Physical biology of the cell:
"Physical Biology of the Cell is a biophysics textbook that explores how the basic tools and insights of physics and mathematics can illuminate the study of molecular and cell biology. Drawing on key examples and seminal experiments from cell biology, the book teaches physical model building th...
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Garland Science
2009
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Physical Biology of the Cell is a biophysics textbook that explores how the basic tools and insights of physics and mathematics can illuminate the study of molecular and cell biology. Drawing on key examples and seminal experiments from cell biology, the book teaches physical model building through a practical, case-study approach, demonstrating how quantitative models derived from basic physical principles can be used to build a more profound, intuitive understanding of cell biology."--BOOK JACKET. |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke. - 2. Aufl. u.d.T.: Physical biology of the cell / Phillips, Rob |
| Beschreibung: | XXIV, 807 S. Ill., graph. Darst. |
| ISBN: | 9780815341635 |
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| 264 | 1 | |a New York, NY [u.a.] |b Garland Science |c 2009 | |
| 300 | |a XXIV, 807 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804138358507569152 |
|---|---|
| adam_text | CONTENTS
Detailed Contents *v
Special Sections xx v
Chapter 1: Why: Biology by the Numbers 3
Chapter 2: What and Where: Construction Plans for Cells
and Organisms 29
Chapter 3: When: Stopwatches at Many Scales 75
Chapter 4: Who: Bless the Little Beasties 119
Chapter 5: Mechanical and Chemical Equilibrium in the
Living Cell l(|7
Chapter 6: Entropy Rules! 215
Chapter 7: Two-State Systems: From Ion Channels to
Cooperative Binding 257
Chapter 8: Random Walks and the Structure
of Macromolecules 281
Chapter 9: Electrostatics for Salty Solutions 327
Chapter 10: Beam Theory: Architecture for Cells
and Skeletons 357
Chapter 11: Biological Membranes: Life in Two Dimensions 407
Chapter 12: The Mathematics of Water 457
Chapter 13: A Statistical View of Biological Dynamics 481
Chapter 14: Life in Crowded and Disordered Environments 513
Chapter IS: Rate Equations and Dynamics in the Cell 539
Chapter 16: Dynamics of Molecular Motors 589
Chapter 17: Biological Electricity and the Hodgkin-Huxley
Model 647
Chapter 18: Sequences, Specificity, and Evolution 681
Chapter 19: Network Organization in Space and Time 721
Chapter 20: Whither Physical Biology? 775
Index 787
DETAILED CONTENTS
Chapter 1 Why: Biology by the Numbers 3
1.1 PHYSICAL BIOLOGY OF THE CELL 3
Model Building Requires a Substrate of Biological
Facts and Physical (or Chemical) Principles 4
1.2 THE STUFF OF LIFE 4
Organisms Are Constructed from Four Great Classes
of Macromolecules 5
Nucleic Acids and Proteins Are Polymer Languages
with Different Alphabets 6
1.3 MODEL BUILDING IN BIOLOGY 9
1.3.1 Models as Idealizations 9
Biological Stuff Can Be Idealized Using Many
Different Physical Models 10
1.3.2 Cartoons and Models 15
Biological Cartoons Select Those Features of
the Problem Thought to be Essential 1 5
Quantitative Models Can Be Built by
Mathematicizing the Cartoons 18
1.4 QUANTITATIVE MODELS AND THE POWER
OF IDEALIZATION 1 9
1.4.1 On the Springiness of Stuff 19
1.4.2 The Toolbox of Fundamental Physical Models 20
1.4.3 The Role of Estimates 22
1.4.4 On Being Wrong 23
1.4.5 Rules of Thumb: Biology by the Numbers 25
1.5 SUMMARY AND CONCLUSIONS 25
1.6 FURTHER READING 27
1.7 REFERENCES 27
Chapter 2 What and Where: Construction
Plans for Cells and Organisms 29
2.1 AN ODE TO E. COU 29
2.1.1 The Bacterial Standard Ruler 30
The Bacterium E. co//Will Serve as Our Standard Ruler 30
2.1.2 Taking the Molecular Census 32
The Cellular Interior Is Highly Crowded with Mean
Spacings Between Molecules That Are
Comparable to Molecular Dimensions 36
2.1.3 Looking Inside Cells 37
2.1.4 Where Does E. coli Fit? 39
Biological Structures Exist Over a Huge Range
of Scales 39
2.2 CELLS AND STRUCTURES WITHIN THEM 40
2.2.1 Cells: A Rogue s Gallery 40
Cells Come in a Wide Variety of Shapes and Sizes
and with a Huge Range of Functions 41
Cells from Humans Have a Huge Diversity of
Structure and Function 45
2.2.2 The Cellular Interior: Organelles 47
2.2.3 Macromolecular Assemblies: The Whole is Greater
than the Sum of the Parts 51
Macromolecules Come Together to Form Assemblies 51
Helical Motifs are Seen Repeatedly in Molecular
Assemblies 51
Macromolecular Assemblies Are Arranged in
Superstructures 53
2.2.4 Viruses as Assemblies 53
2.2.5 The Molecular Architecture of Cells: From Protein
Data Bank (PDB) Files to Ribbon Diagrams 57
Macromolecular Structure Is Characterized
Fundamentally by Atomic Coordinates 57
Chemical Croups Allow Us to Classify Parts of
the Structure of Macromolecules 58
2.3 TELESCOPING UP IN SCALE: CELLS DON T
CO IT ALONE 60
2.3.1 Multicellularity as One of Evolution s Great
Inventions 61
Bacteria Interact to Form Colonies such as Biofilms 61
Teaming Up in a Crisis: Lifestyle of Dictyostelium
discoideum 62
Multicellular Organisms Have Many Distinct
Communities of Cells 64
2.3.2 Cellular Structures from Tissues to Nerve Networks 65
One Class of Multicellular Structures is the
Epithelial Sheets 65
Tissues Are Collections of Cells and Extracellular
Matrix 66
Nerve Cells Form Complex, Multicellular Complexes 66
2.3.3 Multicellular Organisms 67
Cells Differentiate During Development Leading
to Entire Organisms 68
The Cells of the Nematode Worm Caenorhabditis
elegans Have Been Charted Yielding a Cell-by-Cell
Picture of the Organism 69
Higher-Level Structures Exist as Colonies
of Organisms 71
2.4 SUMMARY AND CONCLUSIONS 71
2.5 PROBLEMS 72
2.6 FURTHER READING 73
2.7 REFERENCES 73
Chapter 3 When: Stopwatches at Many
Scales 75
3.1 THE HIERARCHY OF TEMPORAL SCALES 75
3.1.1 The Pageant of Biological Processes 77
Biological Processes Are Characterized by a Huge
Diversity of Time Scales 77
3.1.2 The Evolutionary Stopwatch 83
3.1.3 The Cell Cycle and the Standard Clock 87
The E. coli Cell Cycle Will Serve as Our Standard
Stopwatch 87
3.1.4 Three Views of Time in Biology 89
3.2 PROCEDURAL TIME 90
3.2.1 The Machines (or Processes) of the Central Dogma 90
The Central Dogma Describes the Processes
Whereby the Genetic Information Is Expressed
Chemically 90
The Processes of the Central Dogma Are Carried
Out by Sophisticated Molecular Machines 91
3.2.2 Clocks and Oscillators 93
Developing Embryos Divide on a Regular Schedule
Dictated by an Internal Clock 94
Diurnal Clocks Allow Cells and Organisms to Be
on Time Everyday 94
3.3 RELATIVE TIME 97
3.3.1 Checkpoints and the Cell Cycle 98
The Eukaryotic Cell Cycle Consists of Four Phases
Involving Molecular Synthesis and Organization 98
3.3.2 Measuring Relative Time 100
Genetic Networks Are Collections of Genes Whose
Expression Is Interrelated 100
The Formation of the Bacterial Flagellum Is
Intricately Organized in Space and Time 101
3.3.3 Killing the Cell: The Life Cycles of Viruses 102
Viral Life Cycles Include a Series of Self-Assembly
Processes 102
3.3.4 The Process of Development 104
3.4 MANIPULATED TIME 106
3.4.1 Chemical Kinetics and Enzyme Turnover 107
3.4.2 Beating the Diffusive Speed Limit 108
Diffusion Is the Random Motion of Microscopic
Particles in Solution 109
Diffusion Times Depend upon the Length Scale 109
Molecular Motors Move Cargo over Large
Distances in a Directed Way 110
Membrane Bound Proteins Transport Molecules
from One Side of a Membrane to the Other 11 2
3.4.3 Beating the Replication Limit 11 3
3.4.4 Eggs and Spores: Planning for the Next Generation 114
3.5 SUMMARY AND CONCLUSIONS 115
3.6 PROBLEMS 115
3.7 FURTHER READING 117
3.8 REFERENCES 117
Chapter 4 Who: Bless the Little Beasties 119
4.1 CHOOSING A GRAIN OF SAND 1 19
Modern Genetics Began with the Use of Peas
as a Model System 120
4.1.1 Biochemistry and Genetics 120
4.2 HEMOGLOBIN AS A MODEL PROTEIN 124
4.2.1 Hemoglobin, Receptor—Ligand Binding, and the
Other Bohr 125
The Binding of Oxygen to Hemoglobin Has Served
as a Model System for Ligand—Receptor
Interactions More Generally 125
Quantitative Analysis of Hemoglobin Is Based upon
Measuring the Fractional Occupancy of the Oxygen
Binding Sites as a Function of Oxygen Pressure 125
4.2.2 Hemoglobin and the Origins of Structural Biology 126
The Study of the Mass of Hemoglobin Was Central
in the Development of Centrifugation 127
Structural Biology Has Its Roots in the
Determination of the Structure of Hemoglobin 127
4.2.3 Hemoglobin and Molecular Models of Disease 127
4.2.4 The Rise of Allostery and Cooperativity 128
4.3 BACTERIOPHAGE AND MOLECULAR BIOLOGY 129
4.3.1 Bacteriophage and the Origins of Molecular Biology 129
Bacteriophage Have Sometimes Been Called the
Hydrogen Atoms of Biology 129
Experiments on Phage and Their Bacterial Hosts
Demonstrated That Natural Selection Is
Operative in Microscopic Organisms 130
The Hershey—Chase Experiment Both Confirmed the
Nature of Genetic Material and Elucidated One
of the Mechanisms of Viral DNA Entry into Cells 130
Experiments on Phage T4 Demonstrated the Sequence
Hypothesis of Collinearity of DNA and Proteins 131
The Triplet Nature of the Genetic Code and DNA
Sequencing were Carried Out on Phage Systems 132
Phage Were Instrumental in Elucidating the
Existence of mRNA 133
General Ideas about Gene Regulation Were Learned
from the Study of Viruses as a Model System 133
4.3.2 Bacteriophage and Modern Biophysics 134
Many Single-Molecule Studies of Molecular Motors
Have Been Performed on Motors from Bacteriophage 1 34
4.4 A TALE OF TWO CELLS: E. COLI AS A MODEL SYSTEM 1 36
4.4.1 Bacteria and Molecular Biology 136
4.4.2 E. coli and the Central Dogma 1 36
The Hypothesis of Conservative Replication Has
Falsifiable Consequences 136
Extracts from E. coli Were Used to Perform In Vitro
Synthesis of DNA, mRNA, and Proteins 138
4.4.3 The lac Operon as the Hydrogen Atom of
Genetic Circuits 138
Gene Regulation in E. coli Serves as a Model
for Genetic Circuits in General 138
The lac Operon is a Genetic Network Which
Controls the Production of the Enzymes
Responsible for Digesting the Sugar Lactose 1 39
4.4.4 Signaling and Motility: The Case of Bacterial
Chemotaxis 140
E. coli Has Served as a Model System for the
Analysis of Cell Motility 140
4.5 YEAST: FROM BIOCHEMISTRY TO THE CELL CYCLE 142
Yeast Has Served as a Model System Leading to
Insights in Contexts Ranging from Vitalism to the
Functioning of Enzymes to Eukaryotic Gene
Regulation 142
4.5.1 Yeast and the Rise of Biochemistry 143
4.5.2 Dissecting the Cell Cycle 144
4.5.3 Deciding Which Way Is Up: Yeast and Polarity 145
4.5.4 Dissecting Membrane Traffic 147
4.5.5 Genomics and Proteomics 148
4.6 FLIES AND MODERN BIOLOGY 151
4.6.1 Flies and the Rise of Modern Genetics 151
Drosophila melanogaster Has Served as a Model
System for Studies Ranging from Genetics to
Development to the Functioning of the Brain
and Even Behavior 1 51
4.6.2 How the Fly Cot His Stripes 1 52
4.7 OF MICE AND MEN 154
4.8 THE CASE FOR EXOTICA 155
4.8.1 Specialists and Experts 155
4.8.2 The Squid Giant Axon and Biological Electricity 1 57
There Is a Steady-State Potential Difference Across
the Membrane of Nerve Cells 1 57
Nerve Cells Propagate Electrical Signals and Use
Them to Communicate with Each Other 1 59
4.8.3 Exotica Toolkit 159
4.9 SUMMARY AND CONCLUSIONS 160
4.10 PROBLEMS 161
4.11 FURTHER READING 162
4.12 REFERENCES 164
Chapter 5 Mechanical and Chemical
Equilibrium in the Living Cell 167
5.1 ENERGY AND THE LIFE OF CELLS 167
5.1.1 The Interplay of Deterministic and Thermal Forces 168
Thermal Jostling of Particles Must Be Accounted
for in Biological Systems 169
5.1.2 Constructing the Cell: Managing the Mass and
Energy Budget of the Cell 170
5.2 BIOLOGICAL SYSTEMS AS MINIMIZERS 180
5.2.1 Equilibrium Models for Out of Equilibrium Systems 180
Equilibrium Models Can Be Used for
Nonequilibrium Problems If Certain Processes
Happen Much Faster than Others 180
5.2.2 Proteins in Equilibrium 182
Protein Structures are Free-Energy Minimizers 183
5.2.3 Cells in Equilibrium 184
5.2.4 Mechanical Equilibrium from a Minimization
Perspective 184
The Mechanical Equilibrium State Is Obtained by
Minimizing the Potential Energy 184
5.3 THE MATHEMATICS OF SUPERLATIVES 187
5.3.1 The Mathematization of Judgement: Functions
and Functionals 188
Functionals Deliver a Number for Every Function
They Are Given 188
5.3.2 The Calculus of Superlatives 190
Finding the Maximum and Minimum Values of a
Function Requires That We Find Where the Slope
of the Function Equals Zero 190
5.4 CONFIGURATIONAL ENERGY 192
In Mechanical Problems, Potential Energy
Determines the Equilibrium Structure 192
5.4.1 Hooke s Law: Actin to Lipids 195
There Is a Linear Relation Between Force and
Extension of a Beam 195
The Energy to Deform an Elastic Material Is a
Quadratic Function of the Strain 196
5.5 STRUCTURES AS FREE ENERGY MINIMIZERS 198
The Entropy Is a Measure of the Microscopic
Degeneracy of a Macroscopic State 198
5.5.1 Entropy and Hydrophobicity 201
Hydrophobicity Results from Depriving Water
Molecules of Some of Their Configurational
Entropy 201
Amino Acids Can Be Classified According to Their
Hydrophobicity 203
When in Water, Hydrocarbon Tails on Lipids Have
an Entropy Cost 203
5.5.2 Gibbs and the Calculus of Equilibrium 204
Thermal and Chemical Equilibrium Are Obtained
by Maximizing the Entropy 204
5.5.3 Structure as a Competition 206
Free Energy Minimization Can Be Thought of as an
Alternative Formulation of Entropy Maximization 207
5.5.4 An Ode to AC 208
The Free Energy Reflects a Competition Between
Energy and Entropy 208
5.6 SUMMARY AND CONCLUSIONS 209
5.7 APPENDIX: THE EULER—LACRANGE
EQUATIONS, FINDING THE SUPERLATIVE 210
Finding the Extrema of Functionals is Carried out
Using the Calculus of Variations 210
The Euler—Lagrange Equations Let Us Minimize
Functionals by Solving Differential Equations 210
5.8 PROBLEMS 211
5.9 FURTHER READING 213
5.10 REFERENCES 214
Chapter 6 Entropy Rules! 215
6.1 THE ANALYTICAL ENGINE OF STATISTICAL
MECHANICS 21 5
The Probability of Different Microstates Is
Determined by Their Energy 21 7
6.1.1 A First Look at Ligand—Receptor Binding 219
6.1.2 The Statistical Mechanics of Gene Expression:
RNA Polymerase and the Promoter 222
A Simple Model of Gene Expression Is to Consider
the Probability of RNA Polymerase Binding at
the Promoter 224
Most Cellular RNA Polymerase Molecules Are
Bound to DNA 224
The Binding Probability of RNA Polymerase to Its
Promoter Is a Simple Function of the Number of
Polymerase Molecules and the Binding Energy 226
6.1.3 Classic Derivation of the Boltzmann Distribution 227
The Boltzmann Distribution Gives the Probability
of Microstates for a System in Contact with a
Thermal Reservoir 228
6.1.4 Boltzmann Distribution by Counting 230
Different Ways of Partitioning Energy Among
Particles Have Different Degeneracies 230
6.1.5 Boltzmann Distribution by Guessing 232
Maximizing the Entropy Corresponds to Making a
Best Guess When Faced with Limited Information 232
Entropy Maximization Can Be Used as a Tool for
Statistical Inference 234
The Boltzmann Distribution Is the Maximum
Entropy Distribution in Which the Average Energy
Is Prescribed as a Constraint 236
6.2 ON BEING IDEAL 237
6.2.1 Average Energy of a Molecule in a Gas 238
The Ideal Gas Entropy Reflects the Freedom to
Rearrange Molecular Positions and Velocities 238
6.2.2 Free Energy of Dilute Solutions 240
The Chemical Potential of a Dilute Solution Is a
Simple Logarithmic Function of the Concentration 240
6.2.3 Osmotic Pressure as an Entropic Spring 242
Osmotic Pressure Arises from Entropic Effects 242
Viruses, Membrane-Bound Organelles and Cells
are Subject to Osmotic Pressure 244
Osmotic Forces Have Been Used to Measure the
Interstrand Interactions of DNA 245
6.3 THE CALCULUS OF EQUILIBRIUM APPLIED:
LAW OF MASS ACTION 245
6.3.1 Law of Mass Action and Equilibrium Constants 246
Equilibrium Constants are Determined by Entropy
Maximization 246
6.4 APPLICATIONS OF THE CALCULUS OF EQUILIBRIUM 248
6.4.1 A Second Look at Ligand—Receptor Binding 248
6.4.2 Measuring Ligand—Receptor Binding 250
6.4.3 Beyond Simple Ligand—Receptor Binding:
The Hill Function 250
6.4.4 ATP Power 252
The Energy Released in ATP Hydrolysis Depends
Upon the Concentrations of Reactants and
Products 253
6.5 SUMMARY AND CONCLUSIONS 254
6.6 PROBLEMS 254
6.7 FURTHER READING 256
6.8 REFERENCES 256
Chapter 7 Two-State Systems: From Ion
Channels to Cooperative Binding 257
7.1 MACROMOLECULES WITH MULTIPLE STATES 257
7.1.1 The Internal State Variable Idea 257
The State of a Protein or Nucleic Acid Can Be
Characterized Mathematically Using a State Variable 258
7.1.2 Ion Channels as an Example of Internal State Variables 260
The Open Probability o of an Ion Channel Can Be
Computed Using Statistical Mechanics 261
7.2 STATE VARIABLE DESCRIPTION OF BINDING 264
7.2.1 The Cibbs Distribution: Contact with a Particle
Reservoir 264
The Cibbs Distribution Gives the Probability of
Microstates for a System in Contact with a Thermal
and a Particle Reservoir 264
7.2.2 Simple Ligand—Receptor Binding Revisited 266
7.2.3 Phosphorylation as an Example of Two Internal
State Variables 267
Phosphorylation Can Change the Energy Balance
Between Active and Inactive States 268
7.2.4 Hemoglobin as a Case Study in Cooperativity 269
The Binding Affinity of Oxygen for Hemoglobin
Depends upon Whether or Not Other Oxygens
Are Already Bound 270
A Toy Model of a Dimeric Hemoglobin (Dimoglobin)
Illustrates the Idea of Cooperativity 271
The Monod—Wyman—Changeux (MWC) Model
Provides a Simple Example of Cooperative Binding 272
Statistical Models of the Occupancy of Hemoglobin
Can Be Written Using Occupation Variables 274
There is a Logical Progression of Increasingly
Complex Binding Models for Hemoglobin 274
7.3 SUMMARY AND CONCLUSIONS 278
7.4 PROBLEMS 278
7.5 FURTHER READING 279
7.6 REFERENCES 280
Chapter 8 Random Walks and the
Structure of Macromolecules 281
8.1 WHAT IS A STRUCTURE: PDB OR Rc? 281
8.1.1 Deterministic vs Statistical Descriptions of
Structure 282
PDB Files Reflect a Deterministic Description of
Macromolecular Structure 282
Statistical Descriptions of Structure Emphasize
Average Size and Shape Rather Than Atomic
Coordinates 282
8.2 MACROMOLECULES AS RANDOM WALKS 282
Random Walk Models of Macromolecules View
Them as Rigid Segments Connected by Hinges 282
8.2.1 A Mathematical Stupor 283
In Random Walk Models of Polymers, Every
Macromolecular Configuration Is Equally Probable 283
The Mean Size of a Random Walk Macromolecule
Scales as the Square Root of the Number of
Segments, W 283
The Probability of a Given Macromolecular
Configuration Depends Upon Its Microscopic
Degeneracy 285
Entropy Determines the Elastic Properties of
Polymer Chains 286
The Persistence Length Is a Measure of the Length
Scale Over Which a Polymer Remains Roughly
Straight 289
8.2.2 How Big Is a Genome? 291
8.2.3 The Geography of Chromosomes 292
Genetic Maps and Physical Maps of Chromosomes
Describe Different Aspects of Chromosome Structure 292
Different Structural Models of Chromatin Are
Characterized by the Linear Packing Density of DNA 293
Spatial Organization of Chromosomes Shows
Elements of Both Randomness and Order 294
Chromosomes Are Tethered at Different Locations 295
Chromosome Territories Have Been Observed in
Bacterial Cells 298
Chromosome Territories in Vibrio cholerae Can Be
Explored using Models of Polymer Confinement
and Tethering 299
8.2.4 DNA Looping: From Chromosomes to Gene
Regulation 305
The Lac Repressor Molecule Acts Mechanistically by
Forming a Sequestered Loop in DNA 306
Looping of Large DNA Fragments Is Dictated by the
Difficulty of Distant Ends Finding Each Other 306
8.2.5 PCR, DNA Melting, and DNA Bubbles 307
DNA Melting Is the Result of Competition Between
the Energy Cost and the Entropy Cain of
Separating the Two Complementary Strands 308
DNA Melting Temperatures Can Be Estimated
Using a Random Walk Model 308
8.3 THE NEW WORLD OF SINCLE-MOLECULE MECHANICS 311
Single-Molecule Measurement Techniques Lead
to Force Spectroscopy 311
8.3.1 Force—Extension Curves: A New Spectroscopy 311
Different Macromolecules Have Different Force
Signatures When Subjected to Loading 311
8.3.2 Random Walk Models for Force—Extension Curves 313
The Low-Force Regime in Force—Extension Curves
Can Be Understood Using the Random Walk Model 313
8.4 PROTEINS AS RANDOM WALKS 317
8.4.1 Compact Random Walks and the Size of Proteins 318
The Compact Nature of Proteins Leads to an
Estimate of their Size 318
8.4.2 Hydrophobic and Polar Residues: The HP Model 318
The HP Model Divides Amino Acids into Two
Classes: Hydrophobic and Polar 319
8.4.3 HP Models of Protein Folding 321
8.5 SUMMARY AND CONCLUSIONS 324
8.6 PROBLEMS 324
8.7 FURTHER READING 325
8.8 REFERENCES 326
Chapter 9 Electrostatics for Salty
Solutions 327
9.1 WATER AS LIFE S AETHER 327
9.2 THE CHEMISTRY OF WATER 329
9.2.1 pH and the Equilibrium Constant 329
Dissociation of Water Molecules Reflects a
Competition Between the Energetics of Binding
and the Entropy of Charge Liberation 329
9.2.2 The Charge on DNA and Proteins 330
The Charge State of Biopolymers Depends upon
the pH of the Solution 330
Different Amino Acids Have Different Charge States 331
9.2.3 Salt and Binding 331
9.3 ELECTROSTATICS FOR SALTY SOLUTIONS 332
9.3.1 An Electrostatics Primer 332
A Charge Distribution Produces an Electric Field
Throughout Space 333
The Flux of the Electric Field Measures the
Density of Electric Field Lines 333
The Electrostatic Potential Is an Alternative Basis
for Describing the Electrical State of a System 336
There Is an Energy Cost Associated With
Assembling a Collection of Charges 338
The Energy to Liberate Ions from Molecules Can
Be Comparable to the Thermal Energy 340
9.3.2 The Charged Life of a Protein 341
9.3.3 The Notion of Screening: Electrostatics in Salty
Solutions 342
Ions in Solution Are Spatially Arranged to Shield
Charged Molecules Such as DNA 342
The Size of the Screening Cloud Is Determined
by a Balance of Energy and Entropy of the
Surrounding Ions 343
9.3.4 The Poisson—Boltzmann Equation 346
The Distribution of Screening Ions Can Be Found
by Minimizing the Free Energy 346 :
The Screening Charge Decays Exponentially
Around Macromolecules in Solution 348
9.3.5 Viruses as Charged Spheres 349
9.4 SUMMARY AND CONCLUSION 352
9.5 PROBLEMS 353
9.6 FURTHER READING 355
9.7 REFERENCES 355
Chapter 10 Beam Theory: Architecture
for Cells and Skeletons 357
1 0.1 BEAMS ARE EVERYWHERE: FROM FLACELLA TO
THE CYTOSKELETON 357
One-Dimensional Structural Elements Are the Basis
of Much of Macromolecular and Cellular
Architecture 357
1 0.2 GEOMETRY AND ENERGETICS OF BEAM DEFORMATION 359
10.2.1 Stretch, Bend, and Twist 359
Beam Deformations Result in Stretching, Bending,
and Twisting 359
A Bent Beam Can Be Analyzed as a Collection of
Stretched Beams 359
The Energy Cost to Deform a Beam Is a Quadratic
Function of the Strain 361
10.2.2 Beam Theory and the Persistence Length: Stiffness
is Relative 363
Thermal Fluctuations Tend to Randomize the
Orientation of Biological Polymers 363
The Persistence Length Is the Length Over Which
a Polymer Is Roughly Rigid 363
The Persistence Length Characterizes the
Correlations in the Tangent Vectors at Different
Positions Along the Polymer 364
The Persistence Length Is Obtained by Averaging
Over All Configurations of the Polymer 364
10.2.3 Elasticity and Entropy: The Worm-like Chain 366
The Worm-like Chain Model Accounts for Both
the Elastic Energy and Entropy of Polymer
Chains 366
10.3 THE MECHANICS OF TRANSCRIPTIONAL REGULATION:
DNA LOOPING REDUX 368
10.3.1 The Lac Operon and Other Looping Systems 368
Transcriptional Regulation Can Be Effected by
DNA Looping 369
10.3.2 Energetics of DNA Looping 369
10.3.3 Putting It All Together: The J-Factor 370
10.4 DNA PACKING: FROM VIRUSES TO
EUKARYOTES 372
The Packing of DNA in Viruses and Cells Requires
Enormous Volume Compaction 372
10.4.1 The Problem of Viral DNA Packing 374
Structural Biologists Have Determined the Structure
of Many Parts in the Viral Parts List 375
The Packing of DNA in Viruses Results in a
Free-Energy Penalty 375
A Simple Model of DNA Packing in Viruses Uses
the Elastic Energy of Circular Hoops 377
DNA Self-Interactions Are also Important in
Establishing the Free Energy Associated with
DNA Packing in Viruses 379
DNA Packing in Viruses Is a Competition Between
Elastic and Interaction Energies 380
10.4.2 Constructing the Nucleosome 381
Nucleosome Formation Involves Both Elastic
Deformation and Interactions between Histones
and DNA 383
10.4.3 Equilibrium Accessibility of Nucleosomal DNA 383
The Equilibrium Accessibility of Sites within the
Nucleosome Depends upon How Far They Are
from the Unwrapped Ends 384
10.5 THE CYTOSKELETON AND BEAM THEORY 388
Eukaryotic Cells Are Threaded by Networks of
Filaments 388
10.5.1 The Cellular Interior: A Structural Perspective 388
Prokaryotic Cells Have Proteins Analogous to the
Eukaryotic Cytoskeleton 391
10.5.2 Stiffness of Cytoskeletal Filaments 391
The Cytoskeleton Can Be Viewed as a Collection
of Elastic Beams 391
10.5.3 Cytoskeletal Buckling 393
A Beam Subject to a Large Enough Force Will Buckle 393
10.5.4 Estimate of the Buckling Force 395
Beam Buckling Occurs at Smaller Forces for Longer
Beams 396
10.6 BEAMS AND BIOTECHNOLOGY 396
10.6.1 Biofunctionalized Cantilevers and Molecular
Recognition 397
Biofunctionalized Cantilevers Can Be Used to
Detect Macromolecules, Viruses, and Cells 397
Bending of Biofunctionalized Cantilevers Reflects a
Competition Between Bending Energy and
Surface Free Energy 398
10.7 SUMMARY AND CONCLUSIONS 400
1 0.8 APPENDIX: THE MATHEMATICS OF THE
WORM-LIKE CHAIN 401
10.9 PROBLEMS 403
10.10 FURTHER READING 405
10.11 REFERENCES 406
Chapter 11 Biological Membranes:
Life in Two Dimensions 407
11.1 THE NATURE OF BIOLOGICAL MEMBRANES 407
11.1.1 Cells and Membranes 407
Cells and Their Organelles Are Bound by Complex
Membranes 407
Electron Microscopy Provides a Window on Cellular
Membrane Structures 409
11.1.2 The Chemistry and Shape of Lipids 410
Membranes Are Built from a Variety of Molecules
That Have an Ambivalent Relationship with Water 410
The Shapes of Lipid Molecules Can Induce
Spontaneous Curvature to Membranes 412
11.1.3 The Liveliness of Membranes 414
Membrane Proteins Shuttle Mass Across
Membranes 415
Membrane Proteins Communicate Information
Across Membranes 416
Specialized Membrane Proteins Generate ATP 416
Membrane Proteins Can Be Reconstituted in
Vesicles 417
11.2 ON THE SPRINGINESS OF MEMBRANES 417
11.2.1 An Interlude on Membrane Geometry 417
Membrane Stretching Geometry Can Be Described
by a Simple Area Function 418
Membrane Bending Geometry Can Be Described
by a Simple Height Function, hix,y) 419
Membrane Compression Geometry Can Be
Described by a Simple Thickness Function, w(x,y) 422
Membrane Shearing Can Be Described by an Angle
Variable, 6 422
11.2.2 Free Energy of Membrane Deformation 422
There Is a Free Energy Penalty Associated with
Changing the Area of a Lipid Bilayer 422
There Is a Free Energy Penalty Associated with
Bending a Lipid Bilayer 423
There Is a Free Energy Penalty for Changing the
Thickness of a Lipid Bilayer 424
There Is an Energy Cost Associated with the
Gaussian Curvature 424
11.3 STRUCTURE, ENERGETICS, AND FUNCTION
Of VESICLES 426
11.3.1 Measuring Membrane Stiffness 426
Membrane Elastic Properties Can Be Measured by
Stretching Vesicles 426
11.3.2 Membrane Pulling 427
11.3.3 Vesicles in Cells 431
Vesicles Are Used for a Variety of Cellular Transport
Processes 431
There Is a Fixed Free-Energy Cost Associated with
Spherical Vesicles of All Sizes 433
Vesicle Formation Is Assisted by Budding Proteins 434
There Is an Energy Cost to Disassemble Coated
Vesicles 435
11.3.4 Fusion and Fission 435
1 1.4 MEMBRANES AND SHAPE 436
11.4.1 The Shapes of Organelles 437
The Surface Area of Membranes Due to Pleating Is
So Large That Organelles Can Have Far More Area
than the Plasma Membrane 437
11.4.2 The Shapes of Cells 439
The Equilibrium Shapes of Red Blood Cells Can
Be Found by Minimizing the Free Energy 441
1 1.5 THE ACTIVE MEMBRANE 441
11.5.1 Mechanosensitive Ion Channels and Membrane
Elasticity 441
Mechanosensitive Ion Channels Respond to
Membrane Tension 441
11.5.2 Elastic Deformations of Membranes Produced
by Proteins 443
Proteins Induce Elastic Deformations in the
Surrounding Membrane 443
Protein-induced Membrane Bending Has an
Associated Free-Energy Cost 444
11.5.3 One-Dimensional Solution for MscL 444
Membrane Deformations Can Be Obtained by
Minimizing the Membrane Free Energy 444
The Membrane Surrounding a Channel Protein
Produces a Line Tension 446
11.6 SUMMARY AND CONCLUSIONS 450
11.7 PROBLEMS 450
11.8 FURTHER READING 453
11.9 REFERENCES 453
Chapter 12 The Mathematics of Water 457
12.1 PUTTING WATER IN ITS PLACE 457
12.2 HYDRODYNAMICS OF WATER AND OTHER FLUIDS 458
12.2.1 Water as a Continuum 458
Though Fluids Are Comprised of Molecules It Is
Possible to Treat Them as a Continuous Medium 458
12.2.2 What Can Newton Tell Us? 458
Gradients in Fluid Velocity Lead to Shear Forces 458
12.2.3 F= ma for Fluids 460
12.2.4 The Newtonian Fluid and the Navier—Stokes
Equations 463
The Velocity of Fluids at Surfaces Is Zero 464
1 2.3 THE RIVER WITHIN: FLUID DYNAMICS OF BLOOD 464
12.3.1 Boats in the River: Leukocyte Rolling and Adhesion 466
1 2.4 THE LOW REYNOLDS NUMBER WORLD 468
12.4.1 Stokes Flow: Consider a Spherical Bacterium 468
12.4.2 Stokes Drag in Single-Molecule Experiments 470
Stokes Drag Is Irrelevant for Optical Tweezers
Experiments 470
12.4.3 Dissipative Time Scales and the Reynolds Number 471
12.4.4 Fish Cotta Swim, Birds Gotta Fly, and Bacteria
Gotta Swim Too 472
Reciprocal Deformation of the Swimmer s Body
Does Not Lead to Net Motion at Low Reynolds
Number 474
12.4.5 Centrifugation and Sedimentation: Spin It Down 475
12.5 SUMMARY AND CONCLUSIONS 477
12.6 PROBLEMS 477
12.7 FURTHER READING 479
12.8 REFERENCES 479
Chapter 13 A Statistical View of
Biological Dynamics 481
13.1 DIFFUSION IN THE CELL 481
13.1.1 Active vs Passive Transport 482
13.1.2 Biological Distances Measured in Diffusion Times 482
The Time It Takes a Diffusing Molecule to Travel
a Distance L Crows as the Square of the
Distance 484
Diffusion Is Not Effective Over Large Cellular
Distances 484
13.1.3 Random Walk Redux 486
1 3.2 CONCENTRATION FIELDS AND DIFFUSIVE DYNAMICS 487
Fick s Law Tells Us How Mass Transport Currents
Arise as a Result of Concentration Gradients 488
The Diffusion Equation Results from Fick s Law
and Conservation of Mass 490
1 3.2.1 Diffusion by Summing Over Microtrajectories 491
13.2.2 Solutions and Properties of the Diffusion Equation 496
Concentration Profiles Broaden Over Time in a
Very Precise Way 496
13.2.3 FRAPand FCS 498
1 3.2.4 Drunks on a Hill: The Smoluchowski Equation 502
13.2.5 The Einstein Relation 503
13.3 DIFFUSION TO CAPTURE 505
13.3.1 Modeling the Cell Signaling Problem 506
Perfect Receptors Result in a Rate of Uptake
4nDc0a 507
A Distribution of Receptors Is Almost as Good as a
Perfectly Absorbing Sphere 508
13.3.2 A Universal Rate for Diffusion-Limited Chemical
Reactions 510
1 3.4 SUMMARY AND CONCLUSIONS 51 1
13.5 PROBLEMS 511
13.6 FURTHER READING 512
13.7 REFERENCES 512
Chapter 14 Life in Crowded and
Disordered Environments 513
14.1 CROWDING, LINKAGE, AND ENTANGLEMENT 513
14.1.1 The Cell Is Crowded 514
14.1.2 Macromolecular Networks: The Cytoskeleton
and Beyond 515
14.1.3 Crowding on Membranes 517
14.1.4 Consequences of Crowding 517
Crowding Alters Biochemical Equilibria 517
Crowding Alters the Kinetics within Cells 518
14.2 EQUILIBRIA IN CROWDED ENVIRONMENTS 520
14.2.1 Crowding and Binding 520
Lattice Models of Solution Provide a Simple Picture
of the Role of Crowding in Biochemical Equilibria 520
14.2.2 Osmotic Pressures in Crowded Solutions 523
Osmotic Pressure Reveals Crowding Effects 523
14.2.3 Depletion Forces: Order from Disorder 524
The Close Approach of Large Particles Excludes
Smaller Particles Between Them, Resulting in
an Entropic Force 524
Depletion Forces Can Induce Entropic Ordering! 529
14.2.4 Excluded Volume and Polymers 530
Excluded Volume Leads to an Effective Repulsion
between Molecules 530
Self-avoidance Between the Monomers of a
Polymer Leads to Polymer Swelling 531
14.3 CROWDED DYNAMICS 533
14.3.1 Crowding and Reaction Rates 533
Enzymatic Reactions in Cells Can Proceed Faster
than the Diffusion Limit Using Substrate Channeling 533
Protein Folding Is Facilitated by Chaperones 534
14.3.2 Diffusion in Crowded Environments 535
14.4 SUMMARY AND CONCLUSIONS 536
14.5 PROBLEMS 537
14.6 FURTHER READING 538
14.7 REFERENCES 538
Chapter 15 Rate Equations and
Dynamics in the Cell 539
15.1 BIOLOGICAL STATISTICAL DYNAMICS: A FIRST LOOK 539
15.1.1 Cells as Chemical Factories 540
15.1.2 Dynamics of the Cytoskeleton 541
15.2 A CHEMICAL PICTURE OF BIOLOGICAL DYNAMICS 545
15.2.1 The Rate Equation Paradigm 545
Chemical Concentrations Vary in Both Space and Time 545
Rate Equations Describe the Time Evolution of
Concentrations 546
15.2.2 All Good Things Must End 546
Macromolecular Decay can be Described by a
Simple, First-order Differential Equation 546
1 5.2.3 A Single-Molecule View of Degradation: Statistical
Mechanics Over Trajectories 548
Molecules Fall Apart with a Characteristic Lifetime 548
Decay Processes Can Be Described with Two-state
Trajectories 550
Decay of One Species Corresponds to Growth in the
Number of a Second Species 551
15.2.4 Bimolecular Reactions 553
Chemical Reactions Can Increase the Concentration
of a Given Species 553
Equilibrium Constants Have a Dynamical
Interpretation in Terms of Reaction Rates 555
15.2.5 Dynamics of Ion Channels as a Case Study 555
Rate Equations for Ion Channels Characterize the
Time Evolution of the Open and Closed Probability 556
15.2.6 Rapid Equilibrium 558
Some Chemical Reactions Are Linked Together in a
Sequence Resulting in Coupled Rate Equations 559
15.2.7 Michaelis—Menten and Enzyme Kinetics 563
1 5.3 THE CYTOSKELETON IS ALWAYS UNDER
CONSTRUCTION 566
15.3.1 The Eukaryotic Cytoskeleton 566
The Cytoskeleton Is a Dynamical Structure That Is
Always Under Construction 566
1 5.3.2 The Curious Case of the Bacterial Cytoskeleton 567
1 5.4 SIMPLE MODELS OF CYTOSKELETAL POLYMERIZATION 569
The Dynamics of Polymerization Can Involve Many
Distinct Physical and Chemical Effects 570
15.4.1 The Equilibrium Polymer 571
Equilibrium Models of Cytoskeletal Filaments
Describe the Distribution of Polymer Lengths for
Simple Polymers 571
An Equilibrium Polymer Fluctuates in Time 573
1 5.4.2 Rate Equation Description of Cytoskeletal
Polymerization 575
Polymerization Reactions can be described by
Rate Equations 575
The Time Evolution of the Probability Distribution
Pn(t) can be Written Using a Rate Equation 577
Rates of Addition and Removal of Monomers Are
Often Different on the Two Ends of Cytoskeletal
Filaments 579
1 5.4.3 Nucleotide Hydrolysis and Cytoskeletal
Polymerization 581
ATP Hydrolysis Sculpts the Molecular Interface
Resulting in Distinct Rates at the Ends of
Cytoskeletal Filaments 581
1 5.4.4 Dynamic Instability: A Toy Model of the Cap 583
A Toy Model of Dynamic Instability Assumes That
Catastrophe Occurs When Hydrolyzed Nucleotides
Are Present at the Growth Front 583
15.5 SUMMARY AND CONCLUSIONS 586
15.6 PROBLEMS 587
15.7 FURTHER READING 588
15.8 REFERENCES 588
Chapter 16 Dynamics of Molecular Motors 589
16.1 THE DYNAMICS OF MOLECULAR MOTORS:
LIFE IN THE FAST LANE 589
16.1.1 Translational Motors: Beating the Diffusive Speed Limit 591
The Motion of Eukaryotic Cilia and Flagella Is
Driven by Translational Motors 594
Muscle Contraction Is Mediated by Myosin Motors 595
16.1.2 Rotary Motors 600
16.1.3 Polymerization Motors: Pushing by Growing 603
16.1.4 Translocation Motors: Pushing by Pulling 603
16.2 RECTIFIED BROWNIAN MOTION AND MOLECULAR
MOTORS 605
16.2.1 The Random Walk Yet Again 605
Molecular Motors Can Be Thought of as Random
Walkers 605
16.2.2 The One-state Model 606
The Dynamics of a Molecular Motor Can Be
Written Using a Master Equation 607
The Driven Diffusion Equation Can Be
Transformed into an Ordinary Diffusion Equation 609
16.2.3 Motor Stepping from a Free-Energy Perspective 612
16.2.4 The Two-state Model 616
The Dynamics of a Two-State Motor Is Described
by Two Coupled Rate Equations 617
Internal States Reveal Themselves in the Form
of the Waiting Time Distribution 620
16.2.5 More General Motor Models 622
16.2.6 Coordination of Motor Protein Activity 624
16.2.7 Rotary Motors 626
16.3 POLYMERIZATION AND TRANSLOCATION AS
MOTOR ACTION 629
16.3.1 The Polymerization Ratchet 629
The Polymerization Ratchet Is Based on a
Polymerization Reaction That Is Maintained
Out of Equilibrium 631
The Polymerization Ratchet Force—Velocity Can Be
Obtained by Solving a Driven Diffusion Equation 634
16.3.2 Force Generation by Growth 636
Polymerization Forces Can Be Measured Directly 636
Polymerization Forces Are Used to Center Cellular
Structures 638
16.3.3 The Translocation Ratchet 639
Protein Binding Can Speed up Translocation
through a Ratcheting Mechanism 639
The Translocation Time Can Be Estimated by
Solving a Driven Diffusion Equation 641
16.4 SUMMARY AND CONCLUSIONS 642
16.5 PROBLEMS 643
16.6 FURTHER READING 644
16.7 REFERENCES 645
Chapter 17 Biological Electricity and the
Hodgkin—Huxley Model 647
17.1 THE ROLE OF ELECTRICITY IN CELLS 647
1 7.2 THE CHARGE STATE OF THE CELL 648
17.2.1 The Electrical Status of Cells and Their Membranes 648
1 7.2.2 Electrochemical Equilibrium and the Nernst
Equation 649
Ion Concentration Differences Across Membranes
Lead to Potential Differences 649
17.3 MEMBRANE PERMEABILITY: PUMPS AND CHANNELS 651
A Nonequilibrium Charge Distribution Is Set Up
Between the Cell Interior and the External World 651
Signals in Cells Are Often Mediated by the
Presence of Electrical Spikes Called Action
Potentials 652
17.3.1 Ion Channels and Membrane Permeability 653
Ion Permeability Across Membranes Is Mediated
by Ion Channels 654
A Simple Two-State Model Can Describe Many
of the Features of Voltage Gating of Ion Channels 654
1 7.3.2 Maintaining a Nonequilibrium Charge State 656
Ions Are Pumped Across the Cell Membrane
Against an Electrochemical Gradient 656
17.4 THE ACTION POTENTIAL 659
17.4.1 Membrane Depolarization: The Membrane as a
Bistable Switch 659
Coordinated Muscle Contraction Depends Upon
Membrane Depolarization 659
A Patch of Cell Membrane Can Be Modeled as an
Electrical Circuit 661
The Difference Between the Membrane Potential
and the Nernst Potential Leads to an Ionic Current
Across the Cell Membrane 663
Voltage-gated Channels Result in a Nonlinear
Current—Voltage Relation for the Cell Membrane 663
A Patch of Membrane Acts as a Bistable Switch 666
The Dynamics of Voltage Relaxation Can Be
Modeled Using an RC Circuit 667
1 7.4.2 The Cable Equation 668
17.4.3 Depolarization Waves 670
Waves of Membrane Depolarization Rely on Sodium
Channels Switching into the Open State 670
17.4.4 Spikes 672
17.4.5 Hodgkin—Huxley and Membrane Transport 674
Inactivation of Sodium Channels Leads to
Propagating Spikes 674
17.5 SUMMARY AND CONCLUSIONS 676
17.6 PROBLEMS 676
17.7 FURTHER READING 677
17.8 REFERENCES 677
Chapter 18 Sequences, Specificity, and
Evolution 681
18.1 BIOLOGICAL INFORMATION 681
18.1.1 Why Sequences? 683
18.1.2 Genomes and Sequences by the Numbers 683
18.2 SEQUENCE ALIGNMENT AND HOMOLOGY 685
Sequence Comparison Can Sometimes Reveal Deep
Functional and Evolutionary Relationships Between
Genes, Proteins, and Organisms 686
18.2.1 The HP Model as a Coarse-grained Model for
Bioinformatics 688
18.2.2 Scoring Success 691
A Score Can Be Assigned to Different Alignments
Between Sequences 691
Comparison of Full Amino Acid Sequences
Requires a 20 by 20 Scoring Matrix 692
Even Random Sequences Have a Nonzero Score 694
The Extreme Value Distribution Determines the
Probability That a Given Alignment Score Would
Be Found by Chance 696
False Positives Increase as the Threshold for
Acceptable Expect Values (also Called E-Values)
Is Reduced 698
Structural and Functional Similarity Do Not Always
Guarantee Sequence Similarity 699
18.3 SEQUENCES AND EVOLUTION 701
18.3.1 Evolution by the Numbers: Hemoglobin as a
Case Study in Sequence Alignment 702
Sequence Similarity Is Used as a Temporal
Yardstick to Determine Evolutionary Distances 702
18.3.2 Evolution and Drug Resistance 703
18.3.3 The Evolution of Viruses 706
18.3.4 Phylogenetic Trees 708
18.4 THE MOLECULAR BASIS OF FIDELITY 710
18.4.1 Keeping It Specific: Beating Thermodynamic Specificity 711
The Specificity of Biological Recognition Often Far
Exceeds the Limit Dictated by Free-Energy Differences 711
High Specificity Costs Energy 715
18.5 SUMMARY AND CONCLUSIONS 717
18.6 PROBLEMS 717
18.7 FURTHER READING 719
18.8 REFERENCES 720
Chapter 19 Network Organization in
Space and Time 721
19.1 CHEMICAL AND INFORMATIONAL ORGANIZATION
IN THE CELL 721
Many Chemical Reactions in the Cell are Linked
in Complex Networks 721
Genetic Networks Describe the Linkages Between
Different Genes and Their Products 722
Developmental Decisions Are Made by Regulating
Genes 723
Gene Expression Is Measured Quantitatively in
Terms of How Much, When, and Where 723
19.2 GENETIC NETWORKS: DOING THE RIGHT THING
AT THE RIGHT TIME 726
Promoter Occupancy Is Dictated by the Presence of
Regulatory Proteins Called Transcription Factors 727
19.2.1 The Molecular Implementation of Regulation:
Promoters, Activators, and Repressors 727
Repressor Molecules Are the Proteins That Implement
Negative Control 727
Activators Are the Proteins That Implement Positive
Control 729
Genes Can Be Regulated During Processes Other
Than Transcription 729
19.2.2 The Mathematics of Recruitment and Rejection 729
Recruitment of Proteins Reflects Cooperativity
Between Different DNA Binding Proteins 729
The Regulation Factor Dictates How the Bare RNA
Polymerase Binding Probability Is Altered by
Transcription Factors 732
Activator Bypass Experiments Show That Activators
Work by Recruitment 734
Repressor Molecules Reduce the Probability
Polymerase Will Bind to the Promoter 735 ..
i
19.2.3 Transcriptional Regulation by the Numbers:
Binding Energies and Equilibrium Constants 737
Equilibrium Constants Can be Used To Determine
Regulation Factors 737
19.2.4 A Simple Statistical Mechanics Model of Positive and
Negative Regulation 738
19.2.5 The/ac Operon 740
The lac Operon Has Features of Both Negative
and Positive Regulation 740
The Free Energy of DNA Looping Affects the
Repression of the lac Operon 743
19.3 REGULATORY DYNAMICS 747
19.3.1 The Dynamics of RNA Polymerase and the Promoter 747
The Concentrations of Both RNA and Protein Can
Be Described Using Rate Equations 747
19.3.2 Genetic Switches: Natural and Synthetic 748
19.3.3 Genetic Networks That Oscillate: The Repressilator 753
19.3.4 Putting Space in the Model: Reaction—Diffusion
Models 759
19.4 CELLULAR FAST RESPONSE: SIGNALING 760
19.4.1 Bacterial Chemotaxis 760
19.4.2 Biochemistry on a Leash 765
Tethering Increases the Local Concentration of a
Ligand 765
Signaling Networks Help Cells Decide When and
Where to Grow Their Actin Filaments for Motility 766
Synthetic Signaling Networks Permit a Dissection
of Signaling Pathways 766
19.5 SUMMARY AND CONCLUSIONS 770
19.6 APPENDIX: STABILITY ANALYSIS FOR THE GENETIC
SWITCH 770
19.7 PROBLEMS 772
19.8 FURTHER READINC 773
19.9 REFERENCES 774
Chapter 20 Whither Physical Biology? 775
20.1 QUANTITATIVE DATA DEMAND
QUANTITATIVE MODELS 775
20.2 WRONG AGAIN 778
20.3 ORDER-OF-MAGNITUDE BIOLOGY AND
BEYOND 779
20.4 DIFFICULTIES ON THEORY 780
20.5 A CHARGE TO THE READER 785
20.6 FURTHER READING 785
20.7 REFERENCES 786
|
| adam_txt |
CONTENTS
Detailed Contents *v
Special Sections xx'v
Chapter 1: Why: Biology by the Numbers 3
Chapter 2: What and Where: Construction Plans for Cells
and Organisms 29
Chapter 3: When: Stopwatches at Many Scales 75
Chapter 4: Who: "Bless the Little Beasties" 119
Chapter 5: Mechanical and Chemical Equilibrium in the
Living Cell l(|7
Chapter 6: Entropy Rules! 215 "\
Chapter 7: Two-State Systems: From Ion Channels to
Cooperative Binding 257
Chapter 8: Random Walks and the Structure
of Macromolecules 281
Chapter 9: Electrostatics for Salty Solutions 327
Chapter 10: Beam Theory: Architecture for Cells
and Skeletons 357
Chapter 11: Biological Membranes: Life in Two Dimensions 407
Chapter 12: The Mathematics of Water 457
Chapter 13: A Statistical View of Biological Dynamics 481
Chapter 14: Life in Crowded and Disordered Environments 513
Chapter IS: Rate Equations and Dynamics in the Cell 539
Chapter 16: Dynamics of Molecular Motors 589
Chapter 17: Biological Electricity and the Hodgkin-Huxley
Model 647
Chapter 18: Sequences, Specificity, and Evolution 681
Chapter 19: Network Organization in Space and Time 721
Chapter 20: Whither Physical Biology? 775
Index 787
DETAILED CONTENTS
Chapter 1 Why: Biology by the Numbers 3
1.1 PHYSICAL BIOLOGY OF THE CELL 3
Model Building Requires a Substrate of Biological
Facts and Physical (or Chemical) Principles 4
1.2 THE STUFF OF LIFE 4
Organisms Are Constructed from Four Great Classes
of Macromolecules 5
Nucleic Acids and Proteins Are Polymer Languages
with Different Alphabets 6
1.3 MODEL BUILDING IN BIOLOGY 9
1.3.1 Models as Idealizations 9
Biological Stuff Can Be Idealized Using Many
Different Physical Models 10
1.3.2 Cartoons and Models 15
Biological Cartoons Select Those Features of
the Problem Thought to be Essential 1 5
Quantitative Models Can Be Built by
Mathematicizing the Cartoons 18
1.4 QUANTITATIVE MODELS AND THE POWER
OF IDEALIZATION 1 9
1.4.1 On the Springiness of Stuff 19
1.4.2 The Toolbox of Fundamental Physical Models 20
1.4.3 The Role of Estimates 22
1.4.4 On Being Wrong 23
1.4.5 Rules of Thumb: Biology by the Numbers 25
1.5 SUMMARY AND CONCLUSIONS 25
1.6 FURTHER READING 27
1.7 REFERENCES 27
Chapter 2 What and Where: Construction
Plans for Cells and Organisms 29
2.1 AN ODE TO E. COU 29
2.1.1 The Bacterial Standard Ruler 30
The Bacterium E. co//Will Serve as Our Standard Ruler 30
2.1.2 Taking the Molecular Census 32
The Cellular Interior Is Highly Crowded with Mean
Spacings Between Molecules That Are
Comparable to Molecular Dimensions 36
2.1.3 Looking Inside Cells 37
2.1.4 Where Does E. coli Fit? 39
Biological Structures Exist Over a Huge Range
of Scales 39
2.2 CELLS AND STRUCTURES WITHIN THEM 40
2.2.1 Cells: A Rogue's Gallery 40
Cells Come in a Wide Variety of Shapes and Sizes
and with a Huge Range of Functions 41
Cells from Humans Have a Huge Diversity of
Structure and Function 45
2.2.2 The Cellular Interior: Organelles 47
2.2.3 Macromolecular Assemblies: The Whole is Greater
than the Sum of the Parts 51
Macromolecules Come Together to Form Assemblies 51
Helical Motifs are Seen Repeatedly in Molecular
Assemblies 51
Macromolecular Assemblies Are Arranged in
Superstructures 53
2.2.4 Viruses as Assemblies 53
2.2.5 The Molecular Architecture of Cells: From Protein
Data Bank (PDB) Files to Ribbon Diagrams 57
Macromolecular Structure Is Characterized
Fundamentally by Atomic Coordinates 57
Chemical Croups Allow Us to Classify Parts of
the Structure of Macromolecules 58
2.3 TELESCOPING UP IN SCALE: CELLS DON'T
CO IT ALONE 60
2.3.1 Multicellularity as One of Evolution's Great
Inventions 61
Bacteria Interact to Form Colonies such as Biofilms 61
Teaming Up in a Crisis: Lifestyle of Dictyostelium
discoideum 62
Multicellular Organisms Have Many Distinct
Communities of Cells 64
2.3.2 Cellular Structures from Tissues to Nerve Networks 65
One Class of Multicellular Structures is the
Epithelial Sheets 65
Tissues Are Collections of Cells and Extracellular
Matrix 66
Nerve Cells Form Complex, Multicellular Complexes 66
2.3.3 Multicellular Organisms 67
Cells Differentiate During Development Leading
to Entire Organisms 68
The Cells of the Nematode Worm Caenorhabditis
elegans Have Been Charted Yielding a Cell-by-Cell
Picture of the Organism 69
Higher-Level Structures Exist as Colonies
of Organisms 71
2.4 SUMMARY AND CONCLUSIONS 71
2.5 PROBLEMS 72
2.6 FURTHER READING 73
2.7 REFERENCES 73
Chapter 3 When: Stopwatches at Many
Scales 75
3.1 THE HIERARCHY OF TEMPORAL SCALES 75
3.1.1 The Pageant of Biological Processes 77
Biological Processes Are Characterized by a Huge
Diversity of Time Scales 77
3.1.2 The Evolutionary Stopwatch 83
3.1.3 The Cell Cycle and the Standard Clock 87
The E. coli Cell Cycle Will Serve as Our Standard
Stopwatch 87
3.1.4 Three Views of Time in Biology 89
3.2 PROCEDURAL TIME 90
3.2.1 The Machines (or Processes) of the Central Dogma 90
The Central Dogma Describes the Processes
Whereby the Genetic Information Is Expressed
Chemically 90
The Processes of the Central Dogma Are Carried
Out by Sophisticated Molecular Machines 91
3.2.2 Clocks and Oscillators 93
Developing Embryos Divide on a Regular Schedule
Dictated by an Internal Clock 94
Diurnal Clocks Allow Cells and Organisms to Be
on Time Everyday 94
3.3 RELATIVE TIME 97
3.3.1 Checkpoints and the Cell Cycle 98
The Eukaryotic Cell Cycle Consists of Four Phases
Involving Molecular Synthesis and Organization 98
3.3.2 Measuring Relative Time 100
Genetic Networks Are Collections of Genes Whose
Expression Is Interrelated 100
The Formation of the Bacterial Flagellum Is
Intricately Organized in Space and Time 101
3.3.3 Killing the Cell: The Life Cycles of Viruses 102
Viral Life Cycles Include a Series of Self-Assembly
Processes 102
3.3.4 The Process of Development 104
3.4 MANIPULATED TIME 106
3.4.1 Chemical Kinetics and Enzyme Turnover 107
3.4.2 Beating the Diffusive Speed Limit 108
Diffusion Is the Random Motion of Microscopic
Particles in Solution 109
Diffusion Times Depend upon the Length Scale 109
Molecular Motors Move Cargo over Large
Distances in a Directed Way 110
Membrane Bound Proteins Transport Molecules
from One Side of a Membrane to the Other 11 2
3.4.3 Beating the Replication Limit 11 3
3.4.4 Eggs and Spores: Planning for the Next Generation 114
3.5 SUMMARY AND CONCLUSIONS 115
3.6 PROBLEMS 115
3.7 FURTHER READING 117
3.8 REFERENCES 117
Chapter 4 Who: "Bless the Little Beasties" 119
4.1 CHOOSING A GRAIN OF SAND 1 19
Modern Genetics Began with the Use of Peas
as a Model System 120
4.1.1 Biochemistry and Genetics 120
4.2 HEMOGLOBIN AS A MODEL PROTEIN 124
4.2.1 Hemoglobin, Receptor—Ligand Binding, and the
Other Bohr 125
The Binding of Oxygen to Hemoglobin Has Served
as a Model System for Ligand—Receptor
Interactions More Generally 125
Quantitative Analysis of Hemoglobin Is Based upon
Measuring the Fractional Occupancy of the Oxygen
Binding Sites as a Function of Oxygen Pressure 125
4.2.2 Hemoglobin and the Origins of Structural Biology 126
The Study of the Mass of Hemoglobin Was Central
in the Development of Centrifugation 127
Structural Biology Has Its Roots in the
Determination of the Structure of Hemoglobin 127
4.2.3 Hemoglobin and Molecular Models of Disease 127
4.2.4 The Rise of Allostery and Cooperativity 128
4.3 BACTERIOPHAGE AND MOLECULAR BIOLOGY 129
4.3.1 Bacteriophage and the Origins of Molecular Biology 129
Bacteriophage Have Sometimes Been Called the
"Hydrogen Atoms of Biology" 129
Experiments on Phage and Their Bacterial Hosts
Demonstrated That Natural Selection Is
Operative in Microscopic Organisms 130
The Hershey—Chase Experiment Both Confirmed the
Nature of Genetic Material and Elucidated One
of the Mechanisms of Viral DNA Entry into Cells 130
Experiments on Phage T4 Demonstrated the Sequence
Hypothesis of Collinearity of DNA and Proteins 131
The Triplet Nature of the Genetic Code and DNA
Sequencing were Carried Out on Phage Systems 132
Phage Were Instrumental in Elucidating the
Existence of mRNA 133
General Ideas about Gene Regulation Were Learned
from the Study of Viruses as a Model System 133
4.3.2 Bacteriophage and Modern Biophysics 134
Many Single-Molecule Studies of Molecular Motors
Have Been Performed on Motors from Bacteriophage 1 34
4.4 A TALE OF TWO CELLS: E. COLI AS A MODEL SYSTEM 1 36
4.4.1 Bacteria and Molecular Biology 136
4.4.2 E. coli and the Central Dogma 1 36
The Hypothesis of Conservative Replication Has
Falsifiable Consequences 136
Extracts from E. coli Were Used to Perform In Vitro
Synthesis of DNA, mRNA, and Proteins 138
4.4.3 The lac Operon as the "Hydrogen Atom" of
Genetic Circuits 138
Gene Regulation in E. coli Serves as a Model
for Genetic Circuits in General 138
The lac Operon is a Genetic Network Which
Controls the Production of the Enzymes
Responsible for Digesting the Sugar Lactose 1 39
4.4.4 Signaling and Motility: The Case of Bacterial
Chemotaxis 140
E. coli Has Served as a Model System for the
Analysis of Cell Motility 140
4.5 YEAST: FROM BIOCHEMISTRY TO THE CELL CYCLE 142
Yeast Has Served as a Model System Leading to
Insights in Contexts Ranging from Vitalism to the
Functioning of Enzymes to Eukaryotic Gene
Regulation 142
4.5.1 Yeast and the Rise of Biochemistry 143
4.5.2 Dissecting the Cell Cycle 144
4.5.3 Deciding Which Way Is Up: Yeast and Polarity 145
4.5.4 Dissecting Membrane Traffic 147
4.5.5 Genomics and Proteomics 148
4.6 FLIES AND MODERN BIOLOGY 151
4.6.1 Flies and the Rise of Modern Genetics 151
Drosophila melanogaster Has Served as a Model
System for Studies Ranging from Genetics to
Development to the Functioning of the Brain
and Even Behavior 1 51
4.6.2 How the Fly Cot His Stripes 1 52
4.7 OF MICE AND MEN 154
4.8 THE CASE FOR EXOTICA 155
4.8.1 Specialists and Experts 155
4.8.2 The Squid Giant Axon and Biological Electricity 1 57
There Is a Steady-State Potential Difference Across
the Membrane of Nerve Cells 1 57
Nerve Cells Propagate Electrical Signals and Use
Them to Communicate with Each Other 1 59
4.8.3 Exotica Toolkit 159
4.9 SUMMARY AND CONCLUSIONS 160
4.10 PROBLEMS 161
4.11 FURTHER READING 162
4.12 REFERENCES 164
Chapter 5 Mechanical and Chemical
Equilibrium in the Living Cell 167
5.1 ENERGY AND THE LIFE OF CELLS 167
5.1.1 The Interplay of Deterministic and Thermal Forces 168
Thermal Jostling of Particles Must Be Accounted
for in Biological Systems 169
5.1.2 Constructing the Cell: Managing the Mass and
Energy Budget of the Cell 170
5.2 BIOLOGICAL SYSTEMS AS MINIMIZERS 180
5.2.1 Equilibrium Models for Out of Equilibrium Systems 180
Equilibrium Models Can Be Used for
Nonequilibrium Problems If Certain Processes
Happen Much Faster than Others 180
5.2.2 Proteins in "Equilibrium" 182
Protein Structures are Free-Energy Minimizers 183
5.2.3 Cells in "Equilibrium" 184
5.2.4 Mechanical Equilibrium from a Minimization
Perspective 184
The Mechanical Equilibrium State Is Obtained by
Minimizing the Potential Energy 184
5.3 THE MATHEMATICS OF SUPERLATIVES 187
5.3.1 The Mathematization of Judgement: Functions
and Functionals 188
Functionals Deliver a Number for Every Function
They Are Given 188
5.3.2 The Calculus of Superlatives 190
Finding the Maximum and Minimum Values of a
Function Requires That We Find Where the Slope
of the Function Equals Zero 190
5.4 CONFIGURATIONAL ENERGY 192
In Mechanical Problems, Potential Energy
Determines the Equilibrium Structure 192
5.4.1 Hooke's Law: Actin to Lipids 195
There Is a Linear Relation Between Force and
Extension of a Beam 195
The Energy to Deform an Elastic Material Is a
Quadratic Function of the Strain 196
5.5 STRUCTURES AS FREE ENERGY MINIMIZERS 198
The Entropy Is a Measure of the Microscopic
Degeneracy of a Macroscopic State 198
5.5.1 Entropy and Hydrophobicity 201
Hydrophobicity Results from Depriving Water
Molecules of Some of Their Configurational
Entropy 201
Amino Acids Can Be Classified According to Their
Hydrophobicity 203
When in Water, Hydrocarbon Tails on Lipids Have
an Entropy Cost 203
5.5.2 Gibbs and the Calculus of Equilibrium 204
Thermal and Chemical Equilibrium Are Obtained
by Maximizing the Entropy 204
5.5.3 Structure as a Competition 206
Free Energy Minimization Can Be Thought of as an
Alternative Formulation of Entropy Maximization 207
5.5.4 An Ode to AC 208
The Free Energy Reflects a Competition Between
Energy and Entropy 208
5.6 SUMMARY AND CONCLUSIONS 209
5.7 APPENDIX: THE EULER—LACRANGE
EQUATIONS, FINDING THE SUPERLATIVE 210
Finding the Extrema of Functionals is Carried out
Using the Calculus of Variations 210
The Euler—Lagrange Equations Let Us Minimize
Functionals by Solving Differential Equations 210
5.8 PROBLEMS 211
5.9 FURTHER READING 213
5.10 REFERENCES 214
Chapter 6 Entropy Rules! 215
6.1 THE ANALYTICAL ENGINE OF STATISTICAL
MECHANICS 21 5
The Probability of Different Microstates Is
Determined by Their Energy 21 7
6.1.1 A First Look at Ligand—Receptor Binding 219
6.1.2 The Statistical Mechanics of Gene Expression:
RNA Polymerase and the Promoter 222
A Simple Model of Gene Expression Is to Consider
the Probability of RNA Polymerase Binding at
the Promoter 224
Most Cellular RNA Polymerase Molecules Are
Bound to DNA 224
The Binding Probability of RNA Polymerase to Its
Promoter Is a Simple Function of the Number of
Polymerase Molecules and the Binding Energy 226
6.1.3 Classic Derivation of the Boltzmann Distribution 227
The Boltzmann Distribution Gives the Probability
of Microstates for a System in Contact with a
Thermal Reservoir 228
6.1.4 Boltzmann Distribution by Counting 230
Different Ways of Partitioning Energy Among
Particles Have Different Degeneracies 230
6.1.5 Boltzmann Distribution by Guessing 232
Maximizing the Entropy Corresponds to Making a
Best Guess When Faced with Limited Information 232
Entropy Maximization Can Be Used as a Tool for
Statistical Inference 234
The Boltzmann Distribution Is the Maximum
Entropy Distribution in Which the Average Energy
Is Prescribed as a Constraint 236
6.2 ON BEING IDEAL 237
6.2.1 Average Energy of a Molecule in a Gas 238
The Ideal Gas Entropy Reflects the Freedom to
Rearrange Molecular Positions and Velocities 238
6.2.2 Free Energy of Dilute Solutions 240
The Chemical Potential of a Dilute Solution Is a
Simple Logarithmic Function of the Concentration 240
6.2.3 Osmotic Pressure as an Entropic Spring 242
Osmotic Pressure Arises from Entropic Effects 242
Viruses, Membrane-Bound Organelles and Cells
are Subject to Osmotic Pressure 244
Osmotic Forces Have Been Used to Measure the
Interstrand Interactions of DNA 245
6.3 THE CALCULUS OF EQUILIBRIUM APPLIED:
LAW OF MASS ACTION 245
6.3.1 Law of Mass Action and Equilibrium Constants 246
Equilibrium Constants are Determined by Entropy
Maximization 246
6.4 APPLICATIONS OF THE CALCULUS OF EQUILIBRIUM 248
6.4.1 A Second Look at Ligand—Receptor Binding 248
6.4.2 Measuring Ligand—Receptor Binding 250
6.4.3 Beyond Simple Ligand—Receptor Binding:
The Hill Function 250
6.4.4 ATP Power 252
The Energy Released in ATP Hydrolysis Depends
Upon the Concentrations of Reactants and
Products 253
6.5 SUMMARY AND CONCLUSIONS 254
6.6 PROBLEMS 254
6.7 FURTHER READING 256
6.8 REFERENCES 256
Chapter 7 Two-State Systems: From Ion
Channels to Cooperative Binding 257
7.1 MACROMOLECULES WITH MULTIPLE STATES 257
7.1.1 The Internal State Variable Idea 257
The State of a Protein or Nucleic Acid Can Be
Characterized Mathematically Using a State Variable 258
7.1.2 Ion Channels as an Example of Internal State Variables 260
The Open Probability o of an Ion Channel Can Be
Computed Using Statistical Mechanics 261
7.2 STATE VARIABLE DESCRIPTION OF BINDING 264
7.2.1 The Cibbs Distribution: Contact with a Particle
Reservoir 264
The Cibbs Distribution Gives the Probability of
Microstates for a System in Contact with a Thermal
and a Particle Reservoir 264
7.2.2 Simple Ligand—Receptor Binding Revisited 266
7.2.3 Phosphorylation as an Example of Two Internal
State Variables 267
Phosphorylation Can Change the Energy Balance
Between Active and Inactive States 268
7.2.4 Hemoglobin as a Case Study in Cooperativity 269
The Binding Affinity of Oxygen for Hemoglobin
Depends upon Whether or Not Other Oxygens
Are Already Bound 270
A Toy Model of a Dimeric Hemoglobin (Dimoglobin)
Illustrates the Idea of Cooperativity 271
The Monod—Wyman—Changeux (MWC) Model
Provides a Simple Example of Cooperative Binding 272
Statistical Models of the Occupancy of Hemoglobin
Can Be Written Using Occupation Variables 274
There is a Logical Progression of Increasingly
Complex Binding Models for Hemoglobin 274
7.3 SUMMARY AND CONCLUSIONS 278
7.4 PROBLEMS 278
7.5 FURTHER READING 279
7.6 REFERENCES 280
Chapter 8 Random Walks and the
Structure of Macromolecules 281
8.1 WHAT IS A STRUCTURE: PDB OR Rc? 281
8.1.1 Deterministic vs Statistical Descriptions of
Structure 282
PDB Files Reflect a Deterministic Description of
Macromolecular Structure 282
Statistical Descriptions of Structure Emphasize
Average Size and Shape Rather Than Atomic
Coordinates 282
8.2 MACROMOLECULES AS RANDOM WALKS 282
Random Walk Models of Macromolecules View
Them as Rigid Segments Connected by Hinges 282
8.2.1 A Mathematical Stupor 283
In Random Walk Models of Polymers, Every
Macromolecular Configuration Is Equally Probable 283
The Mean Size of a Random Walk Macromolecule
Scales as the Square Root of the Number of
Segments, W 283
The Probability of a Given Macromolecular
Configuration Depends Upon Its Microscopic
Degeneracy 285
Entropy Determines the Elastic Properties of
Polymer Chains 286
The Persistence Length Is a Measure of the Length
Scale Over Which a Polymer Remains Roughly
Straight 289
8.2.2 How Big Is a Genome? 291
8.2.3 The Geography of Chromosomes 292
Genetic Maps and Physical Maps of Chromosomes
Describe Different Aspects of Chromosome Structure 292
Different Structural Models of Chromatin Are
Characterized by the Linear Packing Density of DNA 293
Spatial Organization of Chromosomes Shows
Elements of Both Randomness and Order 294
Chromosomes Are Tethered at Different Locations 295
Chromosome Territories Have Been Observed in
Bacterial Cells 298
Chromosome Territories in Vibrio cholerae Can Be
Explored using Models of Polymer Confinement
and Tethering 299
8.2.4 DNA Looping: From Chromosomes to Gene
Regulation 305
The Lac Repressor Molecule Acts Mechanistically by
Forming a Sequestered Loop in DNA 306
Looping of Large DNA Fragments Is Dictated by the
Difficulty of Distant Ends Finding Each Other 306
8.2.5 PCR, DNA Melting, and DNA Bubbles 307
DNA Melting Is the Result of Competition Between
the Energy Cost and the Entropy Cain of
Separating the Two Complementary Strands 308
DNA Melting Temperatures Can Be Estimated
Using a Random Walk Model 308
8.3 THE NEW WORLD OF SINCLE-MOLECULE MECHANICS 311
Single-Molecule Measurement Techniques Lead
to Force Spectroscopy 311
8.3.1 Force—Extension Curves: A New Spectroscopy 311
Different Macromolecules Have Different Force
Signatures When Subjected to Loading 311
8.3.2 Random Walk Models for Force—Extension Curves 313
The Low-Force Regime in Force—Extension Curves
Can Be Understood Using the Random Walk Model 313
8.4 PROTEINS AS RANDOM WALKS 317
8.4.1 Compact Random Walks and the Size of Proteins 318
The Compact Nature of Proteins Leads to an
Estimate of their Size 318
8.4.2 Hydrophobic and Polar Residues: The HP Model 318
The HP Model Divides Amino Acids into Two
Classes: Hydrophobic and Polar 319
8.4.3 HP Models of Protein Folding 321
8.5 SUMMARY AND CONCLUSIONS 324
8.6 PROBLEMS 324
8.7 FURTHER READING 325
8.8 REFERENCES 326
Chapter 9 Electrostatics for Salty
Solutions 327
9.1 WATER AS LIFE'S AETHER 327
9.2 THE CHEMISTRY OF WATER 329
9.2.1 pH and the Equilibrium Constant 329
Dissociation of Water Molecules Reflects a
Competition Between the Energetics of Binding
and the Entropy of Charge Liberation 329
9.2.2 The Charge on DNA and Proteins 330
The Charge State of Biopolymers Depends upon
the pH of the Solution 330
Different Amino Acids Have Different Charge States 331
9.2.3 Salt and Binding 331
9.3 ELECTROSTATICS FOR SALTY SOLUTIONS 332
9.3.1 An Electrostatics Primer 332
A Charge Distribution Produces an Electric Field
Throughout Space 333
The Flux of the Electric Field Measures the
Density of Electric Field Lines 333
The Electrostatic Potential Is an Alternative Basis
for Describing the Electrical State of a System 336
There Is an Energy Cost Associated With
Assembling a Collection of Charges 338
The Energy to Liberate Ions from Molecules Can
Be Comparable to the Thermal Energy 340
9.3.2 The Charged Life of a Protein 341
9.3.3 The Notion of Screening: Electrostatics in Salty
Solutions 342
Ions in Solution Are Spatially Arranged to Shield
Charged Molecules Such as DNA 342
The Size of the Screening Cloud Is Determined
by a Balance of Energy and Entropy of the
Surrounding Ions 343
9.3.4 The Poisson—Boltzmann Equation 346
The Distribution of Screening Ions Can Be Found
by Minimizing the Free Energy 346 :
The Screening Charge Decays Exponentially
Around Macromolecules in Solution 348
9.3.5 Viruses as Charged Spheres 349
9.4 SUMMARY AND CONCLUSION 352
9.5 PROBLEMS 353
9.6 FURTHER READING 355
9.7 REFERENCES 355
Chapter 10 Beam Theory: Architecture
for Cells and Skeletons 357
1 0.1 BEAMS ARE EVERYWHERE: FROM FLACELLA TO
THE CYTOSKELETON 357
One-Dimensional Structural Elements Are the Basis
of Much of Macromolecular and Cellular
Architecture 357
1 0.2 GEOMETRY AND ENERGETICS OF BEAM DEFORMATION 359
10.2.1 Stretch, Bend, and Twist 359
Beam Deformations Result in Stretching, Bending,
and Twisting 359
A Bent Beam Can Be Analyzed as a Collection of
Stretched Beams 359
The Energy Cost to Deform a Beam Is a Quadratic
Function of the Strain 361
10.2.2 Beam Theory and the Persistence Length: Stiffness
is Relative 363
Thermal Fluctuations Tend to Randomize the
Orientation of Biological Polymers 363
The Persistence Length Is the Length Over Which
a Polymer Is Roughly Rigid 363
The Persistence Length Characterizes the
Correlations in the Tangent Vectors at Different
Positions Along the Polymer 364
The Persistence Length Is Obtained by Averaging
Over All Configurations of the Polymer 364
10.2.3 Elasticity and Entropy: The Worm-like Chain 366
The Worm-like Chain Model Accounts for Both
the Elastic Energy and Entropy of Polymer
Chains 366
10.3 THE MECHANICS OF TRANSCRIPTIONAL REGULATION:
DNA LOOPING REDUX 368
10.3.1 The Lac Operon and Other Looping Systems 368
Transcriptional Regulation Can Be Effected by
DNA Looping 369
10.3.2 Energetics of DNA Looping 369
10.3.3 Putting It All Together: The J-Factor 370
10.4 DNA PACKING: FROM VIRUSES TO
EUKARYOTES 372
The Packing of DNA in Viruses and Cells Requires
Enormous Volume Compaction 372
10.4.1 The Problem of Viral DNA Packing 374
Structural Biologists Have Determined the Structure
of Many Parts in the Viral Parts List 375
The Packing of DNA in Viruses Results in a
Free-Energy Penalty 375
A Simple Model of DNA Packing in Viruses Uses
the Elastic Energy of Circular Hoops 377
DNA Self-Interactions Are also Important in
Establishing the Free Energy Associated with
DNA Packing in Viruses 379
DNA Packing in Viruses Is a Competition Between
Elastic and Interaction Energies 380
10.4.2 Constructing the Nucleosome 381
Nucleosome Formation Involves Both Elastic
Deformation and Interactions between Histones
and DNA 383
10.4.3 Equilibrium Accessibility of Nucleosomal DNA 383
The Equilibrium Accessibility of Sites within the
Nucleosome Depends upon How Far They Are
from the Unwrapped Ends 384
10.5 THE CYTOSKELETON AND BEAM THEORY 388
Eukaryotic Cells Are Threaded by Networks of
Filaments 388
10.5.1 The Cellular Interior: A Structural Perspective 388
Prokaryotic Cells Have Proteins Analogous to the
Eukaryotic Cytoskeleton 391
10.5.2 Stiffness of Cytoskeletal Filaments 391
The Cytoskeleton Can Be Viewed as a Collection
of Elastic Beams 391
10.5.3 Cytoskeletal Buckling 393
A Beam Subject to a Large Enough Force Will Buckle 393
10.5.4 Estimate of the Buckling Force 395
Beam Buckling Occurs at Smaller Forces for Longer
Beams 396
10.6 BEAMS AND BIOTECHNOLOGY 396
10.6.1 Biofunctionalized Cantilevers and Molecular
Recognition 397
Biofunctionalized Cantilevers Can Be Used to
Detect Macromolecules, Viruses, and Cells 397
Bending of Biofunctionalized Cantilevers Reflects a
Competition Between Bending Energy and
Surface Free Energy 398
10.7 SUMMARY AND CONCLUSIONS 400
1 0.8 APPENDIX: THE MATHEMATICS OF THE
WORM-LIKE CHAIN 401
10.9 PROBLEMS 403
10.10 FURTHER READING 405
10.11 REFERENCES 406
Chapter 11 Biological Membranes:
Life in Two Dimensions 407
11.1 THE NATURE OF BIOLOGICAL MEMBRANES 407
11.1.1 Cells and Membranes 407
Cells and Their Organelles Are Bound by Complex
Membranes 407
Electron Microscopy Provides a Window on Cellular
Membrane Structures 409
11.1.2 The Chemistry and Shape of Lipids 410
Membranes Are Built from a Variety of Molecules
That Have an Ambivalent Relationship with Water 410
The Shapes of Lipid Molecules Can Induce
Spontaneous Curvature to Membranes 412
11.1.3 The Liveliness of Membranes 414
Membrane Proteins Shuttle Mass Across
Membranes 415
Membrane Proteins Communicate Information
Across Membranes 416
Specialized Membrane Proteins Generate ATP 416
Membrane Proteins Can Be Reconstituted in
Vesicles 417
11.2 ON THE SPRINGINESS OF MEMBRANES 417
11.2.1 An Interlude on Membrane Geometry 417
Membrane Stretching Geometry Can Be Described
by a Simple Area Function 418
Membrane Bending Geometry Can Be Described
by a Simple Height Function, hix,y) 419
Membrane Compression Geometry Can Be
Described by a Simple Thickness Function, w(x,y) 422
Membrane Shearing Can Be Described by an Angle
Variable, 6 422
11.2.2 Free Energy of Membrane Deformation 422
There Is a Free Energy Penalty Associated with
Changing the Area of a Lipid Bilayer 422
There Is a Free Energy Penalty Associated with
Bending a Lipid Bilayer 423
There Is a Free Energy Penalty for Changing the
Thickness of a Lipid Bilayer 424
There Is an Energy Cost Associated with the
Gaussian Curvature 424
11.3 STRUCTURE, ENERGETICS, AND FUNCTION
Of VESICLES 426
11.3.1 Measuring Membrane Stiffness 426
Membrane Elastic Properties Can Be Measured by
Stretching Vesicles 426
11.3.2 Membrane Pulling 427
11.3.3 Vesicles in Cells 431
Vesicles Are Used for a Variety of Cellular Transport
Processes 431
There Is a Fixed Free-Energy Cost Associated with
Spherical Vesicles of All Sizes 433
Vesicle Formation Is Assisted by Budding Proteins 434
There Is an Energy Cost to Disassemble Coated
Vesicles 435
11.3.4 Fusion and Fission 435
1 1.4 MEMBRANES AND SHAPE 436
11.4.1 The Shapes of Organelles 437
The Surface Area of Membranes Due to Pleating Is
So Large That Organelles Can Have Far More Area
than the Plasma Membrane 437
11.4.2 The Shapes of Cells 439
The Equilibrium Shapes of Red Blood Cells Can
Be Found by Minimizing the Free Energy 441
1 1.5 THE ACTIVE MEMBRANE 441
11.5.1 Mechanosensitive Ion Channels and Membrane
Elasticity 441
Mechanosensitive Ion Channels Respond to
Membrane Tension 441
11.5.2 Elastic Deformations of Membranes Produced
by Proteins 443
Proteins Induce Elastic Deformations in the
Surrounding Membrane 443
Protein-induced Membrane Bending Has an
Associated Free-Energy Cost 444
11.5.3 One-Dimensional Solution for MscL 444
Membrane Deformations Can Be Obtained by
Minimizing the Membrane Free Energy 444
The Membrane Surrounding a Channel Protein
Produces a Line Tension 446
11.6 SUMMARY AND CONCLUSIONS 450
11.7 PROBLEMS 450
11.8 FURTHER READING 453
11.9 REFERENCES 453
Chapter 12 The Mathematics of Water 457
12.1 PUTTING WATER IN ITS PLACE 457
12.2 HYDRODYNAMICS OF WATER AND OTHER FLUIDS 458
12.2.1 Water as a Continuum 458
Though Fluids Are Comprised of Molecules It Is
Possible to Treat Them as a Continuous Medium 458
12.2.2 What Can Newton Tell Us? 458
Gradients in Fluid Velocity Lead to Shear Forces 458
12.2.3 F= ma for Fluids 460
12.2.4 The Newtonian Fluid and the Navier—Stokes
Equations 463
The Velocity of Fluids at Surfaces Is Zero 464
1 2.3 THE RIVER WITHIN: FLUID DYNAMICS OF BLOOD 464
12.3.1 Boats in the River: Leukocyte Rolling and Adhesion 466
1 2.4 THE LOW REYNOLDS NUMBER WORLD 468
12.4.1 Stokes Flow: Consider a Spherical Bacterium 468
12.4.2 Stokes Drag in Single-Molecule Experiments 470
Stokes Drag Is Irrelevant for Optical Tweezers
Experiments 470
12.4.3 Dissipative Time Scales and the Reynolds Number 471
12.4.4 Fish Cotta Swim, Birds Gotta Fly, and Bacteria
Gotta Swim Too 472
Reciprocal Deformation of the Swimmer's Body
Does Not Lead to Net Motion at Low Reynolds
Number 474
12.4.5 Centrifugation and Sedimentation: Spin It Down 475
12.5 SUMMARY AND CONCLUSIONS 477
12.6 PROBLEMS 477
12.7 FURTHER READING 479
12.8 REFERENCES 479
Chapter 13 A Statistical View of
Biological Dynamics 481
13.1 DIFFUSION IN THE CELL 481
13.1.1 Active vs Passive Transport 482
13.1.2 Biological Distances Measured in Diffusion Times 482
The Time It Takes a Diffusing Molecule to Travel
a Distance L Crows as the Square of the
Distance 484
Diffusion Is Not Effective Over Large Cellular
Distances 484
13.1.3 Random Walk Redux 486
1 3.2 CONCENTRATION FIELDS AND DIFFUSIVE DYNAMICS 487
Fick's Law Tells Us How Mass Transport Currents
Arise as a Result of Concentration Gradients 488
The Diffusion Equation Results from Fick's Law
and Conservation of Mass 490
1 3.2.1 Diffusion by Summing Over Microtrajectories 491
13.2.2 Solutions and Properties of the Diffusion Equation 496
Concentration Profiles Broaden Over Time in a
Very Precise Way 496
13.2.3 FRAPand FCS 498
1 3.2.4 Drunks on a Hill: The Smoluchowski Equation 502
13.2.5 The Einstein Relation 503
13.3 DIFFUSION TO CAPTURE 505
13.3.1 Modeling the Cell Signaling Problem 506
Perfect Receptors Result in a Rate of Uptake
4nDc0a 507
A Distribution of Receptors Is Almost as Good as a
Perfectly Absorbing Sphere 508
13.3.2 A "Universal" Rate for Diffusion-Limited Chemical
Reactions 510
1 3.4 SUMMARY AND CONCLUSIONS 51 1
13.5 PROBLEMS 511
13.6 FURTHER READING 512
13.7 REFERENCES 512
Chapter 14 Life in Crowded and
Disordered Environments 513
14.1 CROWDING, LINKAGE, AND ENTANGLEMENT 513
14.1.1 The Cell Is Crowded 514
14.1.2 Macromolecular Networks: The Cytoskeleton
and Beyond 515
14.1.3 Crowding on Membranes 517
14.1.4 Consequences of Crowding 517
Crowding Alters Biochemical Equilibria 517
Crowding Alters the Kinetics within Cells 518
14.2 EQUILIBRIA IN CROWDED ENVIRONMENTS 520
14.2.1 Crowding and Binding 520
Lattice Models of Solution Provide a Simple Picture
of the Role of Crowding in Biochemical Equilibria 520
14.2.2 Osmotic Pressures in Crowded Solutions 523
Osmotic Pressure Reveals Crowding Effects 523
14.2.3 Depletion Forces: Order from Disorder 524
The Close Approach of Large Particles Excludes
Smaller Particles Between Them, Resulting in
an Entropic Force 524
Depletion Forces Can Induce Entropic Ordering! 529
14.2.4 Excluded Volume and Polymers 530
Excluded Volume Leads to an Effective Repulsion
between Molecules 530
Self-avoidance Between the Monomers of a
Polymer Leads to Polymer Swelling 531
14.3 CROWDED DYNAMICS 533
14.3.1 Crowding and Reaction Rates 533
Enzymatic Reactions in Cells Can Proceed Faster
than the Diffusion Limit Using Substrate Channeling 533
Protein Folding Is Facilitated by Chaperones 534
14.3.2 Diffusion in Crowded Environments 535
14.4 SUMMARY AND CONCLUSIONS 536
14.5 PROBLEMS 537
14.6 FURTHER READING 538
14.7 REFERENCES 538
Chapter 15 Rate Equations and
Dynamics in the Cell 539
15.1 BIOLOGICAL STATISTICAL DYNAMICS: A FIRST LOOK 539
15.1.1 Cells as Chemical Factories 540
15.1.2 Dynamics of the Cytoskeleton 541
15.2 A CHEMICAL PICTURE OF BIOLOGICAL DYNAMICS 545
15.2.1 The Rate Equation Paradigm 545
Chemical Concentrations Vary in Both Space and Time 545
Rate Equations Describe the Time Evolution of
Concentrations 546
15.2.2 All Good Things Must End 546
Macromolecular Decay can be Described by a
Simple, First-order Differential Equation 546
1 5.2.3 A Single-Molecule View of Degradation: Statistical
Mechanics Over Trajectories 548
Molecules Fall Apart with a Characteristic Lifetime 548
Decay Processes Can Be Described with Two-state
Trajectories 550
Decay of One Species Corresponds to Growth in the
Number of a Second Species 551
15.2.4 Bimolecular Reactions 553
Chemical Reactions Can Increase the Concentration
of a Given Species 553
Equilibrium Constants Have a Dynamical
Interpretation in Terms of Reaction Rates 555
15.2.5 Dynamics of Ion Channels as a Case Study 555
Rate Equations for Ion Channels Characterize the
Time Evolution of the Open and Closed Probability 556
15.2.6 Rapid Equilibrium 558
Some Chemical Reactions Are Linked Together in a
Sequence Resulting in Coupled Rate Equations 559
15.2.7 Michaelis—Menten and Enzyme Kinetics 563
1 5.3 THE CYTOSKELETON IS ALWAYS UNDER
CONSTRUCTION 566
15.3.1 The Eukaryotic Cytoskeleton 566
The Cytoskeleton Is a Dynamical Structure That Is
Always Under Construction 566
1 5.3.2 The Curious Case of the Bacterial Cytoskeleton 567
1 5.4 SIMPLE MODELS OF CYTOSKELETAL POLYMERIZATION 569
The Dynamics of Polymerization Can Involve Many
Distinct Physical and Chemical Effects 570
15.4.1 The Equilibrium Polymer 571
Equilibrium Models of Cytoskeletal Filaments
Describe the Distribution of Polymer Lengths for
Simple Polymers 571
An Equilibrium Polymer Fluctuates in Time 573
1 5.4.2 Rate Equation Description of Cytoskeletal
Polymerization 575
Polymerization Reactions can be described by
Rate Equations 575
The Time Evolution of the Probability Distribution
Pn(t) can be Written Using a Rate Equation 577
Rates of Addition and Removal of Monomers Are
Often Different on the Two Ends of Cytoskeletal
Filaments 579
1 5.4.3 Nucleotide Hydrolysis and Cytoskeletal
Polymerization 581
ATP Hydrolysis Sculpts the Molecular Interface
Resulting in Distinct Rates at the Ends of
Cytoskeletal Filaments 581
1 5.4.4 Dynamic Instability: A Toy Model of the Cap 583
A Toy Model of Dynamic Instability Assumes That
Catastrophe Occurs When Hydrolyzed Nucleotides
Are Present at the Growth Front 583
15.5 SUMMARY AND CONCLUSIONS 586
15.6 PROBLEMS 587
15.7 FURTHER READING 588
15.8 REFERENCES 588
Chapter 16 Dynamics of Molecular Motors 589
16.1 THE DYNAMICS OF MOLECULAR MOTORS:
LIFE IN THE FAST LANE 589
16.1.1 Translational Motors: Beating the Diffusive Speed Limit 591
The Motion of Eukaryotic Cilia and Flagella Is
Driven by Translational Motors 594
Muscle Contraction Is Mediated by Myosin Motors 595
16.1.2 Rotary Motors 600
16.1.3 Polymerization Motors: Pushing by Growing 603
16.1.4 Translocation Motors: Pushing by Pulling 603
16.2 RECTIFIED BROWNIAN MOTION AND MOLECULAR
MOTORS 605
16.2.1 The Random Walk Yet Again 605
Molecular Motors Can Be Thought of as Random
Walkers 605
16.2.2 The One-state Model 606
The Dynamics of a Molecular Motor Can Be
Written Using a Master Equation 607
The Driven Diffusion Equation Can Be
Transformed into an Ordinary Diffusion Equation 609
16.2.3 Motor Stepping from a Free-Energy Perspective 612
16.2.4 The Two-state Model 616
The Dynamics of a Two-State Motor Is Described
by Two Coupled Rate Equations 617
Internal States Reveal Themselves in the Form
of the Waiting Time Distribution 620
16.2.5 More General Motor Models 622
16.2.6 Coordination of Motor Protein Activity 624
16.2.7 Rotary Motors 626
16.3 POLYMERIZATION AND TRANSLOCATION AS
MOTOR ACTION 629
16.3.1 The Polymerization Ratchet 629
The Polymerization Ratchet Is Based on a
Polymerization Reaction That Is Maintained
Out of Equilibrium 631
The Polymerization Ratchet Force—Velocity Can Be
Obtained by Solving a Driven Diffusion Equation 634
16.3.2 Force Generation by Growth 636
Polymerization Forces Can Be Measured Directly 636
Polymerization Forces Are Used to Center Cellular
Structures 638
16.3.3 The Translocation Ratchet 639
Protein Binding Can Speed up Translocation
through a Ratcheting Mechanism 639
The Translocation Time Can Be Estimated by
Solving a Driven Diffusion Equation 641
16.4 SUMMARY AND CONCLUSIONS 642
16.5 PROBLEMS 643
16.6 FURTHER READING 644
16.7 REFERENCES 645
Chapter 17 Biological Electricity and the
Hodgkin—Huxley Model 647
17.1 THE ROLE OF ELECTRICITY IN CELLS 647
1 7.2 THE CHARGE STATE OF THE CELL 648
17.2.1 The Electrical Status of Cells and Their Membranes 648
1 7.2.2 Electrochemical Equilibrium and the Nernst
Equation 649
Ion Concentration Differences Across Membranes
Lead to Potential Differences 649
17.3 MEMBRANE PERMEABILITY: PUMPS AND CHANNELS 651
A Nonequilibrium Charge Distribution Is Set Up
Between the Cell Interior and the External World 651
Signals in Cells Are Often Mediated by the
Presence of Electrical Spikes Called Action
Potentials 652
17.3.1 Ion Channels and Membrane Permeability 653
Ion Permeability Across Membranes Is Mediated
by Ion Channels 654
A Simple Two-State Model Can Describe Many
of the Features of Voltage Gating of Ion Channels 654
1 7.3.2 Maintaining a Nonequilibrium Charge State 656
Ions Are Pumped Across the Cell Membrane
Against an Electrochemical Gradient 656
17.4 THE ACTION POTENTIAL 659
17.4.1 Membrane Depolarization: The Membrane as a
Bistable Switch 659
Coordinated Muscle Contraction Depends Upon
Membrane Depolarization 659
A Patch of Cell Membrane Can Be Modeled as an
Electrical Circuit 661
The Difference Between the Membrane Potential
and the Nernst Potential Leads to an Ionic Current
Across the Cell Membrane 663
Voltage-gated Channels Result in a Nonlinear
Current—Voltage Relation for the Cell Membrane 663
A Patch of Membrane Acts as a Bistable Switch 666
The Dynamics of Voltage Relaxation Can Be
Modeled Using an RC Circuit 667
1 7.4.2 The Cable Equation 668
17.4.3 Depolarization Waves 670
Waves of Membrane Depolarization Rely on Sodium
Channels Switching into the Open State 670
17.4.4 Spikes 672
17.4.5 Hodgkin—Huxley and Membrane Transport 674
Inactivation of Sodium Channels Leads to
Propagating Spikes 674
17.5 SUMMARY AND CONCLUSIONS 676
17.6 PROBLEMS 676
17.7 FURTHER READING 677
17.8 REFERENCES 677
Chapter 18 Sequences, Specificity, and
Evolution 681
18.1 BIOLOGICAL INFORMATION 681
18.1.1 Why Sequences? 683
18.1.2 Genomes and Sequences by the Numbers 683
18.2 SEQUENCE ALIGNMENT AND HOMOLOGY 685
Sequence Comparison Can Sometimes Reveal Deep
Functional and Evolutionary Relationships Between
Genes, Proteins, and Organisms 686
18.2.1 The HP Model as a Coarse-grained Model for
Bioinformatics 688
18.2.2 Scoring Success 691
A Score Can Be Assigned to Different Alignments
Between Sequences 691
Comparison of Full Amino Acid Sequences
Requires a 20 by 20 Scoring Matrix 692
Even Random Sequences Have a Nonzero Score 694
The Extreme Value Distribution Determines the
Probability That a Given Alignment Score Would
Be Found by Chance 696
False Positives Increase as the Threshold for
Acceptable Expect Values (also Called E-Values)
Is Reduced 698
Structural and Functional Similarity Do Not Always
Guarantee Sequence Similarity 699
18.3 SEQUENCES AND EVOLUTION 701
18.3.1 Evolution by the Numbers: Hemoglobin as a
Case Study in Sequence Alignment 702
Sequence Similarity Is Used as a Temporal
Yardstick to Determine Evolutionary Distances 702
18.3.2 Evolution and Drug Resistance 703
18.3.3 The Evolution of Viruses 706
18.3.4 Phylogenetic Trees 708
18.4 THE MOLECULAR BASIS OF FIDELITY 710
18.4.1 Keeping It Specific: Beating Thermodynamic Specificity 711
The Specificity of Biological Recognition Often Far
Exceeds the Limit Dictated by Free-Energy Differences 711
High Specificity Costs Energy 715
18.5 SUMMARY AND CONCLUSIONS 717
18.6 PROBLEMS 717
18.7 FURTHER READING 719
18.8 REFERENCES 720
Chapter 19 Network Organization in
Space and Time 721
19.1 CHEMICAL AND INFORMATIONAL ORGANIZATION
IN THE CELL 721
Many Chemical Reactions in the Cell are Linked
in Complex Networks 721
Genetic Networks Describe the Linkages Between
Different Genes and Their Products 722
Developmental Decisions Are Made by Regulating
Genes 723
Gene Expression Is Measured Quantitatively in
Terms of How Much, When, and Where 723
19.2 GENETIC NETWORKS: DOING THE RIGHT THING
AT THE RIGHT TIME 726
Promoter Occupancy Is Dictated by the Presence of
Regulatory Proteins Called Transcription Factors 727
19.2.1 The Molecular Implementation of Regulation:
Promoters, Activators, and Repressors 727
Repressor Molecules Are the Proteins That Implement
Negative Control 727
Activators Are the Proteins That Implement Positive
Control 729
Genes Can Be Regulated During Processes Other
Than Transcription 729
19.2.2 The Mathematics of Recruitment and Rejection 729
Recruitment of Proteins Reflects Cooperativity
Between Different DNA Binding Proteins 729
The Regulation Factor Dictates How the Bare RNA
Polymerase Binding Probability Is Altered by
Transcription Factors 732
Activator Bypass Experiments Show That Activators
Work by Recruitment 734
Repressor Molecules Reduce the Probability
Polymerase Will Bind to the Promoter 735 .
'i
19.2.3 Transcriptional Regulation by the Numbers:
Binding Energies and Equilibrium Constants 737
Equilibrium Constants Can be Used To Determine
Regulation Factors 737
19.2.4 A Simple Statistical Mechanics Model of Positive and
Negative Regulation 738
19.2.5 The/ac Operon 740
The lac Operon Has Features of Both Negative
and Positive Regulation 740
The Free Energy of DNA Looping Affects the
Repression of the lac Operon 743
19.3 REGULATORY DYNAMICS 747
19.3.1 The Dynamics of RNA Polymerase and the Promoter 747
The Concentrations of Both RNA and Protein Can
Be Described Using Rate Equations 747
19.3.2 Genetic Switches: Natural and Synthetic 748
19.3.3 Genetic Networks That Oscillate: The Repressilator 753
19.3.4 Putting Space in the Model: Reaction—Diffusion
Models 759
19.4' CELLULAR FAST RESPONSE: SIGNALING 760
19.4.1 Bacterial Chemotaxis 760
19.4.2 Biochemistry on a Leash 765
Tethering Increases the Local Concentration of a
Ligand 765
Signaling Networks Help Cells Decide When and
Where to Grow Their Actin Filaments for Motility 766
Synthetic Signaling Networks Permit a Dissection
of Signaling Pathways 766
19.5 SUMMARY AND CONCLUSIONS 770
19.6 APPENDIX: STABILITY ANALYSIS FOR THE GENETIC
SWITCH 770
19.7 PROBLEMS 772
19.8 FURTHER READINC 773
19.9 REFERENCES 774
Chapter 20 Whither Physical Biology? 775
20.1 QUANTITATIVE DATA DEMAND
QUANTITATIVE MODELS 775
20.2 WRONG AGAIN 778
20.3 ORDER-OF-MAGNITUDE BIOLOGY AND
BEYOND 779
20.4 "DIFFICULTIES ON THEORY" 780
20.5 A CHARGE TO THE READER 785
20.6 FURTHER READING 785
20.7 REFERENCES 786 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Phillips, Rob 1960- Kondev, Jane Theriot, Julie |
| author_GND | (DE-588)137096372 (DE-588)1017645035 (DE-588)1017645213 |
| author_facet | Phillips, Rob 1960- Kondev, Jane Theriot, Julie |
| author_role | aut aut aut |
| author_sort | Phillips, Rob 1960- |
| author_variant | r p rp j k jk j t jt |
| building | Verbundindex |
| bvnumber | BV035183961 |
| callnumber-first | Q - Science |
| callnumber-label | QH505 |
| callnumber-raw | QH505 |
| callnumber-search | QH505 |
| callnumber-sort | QH 3505 |
| callnumber-subject | QH - Natural History and Biology |
| classification_rvk | WC 2000 WE 2300 |
| classification_tum | PHY 824f |
| ctrlnum | (OCoLC)234234136 (DE-599)BVBBV035183961 |
| dewey-full | 571.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 571 - Physiology & related subjects |
| dewey-raw | 571.6 |
| dewey-search | 571.6 |
| dewey-sort | 3571.6 |
| dewey-tens | 570 - Biology |
| discipline | Physik Biologie |
| discipline_str_mv | Physik Biologie |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV035183961 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:59:00Z |
| indexdate | 2024-07-09T21:26:55Z |
| institution | BVB |
| isbn | 9780815341635 |
| language | English |
| lccn | 2008030748 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016990671 |
| oclc_num | 234234136 |
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| physical | XXIV, 807 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | Garland Science |
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| spelling | Phillips, Rob 1960- Verfasser (DE-588)137096372 aut Physical biology of the cell Rob Phillips ; Jane Kondev ; Julie Theriot New York, NY [u.a.] Garland Science 2009 XXIV, 807 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke. - 2. Aufl. u.d.T.: Physical biology of the cell / Phillips, Rob "Physical Biology of the Cell is a biophysics textbook that explores how the basic tools and insights of physics and mathematics can illuminate the study of molecular and cell biology. Drawing on key examples and seminal experiments from cell biology, the book teaches physical model building through a practical, case-study approach, demonstrating how quantitative models derived from basic physical principles can be used to build a more profound, intuitive understanding of cell biology."--BOOK JACKET. Biophysique Cytologie Biophysics Cells Cells ultrastructure Cytology Molekulare Biophysik (DE-588)4170391-1 gnd rswk-swf Biophysik (DE-588)4006891-2 gnd rswk-swf Cytologie (DE-588)4070177-3 gnd rswk-swf Zelle (DE-588)4067537-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Zelle (DE-588)4067537-3 s Biophysik (DE-588)4006891-2 s DE-604 Cytologie (DE-588)4070177-3 s Molekulare Biophysik (DE-588)4170391-1 s b DE-604 Kondev, Jane Verfasser (DE-588)1017645035 aut Theriot, Julie Verfasser (DE-588)1017645213 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016990671&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Phillips, Rob 1960- Kondev, Jane Theriot, Julie Physical biology of the cell Biophysique Cytologie Biophysics Cells Cells ultrastructure Cytology Molekulare Biophysik (DE-588)4170391-1 gnd Biophysik (DE-588)4006891-2 gnd Cytologie (DE-588)4070177-3 gnd Zelle (DE-588)4067537-3 gnd |
| subject_GND | (DE-588)4170391-1 (DE-588)4006891-2 (DE-588)4070177-3 (DE-588)4067537-3 (DE-588)4123623-3 |
| title | Physical biology of the cell |
| title_auth | Physical biology of the cell |
| title_exact_search | Physical biology of the cell |
| title_exact_search_txtP | Physical biology of the cell |
| title_full | Physical biology of the cell Rob Phillips ; Jane Kondev ; Julie Theriot |
| title_fullStr | Physical biology of the cell Rob Phillips ; Jane Kondev ; Julie Theriot |
| title_full_unstemmed | Physical biology of the cell Rob Phillips ; Jane Kondev ; Julie Theriot |
| title_short | Physical biology of the cell |
| title_sort | physical biology of the cell |
| topic | Biophysique Cytologie Biophysics Cells Cells ultrastructure Cytology Molekulare Biophysik (DE-588)4170391-1 gnd Biophysik (DE-588)4006891-2 gnd Cytologie (DE-588)4070177-3 gnd Zelle (DE-588)4067537-3 gnd |
| topic_facet | Biophysique Cytologie Biophysics Cells Cells ultrastructure Cytology Molekulare Biophysik Biophysik Zelle Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016990671&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT phillipsrob physicalbiologyofthecell AT kondevjane physicalbiologyofthecell AT theriotjulie physicalbiologyofthecell |