Ligand-Binding Basics

A concise and accessible textbook covering ligand-binding theory in chemistry, biology, and drug development

In Ligand-binding Basics: Evaluating Intermolecular Affinity, Specificity, Stoichiometry, and Cooperativity, accomplished chemist Professor Jannette Carey introduces ligand binding in a thorough and practical way for those new to the topic, as well as anyone seeking a connection between theory and experiment. Using a minimum of mathematical formalism, this book offers analytical rigor while remaining accessible to non-specialist practitioners. It provides readers with the skills they need to analyze their own binding data or published results, helping them develop an intuitive grasp of ligand-binding phenomena integrated with structural and thermodynamic understanding.

Topics covered include:

• Application of the principles of equilibrium, mass action, and mass balance to derive the basic equations that describe all binding processes
• Recommended approaches for plotting and graphical analysis of binding data
• Strategies for designing, analyzing, interpreting, and troubleshooting experiments from the perspective of ligand-binding theory
• Review of selected examples that illustrate integration of structural and thermodynamic analysis

Perfect for students and educators in chemistry, biochemistry, molecular biology, and pharmaceutical science, Ligand-binding Basics will also appeal to practitioners who aim to study ligand binding in any molecular system.

About the Cover xi

Introduction xiii

1 The Biology of Molecules 1

Why Study Intermolecular Interactions Quantitatively? 1

Equilibrium and Kinetics 2

Thermodynamic Definitions of Affinity and Specificity 3

The Affinity/Specificity Map 6

Biology Requires Optimization of Affinity and Specificity 8

The Special Case of Protein-DNA Interactions 8

2 General Theory for Reversible Ligand Binding 10

Definition of Ligand and Titration 10

Affinity, Specificity, Stoichiometry, and Cooperativity 10

Ligand-binding Theory: Relationship to Experiment 13

General Theory for Reversible Ligand Binding: Rooted in Chemical Equilibrium 14

General Theory for Reversible Ligand Binding: Quantitative Treatment 14

The Case of 1:1 Binding 15

General Theory for Reversible Ligand Binding: Conservation of Mass 17

Definition of ν 18

The Basic Equation for 1:1 Binding 19

The Single Most Important Thing You Can Learn in This Book 20

The Example of Heme Binding to Apocytochrome c 21

The Rectangular Hyperbola 22

The Binding Isotherm 23

Plot of ν vs. [Hf] 24

General Theory for Reversible Ligand Binding: Role of Mass Action 25

Plot of [AH]vs.[Ht] with Fixed K 27

Determination of Kd from Experiment 28

Plot of [AH]vs.[Ht] with Fixed [At] 29

Determining Molar Ratio from Experiment 29

About Activity 31

3 Graphical Analysis 33

Limitations of Direct Plots 33

The Semi-log Plot 34

Breadth of the Semi-log Plot 36

Myoglobin and Hemoglobin 38

Advantages of the Direct and Semi-log Plots of Binding Data 40

Linear Transforms of the Basic Binding Equation 40

Common Linearizations 41

Requirements of the Linear Regression Model 41

A Linear Model May Misrepresent the Physical Process 43

Deviations from Linearity Are Hard to Detect or Interpret 44

Linear Transforms Distort Data Completeness 44

Linear Transforms Invite – Even Require – Extrapolation 46

Linear Transforms Falsely Promise Both K and Molar Ratio from a Single Dataset 47

Summary about Linear Treatments of Binding Data 47

Simulation Is Just as Good as Fitting, Given Realistic Experimental Errors 50

4 Binding of Multiple Ligands 52

Conservation of Mass Outside the 1:1 Case 52

Redefine ν to Accommodate Any Molar Ratio 53

Accounting for the Definition of Molecule 54

Generalizing to Integer Multiples of 1:1 54

The Langmuir Equation for Any Molar Ratio with Sites of Identical Affinity and No Cooperativity 56

Adair Equation for Any Number of Binding Events 57

The Langmuir Equation vs. the Adair Equation 60

Thermodynamic Linkage 61

Two Classes of Sites with Different Affinities 62

Binding Isotherms for Multiple Sites with Different Affinities 62

Summary 66

5 How to Determine Kd and Molar Ratio Experimentally 67

Stoichiometric Titration First 68

Amounts of Materials 69

Assigning Partners 69

Choice of Experimental Observables 70

Choosing Solution Conditions 70

How Many Data Points? 71

Range-Finding Stoichiometric Titration 72

Visualizing Results 73

Range-Finding Asymptotic Titration to Estimate Kd 74

Data Analysis 75

Practicalities about Experimental Error 75

Statistical Approaches to Estimate the Breakpoint 76

Refined Asymptotic Titration 76

Designing an Experiment to Refine Kd 77

Calculating Free Ligand Concentration 78

Refining the Value of Molar Ratio 79

Example of ArgR/DNA Binding 79

Plotting the Data 81

Deriving Kd from the Data 81

Summary 81

6 Cooperativity 83

Facilitated and Antagonized Binding 83

Free Energy Definition of Cooperative Binding 84

Chemical Potential Diagram for Cooperative Binding 86

Cooperativity as Non-additivity 87

Reciprocity of Cooperative Effects 88

Limitations of Linear Transforms for Cooperative Interactions 88

Microscopic View of Species Distribution 89

Homotropic and Heterotropic Cooperativity 90

Cooperativity Affects Specificity as Well as Affinity 92

Cooperativity Is the Third Axis of the Affinity/Specificity Map 94

Quantifying Homotropic Cooperativity 95

Negative Homotropic Cooperativity 95

A Practical Advantage of Negative Cooperativity 97

Positive Cooperativity and the Ligand Concentration Interval 97

Importance of Individual-site Isotherms and Species Distribution 100

Species Distributions by Specialized Experimental Methods 101

The Many Forms of Cooperativity 103

Emergent Properties 103

Connectivity and Search Entropy 104

Breakdown of Additivity in Complex Systems 105

Statistical Effects 107

Relevance of Non-additivity for Analysis of Mutations 110

Universality and Promiscuity of Cooperativity 111

Proteins as Gestalt Objects 113

Summary 115

7 Theoretical and Method-specific Troubleshooting 116

Equilibrium and Nonequilibrium Methods 116

Accessible Concentration Ranges Limit Accessible Kd Values 116

Signal from Ligand or Target? 118

Separation-based Methods 118

Filter Binding 119

Gel Retardation or EMSA 120

Gel Filtration 121

Hummel and Dreyer Chromatography 121

Equilibrium Dialysis 122

UV Absorbance 123

CD Spectroscopy 123

Fluorescence 124

NMR 124

ITC 125

AUC 129

SPR 129

MS 131

8 Allostery 133

An Historical Overview 133

Facilitated Binding 135

Elaboration of the MWC Model 136

Relaxed Monomers and Tense Multimers 136

Positive Homotropic Cooperativity Only 137

Artifactual Origins of Affinity Heterogeneity 138

Relaxation of Multimers by Ligand Binding 138

Koshland’s Sequential (Asymmetric) Model 140

G3Pase Was Heterogeneous, Not Negatively Cooperative 141

Many Models Fit the Hemoglobin Data 142

Advantages of Negative Cooperativity for Molecular Insight 143

Biology of Negative Cooperativity 145

Structural Analysis Cannot Solve Allostery 146

Allostery without Cooperativity 147

Summary 148

9 Lessons on Affinity and Specificity from Host/Guest Chemistry 149

2D Representations of 3D Objects 149

Early Hosts Were Linear and Flexible 150

Design of Molecular Properties 151

Very Weak Affinity and No Detectable Specificity 151

Later Hosts Pre-organized in Bound Conformation 152

Enormous Gains in Affinity and Specificity 152

Bonds between Host and Guest Are Identical 153

Lessons from the Host/Guest Chemistry 153

Rational Design of Affinity and Specificity 153

Affinity and Specificity Accrue in Parallel 155

Cryptic Contributions Can Dominate Binding 156

10 Reconciling Structure and Thermodynamics in Molecular Interactions 157

Thermodynamics of Molecular Interactions 158

Structural Analysis of Bonding Does Not Predict Binding 160

The Goldilocks Region of Affinity/Specificity Space 162

Conformational Rearrangement upon Binding Decouples Affinity and Specificity 163

A Reservoir of Adaptability 164

No Simple Reconciliation of Structural and Energetic Views 165

Implications for Drug Design 166

11 Applications in Modern Drug Development 167

Background 167

Technological Developments 167

Crystal Structures 168

Trapped High-energy States 168

Another Example 171

Computational Methods 175

High-throughput Assays 177

Druggability 178

Irrational Drug Design 180

A New Workflow 181

Appendix A Ligand-binding Study Questions 182

Appendix B Thought Experiments 195

Appendix C Derivations 197

Appendix D Simulation and Fitting 201

Simulation 201

Fitting 203

Appendix E About the Hill Equation 208

Deriving the Hill Equation 208

The Hill Equation as a Limit of the Adair Equation 209

On Applying the Hill Equation to Quantify Cooperativity 210

Appendix F Stereo Viewing 212

Bibliography 215

Index 227

Jannette Carey has been a member of the Chemistry faculty at Princeton University for over thirty years, where she developed and teaches a two-term sequence in biophysical chemistry that is accessible to early graduate and advanced undergraduate students in a wide range of disciplines. Her biophysical research is focused on unifying the thermodynamic and structural basis for macromolecular interactions.

A concise and accessible textbook covering ligand-binding theory in chemistry, biology, and drug development

In Ligand-binding Basics: Evaluating Intermolecular Affinity, Specificity, Stoichiometry, and Cooperativity, accomplished chemist Professor Jannette Carey introduces ligand binding in a thorough and practical way for those new to the topic, as well as anyone seeking a connection between theory and experiment. Using a minimum of mathematical formalism, this book offers analytical rigor while remaining accessible to non-specialist practitioners. It provides readers with the skills they need to analyze their own binding data or published results, helping them develop an intuitive grasp of ligand-binding phenomena integrated with structural and thermodynamic understanding.

Topics covered include:

• Application of the principles of equilibrium, mass action, and mass balance to derive the basic equations that describe all binding processes
• Recommended approaches for plotting and graphical analysis of binding data
• Strategies for designing, analyzing, interpreting, and troubleshooting experiments from the perspective of ligand-binding theory
• Review of selected examples that illustrate integration of structural and thermodynamic analysis

Perfect for students and educators in chemistry, biochemistry, molecular biology, and pharmaceutical science, Ligand-binding Basics will also appeal to practitioners who aim to study ligand binding in any molecular system.