Laboratory Guide to Enzymology

Geoffrey A. Holdgate is Senior Principal Scientist in Discovery Sciences for BioPharmaceuticals Research and Development at AstraZeneca.

Antonia Turberville, PhD, is a Senior Scientist in Discovery Sciences for Biopharmaceuticals R&D at AstraZeneca.

Alice Lanne, PhD, is a Senior Scientist in Discovery Sciences for BioPharmaceuticals R&D at AstraZeneca.

Preface xiii

Acknowledgments xv

1 Introduction to Proteins and Enzymes 1

1.1 Protein Structure 1

1.1.1 Primary Structure 1

1.1.2 Secondary Structure 1

1.1.3 Tertiary Structure 5

1.1.4 Quaternary Structure 6

1.1.5 Protein Structure Prediction 6

1.2 Enzymes 9

References 15

2 Binding Equilibria and Kinetics 17

2.1 Introduction to Chemical Kinetics 17

2.2 Introduction to Binding Kinetics 22

2.3 Ligand Binding to Single Binding Site 23

2.4 Kinetic Approach to Equilibrium 26

2.5 Methods for Measuring Protein-ligand Binding 27

2.6 Ligand Depletion (Tight Binding) 29

2.8 Ligand Competition 34

References 35

3 Protein QC and Handling 37

3.1 Introduction 37

3.2 Confirming Protein Identity 37

3.2.2 Peptide Mapping 38

3.2.3 Edman Sequencing 39

3.3 Protein Purity 39

3.3.1 Sds-page 40

3.3.2 Dynamic Light Scattering (DLS) 40

3.3.3 Analytical Gel Filtration 41

3.3.4 Analytical Ultracentrifugation 42

3.4 Concentration 43

3.4.1 UV–Vis Spectrum 44

3.4.2 Bradford Assay 44

3.5 Functionality 46

3.5.1 Ligand Binding 46

3.5.1.1 Itc 46

3.5.1.2 Spr 46

3.5.2 Functional Studies 46

3.6 Stability 48

3.6.1 Differential Scanning Calorimetry (DSC) 48

3.6.2 Differential Scanning Fluorimetry (DSF) 49

3.6.3 Circular Dichroism 51

3.6.4 Selwyn’s Test 51

References 52

4 Buffers and their Use in the Study of Enzyme Mechanism 55

4.1 Introduction 55

4.1.1 Ionization and pK a 55

4.1.2 pH 57

4.1.3 Henderson-Hasselbalch Equation 57

4.1.4 Buffers 58

4.2 Buffering Capacity 60

4.3 Ionic Strength 60

4.4 Change in pH with Temperature 62

4.5 Choice of Buffer 63

4.6 Characteristics of Ionizing Groups in Proteins 65

4.7 Effect of pH on Enzyme Activity 66

4.7.1 Assumptions Required for the Analysis of pH Dependence 66

4.7.2 General Rate Equation for pH Dependence 67

4.7.3 Fitting pH Dependence 70

4.7.3.1 Double Ionizing Systems 70

4.7.3.2 Singularly Ionizing Systems 72

4.8 Effect of Solvent and Ionic Strength 73

References 73

5 Steady-state Assays and their Design 75

5.1 Introduction 75

5.2 The Pre-steady State 75

5.3 Steady-state Assays 77

5.4 Assay Development 78

5.4.1 Requirements for Method Development 79

5.4.2 Different Types of Enzymes Assays 79

5.4.2.1 Direct Continuous Assay 79

5.4.2.2 Indirect Assays 80

5.4.2.3 Discontinuous Indirect Assays 80

5.4.2.4 Continuous Indirect Assays 80

5.4.2.5 Coupled Assays 80

5.5 Blank Rates 81

5.6 The Assay Development Process 81

5.6.1 Initial Assay Scoping 81

5.6.2 Substrate Dependence 83

5.6.2.1 Non-Michaelian Kinetics 87

5.6.2.2 Multiple Substrates 89

5.6.3 Plate Type 92

5.7 Assay Optimization 93

5.7.1 Factorial Experimental Design (FED) 93

5.7.2 Coupling Enzyme Considerations 96

5.8 Kinetic Characterization 96

5.8.1 Substrate Concentration 96

5.9 Assay Adaptability 97

5.9.1 Tool Compounds 97

5.9.2 DMSO Tolerance 97

5.9.3 Assay Stability 97

5.9.4 Triage Assays 98

5.10 Assay Evaluation (Validation) 98

5.10.1 Calculations 100

5.10.2 Assessing Plate Uniformity 102

5.10.3 Acceptable Assay Performance Criteria 104

References 105

6 Enzyme Inhibition 107

6.1 Introduction 107

6.2 Substrate and Product Inhibition 108

6.3 Reversibility 109

6.3.1 Testing for Irreversible Inhibition 109

6.3.2 Rapidly Reversible Inhibition 110

6.4 The IC 50 Value 111

6.4.1 Determining the IC 50 Value 111

6.4.2 Use of pIC 50 111

6.4.3 Comparison of Potency 112

6.4.4 Concentration-response Curve Analysis 113

6.4.4.1 Bell-shaped Behavior 115

6.4.4.2 Weakly Active Compounds 116

6.4.4.3 Steep Curves 116

6.4.4.4 Partial Curves 116

6.4.4.5 Noisy Data 117

6.5 Identity of Substrate 117

6.6 Effect of Enzyme Concentration – Tight-binding Inhibition 118

6.7 Slow-binding Inhibition 120

6.7.1 Progress Curves for Slow-binding Inhibition 121

6.8 Slow, Tight-binding Inhibition 126

6.8.1 Conditions where Detection of Slow-binding may be Precluded 128

6.9 Irreversible Inhibition 128

6.10 Presence of Two Inhibitors 131

6.11 Non-specific Inhibition 133

6.11.1 Common Technology Hitters 134

6.11.1.1 UV-light Interference 134

6.11.1.2 Detection System Interference 134

6.11.2 Chemical Reactivity 135

6.11.3 Aggregators 136

6.11.4 Redox Reactivity 137

6.11.4.1 Oxidation of Aromatic Amino Acid Residues 137

6.11.4.2 Protein Unfolding 137

6.11.5 Denaturation 139

6.11.6 Metal Ion Contamination 139

References 140

7 Enzyme Activation and Its Comparison with Inhibition 143

7.1 Introduction 143

7.2 Mechanisms for Enzyme Activation 143

7.2.1 Essential Activation 143

7.2.1.1 Essential Cationic Activation 145

7.2.2 Non-essential Activation 145

7.2.2.1 Non-essential Cationic Activation 146

7.2.3 A Comment on Nomenclature: K-type and V-type Classification 147

7.2.4 De-inhibition 148

7.3 Challenges for Identifying Non-essential Enzyme Activators 148

7.3.1 Enzymes have Evolved to be Active 149

7.3.2 Lack of Tool Compounds 149

7.3.3 Maintaining Steady State 149

7.3.4 Mechanistic Considerations 149

7.3.5 Assay Design and Variability 150

7.4 Addressing the Challenges of Activator Discovery 152

References 153

8 Mechanism of Action 155

8.1 Introduction 155

8.2 Mechanisms of Inhibition 155

8.2.1 Competitive Inhibition 156

8.2.2 Mixed Noncompetitive and Pure Noncompetitive Inhibition 159

8.2.3 Uncompetitive Inhibition 161

8.3 Choosing Between Different Types of Inhibition 162

8.4 Interpretation of Mechanism of Inhibition 163

8.5 Effect of Multiple Substrates and Assignment of Mechanism 164

8.6 Binding Site may not Equal Mechanism 168

8.6.1 Substrate Competitive Inhibitors at Allosteric Sites 169

8.6.2 Noncompetitive Binding giving Competitive Inhibition 169

8.6.3 Competitive Binding giving Uncompetitive Inhibition 170

8.7 Specificity 171

8.7.1 Effect of Increasing [S] 171

8.7.2 Effect of [I] 172

8.8 Activation Mechanisms and Comparison with Inhibition 173

References 175

9 Data Analysis 177

9.1 Introduction 177

9.2 Statistical Analysis of Enzyme Kinetic Data 177

9.3 Least Squares Fitting 177

9.4 Nonlinear Regression 178

9.5 Weighting of Experimental Data 182

9.6 Evaluation of Potential Different Models 183

9.6.1 Distribution of Residuals 183

9.6.1.1 The Runs Test 184

9.6.2 Magnitude of Standard Errors 184

9.6.3 Quantitative Evaluation 185

9.6.3.1 F-test 185

9.6.3.2 Akaike Information Criterion 186

9.6.3.3 Absolute Goodness of Fit 187

9.7 Minimum Significant Ratio 188

9.8 Two Independent Variables 189

9.8.1 Global Fitting 190

9.8.2 Reducing and Repeating and Reducing Only 190

9.8.2.1 Reducing Only 191

9.8.2.2 Reducing and Repeating 191

References 192

10 Molecular Interactions between Proteins and Small Molecules 193

10.1 Introduction 193

10.2 Binding Affinity is a Function of Difference Energy 194

10.3 Interactions between Charged or Polar Groups 196

10.3.1 Electrostatic Interactions 196

10.3.2 Hydrogen Bonds 197

10.4 Nonpolar Interactions 199

10.4.1 van der Waals Interactions 199

10.4.2 Hydrophobic Interactions 202

10.5 Changes in Hydrophobicity on Chemical Substitution 202

10.6 Entropy 203

References 204

11 Applications in Drug Discovery 207

11.1 Introduction 207

11.2 Pre-screening 207

11.2.1 Enzyme Considerations 208

11.2.2 Substrate Considerations 209

11.2.3 Enzyme Mechanism Considerations 210

11.3 Post-screening 211

11.3.1 Measuring Potency 211

11.3.2 Reversibility 212

11.3.3 Inhibitor Mechanistic Characterization 213

11.3.3.1 Combining Enzyme Kinetics and Biophysics 214

11.3.4 Tight Binding 215

11.3.5 Undesired Mechanisms 216

11.4 In Vitro Versus in Cellulo Enzyme Kinetics 217

References 219

Appendix A Basic Math and Statistics 221

A. 1 Algebra 221

A. 2 Fractions 222

A. 3 Indices 222

A. 4 Logarithms 223

A. 5 Quadratic Equations 223

A. 6 Straight Lines 223

A. 7 Functions 223

A. 8 Inequalities 224

A. 9 Differentiation 224

A. 10 Integration 226

A. 11 Series 227

A. 12 Statistics 227

A. 13 Propagation of Errors 228

A. 14 Using Logged Values 228

A. 15 Precision, Accuracy, Significant Figures and Rounding 228

A. 16 Dimensional Analysis 230

Appendix B Some Useful Key Formulas 233

B.1 Assay Reagent Calculations 233

B.2 Assay Statistics 234

B.3 Curve Fitting and Calculation of Parameters 235

B.4 Thermodynamics 236

B.5 Other Useful Formulas 237

Appendix C Constants, Prefixes, Conversions 239

C.1 Useful Physical Constants 239

C.2 Prefixes Used in the SI System 239

C.3 Conversion Factors 240

C.4 Greek Alphabet 241

Appendix D Common Symbols and Abbreviations and Their Units 243

D.1 Common Symbols 243

D.2 Common Abbreviations 245

Appendix E Glossary 247

Appendix F Key Derivations 253

F. 1 Langmuir Isotherm, Assuming Rapid Equilibrium 253

F. 2 Michaelis-Menten, Assuming Rapid Equilibrium 254

F. 3 Michaelis-Menten, Assuming Steady-state 255

F. 4 Rate is Directly Proportional to Free Enzyme 255

F. 5 Two Substrate Reactions 256

F. 6 Dose-response Equation to Calculate K I 257

F. 7 Derivation of Substrate Inhibition, Assuming Rapid Equilibrium 257

F. 8 Competing Ligands, Assuming Rapid Equilibrium 258

F. 9 Tight Binding 259

F. 10 Single Exponential, with First-order Rate Equation 260

F. 11 Protein Double Ionization 261

F. 12 Protein Single Ionization 262

F. 13 Derivation of the Integrated Rate Equation for Slow-binding Inhibition Described by a Two-step Mechanism 263

F. 14 Essential Activation 266

F. 15 Non-essential Activation 267

Appendix G Useful Software Packages for Analyzing Enzyme Kinetic Data 269

G.1 Desktop Based Tools 269

G.2 Web-Based Tools 270

G.3 Other Useful Online Resources 271

Index 273