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Simulating Enzyme Reactivity

Simulating Enzyme Reactivity

Inaki Tunon | Vicent Moliner

(2016)

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Book Details

Abstract

The simulation of enzymatic processes is a well-established field within computational chemistry, as demonstrated by the 2013 Nobel Prize in Chemistry. It has been attracting increasing attention in recent years due to the potential applications in the development of new drugs or new environmental-friendly catalysts. Featuring contributions from renowned authors, including Nobel Laureate Arieh Warshel, this book explores the theories, methodologies and applications in simulations of enzyme reactions. It is the first book offering a comprehensive perspective of the field by examining several different methodological approaches and discussing their applicability and limitations. The book provides the basic knowledge for postgraduate students and researchers in chemistry, biochemistry and biophysics, who want a deeper understanding of complex biological process at the molecular level.

Inaki Tunon is a Professor of Physical Chemistry at the Univeristy of Valencia, Spain. His research focusses on the modelling of chemical reactions in biological environments.

Vicent Moliner is a Professor of Physical Chemistry at the University Jaume I, Spain. His research interests lie in computational chemistry, with an emphasis on the study of enzymatic reactivity.


Table of Contents

Section Title Page Action Price
Cover Cover
Contents xi
Chapter 1 Perspective on Computer Modelling of Enzymatic Reactions 1
1.1 Introduction 1
1.2 Defining and Calculating the Catalytic Effect 2
1.2.1 Using a Logical and Useful Definition 2
1.2.2 Evaluating Reliable Activation Free Energies by Computational Approaches 4
1.2.3 Electrostatic Transition State Stabilisation (TSS) 5
1.3 What was Found by Reliable Computational Studies? 6
1.3.1 General Findings 6
1.3.2 Quantifying the Source of Electrostatic Contributions to Catalysis 8
1.4 What are the Problems with Other Proposals? 12
1.4.1 Ground-state Destabilisation by Steric Strain Does Not Provide a Large Catalytic Effect 12
1.4.2 Dynamical Effects Do Not Contribute Significantly to Enzyme Catalysis 13
1.4.3 Correlated Modes Clearly Exist in Proteins, but They Also Exist in Solution 17
1.4.4 Problems with the Generalised Compression Idea 18
1.4.5 RSD by Desolvation Effects Does Not Provide Large Catalytic Effects 19
1.4.6 Entropy Contributions of Bringing the Reactants Together are Unlikely to Account for Large Catalytic Effects 20
1.4.7 Allosteric Control of Catalytic Activity is Also Associated with Electrostatic Effects 20
1.5 Conclusions and Perspectives 21
Acknowledgments 23
References 23
Section I: Theory 31
Chapter 2 Fundamentals of Enzyme Catalysis: Determination of Rate Constants 33
2.1 Introduction 33
2.2 The Elements of Enzyme Kinetics, in Particular Rate Constants 34
2.2.1 Rate Constants Experimentally Determined 34
2.2.2 Comparison of Experimental Rate Constants with Theoretically Computed Values 36
2.2.3 A Note on Other Approaches 38
2.3 Typical Components of a Simulation Study of Enzyme Catalysis 38
2.3.1 Structural and Other Background 38
2.3.2 Selection of QM and MM Regions and Methods 39
2.3.3 The Border of the QM Region and its Embedding in the MM Region 39
2.3.4 Establishing the Potential-energy Surface 41
2.3.5 Establishing the Reaction Path or Swath 42
2.3.6 Development of a Free-energy Surface 42
2.3.7 Calculation of Rate Constants 42
2.4 Analytical Expressions for Rate Constants 44
2.4.1 The Stable States Picture11,12 44
2.4.2 Variational Transition-state Theory 46
2.4.3 Hammes-Schiffer et al. and Klinman et al. 47
2.5 An Instructive Example: Rate Constants from the Multiconfigurational Molecular Mechanics Approach QM/MM-MCMM 47
2.5.1 Elements of the QM/MM-MCMM Approach 48
2.5.2 The Empirical Valence-bond Technique for the QM Region 49
2.5.3 The Case of the Resonance Integral 50
2.5.4 Identification and Characterisation of Stationary Points 50
2.5.5 Minimum-energy Pathways 51
2.5.6 Toward Good, Cheap Hessians 51
2.6 Good Hessians Give Good Rate Constants 52
Acknowledgments 52
References 52
Chapter 3 A Transition State Theory Perspective for Enzymatic Reactions: Fundamentals and Applications 54
3.1 Introduction 54
3.2 TST and Allied Theories for Enzyme Reactions 55
3.2.1 Assumptions and Structure of TST 55
3.2.2 TS Surface Recrossing Corrections to TST 58
3.3 Classical Enzyme Reactions 60
3.3.1 TST Analysis of an Enzymatic Inverse Menshutkin Reaction: Catechol O-methyltransferase 60
3.3.2 Analysis of Haloalkane Dehalogenase. A Conventional SN2 Reaction 65
3.3.3 Beyond the FE Limit: The Michael Addition Catalysed by Chalcone Isomerase 74
3.4 Enzyme Reactions Involving Quantum Nuclear Motion 76
3.4.1 A Two-dimensional Perspective 77
3.4.2 Adiabatic PT 77
3.4.3 Non-adiabatic PT 79
3.4.4 Examples of Enzyme Reactions Involving Quantum Nuclear Motion 80
3.5 Concluding Remarks 84
Acknowledgments 85
References 85
Chapter 4 Electron Transfer Reactions in Enzymes: Seven Things that Might Break Down in Vanilla Marcus Theory and How to Fix Them if They Do 89
4.1 Introduction 89
4.2 Vanilla MT 92
4.3 Relation Between Microscopic and Macroscopic Concepts and Molecular Simulation 98
4.3.1 Microscopic Derivation of the Marcus Activation Free Energy 98
4.3.2 ET Theories and Molecular Simulations 100
4.4 Beyond the LRA 103
4.4.1 What May Cause the LRA to Break Down? 103
4.4.2 Change of the Polarisability of the Acceptor/Donor Moieties 103
4.4.3 Modification of the ‘Solvation State' upon ET 106
4.4.4 Non-ergodic Effects 109
4.5 Quantum Theories of Electron Transfer 114
4.5.1 The Fermi Golden Rule 114
4.5.2 Mixed Quantum Classical Formulations 116
4.5.3 Spectral Density as a Key Ingredient of ET Rates 119
4.5.4 Quantum Entanglement Between Electronic and Vibrational Degrees of Freedom 120
4.6 Dynamical Effects on ET Kinetics 123
4.6.1 The Chemical Structure of the Bridge Determines HDA 124
4.6.2 ET Mechanism and Electronic Coupling Fluctuations 130
4.6.3 Electron Transfer beyond the Condon Approximation 136
4.7 Beyond the Two-state Approximation 138
4.7.1 Incoherent Hopping Model 139
4.7.2 Flickering Resonance Model 139
4.8 Summary and Perspectives 142
Appendix: Chronology of Contributions to ET Theory 143
Acknowledgments 143
References 144
Chapter 5 Kinetic Isotope Effects 150
5.1 Introduction 150
5.2 The Cut-off Approximation 152
5.3 The Bebo Vibrational Analysis Method for KIE Calculations 154
5.4 QM Cluster Calculations of KIEs 156
5.4.1 Early Examples 156
5.4.2 Dehydrogenases 157
5.4.3 Binding Isotope Effects and Software 158
5.4.4 Glycosyl Transfer 159
5.4.5 Other Enzymes 163
5.5 QM/MM Calculations of KIEs 164
5.5.1 Early Examples 164
5.5.2 Hydride and Hydron Transfer 164
5.5.3 Chorismate Mutase 167
5.5.4 Methyl Transfer 168
5.5.5 Other Enzymes 169
5.6 KIE Calculations in the Supramolecular Age 170
5.6.1 KIEs and Isotopic Partition Function Ratios (IPFRs) for Subsets 170
5.6.2 Conformational Averaging of KIEs and IPFRs 174
5.6.3 Does TS Theory Still Work for KIEs? 176
5.6.4 Cut-off Rules Revisited 177
References 179
Chapter 6 Free Energy Calculation Methods and Rare Event Sampling Techniques for Biomolecular Simulations 185
6.1 Introduction 185
6.2 Reaction Coordinates 189
6.3 Methods 190
6.3.1 Thermodynamic Integration 190
6.3.2 Free Energy Perturbation Approaches 193
6.3.3 Umbrella Sampling 196
6.3.4 Enveloping Distribution Sampling 197
6.3.5 Transition Path Sampling 198
6.3.6 Forward Flux Sampling 200
6.3.7 Metadynamics 202
6.3.8 Averaging Techniques in QM/MM Simulations 205
6.4 Conclusions 206
Acknowledgments 207
References 207
Section II: Methods 215
Chapter 7 Methods to Trace Conformational Transitions 217
7.1 Proteins are Molecular Machines 217
7.2 Computational Methods to Trace Transition Paths 218
7.2.1 Interpolation Schemes 219
7.2.2 Methods Based on Normal Modes 219
7.2.3 Minimum Energy Paths 221
7.3 Transition Paths from Atomistic Simulations 222
7.3.1 MD: Unbiased 222
7.3.2 MD: Biased by a Predefined Coordinate 223
7.3.3 MD: Biased by Energy 225
7.3.4 Advanced Methods 229
7.4 Methods Based on Coarse-grained Simulations 230
7.5 Predicting Conformational Transition Pathways 233
7.5.1 Experimentally Biased Simulation Methods 233
7.5.2 Coevolution Biased Simulation Methods 234
7.6 Discussion 234
References 236
Chapter 8 Key Concepts and Applications of ONIOM Methods 245
8.1 Introduction 245
8.2 Methodological Aspects of ONIOM 246
8.2.1 Energy 246
8.2.2 Treatment of the Boundary 248
8.2.3 Energy Gradients 249
8.2.4 Geometry Optimisation 250
8.2.5 Embedding Schemes 253
8.2.6 Set-up for ONIOM Calculations 255
8.2.7 Preparation of a Decent Initial Orbital Guess for the Model System 260
8.3 Application of ONIOM2(QM:MM) to the Reactions of Iron Enzymes 260
8.3.1 myo-Inositol Oxygenase 261
8.3.2 2-Hydroxyethylphosphonate Dioxygenase 264
8.3.3 Aromatase 269
8.3.4 Fe-MOF-74, a Metal-Organic Framework that has Similarities to Iron Enzymes 272
8.4 Energy Decomposition Analysis of the Core-Environment Interactions Within Enzymes 278
8.5 Application of ONIOM2(QM:MM) to the Reactions of other Types of Enzymes 280
8.5.1 myo-Inositol Monophosphatase 280
8.5.2 QueF Nitrile Reductase 282
8.6 Application of ONIOM2(QM:QM') to Enzymatic Reactions 286
8.6.1 Asparaginase Erwinia chrysanthemi (L-asparaginase II) 287
8.7 Conclusion 289
Acknowledgments 289
References 289
Chapter 9 First Principles Methods in Biology: From Continuum Models to Hybrid Ab initio Quantum Mechanics/Molecular Mechanics 294
9.1 Introduction 294
9.2 First Principles QM/MM Methods 296
9.2.1 Introduction 296
9.2.2 The QM Part 297
9.2.3 The MM Part 298
9.2.4 The EQM/MM Coupling Term 299
9.3 Ab initio QM/MM MD Simulation Techniques 300
9.3.1 DFT Car-Parrinello MD Approach 300
9.3.2 Comparison between Full QM and QM/MM Calculations 301
9.3.3 CPMD/MM Method: Basics 305
9.3.4 Applications to Biological Systems 310
9.3.5 Post-HF Approaches 315
9.3.6 Excited States 316
9.4 Continuum Models 318
9.4.1 Introduction 318
9.4.2 QM/MM MD Simulations with GLOB Approach 319
9.4.3 Applications to Open-shell Systems in Solution 322
References 323
Chapter 10 Nuclear Quantum Effects in Enzymatic Reactions 340
10.1 Introduction 340
10.1.1 Enzymes - the Par Excellence Catalysts of Nature 340
10.1.2 Enzyme Simulations using Hybrid PESs 341
10.1.3 Classical Simulation Methods for Enzyme Modelling 342
10.1.4 Nuclear Quantum Effects in Enzymes 343
10.1.5 The Classical and Quantum Rate Constants 344
10.1.6 Kinetic, Equilibrium and Binding Isotope Effects 348
Summary 348
10.2 How Can We Include NQE in Enzyme Modelling? 349
10.2.1 Semiclassical Approach to Enzyme Modelling 349
10.2.2 Vibrational Wave Function Approach to Enzyme Modelling 352
10.2.3 Path Integral Methods 354
Summary 358
10.3 Applying NQE Methods to Enzymes: Dihydrofolate Reductase (DHFR) - the Gold Standard in Enzymology 358
10.3.1 NQE in Enzyme Reactions 358
10.3.2 DHFR - Background 359
10.3.3 NQE Effects in DHFR 362
Summary 366
10.4 Concluding Words 366
References 367
Section III: Applications 375
Chapter 11 QM/MM Methods for Simulating Enzyme Reactions 377
11.1 Introduction 377
11.2 Applications of QM/MM Methods 380
11.2.1 A Catalytic Role for Methionine Revealed by Computation and Experiment 380
11.2.2 QM/MM Simulations as an Assay for Carbapenemase Activity in Class A β-Lactamases\r 385
11.2.3 QM/MM Simulations Indicate That Asp185 is the Catalytic Base in HIV-1 Reverse Transcriptase 387
11.2.4 The Origins of Catalysis in Chorismate Mutase Analysed by QM/MM Simulations 390
11.3 Conclusions 395
References 396
Chapter 12 Ribozymes 404
12.1 Introduction 404
12.1.1 Natural Ribozymes 404
12.1.2 Artificial Ribozymes 407
12.1.3 Origin of Catalysis in Ribozymes 407
12.2 Methodological Aspects 408
12.3 Mechanisms in Natural Ribozymes 409
12.3.1 Self-cleaving Reaction 410
12.3.2 Peptide Bond Formation Catalysed by the Ribosome 421
12.4 Conclusions, Challenges and Perspectives 426
Acknowledgments 429
References 429
Chapter 13 Effects of Water and Non-aqueous Solvents on Enzyme Activity 436
13.1 Introduction 436
13.2 Traditional Picture: Water Lubricates the Protein Motions 438
13.2.1 Hydration, Protein Flexibility and Enzymatic Activity 438
13.2.2 Inconsistencies 441
13.3 Enzyme Catalysis in Non-aqueous Organic Solvents 443
13.3.1 Overview 443
13.3.2 Solvent Effects on Enzyme Activity and Specificity 443
13.4 Towards a Molecular Picture of Solvent Effects on Catalysis 447
13.4.1 Solvent Polarity 447
13.4.2 Lubrication Picture 447
13.4.3 Competitive Inhibition 449
13.5 Concluding Remarks 450
Acknowledgments 450
References 450
Chapter 14 Modelling Reactivity in Metalloproteins: Hydrogen Peroxide Decomposition by Haem Enzymes 453
14.1 Introduction 453
14.2 Methodology 454
14.3 Catalases and Peroxidases 455
14.3.1 Biological Function 455
14.3.2 Reactivity 456
14.3.3 Monofunctional Catalases and Peroxidases 458
14.3.4 The Catalatic Reaction in KatGs 469
14.4 Conclusions 475
Acknowledgments 476
References 476
Chapter 15 Enzyme Design 481
15.1 Introduction 481
15.2 Scope and Objectives 482
15.3 Man-made Enzymes 483
15.3.1 An Overview of Novel Enzymes 483
15.3.2 Tricking Nature's Enzymes 483
15.3.3 New Folds for New Activities 486
15.3.4 Bringing Homogenous Catalysts into the Game 489
15.4 Computational Tools and Designed Enzymes 492
15.4.1 Accuracy vs. Sampling 492
15.4.2 Reactivity 493
15.4.3 Substrate Binding 495
15.4.4 Folds 497
15.4.5 Chemogenetic Spaces 498
15.4.6 Multi-scale 499
15.5 Applications 501
15.5.1 De novo Enzymes 501
15.5.2 Redesigning, Optimising and Filtering Enzymes 504
15.5.3 Artificial Metalloenzymes 508
15.6 Conclusion and Perspectives 515
Acknowledgments 515
References 516
Subject Index 522