Physical Chemistry for the Biological Sciences

Gordon G. Hammes, PhD, is the Distinguished Service Professor of Biochemistry Emeritus at Duke University. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and has received several national awards, including the American Chemical Society Award in Biological Chemistry and the American Society for Biochemistry and Molecular Biology William C. Rose Award. Dr. Hammes was Editor of the journal Biochemistry from 1992-2003. Sharon Hammes-Schiffer, PhD, is the Swanlund Professor of Chemistry at the University of Illinois at Urbana-Champaign. She is a fellow of the American Physical Society, the American Chemical Society, the Biophysical Society, and the American Association for the Advancement of Science. She is a member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the International Academy of Quantum Molecular Science. Dr. Hammes-Schiffer has served as the Deputy Editor of The Journal of Physical Chemistry B and is currently the Editor-in-Chief of Chemical Reviews.

Preface to First Edition xv

Preface to Second Edition xvii

THERMODYNAMICS 1

1. Heat, Work, and Energy 3

1.1 Introduction 3

1.2 Temperature 4

1.3 Heat 5

1.4 Work 6

1.5 Definition of Energy 9

1.6 Enthalpy 11

1.7 Standard States 12

1.8 Calorimetry 13

1.9 Reaction Enthalpies 16

1.10 Temperature Dependence of the Reaction Enthalpy 18

References 19

Problems 20

2. Entropy and Gibbs Energy 23

2.1 Introduction 23

2.2 Statement of the Second Law 24

2.3 Calculation of the Entropy 26

2.4 Third Law of Thermodynamics 28

2.5 Molecular Interpretation of Entropy 29

2.6 Gibbs Energy 30

2.7 Chemical Equilibria 32

2.8 Pressure and Temperature Dependence of the Gibbs Energy 35

2.9 Phase Changes 36

2.10 Additions to the Gibbs Energy 39

Problems 40

3. Applications of Thermodynamics to Biological Systems 43

3.1 Biochemical Reactions 43

3.2 Metabolic Cycles 45

3.3 Direct Synthesis of ATP 49

3.4 Establishment of Membrane Ion Gradients by Chemical Reactions 51

3.5 Protein Structure 52

3.6 Protein Folding 60

3.7 Nucleic Acid Structures 63

3.8 DNA Melting 67

3.9 RNA 71

References 72

Problems 73

4. Thermodynamics Revisited 77

4.1 Introduction 77

4.2 Mathematical Tools 77

4.3 Maxwell Relations 78

4.4 Chemical Potential 80

4.5 Partial Molar Quantities 83

4.6 Osmotic Pressure 85

4.7 Chemical Equilibria 87

4.8 Ionic Solutions 89

References 93

Problems 93

CHEMICAL KINETICS 95

5. Principles of Chemical Kinetics 97

5.1 Introduction 97

5.2 Reaction Rates 99

5.3 Determination of Rate Laws 101

5.4 Radioactive Decay 104

5.5 Reaction Mechanisms 105

5.6 Temperature Dependence of Rate Constants 108

5.7 Relationship Between Thermodynamics and Kinetics 112

5.8 Reaction Rates Near Equilibrium 114

5.9 Single Molecule Kinetics 116

References 118

Problems 118

6. Applications of Kinetics to Biological Systems 121

6.1 Introduction 121

6.2 Enzyme Catalysis: The Michaelis–Menten Mechanism 121

6.3 α-Chymotrypsin 126

6.4 Protein Tyrosine Phosphatase 133

6.5 Ribozymes 137

6.6 DNA Melting and Renaturation 142

References 148

Problems 149

QUANTUM MECHANICS 153

7. Fundamentals of Quantum Mechanics 155

7.1 Introduction 155

7.2 Schrödinger Equation 158

7.3 Particle in a Box 159

7.4 Vibrational Motions 162

7.5 Tunneling 165

7.6 Rotational Motions 167

7.7 Basics of Spectroscopy 169

References 173

Problems 174

8. Electronic Structure of Atoms and Molecules 177

8.1 Introduction 177

8.2 Hydrogenic Atoms 177

8.3 Many-Electron Atoms 181

8.4 Born–Oppenheimer Approximation 184

8.5 Molecular Orbital Theory 186

8.6 Hartree–Fock Theory and Beyond 190

8.7 Density Functional Theory 193

8.8 Quantum Chemistry of Biological Systems 194

References 200

Problems 201

SPECTROSCOPY 203

9. X-ray Crystallography 205

9.1 Introduction 205

9.2 Scattering of X-Rays by a Crystal 206

9.3 Structure Determination 208

9.4 Neutron Diffraction 212

9.5 Nucleic Acid Structure 213

9.6 Protein Structure 216

9.7 Enzyme Catalysis 219

References 222

Problems 223

10. Electronic Spectra 225

10.1 Introduction 225

10.2 Absorption Spectra 226

10.3 Ultraviolet Spectra of Proteins 228

10.4 Nucleic Acid Spectra 230

10.5 Prosthetic Groups 231

10.6 Difference Spectroscopy 233

10.7 X-Ray Absorption Spectroscopy 236

10.8 Fluorescence and Phosphorescence 236

10.9 RecBCD: Helicase Activity Monitored by Fluorescence 240

10.10 Fluorescence Energy Transfer: A Molecular Ruler 241

10.11 Application of Energy Transfer to Biological Systems 243

10.12 Dihydrofolate Reductase 245

References 247

Problems 248

11. Circular Dichroism, Optical Rotary Dispersion, and Fluorescence Polarization 253

11.1 Introduction 253

11.2 Optical Rotary Dispersion 254

11.3 Circular Dichroism 256

11.4 Optical Rotary Dispersion and Circular Dichroism of Proteins 257

11.5 Optical Rotation and Circular Dichroism of Nucleic Acids 259

11.6 Small Molecule Binding to DNA 260

11.7 Protein Folding 263

11.8 Interaction of DNA with Zinc Finger Proteins 266

11.9 Fluorescence Polarization 267

11.10 Integration of HIV Genome Into Host Genome 269

11.11 α-Ketoglutarate Dehydrogenase 270

References 272

Problems 273

12. Vibrations in Macromolecules 277

12.1 Introduction 277

12.2 Infrared Spectroscopy 278

12.3 Raman Spectroscopy 279

12.4 Structure Determination with Vibrational Spectroscopy 281

12.5 Resonance Raman Spectroscopy 283

12.6 Structure of Enzyme–Substrate Complexes 286

12.7 Conclusion 287

References 287

Problems 288

13. Principles of Nuclear Magnetic Resonance and Electron Spin Resonance 289

13.1 Introduction 289

13.2 NMR Spectrometers 292

13.3 Chemical Shifts 293

13.4 Spin–Spin Splitting 296

13.5 Relaxation Times 298

13.6 Multidimensional NMR 300

13.7 Magnetic Resonance Imaging 306

13.8 Electron Spin Resonance 306

References 310

Problems 310

14. Applications of Magnetic Resonance to Biology 315

14.1 Introduction 315

14.2 Regulation of DNA Transcription 315

14.3 Protein–DNA Interactions 318

14.4 Dynamics of Protein Folding 320

14.5 RNA Folding 322

14.6 Lactose Permease 325

14.7 Proteasome Structure and Function 328

14.8 Conclusion 329

References 329

STATISTICAL MECHANICS 331

15. Fundamentals of Statistical Mechanics 333

15.1 Introduction 333

15.2 Kinetic Model of Gases 333

15.3 Boltzmann Distribution 338

15.4 Molecular Partition Function 343

15.5 Ensembles 346

15.6 Statistical Entropy 349

15.7 Helix-Coil Transition 350

References 353

Problems 354

16. Molecular Simulations 357

16.1 Introduction 357

16.2 Potential Energy Surfaces 358

16.3 Molecular Mechanics and Docking 364

16.4 Large-Scale Simulations 365

16.5 Molecular Dynamics 367

16.6 Monte Carlo 373

16.7 Hybrid Quantum/Classical Methods 373

16.8 Helmholtz and Gibbs Energy Calculations 375

16.9 Simulations of Enzyme Reactions 376

References 379

Problems 379

SPECIAL TOPICS 383

17. Ligand Binding to Macromolecules 385

17.1 Introduction 385

17.2 Binding of Small Molecules to Multiple Identical Binding Sites 385

17.3 Macroscopic and Microscopic Equilibrium Constants 387

17.4 Statistical Effects in Ligand Binding to Macromolecules 389

17.5 Experimental Determination of Ligand Binding Isotherms 392

17.6 Binding of Cro Repressor Protein to DNA 395

17.7 Cooperativity in Ligand Binding 397

17.8 Models for Cooperativity 402

17.9 Kinetic Studies of Cooperative Binding 406

17.10 Allosterism 408

References 412

Problems 412

18. Hydrodynamics of Macromolecules 415

18.1 Introduction 415

18.2 Frictional Coefficient 415

18.3 Diffusion 418

18.4 Centrifugation 421

18.5 Velocity Sedimentation 422

18.6 Equilibrium Centrifugation 424

18.7 Preparative Centrifugation 425

18.8 Density Centrifugation 427

18.9 Viscosity 428

18.10 Electrophoresis 429

18.11 Peptide-Induced Conformational Change of a Major Histocompatibility Complex Protein 432

18.12 Ultracentrifuge Analysis of Protein–DNA Interactions 434

References 435

Problems 435

19. Mass Spectrometry 441

19.1 Introduction 441

19.2 Mass Analysis 441

19.3 Tandem Mass Spectrometry (MS/MS) 445

19.4 Ion Detectors 445

19.5 Ionization of the Sample 446

19.6 Sample Preparation/Analysis 449

19.7 Proteins and Peptides 450

19.8 Protein Folding 452

19.9 Other Biomolecules 455

References 455

Problems 456

APPENDICES 457

Appendix 1. Useful Constants and Conversion Factors 459

Appendix 2. Structures of the Common Amino Acids at Neutral pH 461

Appendix 3. Common Nucleic Acid Components 463

Appendix 4. Standard Gibbs Energies and Enthalpies of Formation at 298 K, 1 atm, pH 7, and 0.25 M Ionic Strength 465

Appendix 5. Standard Gibbs Energy and Enthalpy Changes for Biochemical Reactions at 298 K, 1 atm, pH 7.0, pMg 3.0, and 0.25M Ionic Strength 467

Appendix 6. Introduction to Electrochemistry 469

A6-1 Introduction 469

A6-2 Galvanic Cells 469

A6-3 Standard Electrochmical Potentials 471

A6-4 Concentration Dependence of the Electrochemical Potential 472

A6-5 Biochemical Redox Reactions 473

References 473

Index 475