Theory and Applications of the Empirical Valence Bond Approach

Lynn Kamerlin, Professor, Department of Cell and Molecular Biology, Uppsala University Professor Kamerlin is a full?Professor?of Structural Biology at Uppsala University, as well as an ERC Starting Independent Researcher and a Wallenberg Academy Fellow. She is also the current Chair of the Young Academy of Europe (YAE). Her research interests span theoretical physical organic chemistry, phosphate and sulfate chemistry, the mechanisms of enzyme reactivity, specificity, promiscuity and catalysis, and computational directed evolution. Fernanda Duarte, Department of Cell and Molecular Biology, Uppsala University Dr Duarte is the Newton Fellow at University of Oxford, UK. In November 2015, she was awarded a ?100,000 grant for research into Plagiarizing Proteins: In Silico Evolution of Catalysts for Selective Chemical Synthesis.

List of Contributors xi

Foreword xiii

Acknowledgements xix

1 Modelling Chemical Reactions Using Empirical Force Fields 1
Tibor Nagy and Markus Meuwly

1.1 Introduction 1

1.2 Computational Approaches 3

1.3 Molecular Mechanics with Proton Transfer 3

1.4 Adiabatic Reactive Molecular Dynamics 4

1.5 The Multi-Surface ARMD Method 6

1.6 Empirical Valence Bond 8

1.7 ReaxFF 9

1.8 Other Approaches 10

1.9 Applications 10

1.9.1 ProtonatedWater and Ammonia Dimer 10

1.9.2 Charge Transfer in N2 − N+2 12

1.9.3 Vibrationally Induced Photodissociation of Sulfuric Acid 12

1.9.4 Proton Transfer in Malonaldehyde and Acetyl-Acetone 15

1.9.5 Rebinding Dynamics in MbNO 16

1.9.6 NO Detoxification Reaction in Truncated Hemoglobin (trHbN) 16

1.9.7 Outlook 18

Acknowledgements 19

References 19

2 Introduction to the Empirical Valence Bond Approach 27
Fernanda Duarte, Anna Pabis and Shina Caroline Lynn Kamerlin

2.1 Introduction 27

2.2 Historical Overview 28

2.2.1 From Molecular Mechanics to QM/MM Approaches 28

2.2.2 Molecular Orbital (MO) vs. Valence Bond (VB)Theory 29

2.3 Introduction to Valence BondTheory 30

2.4 The Empirical Valence Bond Approach 32

2.4.1 Constructing an EVB Potential Surface for an SN2 Reaction in Solution 33

2.4.2 Evaluation of Free Energies 36

2.5 Technical Considerations 38

2.5.1 Reliability of the Parametrization of the EVB Surfaces 38

2.5.2 The EVB Off-diagonal Elements 39

2.5.3 The Choice of the Energy Gap Reaction Coordinate 39

2.5.4 Accuracy of the EVB Approach For Computing Detailed Rate Quantities 40

2.6 Examples of Empirical Valence Bond Success Stories 40

2.6.1 The EVB Approach as a Tool to Explore Electrostatic Contributions to Catalysis: Staphylococcal Nuclease as a Showcase System 40

2.6.2 Using EVB to Assess the Contribution of Nuclear Quantum Effects to Catalysis 42

2.6.3 Using EVB to Explore the Role of Dynamics in Catalysis 42

2.6.4 Exploring Enantioselectivity Using the EVB Approach 43

2.6.5 Moving to Large Biological Systems: Using the EVB Approach in Studies of Chemical Reactivity on the Ribosome 44

2.7 Other Empirical Valence Bond Models 47

2.7.1 Chang-Miller Formalism 47

2.7.2 Approximate Valence Bond (AVB) Approach 47

2.7.3 Multistate Empirical Valence Bond (MS-EVB) 48

2.7.4 Multiconfiguration Molecular Mechanics (MCMM) 48

2.7.5 Other VB Approaches for Studying Complex Systems 49

2.8 Conclusions and Future Perspectives 50

References 52

3 Using Empirical Valence Bond Constructs as Reference Potentials For High-Level Quantum Mechanical Calculations 63
Nikolay V. Plotnikov

3.1 Context 64

3.2 Concept 68

3.3 Challenges 69

3.3.1 Different Reference and Target Reaction Paths 69

3.3.2 Convergence of the Free Energy Estimates 70

3.4 Implementation of the Reference PotentialMethods 71

3.4.1 Locating the Target Reaction Path 71

3.4.2 Low-accuracy Target Free Energy Surface from Non-equilibrium Distribution 71

3.4.3 Obtaining a Low-Accuracy Target Free Energy Surface from Free Energy Perturbation 72

3.4.4 Pre-Computing the Reaction Path 73

3.4.5 Reference Potential Refinement: the Paradynamics Model 74

3.4.6 Moving From the Reference to the Target Free Energy Surface at the TS Using Constraints on the Reaction Coordinate 74

3.4.7 High-Accuracy Local PMF Regions from Targeted Sampling 76

3.4.8 Improving Accuracy of Positioning the Local PMF Regions 77

3.5 EVB as a Reference Potential 77

3.5.1 EVB Parameter Refinement 80

3.5.2 EVB Functional Refinement 81

3.6 Estimation of the Free Energy Perturbation 82

3.6.1 Exponential Average 83

3.6.2 Linear Response Approximation (LRA) 84

3.6.3 Bennet’s Acceptance Ratio 84

3.6.4 Free Energy Interpolation 85

3.7 Overcoming Some Limitations of EVB Approach as a Reference Potential 86

3.8 Final Remarks 86

References 87

4 Empirical Valence Bond Methods for Exploring Reaction Dynamics in the Gas Phase and in Solution 93
Jeremy N. Harvey,Michael O’Connor and David R. Glowacki

4.1 Introduction 93

4.2 EVB and Related Methods for Describing Potential Energy Surfaces 94

4.3 Methodology 97

4.4 Recent Applications 100

4.4.1 Cl + CH4 in the Gas Phase 100

4.4.2 CN + c-C6H12 (CH2Cl2 Solvent) 102

4.4.3 CN + Tetrahydrofuran (Tetrahydrofuran Solvent) 103

4.4.4 F+CD3CN (CD3CN Solvent) 104

4.4.5 Diazocyclopropane Ring Opening 107

4.5 Software Implementation Aspects 108

4.5.1 CPU Parallelization Using MPI 109

4.5.2 GPU Parallelization 111

4.6 Conclusions and Perspectives 115

References 117

5 Empirical Valence-BondModels Based on Polarizable Force Fields for Infrared Spectroscopy 121
Florian Thaunay, Florent Calvo, Gilles Ohanessian and Carine Clavaguéra

5.1 Introduction 121

5.2 Infrared Spectra of Aspartate and Non-Reactive Calculations 123

5.2.1 Experimental Approach 123

5.2.2 Quantum Chemical Calculations 124

5.2.3 Finite Temperature IR Spectra Based on AMOEBA 126

5.2.3.1 The AMOEBA Force Field 126

5.2.3.2 Infrared Spectra From Molecular Dynamics Simulations 126

5.2.3.3 Role of the Multipoles 127

5.3 Empirical Valence-Bond Modeling of Proton Transfer 130

5.3.1 Two-State EVB Model 130

5.3.1.1 Implementation of EVB Model with AMOEBA 131

5.3.1.2 Coupling Between Diabatic States 131

5.3.2 Dynamics Under the EVB-AMOEBA Potential 133

5.3.3 Infrared Spectra with the EVB-AMOEBA Approach 136

5.4 Concluding Remarks 140

Acknowledgements 140

References 140

6 Empirical Valence Bond Simulations of Biological Systems 145
Avital Shurki

6.1 Introduction 145

6.2 EVB as a Tool to Unravel Reaction Mechanisms in Biological Systems 147

6.2.1 Hydrolysis of Organophosphate Compounds in BChE 147

6.2.2 Hydrolysis of GTP in Ras/RasGAP 150

6.3 EVB a Comparative Tool 152

6.3.1 Guided Reaction Paths 152

6.3.2 Studies of the Same Reaction in Different Environments 155

6.3.2.1 The Effect of Conformational Changes 155

6.3.2.2 Mutational Studies 156

6.4 EVB – A Sampling Tool 157

6.4.1 EVB – An EfficientWay to Run an Enormous Number of Calculations 157

6.4.2 EVB – An EfficientWay to Sample Conformations for Other QM/MM Approaches 159

6.4.2.1 Copper-Chaperones 159

6.4.2.2 Hybrid Ab Initio VB/MM Approach 161

6.4.2.3 EVB – An Efficient Reference Potential 161

6.5 EVB Provides Simple Yet Superior Definition of Reaction Coordinate 163

6.6 EVB – A Tool with Great Insight 164

6.7 Concluding Remarks 166

Acknowledgements 166

References 166

7 The Empirical Valence Bond Approach as a Tool for Designing Artificial Catalysts 173
Monika Fuxreiter and LetifMones

7.1 Introduction 173

7.2 Proposals for the Origin of the Catalytic Effect 174

7.3 Reorganization Energy 177

7.4 Conventional In Silico Enzyme Design 179

7.5 Computational Analysis of Kemp Eliminases 183

7.6 Using the Empirical Valence Bond Approach to Determine Catalytic Effects 184

7.6.1 General EVB Framework 184

7.6.2 Computing Free Energy ProfilesWithin the EVB Framework 185

7.7 Computing the Reorganization Energy 186

7.8 Egap: A General Reaction Coordinate and its Application on Other PES 187

7.9 Contribution of Individual Residues 189

7.10 Improving Rational Enzyme Design by Incorporating the Reorganization Energy 190

7.11 Conclusions and Outlook 191

Acknowledgements 193

References 193

8 EVB Simulations of the Catalytic Activity of Monoamine Oxidases: From Chemical Physics to Neurodegeneration 199
Robert Vianello and Janez Mavri

8.1 Introduction 199

8.2 Pharmacology of Monoamine Oxidases 200

8.3 Structures of MAO A and MAO B Isoforms 201

8.4 Mechanistic Studies of MAO 202

8.5 Cluster Model of MAO Catalysis 204

8.6 Protonation States of MAO Active Site Residues 211

8.7 EVB Simulation of the Rate Limiting Hydride–Abstraction Step for Various Substrates 215

8.8 Nuclear Quantum Effects in MAO Catalysis 218

8.9 Relevance of MAO Catalyzed Reactions for Neurodegeneration 221

8.10 Conclusion and Perspectives 223

Acknowledgements 223

References 224

Index 233