Physical Biology of the Cell. Rob Phillips, Jane Kondev and Julie Theriot

Transcription

1 Physical Biology of the Cell Rob Phillips, Jane Kondev and Julie Theriot April 4, 2008

2 Contents 0.1 Preface I The Facts of Life 21 1 Why: Biology By the Numbers Physical Biology of the Cell The Stuff of Life Model Building in Biology Models as Idealizations Cartoons and Models Quantitative Models and the Power of Idealization On the Springiness of Stuff The Toolbox of Fundamental Physical Models The Role of Estimates On Being Wrong Rules of Thumb: Biology by the Numbers Summary and Conclusions Further Reading References What and Where: Construction Plans for Cells and Organisms An Ode to E. coli The Bacterial Standard Ruler Taking the Molecular Census Looking Inside of Cells Where Does E. coli Fit? Cells and Structures Within Them Cells: A Rogue s Gallery The Cellular Interior: Organelles Macromolecular Assemblies: The Whole is Greater than the Sum of the Parts Viruses as Assemblies The Molecular Architecture of Cells: From PDB Files to Ribbon Diagrams

3 4 CONTENTS 2.3 Telescoping Up in Scale: Cells Don t Go It Alone Multicellularity As One of Evolution s Great Inventions Cellular Structures From Tissues to Nerve Networks Multicellular Organisms Summary and Conclusions Problems Further Reading References When: Stopwatches at Many Scales The Hierarchy of Temporal Scales The Pageant of Biological Processes The Evolutionary Stopwatch The Cell Cycle and the Standard Clock Three Views of Time in Biology Procedural Time The Machines (or Processes) of the Central Dogma Clocks and Oscillators Relative Time Checkpoints and the Cell Cycle Measuring Relative Time Killing the Cell: The Life Cycles of Viruses The Process of Development Manipulated Time Chemical Kinetics and Enzyme Turnover Beating the Diffusive Speed Limit Beating the Replication Limit Eggs and Spores: Planning for the Next Generation Summary and Conclusions Problems Further Reading References Who: Bless the Little Beasties Choosing a Grain of Sand Biochemistry and Genetics Hemoglobin as a Model Protein Hemoglobin, Receptor-Ligand Binding and the Other Bohr Hemoglobin and the Origins of Structural Biology Hemoglobin and Molecular Models of Disease The Rise of Allostery and Cooperativity Bacteriophage and Molecular Biology Bacteriophage and the Origins of Molecular Biology Bacteriophage and Modern Biophysics A Tale of Two Cells: E. Coli as a Model System Bacteria and Molecular Biology

4 CONTENTS E. coli and The Central Dogma The lac Operon as the Hydrogen Atom of Genetic Circuits Signaling and Motility: The Case of Bacterial Chemotaxis Yeast: From Biochemistry to the Cell Cycle Yeast and the Rise of Biochemistry Dissecting the Cell Cycle Deciding Which Way is Up: Yeast and Polarity Dissecting Membrane Traffic Genomics and Proteomics Flies and Modern Biology Flies and the Rise of Modern Genetics How the Fly Got His Stripes Of Mice and Men The Case for Exotica Specialists and Experts The Squid Giant Axon and Biological Electricity Exotica Toolkit Summary and Conclusions Problems Further Reading References II Life at Rest Mechanical and Chemical Equilibrium in the Living Cell Energy and the Life of Cells The Interplay of Deterministic and Thermal Forces Constructing the Cell: Managing the Mass and Energy Budget of the Cell Biological Systems as Minimizers Equilibrium Models for Out of Equilibrium Systems Proteins in Equilibrium Cells in Equilibrium Mechanical Equilibrium From a Minimization Perspective The Mathematics of Superlatives The Mathematization of Judgement: Functions and Functionals The Calculus of Superlatives Configurational Energy Hooke s Law: Actin to Lipids Structures as Free Energy Minimizers Entropy and Hydrophobicity Gibbs and the Calculus of Equilibrium Structure as a Competition An Ode to G

5 6 CONTENTS 5.6 Summary and Conclusions Appendix: The Euler-Lagrange Equations, Finding the Superlative Problems Further Reading References Entropy Rules! The Analytical Engine of Statistical Mechanics A First Look at Ligand-Receptor Binding The Statistical Mechanics of Gene Expression: RNA Polymerase and the Promoter Classic Derivation of the Boltzmann Distribution Boltzmann Distribution by Counting Boltzmann Distribution by Guessing On Being Ideal Average Energy of a Molecule in a Gas Free Energy of Dilute Solutions Osmotic Pressure as an Entropic Spring The Calculus of Equilibrium Applied: Law of Mass Action Law of Mass Action and Equilibrium Constants Applications of the Calculus of Equilibrium A Second Look at Ligand-Receptor Binding Measuring Ligand-Receptor Binding Beyond Simple Ligand-Receptor Binding: The Hill Function ATP Power Summary and Conclusions Problems Further Reading References Two-State Systems: From Ion Channels to Cooperative Binding Macromolecules With Multiple States The Internal State Variable Idea Ion Channels as an Example of Internal State Variables State Variable Description of Binding The Gibbs Distribution: Contact with a Particle Reservoir Simple Ligand-Receptor Binding Revisited Phosphorylation as an Example of Two Internal State Variables Hemoglobin as a Case Study in Cooperativity Summary and Conclusions Problems Further Reading References

6 CONTENTS 7 8 Random Walks and the Structure of Macromolecules What is a Structure: PDB or R G? Deterministic vs. Statistical Descriptions of Structure Macromolecules as Random Walks A Mathematical Stupor How Big is a Genome? The Geography of Chromosomes DNA Looping: From Chromosomes to Gene Regulation PCR, DNA Melting and DNA Bubbles The New World of Single Molecule Mechanics Force-Extension Curves: A New Spectroscopy Random Walk Models for Force-Extension Curves Proteins as Random Walks Compact Random Walks and the Size of Proteins Hydrophobic and Polar Residues: The HP Model HP Models of Protein Folding Summary and Conclusions Problems Further Reading References Electrostatics for Salty Solutions Water as Life s Aether The Chemistry of Water ph and the Equilibrium Constant The Charge on DNA and Proteins Salt and Binding Electrostatics for Salty Solutions An Electrostatics Primer The Charged Life of a Protein The Notion of Screening: Electrostatics in Salty Solutions The Poisson-Boltzmann Equation Viruses as Charged Spheres Summary and Conclusion Problems Further Reading References Beam Theory: Architecture for Cells and Skeletons Beams are Everywhere: From Flagella to the Cytoskeleton Geometry and Energetics of Beam Deformation Stretch, Bend and Twist Beam Theory and the Persistence Length: Stiffness is Relative Elasticity and Entropy: The Worm-like Chain The Mechanics of Transcriptional Regulation: DNA Looping Redux508

7 8 CONTENTS The Lac Operon and Other Looping Systems Energetics of DNA Looping Putting it all together: The J Factor DNA Packing: From Viruses to Eukaryotes The Problem of Viral DNA Packing Constructing the Nucleosome Equilibrium Accessibility of Nucleosomal DNA The Cytoskeleton and Beam Theory The Cellular Interior: A Structural Perspective Stiffness of Cytoskeletal Filaments Cytoskeletal Buckling Estimate of the Buckling Force Beams and Biotechnology Biofunctionalized Cantilevers and Molecular Recognition Summary and Conclusions Appendix: The Mathematics of the Worm-Like Chain Problems Further Reading References Biological Membranes: Life in Two Dimensions The Nature of Biological Membranes Cells and Membranes The Chemistry and Shape of Lipids The Liveliness of Membranes On the Springiness of Membranes An Interlude on Membrane Geometry Free Energy of Membrane Deformation Structure, Energetics and Function of Vesicles Measuring Membrane Stiffness Membrane Pulling Vesicles in Cells Fusion and Fission Membranes and Shape The Shapes of Organelles The Shapes of Cells The Active Membrane Mechanosensitive Ion Channels and Membrane Elasticity Elastic Deformations of Membranes Produced by Proteins One-Dimensional Solution for MscL Summary and Conclusions Problems Further Reading References

8 CONTENTS 9 III Life in Motion The Mathematics of Water Putting Water in its Place Hydrodynamics of Water and Other Fluids Water as a continuum What Can Newton Tell Us? F = ma For Fluids The Newtonian Fluid and the Navier-Stokes Equations The River Within: Fluid Dynamics of Blood Boats in the River: Leukocyte Rolling and Adhesion The Low-Reynolds Number World Stokes Flow: Consider a Spherical Bacterium Stokes Drag in Single Molecule Experiments Dissipative Time Scales and the Reynolds Number Fish Gotta Swim, Birds Gotta Fly and Bacteria Gotta Swim Too Centrifugation and Sedimentation: Spin it Down Summary and Conclusions Problems Further Reading References A Statistical View of Biological Dynamics Diffusion in the Cell Active versus Passive Transport Biological Distances Measured in Diffusion Times Random Walk Redux Concentration Fields and Diffusive Dynamics Diffusion by Summing Over Microtrajectories Solutions and properties of the diffusion equation FRAP and FCS Drunks on a Hill: The Smoluchowski Equation The Einstein Relation Diffusion to capture Modeling the cell signaling problem A Universal Rate for Diffusion-Limited Chemical Reactions Summary and Conclusions Problems Further Reading References

9 10 CONTENTS 14 Life in Crowded and Disordered Environments Crowding, Linkage and Entanglement The Cell is Crowded Macromolecular Networks: The Cytoskeleton and Beyond Crowding on Membranes Consequences of Crowding Equilibria in Crowded Environments Crowding and binding Osmotic Pressures in Crowded Solutions Depletion Forces: Order from Disorder Excluded Volume and Polymers Crowded Dynamics Crowding and Reaction Rates Diffusion in Crowded Environments Summary and Conclusions Problems Further Reading References Rate Equations and Dynamics in the Cell Biological Statistical Dynamics: A First Look Cells as Chemical Factories Dynamics of the Cytoskeleton A Chemical Picture of Biological Dynamics The Rate Equation Paradigm All Good Things Must End A Single Molecule View of Degradation: Statistical Mechanics Over Trajectories Bimolecular Reactions Dynamics of Ion Channels as a Case Study Rapid equilibrium Michaelis-Menten and Enzyme Kinetics The Cytoskeleton is Always Under Construction The Eukaryotic Cytoskeleton The Curious Case of the Bacterial Cytoskeleton Simple Models of Cytoskeletal Polymerization The Equilibrium Polymer Rate Equation Description of Cytoskeletal Polymerization Nucleotide Hydrolysis and Cytoskeletal Polymerization Dynamic Instability: A Toy Model of the Cap Summary and Conclusions Problems Further Reading References

10 CONTENTS Dynamics of Molecular Motors The Dynamics of Molecular Motors: Life in the Noisy Lane Translational Motors: Beating the Diffusive Speed Limit Rotary Motors Polymerization Motors: Pushing By Growing Translocation Motors: Pushing by Pulling Rectified Brownian Motion and Molecular Motors The Random Walk Yet Again The One-state Model Motor stepping from a free energy perspective The Two-state model More General Motor Models Coordination of Motor Protein Activity Rotary Motors Polymerization and Translocation as Motor Action The Polymerization Ratchet Force Generation by Growth The Translocation Ratchet Summary and Conclusions Problems Further Reading References Biological Electricity and the Hodgkin-Huxley Model The Role of Electricity in Cells The Charge State of the Cell The Electrical Status of Cells and Their Membranes Electrochemical Equilibrium and the Nernst Equation Membrane Permeability: Pumps and Channels Ion Channels and Membrane Permeability Maintaining a Nonequilibrium Charge State The Action Potential Membrane Depolarization: The Membrane as a Bistable Switch The Cable Equation Depolarization waves Spikes Hodgkin-Huxley and Membrane Transport Summary and Conclusions Problems Further Reading References

11 12 CONTENTS IV The Meaning of Life Sequences, Specificity and Evolution Biological Information Why Sequences? Genomes and Sequences by the Numbers Sequence Alignment and Homology The HP Model as a Coarse-Grained Model for Bioinformatics Scoring Success Sequences and Evolution Evolution by the Numbers: Hemoglobin as a Case Study in Sequence Alignment Evolution and Drug Resistance The Evolution of Viruses Phylogenetic Trees The Molecular Basis of Fidelity Keeping it Specific: Beating Thermodynamic Specificity Summary and Conclusions Problems Further Reading References Network Organization in Space and Time Chemical and Informational Organization in the Cell Genetic Networks: Doing the Right Thing at the Right Time The Molecular Implementation of Regulation: Promoters, Activators and Repressors The Mathematics of Recruitment and Rejection Transcriptional Regulation By the Numbers: Binding Energies and Equilibrium Constants A Simple Statistical Mechanics Model of Positive and Negative Regulation The lac Operon Regulatory Dynamics The Dynamics of RNA Polymerase and the Promoter Genetic Switches: Natural and Synthetic Genetic Networks That Oscillate: The Repressilator Putting Space in the Model: Reaction-Diffusion Models Cellular Fast Response: Signaling Bacterial Chemotaxis Biochemistry on a Leash Summary and Conclusions Appendix: Stability Analysis for the Genetic Switch Problems Further Reading

12 CONTENTS References Whither Physical Biology? Quantitative Data Demands Quantitative Models Wrong Again Order-of-Magnitude Biology and Beyond Difficulties on Theory A Charge to the Reader Further Reading References