| Preface |
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vii | |
| Acknowledgments |
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xiii | |
| Special Sections |
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xxix | |
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xxx | |
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1 | (184) |
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Chapter 1 Why: Biology by the Numbers |
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3 | (32) |
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1.1 Biological Cartography |
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3 | (1) |
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1.2 Physical Biology Of The Cell |
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4 | (1) |
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Model Building Requires a Substrate of Biological Facts and Physical (or Chemical) Principles |
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5 | (1) |
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5 | (4) |
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Organisms Are Constructed from Four Great Classes of Macromolecules |
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6 | (1) |
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Nucleic Acids and Proteins Are Polymer Languages with Different Alphabets |
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7 | (2) |
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1.4 Model Building In Biology |
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9 | (11) |
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1.4.1 Models as Idealizations |
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9 | (2) |
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Biological Stuff Can Be Idealized Using Many Different Physical Models |
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11 | (5) |
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1.4.2 Cartoons and Models |
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16 | (1) |
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Biological Cartoons Select Those Features of the Problem Thought to Be Essential |
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16 | (3) |
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Quantitative Models Can Be Built by Mathematicizing the Cartoons |
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19 | (1) |
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1.5 Quantitative Models And The Power Of Idealization |
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20 | (12) |
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1.5.1 On the Springiness of Stuff |
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21 | (1) |
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1.5.2 The Toolbox of Fundamental Physical Models |
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22 | (1) |
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1.5.3 The Unifying Ideas of Biology |
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23 | (2) |
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1.5.4 Mathematical Toolkit |
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25 | (1) |
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1.5.5 The Role of Estimates |
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26 | (3) |
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29 | (1) |
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1.5.7 Rules of Thumb: Biology by the Numbers |
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30 | (2) |
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1.6 Summary And Conclusions |
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32 | (1) |
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32 | (1) |
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33 | (2) |
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Chapter 2 What and Where: Construction Plans for Cells and Organisms |
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35 | (52) |
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35 | (17) |
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2.1.1 The Bacterial Standard Ruler |
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37 | (1) |
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The Bacterium E. coli Will Serve as Our Standard Ruler |
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37 | (1) |
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2.1.2 Taking the Molecular Census |
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38 | (10) |
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The Cellular Interior Is Highly Crowded, with Mean Spacings Between Molecules That Are Comparable to Molecular Dimensions |
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48 | (1) |
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2.1.3 Looking Inside Cells |
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49 | (2) |
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2.1.4 Where Does E. coli Fit? |
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51 | (1) |
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Biological Structures Exist Over a Huge Range of Scales |
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51 | (1) |
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2.2 Cells And Structures Within Them |
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52 | (20) |
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2.2.1 Cells: A Rogue's Gallery |
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52 | (1) |
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Cells Come in a Wide Variety of Shapes and Sizes and with a Huge Range of Functions |
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52 | (5) |
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Cells from Humans Have a Huge Diversity of Structure and Function |
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57 | (2) |
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2.2.2 The Cellular Interior: Organelles |
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59 | (4) |
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2.2.3 Macromolecular Assemblies: The Whole is Greater than the Sum of the Parts |
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63 | (1) |
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Macromolecules Come Together to Form Assemblies |
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63 | (1) |
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Helical Motifs Are Seen Repeatedly in Molecular Assemblies |
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64 | (1) |
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Macromolecular Assemblies Are Arranged in Superstructures |
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65 | (1) |
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2.2.4 Viruses as Assemblies |
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66 | (3) |
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2.2.5 The Molecular Architecture of Cells: From Protein Data Bank (PDB) Files to Ribbon Diagrams |
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69 | (1) |
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Macromolecular Structure Is Characterized Fundamentally by Atomic Coordinates |
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69 | (1) |
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Chemical Groups Allow Us to Classify Parts of the Structure of Macromolecules |
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70 | (2) |
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2.3 Telescoping Up In Scale: Cells Don't Go It Alone |
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72 | (11) |
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2.3.1 Multicellularity as One of Evolution's Great Inventions |
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73 | (1) |
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Bacteria Interact to Form Colonies such as Biofilms |
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73 | (2) |
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Teaming Up in a Crisis: Lifestyle of Dictyostelium discoideum |
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75 | (1) |
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Multicellular Organisms Have Many Distinct Communities of Cells |
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76 | (1) |
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2.3.2 Cellular Structures from Tissues to Nerve Networks |
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77 | (1) |
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One Class of Multicellular Structures is the Epithelial Sheets |
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77 | (1) |
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Tissues Are Collections of Cells and Extracellular Matrix |
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77 | (1) |
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Nerve Cells Form Complex, Multicellular Complexes |
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78 | (1) |
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2.3.3 Multicellular Organisms |
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78 | (1) |
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Cells Differentiate During Development Leading to Entire Organisms |
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78 | (2) |
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The Cells of the Nematode Worm, Caenorhabditis Elegans, Have Been Charted, Yielding a Cell-by-Cell Picture of the Organism |
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80 | (2) |
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Higher-Level Structures Exist as Colonies of Organisms |
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82 | (1) |
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2.4 Summary And Conclusions |
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83 | (1) |
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83 | (1) |
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84 | (1) |
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85 | (2) |
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Chapter 3 When: Stopwatches at Many Scales |
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87 | (50) |
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3.1 The Hierarchy Of Temporal Scales |
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87 | (19) |
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3.1.1 The Pageant of Biological Processes |
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89 | (1) |
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Biological Processes Are Characterized by a Huge Diversity of Time Scales |
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89 | (6) |
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3.1.2 The Evolutionary Stopwatch |
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95 | (4) |
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3.1.3 The Cell Cycle and the Standard Clock |
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99 | (1) |
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The E. coli Cell Cycle Will Serve as Our Standard Stopwatch |
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99 | (6) |
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3.1.4 Three Views of Time in Biology |
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105 | (1) |
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106 | (8) |
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3.2.1 The Machines (or Processes) of the Central Dogma |
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107 | (1) |
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The Central Dogma Describes the Processes Whereby the Genetic Information Is Expressed Chemically |
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107 | (1) |
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The Processes of the Central Dogma Are Carried Out by Sophisticated Molecular Machines |
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108 | (2) |
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3.2.2 Clocks and Oscillators |
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110 | (1) |
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Developing Embryos Divide on a Regular Schedule Dictated by an Internal Clock |
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111 | (1) |
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Diurnal Clocks Allow Cells and Organisms to Be on Time Everyday |
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111 | (3) |
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114 | (11) |
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3.3.1 Checkpoints and the Cell Cycle |
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115 | (1) |
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The Eukaryotic Cell Cycle Consists of Four Phases Involving Molecular Synthesis and Organization |
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115 | (2) |
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3.3.2 Measuring Relative Time |
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117 | (1) |
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Genetic Networks Are Collections of Genes Whose Expression Is Interrelated |
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117 | (2) |
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The Formation of the Bacterial Flagellum Is Intricately Organized In Space and Time |
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119 | (1) |
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3.3.3 Killing the Cell: The Life Cycles of Viruses |
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120 | (1) |
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Viral Life Cycles Include a Series of Self-Assembly Processes |
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121 | (1) |
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3.3.4 The Process of Development |
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122 | (3) |
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125 | (8) |
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3.4.1 Chemical Kinetics and Enzyme Turnover |
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125 | (1) |
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3.4.2 Beating the Diffusive Speed Limit |
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126 | (1) |
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Diffusion Is the Random Motion of Microscopic Particles in Solution |
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127 | (1) |
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Diffusion Times Depend upon the Length Scale |
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127 | (1) |
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Diffusive Transport at the Synaptic Junction Is the Dynamical Mechanism for Neuronal Communication |
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128 | (1) |
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Molecular Motors Move Cargo over Large Distances In a Directed Way |
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129 | (1) |
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Membrane-Bound Proteins Transport Molecules from One Side of a Membrane to the Other |
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130 | (1) |
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3.4.3 Beating the Replication Limit |
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131 | (1) |
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3.4.4 Eggs and Spores: Planning for the Next Generation |
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132 | (1) |
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3.5 Summary And Conclusions |
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133 | (1) |
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133 | (3) |
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136 | (1) |
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136 | (1) |
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Chapter 4 Who: "Bless the Little Beasties" |
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137 | (48) |
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4.1 Choosing A Grain Of Sand |
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137 | (6) |
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Modern Genetics Began with the Use of Peas as a Model System |
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138 | (1) |
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4.1.1 Biochemistry and Genetics |
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138 | (5) |
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4.2 Hemoglobin As A Model Protein |
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143 | (4) |
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4.2.1 Hemoglobin, Receptor-Ligand Binding, and the Other Bohr |
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143 | (1) |
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The Binding of Oxygen to Hemoglobin Has Served as a Model System for Llgand-Receptor Interactions More Generally |
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143 | (1) |
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Quantitative Analysis of Hemoglobin Is Based upon Measuring the Fractional Occupancy of the Oxygen-Binding Sites as a Function of Oxygen Pressure |
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144 | (1) |
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4.2.2 Hemoglobin and the Origins of Structural Biology |
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144 | (1) |
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The Study of the Mass of Hemoglobin Was Central in the Development of Centrifugation |
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145 | (1) |
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Structural Biology Has Its Roots in the Determination of the Structure of Hemoglobin |
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145 | (1) |
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4.2.3 Hemoglobin and Molecular Models of Disease |
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146 | (1) |
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4.2.4 The Rise of Allostery and Cooperativity |
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146 | (1) |
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4.3 Bacteriophages And Molecular Biology |
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147 | (7) |
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4.3.1 Bacteriophages and the Origins of Molecular Biology |
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148 | (1) |
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Bacteriophages Have Sometimes Been Called the "Hydrogen Atoms of Biology" |
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148 | (1) |
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Experiments on Phages and Their Bacterial Hosts Demonstrated That Natural Selection Is Operative in Microscopic Organisms |
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148 | (1) |
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The Hershey-Chase Experiment Both Confirmed the Nature of Genetic Material and Elucidated One of the Mechanisms of Viral DNA Entry into Cells |
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149 | (1) |
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Experiments on Phage T4 Demonstrated the Sequence Hypothesis of Collinearity of DNA and Proteins |
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150 | (1) |
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The Triplet Nature of the Genetic Code and DNA Sequencing Were Carried Out on Phage Systems |
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150 | (1) |
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Phages Were Instrumental in Elucidating the Existence of mRNA |
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151 | (1) |
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General Ideas about Gene Regulation Were Learned from the Study of Viruses as a Model System |
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152 | (1) |
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4.3.2 Bacteriophages and Modern Biophysics |
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153 | (1) |
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Many Single-Molecule Studies of Molecular Motors Have Been Performed on Motors from Bacteriophages |
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154 | (1) |
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4.4 A Tale Of Two Cells: E. Coli As A Model System |
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154 | (7) |
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4.4.1 Bacteria and Molecular Biology |
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154 | (2) |
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4.4.2 E. coli and the Central Dogma |
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156 | (1) |
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The Hypothesis of Conservative Replication Has Falsifiable Consequences |
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156 | (1) |
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Extracts from E. coli Were Used to Perform In Vitro Synthesis of DNA, mRNA, and Proteins |
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157 | (1) |
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4.4.3 The lac Operon as the "Hydrogen Atom" of Genetic Circuits |
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157 | (1) |
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Gene Regulation in E. coli Serves as a Model for Genetic Circuits in General |
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157 | (1) |
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The lac Operon Is a Genetic Network That Controls the Production of the Enzymes Responsible for Digesting the Sugar Lactose |
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158 | (1) |
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4.4.4 Signaling and Motility: The Case of Bacterial Chemotaxis |
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159 | (1) |
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E. coli Has Served as a Model System for the Analysis of Cell Motility |
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159 | (2) |
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4.5 Yeast: From Biochemistry To The Cell Cycle |
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161 | (9) |
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Yeast Has Served as a Model System Leading to Insights in Contexts Ranging from Vitalism to the Functioning of Enzymes to Eukaryotic Gene Regulation |
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161 | (1) |
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4.5.1 Yeast and the Rise of Biochemistry |
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162 | (1) |
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4.5.2 Dissecting the Cell Cycle |
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162 | (2) |
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4.5.3 Deciding Which Way Is Up: Yeast and Polarity |
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164 | (2) |
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4.5.4 Dissecting Membrane Traffic |
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166 | (1) |
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4.5.5 Genomics and Proteomics |
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167 | (3) |
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4.6 Flies And Modern Biology |
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170 | (3) |
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4.6.1 Flies and the Rise of Modern Genetics |
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170 | (1) |
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Drosophila melanogaster Has Served as a Model System for Studies Ranging from Genetics to Development to the Functioning of the Brain and Even Behavior |
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170 | (1) |
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4.6.2 How the Fly Got His Stripes |
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171 | (2) |
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173 | (1) |
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174 | (5) |
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4.8.1 Specialists and Experts |
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174 | (1) |
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4.8.2 The Squid Giant Axon and Biological Electricity |
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175 | (1) |
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There Is a Steady-State Potential Difference Across the Membrane of Nerve Cells |
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176 | (1) |
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Nerve Cells Propagate Electrical Signals and Use Them to Communicate with Each Other |
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176 | (2) |
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178 | (1) |
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4.9 Summary And Conclusions |
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179 | (1) |
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179 | (2) |
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181 | (2) |
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183 | (2) |
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185 | (296) |
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Chapter 5 Mechanical and Chemical Equilibrium in the Living Cell |
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187 | (50) |
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5.1 Energy And The Life Of Cells |
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187 | (13) |
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5.1.1 The Interplay of Deterministic and Thermal Forces |
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189 | (1) |
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Thermal Jostling of Particles Must Be Accounted for in Biological Systems |
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189 | (1) |
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5.1.2 Constructing the Cell: Managing the Mass and Energy Budget of the Cell |
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190 | (10) |
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5.2 Biological Systems As Minimizers |
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200 | (9) |
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5.2.1 Equilibrium Models for Out of Equilibrium Systems |
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200 | (1) |
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Equilibrium Models Can Be Used for Nonequilibrium Problems if Certain Processes Happen Much Faster Than Others |
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201 | (1) |
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5.2.2 Proteins in "Equilibrium" |
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202 | (1) |
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Protein Structures are Free-Energy Minimizers |
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203 | (1) |
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5.2.3 Cells in "Equilibrium" |
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204 | (1) |
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5.2.4 Mechanical Equilibrium from a Minimization Perspective |
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204 | (1) |
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The Mechanical Equilibrium State is Obtained by Minimizing the Potential Energy |
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204 | (5) |
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5.3 The Mathematics Of Superlatives |
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209 | (5) |
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5.3.1 The Mathematization of Judgement: Functions and Functionals |
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209 | (1) |
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Functional Deliver a Number for Every Function They Are Given |
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210 | (1) |
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5.3.2 The Calculus of Superlatives |
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211 | (1) |
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Finding the Maximum and Minimum Values of a Function Requires That We Find Where the 5lope of the Function Equals Zero |
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211 | (3) |
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5.4 Configurational Energy |
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214 | (5) |
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In Mechanical Problems, Potential Energy Determines the Equilibrium Structure |
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214 | (2) |
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5.4.1 Hooke's Law: Actin to Lipids |
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216 | (1) |
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There Is a Linear Relation Between Force and Extension of a Beam |
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216 | (1) |
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The Energy to Deform an Elastic Material is a Quadratic Function of the Strain |
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217 | (2) |
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5.5 Structures As Free-Energy Minimizers |
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219 | (12) |
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The Entropy is a Measure of the Microscopic Degeneracy of a Macroscopic State |
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219 | (3) |
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5.5.1 Entropy and Hydrophobicity |
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222 | (1) |
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Hydrophobicity Results from Depriving Water Molecules of Some of Their Configurational Entropy |
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222 | (2) |
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Amino Acids Can Be Classified According to Their Hydrophobicity |
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224 | (1) |
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When in Water, Hydrocarbon Tails on Lipids Have an Entropy Cost |
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225 | (1) |
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5.5.2 Gibbs and the Calculus of Equilibrium |
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225 | (1) |
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Thermal and Chemical Equilibrium are Obtained by Maximizing the Entropy |
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225 | (2) |
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5.5.3 Departure from Equilibrium and Fluxes |
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227 | (1) |
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5.5.4 Structure as a Competition |
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228 | (1) |
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Free Energy Minimization Can Be Thought of as an Alternative Formulation of Entropy Maximization |
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228 | (2) |
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230 | (1) |
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The Free Energy Reflects a Competition Between Energy and Entropy |
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230 | (1) |
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5.6 Summary And Conclusions |
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231 | (1) |
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5.7 Appendix: The Euler-Lagrange Equations, Finding The Superlative |
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232 | (1) |
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Finding the Extrema of Functionals Is Carried Out Using the Calculus of Variations |
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232 | (1) |
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The Euler-Lagrange Equations Let Us Minimize Functionals by Solving Differential Equations |
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232 | (1) |
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233 | (2) |
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235 | (1) |
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236 | (1) |
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237 | (44) |
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6.1 The Analytical Engine Of Statistical Mechanics |
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237 | (22) |
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The Probability of Different Microstates Is Determined by Their Energy |
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240 | (1) |
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6.1.1 A First Look at Ligand-Receptor Binding |
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241 | (3) |
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6.1.2 The Statistical Mechanics of Gene Expression: RNA Polymerase and the Promoter |
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244 | (1) |
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A Simple Model of Gene Expression Is to Consider the Probability of RNA Polymerase Binding at the Promoter |
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245 | (1) |
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Most Cellular RNA Polymerase Molecules Are Bound to DNA |
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245 | (2) |
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The Binding Probability of RNA Polymerase to its Promoter Is a Simple Function of the Number of Polymerase Molecules and the Binding Energy |
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247 | (1) |
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6.1.3 Classic Derivation of the Boltzmann Distribution |
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248 | (1) |
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The Boltzmann Distribution Gives the Probability of Microstates for a System in Contact with a Thermal Reservoir |
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248 | (2) |
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6.1.4 Boltzmann Distribution by Counting |
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250 | (1) |
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Different Ways of Partitioning Energy Among Particles Have Different Degeneracies |
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250 | (3) |
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6.1.5 Boltzmann Distribution by Guessing |
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253 | (1) |
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Maximizing the Entropy Corresponds to Making a Best Guess When Faced with Limited Information |
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253 | (2) |
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Entropy Maximization Can Be Used as a Tool for Statistical Inference |
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255 | (3) |
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The Boltzmann Distribution is the Maximum Entropy Distribution in Which the Average Energy is Prescribed as a Constraint |
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258 | (1) |
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259 | (8) |
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6.2.1 Average Energy of a Molecule in a Gas |
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259 | (1) |
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The Ideal Gas Entropy Reflects the Freedom to Rearrange Molecular Positions and Velocities |
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259 | (3) |
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6.2.2 Free Energy of Dilute Solutions |
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262 | (1) |
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The Chemical Potential of a Dilute Solution Is a Simple Logarithmic Function of the Concentration |
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262 | (2) |
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6.2.3 Osmotic Pressure as an Entropic Spring |
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264 | (1) |
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Osmotic Pressure Arises from Entropic Effects |
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264 | (1) |
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Viruses, Membrane-Bound Organelles, and Cells Are Subject to Osmotic Pressure |
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265 | (1) |
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Osmotic Forces Have Been Used to Measure the Interstrand Interactions of DNA |
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266 | (1) |
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6.3 The Calculus Of Equilibrium Applied: Law Of Mass Action |
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267 | (3) |
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6.3.1 Law of Mass Action and Equilibrium Constants |
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267 | (1) |
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Equilibrium Constants are Determined by Entropy Maximization |
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267 | (3) |
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6.4 Applications Of The Calculus Of Equilibrium |
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270 | (6) |
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6.4.1 A Second Look at Ligand-Receptor Binding |
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270 | (2) |
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6.4.2 Measuring Ligand-Receptor Binding |
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272 | (1) |
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6.4.3 Beyond Simple Ligand-Receptor Binding: The Hill Function |
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273 | (1) |
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274 | (1) |
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The Energy Released In ATP Hydrolysis Depends Upon the Concentrations of Reactants and Products |
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275 | (1) |
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6.5 Summary And Conclusions |
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276 | (1) |
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276 | (2) |
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278 | (1) |
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278 | (3) |
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Chapter 7 Two-State Systems: From Ion Channels to Cooperative Binding |
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281 | (30) |
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7.1 Macromolecules With Multiple States |
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281 | (8) |
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7.1.1 The Internal State Variable Idea |
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281 | (1) |
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The State of a Protein or Nucleic Acid Can Be Characterized Mathematically Using a State Variable |
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282 | (4) |
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7.1.2 Ion Channels as an Example of Internal State Variables |
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286 | (1) |
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The Open Probability (σ) of an Ion Channel Can Be Computed Using Statistical Mechanics |
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287 | (2) |
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7.2 State Variable Description Of Binding |
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289 | (16) |
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7.2.1 The Gibbs Distribution: Contact with a Particle Reservoir |
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289 | (1) |
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The Gibbs Distribution Gives the Probability of Microstates for a System in Contact with a Thermal and Particle Reservoir |
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289 | (2) |
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7.2.2 Simple Ligand-Receptor Binding Revisited |
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291 | (1) |
|
7.2.3 Phosphorylation as an Example of Two Internal State Variables |
|
|
292 | (1) |
|
Phosphorylation Can Change the Energy Balance Between Active and Inactive States |
|
|
293 | (2) |
|
Two-Component Systems Exemplify the Use of Phosphorylation in Signal Transduction |
|
|
295 | (3) |
|
7.2.4 Hemoglobin as a Case Study in Cooperativity |
|
|
298 | (1) |
|
The Binding Affinity of Oxygen for Hemoglobin Depends upon Whether or Not Other Oxygens Are Already Bound |
|
|
298 | (1) |
|
A Toy Model of a Dimeric Hemoglobin (Dimoglobin) Illustrate the Idea of Cooperativity |
|
|
298 | (2) |
|
The Monod-Wyman-Changeux (MWC) Model Provides a Simple Example of Cooperative Binding |
|
|
300 | (1) |
|
Statistical Models of the Occupancy of Hemoglobin Can Be Written Using Occupation Variables |
|
|
301 | (1) |
|
There is a Logical Progression of Increasingly Complex Binding Models for Hemoglobin |
|
|
301 | (4) |
|
7.3 Ion Channels Revisited: Ligand-Gated Channels And The Mwc Model |
|
|
305 | (3) |
|
7.4 Summary And Conclusions |
|
|
308 | (1) |
|
|
|
308 | (2) |
|
|
|
310 | (1) |
|
|
|
310 | (1) |
|
Chapter 8 Random Walks and the Structure of Macromolecules |
|
|
311 | (44) |
|
8.1 What Is A Structure: PDB Or RG? |
|
|
311 | (1) |
|
8.1.1 Deterministic versus Statistical Descriptions of Structure |
|
|
312 | (1) |
|
PDB Files Reflect a Deterministic Description of Macromolecular Structure |
|
|
312 | (1) |
|
Statistical Descriptions of Structure Emphasize Average Size and Shape Rather Than Atomic Coordinates |
|
|
312 | (1) |
|
8.2 Macromolecules As Random Walks |
|
|
312 | (25) |
|
Random Walk Models of Macromolecules View Them as Rigid Segments Connected by Hinges |
|
|
312 | (1) |
|
8.2.1 A Mathematical Stupor |
|
|
313 | (1) |
|
In Random Walk Models of Polymers, Every Macromolecular Configuration Is Equally Probable |
|
|
313 | (1) |
|
The Mean Size of a Random Walk Macromolecule Scales as the Square Root of the Number of Segments, √N |
|
|
314 | (1) |
|
The Probability of a Given Macromolecular State Depends Upon Its Microscopic Degeneracy |
|
|
315 | (1) |
|
Entropy Determines the Elastic Properties of Polymer Chains |
|
|
316 | (3) |
|
The Persistence Length Is a Measure of the Length Scale Over Which a Polymer Remains Roughly Straight |
|
|
319 | (2) |
|
8.2.2 How Big Is a Genome? |
|
|
321 | (1) |
|
8.2.3 The Geography of Chromosomes |
|
|
322 | (1) |
|
Genetic Maps and Physical Maps of Chromosomes Describe Different Aspects of Chromosome Structure |
|
|
322 | (1) |
|
Different Structural Models of Chromatin Are Characterized by the Linear Packing Density Of DNA |
|
|
323 | (1) |
|
Spatial Organization of Chromosomes Shows Elements of Both Randomness and Order |
|
|
324 | (1) |
|
Chromosomes Are Tethered at Different Locations |
|
|
325 | (2) |
|
Chromosome Territories Have Been Observed in Bacterial Cells |
|
|
327 | (1) |
|
Chromosome Territories in Vibrio cholerae Can Be Explored Using Models of Polymer Confinement and Tethering |
|
|
328 | (5) |
|
8.2.4 DNA Looping: From Chromosomes to Gene Regulation |
|
|
333 | (1) |
|
The Lac Repressor Molecule Acts Mechanistically by Forming a Sequestered Loop in DNA |
|
|
334 | (1) |
|
Looping of Large DNA Fragments Is Dictated by the Difficulty of Distant Ends Finding Each Other |
|
|
334 | (2) |
|
Chromosome Conformation Capture Reveals the Geometry of Packing of Entire Genomes in Cells |
|
|
336 | (1) |
|
8.3 The New World Of Single-Molecule Mechanics |
|
|
337 | (7) |
|
Single-Molecule Measurement Techniques Lead to Force Spectroscopy |
|
|
337 | (2) |
|
8.3.1 Force-Extension Curves: A New Spectroscopy |
|
|
339 | (1) |
|
Different Macromolecules Have Different Force Signatures When Subjected to Loading |
|
|
339 | (1) |
|
8.3.2 Random Walk Models for Force-Extension Curves |
|
|
340 | (1) |
|
The Low-Force Regime in Force-Extension Curves Can Be Understood Using the Random Walk Model |
|
|
340 | (4) |
|
8.4 Proteins As Random Walks |
|
|
344 | (7) |
|
8.4.1 Compact Random Walks and the Size of Proteins |
|
|
345 | (1) |
|
The Compact Nature of Proteins Leads to an Estimate of Their Size |
|
|
345 | (1) |
|
8.4.2 Hydrophobic and Polar Residues: The HP Model |
|
|
346 | (1) |
|
The HP Model Divides Amino Acids into Two Classes: Hydrophobic and Polar |
|
|
346 | (2) |
|
8.4.3 HP Models of Protein Folding |
|
|
348 | (3) |
|
8.5 Summary And Conclusions |
|
|
351 | (1) |
|
|
|
351 | (2) |
|
|
|
353 | (1) |
|
|
|
353 | (2) |
|
Chapter 9 Electrostatics for Salty Solutions |
|
|
355 | (28) |
|
9.1 Water As Life's Aether |
|
|
355 | (3) |
|
9.2 The Chemistry Of Water |
|
|
358 | (2) |
|
9.2.1 pH and the Equilibrium Constant |
|
|
358 | (1) |
|
Dissociation of Water Molecules Reflects a Competition Between the Energetics of Binding and the Entropy of Charge Liberation |
|
|
358 | (1) |
|
9.2.2 The Charge on DNA and Proteins |
|
|
359 | (1) |
|
The Charge State of Biopolymers Depends upon the pH of the Solution |
|
|
359 | (1) |
|
Different Amino Acids Have Different Charge States |
|
|
359 | (1) |
|
|
|
360 | (1) |
|
9.3 Electrostatics For Salty Solutions |
|
|
360 | (19) |
|
9.3.1 An Electrostatics Primer |
|
|
361 | (1) |
|
A Charge Distribution Produces an Electric Field Throughout Space |
|
|
362 | (1) |
|
The Flux of the Electric Field Measures the Density of Electric Field Lines |
|
|
363 | (1) |
|
The Electrostatic Potential Is an Alternative Basis for Describing the Electrical State of a System |
|
|
364 | (3) |
|
There Is an Energy Cost Associated With Assembling a Collection of Charges |
|
|
367 | (1) |
|
The Energy to Liberate Ions from Molecules Can Be Comparable to the Thermal Energy |
|
|
368 | (1) |
|
9.3.2 The Charged Life of a Protein |
|
|
369 | (1) |
|
9.3.3 The Notion of Screening: Electrostatics in Salty Solutions |
|
|
370 | (1) |
|
Ions In Solution Are Spatially Arranged to Shield Charged Molecules Such as DNA |
|
|
370 | (1) |
|
The Size of the Screening Cloud Is Determined by a Balance of Energy and Entropy of the Surrounding Ions |
|
|
371 | (3) |
|
9.3.4 The Poisson-Boltzmann Equation |
|
|
374 | (1) |
|
The Distribution of Screening Ions Can Be Found by Minimizing the Free Energy |
|
|
374 | (2) |
|
The Screening Charge Decays Exponentially Around Macromolecules In Solution |
|
|
376 | (1) |
|
9.3.5 Viruses as Charged Spheres |
|
|
377 | (2) |
|
9.4 Summary And Conclusion |
|
|
379 | (1) |
|
|
|
380 | (2) |
|
|
|
382 | (1) |
|
|
|
382 | (1) |
|
Chapter 10 Beam Theory: Architecture for Cells and Skeletons |
|
|
383 | (44) |
|
10.1 Beams Are Everywhere: From Flagella To The Cytoskeleton |
|
|
383 | (2) |
|
One-Dimensional Structural Elements Are the Basis of Much of Macromolecular and Cellular Architecture |
|
|
383 | (2) |
|
10.2 Geometry And Energetics Of Beam Deformation |
|
|
385 | (9) |
|
10.2.1 Stretch, Bend, and Twist |
|
|
385 | (1) |
|
Beam Deformations Result in Stretching, Bending, and Twisting |
|
|
385 | (1) |
|
A Bent Beam Can Be Analyzed as a Collection of Stretched Beams |
|
|
385 | (2) |
|
The Energy Cost to Deform a Beam Is a Quadratic Function of the Strain |
|
|
387 | (2) |
|
10.2.2 Beam Theory and the Persistence Length: Stiffness Is Relative |
|
|
389 | (1) |
|
Thermal Fluctuations Tend to Randomize the Orientation of Biological Polymers |
|
|
389 | (1) |
|
The Persistence Length Is the Length Over Which a Polymer Is Roughly Rigid |
|
|
390 | (1) |
|
The Persistence Length Characterizes the Correlations in the Tangent Vectors at Different Positions Along the Polymer |
|
|
390 | (1) |
|
The Persistence Length Is Obtained by Averaging Over All Configurations of the Polymer |
|
|
391 | (1) |
|
10.2.3 Elasticity and Entropy: The Worm-Like Chain |
|
|
392 | (1) |
|
The Worm-Like Chain Model Accounts for Both the Elastic Energy and Entropy of Polymer Chains |
|
|
392 | (2) |
|
10.3 The Mechanics Of Transcriptional Regulation: DNA Looping Redux |
|
|
394 | (4) |
|
10.3.1 The lac Operon and Other Looping Systems |
|
|
394 | (1) |
|
Transcriptional Regulation Can Be Effected by DNA Looping |
|
|
395 | (1) |
|
10.3.2 Energetics of DNA Looping |
|
|
395 | (1) |
|
10.3.3 Putting It All Together: The J-Factor |
|
|
396 | (2) |
|
10.4 DNA Packing: From Viruses To Eukaryotes |
|
|
398 | (15) |
|
The Packing of DNA In Viruses and Cells Requires Enormous Volume Compaction |
|
|
398 | (2) |
|
10.4.1 The Problem of Viral DNA Packing |
|
|
400 | (1) |
|
Structural Biologists Have Determined the Structure of Many Parts in the Viral Parts List |
|
|
400 | (2) |
|
The Packing of DNA in Viruses Results in a Free-Energy Penalty |
|
|
402 | (1) |
|
A Simple Model of DNA Packing in Viruses Uses the Elastic Energy of Circular Hoops |
|
|
403 | (1) |
|
DNA Self-Interactions Are also Important in Establishing the Free Energy Associated with DNA Packing in Viruses |
|
|
404 | (2) |
|
DNA Packing in Viruses Is a Competition Between Elastic and Interaction Energies |
|
|
406 | (1) |
|
10.4.2 Constructing the Nucleosome |
|
|
407 | (1) |
|
Nucleosome Formation Involves Both Elastic Deformation and Interactions Between Histones and DNA |
|
|
408 | (1) |
|
10.4.3 Equilibrium Accessibility of Nucleosomal DNA |
|
|
409 | (1) |
|
The Equilibrium Accessibility of Sites within the Nucleosome Depends upon How Far They Are from the Unwrapped Ends |
|
|
409 | (4) |
|
10.5 The Cytoskeleton And Beam Theory |
|
|
413 | (8) |
|
Eukaryotic Cells Are Threaded by Networks of Filaments |
|
|
413 | (1) |
|
10.5.1 The Cellular Interior: A Structural Perspective |
|
|
414 | (2) |
|
Prokaryotic Cells Have Proteins Analogous to the Eukaryotic Cytoskeleton |
|
|
416 | (1) |
|
10.5.2 Stiffness of Cytoskeletal Filaments |
|
|
416 | (1) |
|
The Cytoskeleton Can Be Viewed as a Collection of Elastic Beams |
|
|
416 | (3) |
|
10.5.3 Cytoskeletal Buckling |
|
|
419 | (1) |
|
A Beam Subject to a Large Enough Force Will Buckle |
|
|
419 | (1) |
|
10.5.4 Estimate of the Buckling Force |
|
|
420 | (1) |
|
Beam Buckling Occurs at Smaller Forces for Longer Beams |
|
|
420 | (1) |
|
10.6 Summary And Conclusions |
|
|
421 | (1) |
|
10.7 Appendix: The Mathematics Of The Worm-Like Chain |
|
|
421 | (3) |
|
|
|
424 | (2) |
|
|
|
426 | (1) |
|
|
|
426 | (1) |
|
Chapter 11 Biological Membranes: Life in Two Dimensions |
|
|
427 | (54) |
|
11.1 The Nature Of Biological Membranes |
|
|
427 | (13) |
|
11.1.1 Cells and Membranes |
|
|
427 | (1) |
|
Cells and Their Organelles Are Bound by Complex Membranes |
|
|
427 | (2) |
|
Electron Microscopy Provides a Window on Cellular Membrane Structures |
|
|
429 | (2) |
|
11.1.2 The Chemistry and Shape of Lipids |
|
|
431 | (1) |
|
Membranes Are Built from a Variety of Molecules That Have an Ambivalent Relationship with Water |
|
|
431 | (5) |
|
The Shapes of Lipid Molecules Can Induce Spontaneous Curvature on Membranes |
|
|
436 | (1) |
|
11.1.3 The Liveliness of Membranes |
|
|
436 | (1) |
|
Membrane Proteins Shuttle Mass Across Membranes |
|
|
437 | (2) |
|
Membrane Proteins Communicate Information |
|
|
|
|
|
439 | (1) |
|
Specialized Membrane Proteins Generate ATP |
|
|
439 | (1) |
|
Membrane Proteins Can Be Reconstituted in Vesicles |
|
|
439 | (1) |
|
11.2 On The Springiness Of Membranes |
|
|
440 | (8) |
|
11.2.1 An Interlude on Membrane Geometry |
|
|
440 | (1) |
|
Membrane Stretching Geometry Can Be Described by a Simple Area Function |
|
|
441 | (1) |
|
Membrane Bending Geometry Can Be Described by a Simple Height Function, h(x, y) |
|
|
441 | (3) |
|
Membrane Compression Geometry Can Be Described by a Simple Thickness Function, w(x, y) |
|
|
444 | (1) |
|
Membrane Shearing Can Be Described by an Angle Variable, θ |
|
|
444 | (1) |
|
11.2.2 Free Energy of Membrane Deformation |
|
|
445 | (1) |
|
There Is a Free-Energy Penalty Associated with Changing the Area of a Lipid Bilayer |
|
|
445 | (1) |
|
There Is a Free-Energy Penalty Associated with Bending a Lipid Bilayer |
|
|
446 | (1) |
|
There Is a Free-Energy Penalty for Changing the Thickness of a Lipid Bilayer |
|
|
446 | (1) |
|
There Is an Energy Cost Associated with the Gaussian Curvature |
|
|
447 | (1) |
|
11.3 Structure, Energetics, And Function Of Vesicles |
|
|
448 | (10) |
|
11.3.1 Measuring Membrane Stiffness |
|
|
448 | (1) |
|
Membrane Elastic Properties Can Be Measured by Stretching Vesicles |
|
|
448 | (2) |
|
|
|
450 | (3) |
|
|
|
453 | (1) |
|
Vesicles Are Used for a Variety of Cellular Transport Processes |
|
|
453 | (2) |
|
There Is a Fixed Free-Energy Cost Associated with Spherical Vesicles of All Sizes |
|
|
455 | (1) |
|
Vesicle Formation Is Assisted by Budding Proteins |
|
|
456 | (2) |
|
There Is an Energy Cost to Disassemble Coated Vesicles |
|
|
458 | (1) |
|
|
|
458 | (4) |
|
11.4.1 Pinching Vesicles: The Story of Dynamin |
|
|
459 | (3) |
|
|
|
462 | (5) |
|
11.5.1 The Shapes of Organelles |
|
|
462 | (1) |
|
The Surface Area of Membranes Due to Pleating Is So Large That Organelles Can Have Far More Area than the Plasma Membrane |
|
|
463 | (2) |
|
11.5.2 The Shapes of Cells |
|
|
465 | (1) |
|
The Equilibrium Shapes of Red Blood Cells Can Be Found by Minimizing the Free Energy |
|
|
466 | (1) |
|
|
|
467 | (8) |
|
11.6.1 Mechanosensitive Ion Channels and Membrane Elasticity |
|
|
467 | (1) |
|
Mechanosensitive Ion Channels Respond to Membrane Tension |
|
|
467 | (1) |
|
11.6.2 Elastic Deformations of Membranes Produced by Proteins |
|
|
468 | (1) |
|
Proteins Induce Elastic Deformations in the Surrounding Membrane |
|
|
468 | (1) |
|
Protein-Induced Membrane Bending Has an Associated Free-Energy Cost |
|
|
469 | (1) |
|
11.6.3 One-Dimensional Solution for MscL |
|
|
470 | (1) |
|
Membrane Deformations Can Be Obtained by Minimizing the Membrane Free Energy |
|
|
470 | (2) |
|
The Membrane Surrounding a Channel Protein Produces a Line Tension |
|
|
472 | (3) |
|
11.7 Summary And Conclusions |
|
|
475 | (1) |
|
|
|
476 | (3) |
|
|
|
479 | (1) |
|
|
|
479 | (2) |
|
|
|
481 | (318) |
|
Chapter 12 The Mathematics of Water |
|
|
483 | (26) |
|
12.1 Putting Water In Its Place |
|
|
483 | (1) |
|
12.2 Hydrodynamics Of Water And Other Fluids |
|
|
484 | (7) |
|
12.2.1 Water as a Continuum |
|
|
484 | (1) |
|
Though Fluids Are Composed of Molecules It Is Possible to Treat Them as a Continuous Medium |
|
|
484 | (1) |
|
12.2.2 What Can Newton Tell Us? |
|
|
485 | (1) |
|
Gradients in Fluid Velocity Lead to Shear Forces |
|
|
485 | (1) |
|
|
|
486 | (4) |
|
12.2.4 The Newtonian Fluid and the Navier-Stokes Equations |
|
|
490 | (1) |
|
The Velocity of Fluids at Surfaces Is Zero |
|
|
491 | (1) |
|
12.3 The River Within: Fluid Dynamics Of Blood |
|
|
491 | (4) |
|
12.3.1 Boats in the River: Leukocyte Rolling and Adhesion |
|
|
493 | (2) |
|
12.4 THE Low Reynolds Number World |
|
|
495 | (9) |
|
12.4.1 Stokes Flow: Consider a Spherical Bacterium |
|
|
495 | (3) |
|
12.4.2 Stokes Drag in Single-Molecule Experiments |
|
|
498 | (1) |
|
Stokes Drag Is Irrelevant for Optical Tweezers Experiments |
|
|
498 | (1) |
|
12.4.3 Dissipative Time Scales and the Reynolds Number |
|
|
499 | (1) |
|
12.4.4 Fish Gotta Swim, Birds Gotta Fly, and Bacteria Gotta Swim Too |
|
|
500 | (2) |
|
Reciprocal Deformation of the Swimmer's Body Does Not Lead to Net Motion at Low Reynolds Number |
|
|
502 | (1) |
|
12.4.5 Centrifugation and Sedimentation: Spin It Down |
|
|
502 | (2) |
|
12.5 Summary And Conclusions |
|
|
504 | (1) |
|
|
|
505 | (2) |
|
|
|
507 | (1) |
|
|
|
507 | (2) |
|
Chapter 13 A Statistical View of Biological Dynamics |
|
|
509 | (34) |
|
13.1 Diffusion In The Cell |
|
|
509 | (6) |
|
13.1.1 Active versus Passive Transport |
|
|
510 | (1) |
|
13.1.2 Biological Distances Measured In Diffusion Times |
|
|
511 | (1) |
|
The Time It Takes a Diffusing Molecule to Travel a Distance L Grows as the Square of the Distance |
|
|
512 | (1) |
|
Diffusion Is Not Effective Over Large Cellular Distances |
|
|
512 | (2) |
|
|
|
514 | (1) |
|
13.2 Concentration Fields And Diffusive Dynamics |
|
|
515 | (17) |
|
Fick's Law Tells Us How Mass Transport Currents Arise as a Result of Concentration Gradients |
|
|
517 | (1) |
|
The Diffusion Equation Results from Fick's Law and Conservation of Mass |
|
|
518 | (1) |
|
13.2.1 Diffusion by Summing Over Microtrajectories |
|
|
518 | (6) |
|
13.2.2 Solutions and Properties of the Diffusion Equation |
|
|
524 | (1) |
|
Concentration Profiles Broaden Over Time in a Very Precise Way |
|
|
524 | (1) |
|
|
|
525 | (4) |
|
13.2.4 Drunks on a Hill: The Smoluchowski Equation |
|
|
529 | (1) |
|
13.2.5 The Einstein Relation |
|
|
530 | (2) |
|
13.3 Diffusion To Capture |
|
|
532 | (6) |
|
13.3.1 Modeling the Cell Signaling Problem |
|
|
532 | (1) |
|
Perfect Receptors Result In a Rate of Uptake 4πDcoa |
|
|
533 | (1) |
|
A Distribution of Receptors Is Almost as Good as a Perfectly Absorbing Sphere |
|
|
534 | (2) |
|
Real Receptors Are Not Always Uniformly Distributed |
|
|
536 | (1) |
|
13.3.2 A "Universal" Rate for Diffusion-Limited |
|
|
|
|
|
537 | (1) |
|
13.4 Summary And Conclusions |
|
|
538 | (1) |
|
|
|
539 | (1) |
|
|
|
540 | (1) |
|
|
|
540 | (3) |
|
Chapter 14 Life in Crowded and Disordered Environments |
|
|
543 | (30) |
|
14.1 Crowding, Linkage, And Entanglement |
|
|
543 | (7) |
|
14.1.1 The Cell Is Crowded |
|
|
544 | (1) |
|
14.1.2 Macromolecular Networks: The Cytoskeleton and Beyond |
|
|
545 | (1) |
|
14.1.3 Crowding on Membranes |
|
|
546 | (1) |
|
14.1.4 Consequences of Crowding |
|
|
547 | (1) |
|
Crowding Alters Biochemical Equilibria |
|
|
548 | (1) |
|
Crowding Alters the Kinetics within Cells |
|
|
548 | (2) |
|
14.2 Equilibria In Crowded Environments |
|
|
550 | (16) |
|
14.2.1 Crowding and Binding |
|
|
550 | (1) |
|
Lattice Models of Solution Provide a Simple Picture of the Role of Crowding in Biochemical Equilibria |
|
|
550 | (2) |
|
14.2.2 Osmotic Pressures in Crowded Solutions |
|
|
552 | (1) |
|
Osmotic Pressure Reveals Crowding Effects |
|
|
552 | (2) |
|
14.2.3 Depletion Forces: Order from Disorder |
|
|
554 | (1) |
|
The Close Approach of Large Particles Excludes Smaller Particles Between Them, Resulting in an Entropic Force |
|
|
554 | (5) |
|
Depletion Forces Can Induce Entropic Ordering! |
|
|
559 | (1) |
|
14.2.4 Excluded Volume and Polymers |
|
|
559 | (1) |
|
Excluded Volume Leads to an Effective Repulsion Between Molecules |
|
|
559 | (2) |
|
Self-avoidance Between the Monomers of a Polymer Leads to Polymer Swelling |
|
|
561 | (2) |
|
14.2.5 Case Study In Crowding: How to Make a Helix |
|
|
563 | (2) |
|
14.2.6 Crowding at Membranes |
|
|
565 | (1) |
|
|
|
566 | (3) |
|
14.3.1 Crowding and Reaction Rates |
|
|
566 | (1) |
|
Enzymatic Reactions in Cells Can Proceed Faster than the Diffusion Limit Using Substrate Channeling |
|
|
566 | (1) |
|
Protein Folding Is Facilitated by Chaperones |
|
|
567 | (1) |
|
14.3.2 Diffusion in Crowded Environments |
|
|
567 | (2) |
|
14.4 Summary And Conclusions |
|
|
569 | (1) |
|
|
|
569 | (1) |
|
|
|
570 | (1) |
|
|
|
571 | (2) |
|
Chapter 15 Rate Equations and Dynamics in the Cell |
|
|
573 | (50) |
|
15.1 Biological Statistical Dynamics: A First Look |
|
|
573 | (6) |
|
15.1.1 Cells as Chemical Factories |
|
|
574 | (1) |
|
15.1.2 Dynamics of the Cytoskeleton |
|
|
575 | (4) |
|
15.2 A Chemical Picture Of Biological Dynamics |
|
|
579 | (20) |
|
15.2.1 The Rate Equation Paradigm |
|
|
579 | (1) |
|
Chemical Concentrations Vary in Both Space and Time |
|
|
580 | (1) |
|
Rate Equations Describe the Time Evolution of Concentrations |
|
|
580 | (1) |
|
15.2.2 All Good Things Must End |
|
|
581 | (1) |
|
Macromolecular Decay Can Be Described by a Simple, First-Order Differential Equation |
|
|
581 | (1) |
|
15.2.3 A Single-Molecule View of Degradation: Statistical Mechanics Over Trajectories |
|
|
582 | (1) |
|
Molecules Fall Apart with a Characteristic Lifetime |
|
|
582 | (1) |
|
Decay Processes Can Be Described with Two-State Trajectories |
|
|
583 | (2) |
|
Decay of One Species Corresponds to Growth in the Number of a Second Species |
|
|
585 | (1) |
|
15.2.4 Bimolecular Reactions |
|
|
586 | (1) |
|
Chemical Reactions Can Increase the Concentration of a Given Species |
|
|
586 | (2) |
|
Equilibrium Constants Have a Dynamical Interpretation in Terms of Reaction Rates |
|
|
588 | (1) |
|
15.2.5 Dynamics of Ion Channels as a Case Study |
|
|
589 | (1) |
|
Rate Equations for ton Channels Characterize the Time Evolution of the Open and Closed Probability |
|
|
590 | (1) |
|
|
|
591 | (5) |
|
15.2.7 Michaelis-Menten and Enzyme Kinetics |
|
|
596 | (3) |
|
15.3 The Cytoskeleton Is Always Under Construction |
|
|
599 | (3) |
|
15.3.1 The Eukaryotic Cytoskeleton |
|
|
599 | (1) |
|
The Cytoskeleton Is a Dynamical Structure That Is Always Under Construction |
|
|
599 | (1) |
|
15.3.2 The Curious Case of the Bacterial Cytoskeleton |
|
|
600 | (2) |
|
15.4 Simple Models Of Cytoskeletal Polymerization |
|
|
602 | (16) |
|
The Dynamics of Polymerization Can Involve Many Distinct Physical and Chemical Effects |
|
|
603 | (1) |
|
15.4.1 The Equilibrium Polymer |
|
|
604 | (1) |
|
Equilibrium Models of Cytoskeletal Filaments Describe the Distribution of Polymer Lengths for Simple Polymers |
|
|
604 | (2) |
|
An Equilibrium Polymer Fluctuates in Time |
|
|
606 | (3) |
|
15.4.2 Rate Equation Description of Cytoskeletal Polymerization |
|
|
609 | (1) |
|
Polymerization Reactions Can Be Described by Rate Equations |
|
|
609 | (1) |
|
The Time Evolution of the Probability Distribution Pn(t) Can Be Written Using a Rate Equation |
|
|
610 | (2) |
|
Rates of Addition and Removal of Monomers Are Often Different on the Two Ends of Cytoskeletal Filaments |
|
|
612 | (2) |
|
15.4.3 Nucleotide Hydrolysis and Cytoskeletal Polymerization |
|
|
614 | (1) |
|
ATP Hydrolysis Sculpts the Molecular Interface, Resulting in Distinct Rates at the Ends of Cytoskeletal Filaments |
|
|
614 | (1) |
|
15.4.4 Dynamic Instability: A Toy Model of the Cap |
|
|
615 | (1) |
|
A Toy Model of Dynamic Instability Assumes That Catastrophe Occurs When Hydrolyzed Nucleotides Are Present at the Growth Front |
|
|
616 | (2) |
|
15.5 Summary And Conclusions |
|
|
618 | (1) |
|
|
|
619 | (2) |
|
|
|
621 | (1) |
|
|
|
621 | (2) |
|
Chapter 16 Dynamics of Molecular Motors |
|
|
623 | (58) |
|
16.1 The Dynamics Of Molecular Motors: Life In The Noisy Lane |
|
|
623 | (16) |
|
16.1.1 Translational Motors: Beating the Diffusive Speed Limit |
|
|
625 | (3) |
|
The Motion of Eukaryotic Cilia and Flagella Is Driven by Translational Motors |
|
|
628 | (2) |
|
Muscle Contraction Is Mediated by Myosin Motors |
|
|
630 | (4) |
|
|
|
634 | (3) |
|
16.1.3 Polymerization Motors: Pushing by Growing |
|
|
637 | (1) |
|
16.1.4 Translocation Motors: Pushing by Pulling |
|
|
638 | (1) |
|
16.2 Rectified Brownian Motion And Molecular Motors |
|
|
639 | (24) |
|
16.2.1 The Random Walk Yet Again |
|
|
640 | (1) |
|
Molecular Motors Can Be Thought of as Random Walkers |
|
|
640 | (1) |
|
16.2.2 The One-State Model |
|
|
641 | (1) |
|
The Dynamics of a Molecular Motor Can Be Written Using a Master Equation |
|
|
642 | (2) |
|
The Driven Diffusion Equation Can Be Transformed into an Ordinary Diffusion Equation |
|
|
644 | (3) |
|
16.2.3 Motor Stepping from a Free-Energy Perspective |
|
|
647 | (4) |
|
16.2.4 The Two-State Model |
|
|
651 | (1) |
|
The Dynamics of a Two-State Motor Is Described by Two Coupled Rate Equations |
|
|
651 | (3) |
|
Internal States Reveal Themselves in the Form of the Waiting Time Distribution |
|
|
654 | (2) |
|
16.2.5 More General Motor Models |
|
|
656 | (2) |
|
16.2.6 Coordination of Motor Protein Activity |
|
|
658 | (2) |
|
|
|
660 | (3) |
|
16.3 Polymerization And Translocation As Motor Action |
|
|
663 | (14) |
|
16.3.1 The Polymerization Ratchet |
|
|
663 | (3) |
|
The Polymerization Ratchet Is Based on a Polymerization Reaction That Is Maintained Out of Equilibrium |
|
|
666 | (2) |
|
The Polymerization Ratchet Force-Velocity Can Be Obtained by Solving a Driven Diffusion Equation |
|
|
668 | (2) |
|
16.3.2 Force Generation by Growth |
|
|
670 | (1) |
|
Polymerization Forces Can Be Measured Directly |
|
|
670 | (2) |
|
Polymerization Forces Are Used to Center Cellular Structures |
|
|
672 | (1) |
|
16.3.3 The Translocation Ratchet |
|
|
673 | (1) |
|
Protein Binding Can Speed Up Translocation through a Ratcheting Mechanism |
|
|
674 | (2) |
|
The Translocation Time Can Be Estimated by Solving a Driven Diffusion Equation |
|
|
676 | (1) |
|
16.4 Summary And Conclusions |
|
|
677 | (1) |
|
|
|
677 | (2) |
|
|
|
679 | (1) |
|
|
|
679 | (2) |
|
Chapter 17 Biological Electricity and the Hodgkin-Huxley Model |
|
|
681 | (36) |
|
17.1 The Role Of Electricity In Cells |
|
|
681 | (1) |
|
17.2 The Charge State Of The Cell |
|
|
682 | (3) |
|
17.2.1 The Electrical Status of Cells and Their Membranes |
|
|
682 | (1) |
|
17.2.2 Electrochemical Equilibrium and the Nernst Equation |
|
|
683 | (1) |
|
Ion Concentration Differences Across Membranes Lead to Potential Differences |
|
|
683 | (2) |
|
17.3 Membrane Permeability: Pumps And Channels |
|
|
685 | (8) |
|
A Nonequilibrium Charge Distribution Is Set Up Between the Cell Interior and the External World |
|
|
685 | (1) |
|
Signals in Cells Are Often Mediated by the Presence of Electrical Spikes Called Action Potentials |
|
|
686 | (2) |
|
17.3.1 Ion Channels and Membrane Permeability |
|
|
688 | (1) |
|
Ion Permeability Across Membranes Is Mediated by Ion Channels |
|
|
688 | (1) |
|
A Simple Two-State Model Can Describe Many of the Features of Voltage Gating of Ion Channels |
|
|
689 | (2) |
|
17.3.2 Maintaining a Nonequilibrium Charge State |
|
|
691 | (1) |
|
Ions Are Pumped Across the Cell Membrane Against an Electrochemical Gradient |
|
|
691 | (2) |
|
17.4 The Action Potential |
|
|
693 | (21) |
|
17.4.1 Membrane Depolarization: The Membrane as a Bistable Switch |
|
|
693 | (1) |
|
Coordinated Muscle Contraction Depends Upon Membrane Depolarization |
|
|
694 | (2) |
|
A Patch of Cell Membrane Can Be Modeled as an Electrical Circuit |
|
|
696 | (2) |
|
The Difference Between the Membrane Potential and the Nernst Potential Leads to an Ionic Current Across the Cell Membrane |
|
|
698 | (1) |
|
Voltage-Gated Channels Result in a Nonlinear Current-Voltage Relation for the Cell Membrane |
|
|
699 | (1) |
|
A Patch of Membrane Acts as a Bistable Switch |
|
|
700 | (2) |
|
The Dynamics of Voltage Relaxation Can Be Modeled Using an RC Circuit |
|
|
702 | (1) |
|
17.4.2 The Cable Equation |
|
|
703 | (2) |
|
17.4.3 Depolarization Waves |
|
|
705 | (1) |
|
Waves of Membrane Depolarization Rely on Sodium Channels Switching into the Open State |
|
|
705 | (5) |
|
|
|
710 | (2) |
|
17.4.5 Hodgkin-Huxley and Membrane Transport |
|
|
712 | (1) |
|
Inactivation of Sodium Channels Leads to Propagating Spikes |
|
|
712 | (2) |
|
17.5 Summary And Conclusions |
|
|
714 | (1) |
|
|
|
714 | (1) |
|
|
|
715 | (1) |
|
|
|
715 | (2) |
|
Chapter 18 Light and Life |
|
|
717 | (82) |
|
|
|
718 | (1) |
|
|
|
719 | (40) |
|
Organisms From All Three of the Great Domains of Life Perform Photosynthesis |
|
|
720 | (4) |
|
18.2.1 Quantum Mechanics for Biology |
|
|
724 | (1) |
|
Quantum Mechanical Kinematics Describes States of the System in Terms of Wave Functions |
|
|
725 | (3) |
|
Quantum Mechanical Observables Are Represented by Operators |
|
|
728 | (1) |
|
The Time Evolution of Quantum States Can Be Determined Using the Schrodinger Equation |
|
|
729 | (1) |
|
18.2.2 The Particle-in-a-Box Model |
|
|
730 | (1) |
|
Solutions for the Box of Finite Depth Do Not Vanish at the Box Edges |
|
|
731 | (2) |
|
18.2.3 Exciting Electrons With Light |
|
|
733 | (2) |
|
Absorption Wavelengths Depend Upon Molecular Size and Shape |
|
|
735 | (2) |
|
18.2.4 Moving Electrons From Hitherto Yon |
|
|
737 | (1) |
|
Excited Electrons Can Suffer Multiple Fates |
|
|
737 | (2) |
|
Electron Transfer in Photosynthesis Proceeds by Tunneling |
|
|
739 | (6) |
|
Electron Transfer Between Donor and Acceptor Is Gated by Fluctuations of the Environment |
|
|
745 | (2) |
|
Resonant Transfer Processes in the Antenna Complex Efficiently Deliver Energy to the Reaction Center |
|
|
747 | (1) |
|
18.2.5 Bioenergetics of Photosynthesis |
|
|
748 | (1) |
|
Electrons Are Transferred from Donors to Acceptors Within and Around the Cell Membrane |
|
|
748 | (2) |
|
Water, Water Everywhere, and Not an Electron to Drink |
|
|
750 | (1) |
|
Charge Separation across Membranes Results in a Proton-Motive Force |
|
|
751 | (1) |
|
|
|
752 | (5) |
|
|
|
757 | (1) |
|
18.2.8 Photosynthesis in Perspective |
|
|
758 | (1) |
|
|
|
759 | (26) |
|
18.3.1 Bacterial "Vision" |
|
|
760 | (3) |
|
18.3.2 Microbial Phototaxis and Manipulating Cells with Light |
|
|
763 | (1) |
|
|
|
763 | (2) |
|
There Is a Simple Relationship between Eye Geometry and Resolution |
|
|
765 | (3) |
|
The Resolution of Insect Eyes Is Governed by Both the Number of Ommatidia and Diffraction Effects |
|
|
768 | (1) |
|
The Light-Driven Conformational Change of Retinal Underlies Animal Vision |
|
|
769 | (4) |
|
Information from Photon Detection Is Amplified by a Signal Transduction Cascade in the Photoreceptor Cell |
|
|
773 | (3) |
|
The Vertebrate Visual System Is Capable of Detecting Single Photons |
|
|
776 | (5) |
|
18.3.4 Sex, Death, and Quantum Mechanics |
|
|
781 | (3) |
|
Let There Be Light: Chemical Reactions Can Be Used to Make Light |
|
|
784 | (1) |
|
18.4 Summary And Conclusions |
|
|
785 | (1) |
|
18.5 Appendix: Simple Model Of Electron Tunneling |
|
|
785 | (8) |
|
|
|
793 | (2) |
|
|
|
795 | (1) |
|
|
|
796 | (3) |
|
PART 4 The Meaning of Life |
|
|
799 | (240) |
|
Chapter 19 Organization of Biological Networks |
|
|
801 | (92) |
|
19.1 Chemical And Informational Organization In The Cell |
|
|
801 | (6) |
|
Many Chemical Reactions in the Cell are Linked in Complex Networks |
|
|
801 | (1) |
|
Genetic Networks Describe the Linkages Between Different Genes and Their Products |
|
|
802 | (1) |
|
Developmental Decisions Are Made by Regulating Genes |
|
|
802 | (2) |
|
Gene Expression Is Measured Quantitatively In Terms of How Much, When, and Where |
|
|
804 | (3) |
|
19.2 Genetic Networks: Doing The Right Thing At The Right Time |
|
|
807 | (28) |
|
Promoter Occupancy Is Dictated by the Presence of Regulatory Proteins Called Transcription |
|
|
|
|
|
808 | (1) |
|
19.2.1 The Molecular Implementation of Regulation: Promoters, Activators, and Repressors |
|
|
808 | (1) |
|
Repressor Molecules Are the Proteins That Implement Negative Control |
|
|
808 | (1) |
|
Activators Are the Proteins That Implement Positive Control |
|
|
809 | (1) |
|
Genes Can Be Regulated During Processes Other Than Transcription |
|
|
809 | (1) |
|
19.2.2 The Mathematics of Recruitment and Rejection |
|
|
810 | (1) |
|
Recruitment of Proteins Reflects Cooperativity Between Different DNA-Binding Proteins |
|
|
810 | (2) |
|
The Regulation Factor Dictates How the Bare RNA Polymerase Binding Probability Is Altered by Transcription Factors |
|
|
812 | (1) |
|
Activator Bypass Experiments Show That Activators Work by Recruitment |
|
|
813 | (1) |
|
Repressor Molecules Reduce the Probability Polymerase Will Bind to the Promoter |
|
|
814 | (5) |
|
19.2.3 Transcriptional Regulation by the Numbers: Binding Energies and Equilibrium Constants |
|
|
819 | (1) |
|
Equilibrium Constants Can Be Used To Determine Regulation Factors |
|
|
819 | (1) |
|
19.2.4 A Simple Statistical Mechanical Model of Positive and Negative Regulation |
|
|
820 | (2) |
|
|
|
822 | (1) |
|
The lac Operon Has Features of Both Negative and Positive Regulation |
|
|
822 | (2) |
|
The Free Energy of DNA Looping Affects the Repression of the lac Operon |
|
|
824 | (5) |
|
Inducers Tune the Level of Regulatory Response |
|
|
829 | (1) |
|
19.2.6 Other Regulatory Architectures |
|
|
829 | (1) |
|
The Fold-Change for Different Regulatory Motifs Depends Upon Experimentally Accessible Control Parameters |
|
|
830 | (2) |
|
Quantitative Analysis of Gene Expression In Eukaryotes Can Also Be Analyzed Using Thermodynamic Models |
|
|
832 | (3) |
|
|
|
835 | (37) |
|
19.3.1 The Dynamics of RNA Polymerase and the Promoter |
|
|
835 | (1) |
|
The Concentrations of Both RNA and Protein Can Be Described Using Rate Equations |
|
|
835 | (3) |
|
19.3.2 Dynamics of mRNA Distributions |
|
|
838 | (3) |
|
Unregulated Promoters Can Be Described By a Poisson Distribution |
|
|
841 | (2) |
|
19.3.3 Dynamics of Regulated Promoters |
|
|
843 | (1) |
|
The Two-State Promoter Has a Fano Factor Greater Than One |
|
|
844 | (5) |
|
Different Regulatory Architectures Have Different Fano Factors |
|
|
849 | (5) |
|
19.3.4 Dynamics of Protein Translation |
|
|
854 | (7) |
|
19.3.5 Genetic Switches: Natural and Synthetic |
|
|
861 | (9) |
|
19.3.6 Genetic Networks That Oscillate |
|
|
870 | (2) |
|
19.4 CELLULAR FAST RESPONSE: SIGNALING |
|
|
872 | (16) |
|
19.4.1 Bacterial Chemotaxis |
|
|
873 | (5) |
|
The MWC Model Can Be Used to Describe Bacterial Chemotaxis |
|
|
878 | (3) |
|
Precise Adaptation Can Be Described by a Simple Balance Between Methylation and Demethylation |
|
|
881 | (2) |
|
19.4.2 Biochemistry on a Leash |
|
|
883 | (1) |
|
Tethering Increases the Local Concentration of a Ligand |
|
|
884 | (1) |
|
Signaling Networks Help Cells Decide When and Where to Grow Their Actin Filaments for Motility |
|
|
884 | (1) |
|
Synthetic Signaling Networks Permit a Dissection of Signaling Pathways |
|
|
885 | (3) |
|
19.5 Summary And Conclusions |
|
|
888 | (1) |
|
|
|
889 | (2) |
|
|
|
891 | (1) |
|
|
|
892 | (1) |
|
Chapter 20 Biological Patterns: Order in Space and Time |
|
|
893 | (58) |
|
20.1 Introduction: Making Patterns |
|
|
893 | (3) |
|
20.1.1 Patterns in Space and Time |
|
|
894 | (1) |
|
20.1.2 Rules for Pattern-Making |
|
|
895 | (1) |
|
|
|
896 | (18) |
|
20.2.1 The French Flag Model |
|
|
896 | (2) |
|
20.2.2 How the Fly Got His Stripes |
|
|
898 | (1) |
|
Bicoid Exhibits an Exponential Concentration Gradient Along the Anterior-Posterior Axis of Fly Embryos |
|
|
898 | (1) |
|
A Reaction-Diffusion Mechanism Can Give Rise to an Exponential Concentration Gradient |
|
|
899 | (6) |
|
20.2.3 Precision and Scaling |
|
|
905 | (7) |
|
20.2.4 Morphogen Patterning with Growth in Anabaena |
|
|
912 | (2) |
|
20.3 Reaction-Diffusion And Spatial Patterns |
|
|
914 | (17) |
|
20.3.1 Putting Chemistry and Diffusion Together: Turing Patterns |
|
|
914 | (6) |
|
20.3.2 How Bacteria Lay Down a Coordinate System |
|
|
920 | (6) |
|
20.3.3 Phyllotaxls: The Art of Flower Arrangement |
|
|
926 | (5) |
|
20.4 Turning Time Into Space: Temporal Oscillations In Cell Fate Specification |
|
|
931 | (8) |
|
|
|
932 | (3) |
|
20.4.2 Seashells Forming Patterns in Space and Time |
|
|
935 | (4) |
|
20.5 Pattern Formation As A Contact Sport |
|
|
939 | (8) |
|
20.5.1 The Notch-Delta Concept |
|
|
939 | (5) |
|
|
|
944 | (3) |
|
20.6 Summary And Conclusions |
|
|
947 | (1) |
|
|
|
948 | (1) |
|
|
|
949 | (1) |
|
|
|
950 | (1) |
|
Chapter 21 Sequences, Specificity, and Evolution |
|
|
951 | (72) |
|
21.1 Biological Information |
|
|
952 | (8) |
|
|
|
953 | (4) |
|
21.1.2 Genomes and Sequences by the Numbers |
|
|
957 | (3) |
|
21.2 Sequence Alignment And Homology |
|
|
960 | (16) |
|
Sequence Comparison Can Sometimes Reveal Deep Functional and Evolutionary Relationships Between Genes, Proteins, and Organisms |
|
|
961 | (3) |
|
21.2.1 The HP Model as a Coarse-Grained Model for Bioinformatics |
|
|
964 | (2) |
|
|
|
966 | (1) |
|
A Score Can Be Assigned to Different Alignments Between Sequences |
|
|
966 | (2) |
|
Comparison of Full Amino Acid Sequences Requires a 20-by-20 Scoring Matrix |
|
|
968 | (2) |
|
Even Random Sequences Have a Nonzero Score |
|
|
970 | (1) |
|
The Extreme Value Distribution Determines the Probability That a Given Alignment Score Would Be Found by Chance |
|
|
971 | (2) |
|
False Positives Increase as the Threshold for Acceptable Expect Values (also Called E-Values) Is Made Less Stringent |
|
|
973 | (3) |
|
Structural and Functional Similarity Do Not Always Guarantee Sequence Similarity |
|
|
976 | (1) |
|
21.3 The Power Of Sequence Gazing |
|
|
976 | (17) |
|
21.3.1 Binding Probabilities and Sequence |
|
|
977 | (1) |
|
Position Weight Matrices Provide a Map Between Sequence and Binding Affinity |
|
|
978 | (1) |
|
Frequencies of Nucleotides at Sites Within a |
|
|
|
Sequence Can Be Used to Construct Position Weight Matrices |
|
|
979 | (4) |
|
21.3.2 Using Sequence to Find Binding Sites |
|
|
983 | (5) |
|
21.3.3 Do Nucleosomes Care About Their Positions on Genomes? |
|
|
988 | (1) |
|
DNA Sequencing Reveals Patterns of Nucleosome Occupancy on Genomes |
|
|
989 | (1) |
|
A Simple Model Based Upon Self-Avoidance Leads to a Prediction for Nucleosome Positioning |
|
|
990 | (3) |
|
21.4 Sequences And Evolution |
|
|
993 | (17) |
|
21.4.1 Evolution by the Numbers: Hemoglobin and Rhodopsin as Case Studies in Sequence Alignment |
|
|
994 | (1) |
|
Sequence Similarity Is Used as a Temporal Yardstick to Determine Evolutionary Distances |
|
|
994 | (2) |
|
Modern-Day Sequences Can Be Used to Reconstruct the Past |
|
|
996 | (2) |
|
21.4.2 Evolution and Drug Resistance |
|
|
998 | (2) |
|
21.4.3 Viruses and Evolution |
|
|
1000 | (1) |
|
The Study of Sequence Makes It Possible to Trace the Evolutionary History of HIV |
|
|
1001 | (1) |
|
The Luria-Delbruck Experiment Reveals the Mathematics of Resistance |
|
|
1002 | (6) |
|
21.4.4 Phylogenetic Trees |
|
|
1008 | (2) |
|
21.5 The Molecular Basis Of Fidelity |
|
|
1010 | (6) |
|
21.5.1 Keeping It Specific: Beating Thermodynamic Specificity |
|
|
1011 | (1) |
|
The Specificity of Biological Recognition Often Far Exceeds the Limit Dictated by Free-Energy Differences |
|
|
1011 | (4) |
|
High Specificity Costs Energy |
|
|
1015 | (1) |
|
21.6 Summary And Conclusions |
|
|
1016 | (1) |
|
|
|
1017 | (3) |
|
|
|
1020 | (1) |
|
|
|
1021 | (2) |
|
Chapter 22 Whither Physical Biology? |
|
|
1023 | (16) |
|
22.1 Drawing The Map To Scale |
|
|
1023 | (4) |
|
22.2 Navigating When The Map Is Wrong |
|
|
1027 | (1) |
|
22.3 Increasing The Map Resolution |
|
|
1028 | (2) |
|
22.4 "Difficulties On Theory" |
|
|
1030 | (5) |
|
|
|
1031 | (1) |
|
Is It Biologically Interesting? |
|
|
1031 | (1) |
|
Uses and Abuses of Statistical Mechanics |
|
|
1032 | (1) |
|
Out-of-Equilibrium and Dynamic |
|
|
1032 | (1) |
|
Uses and Abuses of Continuum Mechanics |
|
|
1032 | (1) |
|
|
|
1033 | (1) |
|
|
|
1033 | (1) |
|
|
|
1033 | (1) |
|
|
|
1034 | (1) |
|
|
|
1034 | (1) |
|
|
|
1035 | (1) |
|
22.5 The Rhyme And Reason Of It All |
|
|
1035 | (1) |
|
|
|
1036 | (1) |
|
|
|
1037 | (2) |
| Index |
|
1039 | |
