Equilibria and Kinetics of Biological Macromolecules

Cover......Page 1
Title Page......Page 5
Contents......Page 9
Preface......Page 21
Acknowledgments......Page 23
Part 1 Basic Principles......Page 25
1.1 Introduction......Page 27
1.2 The fundamental postulates or Laws of thermodynamics......Page 28
1.3 Other useful quantities and concepts......Page 38
1.4 Thermodynamics of the ideal gas......Page 43
1.5 Thermodynamics of solutions......Page 44
1.6 Phase equilibria......Page 49
1.7 Chemical equilibria......Page 53
1.9 Microcalorimetry......Page 55
Notes......Page 57
2.1 Introduction......Page 59
2.2 Fundamental hypotheses of quantum theory......Page 60
2.3 Three simple models of nuclear motion......Page 62
2.4 Hydrogen atomic orbitals: A simple model of electronic motion in atoms......Page 68
2.5 Many electron atoms......Page 71
Suggested reading......Page 73
3.2 Chemical bonding: Electronic structure of molecules......Page 75
3.3 Empirical classical energy expressions......Page 82
3.4 Noncovalent forces between atoms and molecules......Page 86
3.5 Molecular mechanics......Page 94
Notes......Page 99
Suggested reading......Page 100
4.1 Introduction......Page 101
4.2 Structure of liquid water......Page 102
4.3 The hydrophobic effect......Page 108
Suggested reading......Page 113
Part 2 Statistical Mechanics: The Molecular Basis of Thermodynamics......Page 115
5.2 The Maxwell-Boltzmann distribution......Page 117
5.3 The molecular partition function and thermodynamic functions......Page 123
5.4 Application to macromolecules......Page 125
Notes......Page 132
Suggested reading......Page 134
6.1 Introduction......Page 135
6.2 Closed systems: The canonical ensemble......Page 136
6.3 The canonical partition function of systems with continuous energy distributions: The phase-space integral......Page 143
6.4 Application: Relation between binding and molecular interaction energy......Page 147
6.5 Application: Binding of ligand to a macromolecule......Page 149
6.6 Open systems: The grand canonical ensemble or grand ensemble......Page 151
6.7 Fluctuations......Page 155
6.8 Application: Light scattering as a measure of fluctuations of concentration......Page 158
Notes......Page 159
Suggested reading......Page 160
7.1 Introduction......Page 161
7.2 Background......Page 162
7.3 Molecular dynamics......Page 163
7.4 Metropolis Monte Carlo......Page 166
7.5 Simulation of a condensed system......Page 167
7.6 Connecting microscopic and macroscopic system properties......Page 168
7.7 An example: Dynamics of Ace-Ala-Nme in solution......Page 170
7.8 Forced transitions......Page 173
7.9 Potential of mean force for changes of chemistry: ``Computer Alchemy''......Page 176
7.10 The potential of mean force and the association equilibrium constant of methane......Page 181
Notes......Page 182
Suggested reading......Page 183
Part 3 Binding to Macromolecules......Page 185
8.2 Single-site model......Page 187
8.3 Measuring ligand activity and saturation......Page 190
8.4 Multiple sites for a single ligand......Page 197
8.5 A few practical recommendations......Page 206
Notes......Page 207
Suggested reading......Page 208
9.1 Introduction......Page 209
9.2 Relation between binding and chemical potential: Unified formulation of binding and ``exclusion''......Page 210
9.3 Free energy of binding......Page 211
9.4 Mutual response......Page 212
9.5 Volume exclusion......Page 213
9.6 Accounting for interactions of macromolecule and solvent components......Page 217
Suggested reading......Page 220
10.1 Introduction......Page 221
10.2 Partition function of ideal solution from thermodynamics......Page 222
10.3 Statistical mechanics of the ideal solution......Page 224
10.4 Formulation of molecular binding interactions in terms of a partition function: Empirical approach based on thermodynamics......Page 226
10.5 A purely statistical mechanical formulation of molecular binding interactions......Page 228
10.6 Statistical mechanical models of nonideal solutions and liquids......Page 232
Suggested reading......Page 235
11.1 Alternate equivalent representations of the partition function......Page 237
11.2 General implications......Page 239
11.3 Site-specific binding: General formulation......Page 240
11.4 Use of single-site binding constants......Page 242
11.5 Partition function for site binding: One type of ligand, independent multiple sites......Page 244
11.6 Site binding to interdependent or coupled sites......Page 245
Suggested reading......Page 246
12.1 Introduction......Page 247
12.2 Simple case: Coupling of binding (one site) and conformation change......Page 248
12.3 Coupling of binding to multiple sites and conformation change......Page 249
12.4 Free energy of binding can ``drive'' conformation change......Page 254
12.5 Formation of oligomers and polymers......Page 256
12.6 Coupled polymerization and ligand binding......Page 261
Suggested reading......Page 262
13.1 Introduction......Page 263
13.2 Background on hemoglobin......Page 264
13.3 The allosteric or induced-fit model of hemoglobin......Page 265
13.4 Simplified allosteric models: Concerted and sequential......Page 266
13.5 Numeric example......Page 268
13.6 Comparison of oxygen binding curves......Page 269
13.7 Separating oxygen binding and conformation change of hemoglobin......Page 270
13.9 Two-site proteins, half-the-sites reactivity, and negative cooperativity......Page 272
13.10 Allosteric effects in protein function......Page 273
13.12 Hill plot......Page 274
Notes......Page 276
Suggested reading......Page 277
14.1 Introduction......Page 279
14.2 Ionizable groups in peptides......Page 280
14.3 pH titration of a protein: Ribonuclease-normal and abnormal ionizable groups......Page 281
14.5 Internal charge-charge interactions: Ion pairs or salt bridges......Page 284
14.6 Measuring stability of salt bridges from double mutant cycles......Page 285
14.7 Salt bridges stabilize proteins from thermophilic organisms......Page 286
14.9 Accounting for charge-charge and charge-solvent interactions......Page 287
14.10 The continuum dielectric model......Page 288
14.11 Application to a charged spherical particle......Page 290
14.12 Accounting for ionic strength: The Poisson-Boltzmann equation and Debye-Huckel theory......Page 291
14.13 Numerical treatment via finite differences......Page 292
14.14 Strengths and limitations of the continuum dielectric model......Page 293
14.15 Applications of the continuum dielectric model to macromolecules......Page 294
Notes......Page 297
Suggested reading......Page 299
Part 4 Conformational Stability and Conformation Change......Page 301
15.1 Introduction......Page 303
15.3 Conformational variation in chain molecules......Page 304
15.4 The ideal random coil and the characteristic ratio......Page 305
15.5 The persistence length as a measure of chain flexibility......Page 306
15.6 Conformation of self-avoiding chains......Page 307
15.7 Dependence of chain conformation on solvent conditions; ``Theta'' conditions......Page 308
15.8 Relating chain statistics to molecular structure......Page 310
15.9 Polyelectrolytes......Page 311
Notes......Page 312
Suggested reading......Page 313
16.2 Single-stranded poly (A): A completely non-cooperative transition......Page 315
16.3 Synthetic polypeptides......Page 316
16.4 Zimm-Bragg, Gibbs-DiMarzio, and Lifson-Roig analyses......Page 319
16.5 Solution of the partition function......Page 321
16.7 Experimental determination of helix propensities in synthetic peptides......Page 323
16.8 Helix stabilization by salt bridges in oligomers containing Glu and Lys......Page 325
16.10 Helix-coil equilibria of nucleic acids......Page 327
16.11 Melting transition of DNA......Page 330
Notes......Page 333
17.1 Introduction......Page 335
17.2 The two-state approximation......Page 336
17.3 Working with the two-state model......Page 338
17.4 Calorimetric measurements of the thermodynamics of protein unfolding......Page 340
17.5 Unfolding thermodynamics of ribonuclease......Page 342
17.7 Solvent-induced unfolding: Guanidine hydrochloride and urea......Page 346
17.8 Mixed solvents: Denaturants and stabilizers......Page 348
17.9 Unfolding is not two-state under native conditions: Hydrogen exchange......Page 352
17.10 Nature of the two states......Page 356
17.11 A third state: The molten globule......Page 360
17.12 Range of stability......Page 362
17.13 Decomposition of the thermodynamic parameters for unfolding......Page 364
Notes......Page 366
Suggested reading......Page 369
18.1 Background......Page 371
18.2 Rubber-like elasticity of polymer networks......Page 372
18.3 Theory of rubber elasticity......Page 373
18.4 Rubber-like elasticity of elastin......Page 375
18.5 Titin and tenascin: Elasticity based on transitions between conformation states......Page 376
18.6 Single-molecule force-extension measurement......Page 378
Notes......Page 379
Part 5 Kinetics and Irreversible Processes......Page 381
19.1 Introduction......Page 383
19.2 Measuring fast kinetics by rapid perturbation......Page 384
19.3 Fast rates from spectroscopic line shape and relaxation times......Page 386
19.4 Relaxation time in a unimolecular reaction......Page 388
19.5 Relaxation time in a bimolecular reaction......Page 389
19.7 Numeric integration of the master equation......Page 391
19.8 Consecutive reactions cause delays......Page 392
19.9 Steady state assumption: Michaelis-Menten model, microscopic reversibility, and cyclic processes......Page 393
19.10 Nucleation and growth mechanisms in phase transitions and biopolymer folding reactions......Page 396
19.11 Kinetic theory and the transition state......Page 397
19.12 Transition state in catalysis......Page 399
19.13 Inhibitor design: Transition state analogs......Page 401
19.14 The diffusion-limited reaction......Page 403
19.15 Estimating reaction rates from simulations......Page 405
Notes......Page 410
Suggested reading......Page 411
20.1 Introduction......Page 413
20.2 Slow folding: Misfolding......Page 414
20.3 Slow folding: Cis-trans isomerization of proline......Page 415
20.4 Slow folding: Disulfide bond formation......Page 416
20.5 Two-state folding kinetics......Page 417
20.6 Folding rates of some peptides and proteins......Page 419
20.7 Probing the transition state: Tanford's β value and Fersht's φ value......Page 422
20.8 Early events in folding......Page 424
20.9 (Free) energy landscape for folding......Page 426
20.10 The ``Levinthal Paradox'' and the folding funnel......Page 427
20.11 Transition state(s), pathway(s), reaction coordinate(s)......Page 428
20.12 Computer simulations of protein folding and unfolding......Page 429
Notes......Page 434
Suggested reading......Page 436
General references......Page 437
21.1 Introduction......Page 439
21.2 Macroscopic treatment of diffusion......Page 440
21.3 Friction force opposes motion......Page 441
21.4 Random walk as a model diffusive process......Page 442
21.5 Equation of motion for stochastic processes: The Langevin equation......Page 443
21.6 Fluctuation-dissipation theorem......Page 444
21.7 Specific examples of fluctuating force......Page 445
21.8 Alternative form of the fluctuation-dissipation theorem......Page 446
21.9 Diffusive motion and the Langevin equation......Page 448
21.10 Smoluchowski and Fokker-Planck equations......Page 449
21.11 Transition state theory revisited......Page 453
21.12 Kramers' theory of reaction rates......Page 456
Notes......Page 459
Suggested reading......Page 460
Appendices......Page 461
A.1 Introduction......Page 463
A.3 Probability distributions......Page 464
A.5 Fitting theory to data: Computer-facilitated ``Least Squares''......Page 466
B.2 Random selection......Page 469
B.3 The central limit theorem......Page 470
B.4 Simple random walk......Page 471
C.1 Introduction......Page 473
C.2 Derivation......Page 474
C.3 Connection with thermodynamic functions......Page 475
C.4 Relation to other types of partition functions......Page 477
D.1 Introduction......Page 481
D.3 Slow growth......Page 482
D.4 Thermodynamic perturbation......Page 483
D.5 Umbrella sampling......Page 484
D.6 Conclusion......Page 485
E.1 Introduction......Page 487
E.2 Maximum term solution......Page 488
E.3 Solution via matrix algebra......Page 490
F.2 The Laplace transform......Page 493
F.3 Two key properties of the Laplace transform......Page 494
F.4 Example 1: The Poisson process (or consecutive reactions)......Page 495
F.5 Example 2: General case of linear kinetic equations......Page 496
F.6 Example 3: Coupled harmonic oscillators-normal modes......Page 498
F.7 Table of inverse Laplace transforms......Page 500
G.1 Formulation......Page 501
G.2 Exact solution for a simple case: The Born model......Page 502
G.3 Accounting for ionic strength: Poisson-Boltzmann equation and Debye-Huckel theory......Page 504
Appendix H Defining Molecular Boundaries......Page 507
I.1 Stirling's formula and combinatorials......Page 509
I.3 Cartesian and spherical polar coordinates......Page 510
I.5 Sums of geometric series......Page 511
I.7 Useful relations between differential quotients......Page 512
I.8 Random numbers......Page 513
Index......Page 515
both......Page 525
bins......Page 526