Contents Preface Chapter 1 Biological Macromolecules 1.1 General PrincipIes 1.1.1 Macrornolecules 1.2 1.1.2 Configuration and Conformation Molecular lnteractions in Macromolecular Structures 1.2.1 Weak lnteractions 1.3 The Environment in the Cell 1.3.1 Water Structure 1.3.2 The lnteraction of Molecules with Water 1.3.3 Nonaqueous Environment of Biological Molecules 1.4 Symmetry Relationships of Molecules 1.4.1 Mirror Symmetry 1.4.2 Rotational Symrnetry 1.4.3 Multiple Syrnmetry Relationships and Point Groups 1.4.4 Screw Symmetry 1.5 The Structure of Proteins 1.5.1 Arnino Acids 1.5.2 The Unique Protein Sequence Application 1.1: Musical Sequences 1.5.3 Secondary Structures of Proteins Application 1.2: Engineering a New Fold 1.5.4 Helical Syrnmetry 1.5.5 1.5.6 Effect of the Peptide Bond on Protein Conforrnations The Structure of Globular Proteins 1.6 The Structure of Nuc1eic Acids 1.6.1 Torsion Angles in the Polynuc1eotide Chain 1.6.2 The Helical Structures of Polynuc1eic Acids 1.6.3 Higher-Order Structures in Polynuc1eotides Application 1.3: Embracing RNA Differences xiii 1 1 2 5 8 8 10 11 15 16 19 21 22 25 26 27 27 31 33 34 35 36 40 42 52 54 55 61 64 68 70 v
vi Contents Chapter 2 Thermodynamics and Biochemistry 2.1 Heat, Work, and Energy-First Law ofthermodynamics 2.2 Molecular Interpretation ofthermodynamic Quantities 2.3 Entropy, Free Energy, and Equilibrium-Second Law of Thermodynamics 2.4 The Standard State 2.5 Experimental Thermochemistry 2.5.1 The van't Hoff Relationship 2.5.2 Calorimetry Application 2.1: Competition Is a Good Thing Chapter 3 Molecular Thermodynamics 3.1 Complexities in Modeling Macromolecular Structure 3.2 3.1.1 Simplifying Assumptions Molecular Mechanics 3.2.1 Basic PrincipIes 3.2.2 Molecular Potentials 3.2.3 Bonding Potentials 3.2.4 Nonbonding Potentials 3.2.5 Electrostatic lnteractions 3.2.6 Dipole-Dipole Interactions 3.2.7 van der Waals Interactions 3.2.8 Hydrogen Bonds 3.3 Stabilizing Interactions in Macromolecules 3.3.1 Protein Structure 3.3.2 3.3.3 Dipole Interactions Side Chain Interactions 3.3.4 Electrostatic Interactions 3.3.5 Nucleic Acid Structure 3.3.6 Base-Pairing 3.3.7 3.3.8 Base-Stacking Electrostatic lnteractions 3.4 Simulating Macromolecular Structure 3.4.1 Energy Minimization 3.4.2 Molecular Dynamics 3.4.3 Entropy 3.4.4 Hydration and the Hydrophobic Effect 3.4.5 Free Energy Methods 72 73 76 80 91 93 93 94 102 104 105 107 107 108 109 109 111 112 115 115 117 118 120 124 125 129 131 131 133 137 139 141 145 146 147 149 153 159 161 163
Contents vii Chapter 4 Statistical Thermodynamics 4.1 General PrincipIes 4.1.1 Statistical Weights and the Partition Function 4.1.2 Models for Structural Transitions in Biopolymers 4.2 Structural Transitions in Polypeptides and Proteins 4.2.1 Coil-Helix Transitions 4.2.2 Statistical Methods for Predicting Pro te in Secondary Structures 4.3 Structural Transitions in Polynucleic Acids and DNA 4.3.1 Melting and Annealing of Polynucleotide Duplexes 4.3.2 HelicaI Transitions in Double-Stranded DNA 4.3.3 Supercoil-Dependent DNA Transitions 4.3.4 Predicting Helical Structures in Genomic DNA 4.4 Nonregular Structures 4.4.1 Random Walk 4.4.2 Average Linear Dimension of a BiopoIymer Application 4.1: LINUS: A Hierarchic Procedure to Predict the Fold of a Protein 4.4.3 Simple Exact Models for Compact Structures Application 4.2: Folding FunneIs: Focusing Down to the Essentials Chapter 5 5.1 5.2 5.3 5.4 Methods for the Separation and Characterization of Macromolecules General PrincipIes Diffusion 5.2.1 5.2.2 Description of Diffusion The Diffusion Coefficient and the Frictional Coefficient 5.2.3 Diffusion Within Cells Application 5.1: Measuring Diffusion of Small DNA Molecules in Cells Sedimentation 5.3.1 Moving Boundary Sedimentation 5.3.2 Zonal Sedimentation 5.3.3 Sedimentation Equilibrium 5.3.4 Sedimentation Equilibrium in a Density Gradient Electrophoresis and Isoelectric Focusing 5.4.1 Electrophoresis: General PrincipIes 5.4.2 Electrophoresis of Nucleic Acids Application 5.2: Locating Bends in DNA by Gel Electrophoresis 5.4.3 SDS-Gel Electrophoresis of Proteins 5.4.4 Methods for Detecting and Analyzing Components on Gels 166 166 167 169 175 175 181 184 184 189 190 197 198 199 201 202 204 208 209 211 213 213 214 215 220 221 222 223 225 237 241 246 248 249 253 257 259 264
viii Contents 5.4.5 Capillary Electrophoresis 5.4.6 Isoelectric Focusing Chapter 6 X-Ray DitTraction 6.1 Structures at Atomic Resolution 6.2 Crystals 6.2.1 What Is a Crystal? 6.2.2 Growing Crystals 6.2.3 Conditions for Macromolecular Crystallization Application 6.1: Crystals in Space! 6.3 Theory of X-Ray Diffraction 6.3.1 Bragg's Law 6.3.2 von Laue Conditions for Diffraction 6.3.3 Reciprocal Space and Diffraction Patterns 6.4 Determining the Crystal Morphology 6.5 Solving Macromolecular Structures by X-Ray Diffraction 6.5.1 The Structure Factor 6.5.2 The Phase Problem Application 6.2: The Crystal Structure of an Old and Distinguished Enzyme 6.6 6.5.3 Resolution in X-Ray Diffraction Fiber Diffraction 6.6.1 The Fiber Unit Cell 6.6.2 Fiber Diffraction of Continuous Helices 6.6.3 Fiber Diffraction of Discontinuous Helices Chapter 7 Scattering from Solutions of Macromolecules 7.1 Light Scattering 7.1.1 Fundamental Concepts 7.1.2 Scattering from a Number of Small Particles: Rayleigh Scattering 7.1.3 Scattering from Particles That Are Not Small Compared to Wavelength of Radiation 7.2 Dynamic Light Scattering: Measurements of Diffusion 7.3 Small-Angle X-Ray Scattering 7.4 Small-Angle Neutron Scattering Application 7.1: Using a Combination of Physical Methods to Determine the Conformation of the Nucleosome 7.5 Summary 266 266 270 274 276 277 279 279 285 286 289 290 292 294 299 304 308 309 317 327 334 338 338 340 343 347 349 351 351 351 355 358 363 365 370 372 376
Contents ix Chapter 8 Quantum Mechanics and Spectroscopy 8.1 Light and Transitions 8.2 Postulate Approach to Quantum Mechanics 8.3 Transition Energies 8.3.1 The Quantum Mechanics of Simple Systems 8.3.2 Approximating Solutions to Quantum Chemistry Problems 8.4 8.3.3 The Hydrogen Molecule as the Mode1 for a Bond Transition Intensities 8.5 Transition Dipole Directions Chapter 9 Absorption Spectroscopy 9.1 Electronic Absorption 9.1.1 Energy of Electronic Absorption Bands 9.1.2 9.1.3 Transition Dipoles Proteins 9.1.4 Nucleic Acids 9.1.5 Applications of Electronic Absorption Spectroscopy 9.2 Vibrational Absorption 9.2.1 Energy ofvibrational Absorption Bands 9.2.2 Transition Dipoles 9.2.3 Instrumentation for Vibrational Spectroscopy 9.2.4 Applications to Biological Molecules Application 9.1: Analyzing IR Spectra of Proteins for Secondary Structure 9.3 Raman Scattering Application 9.2: Using Resonance Raman Spectroscopy to Determine the Mode of Oxygen Binding to Oxygen- Transport Proteins Chapter 10 Linear and Circular Dichroism 10.1 Linear Dichroism of Biological Polymers Application 10.1 Measuring the Base Inclinations in dadt Polynucleotides 10.2 Circular Dichroism of Biological Molecules 10.2.1 Electronic CD of Nucleic Acids Application 10.2: The First Observation of Z-form DNA Was by Use of CD 376 379 380 381 382 386 386 392 400 408 415 418 419 421 421 422 433 435 443 447 449 450 451 453 453 456 457 461 463 464 465 466 471 471 476 478
x Contents 10.2.2 Electronic CD of Proteins 10.2.3 Singular Value Decomposition and Analyzing the CD of Proteins for Secondary Structure 10.2.4 Vibrational CD Chapter 11 Emission Spectroscopy 11.1 The Phenomenon 11.2 Emission Lifetime 11.3 Fluorescence Spectroscopy 11.4 Fluorescence Instrumentation 11.5 11.6 Analytical Applications Solvent Effects 11.7 Fluorescence Decay 11.8 Fluorescence Resonance Energy Transfer 11.9 Linear Polarization of Fluorescence Application 11.1: Visualizing c-amp with Fluorescence 11.10 Fluorescence Applied to Protein Application 11.2: Investigation of the Polymerization of G-Actin 11.11 Fluorescence Applied to Nucleic Acids Application 11.3: The Helical Geometry of Double-Stranded DNA in Solution Chapter 12 Nuclear Magnetic Resonance Spectroscopy 12.1 The Phenomenon 12.2 The Measurable 12.3 Spin-Spin Interaction 12.4 Relaxation and the Nuclear Overhauser Effect 12.5 Measuring the Spectrum 12.6 One-Dimensional NMR of Macromolecules 12.7 Application 12.1: Investigating Base Stacking with NMR Two-Dimensional Fourier Transform NMR 12.8 Two-Dimensional FT NMR Applied to Macromolecules Chapter 13 Macromolecules in Solution: Thermodynamics and Equilibria 13.1 Some Fundamentals of Solution Thermodynamics 13.1.1 Partial Molar Quantities:The Chemical Potential 481 485 496 498 499 501 501 502 504 506 507 509 513 516 517 517 524 528 530 532 533 534 535 535 537 540 542 544 549 553 555 560 575 577 579 580 580
Contents xi 13.1.2 The Chemical Potential and Concentration: Ideal and Nonideal Solutions 13.2 Applications of the Chemical Potential to Physical Equilibria 13.2.1 Membrane Equilibria 13.2.2 Sedimentation Equilibrium 13.2.3 Steady-State Electrophoresis Chapter 14 Chemical Equilibria Iuvolviug Macromolecules 14.1 Thermodynamics of Chemical Reactions in Solution: A Review 14.2 Interactions Between Macromolecules 14.3 Binding of Small Ligands by Macromolecules 14.3.1 General PrincipIes and Methods 14.3.2 Multiple Equilibria Application 14.1: Thermodynamic Analysis of the Binding of Oxygen by Hemoglobin 14.3.3 Ion Binding to Macromolecules 14.4 Binding to Nuc1eic Acids 14.4.1 General PrincipIes 14.4.2 Special Aspects of Nonspecific Binding 14.4.3 Electrostatic Effects on Binding to Nuc1eic Acids Chapter 15 Mass Spectrometry of Macromolecules 15.1 General PrincipIes: The Problem 15.2 Resolving Molecular Weights by Mass Spectrometry 15.3 Determining Molecular Weights of Biomolecules 15.4 Identification of Biomolecules by Molecular Weights 15.5 Sequencing by Mass Spectrometry 15.6 Probing Three-Dimensional Structure by Mass Spectrometry Application 15.1: Finding Disorder in Order Application 15.2: When a Crystal Structure Is Not Enough Chapter 16 Siugle-Molecule Methods 16.1 Why Study Single Molecules? Application 16.1: RNA Folding and Unfolding Observed at the Single-Molecule Level 16.2 Observation of Single Macromolecules by Fluorescence 584 589 589 597 598 600 603 605 605 610 615 615 622 641 644 648 648 648 651 654 658 660 661 664 670 673 676 684 686 687 690 691 693 693 694 695
xii Contents 16.3 Atomic Force Microscopy Application 16.2: Single-Molecule Studies of Active Transcription by RNA Polymerase 16.4 Optical Tweezers 16.5 Magnetic Beads Answers to Odd-Numbered Problems Index 699 701 703 707 708 709 A-l 1-1