physical biology of the cell - content

Physical Biology of the Cell

Rob Phillips, Jane Kondev and Julie Theriot

April 4, 2008

Contents

0.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

I The Facts of Life 21

1 Why: Biology By the Numbers 231.1 Physical Biology of the Cell . . . . . . . . . . . . . . . . . . . . . 231.2 The Stuff of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.3 Model Building in Biology . . . . . . . . . . . . . . . . . . . . . . 28

1.3.1 Models as Idealizations . . . . . . . . . . . . . . . . . . . 281.3.2 Cartoons and Models . . . . . . . . . . . . . . . . . . . . 37

1.4 Quantitative Models and the Power of Idealization . . . . . . . . 411.4.1 On the Springiness of Stuff . . . . . . . . . . . . . . . . . 431.4.2 The Toolbox of Fundamental Physical Models . . . . . . . 441.4.3 The Role of Estimates . . . . . . . . . . . . . . . . . . . . 461.4.4 On Being Wrong . . . . . . . . . . . . . . . . . . . . . . . 481.4.5 Rules of Thumb: Biology by the Numbers . . . . . . . . . 49

1.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 521.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 521.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2 What and Where: Construction Plans for Cells and Organisms 552.1 An Ode to E. coli . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.1.1 The Bacterial Standard Ruler . . . . . . . . . . . . . . . . 572.1.2 Taking the Molecular Census . . . . . . . . . . . . . . . . 592.1.3 Looking Inside of Cells . . . . . . . . . . . . . . . . . . . . 662.1.4 Where Does E. coli Fit? . . . . . . . . . . . . . . . . . . . 67

2.2 Cells and Structures Within Them . . . . . . . . . . . . . . . . . 692.2.1 Cells: A Rogue’s Gallery . . . . . . . . . . . . . . . . . . . 692.2.2 The Cellular Interior: Organelles . . . . . . . . . . . . . . 782.2.3 Macromolecular Assemblies: The Whole is Greater than

the Sum of the Parts . . . . . . . . . . . . . . . . . . . . . 852.2.4 Viruses as Assemblies . . . . . . . . . . . . . . . . . . . . 882.2.5 The Molecular Architecture of Cells: From PDB Files to

Ribbon Diagrams . . . . . . . . . . . . . . . . . . . . . . . 92

3

4 CONTENTS

2.3 Telescoping Up in Scale: Cells Don’t Go It Alone . . . . . . . . . 972.3.1 Multicellularity As One of Evolution’s Great Inventions . 972.3.2 Cellular Structures From Tissues to Nerve Networks . . . 1032.3.3 Multicellular Organisms . . . . . . . . . . . . . . . . . . . 106

2.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 1122.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1132.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 1152.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

3 When: Stopwatches at Many Scales 1193.1 The Hierarchy of Temporal Scales . . . . . . . . . . . . . . . . . 119

3.1.1 The Pageant of Biological Processes . . . . . . . . . . . . 1203.1.2 The Evolutionary Stopwatch . . . . . . . . . . . . . . . . 1263.1.3 The Cell Cycle and the Standard Clock . . . . . . . . . . 1313.1.4 Three Views of Time in Biology . . . . . . . . . . . . . . 135

3.2 Procedural Time . . . . . . . . . . . . . . . . . . . . . . . . . . . 1363.2.1 The Machines (or Processes) of the Central Dogma . . . . 1363.2.2 Clocks and Oscillators . . . . . . . . . . . . . . . . . . . . 140

3.3 Relative Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1453.3.1 Checkpoints and the Cell Cycle . . . . . . . . . . . . . . . 1453.3.2 Measuring Relative Time . . . . . . . . . . . . . . . . . . 1503.3.3 Killing the Cell: The Life Cycles of Viruses . . . . . . . . 1533.3.4 The Process of Development . . . . . . . . . . . . . . . . 156

3.4 Manipulated Time . . . . . . . . . . . . . . . . . . . . . . . . . . 1593.4.1 Chemical Kinetics and Enzyme Turnover . . . . . . . . . 1593.4.2 Beating the Diffusive Speed Limit . . . . . . . . . . . . . 1603.4.3 Beating the Replication Limit . . . . . . . . . . . . . . . . 1663.4.4 Eggs and Spores: Planning for the Next Generation . . . 168


4 Who: “Bless the Little Beasties” 1754.1 Choosing a Grain of Sand . . . . . . . . . . . . . . . . . . . . . . 175

4.1.1 Biochemistry and Genetics . . . . . . . . . . . . . . . . . 1774.2 Hemoglobin as a Model Protein . . . . . . . . . . . . . . . . . . . 180

4.2.1 Hemoglobin, Receptor-Ligand Binding and the Other Bohr1824.2.2 Hemoglobin and the Origins of Structural Biology . . . . 1844.2.3 Hemoglobin and Molecular Models of Disease . . . . . . . 1884.2.4 The Rise of Allostery and Cooperativity . . . . . . . . . . 188

4.3 Bacteriophage and Molecular Biology . . . . . . . . . . . . . . . 1894.3.1 Bacteriophage and the Origins of Molecular Biology . . . 1904.3.2 Bacteriophage and Modern Biophysics . . . . . . . . . . . 195

4.4 A Tale of Two Cells: E. Coli as a Model System . . . . . . . . . 1994.4.1 Bacteria and Molecular Biology . . . . . . . . . . . . . . . 199

CONTENTS 5

4.4.2 E. coli and The Central Dogma . . . . . . . . . . . . . . . 1994.4.3 The lac Operon as the “Hydrogen Atom” of Genetic Circuits2024.4.4 Signaling and Motility: The Case of Bacterial Chemotaxis 205

4.5 Yeast: From Biochemistry to the Cell Cycle . . . . . . . . . . . . 2074.5.1 Yeast and the Rise of Biochemistry . . . . . . . . . . . . . 2084.5.2 Dissecting the Cell Cycle . . . . . . . . . . . . . . . . . . 2094.5.3 Deciding Which Way is Up: Yeast and Polarity . . . . . . 2094.5.4 Dissecting Membrane Traffic . . . . . . . . . . . . . . . . 2124.5.5 Genomics and Proteomics . . . . . . . . . . . . . . . . . . 215

4.6 Flies and Modern Biology . . . . . . . . . . . . . . . . . . . . . . 2184.6.1 Flies and the Rise of Modern Genetics . . . . . . . . . . . 2184.6.2 How the Fly Got His Stripes . . . . . . . . . . . . . . . . 220

4.7 Of Mice and Men . . . . . . . . . . . . . . . . . . . . . . . . . . . 2224.8 The Case for Exotica . . . . . . . . . . . . . . . . . . . . . . . . . 223

4.8.1 Specialists and Experts . . . . . . . . . . . . . . . . . . . 2244.8.2 The Squid Giant Axon and Biological Electricity . . . . . 2254.8.3 Exotica Toolkit . . . . . . . . . . . . . . . . . . . . . . . . 228


II Life at Rest 237

5 Mechanical and Chemical Equilibrium in the Living Cell 2395.1 Energy and the Life of Cells . . . . . . . . . . . . . . . . . . . . . 240

5.1.1 The Interplay of Deterministic and Thermal Forces . . . . 2415.1.2 Constructing the Cell: Managing the Mass and Energy

Budget of the Cell . . . . . . . . . . . . . . . . . . . . . . 2445.2 Biological Systems as Minimizers . . . . . . . . . . . . . . . . . . 254

5.2.1 Equilibrium Models for Out of Equilibrium Systems . . . 2555.2.2 Proteins in “Equilibrium” . . . . . . . . . . . . . . . . . . 2565.2.3 Cells in “Equilibrium” . . . . . . . . . . . . . . . . . . . . 2585.2.4 Mechanical Equilibrium From a Minimization Perspective 259

5.3 The Mathematics of Superlatives . . . . . . . . . . . . . . . . . . 2655.3.1 The Mathematization of Judgement: Functions and Func-

tionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2655.3.2 The Calculus of Superlatives . . . . . . . . . . . . . . . . 267

5.4 Configurational Energy . . . . . . . . . . . . . . . . . . . . . . . 2715.4.1 Hooke’s Law: Actin to Lipids . . . . . . . . . . . . . . . . 274

5.5 Structures as Free Energy Minimizers . . . . . . . . . . . . . . . 2785.5.1 Entropy and Hydrophobicity . . . . . . . . . . . . . . . . 2815.5.2 Gibbs and the Calculus of Equilibrium . . . . . . . . . . . 2855.5.3 Structure as a Competition . . . . . . . . . . . . . . . . . 2885.5.4 An Ode to ∆G . . . . . . . . . . . . . . . . . . . . . . . . 290

6 CONTENTS

5.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 2915.7 Appendix: The Euler-Lagrange Equations, Finding the Superlative2925.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2945.9 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 2985.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

6 Entropy Rules! 3016.1 The Analytical Engine of Statistical Mechanics . . . . . . . . . . 301

6.1.1 A First Look at Ligand-Receptor Binding . . . . . . . . . 3076.1.2 The Statistical Mechanics of Gene Expression: RNA Poly-

merase and the Promoter . . . . . . . . . . . . . . . . . . 3126.1.3 Classic Derivation of the Boltzmann Distribution . . . . . 3186.1.4 Boltzmann Distribution by Counting . . . . . . . . . . . . 3216.1.5 Boltzmann Distribution by Guessing . . . . . . . . . . . . 325

6.2 On Being Ideal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3316.2.1 Average Energy of a Molecule in a Gas . . . . . . . . . . 3326.2.2 Free Energy of Dilute Solutions . . . . . . . . . . . . . . . 3356.2.3 Osmotic Pressure as an Entropic Spring . . . . . . . . . . 337

6.3 The Calculus of Equilibrium Applied: Law of Mass Action . . . . 3416.3.1 Law of Mass Action and Equilibrium Constants . . . . . . 343

6.4 Applications of the Calculus of Equilibrium . . . . . . . . . . . . 3456.4.1 A Second Look at Ligand-Receptor Binding . . . . . . . . 3456.4.2 Measuring Ligand-Receptor Binding . . . . . . . . . . . . 3476.4.3 Beyond Simple Ligand-Receptor Binding: The Hill Function3476.4.4 ATP Power . . . . . . . . . . . . . . . . . . . . . . . . . . 350


7 Two-State Systems: From Ion Channels to Cooperative Bind-ing 3577.1 Macromolecules With Multiple States . . . . . . . . . . . . . . . 358

7.1.1 The Internal State Variable Idea . . . . . . . . . . . . . . 3587.1.2 Ion Channels as an Example of Internal State Variables . 361

7.2 State Variable Description of Binding . . . . . . . . . . . . . . . 3667.2.1 The Gibbs Distribution: Contact with a Particle Reservoir 3677.2.2 Simple Ligand-Receptor Binding Revisited . . . . . . . . 3697.2.3 Phosphorylation as an Example of Two Internal State

Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 3717.2.4 Hemoglobin as a Case Study in Cooperativity . . . . . . . 375


CONTENTS 7

8 Random Walks and the Structure of Macromolecules 3918.1 What is a Structure: PDB or RG? . . . . . . . . . . . . . . . . . 391

8.1.1 Deterministic vs. Statistical Descriptions of Structure . . 3928.2 Macromolecules as Random Walks . . . . . . . . . . . . . . . . . 393

8.2.1 A Mathematical Stupor . . . . . . . . . . . . . . . . . . . 3948.2.2 How Big is a Genome? . . . . . . . . . . . . . . . . . . . . 4038.2.3 The Geography of Chromosomes . . . . . . . . . . . . . . 4058.2.4 DNA Looping: From Chromosomes to Gene Regulation . 4218.2.5 PCR, DNA Melting and DNA Bubbles . . . . . . . . . . . 425

8.3 The New World of Single Molecule Mechanics . . . . . . . . . . . 4308.3.1 Force-Extension Curves: A New Spectroscopy . . . . . . . 4318.3.2 Random Walk Models for Force-Extension Curves . . . . 433

8.4 Proteins as Random Walks . . . . . . . . . . . . . . . . . . . . . 4388.4.1 Compact Random Walks and the Size of Proteins . . . . . 4388.4.2 Hydrophobic and Polar Residues: The HP Model . . . . . 4398.4.3 HP Models of Protein Folding . . . . . . . . . . . . . . . . 443


9 Electrostatics for Salty Solutions 4539.1 Water as Life’s Aether . . . . . . . . . . . . . . . . . . . . . . . . 4539.2 The Chemistry of Water . . . . . . . . . . . . . . . . . . . . . . . 455

9.2.1 pH and the Equilibrium Constant . . . . . . . . . . . . . 4559.2.2 The Charge on DNA and Proteins . . . . . . . . . . . . . 4569.2.3 Salt and Binding . . . . . . . . . . . . . . . . . . . . . . . 458

9.3 Electrostatics for Salty Solutions . . . . . . . . . . . . . . . . . . 4609.3.1 An Electrostatics Primer . . . . . . . . . . . . . . . . . . 4609.3.2 The Charged Life of a Protein . . . . . . . . . . . . . . . 4719.3.3 The Notion of Screening: Electrostatics in Salty Solutions 4739.3.4 The Poisson-Boltzmann Equation . . . . . . . . . . . . . . 4789.3.5 Viruses as Charged Spheres . . . . . . . . . . . . . . . . . 482

9.4 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . 4869.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4869.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 4929.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

10 Beam Theory: Architecture for Cells and Skeletons 49510.1 Beams are Everywhere: From Flagella to the Cytoskeleton . . . . 49610.2 Geometry and Energetics of Beam Deformation . . . . . . . . . . 497

10.2.1 Stretch, Bend and Twist . . . . . . . . . . . . . . . . . . . 49710.2.2 Beam Theory and the Persistence Length: Stiffness is Rel-

ative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50310.2.3 Elasticity and Entropy: The Worm-like Chain . . . . . . . 506

10.3 The Mechanics of Transcriptional Regulation: DNA Looping Redux508

8 CONTENTS

10.3.1 The Lac Operon and Other Looping Systems . . . . . . . 50910.3.2 Energetics of DNA Looping . . . . . . . . . . . . . . . . . 51110.3.3 Putting it all together: The J Factor . . . . . . . . . . . . 511

10.4 DNA Packing: From Viruses to Eukaryotes . . . . . . . . . . . . 51310.4.1 The Problem of Viral DNA Packing . . . . . . . . . . . . 51610.4.2 Constructing the Nucleosome . . . . . . . . . . . . . . . . 52510.4.3 Equilibrium Accessibility of Nucleosomal DNA . . . . . . 528

10.5 The Cytoskeleton and Beam Theory . . . . . . . . . . . . . . . . 53310.5.1 The Cellular Interior: A Structural Perspective . . . . . . 53510.5.2 Stiffness of Cytoskeletal Filaments . . . . . . . . . . . . . 53810.5.3 Cytoskeletal Buckling . . . . . . . . . . . . . . . . . . . . 54210.5.4 Estimate of the Buckling Force . . . . . . . . . . . . . . . 543

10.6 Beams and Biotechnology . . . . . . . . . . . . . . . . . . . . . . 54510.6.1 Biofunctionalized Cantilevers and Molecular Recognition . 546

10.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 54910.8 Appendix: The Mathematics of the Worm-Like Chain . . . . . . 55010.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55210.10Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 55610.11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

11 Biological Membranes: Life in Two Dimensions 56111.1 The Nature of Biological Membranes . . . . . . . . . . . . . . . . 561

11.1.1 Cells and Membranes . . . . . . . . . . . . . . . . . . . . 56111.1.2 The Chemistry and Shape of Lipids . . . . . . . . . . . . 56611.1.3 The Liveliness of Membranes . . . . . . . . . . . . . . . . 570

11.2 On the Springiness of Membranes . . . . . . . . . . . . . . . . . . 57611.2.1 An Interlude on Membrane Geometry . . . . . . . . . . . 57711.2.2 Free Energy of Membrane Deformation . . . . . . . . . . 582

11.3 Structure, Energetics and Function of Vesicles . . . . . . . . . . . 58711.3.1 Measuring Membrane Stiffness . . . . . . . . . . . . . . . 58711.3.2 Membrane Pulling . . . . . . . . . . . . . . . . . . . . . . 59111.3.3 Vesicles in Cells . . . . . . . . . . . . . . . . . . . . . . . . 59511.3.4 Fusion and Fission . . . . . . . . . . . . . . . . . . . . . . 602

11.4 Membranes and Shape . . . . . . . . . . . . . . . . . . . . . . . . 60211.4.1 The Shapes of Organelles . . . . . . . . . . . . . . . . . . 60411.4.2 The Shapes of Cells . . . . . . . . . . . . . . . . . . . . . 607

11.5 The Active Membrane . . . . . . . . . . . . . . . . . . . . . . . . 61111.5.1 Mechanosensitive Ion Channels and Membrane Elasticity 61111.5.2 Elastic Deformations of Membranes Produced by Proteins 61111.5.3 One-Dimensional Solution for MscL . . . . . . . . . . . . 614


CONTENTS 9

III Life in Motion 633

12 The Mathematics of Water 63512.1 Putting Water in its Place . . . . . . . . . . . . . . . . . . . . . . 63512.2 Hydrodynamics of Water and Other Fluids . . . . . . . . . . . . 636

12.2.1 Water as a continuum . . . . . . . . . . . . . . . . . . . . 63612.2.2 What Can Newton Tell Us? . . . . . . . . . . . . . . . . . 63712.2.3 F = ma For Fluids . . . . . . . . . . . . . . . . . . . . . . 63912.2.4 The Newtonian Fluid and the Navier-Stokes Equations . . 643

12.3 The River Within: Fluid Dynamics of Blood . . . . . . . . . . . 64412.3.1 Boats in the River: Leukocyte Rolling and Adhesion . . . 647

12.4 The Low-Reynolds Number World . . . . . . . . . . . . . . . . . 64812.4.1 Stokes Flow: Consider a Spherical Bacterium . . . . . . . 64812.4.2 Stokes Drag in Single Molecule Experiments . . . . . . . . 65312.4.3 Dissipative Time Scales and the Reynolds Number . . . . 65412.4.4 Fish Gotta Swim, Birds Gotta Fly and Bacteria Gotta

Swim Too . . . . . . . . . . . . . . . . . . . . . . . . . . . 65612.4.5 Centrifugation and Sedimentation: Spin it Down . . . . . 659


13 A Statistical View of Biological Dynamics 66913.1 Diffusion in the Cell . . . . . . . . . . . . . . . . . . . . . . . . . 669

13.1.1 Active versus Passive Transport . . . . . . . . . . . . . . . 67013.1.2 Biological Distances Measured in Diffusion Times . . . . . 67213.1.3 Random Walk Redux . . . . . . . . . . . . . . . . . . . . 676

13.2 Concentration Fields and Diffusive Dynamics . . . . . . . . . . . 67813.2.1 Diffusion by Summing Over Microtrajectories . . . . . . . 68213.2.2 Solutions and properties of the diffusion equation . . . . . 68913.2.3 FRAP and FCS . . . . . . . . . . . . . . . . . . . . . . . 69013.2.4 Drunks on a Hill: The Smoluchowski Equation . . . . . . 69513.2.5 The Einstein Relation . . . . . . . . . . . . . . . . . . . . 696

13.3 Diffusion to capture . . . . . . . . . . . . . . . . . . . . . . . . . 69813.3.1 Modeling the cell signaling problem . . . . . . . . . . . . 69913.3.2 A “Universal” Rate for Diffusion-Limited Chemical Reac-

tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70413.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 70513.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70613.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 70713.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709

10 CONTENTS

14 Life in Crowded and Disordered Environments 71114.1 Crowding, Linkage and Entanglement . . . . . . . . . . . . . . . 711

14.1.1 The Cell is Crowded . . . . . . . . . . . . . . . . . . . . . 71214.1.2 Macromolecular Networks: The Cytoskeleton and Beyond 71314.1.3 Crowding on Membranes . . . . . . . . . . . . . . . . . . 71514.1.4 Consequences of Crowding . . . . . . . . . . . . . . . . . . 717

14.2 Equilibria in Crowded Environments . . . . . . . . . . . . . . . . 72114.2.1 Crowding and binding . . . . . . . . . . . . . . . . . . . . 72114.2.2 Osmotic Pressures in Crowded Solutions . . . . . . . . . . 72514.2.3 Depletion Forces: Order from Disorder . . . . . . . . . . . 72914.2.4 Excluded Volume and Polymers . . . . . . . . . . . . . . . 736

14.3 Crowded Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 74014.3.1 Crowding and Reaction Rates . . . . . . . . . . . . . . . . 74014.3.2 Diffusion in Crowded Environments . . . . . . . . . . . . 742


15 Rate Equations and Dynamics in the Cell 75115.1 Biological Statistical Dynamics: A First Look . . . . . . . . . . . 751

15.1.1 Cells as Chemical Factories . . . . . . . . . . . . . . . . . 75215.1.2 Dynamics of the Cytoskeleton . . . . . . . . . . . . . . . . 753

15.2 A Chemical Picture of Biological Dynamics . . . . . . . . . . . . 75815.2.1 The Rate Equation Paradigm . . . . . . . . . . . . . . . . 75815.2.2 All Good Things Must End . . . . . . . . . . . . . . . . . 76015.2.3 A Single Molecule View of Degradation: Statistical Me-

chanics Over Trajectories . . . . . . . . . . . . . . . . . . 76215.2.4 Bimolecular Reactions . . . . . . . . . . . . . . . . . . . . 76815.2.5 Dynamics of Ion Channels as a Case Study . . . . . . . . 77115.2.6 Rapid equilibrium . . . . . . . . . . . . . . . . . . . . . . 77615.2.7 Michaelis-Menten and Enzyme Kinetics . . . . . . . . . . 783

15.3 The Cytoskeleton is Always Under Construction . . . . . . . . . 78615.3.1 The Eukaryotic Cytoskeleton . . . . . . . . . . . . . . . . 78815.3.2 The Curious Case of the Bacterial Cytoskeleton . . . . . . 789

15.4 Simple Models of Cytoskeletal Polymerization . . . . . . . . . . . 79215.4.1 The Equilibrium Polymer . . . . . . . . . . . . . . . . . . 79515.4.2 Rate Equation Description of Cytoskeletal Polymerization 80015.4.3 Nucleotide Hydrolysis and Cytoskeletal Polymerization . 80615.4.4 Dynamic Instability: A Toy Model of the Cap . . . . . . . 808


CONTENTS 11

16 Dynamics of Molecular Motors 82116.1 The Dynamics of Molecular Motors: Life in the Noisy Lane . . . 821

16.1.1 Translational Motors: Beating the Diffusive Speed Limit . 82416.1.2 Rotary Motors . . . . . . . . . . . . . . . . . . . . . . . . 83516.1.3 Polymerization Motors: Pushing By Growing . . . . . . . 83916.1.4 Translocation Motors: Pushing by Pulling . . . . . . . . . 841

16.2 Rectified Brownian Motion and Molecular Motors . . . . . . . . . 84316.2.1 The Random Walk Yet Again . . . . . . . . . . . . . . . . 84416.2.2 The One-state Model . . . . . . . . . . . . . . . . . . . . 84716.2.3 Motor stepping from a free energy perspective . . . . . . 85616.2.4 The Two-state model . . . . . . . . . . . . . . . . . . . . 86116.2.5 More General Motor Models . . . . . . . . . . . . . . . . 86816.2.6 Coordination of Motor Protein Activity . . . . . . . . . . 86916.2.7 Rotary Motors . . . . . . . . . . . . . . . . . . . . . . . . 875

16.3 Polymerization and Translocation as Motor Action . . . . . . . . 87816.3.1 The Polymerization Ratchet . . . . . . . . . . . . . . . . . 87816.3.2 Force Generation by Growth . . . . . . . . . . . . . . . . 88716.3.3 The Translocation Ratchet . . . . . . . . . . . . . . . . . 890


17 Biological Electricity and the Hodgkin-Huxley Model 90317.1 The Role of Electricity in Cells . . . . . . . . . . . . . . . . . . . 90317.2 The Charge State of the Cell . . . . . . . . . . . . . . . . . . . . 905

17.2.1 The Electrical Status of Cells and Their Membranes . . . 90517.2.2 Electrochemical Equilibrium and the Nernst Equation . . 905

17.3 Membrane Permeability: Pumps and Channels . . . . . . . . . . 90817.3.1 Ion Channels and Membrane Permeability . . . . . . . . . 91017.3.2 Maintaining a Nonequilibrium Charge State . . . . . . . . 915

17.4 The Action Potential . . . . . . . . . . . . . . . . . . . . . . . . . 91817.4.1 Membrane Depolarization: The Membrane as a Bistable

Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91817.4.2 The Cable Equation . . . . . . . . . . . . . . . . . . . . . 93117.4.3 Depolarization waves . . . . . . . . . . . . . . . . . . . . . 93317.4.4 Spikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93717.4.5 Hodgkin-Huxley and Membrane Transport . . . . . . . . 939


12 CONTENTS

IV The Meaning of Life 947

18 Sequences, Specificity and Evolution 94918.1 Biological Information . . . . . . . . . . . . . . . . . . . . . . . . 950

18.1.1 Why Sequences? . . . . . . . . . . . . . . . . . . . . . . . 95118.1.2 Genomes and Sequences by the Numbers . . . . . . . . . 952

18.2 Sequence Alignment and Homology . . . . . . . . . . . . . . . . . 95418.2.1 The HP Model as a Coarse-Grained Model for Bioinfor-

matics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96018.2.2 Scoring Success . . . . . . . . . . . . . . . . . . . . . . . . 962

18.3 Sequences and Evolution . . . . . . . . . . . . . . . . . . . . . . . 97318.3.1 Evolution by the Numbers: Hemoglobin as a Case Study

in Sequence Alignment . . . . . . . . . . . . . . . . . . . . 97518.3.2 Evolution and Drug Resistance . . . . . . . . . . . . . . . 97918.3.3 The Evolution of Viruses . . . . . . . . . . . . . . . . . . 98218.3.4 Phylogenetic Trees . . . . . . . . . . . . . . . . . . . . . . 984

18.4 The Molecular Basis of Fidelity . . . . . . . . . . . . . . . . . . . 98718.4.1 Keeping it Specific: Beating Thermodynamic Specificity . 988


19 Network Organization in Space and Time 100519.1 Chemical and Informational Organization in the Cell . . . . . . . 100519.2 Genetic Networks: Doing the Right Thing at the Right Time . . 1012

19.2.1 The Molecular Implementation of Regulation: Promoters,Activators and Repressors . . . . . . . . . . . . . . . . . . 1013

19.2.2 The Mathematics of Recruitment and Rejection . . . . . . 101619.2.3 Transcriptional Regulation By the Numbers: Binding En-

ergies and Equilibrium Constants . . . . . . . . . . . . . . 102619.2.4 A Simple Statistical Mechanics Model of Positive and

Negative Regulation . . . . . . . . . . . . . . . . . . . . . 102719.2.5 The lac Operon . . . . . . . . . . . . . . . . . . . . . . . . 1028

19.3 Regulatory Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 103819.3.1 The Dynamics of RNA Polymerase and the Promoter . . 103819.3.2 Genetic Switches: Natural and Synthetic . . . . . . . . . 103919.3.3 Genetic Networks That Oscillate: The Repressilator . . . 104519.3.4 Putting Space in the Model: Reaction-Diffusion Models . 1051

19.4 Cellular Fast Response: Signaling . . . . . . . . . . . . . . . . . . 105219.4.1 Bacterial Chemotaxis . . . . . . . . . . . . . . . . . . . . 105319.4.2 Biochemistry on a Leash . . . . . . . . . . . . . . . . . . . 1058

19.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 106519.6 Appendix: Stability Analysis for the Genetic Switch . . . . . . . 106619.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106819.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072

CONTENTS 13

19.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073

20 Whither Physical Biology? 107520.1 Quantitative Data Demands Quantitative Models . . . . . . . . . 107520.2 Wrong Again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107920.3 Order-of-Magnitude Biology and Beyond . . . . . . . . . . . . . . 108020.4 “Difficulties on Theory” . . . . . . . . . . . . . . . . . . . . . . . 108120.5 A Charge to the Reader . . . . . . . . . . . . . . . . . . . . . . . 108620.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 108720.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1088

physical biology of the cell - content

Documents

internal state variables

2 free energy

state model

molecular motors

rna polymerase

extension curves

statistical mechanics

lac operon