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 xvPreface to Second Edition xviiTHERMODYNAMICS 11. Heat, Work, and Energy 31.1 Introduction 31.2 Temperature 41.3 Heat 51.4 Work 61.5 Definition of Energy 91.6 Enthalpy 111.7 Standard States 121.8 Calorimetry 131.9 Reaction Enthalpies 161.10 Temperature Dependence of the Reaction Enthalpy 18References 19Problems 202. Entropy and Gibbs Energy 232.1 Introduction 232.2 Statement of the Second Law 242.3 Calculation of the Entropy 262.4 Third Law of Thermodynamics 282.5 Molecular Interpretation of Entropy 292.6 Gibbs Energy 302.7 Chemical Equilibria 322.8 Pressure and Temperature Dependence of the Gibbs Energy 352.9 Phase Changes 362.10 Additions to the Gibbs Energy 39Problems 403. Applications of Thermodynamics to Biological Systems 433.1 Biochemical Reactions 433.2 Metabolic Cycles 453.3 Direct Synthesis of ATP 493.4 Establishment of Membrane Ion Gradients by Chemical Reactions 513.5 Protein Structure 523.6 Protein Folding 603.7 Nucleic Acid Structures 633.8 DNA Melting 673.9 RNA 71References 72Problems 734. Thermodynamics Revisited 774.1 Introduction 774.2 Mathematical Tools 774.3 Maxwell Relations 784.4 Chemical Potential 804.5 Partial Molar Quantities 834.6 Osmotic Pressure 854.7 Chemical Equilibria 874.8 Ionic Solutions 89References 93Problems 93CHEMICAL KINETICS 955. Principles of Chemical Kinetics 975.1 Introduction 975.2 Reaction Rates 995.3 Determination of Rate Laws 1015.4 Radioactive Decay 1045.5 Reaction Mechanisms 1055.6 Temperature Dependence of Rate Constants 1085.7 Relationship Between Thermodynamics and Kinetics 1125.8 Reaction Rates Near Equilibrium 1145.9 Single Molecule Kinetics 116References 118Problems 1186. Applications of Kinetics to Biological Systems 1216.1 Introduction 1216.2 Enzyme Catalysis: The Michaelis–Menten Mechanism 1216.3 α-Chymotrypsin 1266.4 Protein Tyrosine Phosphatase 1336.5 Ribozymes 1376.6 DNA Melting and Renaturation 142References 148Problems 149QUANTUM MECHANICS 1537. Fundamentals of Quantum Mechanics 1557.1 Introduction 1557.2 Schrödinger Equation 1587.3 Particle in a Box 1597.4 Vibrational Motions 1627.5 Tunneling 1657.6 Rotational Motions 1677.7 Basics of Spectroscopy 169References 173Problems 1748. Electronic Structure of Atoms and Molecules 1778.1 Introduction 1778.2 Hydrogenic Atoms 1778.3 Many-Electron Atoms 1818.4 Born–Oppenheimer Approximation 1848.5 Molecular Orbital Theory 1868.6 Hartree–Fock Theory and Beyond 1908.7 Density Functional Theory 1938.8 Quantum Chemistry of Biological Systems 194References 200Problems 201SPECTROSCOPY 2039. X-ray Crystallography 2059.1 Introduction 2059.2 Scattering of X-Rays by a Crystal 2069.3 Structure Determination 2089.4 Neutron Diffraction 2129.5 Nucleic Acid Structure 2139.6 Protein Structure 2169.7 Enzyme Catalysis 219References 222Problems 22310. Electronic Spectra 22510.1 Introduction 22510.2 Absorption Spectra 22610.3 Ultraviolet Spectra of Proteins 22810.4 Nucleic Acid Spectra 23010.5 Prosthetic Groups 23110.6 Difference Spectroscopy 23310.7 X-Ray Absorption Spectroscopy 23610.8 Fluorescence and Phosphorescence 23610.9 RecBCD: Helicase Activity Monitored by Fluorescence 24010.10 Fluorescence Energy Transfer: A Molecular Ruler 24110.11 Application of Energy Transfer to Biological Systems 24310.12 Dihydrofolate Reductase 245References 247Problems 24811. Circular Dichroism, Optical Rotary Dispersion, and Fluorescence Polarization 25311.1 Introduction 25311.2 Optical Rotary Dispersion 25411.3 Circular Dichroism 25611.4 Optical Rotary Dispersion and Circular Dichroism of Proteins 25711.5 Optical Rotation and Circular Dichroism of Nucleic Acids 25911.6 Small Molecule Binding to DNA 26011.7 Protein Folding 26311.8 Interaction of DNA with Zinc Finger Proteins 26611.9 Fluorescence Polarization 26711.10 Integration of HIV Genome Into Host Genome 26911.11 α-Ketoglutarate Dehydrogenase 270References 272Problems 27312. Vibrations in Macromolecules 27712.1 Introduction 27712.2 Infrared Spectroscopy 27812.3 Raman Spectroscopy 27912.4 Structure Determination with Vibrational Spectroscopy 28112.5 Resonance Raman Spectroscopy 28312.6 Structure of Enzyme–Substrate Complexes 28612.7 Conclusion 287References 287Problems 28813. Principles of Nuclear Magnetic Resonance and Electron Spin Resonance 28913.1 Introduction 28913.2 NMR Spectrometers 29213.3 Chemical Shifts 29313.4 Spin–Spin Splitting 29613.5 Relaxation Times 29813.6 Multidimensional NMR 30013.7 Magnetic Resonance Imaging 30613.8 Electron Spin Resonance 306References 310Problems 31014. Applications of Magnetic Resonance to Biology 31514.1 Introduction 31514.2 Regulation of DNA Transcription 31514.3 Protein–DNA Interactions 31814.4 Dynamics of Protein Folding 32014.5 RNA Folding 32214.6 Lactose Permease 32514.7 Proteasome Structure and Function 32814.8 Conclusion 329References 329STATISTICAL MECHANICS 33115. Fundamentals of Statistical Mechanics 33315.1 Introduction 33315.2 Kinetic Model of Gases 33315.3 Boltzmann Distribution 33815.4 Molecular Partition Function 34315.5 Ensembles 34615.6 Statistical Entropy 34915.7 Helix-Coil Transition 350References 353Problems 35416. Molecular Simulations 35716.1 Introduction 35716.2 Potential Energy Surfaces 35816.3 Molecular Mechanics and Docking 36416.4 Large-Scale Simulations 36516.5 Molecular Dynamics 36716.6 Monte Carlo 37316.7 Hybrid Quantum/Classical Methods 37316.8 Helmholtz and Gibbs Energy Calculations 37516.9 Simulations of Enzyme Reactions 376References 379Problems 379SPECIAL TOPICS 38317. Ligand Binding to Macromolecules 38517.1 Introduction 38517.2 Binding of Small Molecules to Multiple Identical Binding Sites 38517.3 Macroscopic and Microscopic Equilibrium Constants 38717.4 Statistical Effects in Ligand Binding to Macromolecules 38917.5 Experimental Determination of Ligand Binding Isotherms 39217.6 Binding of Cro Repressor Protein to DNA 39517.7 Cooperativity in Ligand Binding 39717.8 Models for Cooperativity 40217.9 Kinetic Studies of Cooperative Binding 40617.10 Allosterism 408References 412Problems 41218. Hydrodynamics of Macromolecules 41518.1 Introduction 41518.2 Frictional Coefficient 41518.3 Diffusion 41818.4 Centrifugation 42118.5 Velocity Sedimentation 42218.6 Equilibrium Centrifugation 42418.7 Preparative Centrifugation 42518.8 Density Centrifugation 42718.9 Viscosity 42818.10 Electrophoresis 42918.11 Peptide-Induced Conformational Change of a Major Histocompatibility Complex Protein 43218.12 Ultracentrifuge Analysis of Protein–DNA Interactions 434References 435Problems 43519. Mass Spectrometry 44119.1 Introduction 44119.2 Mass Analysis 44119.3 Tandem Mass Spectrometry (MS/MS) 44519.4 Ion Detectors 44519.5 Ionization of the Sample 44619.6 Sample Preparation/Analysis 44919.7 Proteins and Peptides 45019.8 Protein Folding 45219.9 Other Biomolecules 455References 455Problems 456APPENDICES 457Appendix 1. Useful Constants and Conversion Factors 459Appendix 2. Structures of the Common Amino Acids at Neutral pH 461Appendix 3. Common Nucleic Acid Components 463Appendix 4. Standard Gibbs Energies and Enthalpies of Formation at 298 K, 1 atm, pH 7, and 0.25 M Ionic Strength 465Appendix 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 467Appendix 6. Introduction to Electrochemistry 469A6-1 Introduction 469A6-2 Galvanic Cells 469A6-3 Standard Electrochmical Potentials 471A6-4 Concentration Dependence of the Electrochemical Potential 472A6-5 Biochemical Redox Reactions 473References 473Index 475

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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 xvPreface to Second Edition xviiTHERMODYNAMICS 11. Heat, Work, and Energy 31.1 Introduction 31.2 Temperature 41.3 Heat 51.4 Work 61.5 Definition of Energy 91.6 Enthalpy 111.7 Standard States 121.8 Calorimetry 131.9 Reaction Enthalpies 161.10 Temperature Dependence of the Reaction Enthalpy 18References 19Problems 202. Entropy and Gibbs Energy 232.1 Introduction 232.2 Statement of the Second Law 242.3 Calculation of the Entropy 262.4 Third Law of Thermodynamics 282.5 Molecular Interpretation of Entropy 292.6 Gibbs Energy 302.7 Chemical Equilibria 322.8 Pressure and Temperature Dependence of the Gibbs Energy 352.9 Phase Changes 362.10 Additions to the Gibbs Energy 39Problems 403. Applications of Thermodynamics to Biological Systems 433.1 Biochemical Reactions 433.2 Metabolic Cycles 453.3 Direct Synthesis of ATP 493.4 Establishment of Membrane Ion Gradients by Chemical Reactions 513.5 Protein Structure 523.6 Protein Folding 603.7 Nucleic Acid Structures 633.8 DNA Melting 673.9 RNA 71References 72Problems 734. Thermodynamics Revisited 774.1 Introduction 774.2 Mathematical Tools 774.3 Maxwell Relations 784.4 Chemical Potential 804.5 Partial Molar Quantities 834.6 Osmotic Pressure 854.7 Chemical Equilibria 874.8 Ionic Solutions 89References 93Problems 93CHEMICAL KINETICS 955. Principles of Chemical Kinetics 975.1 Introduction 975.2 Reaction Rates 995.3 Determination of Rate Laws 1015.4 Radioactive Decay 1045.5 Reaction Mechanisms 1055.6 Temperature Dependence of Rate Constants 1085.7 Relationship Between Thermodynamics and Kinetics 1125.8 Reaction Rates Near Equilibrium 1145.9 Single Molecule Kinetics 116References 118Problems 1186. Applications of Kinetics to Biological Systems 1216.1 Introduction 1216.2 Enzyme Catalysis: The Michaelis–Menten Mechanism 1216.3 α-Chymotrypsin 1266.4 Protein Tyrosine Phosphatase 1336.5 Ribozymes 1376.6 DNA Melting and Renaturation 142References 148Problems 149QUANTUM MECHANICS 1537. Fundamentals of Quantum Mechanics 1557.1 Introduction 1557.2 Schrödinger Equation 1587.3 Particle in a Box 1597.4 Vibrational Motions 1627.5 Tunneling 1657.6 Rotational Motions 1677.7 Basics of Spectroscopy 169References 173Problems 1748. Electronic Structure of Atoms and Molecules 1778.1 Introduction 1778.2 Hydrogenic Atoms 1778.3 Many-Electron Atoms 1818.4 Born–Oppenheimer Approximation 1848.5 Molecular Orbital Theory 1868.6 Hartree–Fock Theory and Beyond 1908.7 Density Functional Theory 1938.8 Quantum Chemistry of Biological Systems 194References 200Problems 201SPECTROSCOPY 2039. X-ray Crystallography 2059.1 Introduction 2059.2 Scattering of X-Rays by a Crystal 2069.3 Structure Determination 2089.4 Neutron Diffraction 2129.5 Nucleic Acid Structure 2139.6 Protein Structure 2169.7 Enzyme Catalysis 219References 222Problems 22310. Electronic Spectra 22510.1 Introduction 22510.2 Absorption Spectra 22610.3 Ultraviolet Spectra of Proteins 22810.4 Nucleic Acid Spectra 23010.5 Prosthetic Groups 23110.6 Difference Spectroscopy 23310.7 X-Ray Absorption Spectroscopy 23610.8 Fluorescence and Phosphorescence 23610.9 RecBCD: Helicase Activity Monitored by Fluorescence 24010.10 Fluorescence Energy Transfer: A Molecular Ruler 24110.11 Application of Energy Transfer to Biological Systems 24310.12 Dihydrofolate Reductase 245References 247Problems 24811. Circular Dichroism, Optical Rotary Dispersion, and Fluorescence Polarization 25311.1 Introduction 25311.2 Optical Rotary Dispersion 25411.3 Circular Dichroism 25611.4 Optical Rotary Dispersion and Circular Dichroism of Proteins 25711.5 Optical Rotation and Circular Dichroism of Nucleic Acids 25911.6 Small Molecule Binding to DNA 26011.7 Protein Folding 26311.8 Interaction of DNA with Zinc Finger Proteins 26611.9 Fluorescence Polarization 26711.10 Integration of HIV Genome Into Host Genome 26911.11 α-Ketoglutarate Dehydrogenase 270References 272Problems 27312. Vibrations in Macromolecules 27712.1 Introduction 27712.2 Infrared Spectroscopy 27812.3 Raman Spectroscopy 27912.4 Structure Determination with Vibrational Spectroscopy 28112.5 Resonance Raman Spectroscopy 28312.6 Structure of Enzyme–Substrate Complexes 28612.7 Conclusion 287References 287Problems 28813. Principles of Nuclear Magnetic Resonance and Electron Spin Resonance 28913.1 Introduction 28913.2 NMR Spectrometers 29213.3 Chemical Shifts 29313.4 Spin–Spin Splitting 29613.5 Relaxation Times 29813.6 Multidimensional NMR 30013.7 Magnetic Resonance Imaging 30613.8 Electron Spin Resonance 306References 310Problems 31014. Applications of Magnetic Resonance to Biology 31514.1 Introduction 31514.2 Regulation of DNA Transcription 31514.3 Protein–DNA Interactions 31814.4 Dynamics of Protein Folding 32014.5 RNA Folding 32214.6 Lactose Permease 32514.7 Proteasome Structure and Function 32814.8 Conclusion 329References 329STATISTICAL MECHANICS 33115. Fundamentals of Statistical Mechanics 33315.1 Introduction 33315.2 Kinetic Model of Gases 33315.3 Boltzmann Distribution 33815.4 Molecular Partition Function 34315.5 Ensembles 34615.6 Statistical Entropy 34915.7 Helix-Coil Transition 350References 353Problems 35416. Molecular Simulations 35716.1 Introduction 35716.2 Potential Energy Surfaces 35816.3 Molecular Mechanics and Docking 36416.4 Large-Scale Simulations 36516.5 Molecular Dynamics 36716.6 Monte Carlo 37316.7 Hybrid Quantum/Classical Methods 37316.8 Helmholtz and Gibbs Energy Calculations 37516.9 Simulations of Enzyme Reactions 376References 379Problems 379SPECIAL TOPICS 38317. Ligand Binding to Macromolecules 38517.1 Introduction 38517.2 Binding of Small Molecules to Multiple Identical Binding Sites 38517.3 Macroscopic and Microscopic Equilibrium Constants 38717.4 Statistical Effects in Ligand Binding to Macromolecules 38917.5 Experimental Determination of Ligand Binding Isotherms 39217.6 Binding of Cro Repressor Protein to DNA 39517.7 Cooperativity in Ligand Binding 39717.8 Models for Cooperativity 40217.9 Kinetic Studies of Cooperative Binding 40617.10 Allosterism 408References 412Problems 41218. Hydrodynamics of Macromolecules 41518.1 Introduction 41518.2 Frictional Coefficient 41518.3 Diffusion 41818.4 Centrifugation 42118.5 Velocity Sedimentation 42218.6 Equilibrium Centrifugation 42418.7 Preparative Centrifugation 42518.8 Density Centrifugation 42718.9 Viscosity 42818.10 Electrophoresis 42918.11 Peptide-Induced Conformational Change of a Major Histocompatibility Complex Protein 43218.12 Ultracentrifuge Analysis of Protein–DNA Interactions 434References 435Problems 43519. Mass Spectrometry 44119.1 Introduction 44119.2 Mass Analysis 44119.3 Tandem Mass Spectrometry (MS/MS) 44519.4 Ion Detectors 44519.5 Ionization of the Sample 44619.6 Sample Preparation/Analysis 44919.7 Proteins and Peptides 45019.8 Protein Folding 45219.9 Other Biomolecules 455References 455Problems 456APPENDICES 457Appendix 1. Useful Constants and Conversion Factors 459Appendix 2. Structures of the Common Amino Acids at Neutral pH 461Appendix 3. Common Nucleic Acid Components 463Appendix 4. Standard Gibbs Energies and Enthalpies of Formation at 298 K, 1 atm, pH 7, and 0.25 M Ionic Strength 465Appendix 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 467Appendix 6. Introduction to Electrochemistry 469A6-1 Introduction 469A6-2 Galvanic Cells 469A6-3 Standard Electrochmical Potentials 471A6-4 Concentration Dependence of the Electrochemical Potential 472A6-5 Biochemical Redox Reactions 473References 473Index 475

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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 xvPreface to Second Edition xviiTHERMODYNAMICS 11. Heat, Work, and Energy 31.1 Introduction 31.2 Temperature 41.3 Heat 51.4 Work 61.5 Definition of Energy 91.6 Enthalpy 111.7 Standard States 121.8 Calorimetry 131.9 Reaction Enthalpies 161.10 Temperature Dependence of the Reaction Enthalpy 18References 19Problems 202. Entropy and Gibbs Energy 232.1 Introduction 232.2 Statement of the Second Law 242.3 Calculation of the Entropy 262.4 Third Law of Thermodynamics 282.5 Molecular Interpretation of Entropy 292.6 Gibbs Energy 302.7 Chemical Equilibria 322.8 Pressure and Temperature Dependence of the Gibbs Energy 352.9 Phase Changes 362.10 Additions to the Gibbs Energy 39Problems 403. Applications of Thermodynamics to Biological Systems 433.1 Biochemical Reactions 433.2 Metabolic Cycles 453.3 Direct Synthesis of ATP 493.4 Establishment of Membrane Ion Gradients by Chemical Reactions 513.5 Protein Structure 523.6 Protein Folding 603.7 Nucleic Acid Structures 633.8 DNA Melting 673.9 RNA 71References 72Problems 734. Thermodynamics Revisited 774.1 Introduction 774.2 Mathematical Tools 774.3 Maxwell Relations 784.4 Chemical Potential 804.5 Partial Molar Quantities 834.6 Osmotic Pressure 854.7 Chemical Equilibria 874.8 Ionic Solutions 89References 93Problems 93CHEMICAL KINETICS 955. Principles of Chemical Kinetics 975.1 Introduction 975.2 Reaction Rates 995.3 Determination of Rate Laws 1015.4 Radioactive Decay 1045.5 Reaction Mechanisms 1055.6 Temperature Dependence of Rate Constants 1085.7 Relationship Between Thermodynamics and Kinetics 1125.8 Reaction Rates Near Equilibrium 1145.9 Single Molecule Kinetics 116References 118Problems 1186. Applications of Kinetics to Biological Systems 1216.1 Introduction 1216.2 Enzyme Catalysis: The Michaelis–Menten Mechanism 1216.3 α-Chymotrypsin 1266.4 Protein Tyrosine Phosphatase 1336.5 Ribozymes 1376.6 DNA Melting and Renaturation 142References 148Problems 149QUANTUM MECHANICS 1537. Fundamentals of Quantum Mechanics 1557.1 Introduction 1557.2 Schrödinger Equation 1587.3 Particle in a Box 1597.4 Vibrational Motions 1627.5 Tunneling 1657.6 Rotational Motions 1677.7 Basics of Spectroscopy 169References 173Problems 1748. Electronic Structure of Atoms and Molecules 1778.1 Introduction 1778.2 Hydrogenic Atoms 1778.3 Many-Electron Atoms 1818.4 Born–Oppenheimer Approximation 1848.5 Molecular Orbital Theory 1868.6 Hartree–Fock Theory and Beyond 1908.7 Density Functional Theory 1938.8 Quantum Chemistry of Biological Systems 194References 200Problems 201SPECTROSCOPY 2039. X-ray Crystallography 2059.1 Introduction 2059.2 Scattering of X-Rays by a Crystal 2069.3 Structure Determination 2089.4 Neutron Diffraction 2129.5 Nucleic Acid Structure 2139.6 Protein Structure 2169.7 Enzyme Catalysis 219References 222Problems 22310. Electronic Spectra 22510.1 Introduction 22510.2 Absorption Spectra 22610.3 Ultraviolet Spectra of Proteins 22810.4 Nucleic Acid Spectra 23010.5 Prosthetic Groups 23110.6 Difference Spectroscopy 23310.7 X-Ray Absorption Spectroscopy 23610.8 Fluorescence and Phosphorescence 23610.9 RecBCD: Helicase Activity Monitored by Fluorescence 24010.10 Fluorescence Energy Transfer: A Molecular Ruler 24110.11 Application of Energy Transfer to Biological Systems 24310.12 Dihydrofolate Reductase 245References 247Problems 24811. Circular Dichroism, Optical Rotary Dispersion, and Fluorescence Polarization 25311.1 Introduction 25311.2 Optical Rotary Dispersion 25411.3 Circular Dichroism 25611.4 Optical Rotary Dispersion and Circular Dichroism of Proteins 25711.5 Optical Rotation and Circular Dichroism of Nucleic Acids 25911.6 Small Molecule Binding to DNA 26011.7 Protein Folding 26311.8 Interaction of DNA with Zinc Finger Proteins 26611.9 Fluorescence Polarization 26711.10 Integration of HIV Genome Into Host Genome 26911.11 α-Ketoglutarate Dehydrogenase 270References 272Problems 27312. Vibrations in Macromolecules 27712.1 Introduction 27712.2 Infrared Spectroscopy 27812.3 Raman Spectroscopy 27912.4 Structure Determination with Vibrational Spectroscopy 28112.5 Resonance Raman Spectroscopy 28312.6 Structure of Enzyme–Substrate Complexes 28612.7 Conclusion 287References 287Problems 28813. Principles of Nuclear Magnetic Resonance and Electron Spin Resonance 28913.1 Introduction 28913.2 NMR Spectrometers 29213.3 Chemical Shifts 29313.4 Spin–Spin Splitting 29613.5 Relaxation Times 29813.6 Multidimensional NMR 30013.7 Magnetic Resonance Imaging 30613.8 Electron Spin Resonance 306References 310Problems 31014. Applications of Magnetic Resonance to Biology 31514.1 Introduction 31514.2 Regulation of DNA Transcription 31514.3 Protein–DNA Interactions 31814.4 Dynamics of Protein Folding 32014.5 RNA Folding 32214.6 Lactose Permease 32514.7 Proteasome Structure and Function 32814.8 Conclusion 329References 329STATISTICAL MECHANICS 33115. Fundamentals of Statistical Mechanics 33315.1 Introduction 33315.2 Kinetic Model of Gases 33315.3 Boltzmann Distribution 33815.4 Molecular Partition Function 34315.5 Ensembles 34615.6 Statistical Entropy 34915.7 Helix-Coil Transition 350References 353Problems 35416. Molecular Simulations 35716.1 Introduction 35716.2 Potential Energy Surfaces 35816.3 Molecular Mechanics and Docking 36416.4 Large-Scale Simulations 36516.5 Molecular Dynamics 36716.6 Monte Carlo 37316.7 Hybrid Quantum/Classical Methods 37316.8 Helmholtz and Gibbs Energy Calculations 37516.9 Simulations of Enzyme Reactions 376References 379Problems 379SPECIAL TOPICS 38317. Ligand Binding to Macromolecules 38517.1 Introduction 38517.2 Binding of Small Molecules to Multiple Identical Binding Sites 38517.3 Macroscopic and Microscopic Equilibrium Constants 38717.4 Statistical Effects in Ligand Binding to Macromolecules 38917.5 Experimental Determination of Ligand Binding Isotherms 39217.6 Binding of Cro Repressor Protein to DNA 39517.7 Cooperativity in Ligand Binding 39717.8 Models for Cooperativity 40217.9 Kinetic Studies of Cooperative Binding 40617.10 Allosterism 408References 412Problems 41218. Hydrodynamics of Macromolecules 41518.1 Introduction 41518.2 Frictional Coefficient 41518.3 Diffusion 41818.4 Centrifugation 42118.5 Velocity Sedimentation 42218.6 Equilibrium Centrifugation 42418.7 Preparative Centrifugation 42518.8 Density Centrifugation 42718.9 Viscosity 42818.10 Electrophoresis 42918.11 Peptide-Induced Conformational Change of a Major Histocompatibility Complex Protein 43218.12 Ultracentrifuge Analysis of Protein–DNA Interactions 434References 435Problems 43519. Mass Spectrometry 44119.1 Introduction 44119.2 Mass Analysis 44119.3 Tandem Mass Spectrometry (MS/MS) 44519.4 Ion Detectors 44519.5 Ionization of the Sample 44619.6 Sample Preparation/Analysis 44919.7 Proteins and Peptides 45019.8 Protein Folding 45219.9 Other Biomolecules 455References 455Problems 456APPENDICES 457Appendix 1. Useful Constants and Conversion Factors 459Appendix 2. Structures of the Common Amino Acids at Neutral pH 461Appendix 3. Common Nucleic Acid Components 463Appendix 4. Standard Gibbs Energies and Enthalpies of Formation at 298 K, 1 atm, pH 7, and 0.25 M Ionic Strength 465Appendix 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 467Appendix 6. Introduction to Electrochemistry 469A6-1 Introduction 469A6-2 Galvanic Cells 469A6-3 Standard Electrochmical Potentials 471A6-4 Concentration Dependence of the Electrochemical Potential 472A6-5 Biochemical Redox Reactions 473References 473Index 475

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