158. Simulating Enzyme Reactivity

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158. Simulating Enzyme Reactivity

 

 

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Chapter 1 Perspective on Computer Modelling of Enzymatic

Reactions 1
Arieh Warshel and Ram Prasad Bora
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

RSC Theoretical and Computational Chemistry Series No. 9
Simulating Enzyme Reactivity: Computational Methods in Enzyme Catalysis
Edited by In ̃aki Tun ̃o ́n and Vicent Moliner
r The Royal Society of Chemistry 2017
Published by the Royal Society of Chemistry, www.rsc.org

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
Acknowledgements 23
References 23

Section I: Theory

Chapter 2 Fundamentals of Enzyme Catalysis: Determination of
Rate Constants 33
Richard L. Schowen
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 Picture 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
Acknowledgements 52
References 52

Chapter 3 A Transition State Theory Perspective for Enzymatic

Reactions: Fundamentals and Applications 54
James T. Hynes, Damien Laage, In ̃aki Tun ̃o ́n and Vicent Moliner
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
Acknowledgements 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
Aure ́lien de la Lande, Fabien Cailliez and Dennis R. Salahub
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
Acknowledgements 143
References 144

Chapter 5 Kinetic Isotope Effects 150

I. H. Williams and P. B. Wilson
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
Jens Smiatek, Niels Hansen and Johannes Ka ̈stner
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
Acknowledgements 207
References 207
Contents xv

Section II: Methods

Chapter 7 Methods to Trace Conformational Transitions 217

Pedro Sfriso and Modesto Orozco
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

Hajime Hirao, Kai Xu, Pratanphorn Chuanprasit,
Adhitya Mangala Putra Moeljadi and Keiji Morokuma
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:QM0) to Enzymatic
Reactions 286
8.6.1 Asparaginase Erwinia chrysanthemi
(L-asparaginase II) 287
8.7 Conclusion 289
Acknowledgements 289
References 289

Chapter 9 First Principles Methods in Biology: From Continuum
Models to Hybrid Ab initio Quantum Mechanics/Molecular
Mechanics 294
Jens Dreyer, Giuseppe Brancato, Emiliano Ippoliti,
Vito Genna, Marco De Vivo, Paolo Carloni and
Ursula Rothlisberger
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

Dan Thomas Major, Reuven Eitan, Susant Das,
Anil Mhashal and Vijay Singh
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

Chapter 11 QM/MM Methods for Simulating Enzyme Reactions 377

Kara E. Ranaghan and Adrian J. Mulholland
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
b-Lactamases 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

J. Bertran and A. Oliva
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
Acknowledgements 429
References 429

Chapter 13 Effects of Water and Non-aqueous Solvents on

Enzyme Activity 436
Eva Pluharˇova ́, Nicolas Che ́ron and Damien Laage
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
Acknowledgements 450
References 450

Chapter 14 Modelling Reactivity in Metalloproteins: Hydrogen

Peroxide Decomposition by Haem Enzymes 453
M. Alfonso-Prieto and C. Rovira
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
Acknowledgements 476
References 476
Chapter 15 Enzyme Design 481
Lur Alonso-Cotchico, Jaime Rodrı ́guez-Guerra, Agustı ́ Lledo ́s
and Jean-Didier Mare ́chal
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
Acknowledgements 515
References 516
Subject Index 522

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