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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 |