Ligand-Binding Basics

Chapter 1: The Biology of Molecules

• • Why Study Intermolecular Interactions Quantitatively?
• • Equilibrium and Kinetics
• • Thermodynamic Definitions of Affinity and Specificity
• • The Affinity/Specificity Map
• • Biology Requires Optimization of Affinity and Specificity
• • The Special Case of Protein-DNA Interactions

Chapter 2: General Theory for Reversible Ligand Binding

• • Definition of Ligand and Titration
• • Affinity, Specificity, Stoichiometry, and Cooperativity
• • Ligand-binding Theory: Relationship to Experiment
• • General Theory for Reversible Ligand Binding: Rooted in Chemical Equilibrium
• • General Theory for Reversible Ligand Binding: Quantitative Treatment
• • The Case of 1:1 Binding
• • General Theory for Reversible Ligand Binding: Conservation of Mass
• • Definition of ν
• • The Basic Equation for 1:1 Binding
• • The Single Most Important Thing You Can Learn in This Book
• • The Example of Heme Binding to Apocytochrome c
• • The Rectangular Hyperbola
• • The Binding Isotherm
• • Plot of ν vs. [H f ]
• • General Theory for Reversible Ligand Binding: Role of Mass Action
• • Plot of [AH]vs.[H t ] with Fixed K
• • Determination of K d from Experiment
• • Plot of [AH]vs.[H t ] with Fixed [A t ]
• • Determining Molar Ratio from Experiment
• • About Activity

Chapter 3: Graphical Analysis

• • Limitations of Direct Plots
• • The Semi-log Plot
• • Breadth of the Semi-log Plot
• • Myoglobin and Hemoglobin
• • Advantages of the Direct and Semi-log Plots of Binding Data
• • Linear Transforms of the Basic Binding Equation
• • Common Linearizations
• • Requirements of the Linear Regression Model
• • A Linear Model May Misrepresent the Physical Process
• • Deviations from Linearity Are Hard to Detect or Interpret
• • Linear Transforms Distort Data Completeness
• • Linear Transforms Invite – Even Require – Extrapolation
• • Linear Transforms Falsely Promise Both K and Molar Ratio from a Single Dataset
• • Summary about Linear Treatments of Binding Data
• • Simulation Is Just as Good as Fitting, Given Realistic Experimental Errors

Chapter 4: Binding of Multiple Ligands

• • Conservation of Mass Outside the 1:1 Case
• • Redefine ν to Accommodate Any Molar Ratio
• • Accounting for the Definition of Molecule
• • Generalizing to Integer Multiples of 1:1
• • The Langmuir Equation for Any Molar Ratio with Sites of Identical Affinity and No Cooperativity
• • Adair Equation for Any Number of Binding Events
• • The Langmuir Equation vs. the Adair Equation
• • Thermodynamic Linkage
• • Two Classes of Sites with Different Affinities
• • Binding Isotherms for Multiple Sites with Different Affinities
• • Summary

Chapter 5: How to Determine K d and Molar Ratio Experimentally

• • Stoichiometric Titration First
• • Amounts of Materials
• • Assigning Partners
• • Choice of Experimental Observables
• • Choosing Solution Conditions
• • How Many Data Points?
• • Range-Finding Stoichiometric Titration
• • Visualizing Results
• • Range-Finding Asymptotic Titration to Estimate K d
• • Data Analysis
• • Practicalities about Experimental Error
• • Statistical Approaches to Estimate the Breakpoint
• • Refined Asymptotic Titration
• • Designing an Experiment to Refine K d
• • Calculating Free Ligand Concentration
• • Refining the Value of Molar Ratio
• • Example of ArgR/DNA Binding
• • Plotting the Data
• • Deriving K d from the Data
• • Summary

Chapter 6: Cooperativity

• • Facilitated and Antagonized Binding
• • Free Energy Definition of Cooperative Binding
• • Chemical Potential Diagram for Cooperative Binding
• • Cooperativity as Non-additivity
• • Reciprocity of Cooperative Effects
• • Limitations of Linear Transforms for Cooperative Interactions
• • Microscopic View of Species Distribution
• • Homotropic and Heterotropic Cooperativity
• • Cooperativity Affects Specificity as Well as Affinity
• • Cooperativity Is the Third Axis of the Affinity/Specificity Map
• • Quantifying Homotropic Cooperativity
• • Negative Homotropic Cooperativity
• • A Practical Advantage of Negative Cooperativity
• • Positive Cooperativity and the Ligand Concentration Interval
• • Importance of Individual-site Isotherms and Species Distribution
• • Species Distributions by Specialized Experimental Methods
• • The Many Forms of Cooperativity
• • Emergent Properties
• • Connectivity and Search Entropy
• • Breakdown of Additivity in Complex Systems
• • Statistical Effects
• • Relevance of Non-additivity for Analysis of Mutations
• • Universality and Promiscuity of Cooperativity
• • Proteins as Gestalt Objects
• • Summary

Chapter 7: Theoretical and Method-specific Troubleshooting

• • Equilibrium and Nonequilibrium Methods
• • Accessible Concentration Ranges Limit Accessible K d Values
• • Signal from Ligand or Target?
• • Separation-based Methods
• • Filter Binding
• • Gel Retardation or EMSA
• • Gel Filtration
• • Hummel and Dreyer Chromatography
• • Equilibrium Dialysis
• • UV Absorbance
• • CD Spectroscopy
• • Fluorescence
• • NMR
• • ITC
• • AUC
• • SPR
• • MS

Chapter 8: Allostery

• • An Historical Overview
• • Facilitated Binding
• • Elaboration of the MWC Model
• • Relaxed Monomers and Tense Multimers
• • Positive Homotropic Cooperativity Only
• • Artifactual Origins of Affinity Heterogeneity
• • Relaxation of Multimers by Ligand Binding
• • Koshland’s Sequential (Asymmetric) Model
• • G3Pase Was Heterogeneous, Not Negatively Cooperative
• • Many Models Fit the Hemoglobin Data
• • Advantages of Negative Cooperativity for Molecular Insight
• • Biology of Negative Cooperativity
• • Structural Analysis Cannot Solve Allostery
• • Allostery without Cooperativity
• • Summary

Chapter 9: Lessons on Affinity and Specificity from Host/Guest Chemistry

• • 2D Representations of 3D Objects
• • Early Hosts Were Linear and Flexible
• • Design of Molecular Properties
• • Very Weak Affinity and No Detectable Specificity
• • Later Hosts Pre-organized in Bound Conformation
• • Enormous Gains in Affinity and Specificity
• • Bonds between Host and Guest Are Identical
• • Lessons from the Host/Guest Chemistry
• • Rational Design of Affinity and Specificity
• • Affinity and Specificity Accrue in Parallel
• • Cryptic Contributions Can Dominate Binding

Chapter 10: Reconciling Structure and Thermodynamics in Molecular Interactions

• • Thermodynamics of Molecular Interactions
• • Structural Analysis of Bonding Does Not Predict Binding
• • The Goldilocks Region of Affinity/Specificity Space
• • Conformational Rearrangement upon Binding Decouples Affinity and Specificity
• • A Reservoir of Adaptability
• • No Simple Reconciliation of Structural and Energetic Views
• • Implications for Drug Design

Chapter 11: Applications in Modern Drug Development

• • Background
• • Technological Developments
• • Crystal Structures
• • Trapped High-energy States
• • Another Example
• • Computational Methods
• • High-throughput Assays
• • Druggability
• • Irrational Drug Design
• • A New Workflow

Chapter Appendix A: Ligand-binding Study Questions

Chapter Appendix B: Thought Experiments

Chapter Appendix C: Derivations

Chapter Appendix D: Simulation and Fitting

• • Simulation
• • Fitting

Chapter Appendix E: About the Hill Equation

• • Deriving the Hill Equation
• • The Hill Equation as a Limit of the Adair Equation
• • On Applying the Hill Equation to Quantify Cooperativity

Chapter Appendix F: Stereo Viewing