Metal Fluorides: Tools for Structural and Computational Analysis of Phosphoryl Transfer Enzymes
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The phosphoryl group, PO3 –, is the dynamic structural unit in the biological chemistry of phosphorus. Its transfer from a donor to an acceptor atom, with oxygen much more prevalent than nitrogen, carbon, or sulfur, is at the core of a great majority of enzyme-catalyzed reactions involving phosphate esters, anhydrides, amidates, and phosphorothioates. The serendipitous discovery that the phosphoryl group could be labeled by “nuclear mutation,” by substitution of PO3 – by MgF3 – or AlF4 –, has underpinned the application of metal fluoride (MF x ) complexes to mimic transition states for enzymatic phosphoryl transfer reactions, with sufficient stability for experimental analysis. Protein crystallography in the solid state and 19F NMR in solution have enabled direct observation of ternary and quaternary protein complexes embracing MF x transition state models with precision. These studies have underpinned a radically new mechanistic approach to enzyme catalysis for a huge range of phosphoryl transfer processes, as varied as kinases, phosphatases, phosphomutases, and phosphohydrolases. The results, without exception, have endorsed trigonal bipyramidal geometry (tbp) for concerted, “in-line” stereochemistry of phosphoryl transfer. QM computations have established the validity of tbp MF x complexes as reliable models for true transition states, delivering similar bond lengths, coordination to essential metal ions, and virtually identical hydrogen bond networks. The emergence of protein control of reactant orbital overlap between bond-forming species within enzyme transition states is a new challenging theme for wider exploration.
KeywordsMFx Phosphoryl group surrogates Enzyme mechanisms Transition state analogs QM/MM computation KS-DFT analysis
Alexander Todd1 and Frank Westheimer2 held complementary, and sometime overlapping, views on the centrality of phosphates for life. Todd’s pronouncement: “Where there’s Life, there’s Phosphorus”, encapsulated his conviction that enzymes that manipulate phosphates have been at the heart of biology from the dawn of life anywhere in the universe . Westheimer identified the evolutionary centrality of phosphate . The cellular behavior of phosphate esters and anhydrides provides one of the most remarkable chemical paradoxes: phosphate monoesters hydrolyze spontaneously under physiological conditions with t 1/2 1012 years, yet simple phosphatase enzymes have k cat ca. 30 s−1. The enormous difference corresponds to a remarkable catalytic rate enhancement of 1021 . How do enzymes achieve this? This article focuses on the use of aluminum and magnesium fluoride complexes to mimic structures of transition states of enzymatic reactions that involve the phosphoryl group, PO3 −, and to provide a structural base for quantum chemical computations to describe them in detail.
1.1 Basics of Phosphoryl Transfer
1.2 Historic Development of Mechanisms
2 Development of Metal Fluorides as Phosphate Analogs
2.1 The ‘Burst Phase’ of Analog Discovery
After a short interval, a third class of MF x analog was reported: an aluminum trifluoride complex of magnesium ADP for a dinucleotide kinase, described alongside the corresponding trifluoroberyllate tetrahedral complex. Its great advantage was tbp geometry for the TSA complex that, for the first time, accurately mimicked the TS geometry of the γ-phosphate of ATP undergoing transfer . This was quickly followed by a GDP·AlF 3 0 complex for the small G protein Ras·RasGAP (Fig. 2c)  and then by an ADP·AlF 3 0 ·GDP complex for a quaternary complex of a nucleoside diphosphate kinase from the slime mold, Dictyostelium discoideum . These, and subsequent examples of tbp complexes, recognized that AlF 3 0 was a neutral MF x species and therefore a Coulombic mismatch for an anionic phosphoryl group. It was 5 years before that feature was rectified with the first identification of trifluoromagnesate (MgF3 –) bound to GDP in a complex with the small G protein, RhoA. A key component of that work was the rigorous use of proton-induced X-ray emission spectroscopy (PIXE) to identify magnesium as the atom at the core of the tbp complex (Fig. 2d) .
By this time, there were some 50 structures deposited in the PDB for MF x complexes, usually with anionic oxygen as one axial ligand. Their importance has stimulated a rapid, ongoing growth in their use (Fig. 1). We shall now examine the relative qualities of these four classes and their offshoots on a systematic basis, organized by geometric considerations.
3 MF x Ground State Analogs
3.1 BeF3 – as a Ground State Phosphate Mimic
In aqueous solution, beryllium (II) forms stable fluorides as a mixture of tetrahedral species including BeF2·2H2O, BeF3 –·H2O, and BeF 4 = . 19F NMR studies on fluoroberyllate complexes with ADP identified mixed fluoroberyllate·ADP species for myosin (Fig. 2b). Nearly 130 trifluoroberyllate complexes have now been described, with three structures solved by NMR and 119 X-ray structures having resolutions of ≥1.2 Å, generally having tetrahedral trifluoroberyllate bonded to an anionic oxygen. These comprise two sub-groups: over 70 have Be coordinated to an aspartate carboxylate while some 50 have Be coordinated to a terminal phosphate oxygen of a nucleotide. Just two have Be coordinated to a histidine ring nitrogen, while one has BeF2 bridging two phosphates.
3.1.1 Aspartyl Trifluoroberyllates
3.1.2 BeF3 – Nucleotide Structures
3.1.3 Histidine Trifluoroberyllates
3.1.4 Structural Conclusions
The significant ability of beryllium (II) fluorides to complete tetrahedral coordination by binding to an anionic oxygen has made them good isosteric and electrostatic GSAs of phosphate for a wide range of uses . Bond lengths for Be–F and Be–O are close to those for P–O (1.6 ± 0.5 Å) and the strong ionic character of the Be–F bond means that its fluorines readily accept H-bonds from a range of donors and/or coordinate to Group 2 metal ions . Thus, fluoroberyllates have been used beneficially to study changes in major conformations of proteins by crystallography, NMR, and EM, while studies on ADP·BeF3 – have supported investigations on ATPases that drive various mechanical processes at a molecular level, particularly for myosin [31, 32, 33, 34, 35, 36]. They have proved especially valuable for the identification of near attack conformations (NACs) in enzyme mechanisms, notably for β-phosphoglucomutase (βPGM) .
4 MF x in Transition State Analog Complexes
4.1 Tetrafluoroaluminate TS Complexes—AlF4 –
4.1.1 Aspartyl Tetrafluoroaluminates
Fourteen PDB structures have tetrafluoroaluminate bonded to an aspartate with an essential Mg2+ in a six-membered ring. They align well on the best resolved complex, β-phosphoglucomutase (βPGM, PDB: 2wf7; 1.05-Å resolution (Fig. 6b), with four equatorial oxygen ligands coordinating the catalytic Mg2+. The structures fit into two subsets: six members of the first group have a second aspartate sub-adjacent to the first (Asp8 and Asp10 in βPGM). The OA–Al–OD bonds are “in-line” (167.5˚ ± 7.0˚) with the aluminum midway between the two oxygens (separation 3.9 ± 0.1 Å) and have a catalytic aspartate that accepts a short H-bond from the apical water/hydroxyl group (2.59 ± 0.05 Å) to align this oxygen for nucleophilic attack on phosphorus .
The second subset has ATPases involved in pumping calcium, copper, and zinc ions. They use an aspartyl phosphate intermediate, whose TS for hydrolysis is mimicked by an octahedral AlF4 –. An axial water oxygen forms short H-bonds to an invariant glutamate (2.5 ± 0.1 Å) and to a threonine carbonyl (2.57 ± 0.05 Å), which clearly orientate and polarize the water for “in-line” attack on the aspartyl phosphate .
4.1.2 Nucleotide Guanosine Diphosphate (GDP) Tetrafluoroaluminates
4.1.3 Nucleotide Adenosine Diphosphate (ADP) Tetrafluoroaluminates
4.2 Octahedral Aluminum Trifluoride Phosphate TS Mimics
5 MF3 Improved Geometry Transition State Mimics
5.1 MgF3 –, Trifluoromagnesate
5.2 AlF 3 0 , Aluminum Trifluoride
5.3 A Combined MgF3 −- and AlF 3 0 Structural Analysis
A statistical analysis of the structures of AlF 3 0 and MgF3 − complexes contributes to the resolution of this compositional uncertainty. The near-invariant geometry of octahedral AlF4 − complexes for GDP makes them a useful set for comparison with the corresponding set of tbp MF3 complexes. Thus, eight GDP “AlF 3 0 ” structures for small G proteins align very well with those for five MgF3 − complexes (Fig. 12a). The axial separation for the donor and acceptor oxygens in these combined 13 GDP·MF3 TSAs is 4.38 ± 0.20 Å, significantly distinct from the corresponding average for 19 GDP·AlF4 – complexes, 4.02 ± 0.14 Å, and clearly supported by normal distribution analysis (Fig. 12b). The conclusion is: For “AlF 3 0 ” read MgF3 –!
Taking “AlF 3 0 ” together with trifluoromagnesates, a common general pattern of axial ligands emerges. The MF3 species requires at least one anionic oxygen. β-Oxygens from ADP (33 structures) and GDP (24 structures) provide the overwhelming majority of examples while aspartate (11 structures) is also significant. Water (27 structures) is the dominant neutral axial ligand while serine and threonine hydroxyls appear less frequently. Significantly, there is no example of both axial ligand positions being occupied by two neutral ROH groups.
5.4 MgF 4 = , Tetrafluoromagnesate
Finally, the most remarkable MF x structure is that of a human diphosphoinositol phosphatase, co-crystallized with myo-inositol hexakis-phosphate and then soaked with sodium fluoride (PDB: 2q9p) . This complex has four octahedral magnesiums with nine ligands assigned as fluorines in a complex that embraces MgF2, MgF3, MgF4, and MgF5 species in a single block. It also offers the first example of octahedral MgF x (Fig. 13b). Its core appears related to the Rutile structure of MgF2, which is characterized by octahedral magnesium and trigonal planar fluorine .
6 19F NMR Studies of MF x Complexes
Scalar coupling between nuclei involved with N–H···F H-bonds is an additional parameter that shows details of the coordination of the MF x moiety by the protein. 1 J HF and 2 J NF couplings have been reported for individual NH···F pairs, with values up to 59 and 36 Hz, respectively . All the effects described above, SIIS, NOE, chemical shifts, and scalar couplings, correlate closely with H-bonding orientations and distances obtained from high resolution crystal structure analysis. 19F chemical shifts are invariant over the pH range 6.5–9.5, they signal that there is no detectable change in protonation state of the enzyme in the environment of the TS complex, but the pH dependence of 19F NMR resonances and multiplicity can identify a switch from AlF4 – to MgF3 – complexes above pH 8, as illustrated for cAPK (Fig. 14c) .
NMR measurements of 19F nuclei in the active site of MF x TSA complexes thus provide a picture of charge distribution between the phosphoryl group mimic and the protein. The good relationship between 19F NMR chemical shifts and SIIS values illustrates the dominant influence that very localized H-bonds have on shaping charge density on MF x moieties.
7 Computational Analyses of MF x Complexes
7.1 Balancing Accuracy of Energy/Structure and Conformational Sampling
The solution of accurate molecular energies, ideally with as little parameterization as possible;
The exhaustive consideration of relevant conformations of macromolecules.
For the simulation of biomolecules, it is unavoidable that both criteria must be approximated to varying degrees. In practice, different computational methods put different emphasis on one or the other of these two features. Any useful calculation must meet both criteria adequately. Solutions of the energy of a macromolecule, and thence its structure, should be made for each conformer of the molecule. Hence, the task of achieving reliable energies severely raises the cost of the computation. This constraint therefore drives down the number of conformers to be computed, with the risk that the program may fail to examine the specific conformation most relevant for the reaction under investigation.
To attain a compromise between these two features, the methodology used has to strike a balance between defining a central quantum mechanics (QM) zone and a molecular mechanics (MM) zone dealing with the major part of the macromolecule and environment. The combination of the two regions is called a QM/MM calculation. A QM description is necessary to describe bond–breaking–making processes or electronic excited states because molecular mechanics cannot describe these phenomena. Different balances between these two features are achieved by different choices in the apportionment of resource to the QM region. These include Kohn–Sham density functional theory (KS-DFT) [65, 66, 67, 68, 69] and empirical valence bond (EVB) [70, 71], while similar choices exist for the MM zone. However, the QM zone is the priority region.
7.2 Tradeoff in Accuracy of Energy/Structure: Parameterization Simplification vs. Mathematical Complexity
Accurate molecular energies can be obtained in an unbiased, systematically correctable manner [72, 73, 74] to get the desired accuracy. However, the computational resource required is very expensive, and is usually unacceptable because resource must be apportioned to adequate conformational sampling. In general, either an approximate QM method such as KS-DFT is used, or a heavily parameterized model is designed for a specific system such as EVB. Briefly, parameterization can tailor a QM method specifically to that molecule under analysis—and thereby eliminate many mathematical degrees of freedom. Hence, the calculation can be performed rapidly and can incorporate greater conformational sampling, but it must rely on the assumption that the reduced mathematical form faithfully represents the true quantum mechanics. By contrast, the various KS-DFT forms have parameters which are fixed by the design of the functions, and are completely independent of that particular biomolecule under investigation. Thus, the application of KS-DFT to a specific biomolecule has no freedom to change parameters to suit the target. Hence, KS-DFT deploys a more general mathematical framework, and more faithfully echoes exact quantum mechanics within budget.
7.3 Tradeoffs in Conformational Sampling: Dynamics vs. Statics
In order to balance the budget of the computation program, a choice has to be made between dynamics and statics. On the one hand, a dynamics description delivers an explicit femtosecond-by-femtosecond time evolution of the atoms, boosted by metadynamics . On the other hand, a statics analysis of a few discrete critical points along the reaction identifies TSs and/or intermediates as maxima/minima along the reaction coordinate. Each has its strengths and weaknesses.
A dynamics computation shows the true time-evolution of the molecular system, especially how atoms re-arrange to move along all possible reaction paths, step-by-step. All possible chemical reactions/conformations are sampled in due frequency with the Boltzmann distribution of states. The computation does not “target” a specific reaction path. TSs are rare-events, require long simulations or metadynamics , and so demand a smaller QM zone to allow an adequately fast calculation. This reduction of the QM zone, relative to that for statics described below, makes possible the conformational sampling needed to find the right state. A balance has to be struck between faithfully computing dynamics or prioritizing accurate energy calculations.
The choice for statics in following a reaction path, selected a priori, enables easy identification of the TSs for bond-breaking-making using standard quantum chemistry algorithms. Mathematical properties of energy maxima (TSs) and minima (intermediates) can be sought automatically. Users can seek out any desired pathway, but they have to sacrifice an understanding of the relative values of each path. This requires minimal computational resource compared to that required for a dynamics calculation, and so can accept a much larger QM region and/or a more accurate QM calculation. However, the a priori choice of the conformation is risky: it depends strongly on the accuracy of choice of the true TS conformation, which may or may not be found among existing crystal structures in the PDB.
7.4 KS-DFT as a QM Region Description
A more faithful representation of long-range chemical interactions and a potentially problematic boundary between zones introducing artifacts; and
Neglect of long-range chemical interactions altogether, with no un-physical artifacts introduced by the QM/MM boundary.
The iterative computational procedure delivered a mechanism in which the nucleophilic water is doubly protonated with H-bonds to carbonyl oxygens of both T37 and Q63 residues until after the TS for bond making/breaking, thereby orientating the nucleophilic water for good orbital overlap with the antibonding O3B-PG σ* orbital. PTs are not seen in the TS, but occur subsequently.
7.5 EVB as a QM Region Description
The Empirical Valence Bond method deploys a simplified mathematical framework to achieve the most rigorous possible conformational sampling. In essence, the EVB framework is largely a molecular mechanics based method, with the exception of its representation of a single “orbital” for each molecule, identified as involved in the bond–breaking–making reaction. No other electrons/orbitals are represented explicitly. This framework thus imposes the presumption that only a single orbital is involved in the bond-reorganization for a reaction. The EVB parameterization process is fundamentally chemistry-imposed: it identifies, a priori, what orbitals are involved and dictates chemistry-based molecular mechanics energy functions. This is in sharp contrast to a KS-DFT prescription of a QM region, which is fundamentally agnostic of chemistry, not defining bonds or selecting orbitals targeted for reaction, but merely defining a total number of electrons and nuclei involved, with no presumption of chemistry. As a result of the EVB simplifications, larger-scale changes in molecular conformation can be observed. In this way, the initial conditions of the experimental crystal structure are not a trap; the computational protocol allows the biomolecule to move freely.
7.6 The Use of MF x in Computational Studies of Enzyme Mechanisms
7.6.1 Validation of MF x as a TSA for Phosphoryl Transfer
Relatively few computational studies have been directed at the structural identity of the MF x complex per se. A contentious 1.8 Å resolution structure (PDB: 1o03) focused on a six-atom tbp complex for βPGM, initially described as a pentaoxy-phosphorane . They have converged on identification of (a) the observed crystal structure as a five-coordinate trifluoromagnesate complex rather than a five-coordinate phosphorus , (b) an active site stabilized by an extensive H-bonding network, and (c) a concerted transfer of the phosphoryl group without a stable phosphorane or metaphosphate intermediate [85, 86, 87]. They concluded that MgF3 – is a good TSA that can give insight into the geometry of the phosphoryl transfer TSs. A second example is a QM/MM analysis of the atomic nature of an MF x moiety in a TSA complex for the key kinase, cAPK . The structure of a tbp complex for cAPK·ADP·MF x was originally described as AlF 3 0 (PDB: 1l3r) but QM/MM simulations suggest that MgF3 – is the correct description of the tbp moiety rather than AlF 3 0 , and that MgF3 – is a near isosteric fit to PO3 – in the computed TS for the hydrolysis of ATP [61, 88]. This result agrees with a 19F NMR analysis, have been directed at MF x complexes for cAPK . The computations conclude that this kinase prefers a monoanionic analog (MgF3 − or AlF4 −) over a neutral analog (AlF 3 0 ) to match the −ve charge on the phosphoryl group.
7.6.2 Studies Linking Reaction Mechanisms from Model Systems to MF x Enzyme Complexes
Early QM studies on phosphoryl transfer analyzed the hydrolysis of methyl phosphate  and methyl pyrophosphate , added magnesium , and then transposed the results into the context of the Ras GTPase active site. The result does not match well to the MFx structure for Ras·RasGAP (PDB: 1wq1) because (i) the computed OA—OD separation lies in the region 4.7–5.5 Å and in the MF x structure is 4.4 Å. (ii) The computation calls for a second water to facilitate PT , however, in those (few) instances where a second water is seen in high-resolution MF x structures for Ras, it occupies the site vacated by a displaced or missing Gln61 residue, and is in no position to deliver the proposed catalysis (Fig. 7a).
7.7 Computations Transposing GDP·MF x into GTP Enzyme Complexes
7.7.1 Ras Family and GTP Hydrolysis
The use of MF x TSA structures to identify the TS for hydrolysis of GTP by Ras proteins has been the basis of many computations. Several studies have used PDB: 1wq1 , the 2.5 Å-resolution structure of Ras·RasGAP·GDP·AlF 3 0 as starting point, and have employed both QM/MM [92, 93, 94, 95, 96, 97, 98, 99] and EVB approaches [100, 101]. Some of these have aroused expert criticism of limitations inherent in the QM/MM approach . The results have varied widely, from a two-step reaction mechanism with bond breaking preceding bond making (i.e. a dissociative process; Scheme 1a) , to exclusion of water by the arginine finger , tautomeric catalysis , electrostatic catalysis , a two-water mechanism , and sundry rationalizations of the adverse effects of mutations [97, 99, 101]. The QM zone has generally been limited to 30–40 heavy atoms and, in consequence, has not examined the role of the function of several amino acids in contact with the reactants, most especially the extensive H-bonding network (as in Fig. 16). By contrast, an alternative computational approach using Kohn–Sham DFT analysis for RhoA·RhoGAP hydrolysis of GTP employed a QM zone of 91 heavy atoms, embracing a network of 21 H-bonds, and has attributed catalysis to orbital orientation determined by protein control of H-bonds donated by the nucleophilic water (Fig. 16) . The same study validated the high relevance of MgF3 – as a TSA by back-computing its structure from that of the calculated structure for the true TS complex for GTP hydrolysis.
7.7.2 Other GTPases and GTP Hydrolysis
A study on the structures of a GMP·AlF 3 0 complex (PDB: 2b8w) and a GDP·AlF4 − complex (PDB: 2b92) for hGBP1, has linked a mechanism for the hydrolysis of methyl triphosphate (MTP) to the two-step hydrolysis of GTP to GDP and thence to GMP by this interferon-activated human GTPase (Fig. 7b). The computation employed dated ab initio QM/MM molecular dynamics to simulate the hydrolysis of both GTP and of MTP as a reference system . The study proposes that GTP hydrolysis involves an indirect, substrate-assisted catalysis mechanism, identifying the nearest general base as Glu99, which is 6.2 Å from the nucleophilic water in the TSA complex. This separation problem was resolved by invoking transmission of base catalysis via one water to Ser73, and thence via a second water to the nucleophilic water. These bridging waters are not present in the substantive (3.2 Å resolution) TSA complex but appear to be imported from a structure of hGBP1 with β, γ-imino-GTP that is clearly an NAC complex (PDB: 2bc9; 2.8 Å resolution). This investigation merits a cautionary comment on the frailties of a computational analysis based on structures of poor resolution, under-informed by an adequate grasp of mechanisms of phosphoryl transfer.
7.8 Computations Transposing ADP·MF x into ATP Enzyme Complexes
7.8.1 ATP Hydrolysis by Myosin
7.8.2 ATP Hydrolysis by F1 ATPase
7.8.3 Phosphoryl Transfer in Kinases
The catalytic subunit of cAPK is a serine/threonine kinase responsible for many of the effects of cAMP signaling. It is a prototype for the kinase family that uses two catalytic magnesiums, and has become the most widely studied of all kinases. Many computations have focused on the phosphorylation of a serine in the target peptide by ATP, but recent advances in high-resolution structures of an NAC complex with β,γ-imino-ATP and the products from its slow reaction during crystallization combined with an MgADP·AlF 3 0 TSA, (PDB: 1rl0)  have given new opportunities for computational analysis. One of these, using MP2/aug-cc-pVTZ/CHARMM//B3LYP/6-31 + G(d)/CHARMM electronic structure calculations with a completely solvated model of the cAPKcat–ATPMg2–SP20 system finds that a dissociative concerted mechanism involving two consecutive steps is more favorable than an associative mechanism [110, 111] or a concerted loose mechanism  (Scheme 1b). In step 1, phosphoryl transfer involves a dissociative TS with an O–PG–O distance of 4.7 Å. Then, step 2 follows with back-protonation of the serine phosphate.
7.9 Thoughts from Computations
The first phase of computational studies for phosphoryl transfer was largely focused on finding a close match between computed activation energies and the experimental ones. However, recent advances in computational methodology have cast a shadow on earlier methods, where the energy error might easily lie in the range of 2–10 kcal mol−1, with error spreading as large as 30 kcal mol−1 [78, 114, 115]. Current protocols enable a much larger number of heavy atoms to be embraced in the QM zone, leading to computer results that hinge on geometry of the TS and the H-bond network that it embraces [44, 108, 111]. Such analyses have identified the propensity of nucleotide analogs, particularly β,γ-iminoATP, β,γ-methyleneATP, and their GTP counterparts, to deliver NACs for phosphoryl transfer processes, which is now recognized in recent computational studies as capable of generating small but highly significant conformational changes in kinases and GTPases [44, 108]. Lastly, the belief that enzymes work by optimizing reaction mechanisms that work slowly in solution, as Knowles put it “Not different, Just better” , is proving to be wide of the mark for phosphate reactions. There is growing evidence that phosphoryl transfer takes place in a desolvated environment to enable full protein control of the catalytic region. Water is rigorously excluded to avoid disruption of H-bond networks that are essential for the organization of catalysis.
In-line stereochemistry and concertedness for S N 2(P) reactions has been established at atomic resolution;
Relative priority of charge over geometry in transition state organization is well supported;
Subtle conformational differences between NAC and TS conformations of amino acid functions are increasingly apparent;
The role of H-bond networks to give structural coherence to proteins in transition states is burgeoning;
The propensity of anionic phosphate oxygens to H-bond to ROH nucleophiles explains the need for solvent exclusion from the TS, while its impedance offers a new interpretation of general base catalysis.
Lord Todd of Trumpington, Nobel Laureate 1957, 1702 Professor of Chemistry 1944-71, Cambridge, UK.
Professor of Chemistry, 1953-2007, Harvard, Cambridge, USA.
NB In other computational studies, such four-center PTs for phosphoryl reactions have been deemed to be very high energy.
In literature meant for using DFT in organic, biological, or inorganic applications, “KS-DFT” and “DFT” are used largely interchangeably. Theoreticians draw a distinction between these terms; KS-DFT is a subset of DFT for the given selection of expressing the kinetic energy in terms of orbitals.
A previous study favored a concerted reaction path (Lin et al. ).
It should be added that recent structural studies suggest that one of the catalytic magnesiums is lost from its pre-TS location during the bond-making-breaking process and then appears in a new location (PDB: 4klf and 4klg).
The authors thank Professors Nigel Richards (Cardiff University) and Jon Waltho (Manchester University) for critical comments on and many contributions to this work and Dr. Christian Roth (University of York) for advice on interpretation of some protein structures. We were supported by BBSRC Grant BB/M021637/1 and the Universities of York and Sheffield, UK. Y.J. is funded by ERC Advanced Grant AdG-322942. Multiple structural figures have used data taken from the Protein Data Bank. The use of illustrations from Refs.  and  has been appreciatively acknowledged where appropriate.
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