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Quantum effects in adenosylcobalamin-dependent enzymes Khalilian Boroujeni, M. Hossein 2019

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Quantum Effects in Adenosylcobalamin-dependent Enzymes  by  M. Hossein Khalilian Boroujeni  B.Sc., Chemistry, Razi University, 2014  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF   MASTER OF SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Chemistry)  THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)    April 2019 © M. Hossein Khalilian Boroujeni, 2019  ii  The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis/dissertation entitled:  Quantum Effects in Adenosylcobalamin-dependent Enzymes  submitted by M. Hossein Khalilian Boroujeni in partial fulfillment of the requirements for the degree of Master of Science    Examining Committee:  Gino A. DiLabio, I. K. Barber School of Arts & Sciences Supervisor  W. Stephen McNeil, I. K. Barber School of Arts & Sciences Supervisory Committee Member  Kirsten Wolthers, I. K. Barber School of Arts & Sciences Supervisory Committee Member Michael Deyholos, I. K. Barber School of Arts & Sciences University Examiner  iii  Abstract  The ability of radical enzymes to maintain tight control over the high reactive radical intermediates generated in their active sites is not completely understood. In this thesis, we report on a strategy that radical (B12-dependent) enzymes appear to exploit in order to manipulate and control the reactivity of one of their radical intermediate (5'-deoxyadenosyl radical) contained in the active site. The results of quantum mechanical calculations suggest that these enzymes utilize the little known quantum Coulombic effect (QCE), which causes the radical to acquire an electronic structure that contradicts the Aufbau Principle. This effect causes the energy of the singly-occupied molecular orbital (SOMO) of the radical to be well below that of the highest-occupied molecular orbital (HOMO), which renders the radical less reactive. The dynamic nature of the enzyme and its structure is expected to be such that the reactivity of the radical is not restored until it is moved into close proximity of the target substrate. It was found that the enzyme modulates the magnitude of the QCE and consequently reactivity through elaborate manipulation of the hydrogen bonding between 5'-deoxyadenosyl radical and nearby conserved glutamate residue. To the best of our knowledge, this work is the first study suggesting that both classical and quantum electrostatic factors contribute to both the catalytic power of these enzymes, and to the control of the reactivity and selectivity of the radical intermediates. In addition to B12 enzymes this electrostatic paradigm may be employed by other radical enzymes to attain selectivity of hard to control radical reactions.  iv  Lay Summary  Radical enzymes are a class of proteins that use highly reactive intermediates known as radicals to perform challenging reactions. Exploiting these reactive intermediates requires a sophisticated control mechanism by the enzyme to prevent deleterious side reactions that can potentially damage the enzyme itself. The results of quantum mechanical calculations indicate that the enzymes we studied may use a sophisticated mechanism to control the reactivity of the radicals. This mechanism involves the interaction between charged groups in the enzyme active site and the radical through the quantum Coulombic effect (QCE), and tuning of the QCE through hydrogen bonding. The use of QCE by radical enzymes may be a general phenomenon. This thesis is the first report of the operation of QCE in enzyme systems.    v  Table of Contents  Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Table of Contents ...........................................................................................................................v List of Tables ................................................................................................................................ ix List of Figures .................................................................................................................................x List of Symbols and Abbreviation ............................................................................................ xix Acknowledgements ................................................................................................................... xxii Dedication ................................................................................................................................. xxiii Chapter 1: Introduction ................................................................................................................1 1.1 Radical Enzymes ............................................................................................................. 1 1.2 Cobalamin-dependent Enzymes ...................................................................................... 2 1.2.1 General aspects ........................................................................................................... 2 1.2.2 Classes of B12 Enzymes .............................................................................................. 6 1.2.3 Isomerases ................................................................................................................... 8 1.2.4 Subgroups of Isomerases .......................................................................................... 10 1.2.4.1 Carbon-skeleton Mutases .................................................................................. 12 1.2.4.2 Aminomutases................................................................................................... 14 1.3 Catalytic Power in B12 Enzymes ................................................................................... 17 1.3.1 Hypotheses ................................................................................................................ 17 1.3.1.1 Strain Hypothesis .............................................................................................. 18 1.3.1.2 Electrostatic Effect ............................................................................................ 19 vi  1.3.2 Selectivity in B12 Enzymes ....................................................................................... 22 1.4 Research Questions and Hypothesis ............................................................................. 24 Chapter 2: Orbital Conversion and Quantum Coulombic Effect ...........................................26 2.1 What is Orbital Conversion? ......................................................................................... 26 2.1.1 Orbital Conversion and Radical Stability ................................................................. 30 2.2 The Origin of the Orbital Conversion. Classical or Quantum Effect? .......................... 32 2.3 The Possible Role of QCE in B12 Enzymes .................................................................. 35 Chapter 3: Methods .....................................................................................................................37 3.1 Objective ....................................................................................................................... 37 3.2 Quantum Mechanic/Molecular Mechanic Simulations ................................................ 37 3.2.1 Background and Theory ............................................................................................ 37 3.3 QM/MM Calculations Details....................................................................................... 39 3.4 Molecular Orbital Energy Diagrams ............................................................................. 41 3.5 Transition State Calculations ........................................................................................ 42 3.6 BDE and RSE Calculations .......................................................................................... 43 3.7 Density State Plots (DOS) ............................................................................................ 43 3.8 Multiconfiguration Self-Consistent Field Theory ......................................................... 44 3.8.1 Background and Theory ............................................................................................ 44 Chapter 4: QM/MM Calculations Reveal the Presence of QCE in GM and MCM Enzymes ........................................................................................................................................49 4.1 Objective ....................................................................................................................... 49 4.2 Methodology (GLM Enzyme) ...................................................................................... 49 4.2.1 Models and Calculation Setup .................................................................................. 49 vii  4.2.2 QM/MM Calculations ............................................................................................... 54 4.3 QCE in GLM Enzymes ................................................................................................. 55 4.3.1 Orbital Configurations and Energies Obtained from QM/MM Calculations ........... 55 4.3.2 Analysis and Discussion ........................................................................................... 61 4.4 Methodology (MCM Enzyme) ..................................................................................... 63 4.4.1 Models and Calculation Setup .................................................................................. 63 4.4.2 QM/MM Calculations ............................................................................................... 67 4.5 QCE in MCM ................................................................................................................ 67 4.5.1 Orbital Configurations and Energies Obtained from QM/MM Calculations ........... 67 4.5.2 Analysis and Discussion ........................................................................................... 72 4.6 Summary ....................................................................................................................... 75 Chapter 5: The Relationship between CEE/QCE and Radical Stability/Reactivity .............77 5.1 Objective ....................................................................................................................... 77 5.2 Methodology ................................................................................................................. 77 5.2.1 Models description .................................................................................................... 77 5.3 QCE and Radical Reactivity ......................................................................................... 78 5.3.1 Orbital Configurations and Energies of Small GLM Enzyme Models ..................... 78 5.3.2 Orbital Configurations and Energies of MCM Enzyme ........................................... 83 5.3.3 Verification of UM06-2X Electronic Structure Predictions ..................................... 86 5.3.4 Influence of H-bonds on QCE .................................................................................. 89 5.3.5 Difference between Radical Reactivity and Stability ............................................... 90 5.3.6 Barrier Height Calculations: Assessing Reactivity ................................................... 92 5.3.7 FMO Theory ............................................................................................................. 96 viii  5.3.7.1 Analysis of the Barrier Height Energies Based on FMO Theory ..................... 96 5.4 Radical Stability and CEE ............................................................................................ 97 5.4.1 Stability Calculations in GLM and MCM Enzymes ................................................. 97 5.4.2 Influence of H-bonds on CEE ................................................................................... 99 5.4.3 How CEE Can Contribute to the Catalytic Power of B12 Enzymes? ...................... 102 5.5 Summary ..................................................................................................................... 102 Chapter 6: Conclusions .............................................................................................................104 6.1 A Complete Picture of How QCE and CEE Generate and Control Highly Reactive Species in B12 Enzymes .......................................................................................................... 104 6.2 Conclusions and Future Directions ............................................................................. 108 Bibliography ...............................................................................................................................109  ix  List of Tables  Table 1.1 Subgroups of B12-dependent isomerases with some examples and the reactions they catalyse. ......................................................................................................................................... 11 Table 4.1 Information about GLM model systems that are used for the QM/MM computations. The blue-coloured residues are negatively charged, whereas the red-coloured residues are positively charged. Wat is the Protein Database code for water. .................................................. 55 Table 4.2 Information about MCM model system that is used for the QM/MM computations. The blue-coloured residues are negatively charged and the red-coloured residues are positively charged. ......................................................................................................................................... 67 Table 5.1 CASSCF(9.6)/6-311+G(d,p) results with the percentage of each of the configurations (CSFs) to the total wave function. The configuration numbers (config. no.) are referring to the configurations in figure 5.7. Configurations that are not reported in this table contribute a very small amount to the overall wave function. .................................................................................. 88  x  List of Figures  Figure 1.1 The structure of adenosylcobalamin. The distal ligand is Ado group, while the proximal ligand is DMB. ................................................................................................................ 3 Figure 1.2 Conformations of adenosylcobalamin. .......................................................................... 4 Figure 1.3 Homolytic and heterolytic cleavage of Co-C bond in adenosylcobalamin and methylcobalamin, ............................................................................................................................ 5 Figure 1.4 General rearrangement scheme of B12 isomerases. A hydrogen atom is exchanged with a nearby Y group via a 1,2 shift. Y can be an amino group, a hydroxyl group or a carbon fragment. ......................................................................................................................................... 7 Figure 1.5 Methionine synthase cycle. Using the strong nucleophilic nature of Co(I), in a non-sequential (ping-pong) reaction, the 5-methyltetrahydrofolate (N-methyl-THF) changes to tetrahydrofolate (THF), while homocysteine (Hcy) is replaced by methionine (Met). .................. 7 Figure 1.6 General catalytic scheme of B12-dependent enzymes. .................................................. 9 Figure 1.7 Ado● (left) is compared with its allylic analogue 3,4-anhydro-dAdoCbI (right) ....... 10 Figure 1.8 The intramolecular addition/elimination mechanism in MCM and intermolecular fragmentation/recombination mechanism in GLM. ...................................................................... 14 Figure 1.9 Ornithine 4,5-aminomutase catalytic cycle. ................................................................ 16 Figure 1.10 Proposed rearrangement mechanism for lysine-5,6-aminomutase. ........................... 16 Figure 1.11 Catalytic power of B12 enzymes (isomerases). The BDFE of Co-C is 70 kJ/mol in enzyme compared to 130 kJ/mol in aqueous solution. ................................................................. 17 Figure 1.12 The depiction of upward folding of the corrin ring in distorted adenosylcobalamin in enzyme compared to the undistorted structure in water. The Φ=NCor-Co-NHis bond angle is 76o xi  for adenosylcobalamin in enzyme compared to 91o in adenosylcobalamin in water. Key: red=oxygen, blue=nitrogen, grey=Carbon, white=hydrogen........................................................ 19 Figure 1.13 Demonstration of the electrostatic effect and pre-organized active site in a hypothetical reaction. The red and green circles show the reactant fragments. ........................... 21 Figure 1.14 Demonstration of the origin of electrostatic effects in B12 enzymes. The Ado group has a polar ribose ring that can interact with the charged residues in the active site. The Adenine moiety is abbreviated as Ade. ....................................................................................................... 22 Figure 1.15 Schematic representation of the active site of B12 enzymes. Ado● must migrate approximately 2-10 Å to reach the substrate (Sub.) possessing the target H atom (in magenta). During this migration, Ado● has the potential to react with nearby residues before reacting with the substrate. ................................................................................................................................. 24 Figure 2.1 The expected orbital configuration of TEMPO-dithiolate and its Pt complex based on experimental and theoretical evidence. One electron oxidation of the orbital-converted Pt-complex leads to a triplet electronic state. .................................................................................... 27 Figure 2.2 Structure of NN●TTF and its orbital configuration. The oxidation potential of NN●TTF is similar to that of the TTF moiety suggesting the orbital configuration shown on the right. .............................................................................................................................................. 27 Figure 2.3 An example of a distonic radical anion, COOH-TEMPO (a carboxy-aminoxyl) and its deprotonated form with their associated orbital configurations. One-electron oxidation of the deprotonated structure removes an electron from the doubly-occupied HOMO generating a triplet biradical instead of a closed-shell zwitterion. One-electron oxidation of the protonated structure removes an electron from the singly-occupied HOMO generating the expected closed-xii  shell system. *The orbital configuration provided here is based on calculations performed in this thesis. ............................................................................................................................................ 29 Figure 2.4 Two examples of deprotonated nucleic acids (DNA and RNA). ................................ 29 Figure 2.5 The structure of carboxy-aminoxyl (TEMPO-COO-) and –peroxyl radicals. ............. 30 Figure 2.6 An orbital converted radical (carbene-TEMPO) is compared with a structurally similar unconverted radical (TEMPO). The calculated RSE shows that the stability of both radicals are approximately the same, suggesting that the orbital conversion in carbene-TEMPO does not relate to radical stabilization. .......................................................................................... 33 Figure 2.7 The influence of solvent on the calculated RSE and SOMO-HOMO orbital conversion of TEMPO-COO-. The RSE decreases as the dielectric of the solvent increases. ........................ 33 Figure 3.1 The structure of the vitamin E acetate (also known as tocopheryl acetate), which has been divided into MM and QM regions. The reaction centre of the molecule is included in the QM region, while the carbon chains are treated with the MM approach. .................................... 38 Figure 3.2 Two possible MO diagrams of the singlet O2 (ψ1and ψ2). The correct wavefunction for singlet O2 is a linear combination of ψ1and ψ2. .................................................................... 46 Figure 3.3 A schematic illustration of the CASSCF method. There are three orbitals and four electron in the active space. This can be abbreviated as CASSCF(4,3), which means that all possible configurations of four electrons in three orbitals are considered in the CASSCF calculations. .................................................................................................................................. 48 Figure 4.1 Two models of the GLM enzyme obtained from X-ray crystal structures: A. PHB model B. HB model. ..................................................................................................................... 51 xiii  Figure 4.2 Some of the structural parameters of A) GLM-PHB and B) GLM-HB models. The bond distances of COO- are reported from the centre (between the two oxygen atoms) of the carboxylate groups to the radical center (C2). .............................................................................. 52 Figure 4.3 Initial catalytic steps involved in B12 enzymes. In the first step, the Co-C bond in A breaks to generate the Ado●. This radical then migrates toward the substrate (H-Subs). B is the intermediate structure during the migration. C is the final structure after Ado● migration but before hydrogen abstraction. ......................................................................................................... 53 Figure 4.4  Illustrations of the electronic structure of the GLM-PHB and GLM-HB conformer for Models A, B, and C. The SOMO-HOMO energy gap.................................................................. 58 Figure 4.5 A) The active site of the GLM-HB model (model D) with an illustration of its calculated electronic structure. The SOMO-HOMO energy gap and the absolute SOMO energy are also shown. B) The plot of the HOMO. The orbital is distributed over the base (DMB) of B12 cofactor. No electron density is present on the radical centre in this MO (RCC=0%). C) The plot of the HOMO-59.  The orbital is distributed over the radical centre, indicating that this MO is the SOMO (RCC=10%). ..................................................................................................................... 59 Figure 4.6 A) The active site of the GLM-HB model (model D) with an illustration of its calculated electronic structure. The SOMO-HOMO energy gap and the absolute SOMO energy are also shown. B) The plot of the HOMO. The orbital is distributed over the base (DMB) of B12 cofactor. No electron density is present on the radical centre in this MO (RCC=0%). C) The plot of the HOMO-26. The orbital is distributed over the radical centre, indicating that this MO is the SOMO (RCC=7%). ....................................................................................................................... 60 xiv  Figure 4.7 The distribution of spin density on the Co• and Ado• in GLM-PHB and GLM-HB models. The Mulliken (Hirschfeld) atomic spin density on nominal radical centre carbon in Ado• is 1.34 (0.71) in GLM-HB compared to 1.16 (0.73) in GLM-PHB. ............................................. 61 Figure 4.8 Charged residues in the active sites of GLM-PHB (left) and GLM-HB (right). The dotted lines show the hydrogen bonding interactions between the residues with the substrate and Ado●. Key: red=oxygen, blue=nitrogen, grey=Carbon, white=hydrogen ................................... 63 Figure 4.9 Different models of MCM enzyme: a. PHB model b. HB model ............................... 65 Figure 4.10 Some of the structural parameters of A) MCM-PHB and B) MCM-HB models. The bond distances of COO- are reported from the center of the carboxylate groups to the radical center (C2). ................................................................................................................................... 66 Figure 4.11 The active site of the MCM-PHB model with an illustration of its calculated electronic structure including the SOMO-HOMO energy gap and the absolute SOMO energy. . 69 Figure 4.12 MO plots of high energy MOs in MCM-PHB model. The Ado● RCC values associated with each MO are given in parenthesis. ...................................................................... 70 Figure 4.13 A) The active site of the GLM-HB model (model D) with an illustration of its calculated electronic structure. The SOMO-HOMO energy gap and the absolute SOMO energy are also shown. B) The plot of the HOMO. Electron density of HOMO is distributed over the cobalt centre and the corrin ring of B12 cofactor and no electron density is present on the radical centre in this MO (RCC=0%). C) The plot of the HOMO-1. Electron density of HOMO-1 is distributed over the radical centre, indicating that this MO is the SOMO (RCC=22%). ............. 71 Figure 4.14 Charged residues in the active sites of MCM-PHB (left) and MCM-HB (right). Key: red=oxygen, blue=nitrogen, grey=Carbon, white=hydrogen........................................................ 73 xv  Figure 4.15 The distribution of spin density on the Co• and Ado• in GLM-PHB and GLM-HB models. The Mulliken (Hirschfeld) atomic spin density on carbon-Ado• is 1.34 (0.71) in GLM-HB compared to 1.16 (0.73) in GLM-PHB. In the spin density plot of MCM-HB there is a small spin density on the carbon atom to be hydrogen abstracted, which shows that the MCM-HB model is near TS of hydrogen abstraction. ................................................................................... 74 Figure 5.1 A) The structure of the GLM-PHB(s) model, illustration of the orbital energy diagram, SOMO-HOMO energy gap, and the absolute SOMO energy. MO plots for four highest energy α-MOs for B) HOMO C) HOMO-1 D) HOMO-2 E) HOMO-3. Isovalues of 0.1 were used for the MO plots. .................................................................................................................. 80 Figure 5.2  A) The structure of the GLM-HB(s) model, illustration of the orbital energy diagram, SOMO-HOMO energy gap, and the absolute SOMO energy. MO plots for four highest energy α-MOs for B) HOMO C) HOMO-1 D) HOMO-2 E) HOMO-3. Isovalues of 0.1 were used for the MO plots. ...................................................................................................................................... 81 Figure 5.3  The DOS plots of the A) GLM-PHB and B) GLM-HB models. In the GLM-PHB model the MOs associated with the Glu residue are higher in energy than the SOMO, which is associated with the CH2 fragment. In the GLM-HB the SOMO is the highest energy level MO. 82 Figure 5.4 The structure of the MCM-PHB(s) model, illustration of the orbital energy diagram, SOMO-HOMO energy gap, and the absolute SOMO energy. MO plots for four highest energy α-MOs for B) HOMO C) HOMO-1 D) HOMO-2 E) HOMO-3. Isovalues of 0.1 were used for the MO plots. ...................................................................................................................................... 84 Figure 5.5  The structure of the MCM-HB(s) model, the orbital energy diagram, SOMO-HOMO energy gap, and the absolute SOMO energy. MO plots for four highest energy α-MOs for B) HOMO C) HOMO-1 D) HOMO-2 E) HOMO-3. Isovalues of 0.1 were used for the MO plots. 85 xvi  Figure 5.6  The DOS plots of the A) MCM-PHB and B) MCM-HB models. In the MCM-PHB model the MOs associated with Glu residue are higher in energy than the SOMO, which is associated with the CH2 fragment (SOMO-HOMO gap is 60 kJ/mol).  In the MCM-HB the MOs corresponding to the Glu residue is higher in energy than the SOMO (associated with CH2) but the difference between the two is reduced (SOMO-HOMO gap is 20 kJ/mol). ........................... 86 Figure 5.7 Important electronic configurations that is possible from CASSCF(9,6) calculations........................................................................................................................................................ 87 Figure 5.8 Hydrogen bonding effects on orbital conversion in Ado●. The influence of disrupting the hydrogen bond between the Ado● and the Glu on QCE. At 0o and 180o the H-bonding is maximum and the SOMO is the orbital with the highest energy. When Glu330 is rotated by 60o or 80o, the QCE is present and the SOMO moves to lower energies while the Glu related MOs move to higher energies. ............................................................................................................... 90 Figure 5.9 Comparison between the reactivity of the HB and PHB models of GLM enzyme. The TS structures that are reported for both of the models are as similar as possible. The barrier heights given are based on electronic energies. RC=reactants, TS= transition state, PR=products....................................................................................................................................................... 93 Figure 5.10 Comparison between the reactivity of the HB and PHB models of MCM enzyme. The TS structures for both of the models are calculated to be as similar as possible. The barrier heights given are based on electronic energies. RC=reactants, TS=transition state, PR=products....................................................................................................................................................... 95 Figure 5.11 Simple MO energy diagram illustrating the interaction between the Ado● SOMO in both models (HB and PHB) and the substrate C-H σ*. There is a more favourable interaction between the SOMO of the HB model and the substrate C-H σ*, compared to the interaction xvii  between the SOMO and the substrate C-H σ* in PHB model because the energy gap (ΔE) between Ado● SOMO and C-H σ* is smaller in HB model compared to PHB model (ΔE2 > ΔE1) This favourable interaction reduces the barrier energy for hydrogen abstraction in HB models. 97 Figure 5.12 Illustration of the MO energy diagram of GLM-PHB(s) model (left), and when the Glu residue is replaced with a negative point charge (right). In the right diagram the SOMO is the HOMO-3 and QCE is present in contrast to the left diagram in which the SOMO is the HOMO and QCE is disappeared. However, the RSE value of this system is calculated to be 1.6 kJ/mol suggesting that the CEE is still present. ............................................................................ 99 Figure 5.13 The effect of hydrogen bonding on the stability of Ado● and CEE. Increasing the number of hydrogen bonds by explicit water molecules (W) drops the RSFE values. With inclusion of a bulk solvation model (SMD) the RSE falls below the reference line implying the disappearance of CEE entirely. *The RSE given here for HB model is not the same as the 2.7 kJ/mol reported before in section 5.4.1 for the same system. This difference is because of the geometry optimization performed for these calculations. **Radical stabilization free energies...................................................................................................................................................... 101 Figure 6.1 A model outlining the role of CEE and QCE at different stages of the B12-enzymes catalytic cycle. At stage A the Ado● is bound to the cobalt and CEE and QCE are not present. Stage B shows the Ado● after the Co-C bond dissociation, but before its migration toward the substrate. At this stage the CEE is active, and thus the radical centre is stabilized. Since the Ado:Glu hydrogen bonding is minimum, the QCE is also turned on, which reduces the ability of the Ado● to abstract hydrogen atoms.  At stage C the Ado● has migrated to the substrate. The reactivity of Ado● is restored at this stage by increasing the strength of the Ado:Glu hydrogen bonding, which in turn reduces the QCE and increases the energy level of the Ado● SOMO. xviii  Consequently the ability of the hydrogen abstraction increases due to the better orbital overlap between the Ado●’s SOMO and the σ* LUMO. ........................................................................ 107  xix  List of Symbols and Abbreviation  Ado●  5'-deoxyadenosyl radical APC  azacyclopropylcarbinyl BDFE  bond dissociation free energy BDE  bond dissociation enthalpy BDE´  bond dissociation energy CASSCF complete active space self-consistent field CEE  classical electrostatic effects CPMD  Car–Parrinello molecular dynamics DFT  density functional theory DMB  5,6-dimethylbenzimidazole DOS  density of state EE  electrostatic embedding EPR  electron paramagnetic resonance ESR  electron spin resonance FMO  frontier molecular orbital GLM  glutamate mutase GPA  gas phase acidities GS  ground state HB  hydrogen bonded model Hcy  homocysteine HF  Hartree-Fock theory xx  HOMO highest-energy occupied molecular orbital IRC  intrinsic reaction coordinates LAM  lysine 5,6-aminomutase LUMO lowest-occupied molecular orbital MCSCF multi-configurational self-consistent field Met  methionine MCM  methylmalonyl-CoA mutase MCSCF multi-configurational self-consistent field MM  molecular mechanic MO  molecular orbital OAM  ornithine 4,5-aminomutase ONIOM our Own N-layered Integrated molecular Orbital and molecular Mechanics PDB  protein data bank PDOS  projected density of state PHB  partially hydrogen bonded model PLP  pyridoxal phosphate QCE  quantum Coulombic effect QM  quantum mechanic QM/MM quantum mechanic/molecular mechanic RCC  radical centre contribution RSD  reactant state destabilization RSE  radical stabilization energy RNR  ribonucleotide reductase  xxi  SAM  S-adenosyl methionine SOMO  singly-occupied molecular orbital SMD  universal solvation model STM  scanning tunnelling microscope TEMPO (2,2,6,6-Tetramethylpiperidin-1-yl)oxyl THF  tetrahydrofolate TS  transition state TSS  transition state stabilization TTF  tetrathiafulvalene UFF  universal force field              xxii  Acknowledgements  First and foremost, I must express my profound gratitude to my advisor Prof. Gino A. DiLabio for his continuous support of this research work, and for his valuable guidance and useful critiques at each and every step of my project. In this, his deep knowledge and expertise have been essential for me to complete this thesis. I feel so proud and honored to have him as my supervisor and mentor for the duration of my study. I would also like to thank all the current and past members of the DiLabio group, particularly Dr. Alberto Otero de la Roza, for all of their help and assistance.  Thank you to Dr. W. Stephen McNeil and Dr. Kirsten R. Wolthers as my committee members for their valuable comments and time to review my thesis.  A special thanks to Alireza Sadeghifar for his advice and support during all challenging moments throughout my studies.  I would also like to acknowledge Dr. Elizabeth Brunk from the University of California, San Diego for providing us the coordinates of the MCM enzyme from their simulations.  At the end I would like to thank my previous supervisor Dr. Avat. A. Taherpour and my family members for their encouragement to continue my studies at the graduate level.       xxiii  Dedication      To Yekta,  You mean so much to me        1  Chapter 1: Introduction  1.1 Radical Enzymes  Radicals are species with one or more unpaired electrons and, because of this character, they are generally extremely reactive with low reaction selectivity. It was not until the mid-20th century that researchers discovered that free radicals are also involved in many biological reactions.1,2 It seems very surprising that free radicals are used in biology given the susceptibility of biomaterials to radical damage, such as oxidation by reactive oxygen species. It is also known that free radicals play a role in chronic diseases including Alzheimer's and Parkinson's.3–8 The discovery of ribonucleotide reductase enzyme (RNR), the first enzyme that was found to utilize a radical-based mechanism,9 was a landmark in the development of our understanding of the role of free radicals in biochemical reactions. Developments in EPR spectroscopy led to further discoveries of enzymes that employ radical intermediates to catalyze reactions. These radical enzymes include, but are not limited to, cytochrome P450s, the diverse super-family of S-adenosylmethionine (SAM) dependent enzymes, methane monooxygenase, and several important cobalamin-dependent (vitamin B12-dependent) isomerases.10 Although the involvement of free radical intermediates is confirmed in these enzymes, our knowledge about how they generate free radicals and employ them to catalyze reactions is limited.11 In particular, there is a long-standing question about how radical enzymes use highly reactive radical intermediates without becoming damaged by them.  In this thesis, quantum mechanical simulation techniques are used to explore how radical enzymes control the reactivity of the radicals formed in their active sites. There is a large variety 2  of radical enzymes with different mechanistic and structural features; however in this work, two enzymes from isomerase class of AdoCbl-dependent enzymes were selected for investigation, and the possible generalization of the results to other radical enzymes are left for follow-up studies. In the next section an overview of vitamin B12-dependent enzymes is provided.  1.2 Cobalamin-dependent Enzymes  1.2.1 General aspects  Cobalamin-dependent enzymes, or simply B12 enzymes, function with cobalamin (coenzyme B12) as the cofactor. Dorothy Hodgkin, who won the noble prize in 1956, was the first to uncover the structure of adenosylcobalamin (one of the three biologically active forms) using X-ray crystallography (figure 1.1).12 The coenzyme contains a biologically scarce cobalt element in its +3 oxidation state coordinated to a large, porphyrin-like ring. Unlike porphyrin, cobalamin has an unsymmetrical ring structure composed of three pyrrolines and one pyrrolidine that are not completely conjugated. This semi-aromatic ring, called corrin, is much more flexible than porphyrins due to the presence of several sp3 carbons. The distal ligand is 5′-deoxyadenosyl (Ado), which can be replaced by methyl (CH3) or cyanide (CN) group to generate the methylcobalamin and cyanocobalamin, respectively. The methylcobalamin (MeCbl) and the adenosylcobalamin (AdoCbl) are the bioactive forms of the cobalamins, whereas the cyanocobalamin, which is generally known as vitamin B12, is inactive, but can be converted to one of the bioactive forms in the body. Differences in upper ligand leads to diverse reactivity in B12 enzymes.13 The proximal axial ligand is 5,6-dimethylbenzimidazole (DMB), which is appended from the saturated 3  pyrrolidine ring and is connected to the cobalt center through a 19-membered loop. In the active site of some of the cobalamin-dependent enzymes (e.g.  aminomutases), a histidine residue can take the place of DMB, resulting in a conformation called His-on/base(dmb)-off. In aqueous solution and in eliminases the B12 coenzyme maintains the His-off/base-on mode (figure 1.2).14      Figure 1.1 The structure of adenosylcobalamin. The distal ligand is Ado group, while the proximal ligand is DMB.  5'-deoxyadenosyl (Ado)                                            5,6-dimethylbenzimidazole (DMB)                                  4  CoIII CoIIICoIIIAdo AdoAdoBaseBaseBaseHisbase-on/his-off 11base-off/his-on  Figure 1.2 Conformations of adenosylcobalamin.  An intriguing aspect of cobalamin-dependent enzymes is the key role played by Co-C bond in enzyme activity. These enzymes are the only known biological occurrence in which the cobalt ion is covalently bonded to a carbon atom. The relatively weak Co-C bond allows for the dissociation of this organometallic bond either heterolytically or homolytically in the enzyme’s active site, depending on whether the upper ligand is Ado or CH3 (figure 1.3). The Co-C bond must be first cleaved to initiate catalysis. In the case of adenosylcobalamin, the homolytic dissociation of the Co-C bond generates the Ado radical (Ado●), which is then employed for catalysis. In other words, the adenosylcobalamin is a latent radical source.14 However, in methylcobalamin-dependent enzymes, the Co-C bond is cleaved heterolytically, and the resulting Co (I) engages in nucleophilic enzyme catalysis (some MeCbl dependent enzymes will generate ●CH3, but these are not well studied).12,15–17      5  CoIIICoIII CH3AdoCoICoII  Figure 1.3 Homolytic and heterolytic cleavage of Co-C bond in adenosylcobalamin and methylcobalamin,  CoIII, CoII, CoI-corrins The Cobalt ion in intact cobalamins (CoIII-corrins) has a pseudooctahedral hexacoordinated structure with a +3 oxidation state and is in a low-spin, d6 configuration.18 Spectroscopic studies also confirm that the cobalt ion is diamagnetic and hexacoordinated.12 However, the CoII-corrins are found to be pentacoordinated and paramagnetic (low-spin). The reduction of CoIII-corrins to CoII-corrins can be achieved by homolytic cleavage of Co-C bond and removal of the distal ligand. Further reduction of the corrins (by heterolytic cleavage of Co-C) leads to the formation of CoI-corrins. Although CoIII and CoII corrins are relatively stable, the high nucleophilic character of the CoI-corrins makes them prone to oxidation. The latter species has yet to be crystallized.12,19 However, there is evidence to suggest that the CoI corrins have a tetracoordinated and square planar structure in which both of the axial ligands are missing.12,18   The structural features of the CoIII-corrins were also the subject of X-ray analytical studies. The flexibility of the cobalamin leads to the non-planar, upwardly-folded corrin ring15,20 and the degree of the non-planarity can be determined from the angle between the corrin ring and its axial ligands. 6  Corrin ring folding has been measured for different B12 enzymes and their corresponding dissociated species: Cobalamins with bulky ligands were found to have higher nonplanarity. These results suggest that there is strain in adenosylcobalamins. This point will be discussed in more details later in the chapter.21  1.2.2 Classes of B12 Enzymes  There are three classes of B12 dependent enzymes: isomerses, methyltransferases and reductive dehalogenases. Isomerases, which have adenosylcobalamin cofactor in their active site, employ a radical-based mechanism to catalyze thermodynamically challenging rearrangements (see figure 1.4). Methyltransferases employ the methylcobalamin cofactor and they catalyze nucleophilic/electrophilic reactions. The last class of B12 enzymes are the reductive dehalogenases in which the Co is connected to a halogen atom. Owing to the oxygen sensitivity of this group, they have not been studied in great detail.22–24 Since the focus of this thesis is radical enzymes, only the isomerases will be discussed further. For comparison purposes, the overall mechanism of one of the methyltransferases, methionine synthase, is shown in figure 1.5. Methionine synthase converts homocysteine to methionine and 5-methyltetrahydrofolate to tetrahydrofolate.     7  Adenosylcobalamin  Figure 1.4 General rearrangement scheme of B12 isomerases. A hydrogen atom is exchanged with a nearby Y group via a 1,2 shift. Y can be an amino group, a hydroxyl group or a carbon fragment.   CoICoIIICH3THF N-methyl-THFHcy Met  Figure 1.5 Methionine synthase cycle. Using the strong nucleophilic nature of Co(I), in a non-sequential (ping-pong) reaction, the 5-methyltetrahydrofolate (N-methyl-THF) changes to tetrahydrofolate (THF), while homocysteine (Hcy) is replaced by methionine (Met).19,20,25   8  1.2.3 Isomerases  Isomerases, which are the largest class of B12 enzymes, catalyze a number of rearrangements by exchanging a hydroxyl, an amino group, or a carbon fragment with a vicinal hydrogen atom (figure 1.4). In these rearrangements, it is difficult to induce migration of the hydrogen atom because it is not adjacent to an activated carbon. The lack of reactivity toward rearrangements explains why nature uses a highly reactive free radical to achieve the isomerizations.  B12 isomerases are subdivided into three categories depending on the nature of the substrate and the migrating group (see below). As summarized in figure 1.6, all these categories of B12 isomerases employ homolytic Co-C bond scission as the first step in their catalytic cycle, followed by hydrogen abstraction.26 The homolysis of adenosylcobalamin generates cob(II)alamin and a reactive 5′-deoxyadenosyl radical (Ado●) that is able to abstract a hydrogen atom from an unactivated C-H bond in the substrate. The radical substrate generated subsequently undergoes a 1,2 rearrangement by a mechanism that is dependent upon the specific isomerase. In the last step of the catalytic cycle the rearranged substrate radical abstracts a hydrogen atom from 5’-deoxyadenosine to form the Ado●, which then recombines with cob(II)alamin to complete the enzyme cycle (figure 1.6).20 During this catalytic cycle it is possible for the enzyme to become deactivated due to the loss of Ado●. The loss of Ado● or other radical intermediates disrupts the catalytic cycle and prevents the rearrangement reaction from occurring. However, B12 enzymes have evolved some repair systems (adenosyltransferase and G-protein chaperone) that can help the enzymes to recover from the infrequent loss of radical intermediates by exchanging a defective cofactor with a new one. When the inactivation occurs, the repair systems bind with ATP and 9  convert it to ADP. The ADP-bound repair system in turn attaches to the inactive enzyme and releases the damaged cofactor. A free cofactor (adenosylcobalamin) is then transferred to the enzyme, which eventually reactivates the enzyme catalysis.27,28   CoIICoIICoIIIAdo Ado AdoH  Figure 1.6 General catalytic scheme of B12-dependent enzymes.  Although the general mechanism associated with figure 1.6 and the involvement of substrate-derived radicals has been confirmed using electron paramagnetic resonance (EPR) spectroscopy, Ado● has not been detected spectroscopically due to its short lifetime14. Nevertheless, evidence for the participation of Ado● has been provided using ultrafast photolysis experiments in conjunction with an Ado● synthetic analogue, 3,4-anhydro-dAdoCbI. This analogue contains an allylic system in which the unpaired electron is strongly delocalized (figure 1.7).29–33 The stabilization induced by the delocalization is sufficient to increase the lifetime of the radical, making the EPR detection possible. 10      Figure 1.7 Ado● (left) is compared with its allylic analogue 3,4-anhydro-dAdoCbI (right)  1.2.4 Subgroups of Isomerases  There are 10 known isomerases that depend on AdoCbl to facilitate rearrangement reactions.34 As mentioned above, these isomerases are subdivided into three categories; carbon-skeleton mutases, aminomutases and eliminases (dehydratases and deaminases). This classification is based on the substrate and its migrating group.14 Table 1.1 summarizes this classification with examples of each group. The following section will provide a brief review of the carbon-skeleton mutases, which are the subject of this thesis. A very brief description of aminomutases is also provided.      11   Table 1.1 Subgroups of B12-dependent isomerases with some examples and the reactions they catalyse.      Carbon-skeleton Mutases Enzyme Catalytic function Methylmalonyl-CoA Mutase (MCM) Conversion of methylmalonyl CoA to succinyl CoA Glutamate Mutase (GLM) Conversion of glutamate to methylaspartate Methyleneglutarate Mutase Conversion of L-threo-3-methylaspartate to L-glutamate. Isobutyryl-CoA Mutase Conversion of 2-methylpropanoyl-CoA to butanoyl-CoA Amino Mutases Enzyme Catalytic function Lysine-5,6-aminomutase Conversion of D-lysine to 2,5-diaminohexanoate. Ornithine 4,5-aminomutase Conversion of D-ornithine to (2R,4S)-2,4-diaminopentanoate. Leucine 2,3-aminomutase Conversion of L-leucine to β-leucine Eliminases Enzyme Catalytic function Diol-dehydrase Conversion of diols into aldehydes Glycerol-dehydrase Conversion of glycerol to 3-hydroxypropanal and H2O. Ethanolamine-ammonia-lyase Conversion of ethanolamine to acetaldehyde and NH3. 12  1.2.4.1 Carbon-skeleton Mutases  The most studied B12-dependent coenzymes are those that catalyze carbon-skeleton rearrangements. In particular, the methylmalonyl-CoA mutase (MCM), which is the only mammalian B12-dependent isomerase, catalyzes the conversion of methylmalonyl CoA to the valuable metabolite succinyl CoA.35,36 Methylmalonyl CoA is produced from degradation of amino acids with branched-chains, odd-numbered fatty acids, and cholesterol.26 MCM rearranges methylmalonyl CoA into succinyl CoA, which then enters the Krebs cycle where it is involved in ATP metabolism. Deficiencies of MCM leads to the accumulation of methylmalonyl CoA, which can cause a metabolic disorder known as methylmalonic aciduri.16,34  Another important enzyme among the carbon-skeleton mutases is methylaspartate mutase, which is more commonly known as glutamate mutase (GLM). GLM (from C. tetanomorphum) was the first enzyme that was found to rely on B12 coenzyme.37 GLM catalyzes the conversion of glutamate to methylaspartate and has been studied as a prototype for carbon-skeleton mutases.  The protein structures of both GLM and MCM have been crystallized under different conditions including the substrate-bound and substrate-free forms.37,38 The substrate-free enzyme is referred to as an “open”, unreactive conformation, whereas the substrate-bound enzyme is known as “closed” or reactive conformation. Comparison of the open and closed conformations in both of the MCM and GLM shows that the two conformers differ significantly from each other.35 This suggests that the protein structures undergo major conformational changes upon substrate binding. The conformational change creates a somewhat hydrophobic cavity inside the protein that can accommodate the substrate and protects the radical reservoir from side reactions with enzyme’s environment. In other words, the architecture of closed conformation isolates the substrate inside 13  the active site. Similar to other carbon-skeleton mutases, both GLM and MCM were crystalized in the His-on mode with the DMB detached from the cobalt centre.  Both MCM and GLM follow the same general mechanism as all of the AdoCbl-dependent enzymes (see figure 1.6). The rearrangement mechanism, however, is specific to a particular enzyme system.14,39 Computational simulations have been used to study the rearrangement mechanisms of MCM and GLM, and these provide an atomistic view of the ground states and transition states involving radical intermediates.40–42 In the case of MCM, the rearrangement mechanism could take place via intramolecular (associative) or intermolecular (dissociative) pathways. In the associative mechanism, an sp2 hybridized thioester group (blue-colored fragment in figure 1.8) migrates to the vicinal carbon by forming a 3-membered ring (MCM-TS in figure 1.8). It is also possible that the thioester group completely dissociates to form an acrylate and a corresponding radical. The radical then reattaches to the acrylate in a different position. The calculated transition states and the associated barrier heights show that forming the 3-membered ring is energetically more favourable (15.4 kcal/mol) compared to the dissociative pathway (17.1 kcal/mol). The active site residues play a role in lowering the energy barrier by forming hydrogen bonds with the carbonyl group of the substrate.  The formation of the three-membered ring and the intramolecular mechanism in MCM is not possible for the GLM enzyme, as the migrating group is a saturated sp3 carbon fragment. Therefore, the only mechanism by which the saturated carbon could migrate is the fragmentation/addition pathway (see figure 1.8). Active site residues in GLM also facilitate the rearrangement by interacting with the carboxylate moiety of the substrate.14,43      14  MCM-TSGM-TSMethylmalonyl-CoA mutaseGlutamate mutase‡‡  Figure 1.8 The intramolecular addition/elimination mechanism in MCM and intermolecular fragmentation/recombination mechanism in GLM.  1.2.4.2 Aminomutases  Another group of rearrangements can be catalyzed by aminomutases, which have exceptional catalytic power and selectivity.  These enzymes activate unreactive carbon-hydrogen bonds and convert one chiral molecule to another. This specificity makes these enzymes a potentially powerful tool for biocatalytic applications.  There are currently three known aminomutases that depend on the B12 cofactor: lysine 5,6-aminomutase (5,6-LAM), ornithine 4,5-aminomutase (OAM) and leucine 2,3-aminomutase. However, the existence of the latter has been disputed since reports of this enzyme appears in very few papers, dating back about 30 years.44,45  It should be noted that the aminomutase family is not just limited to B12 aminomutases: For example, there exist SAM-dependent aminomutases, which catalyse reactions using S-adenosyl methionine (SAM).  15  Aminomutases utilize coenzyme B12 to accomplish the rearrangements but also require another complementary cofactor, pyridoxal phosphate (PLP), which helps the aminomutases to exchange an amino substituent with its proximal hydrogen atom. The mechanism by which the aminomutases and carbonmutases perform rearrangements are nevertheless quite similar and involves an Ado● generated from the Co-C bond dissociation. A detailed mechanism for OAM is provided in figure 1.9, which shows the conversion of chiral D-ornithine to (2R,4S)-2,4-diaminopentanoate (see table 1.1).34,44 Since this conversion occurs through a cyclic intermediate (azacyclopropylcarbinyl radical, APC in figure 1.9), the mechanism is either associative or intramolecular.  Another enzyme of this group is 5,6-LAM, which catalyzes the rearrangement of D-lysine to 2,5-diaminohexanoate.46 As can be seen from figure 1.10, its rearrangement mechanism resembles that which occurs in OAM.     16    Figure 1.9 Ornithine 4,5-aminomutase catalytic cycle.      Figure 1.10 Proposed rearrangement mechanism for lysine 5,6-aminomutase.  HOrnithineAdo AdoHPLPAdo HAdoAPC17  1.3 Catalytic Power in B12 Enzymes  1.3.1 Hypotheses  Enzymes are known for their ability to increase reaction rates relative to those occurring in solution.47 However, the cause and origin of their catalytic power are not always clearly understood.48 A number of mechanisms have been proposed to explain enzyme-induced reaction rate enhancement.49 Proposed mechanisms are based on transition state stabilization (TSS) or reactant state destabilization (RSD). In both cases, the barrier height of the reaction is reduced. Often both mechanisms are invoked to account for a large rate increase in an enzyme.  A component of the catalytic efficiency of B12 enzymes comes from its low Co-C bond dissociation free energy (BDFE): In water the Co-C BDFE is approximately 130 kJ/mol and in the enzyme it reduces to 70 kJ/mol. The reduction of the Co-C BDFE corresponds to a scission rate increase of more than 10 orders of magnitude (figure 1.11).50–53 Understanding how B12 enzymes are able to achieve this rate enhancement has been a major challenge for almost 50 years. In this regard, several hypotheses have been put forward, including the “strain hypothesis” and “electrostatic hypothesis”.54  CoIIIAdoCoII  Figure 1.11 Catalytic power of B12 enzymes (isomerases). The BDFE of Co-C is 70 kJ/mol in enzyme compared to 130 kJ/mol in aqueous solution.  18  1.3.1.1 Strain Hypothesis  The strain hypothesis (or mechanochemical triggering hypothesis) has been advanced through the work of Halpern and coworkers.21  According to this hypothesis, the enzyme distorts and compresses the corrin ring and the Ado fragment to some degree, resulting in an increase in the corrin ring folding and a destabilization of the ground state (RSD mechanism). The degree of the upward folding of the corrin ring is reflected by the CAdo-Co-NCor or the NCor-Co-NHis bond angles. X-ray measurements show a large distortion in enzyme-bound adenosylcobalamin compared to the isolated adenosylcobalamin in aqueous solution.20 Later studies found that upward folding of the corrin ring is also present in the methylcobalamins in which the bulky Ado group is replaced with a significantly smaller methyl group. Changing the proximal ligand from the native DMB to a smaller sized imidazole ligand, leads to a slightly less efficient Co-C cleavage.15 These studies cast some doubt upon the strain hypothesis and suggest that the strain factor may only make a small contribution to the enzymatic activation of the adenosylcobalamins. Figure 1.12 shows the structure of distorted adenosylcobalamin in enzyme compared with the water structure.          19            Figure 1.12 The depiction of upward folding of the corrin ring in distorted adenosylcobalamin in enzyme compared to the undistorted structure in water. The Φ=NCor-Co-NHis bond angle is 76o for adenosylcobalamin in enzyme compared to 91o in adenosylcobalamin in water. The water structure was obtained from calculations performed as part of this work. Key: red=oxygen, blue=nitrogen, grey=Carbon, white=hydrogen  1.3.1.2 Electrostatic Effect  The electrostatic hypothesis was first proposed by Vernon,55 however in the original report it was not clear how the electrostatic effects are more pronounced in enzyme rather than in aqueous solutions. Warshel modified the original hypothesis and put forward the concept of the pre-organized active sites (see below).  The electrostatic hypothesis, contrary to the strain hypothesis is based on TSS. In order to explain the origin of the enzyme catalysis by the electrostatic effects, the enzyme reaction must be compared that which occurs in aqueous solution. Figure 1.12 shows that in the non-enzymatic Cobalamin structure in Water Cobalamin structure in Enzyme 20  reaction the orientation of the water molecules around the ground state (GS) changes significantly in the transition state (TS). This change allows the water molecule to interact with the partial charges of the reactant fragments that are formed in the TS. About half of the energy gained by the favourable interactions between the partial charges and the water molecules is spent on the reorganization of the water molecules. In the enzymatic reaction, however, the polar amino acid residues, charged residues, and internal water molecules in the enzyme active site are already oriented such that they stabilize the TS structure (figure 1.12). Therefore, less energy is required for reorganization and the favourable interaction between the partial charges of the reactant fragments and the active site residues in the TS structure results in a lower activation barrier.47,49,56,57 Although the electrostatic hypothesis appears to reasonably explain the rate enhancement in many enzyme systems, one cannot easily generalize this proposal to radical enzymes such as B12 enzymes. This is due to the fact that the change in charge distribution or the change in dipoles is almost zero (negligible) upon moving from the GS to the TS associated with Co-C bond dissociation. Therefore no rate enhancement is expected to occur as a consequence of electrostatic effects.  However, a computational study by Warshel et al. demonstrated that the reduction in BDFE of Co-C bond in the MCM enzyme is in fact due to the charged residues in the active site.58 The reaction profile of the Co-C bond cleavage was calculated with and without the charged residues and was compared with the Co-C BDFE in solution. Upon inclusion of the active site charges they were able to reproduce the ~60 kJ/mol reduction in BDFE. However, it was found that the BDFE in the protein and in water is the same when the charges of active site residues were set to zero. This suggests that the bond scission catalysis by AdoCbl-enzymes is due to the charged residues and their corresponding electrostatic effects with the cofactor. The authors stated that 21  “Electrostatic catalysis can… be obtained by attaching a polar group to the leaving fragment and designing an active site that interacts more strongly with this group in the product state than in the reactant state.”58 Figure 1.14 schematically shows how the electrostatic effects are achieved by the interactions between the polar ribose ring and the negatively charged active site residues in the TS structure.          Figure 1.13 Demonstration of the electrostatic effect and pre-organized active site in a hypothetical reaction. The red and green circles show the reactant fragments.  +δ -δGround state Transition state+δ -δGround state Transition stateNon-enzymatic Reaction Enzymatic Reaction 22    Figure 1.14 Demonstration of the origin of electrostatic effects in B12 enzymes. The Ado group has a polar ribose ring that can interact with the charged residues in the active site. The adenine moiety is abbreviated as Ade.    1.3.2 Selectivity in B12 Enzymes  Selectivity in enzyme catalysis is the ability of a reagent to attack the intended substrate rather than nearby spectator species. Enzymes were once thought to act in analogy to a lock and a key. Only a specific key (substrate) fits into the specific shape of the lock’s key hole (enzyme active site). This analogy, though naïve, implies that enzymes are selective toward their substrates and they control the reaction outcome by their three-dimensional structure. However, the mechanism by which this selectivity and control is enabled differs from one enzyme to another.59  In the case of B12 enzymes, the control mechanism must be highly sophisticated because the radicals that are generated in the active site of these enzymes are extremely reactive and therefore unselective. For instance, the Ado● generated in the initial stage of the B12 catalytic cycle is a 23  highly reactive primary carbon-centred radical. The enzyme must therefore employ a strategy to prevent Ado● from engaging in unintended reactions that can damage the enzyme’s interior. The need for a radical control mechanism is underscored by the fact that the target substrate can be as far as 10 Å away from the Ado●. 60 Figure 1.14 illustrates a simple schematic representation of the active site of B12 enzymes.   The seemingly contradictory challenge faced by B12 enzymes is to preserve the selectivity without sacrificing the reactivity. Recall that the main objective of deploying a free radical in enzyme systems is to exploit their high reactivity to catalyze thermodynamically challenging reactions. Therefore, radical enzymes must maintain a balance between the reactivity and selectivity.  Given the importance of radical control in B12 enzymes, it is surprising that little attention has been dedicated to this subject. Rétey attempted to explain the control strategy employed by B12 enzymes. According to Rétey’s “negative catalysis” hypothesis, B12 enzymes function by suppressing undesired reactions rather than facilitating the target reactions. Rétey’s hypothesis does not provide molecular-level (e.g. by TSS or RSS) insights on how negative catalysis operates  in an enzyme system.61    24  1CoLysAdoAspArgTyrSub.GluAla Wat1~ 2-10 Å  Figure 1.15 Schematic representation of the active site of B12 enzymes. Ado● must migrate approximately 2-10 Å to reach the substrate (Sub.) possessing the target H atom (in magenta). During this migration, Ado● has the potential to react with nearby residues before reacting with the substrate.   1.4 Research Questions and Hypothesis  Two important aspects of B12 enzymes were discussed in the previous sections. The first relates to the reduction of the Co-C bond strength in the enzyme active site. The second relates to the selectivity and reactivity of highly reactive Ado● generated during the B12 enzyme catalytic cycle. The latter aspect of radical enzyme behaviour, despite its significance, has received far less attention than the former. These two aspects are complementary in that investigating one of them may provide valuable insights to the other and can help to put together a clear picture of how B12 enzymes work.  A novel hypothesis that explains how MCM and GLM control the reactivity and selectivity of Ado● was tested in this thesis. We hypothesize that a negatively charged glutamate residue, which 25  is conserved in AdoCbl-dependent mutases and aminomutases, is the origin of a quantum Coulombic effect (QCE). This effect decreases the reactivity of Ado● by reducing the energy of its carbon-centred, singly-occupied molecular orbital (SOMO). In doing so, the QCE causes the Ado● to acquire an “orbital converted” electronic structure wherein the SOMO is not the highest occupied orbital.62 When the QCE is active, the radical becomes less reactive toward neighbouring side-chains. The dynamic nature of the enzyme is expected to be such that QCE is “turned off” when the Ado● is near the intended substrate so that the reactivity of the radical is restored.  Coulombic effects also impart thermodynamic stability to Ado●, thereby lower the Co-C BDFE and contribute to the catalytic power of B12 enzymes, and this has also been explored in this thesis. If it can be shown that the QCE is used by GLM and MCM enzymes, it may be the case that the QCE is a mechanism general employed in radical enzymes. The next chapter will discuss the QCE and its consequences for radical reactivity.            26  Chapter 2: Orbital Conversion and Quantum Coulombic Effect  2.1 What is Orbital Conversion?  The Aufbau principle suggests that the electronic configuration of a radical will have the unpaired electron in the highest-energy occupied molecular orbital (HOMO). However, there are some radicals that have electronic configurations in which the singly-occupied molecular orbital (SOMO) is lower in energy than one or more doubly-occupied molecular orbitals.62–68 This kind of electronic configuration is called SOMO-HOMO conversion. One electron oxidation of orbital-converted radical systems will remove an electron from the doubly occupied HOMO to yield a triplet biradical.62–68 Orbital conversion (sometimes called quasi-closed-shell state) is found to occur in number of organometallic systems. Recently, orbital conversion was observed in several distonic radical anions,62–68 that is chemical species possessing both a negative charge close to a non-conjugated unpaired electron. For instance, the (2,2,6,6-tetramethylpiperidin-1-yl)oxyl dithiolate (TEMPO-dithiolate) radical, shown in figure 2.1, upon complexation with Pt(II) ion was reported to show orbital conversion.63 Orbital configuration in this system was verified by one electron oxidation, which led to a triplet signal in electron spin resonance (ESR) spectroscopy. Another example is the stable nitronyl nitroxide (NN●) radical, which combines with tetrathiafulvalene (TTF) to generate triplet cation biradical (NN●TTF) upon one electron oxidation.65 The oxidation potential of NN●TTF was found to be similar to the oxidation potential of TTF rather than NN● (figure 2.2). These findings support the notion that NN●TTF has a SOMO that is not the HOMO. Theoretical studies also predicted that the SOMO in NN●TTF is lower in energy than the HOMO. 65  27    Figure 2.1 The expected orbital configuration of TEMPO-dithiolate and its Pt complex based on experimental and theoretical evidence. One electron oxidation of the orbital-converted Pt-complex leads to a triplet electronic state.     Figure 2.2 Structure of NN●TTF and its orbital configuration. The oxidation potential of NN●TTF is similar to that of the TTF moiety suggesting the orbital configuration shown on the right.  28  Coote et al. showed that a certain aminoxyl- and peroxy-based distonic radical anions have orbital-converted electronic configurations in which the SOMO is lower in energy than several doubly-occupied MOs, at least one of which is associated with the anionic center.62 One electron oxidation of these systems generates a triplet biradical instead of a closed-shell zwitterion (one example of aminoxyl is shown in figure 2.3). Upon neutralization of the negative charge by protonation, the SOMO becomes the HOMO and orbital conversion disappears (figure 2.3). Therefore it is possible to alter the relative energy level of a SOMO by simply changing the pH of the system. This may have various industrial application in pH-switchable polymerization. In addition, orbital conversion might be a common phenomenon in biologically important distonic radical anions such as deprotonated nucleic acids that are formed via oxidative damage by hydrogen abstraction62 (figure 2.4).  Coote et al. confirmed their results using a variety of ab initio computational approaches including multi-configurational self-consistent field (MCSCF), complete active space self-consistent field (CASSCF), and various density functional theory (DFT) methods. Experimental gas-phase acidities (see next section) also support the presence and absence of orbital conversion in deprotonated and protonated molecules, respectively.  Another system that is worth noting among the orbital converted species is superoxide anion. O2- is the product of one electron reduction of molecular oxygen (O2) and is considered to be a reactive oxygen species. It has been found that the SOMO of O2- is not the HOMO.67 The fact that O2 is in a triplet state provides a strong rationale for orbital conversion in O2-. Upon oxidation of O2-, one electron must be removed from the HOMO rather than the energetically lower SOMO yielding two unpaired electrons and hence the triplet O2. If ionization of the SOMO electron occurred, the high-energy 1O2 molecule would be generated.  29    Figure 2.3 An example of a distonic radical anion, COOH-TEMPO (a carboxy-aminoxyl) and its deprotonated form with their associated orbital configurations. One-electron oxidation of the deprotonated structure removes an electron from the doubly-occupied HOMO generating a triplet biradical instead of a closed-shell zwitterion. One-electron oxidation of the protonated structure removes an electron from the singly-occupied HOMO generating the expected closed-shell system.62 *The orbital configuration provided here is based on calculations performed in this thesis.      Figure 2.4 Two examples of deprotonated nucleic acids (DNA and RNA). 30    Figure 2.5 The structure of carboxy-aminoxyl (TEMPO-COO-) and –peroxyl radicals.  2.1.1 Orbital Conversion and Radical Stability  It has been found that distonic anion radicals have unexpectedly high stability, which correlates with high proton acidities in their conjugate acids. This stability arises from the interaction between the negative charge and the radical centre has been explored in the case of two distinct radicals shown in figure 2.5.62 In order to quantify the stability in distonic radicals, methyl bond dissociation free energies (BDFE) were calculated for both deprotonated (orbital converted) and protonated (unconverted) forms of the radicals. The radical stabilization energy (RSE), which is defined as BDFEprotonated ─ BDFEdeprotonated, gives a measure of how orbital conversion (or any other effect) stabilizes the radical. The magnitude of this RSE (also known as BDE switch)62,68,69 amounts to 15 and 20 kJ/mol in carboxy aminoxyl and carboxy peroxyl radicals, respectively. The magnitude of these RSE values were confirmed experimentally by the measured differences in gas phase acidities (DGPA), which relates to RSE by the thermodynamic cycle shown in scheme 1.    31   Scheme 1 Thermodynamic cycle relating RSE to DGPA.  From this cycle, the following relationship can be obtained:   BDFE(HOOCR─Me) ─ BDFE (─OOCR─Me) = GPA(HOOCR●) ─ GPA(HOOCR─Me)    Eq. 1  The left-hand side of eq. 1 is the RSE, while the right-hand side is the DGPA. The DGPA can be measured experimentally using mass spectrometry and can be compared with theoretically calculated RSEs. The measured DGPAs were found to be in agreement with the theoretical calculations for the two radicals shown in figure 2.5.   The two radical anions described above have the negative charge far from the radical centre and there is no σ or π conjugation between the charge and the spin, making the 15 and 20 kJ/mol stabilization rather surprising. There remains the question of whether the RSE is related to orbital conversion. This is discussed in the next section.  32  2.2 The Origin of the Orbital Conversion. Classical or Quantum Effect?   We have seen so far that the phenomenon known as orbital conversion exists in several distonic radical anions, and that distonic radicals are significantly stabilized relative to their uncharged counterparts. What is the relationship between the orbital conversion that is observed in the distonic radicals and radical stabilization? To answer this question, Coote and coworkers selected two groups of neutral aminoxyl radicals, similar to the -OOC-TEMPO radical structure.69 In the first group of radicals, the negatively charged group (-OOC) was substituted with a non-conjugated heterocyclic carbene that has a high energy HOMO to ensure that the radical displays orbital conversion (figure 2.6). In the second group, the same radicals were included, but this time the carbene moiety was removed in order to eliminate orbital conversion. The RSEs were calculated by subtracting the methyl BDFEs of the first group from the methyl BDFEs of the second group. The RSEs acquired show that the stability of both groups of radicals are approximately the same. This suggests that the orbital conversion in the first group does not stabilize the radical center. Furthermore, replacement of the COO- group in -OOC-TEMPO radical with a classical negative point charge, which does not have orbitals associated with it, results in the stabilization effect being preserved (or even increased) in the absence of the orbital conversion. These two results indicate that orbital conversion is not the primary cause of the stabilization in distonic radical anions, though they seem to accompany each other. This strong correlation can be seen in figure 2.7, where the effects of the solvent polarity on the orbital conversion and RSE has been shown. Both of the RSE and the SOMO-HOMO energy gap (i.e. the magnitude of orbital conversion) is decreased in high polarity solvents.   33     Figure 2.6 An orbital converted radical (carbene-TEMPO) is compared with a structurally similar unconverted radical (TEMPO). The calculated RSE shows that the stability of both radicals are approximately the same, suggesting that the orbital conversion in carbene-TEMPO does not relate to radical stabilization.     Figure 2.7 The influence of solvent on the calculated RSE and SOMO-HOMO orbital conversion of TEMPO-COO-. The RSE decreases as the dielectric of the solvent increases.69 34  Coote and co-workers investigated the origin of the RSE in distonic radical anions through a series of theoretical calculations. It was found that the major part of the RSE cannot be explained by conventional polar effects such as inductive, mesomeric, and stereoelectronic effects, which are well-known in physical organic chemistry. The RSE is caused by a through-space interaction between the negative charge and the spin, contrary to inductive effects, which are through bond interactions. This conclusion was drawn by comparing RSE of TEMPO-COO- radical with RSE of a similar system in which the chemical bond between the TEMPO and COO- is removed and hydrogen atoms are added to cap the dangling bonds. The distonic radical anions that were studied lack π conjugations and so mesomeric effects can also excluded as the cause of the stabilization.  It was argued by Coote et al. that the origin of the RSE in distonic radical anions is electrostatic in nature and arises from the interaction between the negative charge and an induced dipole or quadruple moment. The authors stated that the negative charge in these systems pushes the electron density to the extremities of the molecule and thereby creates the induced dipole/quadruple moment that interacts with the negative charge to stabilize the system. The magnitude of this interaction in distonic radical anions was found to strengthen when (i) the unpaired electron is delocalized (ii) the charge on the anion is increased (iii) the distance between the anion and the radical centre is decreased (iv) the radical anion is in the gas-phase or low-polarity media. The latter factor was illustrated in figure 2.7. The above discussion points to the fact that the nature of the orbital conversion is different from the enhanced stabilization experienced by the distonic radicals despite the fact that they are closely related. The extra stabilization can be explained in terms of classical Coulombic effects (CEE) and so it can be assessed to some degree by classical equations such as Coulomb's Law. On the other hand, orbital conversion is the direct consequence of quantum mechanics and its evaluation must 35  be carried out by solving the Schrödinger equation.70 The fact that the orbital conversion disappears (unlike CEE) when an orbital-less point charge replaces the negatively charged group supports the notion that the orbital conversion is a quantum effect, and thus it can be said to result from a quantum Coulombic effect (QCE). Although the QCE and CEE accompany each other, these two effects, as will be discussed, can have different consequences in B12 enzymes and should be considered separately.   2.3 The Possible Role of QCE in B12 Enzymes  Several approaches have been devised to enhance and control the outcome (selectivity) of reactions.71,72 Among these approaches, electrostatic catalysis has received less attention compared to the other forms of the catalysis because electric fields are direction-dependent, and it is difficult to orient them with the reaction centre.73,74 However, this issue has been recently overcome for a Diels-Alder reaction by fixing the dienes on the tip of a scanning tunnelling microscope (STM) and the dieneophiles on a surface.75 It has been found that the electric field between the tip and surface enhances the rate of the Diels-Alder reaction by fivefold, through TSS.   It is also known that nature exploits field-induced chemistry in many biological catalysts.47,76 Enzymes carry out their reactions in an active site in which the charged residues are pre-organized to create an electric field that can catalyze the reaction.47 For example, ketosteroid isomerase was shown to utilize electrostatic fields to catalyze the isomerization of a C=C bond through an enolate intermediate.77,78 The basis of this enzyme catalysis is the difference in the dipole moment of the GS and the TS. In the TS the dipole moment of the elongated C=O bond (+δC=O-δ) is larger than that in the GS. It was suggested that the charged and polar residues in the active site directly 36  stabilize the C=O bond in the TS more than the GS by interacting with the stronger dipole moment in the TS.77,78 The major portion of the ketosteroid isomerase’s catalytic power was found experimentally to have electrostatic origin.   This is the first direct experimental evidence that shows that electrostatic catalysis is exploited by enzymes, though the importance of the electric fields was previously shown in P450 enzymes by computational approaches.73,76,79–81      Analysis of the crystal structures of GLM (pdb:1I9C) and MCM (pdb:4REQ) enzymes reveals the presence of a negatively charged glutamate residue in the active site of the both enzymes. This residue, which  is conserved in many B12 enzymes, was found to be related to the catalytic efficiency and selectivity of B12 enzymes.82–84 Enzyme structures show that the conserved glutamate residue interacts non-covalently with Ado● (in substrate-bound state). We hypothesize that the Glu----Ado● system may display some of the same properties as a distonic radical anion. Since the QCE and the CEE present in most distonic radical anions, the B12 enzymes might employ these effects to electrostatically catalyse and control the radical reactions. It would be difficult to quantify these effects with experimental approaches in enzymes, but quantum mechanical calculations and computational simulations are ideally suited to explore this hypothesis. This is the central theme of this thesis.     37  Chapter 3: Methods  3.1 Objective  In this chapter the technical details of the quantum chemical calculations are summarized. These include details of barrier height (TS), and QM/MM calculations in addition to information on how the molecular orbital energy diagrams and electron configurations were obtained. Background and theory behind the QM/MM calculations and high level MCSCF/CASSCF calculations, which confirm the electronic structures obtained by means of DFT methods, are also provided.   3.2 Quantum Mechanic/Molecular Mechanic Simulations  3.2.1 Background and Theory  Quantum mechanical (QM) calculations such as density functional theory (DFT), which is used in this thesis, can rapidly become computationally expensive as the size of the molecular system increases. This makes the QM calculations impractical for large sized systems such as proteins or enzymes. On the other hand molecular mechanical (MM) methods can treat very large systems with significantly less computational time. However, MM methods are not capable of treating chemical systems where bond forming/breaking occur. In order to take advantage of the QM accuracy and the speed of MM, we can divide a large system into two parts; one is where the chemistry happens (reaction centre) and one is the other parts of the system in which are not engaged in the chemical process. The former region can then be treated by full QM calculations, 38  while the latter can be treated using the computationally cheaper MM approach. This strategy, which was originally introduced by Warshel and Levitt is known as hybrid QM/MM formalism.85 Figure 3.1 illustrates the QM/MM concept for an example molecule vitamin E acetate.       Figure 3.1 The structure of the vitamin E acetate (also known as tocopheryl acetate), which has been divided into MM and QM regions. The reaction centre of the molecule is included in the QM region, while the carbon chains are treated with the MM approach.  A challenge associated with QM/MM calculations is to treat the interactions between the particles in the QM and MM regions. Various QM/MM schemes have been developed to assess these interactions. The QM/MM formalism that is used in this thesis is ONIOM (our Own N-layered Integrated molecular Orbital and molecular Mechanics) approach, which was devised by Morokuma and co-workers.86,87 In ONIOM the total energy of the system is calculated by the following equation88                             𝐸𝑡𝑜𝑡𝑎𝑙 = 𝐸𝑀𝑀(𝑀𝑀 + 𝑄𝑀) +  𝐸𝑄𝑀(𝑄𝑀) −  𝐸𝑀𝑀 (𝑄𝑀)                                  (3.56)  39  where EMM (QM+MM) is the energy of both QM and MM regions (i.e. the whole system) calculated at MM level of treatment, while the EQM (QM) and EMM (QM) are the energies of the QM region, at QM and MM levels of treatment, respectively. One of the shortcomings of this approach is the fact that the ONIOM method does not correctly take into account the influence of the MM environment on the QM region. To better describe this influence, electrostatic embedding (EE) can be used with ONIOM method. ONIOM with electrostatic embedding (ONIOM-EE) includes polarization effects induced by the charges associated with the atoms inside the MM region on the QM system.89  Single point calculations were performed on our protein systems at the ONIOM-EE(UM06-2X:UFF) level. That is, the atoms inside the QM region are treated using UM06-2X, which is a DFT method, and atoms inside the MM region are treated with an MM method called universal force field (UFF). For geometry optimizations two methods were employed: ONIOM-EE(UM06-2X:UFF) and ONIOM-EE(PM6:UFF) - see the next section. PM6 is a semi-empirical method that has a computational cost that is intermediate to DFT and MM methods.   3.3 QM/MM Calculations Details  The GLM-HB and GLM-PHB models, which were obtained using GLM enzyme crystal structures (see Chapter 5 for more information about these models), were modified by the following steps to acquire the initial structures for our final QM/MM calculations. Starting from these crystal structures, hydrogen atoms and protons on the standard residues were added using the PROPKA 3.190 and PDBPQR91 programs, with the pH set to 7.0. Hydrogens atoms on the Ado●, the substrate and the B12 cofactor (the non-standard residues) were added using the Gaussview version 3 40  software package.92 The prepared structures were then subjected to QM/MM calculations using a two-layer ONIOM scheme93 with electronic embedding. For this purpose the atoms within 10 Å of the cobalt centre incorporated in the QM layer, while all other atoms included in the MM layer. Geometry optimizations were then performed at ONIOM-EE(PM6:UFF) level to relax the positions of the added hydrogens inside the QM region. During the optimization all of the atoms were kept fixed expect the added hydrogen atoms. Additional QM/MM geometry optimizations using ONIOM-EE(UM06-2X/6-31+G(d):UFF) were performed on only the hydrogen atoms of Ado● group, glutamate (Glu330) and the substrate, which constituted the QM region to refine the position of the hydrogens on these residues using a more accurate DFT (UM06-2X) method. The resulting final structures were employed for several single-point QM/MM computations with QM regions of different sizes in order to obtain the MOs and the electronic configurations (see section 4.2.2 for the residues that are included in the QM region). For these single point calculations, the unrestricted DFT calculations with the UM06-2X functional and 6-31+G* basis sets with 6 d-functions were applied to atoms within the QM region, while the atoms in the MM region were described using UFF to incorporate the partial charges of all protein residues. It is expected that the inclusion of the partial charges associated with the MM region will allow for an assessment of their electrostatic influence on the orbital ordering and the QCE.  For MCM, the model systems were obtained from a previous theoretical study94, thus no extra steps were required to optimize or add the hydrogen atoms. On these model systems single point QM/MM calculations were performed at the same ONIOM-EE(UM06-2X/6-31+G(d):UFF) level as in the GLM enzyme computations in order to obtain MOs and orbital energy diagrams (see section 4.4.2 for the residues that are included in the QM region). All of the ONIOM calculations 41  described above for GLM and MCM enzymes were performed using the Gaussian 09 and 16 software packages95,96. The choice of UM06-2X DFT functional is based on the fact that this method was shown to perform well in previous related orbital conversion studies.62,66,69 Nevertheless, we also performed our own benchmarking with high level ab initio multi-reference approaches (MCSCF/CASSCF), which are described in the Chapter 5. The Minnesota functional, UM06-2X with 54% HF exchange, is designed mostly for the main group elements in the periodic table. For systems that include transition metals, the M06-L functional, which has zero HF exchange, is recommended.97,98 However, since the purpose of our calculations is to obtain the MO energy diagrams and not to calculate the energy or thermochemistry of MCM and GLM enzymes, M06-2X was selected. The local functionals such as M06-L are known to predict inaccurate MO energies compared to hybrid functionals like UM06-2X.99–101  3.4 Molecular Orbital Energy Diagrams    The foregoing QM/MM [ONIOM (UM06-2X/6-31+G*:UFF)] unrestricted computations were used to extract the Kahn-Sham(DFT) molecular orbitals (MO). In unrestricted calculations, in contrast to restricted ones, α and β orbitals are represented by separate wave functions. Therefore, α and β orbitals calculated for a doubly occupied orbital will not necessarily have identical shapes or energies but are expected to be approximately the same. In order to determine if an MO is doubly or singly occupied, the α orbitals and β orbitals should be matched in terms of energy and MO shape (by visual inspection) as far as it is possible. An MO is doubly occupied if an occupied α orbital matches an occupied β orbital (approximately). If an occupied α orbital has a β counterpart 42  that is unoccupied, the α orbital is the SOMO. SOMOs are expected to be localized largely on the radical centre, where the most spin density is located. Thus, the spin density plots would help to verify this MO as the SOMO. In the case of MCM and GLM enzymes, one of the radical centres corresponds to a carbon atom in the Ado● moiety and the other radical centre is the Co● atom. The radical centre contribution (RCC) to the SOMO or HOMO is another tool that can be helpful for the verification of the radical centre. RCC estimates the contribution of a particular atomic orbital – the carbon-centred radical in this case – to the MO of interest, for example the SOMO or HOMO. RCC can be determined using the following expression (known as Simple scheme):                                                         𝑅𝐶𝐶 (𝑀𝑂) =𝐶𝜆2∑ 𝐶𝜇2𝜇 × 100%                                                          (3.1)  where Cλ is the particular atomic orbital coefficients associated with the radical center in a given MO, and Cμ is the atomic orbital coefficients of all of the atoms contribute to the MO. For a particular MO, Cλ is the sum of the coefficients of the p-type orbitals on the carbon radical centre in which the unpaired radical is nominally contained, while the Cμ is the atomic orbital coefficients of other atoms. The Cλ and Cμ coefficients needed for the RCC calculations were obtained from the QM/MM single point computations described at the beginning of this section.    3.5 Transition State Calculations   The transition state (TS) calculations in Chapter 5 were performed on the truncated models of GLM and MCM enzymes. For these calculations, the DFT UM06-2X with 6-311+G(d,p) basis 43  sets were employed. The TS optimizations were performed by constraining the geometry of the glutamate and the Ado● (except its CH2 group) and relaxing the coordinates of the substrate (more information is given in Chapter 5). The calculated intrinsic reaction coordinates (IRC) verified that the TS coordinates that were obtained using this approach correctly connects reactants to products, thus validating the TS structures. The barrier heights reported in the thesis are based on electronic energies rather than free energies because of the constrained TS computations.   3.6 BDE and RSE Calculations  The BDE and RSE values reported in Chapter 5 were obtained by performing constrained optimization at the same UM06-2X/6-311+G(d,p) level: The coordinates of Ado● was fixed except for the hydrogen atoms of the CH2 group (or CH3 group for the parent molecule). The constrained optimizations ensure that the geometry of the studied systems stays the same as in the wild-type enzyme. The reported BDE and RSE values are based on the electronic energies, unless otherwise stated. For the RSE values calculated in the bulk solvation (Section 6.4.2), the universal solvation model (SMD) is used.102 These and the TS calculations were performed with the Gaussian 09 program95.  3.7 Density State Plots (DOS)  In order to understand how the MOs composition derived from different chemical fragments in the systems studied, DOS plots were computed. The total DOS at energy E can be calculated by the following equation: 44                                                                   𝑁(𝐸) = ∑ 𝛿(𝐸 − 𝜖𝑛)𝑖                                                            (3.2)  where N(E) is the number of states, 𝛿 is the Dirac delta function, and ϵn is the MO energies.103,104 The type of DOS analysis performed in this thesis is known as projected DOS (PDOS). In PDOS the total density is projected out into certain fragments using the following equation:                                                      𝑁𝑚(𝐸) = ∑ < 𝜒𝜎|𝜙𝑛 > 𝛿(𝐸 − 𝜖𝑛)𝑖                                              (3.3)   The function χσ here shows the contribution of each fragment in the orbital φn. These calculations were performed using GaussSum version 3.0.105  3.8 Multiconfiguration Self-Consistent Field Theory   3.8.1 Background and Theory  Hartree-Fock (HF) theory is the starting point for most wave function-based electronic structure methods. However, HF provides an inadequate description of many systems because it lacks electronic correlation and because it is based on a single electronic configuration. Multi-configuration Self-Consistent Field Theory (MCSCF) methods provide a means of introducing multiple configurations in the description of the wave function of chemical systems and thus it 45  better represents the electronic structure. An example of a challenging problem for single configuration methods is singlet O2:  according to the MO energy diagram the last two electrons of O2 can exist in either the πx* or πy* orbitals to form the singlet electronic state (see figure 3.2):                                                                     𝜓1 = ⋯   𝜋𝑥∗0𝜋𝑦∗ 2                                                                   (3.4) or                                                                    𝜓2 = ⋯   𝜋𝑥∗2𝜋𝑦∗ 0                                                                   (3.5)  Since the electrons have equal probability of being in either π1* or π2*, the proper description of the 1O2 wave function is:                                        Ψ (𝑠𝑖𝑛𝑔𝑙𝑒𝑡 𝑂2)  =  𝑎1 (… 𝜋𝑥∗0𝜋𝑦∗ 2) + 𝑎2 (… 𝜋𝑥∗2𝜋𝑦∗ 0)                                 (3.6)   where 𝑎1 and 𝑎2 are the weights of each configuration, which are the same in this case. HF theory cannot provide a correct description of the 1O2 wave function because it is a single electronic configuration method.  46    Figure 3.2 Two possible MO diagrams of the singlet O2 (𝝍𝟏and 𝝍𝟐). The correct wavefunction for singlet O2 is a linear combination of 𝝍𝟏and 𝝍𝟐.  The MCSCF method can also incorporate electronic correlation missing from HF theory by including additional configurations in the wave function expansion, i.e.:                                                     Ψ𝑀𝐶𝑆𝐶𝐹 = 𝑎0𝜓𝐻𝐹 + 𝑎1𝜓1 +  𝑎2𝜓2 + ⋯                                      (3.7)  The coefficients 𝑎n in equation 3.7 are weighing factors that indicate the relative importance of the nth configuration in the description of the overall wave function. The different configuration wave functions (𝜓1, 𝜓2, …) are generated by exciting electrons to the unoccupied MOs. The MCSCF calculations are computationally intensive and are only possible for a small number of systems unless additional constraints are introduced.  47  The Complete Active Space Self-consistent Field (CASSCF) method is a subset of MCSCF and it allows for a selection of a manageable number of configurations to be introduced into the wave function expansion. MOs within an energy window that straddles the HOMO-LUMO gap are usually selected to comprise the “active space”, and configurations are generated by permuting the electrons within the active space amongst all orbitals in the active space window. Other MOs that are not included in the active space are enforced to be either doubly occupied or empty (Figure 3.3 schematically illustrates the CASSCF formalism). CASSCF calculations were performed on several systems in this thesis to ensure that the results that were obtained with DFT are reasonable. The results of these CASSCF calculations are given in Chapter 5 (section 5.3.3).          48    Figure 3.3 A schematic illustration of the CASSCF method. There are three orbitals and four electron in the active space. This can be abbreviated as CASSCF(4,3), which means that all possible configurations of four electrons in three orbitals are considered in the CASSCF calculations.    49  Chapter 4: QM/MM Calculations Reveal the Presence of QCE in GM and MCM Enzymes  4.1 Objective  Atomistic modelling was performed on two examples of AdoCbl-dependent enzymes (MCM and GLM) in order to test the hypothesis that these enzymes exploit QCE to control the selectivity and maintain the catalytic efficiency. The first step is to determine if orbital conversion is present in these enzymes, and this is the focus of this chapter.  Hybrid quantum mechanics/molecular mechanics (QM/MM) calculations were performed on two model systems of each MCM and GLM enzymes. The models represent two stages of the catalytic cycle of B12 enzymes. The first stage is when the Ado● is formed after the Co-C bond dissociation and the second is when the Ado● is in position to abstract the target hydrogen atom from the substrate. These models can provide insights on how the reactivity of Ado● might differ at different stages.  4.2 Methodology (GLM Enzyme)  4.2.1 Models and Calculation Setup   Since it is known that the B12 enzymes undergo significant conformational changes upon binding to a substrate, it is important to have a starting structure that has the substrate bound to the active 50  site (closed form) rather than an unreactive open form in which the substrate does not exist.106 The GLM X-ray crystallographic structure (Protein Data Bank entry code 1I9C) was selected as a starting structure for all of the GLM calculations. In this crystal structure, the substrate is bound to the active site and therefore the enzyme is in its reactive form. The 1I9C X-ray structure also shows two distinct conformations for Ado group, which correspond to two different stages of the catalytic cycle (see figure 4.1).107  The two conformers differ from each other by only the geometry and the position of Ado group which leads to differences in Co-C(Ado) bond distance, the geometry of ribose ring, and the degree to which Ado● interacts with the nearby conserved glutamate residue. In the first conformation, the Co-C(Ado) bond length is approximately 3.2 Å and the ribose group has a C2′-endo sugar ring orientation. We name this conformation “GLM partially hydrogen bonded model” (GLM-PHB), as it forms a hydrogen bond with O…H distance of 2.1 Å with one of the oxygen atoms of Glu330 in the active site (figure 4.1-A). In the second conformation, the Co-C(Ado) distance is 4.5 Å and the Ado● group closer to the substrate. The ribose group in this conformation is in the C3′-endo puckered state. This orientation helps the ribose group to form a pair of hydrogen bonds with both oxygen atoms of Glu330 (figure 4.1-B). The O…H distances associated with the hydrogen bonds are 1.5 and 1.7 Å, and this conformation is labelled “GLM hydrogen bonded model” (GLM-HB). Figure 4.2-A and B show the important structural parameters for GLM-PHB and GLM-HB models, respectively.      51     Figure 4.1 Two models of the GLM enzyme obtained from X-ray crystal structures: A. PHB model B. HB model. A B 52      Figure 4.2 Some of the structural parameters of A) GLM-PHB and B) GLM-HB models. The bond distances of COO- are reported from the centre (between the two oxygen atoms) of the carboxylate groups to the radical center (C2). A B 53  The GLM-PHB conformer is believed to be an intermediate during the Ado● migration, so it embodies the characteristics of Ado● during migration (stage B in figure 4.3). The HB conformer aligns with a stage in which the Ado● is within the van der Waals distance of the substrate and it is ready to abstract the intended hydrogen, and thus relates to the hydrogen abstraction step (C in figure 4.3). As can be seen from figure 4.2, the radical centre of Ado● is oriented toward the target hydrogen atom, and is within a distance of 2.2 Å, of the substrate. The analogous distance in the PHB model is 3.8 Å. The H4-C2-H1-C1 dihedral angle in HB model is also approximately 90o, which indicates that Ado● is appropriately oriented for hydrogen abstraction.       Figure 4.3 Initial catalytic steps involved in B12 enzymes. In the first step, the Co-C bond in A breaks to generate the Ado●. This radical then migrates toward the substrate (H-Subs). B is the intermediate structure during the migration. C is the final structure after Ado● migration but before hydrogen abstraction.  The HB and PHB conformations provide a somewhat ideal model systems for exploring our hypothesis in GLM enzyme: The PHB model represents the migration step in which the reactivity of Ado● should be controlled in order to prevent unintended reactions, while the HB model A                                                        B                                               C 54  represents hydrogen abstraction step in which the Ado● should be exploited for its reactivity in order to effectively catalyze the hydrogen atom abstraction.   4.2.2 QM/MM Calculations  We performed several QM/MM single-point calculations on the GLM-HB and GLM-PHB models described in the methodology section). In order to mitigate any uncertainties that could arise due to the charge and size of our QM region (QM region sensitivity), four models with different QM sizes and different total charge were prepared. These models are: negatively-charged model A, neutral model B, positively-charged model C and neutral model D with 45, 67, 91, and 643 atoms in the QM region, respectively. More details on what residues are included in the QM region of these models are given in table 4.1. These models were used to confirm the fact that QCE pattern in all of the models are consistent regardless of the charge or the size of the QM system.        55  Table 4.1 Information about GLM model systems that are used for the QM/MM computations. The blue-coloured residues are negatively charged, whereas the red-coloured residues are positively charged. Wat is the Protein Database code for water.    4.3 QCE in GLM Enzymes   4.3.1 Orbital Configurations and Energies Obtained from QM/MM Calculations  A total of eight QM/MM calculations with different QM sizes and charges were performed on the GLM-HB and GLM-PHB models. The smallest model in terms of QM region size – model A - consists of Ado●, 3 nearby water molecules and side chain of Glu330, which is capped with a link hydrogen atom at Cβ. The orbital configuration diagrams of this negatively-charged model are reported in figure 4.4 for GLM-HB and GLM-PHB models. Both models display orbital conversion, which indicates that the QCE is active in these systems. However, the degree of orbital conversion in the GLM-PHB and GLM-HB models is very different, suggesting that the magnitude 56  of the QCE operating in the two models is quite different. The SOMO-HOMO energy gap can be used as an indication of the magnitude of the QCE. In GLM-PHB, the SOMO is HOMO-6 and the SOMO-HOMO energy gap is 265 kJ/mol, whereas in GLM-HB model the SOMO is HOMO-3 and the energy gap is 47 kJ/mol. Therefore, the QCE is significantly larger in GLM-PHB than GLM-HB model. As is illustrated in figure 4.4, increasing the QM size and altering the total charge of the QM region does not change this behaviour and the neutral model B and positively charged model C follow the same trend. Note that the absolute energy of the SOMO is lower (i.e. more negative) in all of the PHB models compared to their corresponding HB conformers.  These results are also supported by the largest models (D), which are constructed by including 24 active site amino acids, 14 water molecules and the non-standard residues in the QM layer (see table 4.1). The orbital energy diagrams that were obtained for Model D (figures 4.5-A and 4.6-A) show that the HOMO does not correspond to the radical centre (see spin density plots in figure 4.7) in either GLM-PHB or GLM-HB, and the electron density of HOMO is distributed over the base (DMB) of B12 cofactor (figure 4.5B and 4.6B). In the GLM-PHB model the radical center contribution (RCC) to the HOMO is found to be zero, which verifies that the SOMO is not the HOMO. Visualization of α orbitals show that the MO that is associated with the radical center is HOMO-59 (SOMO-HOMO energy gap= 240 kJ/mol) with RCC value of 10% (figure 4.5C). Although this percentage may seem small, this RCC value is the largest amongst the 59 highest energy MOs. It should also be kept in mind that the RCC value is weighted by the large number of atoms present in the QM region of Model D (see equation 3.1). Similarly, in the GLM-HB model the HOMO is not associated with the radical center (RCC=0%). The largest RCC value found amongst the occupied MOs is associated with HOMO-26 for which the RCC is 7%. The magnitude of QCE expressed in terms of SOMO-HOMO energy gap in this 57  model is 170 kJ/mol. In agreement with our small model systems, the magnitude of QCE in this model is smaller than GLM-PHB. The calculated results obtained for all of the model systems point to the fact that the magnitude of the QCE, as measured by the SOMO-HOMO energy gap, is larger in the GLM-PHB model than in the GLM-HB models. The differences in QCE between the two models is explored in the following section.58  Figure 4.4  Illustrations of the electronic structure of the GLM-PHB and GLM-HB conformer for Models A, B, and C. The SOMO-HOMO energy gap  and the absolute SOMO energy (red colored energy level and electron) are also shown. The SOMO-HOMO energy gap is larger in all PHB models compared to the HB models, regardless of the size and the charge of the QM layer. This suggests that and the magnitude of the QCE is larger in the PHB models compared to the HB models. To reiterate that the diagrams were obtained by means of unrestricted calculations, on the orbital representations α and β signs are shown (see section 3.4)59     Figure 4.5 A) The active site of the GLM-HB model (model D) with an illustration of its calculated electronic structure. The SOMO-HOMO energy gap and the absolute SOMO energy are also shown. B) The plot of the HOMO. The orbital is distributed over the base (DMB) of B12 cofactor. No electron density is present on the radical centre in this MO (RCC=0%). C) The plot of the HOMO-59.  The orbital is distributed over the radical centre, indicating that this MO is the SOMO (RCC=10%).   A B C 60      Figure 4.6 A) The active site of the GLM-HB model (model D) with an illustration of its calculated electronic structure. The SOMO-HOMO energy gap and the absolute SOMO energy are also shown. B) The plot of the HOMO. The orbital is distributed over the base (DMB) of B12 cofactor. No electron density is present on the radical centre in this MO (RCC=0%). C) The plot of the HOMO-26. The orbital is distributed over the radical centre, indicating that this MO is the SOMO (RCC=7%).   B C A 61    Figure 4.7 The distribution of spin density on the Co• and Ado• in GLM-PHB and GLM-HB models. The Mulliken (Hirschfeld) atomic spin density on nominal radical centre carbon in Ado• is 1.34 (0.71) in GLM-HB compared to 1.16 (0.73) in GLM-PHB.      4.3.2 Analysis and Discussion  The results from the QM/MM calculations demonstrate that orbital conversion occurs in both the GLM-HB and GLM-PHB models. However, the magnitude of the orbital conversion and QCE in these systems were found to be much larger than that found in distonic radical anions (see chapter 2). The magnitude of QCE in GLM-HB is notably smaller than that in GLM-PHB. The differences in the QCE in the two models likely a consequence of the differences in the quantum electrostatic interactions that arise from the differences in the structures of the models. Recall that the only significant difference between these models is the position of Ado●, which leads to different hydrogen bonding interactions with the Glu330 in the active site (figure 4.1). Although the difference in hydrogen bonding interactions appears to be the cause of the dissimilarity in orbital 62  configurations, the unusual, relatively low energy of the SOMOs in both models is another issue that has to be addressed. In this regard, a closer look at the models shows that there are several active site charged residues (negative and positive) located near the Ado● (figure 4.8). These charged residues, in addition to Glu330, can induce a strong QCE on Ado●, which would lead to the large orbital conversions found in the GLM models. The strong hydrogen bonding between Ado● and Glu330 in GLM-HB model, however, offsets part of the influence of Glu330 on the orbital ordering, and reduces the magnitude of QCE compared to GLM-PHB. This is consistent with previous results that found that the implicit bulk-water solvation of distonic radicals quenches orbital conversion.69,108 In the active site of the enzyme, the residues are oriented in such a way so that they create an environment that precludes full solvation, allowing QCE to operate. Key residues in the active site allow the magnitude of the QCE to be controlled through specific hydrogen bonding interactions. In the case of the GLM enzyme, it seems that the explicit hydrogen bonds between the Ado● and the Glu330 directly controls the magnitude of the QCE. Since the Glu330 was also found to be related to B12 enzymes reactivity and efficiency, it seems reasonable to hypothesize that B12 enzyme catalysis and the magnitude of QCE, might be linked in some way. This relationship is investigated in more detail in Chapter 5. In the next section, the relationship between active site hydrogen bonding with Ado● in another B12 enzyme, MCM, is explored.     63   Figure 4.8 Charged residues in the active sites of GLM-PHB (left) and GLM-HB (right). The dotted lines show the hydrogen bonding interactions between the residues with the substrate and Ado●. Key: red=oxygen, blue=nitrogen, grey=Carbon, white=hydrogen  4.4 Methodology (MCM Enzyme)  4.4.1 Models and Calculation Setup   The study was extended to the MCM in order to determine if the electronic structure found in GLM is present in another enzyme in AdoCbl-dependent mutase. Rothlisberger’s group performed classical molecular dynamic (MD) and QM/MM MD simulations using Car–Parrinello molecular dynamics (CPMD) on the MCM enzyme at different stages of catalysis.94 They employed DFT/BLYP with 6-31G* functional for treating atoms inside the QM region and other atoms were treated using the classical AMBER 99sb force field (for complete information see reference 94).94 Two structures having similar character to the GLM models were extracted from the simulations and provided to us by the authors upon our request. Note that the authors used lactoyl-CoA as the substrate instead of the wild-type MCM substrate, L-methylmalonyl-CoA. No rationale for this 64  choice was offered in reference 94. The first model has a structure that corresponds to Co-C bond dissociation where the Ado● is at the beginning of its migration to the substrate and the second model has the Ado● close to the hydrogen abstraction transition state.  Similar to the GLM models, the MCM models have the Ado● moiety non-covalently interacting with a conserved nearby glutamate residue (Glu370). In the first model this interaction is not a hydrogen bonding interaction, however in the second model the Glu370 makes a partial hydrogen bond with one of the oxygen atoms of Glu370 (the O…H distance is 1.6 Å). To be consistent with our GLM models we name these models MCM partially hydrogen bonded model (MCM-PHB) and MCM hydrogen bonded model (MCM-HB), despite the fact that the Ado● is not forming a significant hydrogen bond with Glu370 in MCM-PHB and only forms a partial hydrogen bonding in MCM-HB. Figure 4.9 and figure 4.10 illustrates the two MCM models with several important structural parameters.      65    Figure 4.9 Different models of MCM enzyme: a. PHB model b. HB model  A B 66     Figure 4.10 Some of the structural parameters of A) MCM-PHB and B) MCM-HB models. The bond distances of COO- are reported from the center of the carboxylate groups to the radical center (C2).    67  4.4.2 QM/MM Calculations  The MCM models were taken from a previous computational study94, and therefore no model preparation was required. QM/MM single point calculations were performed using ONIOM(UM06-2X/6-31+G*:UFF), as was done for the GLM  models. For the MCM models, only one set of calculations were done on one model (model A) containing a large QM region consisting of 507 atoms. The residues that are included in the QM layer are given below in the table 4.2.  Table 4.2 Information about MCM model system that is used for the QM/MM computations. The blue-coloured residues are negatively charged and the red-coloured residues are positively charged.     4.5 QCE in MCM   4.5.1 Orbital Configurations and Energies Obtained from QM/MM Calculations  68  The electronic configuration that was obtained from single point QM/MM calculations for MCM-PHB is illustrated in figure 4.11. This figure shows that the HOMO in MCM-PHB is not associated with the radical centre (the Ado● RCC to HOMO is 0%), suggesting that the QCE is active in Ado● before its migration toward the substrate. The calculated RCCs and MO plots of high energy MOs (figure 4.12) show that the unpaired electron that is associated with the radical centre resides in HOMO-6. This MO has the highest RCC (5.5%) amongst the six highest energy occupied MOs shown in figure 4.12. The SOMO-HOMO energy gap in this model is approximately 60 kJ/mol.  The MCM-HB model also shows that the HOMO is not associated with the Ado● centre (figure 4.13). Indeed the electron density of HOMO is found to be distributed on the cobalt centre. The MO associated with the unpaired electron on the Ado● is HOMO-1 and it has an RCC of 22%. In this case the SOMO-HOMO energy gap is just 15 kJ/mol, which indicates that the magnitude of the QCE is very small. Although the degree of orbital conversion that occurs in the MCM models is smaller than that in the GLM models, the pattern of behaviour is quite similar. This will be discussed in more detail in the following section. The MO plots of HOMO and HOMO-1 (SOMO) of MCM-HB model are given figure 4.13.     69    Figure 4.11 The active site of the MCM-PHB model with an illustration of its calculated electronic structure including the SOMO-HOMO energy gap and the absolute SOMO energy.   70    Figure 4.12 MO plots of high energy MOs in MCM-PHB model. The Ado● RCC values associated with each MO are given in parenthesis.  71     Figure 4.13 A) The active site of the GLM-HB model (model D) with an illustration of its calculated electronic structure. The SOMO-HOMO energy gap and the absolute SOMO energy are also shown. B) The plot of the HOMO. Electron density of HOMO is distributed over the cobalt centre and the corrin ring of B12 cofactor and no electron density is present on the radical centre in this MO (RCC=0%). C) The plot of the HOMO-1. Electron density of HOMO-1 is distributed over the radical centre, indicating that this MO is the SOMO (RCC=22%).   B C A 72  4.5.2 Analysis and Discussion  According to the calculated orbital configurations, the QCE is operating in MCM-PHB model. However, the magnitude of this QCE is much smaller in MCM-PHB than in both of the GLM models. This prompted us to seek an explanation for the differences based on the structures of the models. Only two residues (Glu370 and Glu247) in the QM layer of MCM enzyme are negatively or positively charged, in contrast to the GLM models in which several charged residues, and negatively charged substrate are present in the QM region (see the charged residues that were included in the QM region in table 4.1). As mentioned, in the MCM models the neutral lactoyl-CoA was used instead of the wild-type negatively charged substrate, which reduces the number of the charged groups in the active site. We were unable to test the impact associated with the use of the non-wild type substrate, but we suspect that the absence of the carboxylate would likely result in lower QCE.   Moreover, most of the charged residues in the GLM models are located near the Ado●. For instance, the positively charged Lys326, and the negatively charged substrate that are positioned only 4.7, and 4.9 Å away from the radical centre, respectively. In comparison, the distance between Glu247 and the radical centre in MCM models is much longer at approximately 7.0 Å. The position of the charged residues in MCM models are illustrated in figure 4.14, and these can be compared with the positions of the nearby charged residues in the GLM models (figure 4.8). The differences in the number and the position of the charged residues in the active site of MCM and GLM accompanied by the fact that the magnitude of the QCE differs significantly between these models suggest that the QCE is related to the strength of the electric field induced by the charges in the 73  active site (E ∝ q and 1/r2). Thus, it seems that the electric field is stronger in GLM, and this leads to a greater QCE in GLM.     Figure 4.14 Charged residues in the active sites of MCM-PHB (left) and MCM-HB (right). Key: red=oxygen, blue=nitrogen, grey=Carbon, white=hydrogen  74    Figure 4.15 The distribution of spin density on the Co• and Ado• in GLM-PHB and GLM-HB models. The Mulliken (Hirschfeld) atomic spin density on carbon-Ado• is 1.34 (0.71) in GLM-HB compared to 1.16 (0.73) in GLM-PHB. In the spin density plot of MCM-HB there is a small spin density on the carbon atom to be hydrogen abstracted, which shows that the MCM-HB model is near TS of hydrogen abstraction.  Besides the fact that the magnitude of the QCE defers significantly between the MCM and GLM models, both of the PHB models (GLM-PHB and MCM-PHB) demonstrated a larger QCE compared to their corresponding HB models. The major difference between the PHB and HB models is their hydrogen bonding interactions between the conserved glutamate residue and the Ado●, implying that the hydrogen bonding is controlling the magnitude of QCE. Recall that PHB models represent a stage in which the Ado● just dissociated from the cobalt prior to its migration toward the substrate, while in HB models the Ado● has migrated toward the substrate in an approach to the hydrogen atom abstraction transition state. Therefore, the QCE is large in the GLM and MCM models in which the Ado● is minimally hydrogen bonded and ready to migrate toward the substrate. After the migration, the Ado● is engaged in more hydrogen bonding and the 75  magnitude of the QCE is relatively low. The consequences that these results might have on enzyme’s efficiency and reactivity are discussed in the next chapter.   4.6 Summary  The possibility of the existence of the QCE and SOMO-HOMO orbital conversion in two B12 enzymes, MCM and GLM, was explored by hybrid QM/MM calculations. Calculations were performed to assess the sensitivity of orbital conversion to the size and overall charge of the QM part of the models employed. The results indicate that the general behaviour of the QCE does not change as the function of the size or the total charge of the system.  The largest models employed for the GLM and MCM enzymes included 643 and 507 atoms, respectively. The models were associated with two important stages of the B12 catalytic cycle: (i) the stage in which the Ado● is migrating toward the substrate (B in figure 4.3) (ii) the stage in which the Ado● is close to a position to abstract the intended hydrogen atom from the substrate (C in figure 4.3). It was found that in the models (labelled “PHB”) that correspond to the first stage (B in figure 4.3), the hydroxide groups of ribose ring of Ado● are partially hydrogen bonded to a conserved glutamate residue. In contrast, in the models (labelled “HB”) corresponding to the second stage (C in figure 4.3) the magnitude of the aforementioned hydrogen bonding is increased. The calculated electronic configurations of the PHB models demonstrate a significant degree of orbital conversion, whereas orbital conversion occurs to a far less degree or not at all in the HB models. The magnitude of the QCE, as demonstrated by the SOMO-HOMO energy gap, was larger for PHB models compared to HB models regardless of the nature of the enzyme system. These results suggest that the Ado●:Glu330 hydrogen bonding is reducing the QCE in HB models 76  compared to the PHB models. Therefore, QCE is operating at a higher level in stage (B) of the catalysis than at stage (C). The difference in the QCE has several consequences with regard to the Ado● reactivity, and this is discussed in details in the next chapter. We also found that the magnitude of the QCE is much more significant in GLM models compared to the MCM. This may be explained by the fact that the Ado● is surrounded by several charged residues in GLM enzyme, while in the MCM enzyme there are only two charged residues. Since the QCE is an electrostatic effect, we expect its magnitude is determined by the number and the proximity of the charged residues.  77  Chapter 5:  The Relationship between CEE/QCE and Radical Stability/Reactivity  5.1 Objective  It was seen in the previous chapter that quantum effects, as indicated by orbital conversion, are operating in both GLM and MCM. The magnitude of the quantum effects were found to be significantly smaller in the GLM-HB or MCM-HB models compared to the GLM-PHB or MCM-PHB. Since the two PHB and HB models describe different stages of the B12 enzymes catalytic cycle, it might be possible for these enzymes to utilize the quantum effects to control the reactivity of Ado●. This chapter is focused on developing more insights into how B12 enzymes might exploit quantum effects to exert tight control on the Ado● reactivity and contribute to the catalytic power. For this purpose, the protein structures of GLM and MCM enzymes are truncated to smaller models and these models are subjected to stability and reactivity computations by QM DFT approaches.     5.2 Methodology  5.2.1 Models description   The GLM and MCM enzyme models used previously to determine the QCE in protein structures were employed as starting models for the calculations in this chapter. These models were truncated to small systems containing 37 atoms, which were subjected to full QM calculations. For our first 78  set of computations the GLM-PHB and GLM-HB models were reduced without any modification to the structures to only the Ado● and the side chain of the conserved glutamate residue (Glu330). Similarly, the MCM-PHB and MCM-HB models were truncated to the Ado● and the glutamate side chain (Glu370). For the nomenclature purposes, we added an (s) at the end of the name of these models to distinguish them from the large enzyme models. The small model systems allow for a detailed analysis of QCE and CEE through full QM calculations based on DFT method. In order to validate the DFT results and verify the presence of the orbital conversion, high-level CASSCF calculations were performed on these systems and the results are reported in section 5.3.3. Since the results of the DFT calculations are in line with the CASSCF results, only the DFT approach is used for the rest of the calculations in this chapter.  Another set of models were prepared for the barrier height calculations associated with the hydrogen abstraction step. These models are similar to the small models described above, but the substrate is included. More information is given later in the chapter on how these models are used in the barrier height calculations.  5.3 QCE and Radical Reactivity  5.3.1 Orbital Configurations and Energies of Small GLM Enzyme Models  The orbital energy diagrams and the high energy level MOs that were acquired from the calculations on small GLM models are illustrated in figure 5.1 and figure 5.2. As can be seen from the MO plots in figure 5.1, the HOMO of the GLM-PHB(s) is not associated with the radical centre (RCC=0%) indicating the presence of the QCE. The MO with the highest RCC (33%) was found 79  to be HOMO-3, which also has electron density distributed over the ribose ring. The magnitude of the QCE in the GLM-PHB(s) model is 140 kJ/mol, based on the orbital energy difference between the HOMO and HOMO-3 (SOMO-HOMO energy gap). On the other hand, the orbital energy illustration of the GLM-HB(s) model shows that the QCE is not present in this system because the HOMO is the SOMO (figure 5.2). The RCC associated with the HOMO is 17%, which implies that the electron density is distributed on other parts of the molecule as well as the radical centre (see the MO plot of HOMO in figure 5.2). We note that this HOMO has the highest RCC value among the MOs illustrated in figure 5.2, with the next highest RCC value of 7% belonging to HOMO-2. The results obtained from the small model GLM calculations suggest that the QCE is stronger in PHB models than in the HB models. This is consistent with the results obtained for the complete enzyme models that were the subject of Chapter 4.      80    Figure 5.1 A) The structure of the GLM-PHB(s) model, illustration of the orbital energy diagram, SOMO-HOMO energy gap, and the absolute SOMO energy. MO plots for four highest energy α-MOs for B) HOMO C) HOMO-1 D) HOMO-2 E) HOMO-3. Isovalues of 0.1 were used for the MO plots. A B D C E 81     Figure 5.2  A) The structure of the GLM-HB(s) model, illustration of the orbital energy diagram, SOMO-HOMO energy gap, and the absolute SOMO energy. MO plots for four highest energy α-MOs for B) HOMO C) HOMO-1 D) HOMO-2 E) HOMO-3. Isovalues of 0.1 were used for the MO plots.  A B D C E 82          Figure 5.3  The DOS plots of the A) GLM-PHB and B) GLM-HB models. In the GLM-PHB model the MOs associated with the Glu residue are higher in energy than the SOMO, which is associated with the CH2 fragment. In the GLM-HB the SOMO is the highest energy level MO.   The MO composition and MO character in the small models were also analysed using density of state (DOS) plots (figure 5.3). The DOS plots provide a pictorial representation of the MO character in terms of chemical moiety as a function of MO energies. These plots make it possible to see which fragments contribute to a particular MO (see section 3.7 for more information). In the case of our model systems, the contribution of the CH2 (radical centre), Glu residue (side chain), and the rest of the Ado● to the MOs were examined. In the GLM-HB(s) model, the MO associated with the CH2 group in Ado● (SOMO) has the highest energy, while the other MO(s) associated with the Glu residue is lower in energy. In the GLM-PHB(s) DOS, the MO associated with the CH2 moiety is lower in energy than those associated with the Glu moiety. These results indicate that the orbital conversion does not simply reflect a stabilization of the SOMO but also the A B 83  destabilization of fully occupied orbitals, in particular those associated with the negatively-charged residue side chain.  5.3.2 Orbital Configurations and Energies of MCM Enzyme  Calculations were also performed on small models of the MCM enzyme. According to the energy diagrams and MO plots of MCM-PHB(s) model illustrated in figure 5.4, the SOMO is HOMO-3 and the SOMO-HOMO energy gap is 60 kJ/mol. The RCC values found are also consistent with the MO energy diagram: i.e. the RCC associated with the HOMO and HOMO-3 are 0% and 28%, respectively. In contrast, the SOMO is HOMO-1 in the MCM-HB(s) model and the SOMO-HOMO energy gap is much smaller at 20 kJ/mol. The RCC values and the MO plots for MCM-HB(s) are given in figure 5.5. Among these MOs the HOMO-1 has the largest RCC with 23%, and the next largest RCC belongs to HOMO-3 with only 2%.  In agreement with the MCM large protein models, these results imply that the QCE is larger in the PHB model compared to the HB model. This is despite the fact that both of our MCM models show a degree of QCE, which is not the case in both of the GLM models. We hypothesize that the stronger hydrogen bonding in the GLM-HB results in the complete mitigation of the QCE, while the relatively weaker hydrogen bond in MCM-HB results in the some small impacts due to QCE. Note that in GLM-HB model the Glu residue makes a hydrogen bond with both of the hydroxide groups of the Ado● compared to the MCM-HB in which only one of the hydroxides is engaged in hydrogen bonding. The DOS plots for the two models of MCM enzyme were also calculated and they are illustrated in figure 5.6.  Based on this figure, we suggest that the larger QCE in the PHB model leads to a 84  decrease in the SOMO energy and an increase in the Glu related MOs. These results are similar to the DOS plots of the GLM models discussed previously.    Figure 5.4 The structure of the MCM-PHB(s) model, illustration of the orbital energy diagram, SOMO-HOMO energy gap, and the absolute SOMO energy. MO plots for four highest energy α-MOs for B) HOMO C) HOMO-1 D) HOMO-2 E) HOMO-3. Isovalues of 0.1 were used for the MO plots. A B D C E 85    Figure 5.5  The structure of the MCM-HB(s) model, the orbital energy diagram, SOMO-HOMO energy gap, and the absolute SOMO energy. MO plots for four highest energy α-MOs for B) HOMO C) HOMO-1 D) HOMO-2 E) HOMO-3. Isovalues of 0.1 were used for the MO plots.  A B D C E 86           Figure 5.6  The DOS plots of the A) MCM-PHB and B) MCM-HB models. In the MCM-PHB model the MOs associated with Glu residue are higher in energy than the SOMO, which is associated with the CH2 fragment (SOMO-HOMO gap is 60 kJ/mol).  In the MCM-HB the MOs corresponding to the Glu residue is higher in energy than the SOMO (associated with CH2) but the difference between the two is reduced (SOMO-HOMO gap is 20 kJ/mol).   5.3.3 Verification of UM06-2X Electronic Structure Predictions In order to verify the electronic structures that was predicted from the single-referenced UM06-2X calculations on the small model systems of the enzyme active site, CASSCF calculations were performed on the GLM-PHB(s), GLM-HB(s), MCM-PHB(s), and MCM-HB(s) models. For our CASSCF computations, we included five highest energy occupied MOs to active space involving those related to the glutamate residue and the radical centre, and one unoccupied MO associated with the β counterpart of the α-SOMO. Therefore the active space of our CASSCF has nine electrons and six orbitals: The full calculation method can be summarized as CASSCF(9,6)/6-311+G(d,p). Some of the possible electronic configurations that can be occupied are given in figure A B 87  5.7. The contribution of these configurations to the total wave function is summarized in table 5.1. For these CASSCF calculations GAMESS 2017 program was used.109              Figure 5.7 Important electronic configurations that is possible from CASSCF(9,6) calculations.    88  Table 5.1 CASSCF(9.6)/6-311+G(d,p) results with the percentage of each of the configurations (CSFs) to the total wave function. The configuration numbers (config. no.) are referring to the configurations in figure 5.7. Configurations that are not reported in this table contribute a very small amount to the overall wave function.      According to the results summarized in the table 5.1, the electronic configuration predicted by the DFT calculations (see figures 5.1, 5.2, 5.3, and 5.4) is the configuration that contributes the most to the CASSCF wave functions. These results, consistent with previous studies, justifies that the use of the unrestricted DFT calculations with M06-2X functional for predicting the electronic structures.       89  5.3.4 Influence of H-bonds on QCE  It was shown above that the magnitude of the QCE in the PHB models is larger than that in the HB models for both enzymes studied. This finding is independent of the size of the model used for the calculations. The major difference between the HB and PHB models is the degree of Ado●:Glu hydrogen bonding, suggesting that this is the source of differences in the magnitude of the QCE.  In this section, the role of hydrogen bonding in mediating QCE was explored in GLM-HB(s) by rotating the –COO- moiety of Glu residue. For these calculations, we optimized the GLM-HB(s) geometry and performed single-point calculations at each rotation about the plane of the hydrogen bond. As can be seen in figure 5.8, at Φ=80o the hydrogen bond is largely broken and the QCE is at its highest. As the Glu is rotated towards Φ=180o and the hydrogen bond is reformed, the QCE diminishes. The appearance of the QCE when the hydrogen bond is lost is due to the stabilization of the SOMO and destabilization of the MOs that correspond to the Glu residue. This is in agreement with the DOS plots shown in the previous sections. All of these findings point to the fact that the magnitude of QCE in these systems is significantly influenced by hydrogen bond interactions between the Ado● and Glu. The hydrogen bond interactions result in a mixing of the orbitals of the glutamate and Ado●, which leads to the elimination of the orbital conversion. This suggests that B12 enzymes use Ado●:Glu hydrogen bonding to control the magnitude of the QCE.   90    Figure 5.8 Hydrogen bonding effects on orbital conversion in Ado●. The influence of disrupting the hydrogen bond between the Ado● and the Glu on QCE. At 0o and 180o the H-bonding is maximum and the SOMO is the orbital with the highest energy. When Glu330 is rotated by 60o or 80o, the QCE is present and the SOMO moves to lower energies while the Glu related MOs move to higher energies.   5.3.5 Difference between Radical Reactivity and Stability  Before discussing the consequences of the QCE on the reactivity of Ado●, it is worthwhile to distinguish between chemical reactivity and chemical stability. Throughout this thesis we use the term chemical reactivity, which refers to the tendency of a molecule to undergo a chemical 91  reaction, or the speed with which such reactions occur. Computationally, reactivity can be determined by calculating reaction barrier height and/or reaction rate constants. Chemical stability, on the other hand, is related to thermodynamics in the sense that it reflects the free energy difference between a particular chemical species and some other compound.  In the case of radicals, stability can be evaluated by RSE/RSFE in which the BDFE/BDE of the parent radical will be compared with BDE/BDFE of a reference system, such as methane (CH4).*                 *In some cases reactivity and stability are related to each other. For instance, in electron transfer reactions the rate of the electron transfer depends on both thermodynamic and kinetic factors. Marcus theory is a key example of this, which states that the rate of redox reactions increases with the reaction cell potentials (ΔEo) becomes more negative up to a certain point known as inverted region. After this critical point any increase in the ΔEo would lead to a slower reaction. Therefore, the thermodynamic factor ΔEo influences the rate of the reaction.110 Moreover, it has been also found that there is a correlation between the hydrogen BDE and the rate of hydrogen atom transfer in many radical systems.111–114  92  5.3.6 Barrier Height Calculations: Assessing Reactivity   In order to derive insights in to how the reactivity can be affected by the QCE, the barrier height of the hydrogen abstraction by Ado● was calculated using the small model systems of GLM. In order to obtain hydrogen abstraction TSs, the protonated version of the substrate for the wild-type GLM, L-threo-3-methylaspartic acid, was used in both the GLM-PHB(s) and GLM-HB(s) models. In the enzyme the substrate is normally deprotonated but the presence of two negative charges in our small reaction model would result in unrealistically large Coulombic repulsions. In the full enzyme, the presence of many residues including positively charged amino acid side-chains in the active site reduces the degree of Coulombic repulsion. Given that the purpose of the TS calculations is to compare the relative reactivity of Ado● in HB and PHB configurations, protonation of the substrate is a reasonable simplification.  For the barrier height calculations, the geometries of the Glu330, Ado● (except the ●CH2 group) were kept fixed and the coordinates of the substrate were relaxed. This constrained optimization was performed in order to keep the geometry of Ado● and Glu the same as in the full enzyme system. This reduces the uncertainties associated with the use of small model structures and it better represents Ado● in enzymes.  The conformational flexibility of the substrate makes it possible to obtain several TS structures for the PHB and HB models, and this may introduce another uncertainty on the barrier heights. To mitigate this uncertainty we chose TS structures in which the substrate had the same conformation in both of the HB and PHB models. Moreover, as the position of the Ado● (+Glu) relative to the substrate could differ in the TS structures, the TSs are selected in which both of the HB and PHB models had the same orientation relative to the substrate (see figure 5.9). Note that we are 93  interested in the relative reactivity of the two models, so choosing any of the TS structures would be sufficient for our purpose as long as they are similar. The energy barriers that were acquired from the QM calculations for the Ado● hydrogen abstraction are reported in figure 5.9. It was found that the barrier height for hydrogen abstraction in GLM-HB(s) model is 24.7 kJ/mol and 31.8 kJ/mol in the GLM-PHB(s) model. Therefore, the Ado●-Glu in HB model is more reactive than that in the PHB model by 7.1 kJ/mol. This translates into a difference in reaction rate constant of more than one order of magnitude.   Figure 5.9 Comparison between the reactivity of the HB and PHB models of GLM enzyme. The TS structures that are reported for both of the models are as similar as possible. The barrier heights given are based on electronic energies. RC=reactants, TS= transition state, PR=products 94  Analogous calculations were also performed on the small models of MCM. The substrate for the wild-type enzyme, methylmalonyl-CoA, which was truncated to reduce its size was included in the MCM-PHB(s), MCM-HB(s) models. In these cases, the CoA tail is capped after the carbon atom next to the sulfur atom. Constrained hydrogen abstraction TS optimizations were performed on these structures by relaxing the coordinates of the substrate, and freezing the geometries of Ado● (except the ●CH2 group) and Glu residue. The negatively-charged substrate was protonated to eliminate the Coulombic repulsion between the Ado● and the Glu residue and TS structures are chosen that were similar in both HB and PHB models (figure 5.10). The barrier heights that were obtained from these calculations are similar to those for GLM enzyme: The reactivity of Ado●-Glu is 15.3 kJ/mol for MCM-HB(s) compared to 27.0 kJ/mol for MCM-PHB(s), a difference that corresponds to almost three orders of magnitude in rate constant.  The barrier heights that were acquired from the calculations on the PHB model systems for both enzyme systems support the hypothesis that at the early stages of the catalysis when Ado● is first formed, the reactivity of the radical is lowered to prevent aberrant side reactions. Likewise, the calculated barrier heights associated with the HB models align with the notion that the reactivity of Ado● must be relatively higher in order to effectively abstract the target hydrogen atom. We will see in the next section, the stability of the HB and PHB models are approximately the same, so the thermodynamic factors cannot be the major reason for the observed barrier height difference between the models.  It was demonstrated earlier in the thesis that the calculated magnitude of the QCE is smaller in all HB models relative to their analogous PHB models. This suggests that the reactivity of Ado● can be related to the magnitude of the QCE, which supports our hypothesis that the B12 enzymes employ QCE to control the reactivity of the Ado● radical. When the magnitude of QCE is large, 95  the reactivity of Ado● is lowered, but when the enzyme decreases the magnitude of the QCE by increasing the hydrogen bonding interactions, the reactivity of Ado● restores a higher level or reactivity.  A remaining question is how the magnitude of QCE is related to the Ado● reactivity. This question will be addressed in the next section using the frontier molecular orbital (FMO) theory.     Figure 5.10 Comparison between the reactivity of the HB and PHB models of MCM enzyme. The TS structures for both of the models are calculated to be as similar as possible. The barrier heights given are based on electronic energies. RC=reactants, TS=transition state, PR=products   96  5.3.7 FMO Theory  5.3.7.1 Analysis of the Barrier Height Energies Based on FMO Theory  Pioneered by Kenichi Fukui,  FMO theory can be used to predict the reactivity and selectivity of many organic compounds based on interactions involving their frontier (highest occupied/lowest unoccupied) orbitals .115,116 FMO theory generally focuses on the LUMO and HOMO interactions, since they are the most likely to participate in chemical reactions. However, in the case of radicals reacting with closed-shell systems, as in the case of the reactions focussed on in this thesis, SOMO-LUMO and SOMO-HOMO interactions are most likely to be involved in chemical reactivity. The substrates in the B12 enzymes studied, specifically the C-H groups where hydrogen atom abstraction occurs, are electrophilic. This means that the SOMO of Ado● (C p-orbital) will interact with σ* orbital of the C-H group on the substrate in the transition state.  Figure 5.11 is a simple schematic illustrating the interaction between the SOMO of the Ado● and the substrate C-H σ* orbital. As can be seen in this figure, a higher energy Ado● SOMO can interact more strongly with the substrate C-H σ* orbital compared to a lower energy SOMO. Our calculations in all cases show that the PHB models of both enzymes have lower energy SOMOs compared to the SOMOs in the HB models, as a consequence of enhanced QCE in the former structures. Consequently, FMO predicts that the barrier heights of hydrogen abstraction in PHB models will be higher than those associated with the HB models, in agreement with the result of the barrier height calculations.   97    Figure 5.11 Simple MO energy diagram illustrating the interaction between the Ado● SOMO in both models (HB and PHB) and the substrate C-H σ*. There is a more favourable interaction between the SOMO of the HB model and the substrate C-H σ*, compared to the interaction between the SOMO and the substrate C-H σ* in PHB model because the energy gap (ΔE) between Ado● SOMO and C-H σ* is smaller in HB model compared to PHB model (ΔE2 > ΔE1) This favourable interaction reduces the barrier energy for hydrogen abstraction in HB models.   5.4 Radical Stability and CEE  5.4.1 Stability Calculations in GLM and MCM Enzymes  As mentioned in the previous chapters, the thermodynamic stabilization caused by CEE is accompanied by the QCE in distonic anion radicals. In order to see if the CEE present in our systems, the stability of the small PHB and HB models in both enzymes were explored by calculating RSEs. These RSE values were determined by comparing their calculated bond dissociation energies (BDE´) with those of the corresponding Ado●-only system: 98                                    𝑅𝑆𝐸 (𝐻𝐵 𝑚𝑜𝑑𝑒𝑙) = 𝐵𝐷𝐸´𝐴𝑑𝑜−𝐻𝐵 −  𝐵𝐷𝐸´𝑒𝑛𝑧𝑦𝑚𝑒−𝐻𝐵(𝑠)                            (5.1)                                  𝑅𝑆𝐸 (𝑃𝐻𝐵 𝑚𝑜𝑑𝑒𝑙) = 𝐵𝐷𝐸´𝐴𝑑𝑜−𝑃𝐻𝐵 −  𝐵𝐷𝐸´𝑒𝑛𝑧𝑦𝑚𝑒−𝑃𝐻𝐵(𝑠)                         (5.2)  The Ado-HB/PHB system is the same molecule as enzyme-HB(s)/PHB(s), but with the Glu residue removed.  The RSE value calculated for the HB model of GLM is 2.7 kJ/mol and is 2.2 kJ/mol for the corresponding PHB model. The results obtained may seem surprising at first because the QCE is present in only the PHB model and thus one might expect that only this system would be stabilized. However, as mentioned earlier, although there is a connection between the QCE and CEE, the QCE is not necessarily accompanied by CEE. Analogously the stabilization in distonic ion radicals could occur without the presence of QCE as we saw in the case when the negatively charged fragment of TEMPO-COO- is replaced by an orbital-less negative charge (see Chapter two).  Consistently here in both of the HB and PHB models, regardless of the presence of the QCE, the CEE emanating from the negative charge stabilizes the Ado●. Also, replacing the Glu residue with a negative point charge eliminates the QCE, but the CEE is still present. This is shown in figure 5.12. These results again verify the fact that the CEE and QCE are two distinct effects and indeed the CEE is classical in contrast to QCE, which is quantum effect. Furthermore, it appears that the hydrogen bonding in GLM-HB model only quenches the QCE, but it does not have a same effect on CEE. In the next section the hydrogen bonding effect on CEE will be discussed.  The same stability calculations were also performed for the MCM small model systems using the equations 5.1 and 5.2. The RSE values that were obtained from the calculations, similar to the 99  GLM RSEs, demonstrate that CEE is present in both MCM models. The RSE value for the MCM-PHB(s) and MCM-HB(s) is 2.1 kJ/mol and 2.5 kJ/mol, respectively. Approximately the same RSE values in the MCM models provide additional evidence that the QCE and CEE are related, but distinct effects.     Figure 5.12 Illustration of the MO energy diagram of GLM-PHB(s) model (left), and when the Glu residue is replaced with a negative point charge (right). In the right diagram the SOMO is the HOMO-3 and QCE is present in contrast to the left diagram in which the SOMO is the HOMO and QCE is disappeared. However, the RSE value of this system is calculated to be 1.6 kJ/mol suggesting that the CEE is still present.    5.4.2 Influence of H-bonds on CEE  The influence of the hydrogen bonding on the magnitude of the CEE in Ado● was investigated by calculating the RSEs for several systems. For this effort, the GLM-HB(s) model was chosen as the 100  reference system, however the coordinates were relaxed to fully optimize the geometry. In order to increase the magnitude of hydrogen bonding, we added one, two and three explicit water molecules around the GLM-HB(s) model and performed geometry optimization. The structures of these systems and their associated RSEs are given in Figure 5.13 as a function of the number of explicit water molecules added. As can be seen from this plot, the increase in the amount of hydrogen bonding is accompanied by the incremental decrease in the calculated RSEs. In the limiting case of bulk-water solvation, the RSE value becomes negative which implies that the CEE is a destabilizing effect in full water solvation. This is consistent with previous experimental observations and QM calculations that show that hydrogen bonding solvents can completely mitigate CEE. The effect of hydrogen bonding on CEE appears to be less significant than on QCE, as more hydrogen bonds are required to attenuate the CEE to a negligible magnitude, whereas for QCE the hydrogen bonding in HB models is sufficient to reduce the magnitude of QCE significantly as can be seen from comparing small HB and PHB models.   101     Figure 5.13 The effect of hydrogen bonding on the stability of Ado● and CEE. Increasing the number of hydrogen bonds by explicit water molecules (W) drops the RSFE values. With inclusion of a bulk solvation 102  model (SMD) the RSE falls below the reference line implying the disappearance of CEE entirely. *The RSE given here for HB model is not the same as the 2.7 kJ/mol reported before in section 5.4.1 for the same system. This difference is because of the geometry optimization performed for these calculations. **Radical stabilization free energies.  5.4.3 How CEE Can Contribute to the Catalytic Power of B12 Enzymes?  According to the calculated RSEs of our small model systems, CEE is present in both HB and PHB models with approximately the same magnitude. This implies that the glutamate residue is stabilizing the Ado● to a small extent over its course toward the substrate. Therefore, the CEE can be regarded as one of the factors that lowers the Co-C bond scission by stabilizing Ado● and thereby contributes to the catalytic power of the B12 enzymes. In fact, CEE provides a way to stabilize a non-polar Ado● radical through electrostatic effects and also it explains how radical enzymes can exploit electrostatic effects during the course of an enzymatic radical reaction in which the change in charge distribution is not significant compared to reactions from which charged species are formed. Although the magnitude of the CEE in Ado● is not very large based on our small models, we expect it to increase in the actual enzyme system as there are more charged residues located near the Ado● (particularly in GLM enzyme).      5.5 Summary  The stability and reactivity of the Ado● at different stages of migration toward substrate was assessed computationally on small PHB and HB models of GLM and MCM. The barrier height calculations suggest that the presence of QCE in PHB model reduces the Ado● reactivity. The 103  reactivity of Ado● increases however when the QCE is reduced as a consequence of increased hydrogen bonding between glutamate and the Ado● when the radical is near the substrate. These findings support the hypothesis that QCE may be used by the enzyme to control the reactivity of Ado● at different stages of the Ado● migration toward the substrate.  The stability of Ado● was also evaluated in this chapter. The RSEs were calculated for both HB and PHB models, and showed that both of the HB and PHB models are stabilized by approximately a same amount despite the fact that their reactivity is very different. The results were understood on the basis that the RSE is caused by the CEE, which arises from the classical effects, but the reactivity mainly depends on the QCE. The magnitude of the CEE also has been found to be related to the hydrogen bonding; however, the influence of the hydrogen bonding appears to be less significant compared to QCE. It should be mentioned that this conclusion is drawn based on the small HB and PHB models, as we have not evaluated the CEE in the enzyme systems.           104  Chapter 6: Conclusions   6.1 A Complete Picture of How QCE and CEE Generate and Control Highly Reactive Species in B12 Enzymes  Based on the small model calculations performed as part of this thesis, it is clear that both the QCE and CEE play a significant role in controlling the reactivity and stabilizing the Ado● in two of the vitamin B12-dependent enzymes. In the first step of the catalytic cycle of B12 enzymes, the Co-C(Ado) bond breaks and Ado● is generated. This process requires approximately 130 kJ/mol in aqueous solution. However, the enzyme environment reduces this BDFE to 70 kJ/mol. The mechanism by which B12 enzymes accomplish this BDFE lowering has been the subject of debate. In this connection, Warshel’s “Electrostatic” proposal is the most widely accepted proposal. In one study on MCM, it was shown through theoretical calculations that the reduction in the BDFE is due to the electric field exerted by the charged residues in this B12 enzyme (see Chapter one). In support of this study our calculations on small model systems demonstrated that a CEE caused by the interaction between the glutamate residue and the Ado● stabilizes the radical centre to a small extent, which can contribute to the Co-C(Ado) bond dissociation. Although the magnitude of the CEE in these small systems ranges from 2.1 to 2.7 kJ/mol, the previous study by Warshel et. al suggests that the contribution of the classical Coulombic interactions increase to a more appreciable amount when the whole enzyme with all residues are considered. Thus we speculate that using a larger model increases the CEE magnitude. Further, the CEE provides an electrostatic means to facilitate the Co-C homolytic cleavage, where the change in charge distribution is not as much as when the bond is broken heterolytically.   105  It has been shown that this CEE is associated with a phenomenon known as SOMO-HOMO orbital conversion, which is a consequence of the QCE. Therefore the orbital conversion not only indicates that QCE is active, but also it signals the potential presence of the CEE. However, the orbital conversion and the QCE can be modulated by Ado●:Glu hydrogen bonding, while the CEE is still present. For instance, in the HB model of the GLM enzyme it was found that the orbital conversion is quenched by the strong Ado●:Glu hydrogen bonding, but this interaction does not change the CEE significantly. This weak influence of the Ado●:Glu hydrogen bond on CEE has two main advantages for the enzyme catalysis: (i) it ensures that the CEE is present and stabilizes the Ado● over the whole catalytic cycle, and (ii) it reduces the rate of reformation of the Co-C(Ado) bond.   In the second step of the catalytic cycle, the generated Ado● must migrate toward the substrate in order to engage in hydrogen atom abstraction. It is during this migration that the reactivity of Ado● must be controlled in order to prevent the erroneous side reactions that can disrupt the catalytic cycle and/or damage the enzyme’s interior. The results of the calculations presented in this thesis suggest that the magnitude of the QCE is related to the reactivity of the Ado●. At the beginning of the Ado● migration, immediately after the Co-C bond scission, the magnitude of the QCE is large and this lowers the energy of the SOMO. The low energy SOMO interacts less effectively with the C-H σ* MO of the substrate, resulting in lower Ado● reactivity. When the Ado● is closer to the intended substrate and in position to abstract the correct hydrogen atom, the magnitude of the QCE decreases. The decrease in the QCE is caused by increases in the degree of hydrogen bonding between the nearby glutamate and the Ado● and results in an increase in the energy of the SOMO. The higher energy SOMO can overlap more effectively with the substrate C-H σ* LUMO by 106  taking advantage of the high reactivity of the primary Ado●, and this decreases the barrier height associated with hydrogen atom abstraction.  The magnitude of the QCE is significantly influenced by the Ado●:Glu hydrogen bonding. The stronger the hydrogen bond, the weaker the QCE. This gives the enzyme the ability to manipulate the reactivity (or the QCE) of the Ado● at different stages of the catalytic cycle by simply controlling the magnitude of Ado●:Glu hydrogen bond in order to improve target selectivity in hydrogen atom abstraction reactions. Figure 6.1 illustrates a model that summarizes what the calculations suggest is happening in the B12 enzyme systems in terms of stabilizing and controlling the Ado● species.                 107     Figure 6.1 A model outlining the role of CEE and QCE at different stages of the B12-enzymes catalytic cycle. At stage A the Ado● is bound to the cobalt and CEE and QCE are not present. Stage B shows the Ado● after the Co-C bond dissociation, but before its migration toward the substrate. At this stage the CEE is active, and thus the radical centre is stabilized. Since the Ado:Glu hydrogen bonding is minimum, the QCE is also turned on, which reduces the ability of the Ado● to abstract hydrogen atoms.  At stage C the Ado● has migrated to the substrate. The reactivity of Ado● is restored at this stage by increasing the strength of the Ado:Glu hydrogen bonding, which in turn reduces the QCE and increases the energy level of the Ado● SOMO. Consequently the ability of the hydrogen abstraction increases due to the better orbital overlap between the Ado●’s SOMO and the σ* LUMO.  Stage A Stage B Stage C 108  6.2 Conclusions and Future Directions  The quantum Coulombic effect, which manifests through orbital conversion, appears to be a remarkable phenomenon that might be exploited by B12 enzymes to control and manipulate the reactivity of Ado●. The characteristics of QCE are such that it gives the B12 enzymes the ability to control the reactivity Ado● simply by changing the hydrogen bonding between Ado● and a nearby conserved glutamate residue. The work presented here shows for the first time that the electrostatics not only play a critical role in catalytic power of enzymes, but also demonstrates they can be responsible for controlling the reactivity of radical intermediates and preventing the enzyme from being damaged by deleterious side reactions.  We also provided evidence in support of the contribution of classical electrostatic effects in B12-enzymes’s catalytic power. Consistent with previous studies, classical Coulombic effects were also found to stabilize Ado●, and so this can be a factor in facilitating the dissociation of the Co-C(Ado) bond, which results in the easier formation of Ado● (lowers the BDFE).   At this stage, we cannot say that this effect is also present in other radical enzymes. More studies are required in order to elucidate the full scope of the role of QCE in B12 enzymes, and the potential for QCE to be active in other radical enzymes, such as RNR and SAM-dependent enzymes. 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