Computational Modeling of Catalytic Mechanisms of Glycyl Radical Enzymes

Computational Modeling of Catalytic Mechanisms of Glycyl Radical Enzymes Dissertation zur Erlangung der Doktorw¨urde der Fakult¨at f¨ur Biologie, Chemie und Geowissenschaften der Universit¨at Bayreuth vorgelegt von Mikolaj Feliks January 29, 2014 2 This doctoral thesis was prepared at the University of Bayreuth between March 2009 until June 2013, supervised by Prof. Dr. G. Matthias Ullmann. This is a full reprint of the dissertation submitted to obtain the academic degree of Doctor of Natural Sciences (Dr. rer. nat.) and approved by the Faculty of Biology, Chemistry and Geosciences of the University of Bayreuth. Acting dean: Prof. Dr. Rhett Kempe Date of submission: 03.07.2013 Date of defence (disputation): 09.01.2014 Doctoral committee: Prof. Dr. G. Matthias Ullmann 1st reviewer: Prof. Dr. G. Matthias Ullmann Prof. Dr. Franz Xavier Schmid 2nd reviewer: Prof. Dr. Holger Dobbek Prof. Dr. J¨urgen Senker Chairman: Prof. Dr. Rainer Schobert Prof. Dr. Rainer Schobert 3 I would like to express my gratitude to people without whom this thesis would not have been possible: • Prof. Dr. G. Matthias Ullmann (supervisor) for guidance, constructive advice and constant support • Dr. Berta Martins for disclosing unpublished experimental results and many valuable discussions •Dr. Martin J. Field for the pDynamo software library • Prof. Dr. W. Andrzej Sokalski for introducing me into the quite exciting field of computational chemistry •Colleagues from the Computational Biochemistry Group, in particular Lars M¨uller and Timm Essigke, for creating a friendly and supportive work environment • Friends from the Welcome Center of the Univeristy of Bayreuth for the great time spent together exploring Oberfranken • My parents Maria and Jerzy Feliks for their continuous support throughout my student years 4 Contents Abstract 5 List of Abbreviations 7 1 Introduction 8 2 Computer simulations of enzyme catalysis 11 2.1 The principles of enzymatic catalysis 12 2.2 Computational methods 13 2.3 Three approaches to the modeling of enzymatic catalysis 17 3 The chemistry of radical enzymes from anaerobic bacteria 21 3.1 Vitamin B12-dependent enzymes 23 3.2 S-adenosylmethionine radical enzymes 24 3.3 Glycyl radical enzymes 25 4 Synopsis of published and submitted manuscripts 33 4.1 Cleavage of the C−O bond in glycerol 33 4.2 Cleavage of the C−C bond in 4-hydroxyphenylacetate 35 4.3 Cleavage of the C−C bond in pyruvate 36 4.4 List of published and submitted manuscripts 37 Bibliography 39 Manuscript A 49 Manuscript B 50 Manuscript C 51 Manuscript D 52 Appendix: Python QC/MM scripts 76 5 Abstract In this thesis, different computational methods have been used to study the catalytic mechanisms of three glycyl radical enzymes. The mechanism of the B12 -independent glycerol dehydratase has been elucidated by combining continuum electrostatic and density functional theory calculations. A mechanism for the dehydration of glycerol is proposed that does not involve a complex intramolecular 1 → 2 shift of the middle hydroxyl group, as previously suggested. Instead, the enzyme uses a pair of residues in the active site, glutamate and histidine, to facilate direct release of a water molecule from glycerol. The mechanism of 4-hydroxyphenylacetate decarboxylase has been explored based on continuum electrostatic and hybrid quantum chemical/molecular mechanical calculations. The calculations suggest that the substrate is activated to a radical form by two simultaneous transfers, one of an electron to the thiyl radical and second of a proton to the active site glutamate. This activation mode has not been reported for any known radical enzyme. The mechanism of pyruvate formate-lyase has been investigated based for the first time on the complete enzyme model. The key new finding is that quenching of the formyl radical is performed by one of the active site cysteines and not by coenzyme A, as previously suggested. Zusammenfassung In der vorliegenden Arbeit werden unterschiedliche Berechnungsmethoden angewendet, um die katalytischen Mechanismen von drei Glycyl-Radikalenzyme zu untersuchen. Der Mechanismus der B12 -unabh¨angigen Glyceroldehydratase wurde mit Hilfe von Kontinuumselektrostatikund Quantenchemierechnungen untersucht. Der vorgeschlagene Dehydratisierungsmechanismus ben¨otigt nicht die komplexe 1 → 2 Migration der mittleren Hydroxyl-Gruppe des Glycerins. Die Dehydratisierung des Glycerins involvierte einige Reste im aktiven Zentrum des Enzyms, im speziellen ein Glutamat und ein Histidin. Der Mechanismus der 4-Hydroxyphenylacetat-Decarboxylase wurde mit Hilfe von Kontinuumselektrostatik und Quantenchemischen/Molek¨ulmechanischen Rechnungen untersucht. Die Berechnungen zeigen, dass das Substrat zu einer radikalen Form durch zwei gleichzeitige Transfers aktiviert wird. Zum einen wird ein Elektron zum Thiylradikal transferiert und zum anderen ein Proton zu einem Glutamat im aktiven Zentrum. Dieser Aktivierungs- 6 mechanismus wurde bisher in keinem anderen Radikalenzym beobachtet. Der Mechanismus der Pyruvat-Formiat-Lyase wurde zum ersten Mal mit einem kompletten Enzymsmodell untersucht. Die wichtigste neue Erkenntnis ist, dass die Deaktivierung des FormylIntermediats nicht durch Koenzym A durchgef¨uhrt wird, sondern durch ein Cystein im aktiven Zentrum. 7 List of Abbreviations 4Hpad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-Hydroxyphenylacetate decarboxylase ARNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Anaerobic (class III) ribonucleotide reductase BDE .........................................................Bond dissociation energy BSS ..........................................................Benzylsuccinate synthase CTL .....................................................Choline trimethylamine-lyase DFT .........................................................Density functional theory EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron paramagnetic resonance spectroscopy GDH ..............................................B12-dependent glycerol dehydratase iGDH ............................................B12-independent glycerol dehydratase GRE ............................................................Glycyl radical enzyme NMR ......................................................Nuclear magnetic resonance NEB .....................................................Nudged elastic band method PBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Poisson-Boltzmann electrostatics PES ...........................................................Potential energy surface PFL ...........................................................Pyruvate formate-lyase QC/MM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Quantum chemistry/molecular mechanics SAM ............................................................S-adenosylmethionine TMA ..................................................................Trimethylamine TST ...........................................................Transition state theory 8Introduction 1 Introduction Radical enzymes have been recognized as extremely robust catalysts in many biological systems. 1–4 These enzymes use the high reactivity of radicals to initiate reactions of practically nonreactive compounds. The ability of radical enzymes to catalyze chemically demanding reactions is particularly interesting for industry due to their potential use in organic synthesis. 5,6 Over the years, considerable efforts have been made to understand at the molecular level the intriguing chemistry of radical enzymes. 7,8 However, many aspects of the radical-based catalysis still remain unknown because the reactions catalyzed by radical enzymes involve unstable, short-lived intermediates that are difficult to study experimentally. On the other hand, the methods of computational chemistry for studying enzymatic reactions have in the past decade evolved to a degree that they can compete with experiments offering reasonable accuracy and reliability. 9–12 These methods provide insights into the intrinsic chemistry of the catalyzed reaction that are beyond the scope of most experimental techniques, for example the determination of transition states on the reaction path. It is in this context that I employ electrostatic, 13–15 quantum chemical, 16–18 and combined quantum chemical/molecular mechanical calculations 19–22 to study the catalytic mechanisms of three glycyl radical enzymes, 23,24 namely the B12 -independent glycerol dehydratase (iGDH), 4-hydroxyphenylacetate decarboxylase (4Hpad) and pyruvate formatelyase (PFL). The mechanisms of the former two enzymes have not been studied before experimentally nor computationally. My calculations show that both iGDH and 4Hpad adopt catalytic mechanisms that are without precedence among the radical enzymes discovered to date. Although the mechanism of PFL is thought to be well understood, the performed calculations are able to explain some of the still confusing aspects of the catalyzed reaction. The B12 -independent glycerol dehydratase is a novel glycyl radical enzyme catalyzing the conversion of glycerol into 3-hydroxylpropionaldehyde. 25,26 The previously suggested reaction mechanism assumed that the dehydration of glycerol is accomplished by an intramolecular 1 → 2 shift of the middle hydroxyl group, as seen in the catalysis by B12 - dependent enzymes. The shift was postulated to involve a cyclic transition state and result in a 1,2-diol intermediate that spontaneously releases a water molecule. 26–28 However, the electrostatic and density functional theory calculations suggest that the mechanistically Introduction 9 complicated migration of the middle hydroxyl group can be avoided 29 (Manuscript A). One of the histidine residues in the active site of iGDH donates a proton to the leaving hydroxyl group, which leads to the immediate formation of a water molecule. The release of water is coupled to a proton transfer from one of the terminal hydroxyl groups of glycerol to glutamate in the active site, which generates a C=O double bond of the future product. Despite many structural similarities between the active sites of iGDH and its B12 -dependent counterpart, 30,31 GDH, these enzymes seem to adopt totally different catalytic mechanisms for the dehydration of glycerol. 32–34 The key histidine residue, whose protonation state seems to determine the reaction route taken by the enzyme, is doubly-protonated in iGDH and singly-protonated in GDH. The unexpected catalytic mechanism of iGDH derived from the calculations is one of the highlights of the present thesis. 4-hydroxyphenylacetate decarboxylase catalyzes the production of p-cresol from its substrate. 35,36 The electrostatic and hybrid quantum chemical/molecular mechanical calculations performed on the full-enzyme model of 4Hpad reveal a catalytic mechanism that involves an unusual activation mode of the substrate, which has not been described for any of the known radical enzymes (Manuscripts B and C). Usually, the substrate in radical enzymes is activated to a radical form by abstraction of a hydrogen atom by transient radical species in the active site, such as the thiyl radical. The calculations indicate, however, that the activation of 4-hydroxyphenylacetate is accomplished by two simultaneous transfers from the substrate, first of an electron to the radical cysteine and second of the phenolic proton to the active site glutamate. The substrate is therefore activated by the netto abstraction of a hydrogen atom. The exceptional separation of proton and electron during the substrate activation by 4Hpad as suggested by the calculations is another highlight of this thesis. Pyruvate formate-lyase was the first glycyl radical enzyme to be discovered and its mechanism of action has been extensively studied since then. 37,38 The calculations done for the first time on the complete enzyme model attempt to answer the questions regarding some of the unrevealed mechanistic aspects of the PFL-catalyzed reaction (Manuscript D). One of the new findings is that the reaction proceeds through a stable protein-bound tetrahedral intermediate formed by pyruvate and the radical cysteine in the active site. Moreover, the calculations indicate that another active site cysteine is responsible for quenching of the formyl radical. It is therefore quite likely that the release of formate 16 Computer simulations of enzyme catalysis to the charge density and dielectric constant. The system of interest is described starting from the available crystal structure. A set of partial atomic charges, usually taken from the force field, is used to calculate the charge distribution ρprotein ( ~r ). Mobile ions outside the protein are assumed to adopt a Boltzmann distribution. Different dielectric constants are assigned to the protein (usually  =4) and the outer medium (  =80 for aqueous solution) to account for the lower polarizability of protein environment. The electrostatic potential φ(~r) can be calculated from the linearised Poisson-Boltzmann equation: ~ ∇h(~r)~ ∇φ(~r)i=1 0"ρprotein(~r) + I X iciz2 ie2 RT φ(~r)#(5) where ci is the concentration of ions of type i, zi is the formal charge of an ion, e is the elementary charge, R is the universal gas constant and T is the temperature. The summation is performed for I different types of ions. 72,73 Because of its complexity, the Poisson-Boltzmann equation is usually solved by using numerical methods that map the protein model onto a cubic lattice, for example the finite difference method. For a protein with N titratable sites, there can be 2 N different protonation states. On top of the previously calculated electrostatic potential, the energy G(n) of state n in the function of pH can be evaluated as: G(n)(pH) = N X i (x(n) i−x(0) i)(pH −pKintr i) +1 2 N X i N X j (x(n) i−x(0) i)(x(n) j−x(0) j)Wi,j (6) where x(n) i and x(0) i are the state vectors representing the present and the reference macroscopic protonation state, respectively, collecting the microscopic protonation states of individual sites, p Kintr i is the intrinsic p K of site i and Wi,j is the interaction energy between two sites. For most proteins, the calculation of all protonation states is not possible because 2 N can be a very large number. Instead, the protonation state energies can be sampled by using the Metropolis Monte Carlo method.70, 74 Computer simulations of enzyme catalysis 17 2.3 Three approaches to the modeling of enzymatic catalysis Theoretical modeling of an enzyme-catalyzed reaction mechanism can in general be accomplished at one of the three levels of approximation, i.e. increasing complexity. Small-molecule approach The first option is to focus on a small-molecule model of isolated reactants in the gas-phase, neglecting the remaining parts of the enzyme. 42 Obviously, a gas-phase model cannot account for the actual enzymatic mechanism, because it does not include the catalytic effects that arise from the protein environment. These effects can be steric, electrostatic and of different nature. However, calculations on small models allow to investigate the intrinsic chemistry of the catalyzed reaction with accurate methods and at relatively low computational cost. These calculations can serve as a reference for the studies on larger and more realistic models. Because of the limited computing power in the past, calculations on gas-phase models were the first available method for studying enzymatic systems. Some of the radical enzymes have been investigated computationally by using the small-molecule approach, for example pyruvate formate-lyase 75,76 or the enzymes from the B12-dependent family.8 Cluster model approach To better reproduce the behavior of the actual enzymatic system, the model can be extended by inclusion of additional, nonreactive parts of the active site. In the cluster model approach, 16–18,77, 78 a model is constructed based on the crystal structure of the enzyme by selecting a discreet number of atoms from the residues that make up the active site. If only a structure of the substrate-free form of the enzyme is available, molecular docking can be used to position the substrate in the active site. 79 In addition to the intrinsic chemistry of the catalyzed reaction, a cluster model also tries to capture the effect of surrounding residues on the reacting region. Since a truncated enzyme model is used, two procedures are employed to account for the missing outer parts of the enzyme. To compensate for the lack of steric effects, selected atoms are kept constrained at their crystallographic positions during the geometry optimizations. The selection of fixed atoms often requires a large number of calculations with different sets of constraints until a 18 Computer simulations of enzyme catalysis model is found that can keep the integrity of the initial active site during the geometry optimizations in vacuum. Errors that arise due to the coordinate-locking procedure, for example an increased strain of the model, can be avoided by shifting the constrained atoms further away from the reacting center. To simulate the electrostatic polarization effects exerted by the protein surrounding on the cluster, dielectric cavity techniques can be used, for example the polarizable-like continuum model 80,81 (PCM). The missing outer parts of the enzyme are mimicked by a homogeneous medium with a dielectric constant usually set to  =4. For large cluster models, the solvation effects usually saturate, i.e. with an increasing size of the model the choice of the dielectric constant becomes less critical.82 The cluster model approach has been demonstrated very successful in studies on different enzymes. Cluster models are easiest to setup for systems like metalloenzymes where the chemistry at the active site is dominated by strong electrostatic interactions due to the presence of the central metal ion. In such cases, further located parts of the enzyme are quite unimportant for the catalyzed reaction and the use of a small cluster model is usually sufficient for proper description of the enzymatic system. Full-enzyme (QC/MM) approach Although the performance of the cluster model approach is sufficient for the identification of key features of the catalytic mechanism, it may sometimes be necessary to include additional parts of the enzyme into the model. However, the use of a full-enzyme model requires that the system is partitioned into two parts, the reacting one described quantum chemically and the non-reacting one that can be handled at a simpler molecular mechanical level. That is because the size of a complete enzyme model, which usually exceeds thousands of atoms, would be prohibitive for pure quantum chemical treatment. Given the present computer speed and the available theoretical methods, a model of ∼ 300 atoms is the maximum that can be studied in a reasonable time using density functional theory. For more sophisticated ab inito quantum chemical methods, the maximum available size of the model is usually far less than 100 atoms. On the other hand, force fields such as Amber or CHARMM have been well-parametrized for studying proteins. 62,63 These force fields are known to reproduce ground-state geometries of proteins more accurately than semi-empirical methods of quantum chemistry.83 In the hybrid quantum chemical/molecular mechanical approach, 19–22,84 a model of Computer simulations of enzyme catalysis 19 the enzyme is constructed, usually on top of the available crystal structure, by dividing the system (S) into two parts. The inner part (I) consists of the reacting region and is treated at a quantum chemical level. The outer part (O), which encompasses the rest of the enzyme, is treated at a molecular mechanics level. The QC/MM concept was first introduced in 1976 by Warshel and Levitt 85 but the method has only become popular in the last years. Fig. 2 shows the principle of the QC/MM method. Due to the strong interactions between the inner (QC) and the outer (MM) regions, the total energy of the system cannot be written as a simple sum of the energies of the subsystems. To account for these interactions, coupling terms are introduced. Two different energy partitioning schemes have been developed within the QC/MM framework, namely the subtractive 86 (ONIOM) and additive scheme. For the calculations described in this thesis, the additive scheme was always used. The additive scheme takes the following form: Eadd QC/MM(S) = EMM(O) + EQC(I + L) + EQC−MM(I,O) (7) where Eadd QC/MM ( S ) is the total energy of the system, EMM ( O ) is the energy of the outer region treated at the MM-level, EQC ( I + L ) is the energy of the inner region including link-atoms treated at the QC-level and EQC−MM ( I, O ) is the coupling term collecting the interactions between the two regions. For a given reaction step, the difference in electronic energy (∆ Eadd QC/MM (S)) between the intermediate and the transition state gives the potential energy barrier. The QC/MM method can in principle accommodate any combination of QCand MM-potentials. From a technical point of view, the applied QC-method must be able to account for the external point charges that represent the outer region. The wavefunction at the reacting region is solved in the presence of point charges. Usually, semi-empirical or DFT methods are used as QC-potentials. The energy of the outer region is calculated from the potential energy function of a force field, for example Amber or CHARMM. 62,63 The energy of these force fields is calculated from the general equation: EMM (O) = Ebond +Eangle +Edihedral +Etorsion +Eelec +EvdW (8) The consecutive energy terms correspond to the extension of bonds, bending of angles, 20 Computer simulations of enzyme catalysis Figure 2: Conceptual drawing showing the principle of the QC/MM approach. rotation of dihedral angles, electrostatic interactions and Van der Waals interactions, respectively. The key problem of the QC/MM method is the proper treatment of the boundary between the inner and outer regions. 21 If the boundary cuts through covalent bonds, the valencies of these bonds must be saturated. This is usually done by introducing link-atoms similar to hydrogen atoms that cap the QC-region at the boundary. Other approaches include boundary atoms or frozen localized orbitals.87 The exploration of the potential energy surface (PES) of an enzyme model is the central issue in the modeling of enzymatic reactions. Stable structures on the reaction path, i.e. reactants and intermediates, are represented by minima on the PES, whereas transition states are represented by saddle points. Finding the transition state geometry is probably the most challenging aspect in studies on enzymatic reaction paths. A variety of geometry optimization methods have been developed for this purpose. 88,89 To be able to properly characterize the transition state, it is required to calculate a matrix of secondorder derivatives of energy (Hessian). However, for large QC/MM models, obtaining and manipulating this matrix becomes computationally too expensive and approximate techniques for localizing transition states have to be used. One approach is the so-called linear transit, where a relaxed PES scan is performed in steps along the assumed major component of the reaction coordinate, for example a distance between two atoms. More sophisticated methods involve generation of a chain of frames interpolated between two energy minima that are bound with a special merit function and optimized together to converge on the minimum energy path, for example the nudged elastic band method 90,91 (NEB). The NEB method has been used in the present work to study the reaction paths in 4Hpad and PFL. The chemistry of radical enzymes from anaerobic bacteria 21 3 The chemistry of radical enzymes from anaerobic bacteria Radicals are highly reactive atoms, molecules or ions that have an open electron shell, i.e. a single valence electron. This single electron seeks to pair with another electron, which can be derived from the second radical or a σ - or π -bond. To date, many enzymes have been identified that employ a radical-mediated catalytic mechanism. 1–4,24, 27,92, 93 The protein environment protects reactive radical species from quenching agents, dimerizations and other side reactions and allows the radicals to persist. 92 On the other hand, reactions involving small ligands such as molecular oxygen are difficult to avoid, since these ligands can easily penetrate the protein matrix. For example, glycyl radical enzymes lose their activity due to the cleavage of the protein backbone at the glycyl radical site after exposure to molecular oxygen. Therefore, radical enzymes are usually found in anaerobic microorganisms where the risk of oxygen-induced side reactions is minimal. Whenever possible, nature has evolved enzymes to catalyze biochemical transformations via simple acid-base mechanisms. Since radical chemistry is more demanding in terms of generation, storage and controlled decomposition of open-shell species, radical enzymes are used only when there is no alternative.4 Radicals can be introduced into proteins either by homolysis of weak σ -bonds or by electron transfer. There are two radical generators in proteins, namely the vitamin B12 (adenosylcobalamin) and S-adenosylmethionine (SAM). Alternatively, the radical can sometimes be introduced into the protein by one-electron transfer to coenzyme A or thymidine, leading to the formation of a ketyl radical anion. In such cases, the energy for generating the radical is usually provided by ATP or light. For some enzymes the mechanism by which they obtain the radical is still uncertain, for example acyl-CoA dehydrogenase and 4-hydroxybutyryl-CoA. The concept of enzymatic radical catalysis is depicted on Fig. 3. Although the conversion of a substrate is thermodynamically feasible, the reaction cannot proceed due to the high energy barrier (A). The situation changes after a catalytic radical (R • ), for example the thiyl radical, has been introduced into the active site (B). The substrate is now activated to a reactive radical form by abstraction of a hydrogen atom by the catalytic radical. The energy barrier for the conversion of the substrate-derived radical intermediate 22 The chemistry of radical enzymes from anaerobic bacteria Figure 3: A simplified potential energy diagram showing the principles of enzymatic radical catalysis. 94 (A) Reaction without a catalytic radical. (B) Reaction with a catalytic radical. SH, substrate; PH, product; S ‡ , transition state; R • , catalytic radical; ∆ G‡ , energy barrier for substrate conversion. (S • ) is significantly lower than that for the substrate. The conversion S •→ P • gives a product-related radical intermediate. In the last step, P • abstracts a hydrogen atom from the enzyme, which gives the final product (P) and regenerates the initial catalytic radical. In summary, a radical-mediated reaction mechanism usually involves three reaction steps, namely the activation of a substrate by radical species in the active site, conversion of a substrate-derived radical intermediate and deactivation of a product-related intermediate into the final product. In the following sections, three different classes of radical enzymes from anaerobic bacteria are briefly outlined. Although the present thesis deals specifically with modeling of catalysis by glycyl radical enzymes, there are structural and functional connections between the members of all three classes. For example, SAM-dependent enzymes are essential activators of glycyl radical enzymes. The knowledge of these connections is key for understanding the chemistry of glycyl radical enzymes. The chemistry of radical enzymes from anaerobic bacteria 23 3.1 Vitamin B12-dependent enzymes Vitamin B12 (adenosylcobalamin) is a complex organometallic compound that assists many enzymatic reactions. The octahedral structure of vitamin B12 shows a Co 3+ ion embedded in a corrin ring and two axial ligands interacting with the central ion (Fig. 4). The binding of the cobalt ion is provided by four in-plane nitrogen atoms of corrin. The first ligand is a 5’-deoxyadenosyl residue bound to the cobalt ion via a weak σ -bond. This unusual metal-carbon bond has a dissociation energy of only ∼ 31 kcal/mol in solution and ∼ 15 kcal/mol in protein environment. The nature of the Co − C bond in vitamin B12 has been extensively studied 8,95, 96 but remains poorly understood. One of the key questions still to be addressed is why the bond dissociation energy (BDE) of this bond is significantly different between solution and protein environment. The second ligand can be either 5,6-dimethylbenzimidazole (”base on”), which connects with the corrin ring D, or the imidazole ring of histidine (”base off, his on”). All reactions catalyzed by B12 -dependent enzymes start from the homolytic cleavage of the weak Co − C bond of the coenzyme. The cleavage gives Co +2 and 5’-deoxyadenosyl radical (Ado-CH • 2 ), which abstracts a hydrogen atom from the substrate, generating a substrate-derived radical intermediate. This intermediate rearranges into a product-related radical intermediate and abstracts a hydrogen atom back from 5’-deoxyadenosine, which leads to the final product. The rearrangement usually involves an intramolecular 1 → 2 shift of the functional group, for example the middle hydroxyl group of glycerol as in the reaction catalyzed by the B12 -dependent glycerol dehydratase. 32,33 Finally, Ado-CH • 2 and the Co +2 ion can recombine to complete the catalytic cycle. The reactions catalyzed by the B12 -dependent enzymes have been extensively studied, both experimentally and computationally.8 There are two groups of B12 -dependent enzymes. One group comprises of ”base on” irreversible eliminases, for example ethanolamine ammonia-lyase, class II ribonucleotide reductase and glycerol dehydratase. Class II RNR is somewhat exceptional, since it uses a cysteine residue in the active site to relay the radical between 5’-deoxyadenosine and the substrate. In all other enzymes from this family, the 5’-deoxyadenosyl radical directly attacks the substrate. Another interesting feature of class II RNR is that the nucleotide reduction by this enzyme does not seem to be accompanied by a 1 → 2 rearrangement reaction that is typical for other B12-dependent enzymes. 24 The chemistry of radical enzymes from anaerobic bacteria Figure 4: Vitamin B12 analog as seen in the crystal structure of diol dehydratase (PDB code 1EEX30). The cobalt ion is depicted in pink color. The second group is represented by ”base off, his on” reversible mutases catalyzing rearrangements of the carbon skeleton and migrations of the amino group. Examples of mutases include methylmalonyl CoA mutase and glutamate mutase. Interestingly, all known eliminases have counterparts in the B12 -independent enzyme family. These counterparts are either SAM-dependent or glycyl radical enzymes, as in the case of glycerol dehydratase. On the other hand, counterparts of mutases have not been reported and may not exist at all. A unique feature of the enzymes from the B12 -dependent family is that the radical disappears by reformation of the Co − C bond in the coenzyme. Other enzymes can only carry a permanent radical. However, some of the B12 -dependent enzymes become inactive after a few thousands of turnovers. For example, diol dehydratase can survive only about 10 4 turnovers. The advantage of these enzymes is that they are much less sensitive to molecular oxygen, unlike glycyl radical and [4Fe−4S] cluster/SAM-containing enzymes. 3.2 S-adenosylmethionine radical enzymes The S-adenosylmethionine cofactor (SAM) undergoes transient cleavage to methionine and 5’-deoxyadenosyl radical, which can further propagate the radical by abstracting The chemistry of radical enzymes from anaerobic bacteria 25 Figure 5: Activation of SAM by addition of an extra electron, leading to methionine and 5’-deoxyadenosyl radical. hydrogen atoms from substrate molecules or precursor proteins of glycyl radical enzymes. Cleavage of the rather strong sulfur–adenosyl bond in SAM (BDE ∼ 60 kcal/mol) is only possible if assisted by a low-potential one-electron donor, such as ferredoxin or flavodoxin. These donors contain iron-sulfur clusters ([4Fe − 4S]) that reduce SAM by supplying an extra electron to the cofactor, as depicted on Fig. 5. After the cleavage of the S − C bond, the resulting 5’-deoxyadenosyl radical can be irreversibly released or recycled after each turnover to regenerate the cofactor. More than 3000 potential SAM-dependent enzymes have been detected in genomes of anaerobic and aerobic bacteria, fungi, plants and animals. However, only a few of these enzymes have been studied in detail. These include the reversible lysine-2,3-aminomutase (the first discovered SAM-dependent enzyme) and spore photoproduct-lyase 97–99 (a DNA repair enzyme) as well as irreversible biotin synthase, oxygen-independent coproporphyrinogen III oxidase and Mo-cofactor biosynthesis protein A (MoaA). The latter three enzymes together with MoaC are involved in the synthesis of molybdopterin, which is a crucial cofactor for many metalloenzymes. An important group of irreversible SAM-dependent enzymes are the activases of glycyl radical enzymes. 3.3 Glycyl radical enzymes As of this writing, six glycyl radical enzymes (GRE) of known function have been identified, 24,100–102 namely pyruvate formate-lyase (PFL), anaerobic ribonucleotide reductase (ARNR), benzylsuccinate synthase (BSS), B12 -independent glycerol dehydratase (iGDH), 4-hydroxyphenylacetate decarboxylase (4Hpad) and choline trimethylamine-lyase (CTL). These enzymes are able to perform chemically difficult transformations, such as cleavage of C − C bonds (PFL, 4Hpad), cleavage of C − O bonds (iGDH, ARNR), addition to double bonds (BSS) or cleavage of C − N bonds (CTL). Fig. 6 shows reactions catalyzed by these 32 The chemistry of radical enzymes from anaerobic bacteria has been examined by means of experimental and theoretical methods. 75,76, 107,127, 128 An interesting feature of PFL is that the enzyme employs two active site cysteines that can relay the radical. Other GRE enzymes use only one cysteine. The currently accepted catalytic mechanism starts from the radical transfer between the glycyl radical storage and one of the cysteines. The radical is further propagated to the second cysteine, which attacks the carbonyl moiety of pyruvate, forming a protein-bound radical intermediate (see Manuscript D). The subsequent cleavage of the C − C bond in the intermediate yields a free formyl radical. To complete the reaction, the first cysteine donates a hydrogen atom to the formyl radical, generating formate. Since there is no structural information available on binding of CoA to the active site of PFL, less is known about the second stage of the reaction. Most likely, once formate has left the active site, a molecule of CoA binds in the vicinity of the acylated cysteine. Transacylation between these two results in acetyl-CoA and regenerates the thiyl radical. Unlike for ARNR, iGDH and 4Hpad, the catalytic machinery of PFL is rather simple, since it does not involve residues in the active site other than the two radical cysteines. Choline trimethylamine-lyase CTL from the anaerobic bacterium Desulfovibrio desulfuricans is a novel glycyl radical enzyme catalyzing the production of trimethylamine (TMA). 101,102 Choline is an important compound for functioning of cell membranes, methyl transfer reactions and neurotransmission. On the other hand, TMA can be used by the bacterium as a source of carbon. The CTL-catalyzed reaction involves cleavage of the C − N bond in choline. This type of reaction has not been described for any of the known GREs. Initially, the conversion of choline was postulated to be catalyzed by a hypothetical B12 -dependent enzyme, since the breakdown of a cognate compound, ethanolamine, is catalyzed by the B12 -dependent ethanolamine ammonia-lyase. However, the EPR experiments as well as the analysis of the bacterial genome clearly indicate the involvement of a glycyl radical enzyme in this reaction.101 Synopsis of published and submitted manuscripts 33 4 Synopsis of published and submitted manuscripts Glycyl radical enzymes have evolved to perform a variety of chemically difficult transformations. The focus of this work was on the computational investigation of enzymes catalyzing the cleavage of C − O and C − C bonds. Because of the evident structural and functional similarities between the enzymes from the glycyl radical family, one of the important issues of the present work was to study whether the catalytic mechanisms of these enzymes share some common features. For example, the crystal structures of the B12 -independent glycerol dehydratase and 4-hydroxyphenylacetate decarboxylase show the presence of aspartic and glutamic acid residues in the active site. These residues have been computationally shown to be crucial for the catalysis by both enzymes, acting as proton donors and acceptors. Manuscript A covers a computational study (electrostatic and cluster model DFT calculations) on the catalytic mechanism of the B12 -independent glycerol dehydratase. Manuscript B discusses a crystallographic study, with some support from electrostatic calculations, on the structure of 4-hydroxyphenylacetate decarboxylase. Manuscript C extends this discussion by presenting a combined electrostatic and QC/MM study on the full-enzyme model. In manuscript D, QC/MM calculations are discussed that provide updates to the previously studied mechanism of pyruvate formate-lyase. 4.1 Cleavage of the C−O bond in glycerol The growing biofuel industry is interested in methods for biochemical degradation of glycerol. This has motivated a study (Manuscript A) on the mechanism of the B12 -independent glycerol dehydratase (iGDH), a novel glycyl radical enzyme catalyzing the dehydration of glycerol. The other enzyme capable of converting glycerol is the B12 -dependent glycerol dehydratase (GDH). Both enzymes employ radical-mediated mechanisms. For radical storage and activation of the substrate, however, GDH uses the adenosylcobalamin cofactor and iGDH uses a glycyl/thiyl radical diad. Although GDH and iGDH belong to different enzyme families, their active sites are somewhat similar. For example, Glu435, Asp447 and His164 in iGDH are equivalent to Glu170, Asp335 and His143 in GDH. The key structural difference between the two active sites is that the additional histidine in iGDH, His281, is replaced by a potassium ion in GDH. 34 Synopsis of published and submitted manuscripts Enzymes from the B12 -dependent family are believed to adopt a common catalytic mechanism that involves an intramolecular 1 → 2 shift of the functional group of the substrate, for example the middle hydroxyl group of glycerol as in the reaction catalyzed by GDH. It has been established that two effects facilitate the GDH-catalyzed reaction by lowering the energy barrier for the critical 1 → 2 shift. These effects are the so-called 1) partial protonation of the migrating hydroxyl group by acidic species in the active site, such as histidine, and 2) partial deprotonation of one the terminal groups of glycerol by basic species, such as aspartate or glutamate. However, the migrating/spectator hydroxyl groups never get fully protonated/deprotonated during the 1 → 2 shift because the deprotonation of neutral histidine would be energetically too unfavorable. The hydroxyl group migration proceeds through a cyclic transition state and gives an unstable 1,2-diol intermediate, which readily collapses into the corresponding aldehyde and water. To explore the catalytic mechanism of iGDH, the protonation states of titratable residues in the protein were in the first step studied by electrostatic and Monte Carlo calculations on the crystal structure of the substrate-bound form of the enzyme. The calculations indicate that in the lowest energy state at pH=7, both Glu435 and Asp447 are deprotonated and His164 is doubly protonated. The positive charge on His164 is counterbalanced by the negative charges on Glu435 and Asp447. A network of hydrogen bonds inside the active site provides contacts between these residues, the ligand and the rest of the enzyme. The DFT calculations performed on the cluster model of the enzyme show that the dehydration of glycerol by iGDH does not require a complicated intramolecular shift of the middle hydroxyl group, as previously suggested by analogy to the B12-dependent enzyme. Instead, the iGDH-catalyzed reaction seems to involve three elementary steps: 1) activation of glycerol to a radical form by Cys433, 2) dehydration of the substrate-derived radical intermediate, 3) deactivation of the product-related radical intermediate by Cys433. During the second step, a water molecule is released directly from glycerol by full protonation of the leaving hydroxyl group by His164. The dehydration is coupled to a proton transfer from the C1 hydroxyl group of glycerol to Glu435, which generates a C=O double bond of the future aldehyde product. The energetics of all three reaction steps were calculated to be very feasible, i.e. the energy barriers were found to be very low. The barrier for the direct release of water does not exceed 6 kcal/mol. The calculations also suggest the possibility of an alternative reaction mechanism, in which Synopsis of published and submitted manuscripts 35 first His164 and Asp447 exchange a proton and second Asp447 donates the proton to the leaving hydroxyl group of glycerol. On the basis of the performed calculations, isotope labeling experiments are proposed that could support the theoretical mechanism. The most interesting finding is that the B12 -dependent and -independent enzymes adopt fundamentally different mechanisms for the dehydration of glycerol, which is mostly due to a different protonation state of a single histidine in the active site. Moreover, the calculations are able to pinpoint the origins of catalytic efficiency of iGDH. These are: 1) the Cys433 radical that activates the substrate to a reactive radical form, 2) the proton donating/accepting system of His164 (Asp447) and Glu435 that facilitates the release of water from the activated substrate, 3) the hydrogen bond network made up by Asn156, Ser232 and His281 that stabilizes the transition state for the dehydration. 4.2 Cleavage of the C−C bond in 4-hydroxyphenylacetate Decarboxylation processes are of high significance in biological systems. 4-hydroxyphenylacetate decarboxylase (4Hpad) is a glycyl radical enzyme involved in the fermentative metabolism of tyrosine in clostridia. The enzyme catalyzes the production of p-cresol from its substrate. The previously postulated decarboxylation mechanism assumed that the reaction starts from the hydrogen atom transfer between the hydroxyl group of the substrate and the radical cysteine Cys503. However, the recently solved crystal structure of the substrate-bound form of 4Hpad shows an unexpected binding mode of 4-hydroxyphenylacetate in the active site (Manuscript B). Namely, the substrate binds to the enzyme with its carboxyl group close to the radical cysteine Cys503, while the substrate’s hydroxyl group is hydrogen-bound to Glu637 at the opposite end of the active site. This finding suggests that the enzyme performs the decarboxylation of 4-hydroxyphenylacetate via a Kolbe-type mechanism. On the other hand, the analysis of the crystal structure alone is insufficient for the determination of the exact enzymatic mechanism. Therefore, electrostatic and quantum chemical/molecular mechanical calculations were used to study the 4Hpad-catalyzed reaction in detail (Manuscript C). The electrostic calculations indicate that the carboxyl group of the bound substrate is deprotonated and the substrate’s hydroxyl group is protonated. The negative charge on the carboxyl group is stabilized by a network of hydrogen bonds from the protonated Glu505, 36 Synopsis of published and submitted manuscripts the protein backbone and Ser344. Based on the QC/MM calculations, the activation of the substrate was found to follow a nonstandard reaction scheme, in which the radical cysteine Cys503 abstracts an electron from the substrate and the active site glutamate Glu637 abstracts a proton from the substrate’s hydroxyl group. The activation is hence accomplished by the netto abstraction of a hydrogen atom from the substrate and requires that two active site residues are simultaneously involved in this processes. In the next step, the activated substrate readily decarboxylates. The remaining steps of the reaction involve rotation of the Cys503 side-chain, a proton transfer from Glu505 to Cys503 and a hydrogen atom transfer from Cys503 to the product-related intermediate. All reaction steps were found to be energetically very feasible. The highest energy barrier of about 7 kcal/mol was calculated for the decarboxylation step. 4.3 Cleavage of the C−C bond in pyruvate Pyruvate formate-lyase catalyzes the conversion of pyruvate and coenzyme A (CoA) into formate and acetyl-CoA, which is a key reaction in the carbon metabolism of various anaerobic bacteria. The reaction catalyzed by PFL has been computationally studied before but only using small-molecule or cluster models of the active site. To better understand the role of protein environment in the catalyzed reaction, not accounted for by the previously used computational methods, I have performed quantum chemical/molecular mechanical calculations on the full-enzyme model (Manuscript D). In general, the present QC/MM calculations support the mechanism derived from the earlier computational studies but introduce some novelties. The crucial step in the catalysis by PFL is a thiyl attack of the active site cysteine Cys418 on the carbonyl moiety of pyruvate. This step leads to the formation of a proteinbound intermediate. However, the exact nature of this intermediate remained elusive. The study on small-molecule models using deprotonated pyruvate suggests that the thiyl attack of Cys418 on pyruvate’s carbonyl moiety and release of the formyl radical are coupled. The studies involving pyruvate in a protonated form or stabilized by two active site arginines, Arg176 and Arg435, show the occurrence of an unstable oxy-radical tetrahedral intermediate of pyruvate bound to Cys418. On the other hand, the present QC/MM calculations indicate that first the energy barrier for the formation of the tetrahedral intermediate is as low as 5 kcal/mol (twice lower than for the earlier models) and second Synopsis of published and submitted manuscripts 37 the intermediate is a relatively stable species on the potential energy surface. The other new observation is that the collapse of the tetrahedral intermediate induces a conformational change of the Cys419 side-chain in the active site. With the extension of the C − C bond of pyruvate, the Cys419 side-chain rotates towards the leaving formyl radical. After the collapse of the tetrahedral intermediate, Cys419 is perfectly positioned for the hydrogen atom abstraction by the formyl radical. Thus, Cys419 rather than CoA is responsible for quenching of the formyl radical. Moreover, this may suggest that the release of formate precedes binding of the CoA molecule to the active site. 4.4 List of published and submitted manuscripts A. Mikolaj Feliks, G. Matthias Ullmann “Glycerol Dehydratation by the B12independent Enzyme May Not Involve the Migration of a Hydroxyl Group – A Computational Study” J. Phys. Chem. B 116, 7076–7087 (2012) The project was initiated by myself. All electrostatic and quantum chemical (DFT) calculations for modeling of the enzymatic reaction path described in the paper were designed and performed by myself. The results from the calculations were analyzed and interpreted by myself with support from Matthias Ullmann. The manuscript was written by myself and corrected to the final version by Matthias Ullmann. B. Berta M. Martins, Martin Blaser, Mikolaj Feliks, G. Matthias Ullmann, Wolfgang Buckel, Thorsten Selmer “Structural Basis for a Kolbe-Type Decarboxylation Catalyzed by a Glycyl Radical Enzyme” J. Am. Chem. Soc. 133, 14666–14674 (2011) The experimental part of the paper involving the elucidation of the protein crystal structure was done by Berta Martins and Martin Blaser. The electrostatic calculations and the analysis of protonation states of titratable residues were performed on top of the crystal structure by myself with support from Matthias Ullmann. These calculations were used to formulate the putative catalytic mechanism for the enzyme. The manuscript was written by Berta Martins. All authors were involved in discussions and also contributed to the final version of the manuscript. 38 Synopsis of published and submitted manuscripts C. Mikolaj Feliks, Berta M. Martins, G. Matthias Ullmann “Catalytic Mechanism of the Glycyl Radical Enzyme 4-Hydroxyphenylacetate Decarboxylase from Continuum Electrostatic and QC/MM Calculations” J. Am. Chem. Soc. 135, 14574–14585 (2013) All electrostatic and quantum chemical/molecular mechanical (DFT) calculations discussed in the paper were performed by myself. The calculations were designed by myself and Matthias Ullmann. The software for studying the enzymatic mechanism was written by myself using the Python programming language and the framework of the pDynamo library by Martin Field. The results from the calculations (reaction paths, catalytic effects) were analyzed by myself together with Matthias Ullmann. The manuscript was written by myself. Matthias Ullmann and Berta Martins contributed to discussions and helped prepare the final version of the manuscript. D. Mikolaj Feliks, G. Matthias Ullmann “New Insights into the Catalytic Mechanism of Pyruvate Formate-Lyase from QC/MM Calculations” (Manuscript to be submitted) The project was initiated by myself. All QC(DFT)/MM calculations described in the paper were carried out by myself. 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Deckwer (1995): Microbial conversion of glycerol to 1,3-propanediol. Fems Microbiol. Rev. 16, 143–149 [121] M. Gonzalez-Pajuelo, I. Meynial-Salles, F. Mendes, P. Soucaille and I. Vasconcelos (2006): Microbial conversion of glycerol to 1,3-propanediol: Physiological comparison of a natural producer, Clostridium butyricum VPI 3266, and an engineered strain, Clostridium acetobutylicum DG1(pSPD5). Appl. Environ. Microbiol. 72, 96–101 [122] D. Logan, J. Andersson, B. Sjoberg and P. Nordlund (1999): A glycyl radical site in the crystal structure of a class III ribonucleotide reductase. Science 283, 1499–1504 [123] P. Nordlund and P. Reichard (2006): Ribonucleotide reductases. Annu. Rev. Biochem. 75, 681–706 [124] K. Cho, F. Himo, A. Graslund and P. Siegbahn (2001): The substrate reaction mechanism of class III anaerobic ribonucleotide reductase. J. Phys. Chem. B 105, 6445–6452 [125] K. Cho, V. Pelmenschikov, A. Graslund and P. 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Theory Comput. 4, 1151–1161 Manuscript A 49 Manuscript A “Glycerol Dehydratation by the B12-Independent Enzyme May Not Involve the Migration of a Hydroxyl Group: A Computational Study” Mikolaj Feliks, G. Matthias Ullmann J. Phys. Chem. B 116, 7076–7087 (2012) Permanent link: http://pubs.acs.org/doi/abs/10.1021/jp301165b Abstract Continuum electrostatic and density functional calculations have been combined to explore the catalytic mechanism of the B12 -independent glycerol dehydratase. In sharp contrast to the previously suggested mechanism, the calculations indicate that the release of water from glycerol is accomplished without the intermediacy of a geminal diol species. Instead, the enzyme employs two active site residues, histidine and glutamate, as a proton donating/accepting system. The glutamate accepts a proton from the terminal hydroxyl group of glycerol, whereas the histidine donates a proton to the leaving middle hydroxyl group of glycerol, forming a water molecule. The calculations also show a key role of the active site residues in stabilization of the transition state of the water release step. 50 Manuscript B Manuscript B “Structural Basis for a Kolbe-Type Decarboxylation Catalyzed by a Glycyl Radical Enzyme” Berta M. Martins, Martin Blaser, Mikolaj Feliks, G. Matthias Ullmann, Wolfgang Buckel, Thorsten Selmer J. Am. Chem. Soc. 133, 14666–14674 (2011) Permanent link: http://pubs.acs.org/doi/abs/10.1021/ja203344x Abstract In the present study, we report on the high-resolution crystal structure of 4-hydroxyphenylacetate decarboxylase, a novel glycyl radical enzyme proposed to catalyze the last step of tyrosine fermentation in clostridia. The structure shows an unexpected binding mode of 4-hydroxyphenylacetate to the enzyme active site. In this mode, the carboxyl group of the substrate is in close contact to the thiyl radical and the phenolic group is hydrogen-bound to the glutamate on the opposite end of the active site. A Kolbe-type decarboxylation mechanism is suggested for the formation of the p-cresol product. This mechanism is supported by our continuum electrostatic calculations. Manuscript C 51 Manuscript C “Catalytic Mechanism of the Glycyl Radical Enzyme 4-Hydroxyphenylacetate Decarboxylase from Continuum Electrostatic and QC/MM Calculations” Mikolaj Feliks, Berta M. Martins, G. Matthias Ullmann J. Am. Chem. Soc. 135, 14574–14585 (2013) Permanent link: http://pubs.acs.org/doi/abs/10.1021/ja402379q Abstract The catalytic mechanism of 4-hydroxyphenylacetate decarboxylase has been studied based on continuum electrostatic and QC/MM calculations. The calculations suggest an unconventional activating mode of 4-hydroxyphenylacetate. The substrate is activated to a radical form by two simultaneous transfers, first of an electron and second of a proton. The electron is transferred from the substrate to the thiyl radical and the proton is abstracted from the phenolic group of the substrate by the active site glutamate. The activation generates a radical anion intermediate. The release of CO 2 from the intermediate is coupled to a proton back-transfer from the glutamate to the phenolic group. The mechanism based on the calculations corroborates previous experiments showing that the hydroxyl group in the p-position of the substrate is crucial for the catalysis. 52 Manuscript D New Insights into the Catalytic Mechanism of Pyruvate Formate-Lyase from QC/MM Calculations Mikolaj Feliks,1G. Matthias Ullmann1,† 1) Computational Biochemistry Group, University of Bayreuth, Universit¨atsstr. 30, BGI, 95447 Bayreuth, Germany †)to whom correspondence should be addressed; e-mail: [email protected] January 29, 2014 1 Manuscript D 53 Abstract We have revisited, by performing quantum chemical/molecular mechanical calculations on the full-enzyme model, the first part of the enzymatic reaction catalyzed by the glycyl radical enzyme puruvate formate-lyase. Based on our model, we propose several modifications to the previously studied mechanism, which now agrees well with experimental data. First, we present an energy profile which can better explain the reversibilty of the PFL-catalyzed reaction. Second, the calculations suggest that the thiyl attack on pyruvate results in the formation of the protein-bound tetrahedral radical intermediate. The occurance of this intermediate on the reaction path was often questioned in the previous studies on PFL. In our study, the barrier for the formation step was calculated to be as low as 5 kcal/mol. Moreover, the intermediate appears to be quite stable thanks to the stabilizing interactions from the enzyme. Third, the barrier for the release of the formyl radical was found to be 9 kcal/mol. Fourth, from the calculated reaction path, we provide evidence that not CoA but rather Cys419 is responsible for the quenching of the formyl radical. That is, the function of Cys419 is not limited to the hydrogen atom relay between Gly734 and Cys418, as thought before. Keywords: glycyl radical enzyme, enzymatic reaction mechanism, quantum chemical calculation, continuum electrostatics, proton transfer 2 54 Manuscript D Introduction Radical enzymes are interesting because of their ability to catalyze transformations of generally unreactive compounds.1–4 There exist many enzymes that employ a radicalbased reaction mechanism but only a few glycyl radical enzymes (GRE) have been identified to date.5–8 The first glycyl radical enzyme to be discovered was pyruvate formatelyase9(PFL), which catalyzes the reversible conversion of pyruvate and CoA into formate and acetyl-CoA. This essential reaction is part of the anaerobic glucose metabolism in various bacteria. Like the other enzymes from the glycyl radical family, PFL is activated to a reactive radical form by a dedicated S-adenosylmethionine-dependent activating enzyme. During the activation, the radical is introduced into PFL by the homolytic cleavage of the C–H bond at Gly734. Upon binding of pyruvate, the radical moves from Gly734 to Cys419 in the active site, where it can initiate substrate reactions. This activation mechanism is thought to be a common step in the catalysis by all members of the GRE family. However, the consecutive reaction steps may be very different depending on the particular enzyme as, for example, shown in the recent mechanistic studies on the B12-independent glycerol dehydratase10–12 (iGDH) and 4-hydroxyphenylacetate decarboxylase13 (4-Hpad) as well as the earlier studies on benzylsuccinate synthase14 (BSS) and anaerobic ribonucleotide reductase15 (ARNR). Since the discovery of PFL in 1985, the enzyme has been extensively studied, both experimentally and computationally.15–18 Although the catalytic mechanism of PFL is now believed to be well understood, questions remain concerning some of the mechanistic details of the catalyzed reaction. For example, it is not clear which of CoA or Cys419 is responsible for quenching of the formyl radical, i.e. whether the binding of CoA to the active site preceeds the release of formate. Revisiting the mechanism of PFL in the light of the recent studies on iGDH and 4-Hpad may in general provide better understanding of chemistry involved in the catalysis by glycyl radical enzymes. The currently discussed catalytic mechanism of PFL, which was originally proposed 3 Manuscript D 55 by Knappe and co-workers,19 involves four reaction steps. After the substrate binding, the radical is transferred from Cys419 to Cys418. The presence of two cysteine residues in the active site of PFL that actively participate in the catalysis is unique compared to the other members of the GRE family. In the next step, the thiyl radical on Cys418 attacks the carbonyl carbon atom of pyruvate, which leads to the formation of a S–C bond. The so-generated enzyme-bound radical intermediate is unstable and collapses into the acylated Cys418 and a formyl radical. The formyl radical abstracts a hydrogen atom from Cys419, which gives formate and regenerates the radical on Cys419. Alternatively, the formyl radical may abstract a hydrogen atom from CoA that binds in the active site during the second stage of the reaction. The reaction is completed by the transfer of the acetate moiety from Cys418 to CoA. The PFL-catalyzed reaction has been computationally studied three times before. In their work on PFL, Himo and co-workers calculated the mechanism for a simple gas-phase model of the active site.16 The X-ray structure of the enzyme was not available at the time of their study. They used a model of protonated pyruvate. The rationale for using neutral pyruvate was that charge separation in the protein environment is usually very small. Following similar methodology, Lucas and co-workers recalculated the mechanism of PFL using a deprotonated model of pyruvate.17 They found that the reaction steps involving the attack of the Cys418 thiyl radical on pyruvate and the release of the formyl radical anion are concerted. Clearly, studying isolated reactants in vacuum is the simplest approach to the modeling of enzymatic catalysis. Although this method can provide some insights into the intrinsic chemistry of the reaction, it cannot account for the precise catalytic mechanism, because the protein environment is not included in the model. The lack of protein surrounding allows reactants to move freely during the reaction, which is not possible inside the enzyme active site. In their second study on PFL,18 Himo and co-workers employed the socalled cluster model approach20–22 to better represent the actual conditions of protein 4 56 Manuscript D interior. The cluster models consisted of up to 75 atoms and were based on the crystal structure of PFL by Becker and co-workers.23 To compensate for the missing parts of the enzyme, selected atoms were kept fixed at their X-ray positions during the geometry optimizations. However, the cluster models used by Himo still suffered from too much flexibility. Because of this, the exothermic energies of some of the reaction steps were found to be overestimated, i.e. they were not in line with experimental data. Although the cluster model approach works reasonably well for the identification of key features of the mechanism, it cannot provide full insight into long-range interactions between the active site and the rest of the enzyme. Do these interactions influence the chemistry at the active site? If so, to what extent can they modify the mechanism derived from the cluster model calculations? To address these questions and to overcome the limitations of the previously used methods, one has to go beyond small molecule models of the enzymatic system. Therefore, we have employed hybrid quantum chemical/molecular mechanical (QC/MM) calculations24–26 to study the mechanism of PFL for the first time in a fullprotein model. The QC/MM (ONIOM) method was previously used by Condic-Jurkic and co-workers to study some aspects of the PFL-catalyzed reaction but they still used only small gas-phase models of the active site.27,28 The key problem in modeling of enzymatic reactions is the treatment of titratable residues.29 These residues can adopt different protonation states depending on the pH, interactions with local environment etc. The presence of charged groups close to the active site, even if they do not participate directly in the catalysis, may have a considerable influence on the reaction mechanism.30 Therefore, prior to the QC/MM exploration of the reaction path, we performed Poisson-Boltzmann electrostatic calculations combined with a Monte Carlo titration to study the protonation behavior of titratable residues in PFL. We explored the catalytic mechanism of PFL by systematic build-up of the reaction path from potential energy surface scans and geometry optimizations. Reaction profiles 5 Manuscript D 57 connecting the optimized minima of intermediates were studied by the nudged elastic band method (NEB).31,32 Transition states were taken as points of the highest energy on the NEB-calculated reaction profiles. Based on our calculations, we are able to present a mechanism that is in general consistent with the previously studied ones but introduces several corrections and novel observations. Methods Preparation of the full-enzyme model. The crystal structure of the pyruvatebound form of PFL by Becker and co-workers23 (PDB code 1H16) was used to build the complete enzyme model. At the resolution of 1.53 ˚ A, this is the most accurate structure of PFL availabe to date. In addition to puruvate, the crystal structure shows a molecule of CoA bound at the protein surface. The binding mode of CoA allows to study only the first stage of the PFL-catalyzed reaction (see Fig. 1). The initial model of the reactant state was prepared in CHARMM.33,34 D-treitol, tetraethylene glycol, sodium and magnesium ions as well as CoA were removed from the model. The CHARMM27 force field35 was used to describe the protein and the waters. The MM-parameters for pyruvate were taken from the force field based on analogy to similar structures. Setup of the continuum electrostatic model. The protonation states of all titratable residues were set to their standard values at pH 7. CHARMM program was used to add missing hydrogens atoms and to optimize their positions. Crystallographic water molecules were removed from the model. A Poisson-Boltzmann continuum electrostatic model combined with a Monte Carlo titration was used to calculate the protonation probabilities of titratable residues in the protein. The electrostatic calculations were carried out in MEAD36 with the following parameters. Dielectric constants of p= 4 and s= 80 were assigned to the interior of the protein and to the solvent, respectively. The ionic strength of solvent was set to I= 100 mM and the temperature was set to T= 300 K. An ion exclusion layer of 2.0 ˚ A and a solvent probe radius of 1.4 ˚ A were 6 64 Manuscript D normal conditions. In the case of PFL, however, Cys418 attacks the carbonyl group of pyruvate, forming a radical intermediate covalently bound to the protein. Another example of a glycyl radical enzyme that performs unusual activation of its substrate is the recently studied 4-hydroxyphenylacetate decarboxylase.13 Collapse of the tetrahedral radical intermediate. After the addition of the Cys418 thiyl radical to pyruvate, the reaction can proceed to the next stage, which is the cleavage of the C–C bond in pyruvate that gives the formyl radical and acylated Cys418. To model the collapse of the tetrahedral intermediate, a PES was first performed along the C1Pyr—C2Pyr bond; the distance between the two atoms was gradually extended by 0.1 kcal/mol. The scan was followed by the NEB calculation. Mechanistically, this reaction step was found to involve several simultaneous events. First, the distance between the atoms C1Pyr and C2P yr extends from 1.8 ˚ A (In2) to 2.9 ˚ A (In3). Second, the SCys418— C2Pyr bond is shortened from 1.9 ˚ A to 1.8 ˚ A. Third, the side-chain of Cys419 that pointed towards Cys418 rotates in the direction of the newly formed formyl radical. From the NEB-calculated reaction path it can be seen that the Hγatom of Cys419 follows the moving carboxylic moiety of pyruvate. The distance between the atoms Hγ,Cys418 and C1Pyr is shortened from 3.8 ˚ A (In2) to 3.0 ˚ A (In3). That is, after the splitting of pyruvate, the formyl radical is perfectly positioned for the hydrogen abstraction from Cys419 (see In3 on Fig. 4). This observation suggests that not CoA but rather Cys419 is responsible for quenching of the formyl radical. In the small-molecule studies on the mechanism of PFL, such movement of the Cys419 side-chain was not visible. Unlike for the In1→In2 addition step, the energetics of the C–C bond cleavage were found to be considerably dependent on the applied level of theory. Namely, the barrier calculated for the smaller basis set (5.7 kcal/mol) is twice as high as the one obtained using the larger basis set (2.6 kcal/mol; see Fig. 6 for detailed energy profiles). The resulting cleaved intermediate (In3) is virtually isoenergetic with the preceeding transition state (TS3), i.e. In3 lies in a very shallow energy minimum on the PES. Namely, the energy 13 Manuscript D 65 difference between TS3 and In3 does not exceed 0.5 kcal/mol. Taking the small energy difference between TS3 and In3, the similarity between the two geometries is consistent with the Hammond’s postulate.45 With the extension of the C1Pyr—C2Pyr bond, the radical shifts from the enzymebound part towards the leaving carboxylic moiety of pyruvate. Since the transition state TS3 is geometrically and energetically very close to the intermediate In3, the spin distributions of the two are nearly the same. The radical in TS3/In3 is localized entirely on the newly created formyl moiety and is shared between the atoms C1Pyr (0.70), O12P yr (0.14) and O11Pyr (0.16; see In2→In3 on Fig. 4). The acetyl-Cys418 moiety is free of the radical. Quenching of the formyl radical. In the last reaction step of the first part of the PFL-catalyzed reaction, the formyl radical has only to abstract a hydrogen atom from the enzyme. The nearest accessible hydrogen atom is Hγ,Cys419, as mentioned before. The abstraction of hydrogen from Cys419 was in the first step modeled with a PES scan by shortening the C2Pyr · · ·Hγ,Cys419 distance by 0.1 ˚ A in each step and subsequently refined by using the NEB method. For the last reaction step, the calculated barrier is 10.0 kcal/mol (or 8.8kcal/mol if only the smaller basis set is used). The relatively high barrier obtained for our QC/MM model in comparison to the previous isolated models can be related to the rather long distance of 3.0 ˚ A that the hydrogen atom has to overcome to transfer between Cys419 and the formyl radical. Moreover, pyruvate inside the active site of PFL is involved in a network of hydrogen bonds with Arg176 and Arg435. These bonds have to be streched during the radical transfer formyl→Cys418, as visible from the NEBcalculated reaction path. Stretching of the hydrogen bond network requires some energy and increases the activation energy for the last reaction step. After the abstraction of hydrogen is complete, the radical is localized back on Cys419. The Mulliken spin density was calculated to be 0.97 for the Sγ,Cys419 atom. Geometrically, the difference between In3 and Pro is only the new position of the hydrogen atom from Cys419. The first part 14 66 Manuscript D of the PFL catalytic reaction ends with acylated Cys418, free formate and the Cys419 thiyl radical. On the basis of our observations for the QC/MM model, we propose that the reaction continues with the release of formate from the active site, binding of CoA and abstraction of hydrogen from CoA by the Cys419 thiyl radical. Conclusions In the present work, we have investigated the first part of the PFL catalytic cycle by performing QC/MM calculations on the full-enzyme model. The use of a complete enzyme eliminates some of the problems of small-molecule models, since the protein environment is taken into account during the calculations. For example, the orientation of reactants throughout the catalytic cycle is more realistic because of the spatial restraints imposed by the enzyme. There are two highlights of this work. First, our calculations indicate that the tetrahedral radical intermediate that results from the thiyl attack of Cys418 on pyruvate is a relatively stable species. The barrier required for the formation of this intermediate was calculated to be as low as 5 kcal/mol, which translates into a twice lower barrier in comparison to the previously studied small-molecule models. Second, we propose that quenching of the formyl radical is performed by Cys419 and a molecule of CoA binds to the active site only after the release of formate. The calculated reaction path shows that the cleavage of the C–C bond in pyruvate is coupled to the movement of the Cys419 side-chain towards the leaving formyl radical. After the cleavage, Cys419 is perfectly positioned for the formyl→Cys419 radical transfer. Acknowledgments. This work was supported by the DFG grant UL 174/8-2 and the BioMedTec International Graduate School of the Elitenetwork Bavaria. Supplementary materials. Cartesian coordinates and Mulliken atomic spin densities and charges for the optimized structures (only the active site region). This material is available free of charge via the Internet at http://pubs.acs.org. 15 Manuscript D 67 References [1] Buckel, W.; Golding, B. Fems Microbiol. Rev.,1998,22(5), 523–541. [2] Frey, P. Annu. Rev. Biochem.,2001,70, 121–148. [3] Buckel, W.; Golding, B. T. Annu. Rev. Microbiol.,2006,60, 27–49. [4] Buckel, W. Angew. Chem.-Int. Edit.,2009,48(37), 6779–6787. [5] Eklund, H.; Fontecave, M. Struct. Fold. Des.,1999,7(11), R257–R262. [6] Selmer, T.; Pierik, A.; Heider, J. Biol. Chem.,2005,386(10), 981–988. [7] Craciun, S.; Balskus, E. P. Proc. Nat. Acad. Sci. USA,2012,109, 21307–21312. [8] Thibodeaux, C.; van der Donk, W. A. Proc. Nat. Acad. Sci. USA,2012,109, 21184– 21185. 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J. Phys.,1980,58(8), 1200–1211. [41] Lee, C.; Yang, W.; Parr, R. Phys. Rev. B,1988,37(2), 785–789. [42] Becke, A. J. Chem. Phys.,1993,98(7), 5648–5652. [43] Stephens, P.; Devlin, F.; Chabalowski, C.; Frisch, M. J. Phys. Chem.,1994,98(45), 11623–11627. [44] Himo, F. Biochim Biophys Acta,2005,1707(1), 24–33. [45] Hammond, G. J. Am. Chem. Soc.,1955,77(2), 334–338. [46] Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graph.,1996,14(1), 33–38. 18 70 Manuscript D Figure 1: The PFL-catalyzed reaction cycle. The first part of the cycle studied in this paper is depicted in black and red color. The second part not included in this study is shown in grey color. The first part involves four elementary steps. In the first step, a hydrogen atom is transferred from Cys418 to Cys419. In the second step, Cys418 attacks the carbonyl carbon atom of pyruvate, which leads to the formation of a radical tetrahedral intermediate. Next, the intermediate collapses into the formyl radical and acylated Cys418. In the last step, the formyl radical abstracts a hydrogen atom from Cys419, which gives formate and regenerates the radical at Cys419. 19 Manuscript D 71 Figure 2: QC-part of the QC/MM model used in the calculations (optimized geometry of In1). The rest of the protein was omitted for clarity. The QC-part encompasses pyruvate, Cys418 and Cys419, the protein backbone link between the cysteines, the side-chains of Arg176 and Arg435 and two water molecules Wat2859 and Wat3252 (64 QC-atoms atoms in total including link-atoms). Dashed lines depict hydrogen bonds. Atoms discussed in the text are labeled. The label Lindicates atoms replaced by hydrogen-type link-atoms during the QC/MM calculations. 20 72 Manuscript D Figure 3: QC/MM-optimized geometries of intermediates and transition states for the radical transfer Cys419→Cys418. Since there are two possible substrate states, the energies (in kcal/mol) are given with respect to the first intermediate (In1; radical localized on Cys418). The transition states were taken from the NEB-derived reaction profiles as the highest energy points. Numbers at the arrows indicate changes of the energy on the reaction path. Relevant interand intramolecular distances (in ˚ A) are depicted in italics. The Mulliken atomic spin densities (for clarity, only the ones of the absolute value ≥0.1) are depicted in bold. The 3D spin denisity is shown in magenta color at the isovalue of 0.01 a.u. The model was visualized in VMD.46 21 Manuscript D 73 Figure 4: QC/MM-optimized geometries of intermediates and transition states for the formation of the S–C bond between pyruvate and Cys418 (In1→In2), cleavage of the C–C bond of pyruvate (In2→In3) and formation of formate and regeneration of the radical on Cys419 (In3→Pro). See description under Fig. 3 for details. 22 80 Appendix: Python QC/MM scripts 27 for a in co. keys (): 28 c = co[a] 29 cm = SoftConstraintEnergyModelHarmonic (0., c) 30 SCC["%s" % a] = SoftConstraintTether (a, ref . GetRow (a), cm) 31 mol . DefineSoftConstraints ( SCC) 33 op = "/ home /41/ bt260941 / local / orca_2_9_0_linux_x86 -64/ orca " 34 sp = "/tmp" 35 PID = getpid () 36 time = strftime ("%y%m%d%H%M%S") 37 f = argv [0] 38 fl = basename (f[: f. rfind (".") ]) 39 user = getuser () 40 sp = "%s/% s_pdynamo /%s -%s -%s" % (sp , user , fl , time , PID) 42 makedirs (sp) 43 logFile .Text (" Scratch directory : %s\n" % sp) 45 mol . electronicState = ElectronicState ( charge = -1, multiplicity = 2) 47 qcm = QCModelORCA ( 48 "B3LYP :6 -31G*", " PAL8 ", " SCFCONV10 ", 49 command = op , 50 scratch = sp , 51 job = "job", 52 deleteJobFiles = False ) 53 mol . DefineQCModel (qcm , qcSelection = Selection (qc)) 55 mol . DefineNBModel ( NBModelORCA () ) 57 tdir = "%s/ qcmmopt_traj " % sp 58 traj = SystemGeometryTrajectory (tdir , mol , mode = "w") 59 Conv , a = False , 1 61 while not Conv: 62 logFile . Text (" Optimizing the system ( attempt %d) ...\ n" % a) 63 r = ConjugateGradientMinimize_SystemGeometry (mol , logFrequency = 1, maximumIterations = 9999 , rmsGradientTolerance = TolCrit , trajectories = [( traj , 1) ]) 64 Conv = r[" Converged "] 65 a += 1 67 XYZFile_FromSystem (" after_qcmm . xyz ", mol , label = "QC /MM - optimized geometry ") 68 logFile . Footer () The script scan.py performs a relaxed potential energy surface scan along the distance between two specified atoms. The first part of the script involves the QC/MM model setup and is the same as in the qcmmopt.py script. However, Vector3 and SoftConstraintDistance have to be additionally imported from the modules pCore and pMolecule, Appendix: Python QC/MM scripts 81 respectively. Lines 1-2 define a helper function converting atomic patterns into indices. Lines 4-8 contain the definitions of two atoms along which the scan is performed, step in ˚ A and the final distance between the atoms at which the scan is terminated. Line 10 starts the main loop. First, the current distance between the atoms is calculated. This distance is used as an additional restraint that is added to the restraint container (lines 12-14). A restrained geometry optimization is performed for every step along the scan (lines 19-24). The resulting intermediate geometry is written out as an XYZ file (line 27). In lines 29-30, a check is performed whether the scan has been completed. If not, a vector is calculated between the two atoms (lines 32-37). Based on the vector, the positions of the atoms are updated. The atoms are moved further or closer depending on the variable step. scan.py 1 def I (m, t): 2 return m. sequence . AtomIndex ("%s:%s.% s :%s" % t) 4 a = I (mol , (" PRTA", " GLY ", "734", " HA1")) 5 b = I (mol , (" PRTA", " CYS ", "419", "SG")) 6 step = -0.10 7 D_fin = 1.35 8 i = 0 10 while 1: 11 D = mol. coordinates3 . Distance (a , b) 12 cm = SoftConstraintEnergyModelHarmonic (D, 10000.0) 13 SCC [" distance "] = SoftConstraintDistance (a, b , cm) 14 mol. DefineSoftConstraints ( SCC) 16 logFile .Text (" *** Optimizing step %d ***\ n" % i) 17 XYZFile_FromSystem (" scan %03d. xyz" % i, mol ) 19 while 1: 20 r = ConjugateGradientMinimize_SystemGeometry (mol , logFrequency = 1, maximumIterations = 9999 , rmsGradientTolerance = TolCrit ) 21 if r[" Converged " ]: 22 break 23 else : 24 logFile . Text (" *** Restarting the optimization ... ***\ n") 26 logFile .Text (" *** Done with step %d ***\ n" % i) 27 XYZFile_FromSystem (" scan %03 d_optimized .xyz " % i, mol) 29 N = abs (( D_fin - D) / step ) 30 if N < 1: break 32 A = mol . coordinates3 . GetRow (a) 82 Appendix: Python QC/MM scripts 33 B = mol. coordinates3 . GetRow (b) 34 V = Vector3 () 35 B. CopyTo (V) 36 V. AddScaledVector3 ( -1. , A) 37 V. Normalize () 39 f = step * .5 40 mol. coordinates3 . AddScaledVector3 (a, -f , V) 41 mol. coordinates3 . AddScaledVector3 (b, f, V) 42 i += 1 The nudged elastic band method 90,91 provides a better approximation of the reaction path than a potential energy surface (PES) scan but requires that the geometries of both the initial and the final states are known. The geometry of the latter can be generated by performing a PES scan. The script neb.py provides access to the NEB method in pDynamo. The first part of the script is the same as in the qcmmopt.py or scan.py scripts. Two functions, GrowingStringInitialPath and NudgedElasticBandSplineOptimize SystemGeometry, have to be imported from the module pMoleculeScripts. Line 1 defines a directory where the NEB-calculated trajectory will be stored. The following lines specify the number of frames and the previously optimized geometries of two energy minima. In line 5, an initial chain of frames is generated by linearly interpolating between the two geometries. Next, the trajectory object is initialized (line 7). Finally, a function is called that performs the calculation of the minimum energy path by using the NEB method. neb.py 1 traj_path = " neb_traj " 2 N = 11 3 reac = XYZFile_ToCoordinates3 (" sub_after_qcmm .xyz ") 4 prod = XYZFile_ToCoordinates3 (" in1_after_qcmm .xyz ") 5 GrowingStringInitialPath (mol , N, reac , prod , traj_path , log = logFile ) 7 traj = SystemGeometryTrajectory ( traj_path , mol , mode = "a+") 9 NudgedElasticBandSplineOptimize_SystemGeometry(mol, traj, log = logFile , maximumIterations = 5000 , rmsGradientTolerance = TolCrit ) The script cube.py can be used for the generation of volumetric data containing spin density. The initialization of the QC/MM model follows the same procedure as in the previous scripts. After the scratch space has been set up, a check is performed (lines 3-5) Appendix: Python QC/MM scripts 83 whether there exists a file containing the parameters of the cube. If so, the parameters in the form of Python commands are loaded. Otherwise, the geometrical center of the QC-region is calculated (lines 7-13). In lines 15-23, a distance is calculated from the center to the furthermost atom. This distance is used to determine the dimensions of the cube (lines 25-31). The calculated cube is 25% larger than the one bonding the QC-region. Lines 33-35 define the resolution (in ˚ A) and evaluate the number of nodes in each direction. In the following lines, an XYZ file is generated for visualization purposes containing the cube vertices. The dimensions are converted into Bohrs (lines 52-58) and a DEF file is written (lines 60-63). Finally, the parameters are passed to the ORCA object (lines 65-70). A single point energy calculation (line 75) generates a cube file in the scratch directory. cube.py 1 cubef = "cube .def" 3 if exists ( cubef ): 4 f = open ( cubef ). readlines () 5 for c in f: exec (c) 7 else : 8 C = Vector3 () 9 for q in qc: 10 Q = mol . coordinates3 . GetRow (q) 11 C. AddScaledVector3 (1. , Q) 12 C.Scale (1. / len (qc)) 13 cx , cy , cz = C 15 R = 0. 16 V = Vector3 () 17 for q in qc: 18 Q = mol . coordinates3 . GetRow (q) 19 C. CopyTo (V) 20 V. AddScaledVector3 ( -1., Q) 21 r = sqrt (V.Dot (V)) 22 if r > R: 23 R = r 25 Scale = 1.25 26 minx = -R * Scale + cx 27 maxx = R * Scale + cx 28 miny = -R * Scale + cy 29 maxy = R * Scale + cy 30 minz = -R * Scale + cz 31 maxz = R * Scale + cz 33 Res = 0.10 84 Appendix: Python QC/MM scripts 34 t = (maxx - minx ) / Res 35 np = floor (t) 37 O = open (" cube . xyz ", "w") 38 O. write (" 9\ nCube in Angstroems \n") 39 for a in ( 40 (cx , cy , cz), 41 (minx , miny , minz), 42 (minx , miny , maxz), 43 (minx , maxy , minz), 44 (minx , maxy , maxz), 45 (maxx , miny , minz), 46 (maxx , miny , maxz), 47 (maxx , maxy , minz), 48 (maxx , maxy , maxz)): 49 O. write ("Xx %6.2 f %6.2f %6.2 f\n" % a) 50 O. close () 52 toBohr = 1. / 0.5291772 53 minx = minx * toBohr 54 maxx = maxx * toBohr 55 miny = miny * toBohr 56 maxy = maxy * toBohr 57 minz = minz * toBohr 58 maxz = maxz * toBohr 60 f = open (" cube . def ", "w") 61 f. write ("# Cube parameters in a.u.\ n") 62 f. write (" minx = %6.2 f\ nmaxx = %6.2 f\ nminy = %6.2 f\ nmaxy = %6.2 f\ nminz = %6.2 f\ nmaxz = %6.2 f\ nnp = %6 d\n" % ( minx , maxx , miny, maxy, minz, maxz, np)) 63 f. close () 65 qcm = QCModelORCA (" B3LYP :6 -311++ G (2d ,2p)", " PAL4 ", " SCFCONV10 " , "\n%% plots \n dim1 %d\n dim2 %d\n dim3 %d\n min1 %f\n max1 %f\n min2 %f\n max2 %f\n min3 %f\n max3 %f\n Format Gaussian_Cube \n SpinDens (\" spin_dens .cube \") ;\n end" % (np , np , np , minx , maxx , miny , maxy , minz , maxz ), 66 command = op , 67 scratch = sp , 68 job = "job", 69 deleteJobFiles = False 70 ) 71 mol . DefineQCModel (qcm , qcSelection = Selection (qc)) 72 mol . DefineNBModel ( NBModelORCA () ) 74 mol . Energy () 76 logFile . Footer () 85 Apart from the main research topic that is modeling of catalysis by radical enzymes, I have also contributed to the following papers that in general deal with the problem of enzymatic catalysis: 1. Wiktor Beker, Karol M. Langner, Edyta Dyguda-Kazimierowicz, Mikolaj Feliks, W. Andrzej Sokalski “Predicting relative stabilities of biomolecular complexes from electrostatic multipole interactions at shortened intermolecular distances” J. Comput. Chem. 34, 1797–1799 (2013) 2. Renata Grzywa, Edyta Dyguda-Kazimierowicz, Michal Sienczyk, Mikolaj Feliks, W. Andrzej Sokalski, Jozef Oleksyszyn “The molecular basis of urokinase inhibition: from the nonempirical analysis of intermolecular interactions to the prediction of binding affinity” J. Mol. Model. 13, 677–683 (2007) 3. Jing Wang, Juo Gu, Jerzy Leszczynski, Mikolaj Feliks, W. Andrzej Sokalski “Oximeinduced reactivation of sarin-inhibited AChE: A theoretical mechanism study” J. Phys. Chem. B 111, 2404–2408 (2007) 86 I declare that this thesis titled, “Computational Modeling of Catalytic Mechanisms of Glycyl Radical Enzymes” and the work presented in it are my own. I confirm that: • This thesis was prepared entirely while in candidature for a Ph. D. degree at the University of Bayreuth. • This thesis has not been submitted previously for a Ph. D. degree at any other institution. • Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. •I have acknowledged all main sources of help. • Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself. Bayreuth, January 2014