Preface |
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xix | |
Acknowledgments |
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xxi | |
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1 | (90) |
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3 | (32) |
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3 | (1) |
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1.2 The fundamental postulates or Laws of thermodynamics |
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4 | (10) |
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1.3 Other useful quantities and concepts |
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14 | (5) |
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1.4 Thermodynamics of the ideal gas |
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19 | (1) |
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1.5 Thermodynamics of solutions |
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20 | (5) |
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25 | (4) |
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29 | (2) |
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1.8 Temperature dependence of chemical equilibria: The van't Hoff equation |
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31 | (1) |
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31 | (4) |
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33 | (2) |
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2 Four Basic Quantum Mechanical Models of Nuclear and Electronic Motion: A Synopsis |
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35 | (16) |
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35 | (1) |
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2.2 Fundamental hypotheses of quantum theory |
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36 | (2) |
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2.3 Three simple models of nuclear motion |
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38 | (6) |
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2.4 Hydrogen atomic orbitals: A simple model of electronic motion in atoms |
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44 | (3) |
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47 | (4) |
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49 | (1) |
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49 | (2) |
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3 Molecular Structure and Interactions |
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51 | (26) |
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51 | (1) |
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3.2 Chemical bonding: Electronic structure of molecules |
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51 | (7) |
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3.3 Empirical classical energy expressions |
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58 | (4) |
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3.4 Noncovalent forces between atoms and molecules |
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62 | (8) |
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70 | (7) |
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75 | (1) |
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76 | (1) |
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4 Water and the Hydrophobic Effect |
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77 | (14) |
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77 | (1) |
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4.2 Structure of liquid water |
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78 | (6) |
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4.3 The hydrophobic effect |
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84 | (7) |
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89 | (1) |
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89 | (2) |
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PART 2 STATISTICAL MECHANICS: THE MOLECULAR BASIS OF THERMODYNAMICS |
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91 | (70) |
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5 The Molecular Partition Function |
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93 | (18) |
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93 | (1) |
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5.2 The Maxwell--Boltzmann distribution |
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93 | (6) |
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5.3 The molecular partition function and thermodynamic functions |
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99 | (2) |
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5.4 Application to macromolecules |
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101 | (10) |
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108 | (2) |
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110 | (1) |
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6 System Ensembles and Partition Functions |
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111 | (26) |
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111 | (1) |
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6.2 Closed systems: The canonical ensemble |
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112 | (7) |
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6.3 The canonical partition function of systems with continuous energy distributions: The phase-space integral |
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119 | (4) |
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6.4 Application: Relation between binding and molecular interaction energy |
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123 | (2) |
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6.5 Application: Binding of ligand to a macromolecule |
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125 | (2) |
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6.6 Open systems: The grand canonical ensemble or grand ensemble |
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127 | (4) |
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131 | (3) |
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6.8 Application: Light scattering as a measure of fluctuations of concentration |
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134 | (3) |
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135 | (1) |
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136 | (1) |
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7 Sampling Molecular Systems with Simulations |
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137 | (24) |
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137 | (1) |
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138 | (1) |
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139 | (3) |
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7.4 Metropolis Monte Carlo |
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142 | (1) |
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7.5 Simulation of a condensed system |
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143 | (1) |
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7.6 Connecting microscopic and macroscopic system properties |
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144 | (2) |
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7.7 An example: Dynamics of Ace-Ala-Nme in solution |
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146 | (3) |
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149 | (3) |
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7.9 Potential of mean force for changes of chemistry: "Computer Alchemy" |
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152 | (5) |
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7.10 The potential of mean force and the association equilibrium constant of methane |
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157 | (4) |
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158 | (1) |
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159 | (2) |
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PART 3 BINDING TO MACROMOLECULES |
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161 | (116) |
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163 | (22) |
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163 | (1) |
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163 | (3) |
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8.3 Measuring ligand activity and saturation |
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166 | (7) |
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8.4 Multiple sites for a single ligand |
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173 | (9) |
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8.5 A few practical recommendations |
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182 | (3) |
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183 | (1) |
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184 | (1) |
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9 Thermodynamics of Molecular Interactions |
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185 | (12) |
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185 | (1) |
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9.2 Relation between binding and chemical potential: Unified formulation of binding and "exclusion" |
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186 | (1) |
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9.3 Free energy of binding |
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187 | (1) |
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188 | (1) |
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189 | (4) |
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9.6 Accounting for interactions of macromolecule and solvent components |
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193 | (4) |
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196 | (1) |
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196 | (1) |
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10 Elements of Statistical Mechanics of Liquids and Solutions |
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197 | (16) |
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197 | (1) |
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10.2 Partition function of ideal solution from thermodynamics |
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198 | (2) |
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10.3 Statistical mechanics of the ideal solution |
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200 | (2) |
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10.4 Formulation of molecular binding interactions in terms of a partition function: Empirical approach based on thermodynamics |
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202 | (2) |
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10.5 A purely statistical mechanical formulation of molecular binding interactions |
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204 | (4) |
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10.6 Statistical mechanical models of nonideal solutions and liquids |
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208 | (5) |
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211 | (1) |
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211 | (2) |
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11 Analysis of Binding Equilibria in Terms of Partition Functions |
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213 | (10) |
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11.1 Alternate equivalent representations of the partition function |
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213 | (2) |
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11.2 General implications |
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215 | (1) |
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11.3 Site-specific binding: General formulation |
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216 | (2) |
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11.4 Use of single-site binding constants |
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218 | (2) |
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11.5 Partition function for site binding: One type of ligand, independent multiple sites |
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220 | (1) |
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11.6 Site binding to interdependent or coupled sites |
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221 | (2) |
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222 | (1) |
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223 | (16) |
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223 | (1) |
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12.2 Simple case: Coupling of binding (one site) and conformation change |
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224 | (1) |
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12.3 Coupling of binding to multiple sites and conformation change |
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225 | (5) |
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12.4 Free energy of binding can "drive" conformation change |
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230 | (2) |
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12.5 Formation of oligomers and polymers |
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232 | (5) |
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12.6 Coupled polymerization and ligand binding |
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237 | (2) |
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238 | (1) |
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238 | (1) |
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239 | (16) |
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239 | (1) |
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13.2 Background on hemoglobin |
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240 | (1) |
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13.3 The allosteric or induced-fit model of hemoglobin |
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241 | (1) |
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13.4 Simplified allosteric models: Concerted and sequential |
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242 | (2) |
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244 | (1) |
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13.6 Comparison of oxygen binding curves |
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245 | (1) |
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13.7 Separating oxygen binding and conformation change of hemoglobin |
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246 | (2) |
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13.8 Experiments with hybrid hemoglobins |
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248 | (1) |
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13.9 Two-site proteins, half-the-sites reactivity, and negative cooperativity |
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248 | (1) |
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13.10 Allosteric effects in protein function |
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249 | (1) |
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13.11 Sickle cell hemoglobin |
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250 | (1) |
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250 | (5) |
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252 | (1) |
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253 | (2) |
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14 Charged Groups: Binding of Hydrogen Ions, Solvation, and Charge--Charge Interactions |
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255 | (22) |
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255 | (1) |
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14.2 Ionizable groups in peptides |
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256 | (1) |
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14.3 pH titration of a protein: Ribonuclease---normal and abnormal ionizable groups |
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257 | (3) |
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14.4 Local interactions cause pKaS to be abnormal |
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260 | (1) |
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14.5 Internal charge--charge interactions: Ion pairs or salt bridges |
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260 | (1) |
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14.6 Measuring stability of salt bridges from double mutant cycles |
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261 | (1) |
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14.7 Salt bridges stabilize proteins from thermophilic organisms |
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262 | (1) |
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14.8 Charged side chains in enzyme catalysis and protein solubility |
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263 | (1) |
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14.9 Accounting for charge--charge and charge--solvent interactions |
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263 | (1) |
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14.10 The continuum dielectric model |
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264 | (2) |
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14.11 Application to a charged spherical particle |
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266 | (1) |
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14.12 Accounting for ionic strength: The Poisson--Boltzmann equation and Debye--Huckel theory |
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267 | (1) |
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14.13 Numerical treatment via finite differences |
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268 | (1) |
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14.14 Strengths and limitations of the continuum dielectric model |
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269 | (1) |
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14.15 Applications of the continuum dielectric model to macromolecules |
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270 | (7) |
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273 | (2) |
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275 | (2) |
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PART 4 CONFORMATIONAL STABILITY AND CONFORMATION CHANGE |
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277 | (80) |
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15 Some Elements of Polymer Physics |
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279 | (12) |
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279 | (1) |
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15.2 Conformational variation in small molecules |
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280 | (1) |
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15.3 Conformational variation in chain molecules |
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280 | (1) |
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15.4 The ideal random coil and the characteristic ratio |
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281 | (1) |
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15.5 The persistence length as a measure of chain flexibility |
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282 | (1) |
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15.6 Conformation of self-avoiding chains |
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283 | (1) |
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15.7 Dependence of chain conformation on solvent conditions; "Theta" conditions |
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284 | (2) |
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15.8 Relating chain statistics to molecular structure |
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286 | (1) |
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287 | (4) |
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288 | (1) |
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289 | (2) |
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291 | (20) |
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16.1 Introduction: Multistate transitions of helical polymers |
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291 | (1) |
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16.2 Single-stranded poly (A): A completely non-cooperative transition |
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291 | (1) |
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16.3 Synthetic polypeptides |
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292 | (3) |
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16.4 Zimm--Bragg, Gibbs--DiMarzio, and Lifson--Roig analyses |
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295 | (2) |
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16.5 Solution of the partition function |
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297 | (2) |
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16.6 Experiments on synthetic homo-polypeptides and protein fragments |
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299 | (1) |
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16.7 Experimental determination of helix propensities in synthetic peptides |
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299 | (2) |
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16.8 Helix stabilization by salt bridges in oligomers containing Glu and Lys |
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301 | (2) |
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16.9 Helix stabilization by charged groups interacting with the helix dipole |
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303 | (1) |
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16.10 Helix-coil equilibria of nucleic acids |
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303 | (3) |
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16.11 Melting transition of DNA |
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306 | (5) |
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309 | (2) |
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17 Protein Unfolding Equilibria |
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311 | (36) |
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311 | (1) |
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17.2 The two-state approximation |
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312 | (2) |
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17.3 Working with the two-state model |
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314 | (2) |
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17.4 Calorimetric measurements of the thermodynamics of protein unfolding |
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316 | (2) |
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17.5 Unfolding thermodynamics of ribonuclease |
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318 | (4) |
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322 | (1) |
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17.7 Solvent-induced unfolding: Guanidine hydrochloride and urea |
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322 | (2) |
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17.8 Mixed solvents: Denaturants and stabilizers |
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324 | (4) |
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17.9 Unfolding is not two-state under native conditions: Hydrogen exchange |
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328 | (4) |
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17.10 Nature of the two states |
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332 | (4) |
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17.11 A third state: The molten globule |
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336 | (2) |
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338 | (2) |
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17.13 Decomposition of the thermodynamic parameters for unfolding |
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340 | (7) |
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342 | (3) |
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345 | (2) |
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18 Elasticity of Biological Materials |
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347 | (10) |
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341 | (7) |
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18.2 Rubber-like elasticity of polymer networks |
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348 | (1) |
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18.3 Theory of rubber elasticity |
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349 | (2) |
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18.4 Rubber-like elasticity of elastin |
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351 | (1) |
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18.5 Titin and tenascin: Elasticity based on transitions between conformation states |
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352 | (2) |
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18.6 Single-molecule force-extension measurement |
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354 | (3) |
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355 | (2) |
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PART 5 KINETICS AND IRREVERSIBLE PROCESSES |
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357 | (80) |
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359 | (30) |
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359 | (1) |
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19.2 Measuring fast kinetics by rapid perturbation |
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360 | (2) |
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19.3 Fast rates from spectroscopic line shape and relaxation times |
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362 | (2) |
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19.4 Relaxation time in a unimolecular reaction |
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364 | (1) |
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19.5 Relaxation time in a bimolecular reaction |
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365 | (2) |
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367 | (1) |
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19.7 Numeric integration of the master equation |
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367 | (1) |
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19.8 Consecutive reactions cause delays |
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368 | (1) |
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19.9 Steady state assumption: Michaelis--Menten model, microscopic reversibility, and cyclic processes |
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369 | (3) |
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19.10 Nucleation and growth mechanisms in phase transitions and biopolymer folding reactions |
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372 | (1) |
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19.11 Kinetic theory and the transition state |
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373 | (2) |
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19.12 Transition state in catalysis |
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375 | (2) |
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19.13 Inhibitor design: Transition state analogs |
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377 | (2) |
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19.14 The diffusion-limited reaction |
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379 | (2) |
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19.15 Estimating reaction rates from simulations |
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381 | (8) |
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386 | (1) |
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387 | (2) |
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20 Kinetics of Protein Folding |
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389 | (26) |
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389 | (1) |
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20.2 Slow folding: Misfolding |
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390 | (1) |
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20.3 Slow folding: Cis-trans isomerization of proline |
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391 | (1) |
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20.4 Slow folding: Disulfide bond formation |
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392 | (1) |
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20.5 Two-state folding kinetics |
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393 | (2) |
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20.6 Folding rates of some peptides and proteins |
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395 | (3) |
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20.7 Probing the transition state: Tanford's β value and Fersht's φ value |
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398 | (2) |
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20.8 Early events in folding |
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400 | (2) |
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20.9 (Free) energy landscape for folding |
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402 | (1) |
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20.10 The "Levinthal Paradox" and the folding funnel |
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403 | (1) |
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20.11 Transition state(s), pathway(s), reaction coordinate(s) |
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404 | (1) |
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20.12 Computer simulations of protein folding and unfolding |
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405 | (5) |
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410 | (5) |
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410 | (2) |
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412 | (1) |
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413 | (2) |
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21 Irreversible and Stochastic Processes |
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415 | (22) |
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415 | (1) |
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21.2 Macroscopic treatment of diffusion |
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416 | (1) |
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21.3 Friction force opposes motion |
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417 | (1) |
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21.4 Random walk as a model diffusive process |
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418 | (1) |
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21.5 Equation of motion for stochastic processes: The Langevin equation |
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419 | (1) |
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21.6 Fluctuation--dissipation theorem |
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420 | (1) |
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21.7 Specific examples of fluctuating force |
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421 | (1) |
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21.8 Alternative form of the fluctuation--dissipation theorem |
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422 | (2) |
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21.9 Diffusive motion and the Langevin equation |
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424 | (1) |
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21.10 Smoluchowski and Fokker--Planck equations |
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425 | (4) |
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21.11 Transition state theory revisited |
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429 | (3) |
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21.12 Kramers' theory of reaction rates |
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432 | (5) |
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435 | (1) |
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436 | (1) |
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437 | (54) |
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439 | (6) |
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439 | (1) |
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440 | (1) |
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A.3 Probability distributions |
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440 | (2) |
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442 | (1) |
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A.5 Fitting theory to data: Computer-facilitated "Least Squares" |
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442 | (3) |
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B Random Walk and Central Limit Theorem |
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445 | (4) |
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445 | (1) |
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445 | (1) |
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B.3 The central limit theorem |
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446 | (1) |
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447 | (2) |
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C The Grand Partition Function: Derivation and Relation to Other Types of Partition Functions |
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449 | (8) |
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449 | (1) |
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450 | (1) |
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C.3 Connection with thermodynamic functions |
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451 | (2) |
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C.4 Relation to other types of partition functions |
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453 | (4) |
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D Methods to Compute a Potential of Mean Force |
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457 | (6) |
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457 | (1) |
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D.2 Thermodynamic integration |
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458 | (1) |
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458 | (1) |
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D.4 Thermodynamic perturbation |
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459 | (1) |
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460 | (1) |
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461 | (2) |
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E Theory of the Helix-Coil Transition |
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463 | (6) |
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463 | (1) |
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E.2 Maximum term solution |
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464 | (2) |
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E.3 Solution via matrix algebra |
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466 | (3) |
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469 | (8) |
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F.1 Solving linear differential equations with the Laplace transform |
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469 | (1) |
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F.2 The Laplace transform |
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469 | (1) |
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F.3 Two key properties of the Laplace transform |
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470 | (1) |
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F.4 Example 1: The Poisson process (or consecutive reactions) |
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471 | (1) |
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F.5 Example 2: General case of linear kinetic equations |
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472 | (2) |
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F.6 Example 3: Coupled harmonic oscillators'normal modes |
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474 | (2) |
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F.7 Table of inverse Laplace transforms |
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476 | (1) |
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477 | (6) |
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477 | (1) |
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G.2 Exact solution for a simple case: The Born model |
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478 | (2) |
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G.3 Accounting for ionic strength: Poisson--Boltzmann equation and Debye--Huckel theory |
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480 | (3) |
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H Defining Molecular Boundaries |
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483 | (2) |
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485 | (6) |
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I.1 Stirling's formula and combinatorials |
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485 | (1) |
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I.2 Integrals of Gaussian distributions |
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486 | (1) |
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I.3 Cartesian and spherical polar coordinates |
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486 | (1) |
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I.4 Laplace operator in three-dimensional cartesian, polar, and cylindrical coordinates |
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487 | (1) |
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I.5 Sums of geometric series |
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487 | (1) |
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I.6 The Kronecker and Dirac delta functions |
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488 | (1) |
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I.7 Useful relations between differential quotients |
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488 | (1) |
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489 | (2) |
Index |
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491 | |