Contents in Detail xix - xxviii
Preface vii
Acknowledgments xiii
Special Sections xxix
Map of the Maps xxx
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 G 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 \sigma 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 RG? 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, Every Macromolecular Configuration Is Equally Probable 313
The Mean Size of a Random Walk Macromolecule Scales as the Square Root of the Number of Segments, vN 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 Observed 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 lac 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, \theta 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 $4\pi D c_0 a$ 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 P_n(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 Diffusion 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 lac Operon 822
The lac Operon Has Features of Both Negative and Positive Regulation 822
The Free Energy of DNA Looping Affects the Repression of the lac 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