Kinetics and Dynamics (eBook)

P. Paneth is Professor of Physical and Theoretical Chemistry at the Technical University of Lodz. A. Dybala-Defratyka is Assistant Professor at the Technical University of Lodz.

Preface 6
Contents 10
CHAPTER 1: Ca2+ REACTIVITY IN THE GAS PHASE. BONDING, CATALYTIC EFFECTS AND COULOMB 20
1.1 INTRODUCTION 21
1.2 STRUCTURE AND BONDING OF Ca2+ COMPLEXES 22
1.3 STABILITY OF Ca2+ COMPLEXES IN THE GAS PHASE 30
1.4 REACTIVITY OF Ca2+ IONS IN THE GAS PHASE 33
REFERENCES 48
CHAPTER 2: FROM THE GAS PHASE TO A LIPID MEMBRANE ENVIRONMENT: DFT AND MD SIMULATIONS OF STRUCTURE AND DYNAMICS OF HYDROGEN-BONDED SOLVATES OF BIFUNCTIONAL HETEROAZAAROMATIC COMPOUNDS 53
2.1 INTRODUCTION 54
2.2 ELECTRONIC STRUCTURE OF 1H-PYRROLO[3,2-h]QUINOLINE 56
2.3 STRUCTURE OF GAS-PHASE COMPLEXES 59
2.3.1 Hydrogen-Bonded Complexes with Water 59
2.3.2 Excited-State Proton Transfer Through Water Bridges 61
2.3.3 Hydrogen-Bonded Complexes with Methanol 64
2.3.4 Cluster Size Effect on Fluorescence Quenching in Hydrogen-Bonded Complexes of PQ with Methanol 68
2.4 HYDROGEN BONDING OF HETEROAZAAROMATICS IN SOLUTION 69
2.4.1 Hydrogen-Bonded Complexes with Methanol and Water 70
2.4.2 Hydrogen-Bonding Dynamics in Bulk Solvents 74
2.5 HYDROGEN-BONDING-INDUCED AND EXCITED-STATE PHENOMENA IN BIFUNCTIONAL DONOR-ACCEPTOR MOLECULES 76
2.6 INTERACTION OF HETEROAZAAROMATICS WITH LIPID MEMBRANES 78
2.6.1 Hydrogen-Bonding at the Membrane Interface 81
2.7 PROBING THE ACID-BASE EQUILIBRIUM AT THE MEMBRANE INTERFACE 85
2.8 CONCLUSIONS 89
REFERENCES 90
CHAPTER 3: FORMAMIDE AS THE MODEL COMPOUND FOR PHOTODISSOCIATION STUDIES OF THE PEPTIDE BOND 94
3.1 INTRODUCTION 95
3.2 AN OVERVIEW OF COMPUTATIONAL METHODS FOR STUDYING DYNAMICS OF FAST PHOTODISSOCIATION PROCESSES 96
3.3 COMPUTATIONAL DETAILS 99
3.4 SIMULATIONS OF NON-ADIABATIC PHOTODYNAMICS OF FORMAMIDE 100
3.4.1 Gas Phase Studies 100
3.4.2 Photodissociation of Substituted Formamides 106
3.4.2.1 N,N-Dimethylformamide 106
3.4.2.2 Acetamide 110
3.4.2.3 Phenyl Substituted Formamides 113
3.5 EFFECT OF PROTONATION ON PHOTODISSOCIATION OF FORMAMIDE 113
3.6 EFFECT OF ENVIRONMENT ON PHOTODISSOCIATION OF FORMAMIDE 117
3.7 CONCLUSIONS AND FINAL REMARKS 119
REFERENCES 121
CHAPTER 4: DESIGN OF CATALYSTS FOR ASYMMETRIC ORGANIC REACTIONS THROUGH DENSITY FUNCTIONAL CALCULATIONS 124
4.1 INTRODUCTION 124
4.1.1 Organocatalytic Reactions and Theoretical Models 125
4.1.1.1 Proline Catalyzed Intermolecular Aldol Reaction 126
4.1.1.2 Modified Proline Analogues as Catalysts 127
4.1.2 Sulfur Ylide Promoted Reactions 128
4.2 COMPUTATIONAL METHODS 130
4.2.1 Terminology 131
4.2.1.1 Bicyclic Proline Analogues as Catalyst for Intermolecular Aldol Reaction 131
4.2.1.2 Design of Catalyst for Sulfur Ylide Mediated Reaction 131
4.3 RESULTS AND DISCUSSION 131
4.3.1 Intermolecular Aldol Reaction 131
4.3.1.1 Bicyclic Systems Where -NH Is Out-of-Plane in the Envelope Conformer of Proline 133
4.3.1.2 Structural Modification of N Out-of-Plane Bicyclic Proline Analogues by Fine-Tuning the Weak Interactions 136
4.3.1.3 Bicyclic Systems Where C-beta Is Out-of-Plane in the Envelope Conformer of Proline 137
4.3.1.4 Bicyclic Systems Where C-gamma Is Out-of-Plane in the Envelope Conformer of Proline 138
4.3.1.5 Bicyclic System Where C-beta Is Out-of-Plane in the Envelope Conformer of beta-Proline 139
4.3.2 Sulfur Ylide Promoted Reactions 140
4.3.2.1 Mechanism and Diastereoselectivity Studies on Achiral Models 140
4.3.2.2 Designing Catalyst for Asymmeric Aziridination 145
4.3.2.2.1 Aziridines from Stabilized Chiral S-Ylides 146
4.3.2.2.2 Aziridines from Semistabilized Chiral S-Ylides 146
4.4 SUMMARY 150
REFERENCES 151
CHAPTER 5: REACTIVE PROCESSES WITH MOLECULAR SIMULATIONS 154
5.1 INTRODUCTION 154
5.2 CONCEPTUAL APPROACHES 157
5.2.1 Molecular Mechanics with Proton Transfer 157
5.2.2 Reactive Molecular Dynamics 158
5.2.3 Empirical Valence Bond 159
5.2.4 ReaxFF 160
5.2.5 Other Approaches 162
5.3 APPLICATIONS 162
5.3.1 Proton Transfer Reactions 162
5.3.2 Ligand Binding in Heme Proteins 165
5.4 OUTLOOK 168
REFERENCES 170
CHAPTER 6: THEORETICAL STUDIES OF POLYMERISATION REACTIONS 173
6.1 INTRODUCTION 173
6.1.1 Methods for Modelling of Polymers 174
6.1.1.1 Ab Initio Calculations 174
6.1.1.2 DFT Methods 175
6.1.1.3 Semiempirical Methods 176
6.1.1.4 Molecular Mechanics 176
6.1.1.5 Coarse Grained Models 177
6.1.1.6 Hybrid Methods 177
6.1.1.7 Molecular Dynamics 179
6.1.2 Large-Scale Molecular Modelling Calculations on Biological Systems 179
6.1.3 Molecular Modelling Software for Describing Structures and Energies 180
6.2 COMPUTATIONAL QUANTUM CHEMISTRY STUDIES OF POLYMERISATION MECHANISMS 180
6.2.1 Solvent Effects 182
6.2.2 Free-Radical Polymerisation 182
6.2.2.1 General Remarks 182
6.2.2.2 Controlled Radical Polymerisation 184
6.2.2.3 Radical Ring-Opening Polymerisation 185
6.2.3 Ionic Polymerisation 185
6.2.3.1 General Remarks 185
6.2.3.2 Ionic Polymerisation of Olefins 187
6.2.3.3 Ring Opening Polymerisation (ROP) of Cyclic Monomers 188
6.2.4 Coordination Polymerisation 191
6.2.5 Polycondensation 193
6.3 ENZYMATIC REACTIONS 193
6.4 STRUCTURAL STUDIES 195
6.5 SUMMARY 196
REFERENCES 196
CHAPTER 7: EVALUATION OF PROTON TRANSFER IN DNA CONSTITUENTS: DEVELOPMENT AND APPLICATION OF AB INITIO BASED REACTION KINETICS 203
7.1 INTRODUCTION 204
7.2 METHODOLOGY 205
7.2.1 Ab Initio Based Computation of Reaction Rates 205
7.2.2 Numerical Solution of a System of Rate Equations 207
7.3 APPLICATIONS OF THE REACTION KINETICS MODELS TO THE STUDIES OF PROTON TRANSFER IN DNA CONSTITUENTS 208
7.3.1 Tautomerization of Nucleobases in the Gas Phase 208
7.3.1.1 Kinetic Model for the Gas Phase Experiments 211
7.3.1.2 Ab Initio Based Kinetics of Laser-Induced Desorption 214
7.3.2 Tautomerization of Isolated and Monohydrated Cytosine and Guanine at Room Temperature 218
7.3.2.1 Tautomerization of Isolated Species 218
7.3.2.2 Tautomerization of Monohydrated Species 219
7.3.3 Role of Hydrated Metal Ions for Nucleic Acids Stabilization 220
7.3.4 Gas Phase Tautomerization in AT and GC Pairs of DNA Bases 224
7.4 CONCLUSIONS 225
REFERENCES 226
CHAPTER 8: SIMULATION OF CHARGE TRANSFER IN DNA 228
8.1 INTRODUCTION 228
8.1.1 Basics of Hole Transfer in DNA 229
8.1.2 Experimental Studies 229
8.1.2.1 Rate of Hole Transfer 229
8.1.2.2 Mechanism of Charge Migration 231
8.1.3 Theory and Computation 232
8.1.3.1 Phenomenological Description: Marcus´ Theory 233
8.1.3.2 Kinetic Studies 234
8.1.3.3 Stochastic Approaches 234
8.1.4 Subject of This Contribution 235
8.2 CHARGE-TRANSFER PARAMETERS 235
8.2.1 Ionization Potentials 235
8.2.2 Electronic Couplings 235
8.2.3 CT Parameters Within the Fragment-Orbital Approach 236
8.2.3.1 Fragment-Orbital Approach 236
8.2.3.2 The SCC-DFTB Method 237
8.2.3.3 Coupling to the Environment: QM/MM SCC-DFTB 238
8.2.4 Summary 239
8.3 EFFECT OF DYNAMICS AND ENVIRONMENT ON CT PARAMETERS 239
8.3.1 Electronic Couplings 240
8.3.2 Ionization Potentials 240
8.3.3 Computation of CT Parameters Along MD Trajectories 241
8.3.3.1 Magnitude of Oscillations of CT Parameters 241
8.3.3.2 The Electrostatic Potential Induced by the Environment 242
8.3.3.3 Correlation of CT Parameters 244
8.3.4 Summary 245
8.4 QUANTUM DYNAMICS OF A HOLE IN DNA 245
8.4.1 Integration of the Time-Dependent Schrödinger Equation 245
8.4.2 Simulation of Hole Transfer Over Adenine Bridges 246
8.4.2.1 Effect of Dynamics 247
8.4.2.2 On the Mechanism and Rate of the Transfer 248
8.4.2.3 Effect of the Features of CT Parameters on the Rate of Transfer 249
8.4.3 Summary 250
8.5 SOLVENT REORGANIZATION ENERGY AND DE-LOCALIZATION OF THE HOLE 251
8.5.1 Polarization of the Environment by the Hole Charge 251
8.5.2 Solvent Reorganization Energy 252
8.5.3 Spatial Extent of the Hole 253
8.5.4 How to Include the Response of Solvent in the Simulation? 254
8.6 SUMMARY, CONCLUSIONS AND OUTLOOK 255
8.6.1 Fundamental Mechanism of Charge Transfer 256
8.6.2 De/localization of the Hole 256
8.6.3 Requirements on a Computational Model 257
REFERENCES 257
CHAPTER 9: QUANTUM-MECHANICAL MOLECULAR DYNAMICS OF CHARGE TRANSFER 261
9.1 INTRODUCTION 262
9.2 THEORETICAL PART 263
9.3 THE NOTION OF CHARGE TRANSFER 265
9.3.1 QM MD of Ubiquitin in Explicit Water 267
9.3.2 Charge Transfer Inside Protein 268
9.3.3 Charge Transfer Channel 269
9.3.4 Inequality Among Same-Type Amino Acids 271
9.3.5 Protein-Solvent Charge Transfer 275
9.4 IMPLICATIONS OF CHARGE TRANSFER 278
REFERENCES 279
CHAPTER 10: BEYOND STANDARD QUANTUM CHEMICAL SEMI-CLASSIC APPROACHES: TOWARDS A QUANTUM THEORY OF ENZYME CATALYSIS 281
10.1 INTRODUCTION 282
10.2 ENZYME CATALYZED REACTIONS 283
10.2.1 Transition Structures and Chemical Mechanisms 285
10.3 EXACT QUANTUM SCHEMES 286
10.4 SEMI-CLASSIC SCHEMES AND BEYOND 288
10.4.1 Semi-classic Hamiltonian Models 288
10.4.2 Invariant Electronic Configuration Space Models 291
10.4.3 ``Mobile´´ Electronic-Configuration-Space: Nodal Envelope States 292
10.5 QUANTUM ASPECTS OF CATALYSIS 293
10.5.1 Model Quantum Catalyst: H + H and H2 293
10.5.2 Quantum Transition States 295
10.5.3 Abstract BO Transition Structures 297
10.5.3.1 One-Electron Basis Sets 298
10.6 ANGULAR MOMENTUM (SPIN) AND CHEMICAL REACTIVITY 299
10.6.1 Spin-Space Separation and Chemical Reactivity 300
10.6.1.1 Ethylene 301
10.6.1.2 Carbene Fragments: Basis States 305
10.7 PHOTORESPIRATION: DIOXYGEN 307
10.8 MORE LIGHT 309
REFERENCES 312
CHAPTER 11: MOLECULAR DYNAMICS SIMULATIONS: DIFFICULTIES, SOLUTIONS AND STRATEGIES FOR TREATING METALLOENZYMES 313
11.1 INTRODUCTION 313
11.2 BIOMOLECULAR FORCE FIELDS 315
11.2.1 AMBER 316
11.2.2 CHARMM 317
11.2.3 OPLS 318
11.3 DIFFICULTIES IN TREATING A METALLOENZYME 319
11.4 PARAMETERIZATION STRATEGIES FOR METALLOPROTEINS 319
11.4.1 The Non-Bonded Model Approach 320
11.4.2 The Bonded Model Approach 322
11.4.3 Cationic Dummy Atom Approach 323
11.4.4 Alternative Formulations 324
11.5 FARNESYLTRANSFERASE AS A TEST CASE 325
11.5.1 The Target Protein 325
11.5.2 Initial Strategies 327
11.5.3 Setting a Bonded Model Simulation 328
11.5.3.1 Atom Types 328
11.5.3.2 Bond Parameters 329
11.5.3.3 Angle Parameters 332
11.5.3.4 Dihedral Parameters 333
11.5.3.5 Van der Waals Parameters 334
11.5.3.6 Electrostatic Parameters 335
11.5.4 Validation and Application 337
11.6 SUMMARY 340
REFERENCES 341
CHAPTER 12: QM/MM ENERGY FUNCTIONS, CONFIGURATION OPTIMIZATIONS, AND FREE ENERGY SIMULATIONS OF ENZYME CATALYSIS 345
12.1 ENZYME CATALYSIS AND QM/MM MODELING 345
12.1.1 Non-Covalent Contributions to Enzyme Catalysis 345
12.1.2 Modeling Non-Covalent Interactions in Enzyme Reactions by QM/MM 347
12.2 QM/MM AS POTENTIAL ENERGY MODELS 347
12.2.1 Mechanical Embedding QM/MM 347
12.2.2 Electrostatic QM/MM 348
12.2.3 QM/MM Partitioning and the Treatment of Boundaries 349
12.2.3.1 Partitioning Between QM and MM 349
12.2.3.2 The Link Atom Approach 350
12.2.3.3 The Pseudo-Bond Approach 350
12.2.3.4 Treating Immediate Neighbors Between QM and MM 351
12.2.3.5 QM/MM Boundaries in the Modeling of Enzymatic Reactions 351
12.2.4 Long Range Electrostatic Effects 352
12.2.4.1 Finite Size Effects and Charge Scaling 352
12.2.4.2 Periodic QM/MM Systems 352
12.2.4.3 Incorporating QM/MM with Continuum Models 353
12.3 OPTIMIZATION AND SAMPLING IN QM/MM CONFIGURATION SPACES 353
12.3.1 Effects of System Sizes and Computational Characteristics of QM/MM 354
12.3.2 Optimization on QM/MM Potential Energy Surfaces 354
12.3.2.1 Meaning of Stationary Points and Minimum Energy Paths in QM/MM 354
12.3.2.2 Iterative Optimizations of QM and MM Subsystems 355
12.3.2.3 Reaction Path Optimizations and the Nudged Elastic Band (NEB) Method 356
12.3.3 Free Energies and Sampling in QM/MM Configuration Spaces 358
12.3.3.1 The Basic Concept of Potential of Mean Force 358
12.3.3.2 Determining PMFs Through Umbrella Sampling 359
12.3.3.3 QM/MM Free Energy Perturbations 360
12.4 APPLYING QM/MM TO ENZYMATIC SYSTEMS 361
12.4.1 Practical Issues 361
12.4.1.1 Choosing a QM/MM Model 361
12.4.1.2 Defining QM and MM Subsystems 362
12.4.1.3 Setting up Initial Configurations 362
12.4.2 Learning How Enzymes Work Through QM/MM Modeling 363
12.4.2.1 Structures, Energetic, and Transition State Stabilization 363
12.4.2.2 Roles of Enzyme Dynamics 364
REFERENCES 365
CHAPTER 13: COMPUTATIONAL MODELING OF BIOLOGICAL SYSTEMS: THE LDH STORY 368
13.1 INTRODUCTION 369
13.2 GAS PHASE CALCULATIONS 371
13.3 INCLUSION OF ENVIRONMENT EFFECTS 371
13.3.1 Cluster Models 371
13.3.2 QM/MM Methods 372
13.4 STATISTICAL SIMULATIONS 378
13.4.1 Free Energy Perturbation (FEP) 378
13.4.2 Potential of Mean Force (PMF) 381
13.5 LARGE SCALE CONFORMATIONAL CHANGES AND AVERAGED KINETIC PROPERTIES 383
13.6 CONCLUSIONS 385
REFERENCES 386
CHAPTER 14: ENZYME DYNAMICS AND CATALYSIS: INSIGHTS FROM SIMULATIONS 388
14.1 INTRODUCTION 388
14.2 CHALLENGES IN BIOMOLECULAR SIMULATION 389
14.3 PROTEIN DYNAMICS AND ENZYME CONFORMATIONAL CHANGES 392
14.3.1 Scavenger Decapping Enzyme (DcpS) 394
14.3.2 Phosphomannomutase/Phosphoglucomutase 396
14.4 ENZYME CATALYSIS 397
14.4.1 Chorismate Mutase 398
14.5 ENZYME REACTION MECHANISMS 400
14.5.1 Citrate Synthase 400
14.5.2 Hen Egg White Lysozyme 402
14.5.3 Aromatic Amine Dehydrogenase 404
14.6 CONCLUSIONS 404
REFERENCES 406
CHAPTER 15: TRANSPORT MECHANISM IN THE ESCHERICHIA COLI AMMONIA CHANNEL AMTB: A COMPUTATIONAL STUDY 409
15.1 OVERVIEW 410
15.2 EXPERIMENTAL EVIDENCES ON ESCHERICHIA COLI AMTB CHANNEL 412
15.3 COMPUTATIONAL METHODS 415
15.4 COMPUTATIONAL STUDIES 417
15.4.1 Molecular Dynamics at the Molecular Mechanical Level 417
15.4.1.1 Computational Model 417
15.4.1.2 Energy Profiles for the Transduction of Ammonium 419
15.4.1.3 Gating Mechanism 421
15.4.1.4 Specific Role of Asp160 422
15.4.1.5 Homology Model of the D160A Mutant 423
15.4.1.6 The Transduction of Ammonia 425
15.4.1.7 The Transduction of Water 428
15.4.2 Combined QM(DFT)/MM Studies 429
15.4.2.1 Computational Model 430
15.4.2.2 Geometries and Energetics in the NH4+ Deprotonation Process 430
15.4.3 Combined QM(PM3)/MM Molecular Dynamics Simulations 433
15.5 SUMMARY 436
REFERENCES 437
CHAPTER 16: CHALLENGES FOR COMPUTER SIMULATIONS IN DRUG DESIGN 442
16.1 INTRODUCTION 442
16.2 MD SIMULATIONS 446
16.3 THE ROLE OF SIMULATIONS IN THE DRUG DISCOVERY PROCESS 447
16.4 VIRTUAL SCREENING AND MD SIMULATIONS 448
16.4.1 Pharmacophore Modelling 448
16.4.1.1 Ligand-Based Approach 448
16.4.1.2 Structure-Based Approach 449
16.4.2 Docking 450
16.5 PREDICTION OF GIBBS FREE ENERGY OF BINDING 454
16.5.1 MM/PB(GB)SA 455
16.5.1.1 Electrostatic Contribution DeltaGpol 456
16.5.1.2 Non-polar Interactions DeltaGnpol 457
16.5.1.3 Entropic Contributions 457
16.5.1.4 Applications 458
16.5.2 LIE Approach 458
16.5.3 FEP/TI 461
16.6 ELUCIDATION OF STRUCTURAL FUNCTION USING SIMULATIONS 463
16.6.1 GPCRs 463
16.6.2 Water 465
16.7 PERSPECTIVE 466
REFERENCES 468
CHAPTER 17: INTERPRETATION OF KINETIC ISOTOPE EFFECTS IN ENZYMATIC CLEAVAGE OF CARBON-HYDROGEN BONDS 475
17.1 INTRODUCTION 475
17.2 MODEL 478
17.3 PHYSICAL PARAMETERS 483
17.4 APPLICATION TO LIPOXYGENASE-1 484
17.5 APPLICATION TO FREE RADICAL TRANSFER 485
17.6 APPLICATION TO METHYLAMINE DEHYDROGENASE 487
17.7 DISCUSSION 488
REFERENCES 489
CHAPTER 18: TUNNELING TRANSMISSION COEFFICIENTS: TOWARD MORE ACCURATE AND PRACTICAL IMPLEMENTATIONS 490
18.1 INTRODUCTION 490
18.2 TUNNELING TRANSMISSION COEFFICIENTS 493
18.3 PRACTICAL IMPLEMENTATION OF THE LCG4 AND LAG4 METHODS 500
18.4 TRANSMISSION COEFFICIENTS AND KIES 505
REFERENCES 507
CHAPTER 19: INTEGRATING COMPUTATIONAL METHODS WITH EXPERIMENT UNCOVERS THE ROLE OF DYNAMICS IN ENZYME-CATALYSED H-TUNNELLING REACTIONS 510
19.1 INTRODUCTION 510
19.2 H-TUNNELING REACTIONS AS PROBES OF DYNAMICS 511
19.2.1 Hydrogen Atom Transfer in Soybean Lipoxygenase-1 514
19.2.2 Hydride Transfer in Morphinone Reductase 516
19.2.2.1 High-Pressure Molecular Dynamics Confirm the Effect of Pressure 516
19.2.2.2 Further Insights from Molecular Modelling of the H-Transfer 518
19.3 COMPUTATIONAL TECHNIQUES FOR ATOMISTIC ANALYSIS OF PROMOTING VIBRATIONS 518
19.3.1 Spectral Density Analysis Reveals a Promoting Vibration in Horse Liver Alcohol Dehydrogenase 518
19.3.2 Spectral Densities Coupled with Digital Filtering of Atomic Motions Reveal a Complicated Picture in Aromatic Amine Dehy. 519
19.3.3 Potential Energy Scans Reveal the Effect of the Promoting Vibration on Barrier Scaling in AADH 521
19.4 THE ROLE OF LONG-RANGE COUPLED MOTIONS 523
19.4.1 Coupled Motions of Different Timescales in DHFR 523
19.4.2 A Proposed Conserved Network of Vibrations in HLADH 524
19.4.3 A Small-Scale, Local Promoting Vibration in AADH 525
19.5 DISCUSSION AND FUTURE PERSPECTIVES 526
REFERENCES 527
Index 529