cytoskeleton Is a Dynamical Structure That Is Always Under Construction 599

15.3.2 The Curious Case of the Bacterial Cytoskeleton 600

15.4 SIMPLE MODELS OF CYTOSKELETAL POLYMERIZATION 602

The Dynamics of Polymerization Can Involve Many Distinct Physical and Chemical Effects 603

15.4.1 The Equilibrium Polymer 604

Equilibrium Models of Cytoskeletal Filaments Describe the Distribution of Polymer Lengths for Simple Polymers 604

An Equilibrium Polymer Fluctuates in Time 606

15.4.2 Rate Equation Description of Cytoskeletal Polymerization 609

Polymerization Reactions Can Be Described by Rate Equations 609

The Time Evolution of the Probability Distribution Pn（t） Can Be Written Using a Rate Equation 610

Rates of Addition and Removal of Monomers Are Often Different on the Two Ends of Cytoskeletal Filaments 612

15.4.3 Nucleotide Hydrolysis and Cytoskeletal Polymerization 614

ATP Hydrolysis Sculpts the Molecular Interface，Resulting in Distinct Rates at the Ends of Cytoskeletal Filaments 614

15.4.4 Dynamic Instability：A Toy Model of the Cap 615

A Toy Model of Dynamic Instability Assumes That Catastrophe Occurs When Hydrolyzed Nucleotides Are Present at the Growth Front 616

15.5 SUMMARY AND CONCLUSIONS 618

15.6 PROBLEMS 619

15.7 FURTHER READING 621

15.8 REFERENCES 621

Chapter 16 Dynamics of Molecular Motors 623

16.1 THE DYNAMICS OF MOLECULAR MOTORS：LIFE IN THE NOISY LANE 623

16.1.1 Translational Motors：Beating the Diffusive Speed Limit 625

The Motion of Eukaryotic Cilia and Flagella Is Driven by Translational Motors 628

Muscle Contraction Is Mediated by Myosin Motors 630

16.1.2 Rotary Motors 634

16.1.3 Polymerization Motors：Pushing by Growing 637

16.1.4 Translocation Motors：Pushing by Pulling 638

16.2 RECTIFIED BROWNIAN MOTION AND MOLECULAR MOTORS 639

16.2.1 The Random Walk Yet Again 640

Molecular Motors Can Be Thought of as Random Walkers 640

16.2.2 The One-State Model 641

The Dynamics of a Molecular Motor Can Be Written Using a Master Equation 642

The Driven Diff usion Equation Can Be Transformed into an Ordinary Diffusion Equation 644

16.2.3 Motor Stepping from a Free-Energy Perspective 647

16.2.4 The Two-State Model 651

The Dynamics of a Two-State Motor Is Described by Two Coupled Rate Equations 651

Internal States Reveal Themselves in the Form of the Waiting Time Distribution 654

16.2.5 More General Motor Models 656

16.2.6 Coordination of Motor Protein Activity 658

16.2.7 Rotary Motors 660

16.3 POLYMERIZATION AND TRANSLOCATION AS MOTOR ACTION 663

16.3.1 The Polymerization Ratchet 663

The Polymerization Ratchet Is Based on a Polymerization Reaction That Is Maintained Out of Equilibrium 666

The Polymerization Ratchet Force -Velocity Can Be Obtained by Solving a Driven Diffusion Equation 668

16.3.2 Force Generation by Growth 670

Polymerization Forces Can Be Measured Directly 670

Polymerization Forces Are Used to Center Cellular Structures 672

16.3.3 The Translocation Ratchet 673

Protein Binding Can Speed Up Translocation through a Ratcheting Mechanism 674

The Translocation Time Can Be Estimated by Solving a Driven Diffusion Equation 676

16.4 SUMMARY AND CONCLUSIONS 677

16.5 PROBLEMS 677

16.6 FURTHER READING 679

16.7 REFERENCES 679

Chapter 17 Biological Electricity and the Hodgkin-Huxley Model 681

17.1 THE ROLE OF ELECTRICITY IN CELLS 681

17.2 THE CHARGE STATE OF THE CELL 682

17.2.1 The Electrical Status of Cells and Their Membranes 682

17.2.2 Electrochemical Equilibrium and the Nernst Equation 683

Ion Concentration Differences Across Membranes Lead to Potential Differences 683

17.3 MEMBRANE PERMEABILITY：PUMPS AND CHANNELS 685

A Nonequilibrium Charge Distribution Is Set Up Between the Cell Interior and the External World 685

Signals in Cells Are Often Mediated by the Presence of Electrical Spikes Called Action Potentials 686

17.3.1 Ion Channels and Membrane Permeability 688

Ion Permeability Across Membranes Is Mediated by Ion Channels 688

A Simple Two-State Model Can Describe Many of the Features of Voltage Gating of Ion Channels 689

17.3.2 Maintaining a Nonequilibrium Charge State 691

Ions Are Pumped Across the Cell Membrane Against an Electrochemical Gradient 691

17.4 THE ACTION POTENTIAL 693

17.4.1 Membrane Depolarization：The Membrane as a Bistable Switch 693

Coordinated Muscle Contraction Depends Upon Membrane Depolarization 694

A Patch of Cell Membrane Can Be Modeled as an Electrical Circuit 696

The Difference Between the Membrane Potential and the Nernst Potential Leads to an Ionic Current Across the Cell Membrane 698

Voltage-Gated Channels Result in a Nonlinear Current-Voltage Relation for the Cell Membrane 699

A Patch of Membrane Acts as a Bistable Switch 700

The Dynamics of Voltage Relaxation Can Be Modeled Using an RC Circuit 702

17.4.2 The Cable Equation 703

17.4.3 Depolarization Waves 705

Waves of Membrane Depolarization Rely on Sodium Channels Switching into the Open State 705

17.4.4 Spikes 710

17.4.5 Hodgkin-Huxley and Membrane Transport 712

Inactivation of Sodium Channels Leads to Propagating Spikes 712

17.5 SUMMARY AND CONCLUSIONS 714

17.6 PROBLEMS 714

17.7 FURTHER READING 715

17.8 REFERENCES 715

Chapter 18 Light and Life 717

18.1 INTRODUCTION 718

18.2 PHOTOSYNTHESIS 719

Organisms From All Three of the Great Domains of Life Perform Photosynthesis 720

18.2.1 Quantum Mechanics for Biology 724

Quantum Mechanical Kinematics Describes States of the System in Terms of Wave Functions 725

Quantum Mechanical Observables Are Represented by Operators 728

The Time Evolution of Quantum States Can Be Determined Using the Schrodinger Equation 729

18.2.2 The Particle-in-a-Box Model 730

Solutions for the Box of Finite Depth Do Not Vanish at the Box Edges 731

18.2.3 Exciting Electrons With Light 733

Absorption Wavelengths Depend Upon Molecular Size and Shape 735

18.2.4 Moving Electrons From Hither to Yon 737

Excited Electrons Can Suffer Multiple Fates 737

Electron Transfer in Photosynthesis Proceeds by Tunneling 739

Electron Transfer Between Donor and Acceptor Is Gated by Fluctuations of the Environment 745

Resonant Transfer Processes in the Antenna Complex Efficiently Deliver Energy to the Reaction Center 747

18.2.5 Bioenergetics of Photosynthesis 748

Electrons Are Transferred from Donors to Acceptors Within and Around the Cell Membrane 748

Water，Water Everywhere，and Not an Electron to Drink 750

Charge Separation across Membranes Results in a Proton-Motive Force 751

18.2.6 Making Sugar 752

18.2.7 Destroying Sugar 757

18.2.8 Photosynthesis in Perspective 758

18.3 THE VISION THING 759

18.3.1 Bacterial “Vision” 760

18.3.2 Microbial Phototaxis and Manipulating Cells with Light 763

18.3.3 Animal Vision 763

There Is a Simple Relationship between Eye Geometry and Resolution 765

The Resolution of Insect Eyes Is Governed by Both the Number of Ommatidia and Diffraction Effects 768

The Light-Driven Conformational Change of Retinal Underlies Animal Vision 769

Information from Photon Detection Is Amplified by a Signal Transduction Cascade in the Photoreceptor Cell 773

The Vertebrate Visual System Is Capable of Detecting Single Photons 776

18.3.4 Sex，Death，and Quantum Mechanics 781

Let There Be Light：Chemical Reactions Can Be Used to Make Light 784

18.4 SUMMARY AND CONCLUSIONS 785

18.5 APPENDIX：SIMPLE MODEL OF ELECTRON TUNNELING 785

18.6 PROBLEMS 793

18.7 FURTHER READING 795

18.8 REFERENCES 796

PART 4 THE MEANING OF LIFE 799

Chapter 19 Organization of Biological Networks 801

19.1 CHEMICAL AND INFORMATIONAL ORGANIZATION IN THE CELL 801

Many Chemical Reactions in the Cell are Linked in Complex Networks 801

Genetic Networks Describe the Linkages Between Different Genes and Their Products 802

Developmental Decisions Are Made by Regulating Genes 802

Gene Expression Is Measured Quantitatively in Terms of How Much，When，and Where 804

19.2 GENETIC NETWORKS：DOING THE RIGHT THING AT THE RIGHT TIME 807

Promoter Occupancy Is Dictated by the Presence of Regulatory Proteins Called Transcription Factors 808

19.2.1 The Molecular Implementation of Regulation：Promoters，Activators，and Repressors 808

Repressor Molecules Are the Proteins That Implement Negative Control 808

Activators Are the Proteins That Implement Positive Control 809

Genes Can Be Regulated During Processes Other Than Transcription 809

19.2.2 The Mathematics of Recruitment and Rejection 810

Recruitment of Proteins Reflects Cooperativity Between Different DNA-Binding Proteins 810

The Regulation Factor Dictates How the Bare RNA Polymerase Binding Probability Is Altered by Transcription Factors 812

Activator Bypass Experiments Show That Activators Work by Recruitment 813

Repressor Molecules Reduce the Probability Polymerase Will Bind to the Promoter 814

19.2.3 Transcriptional Regulation by the Numbers：Binding Energies and Equilibrium Constants 819

Equilibrium Constants Can Be Used To Determine Regulation Factors 819

19.2.4 A Simple Statistical Mechanical Model of Positive and Negative Regulation 820

19.2.5 The Iac Operon 822

The Iac Operon Has Features of Both Negative and Positive Regulation 822

The Free Energy of DNA Looping Affects the Repression of the Iac Operon 824

Inducers Tune the Level of Regulatory Response 829

19.2.6 Other Regulatory Architectures 829

The Fold-Change for Different Regulatory Motifs Depends Upon Experimentally Accessible Control Parameters 830

Quantitative Analysis of Gene Expression in Eukaryotes Can Also Be Analyzed Using Thermodynamic Models 832

19.3 REGULATORY DYNAMICS 835

19.3.1 The Dynamics of RNA Polymerase and the Promoter 835

The Concentrations of Both RNA and Protein Can Be Described Using Rate Equations 835

19.3.2 Dynamics of mRNA Distributions 838

Unregulated Promoters Can Be Described By a Poisson Distribution 841

19.3.3 Dynamics of Regulated Promoters 843

The Two-State Promoter Has a Fano Factor Greater Than One 844

Different Regulatory Architectures Have Different Fano Factors 849

19.3.4 Dynamics of Protein Translation 854

19.3.5 Genetic Switches：Natural and Synthetic 861

19.3.6 Genetic Networks That Oscillate 870

19.4 CELLULAR FAST RESPONSE：SIGNALING 872

19.4.1 Bacterial Chemotaxis 873

The MWC Model Can Be Used to Describe Bacterial Chemotaxis 878

Precise Adaptation Can Be Described by a Simple Balance Between Methylation and Demethylation 881

19.4.2 Biochemistry on a Leash 883

Tethering Increases the Local Concentration of a Ligand 884

Signaling Networks Help Cells Decide When and Where to Grow Their Actin Filaments for Motility 884

Synthetic Signaling Networks Permit a Dissection of Signaling Pathways 885

19.5 SUMMARY AND CONCLUSIONS 888

19.6 PROBLEMS 889

19.7 FURTHER READING 891

19.8 REFERENCES 892

Chapter 20 Biological Patterns：Order in Space and Time 893

20.1 INTRODUCTION：MAKING PATTERNS 893

20.1.1 Patterns in Space and Time 894

20.1.2 Rules for Pattern-Making 895

20.2 MORPHOGEN GRADIENTS 896

20.2.1 The French Flag Model 896

20.2.2 How the Fly Got His Stripes 898

Bicoid Exhibits an Exponential Concentration Gradient Along the Anterior-Posterior Axis of Fly Embryos 898

A Reaction-Diffusion Mechanism Can Give Rise to an Exponential Concentration Gradient 899

20.2.3 Precision and Scaling 905

20.2.4 Morphogen Patterning with Growth in Anabaena 912

20.3 REACTION-DIFFUSION AND SPATIAL PATTERNS 914

20.3.1 Putting Chemistry and Diffusion Together：Turing Patterns 914

20.3.2 How Bacteria Lay Down a Coordinate System 920

20.3.3 Phyllotaxis：The Art of Flower Arrangement 926

20.4 TURNING TIME INTO SPACE：TEMPORAL OSCILLATIONS IN CELL FATE SPECIFICATION 931

20.4.1 Somitogenesis 932

20.4.2 Seashells Forming Patterns in Space and Time 935

20.5 PATTERN FORMATION AS A CONTACT SPORT 939

20.5.1 The Notch-Delta Concept 939

20.5.2 Drosophila Eyes 944

20.6 SUMMARY AND CONCLUSIONS 947

20.7 PROBLEMS 948

20.8 FURTHER READING 949

20.9 REFERENCES 950

Chapter 21 Sequences，Specificity，and Evolution 951

21.1 BIOLOGICAL INFORMATION 952

21.1.1 Why Sequences？ 953

21.1.2 Genomes and Sequences by the Numbers 957

21.2 SEQUENCE ALIGNMENT AND HOMOLOGY 960

Sequence Comparison Can Sometimes Reveal Deep Functional and Evolutionary Relationships Between Genes，Proteins，and Organisms 961

21.2.1 The HP Model as a Coarse-Grained Model for Bioinformatics 964

21.2.2 Scoring Success 966

A Score Can Be Assigned to Different Alignments Between Sequences 966

Comparison of Full Amino Acid Sequences Requires a 20-by-20 Scoring Matrix 968

Even Random Sequences Have a Nonzero Score 970

The Extreme Value Distribution Determines the Probability That a Given Alignment Score Would Be Found by Chance 971

False Positives Increase as the Threshold for Acceptable Expect Values （also Called E-Values） Is Made Less Stringent 973

Structural and Functional Similarity Do Not Always Guarantee Sequence Similarity 976

21.3 THE POWER OF SEQUENCE GAZING 976

21.3.1 Binding Probabilities and Sequence 977

Position Weight Matrices Provide a Map Between Sequence and Binding Affinity 978

Frequencies of Nucleotides at Sites Within a Sequence Can Be Used to Construct Position Weight Matrices 979

21.3.2 Using Sequence to Find Binding Sites 983

21.3.3 Do Nucleosomes Care About Their Positions on Genomes？ 988

DNA Sequencing Reveals Patterns of Nucleosome Occupancy on Genomes 989

A Simple Model Based Upon Self-Avoidance Leads to a Prediction for Nucleosome Positioning 990

21.4 SEQUENCES AND EVOLUTION 993

21.4.1 Evolution by the Numbers：Hemoglobin and Rhodopsin as Case Studies in Sequence Alignment 994

Sequence Similarity Is Used as a Temporal Yardstick to Determine Evolutionary Distances 994

Modern-Day Sequences Can Be Used to Reconstruct the Past 996

21.4.2 Evolution and Drug Resistance 998

21.4.3 Viruses and Evolution 1000

The Study of Sequence Makes It Possible to Trace the Evolutionary History of HIV 1001

The Luria-Delbruck Experiment Reveals the Mathematics of Resistance 1002

21.4.4 Phylogenetic Trees 1008

21.5 THE MOLECULAR BASIS OF FIDELITY 1010

21.5.1 Keeping It Specific：Beating Thermodynamic Specificity 1011

The Specificity of Biological Recognition Often Far Exceeds the Limit Dictated by Free-Energy Differences 1011

High Specificity Costs Energy 1015

21.6 SUMMARY AND CONCLUSIONS 1016

21.7 PROBLEMS 1017

21.8 FURTHER READING 1020

21.9 REFERENCES 1021

Chapter 22 Whither Physical Biology？ 1023

22.1 DRAWING THE MAP TO SCALE 1023

22.2 NAVIGATING WHEN THE MAP IS WRONG 1027

22.3 INCREASING THE MAP RESOLUTION 1028

22.4 “DIFFICULTIES ON THEORY” 1030

Modeler’ s Fantasy 1031

Is It Biologically Interesting？ 1031

Uses and Abuses of Statistical Mechanics 1032

Out-of-Equilibrium and Dynamic 1032

Uses and Abuses of Continuum Mechanics 1032

Too Many Parameters 1033

Missing Facts 1033

Too Much Stuff 1033

Too Little Stuff 1034

The Myth of “THE” Cell 1034

Not Enough Thinking 1035

22.5 THE RHYME AND REASON OF IT ALL 1035

22.6 FURTHER READING 1036

22.7 REFERENCES 1037

Index 1039