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      Quantum Chemistry as a Tool in Asymmetric Biocatalysis: Limonene Epoxide Hydrolase Test Case**

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          Quantum chemical models of enzyme active sites have in recent years proven to be a very powerful tool in the elucidation of enzymatic reaction mechanisms.1 In the so-called cluster approach, a limited part of the enzyme around the active site is cut out and treated using relatively accurate electronic structure methods, typically hybrid density functional theory (DFT). The missing enzyme surrounding is approximated by a homogeneous polarizable continuum model with some assumed dielectric constant.2 A large variety of enzymatic systems have been investigated quite successfully using this approach and a wealth of mechanistic insight has been gained.3 A few years ago, active site models consisted typically of less than 100 atoms. However, with today’s computers and using the same computational protocol, it is possible to treat more than 250 atoms quite routinely. These developments have paved the way for wider applications of the cluster approach, beyond the pure mechanistic investigations. To investigate and explain sources of various kinds of selectivities, in particular enantioselectivity, one has typically to reproduce relative transition-state energies on the order of 1 kcal mol−1. The accuracy of modern DFT methods has been proven to be sufficiently high to achieve this. In particular, these methods have in recent years been applied very successfully to a multitude of problems in the field of asymmetric homogenous catalysis.4 Modeling enzymatic enantioselectivity with the cluster approach has remained somewhat out of reach because larger active-site models are in general required to create the chiral environment provided by the enzyme. Herein, we will demonstrate that this kind of modeling approach is indeed able to reproduce and rationalize enantioselectivity in enzymes and has thus the potential to become a valuable tool also in the field of asymmetric biocatalysis. Today enzymes are increasingly used in synthetic chemistry for the production of base and fine chemicals.5 Indeed, biocatalytic processes are starting to replace transition-metal-catalyzed reactions for large-scale production of drug compounds.6 One of the most attractive features of enzymes in this respect is their high levels of selectivity. Various engineering techniques have been developed to manipulate the properties of enzymes to achieve the desired function. These techniques range from pure combinatorial approaches to semi-rational and fully rational designs, which are based on the detailed knowledge of the structure and mechanism of the enzymes. Theoretical methodology in asymmetric biocatalysis has relied mainly on substrate docking or molecular dynamics simulations of the enzyme–substrate (ES) complexes in the ground state.7, 8 To some extent, this has been successful in qualitatively guiding the experimental work as to which parts of the active site to manipulate and also to provide some rationalization for observed trends. These approaches are, however, inherently deficient since they do not consider the transition states and can thus not be fully quantitative. In recent years, the quantum mechanical/molecular mechanical (QM/MM) approach9 has been employed in this field to obtain a more quantitative description.10 In particular, the empirical valence bond (EVB) method has been shown to yield very promising results for the case of Candida antarctica lipase A.11 To examine the capabilities of the cluster approach in terms of reproducing enantioselectivity and mutational effects we have chosen to focus on the enzyme limonene epoxide hydrolase (LEH) from rhodoccoccus erythropolis as a test case. The natural substrate for this enzyme is limonene-1,2-epoxide, but the enzyme can catalyze the hydrolysis of a range of other epoxides to their corresponding vicinal diols.12 The reaction mechanism of LEH is quite well understood and consists of a single concerted step in which an aspartate (Asp132) abstracts a proton from the nucleophilic water molecule which attacks the epoxide, while another Asp residue (Asp101) protonates the oxirane ring of the substrate. Arg99 positions the carboxylate groups of the two aspartates, while the water molecule is properly positioned in the active site by hydrogen bonds to the Tyr53, Asn55, and Asp132 residues. The potential for the enzyme to be useful in biocatalysis is limited by the poor enantioselectivity it displays for substrates other than the natural limonene epoxide. For example, cyclopentene oxide (Scheme 1) is hydrolyzed with an enantiomeric excess (ee) of only 14 % in favor of the R,R-configured product.13 Recently, Zheng and Reetz employed iterative saturation mutagenesis techniques to engineer LEH mutants which were able to catalyze the desymmetrization of meso-cyclopentene oxide to produce either of the R,R- or S,S-configured diols with high enantioselectivities (Figure 1).13 The ability to generate R- or S-selective mutants using directed evolution techniques is indeed an impressive success of the experimental procedures. These well-defined experimental results constitute an interesting case to assess the usefulness of the cluster approach. It should be pointed out that as the substrate is a meso compound it makes the task of the investigation of the enantioselectivity somewhat easier, since one in fact does not need to consider the differential binding energies of enantiomeric substrates. The latter case is of course a more common scenario in asymmetric biocatalytic applications. Nevertheless, we have in the current work chosen to study LEH-catalyzed desymmetrization of cyclopentene oxide to separate the effects of the mutations on the chemical step from those on the binding step, which will help to better analyze possible sources of errors associated with the cluster approach. Figure 1 Experimental results of iterative saturation mutagenesis experiments.13 Scheme 1 A) LEH-catalyzed desymmetrization reaction considered in the present work. B) Reaction mechanism of LEH. Previous quantum chemical calculations using a relatively small model of the active site (80 atoms) confirmed the reaction mechanism shown in Scheme 1 and resolved some issues regarding the stereoselectivity of limonene hydrolysis, issues which were shown to be inherent to the limonene substrate itself.14 QM/MM calculations have also been performed recently, reaching similar conclusions regarding the reaction mechanism.15 Here, a large active-site model of LEH was designed based on the X-ray crystal structure of the wild-type (WT) enzyme crystallized with heptanamide as a ligand (PDB 1NWW).12d It consists of 259 atoms and includes the following groups (Figure 2): the Asp132-Arg99-Asp101 catalytic triad, the nucleophilic water and the two residues hydrogen-bonding to it, Tyr53 and Asn55, as well as other groups that define the active-site cavity, namely Met78, Leu74, Ile80, Leu35, Leu103, Met32, Val83, Leu114, and Ile116. Hydrogen atoms were added manually and the ligand in the active site was replaced by the substrate with the epoxide oxygen atom positioned within hydrogen-bonding distance to Asp101. As shown in Figure 2, the various amino acids were truncated to reduce the size of the model. The truncation points (asterisks in Figure 2) were kept fixed during the geometry optimizations to maintain the overall structure of the active site (see the Supporting Information for a list of locked centers in all models). This coordinate-locking scheme is a very common, and in many cases necessary, procedure in the cluster approach and has over the years been shown to yield very good results, in particular when the model is large enough.1 The geometries were optimized at the B3LYP/6-31G(d,p) level of theory (see Computational Details in the Supporting Information). Large models of the size used here suffer very commonly from multiple-minima problems which can be quite severe, and can lead to unreliable energies. In the present work, we have very carefully, by visual inspection and by overlaying the optimized structures of the stationary points, made sure that groups which are not directly participating in the reaction are in the same local minima throughout the reaction. Figure 2 Optimized structure of the active-site model of LEH. The catalytically active residues are shown in yellow. Asterisks indicate positions fixed to their crystallographic coordinates. For clarity, only selected hydrogen atoms are shown. The optimized structure of the ES complex is displayed in Figure 2. Cyclopentene oxide is somewhat smaller than the natural limonene epoxide substrate and therefore fits in the active-site cavity without major conformational changes of the side chains as compared to the crystal structure. As expected, the substrate is positioned through a hydrogen bond to Asp101 while the water molecule forms hydrogen bonds to Tyr53 and Asn55, as well as to Asp132, which will act as the general base. Next, we optimized the transition states (TSs) for the opening of the oxirane ring at either of the two carbon centers which we will refer to as C1 and C2, respectively, thus leading to either the S,S- or R,R-configured products (see Figure 2 for labeling). As demonstrated in the previous quantum chemical study,14 the reaction is calculated to take place in one concerted step in which the nucleophilic attack and ring-opening take place at the same time as the activation of the water molecule by Asp132 and the protonation of the epoxide oxygen atom by Asp101 (Figure 3). Figure 3 Optimized transition-state structures, for the WT, of TSC1 and TSC2, which result in the S,S- or R,R-configured products, respectively. Selected distances are given in Angstroms. Note that for clarity the figures show only a small part of the active-site model. The energy barriers were calculated at the B3LYP/6-311+G(2d,2p) level of theory and include corrections for the zero-point, solvation, and dispersion effects (see the Supporting Information). For the WT structure, the computed barriers were found to be almost identical, 15.7 and 15.6 kcal mol−1, for obtaining the S,S- and R,R-configured products, respectively. This result is in a very good agreement with the experimental observation of a small 14 % ee obtained in favor of the R,R-configured product, and corresponds to an energy difference of 0.2 kcal mol−1. As mentioned above, the active-site cavity of the WT is somewhat too large for the cyclopentene oxide substrate and can therefore accommodate attacks at C1 and C2 equally well because the substrate can be displaced in one direction or the other (Figure 3) with the same energetic penalty. This scenario results in very similar barriers and hence very poor selectivity. The results so far show that the active-site model can reproduce and rationalize the enantioselectivity of the WT enzyme. Next, the cluster model was altered according to the experimental mutations (see Figure 1 for definitions) and all TSs for attacks on C1 and C2 were re-optimized. The calculated barriers are presented in Table 1 and the barrier differences are compared to the experimentally determined enantioselectivities in Figure 4. Figure 4 Comparison between experimental and calculated differences in activation barriers for WT and mutants. Table 1 Calculated absolute and relative activation barriers (in kcal mol−1) for WT and all mutants TSC1 TSC2 ΔΔE ≠ calc. ΔΔG ≠ expt [a] WT 15.7 15.6 −0.1 −0.2 Mutant R1 14.3 13.1 −1.2 −0.9 Mutant R2 14.0 13.6 −0.4 −1.1 Mutant R3 15.3 14.3 −1.0 −1.3 Mutant S1 14.7 16.1 +1.4 +1.0 Mutant S2 13.9 17.5 +3.6 +1.8 Mutant S3 13.2 16.6 +3.4 +2.0 [a] Energies as converted from the experimental enantiomeric excesses. The comparison shows that the cluster model yields very good agreement with the experimental observations. That is, the mutants that experimentally result in improved R,R selectivity are indeed calculated to have lower barriers for opening at C2, while the mutants that show S,S selectivity have lower barriers for opening at C1. Taken together, these results must be regarded as outstanding indeed, especially considering that some of the variants contain up to five point mutations. The energetic preference for the S,S- or R,R-configured products can be rationalized by scrutinizing the optimized transition-state structures of the mutants. It turns out that, to a large extent, the mutational effects can be explained by how much steric hindrance they introduce or relieve to prevent or allow the substrate from moving to accommodate attacks on either of the two carbon centers. For example, both the Leu74Ile and Ile80Cys mutations in the double-mutant R1 variant introduce smaller side chains and make one side of the active site slightly less crowded, and in turn makes the attack on C2 somewhat less hindered because the substrate now can be displaced more easily in that direction. Overall, this double mutation leads to lower barriers for both attacks compared to the WT, but the C2 attack is more favorable (13.1 and 14.3 kcal mol−1 for attacks at C2 and C1, respectively), thus yielding a higher selectivity for the R,R-configured product. Conversely, in the S1 mutant both the Leu114Cys and Ile116Val mutations are located on the other side of the substrate and result in decreased bulk there. Therefore, these mutations will now lower the barrier for attack on C1 compared to C2 (14.7 and 16.1 kcal mol−1 for attacks at C1 and C2, respectively), thus leading to the S,S-configured product. The additional mutation introduced in S2, Ile80Phe, is located on the other side compared to the two mutations of S1 and introduces additional bulk there. This mutation results in a higher barrier for attack at C2 and thus the more favorable C1 attack (13.9 and 17.5 kcal mol−1 for attacks at C1 and C2, respectively) leads to an increased S,S selectivity. The calculated effect of the Ile80Phe mutation is however somewhat overestimated compared to experiments (Figure 4). One reason for this could be that the locking scheme makes that residue too rigid in the cluster model. Interestingly, the Met32Cys mutation appears experimentally in both branches of mutations, that is, it helps in improving both the R,R and S,S selectivities (R1→R2 and S2→S3). The improvement is quite small (66 to 73 % ee for R1→R2 and 91 to 93 % ee for S2→S3). Its role is unclear and it is evident that the calculations cannot reproduce the trends correctly (Figure 4). One reason for this discrepancy could be that the Met32Cys introduces a hydrogen-bonding thiol group at the periphery of the cluster model. In the absence of other residues outside, this group turns inward and forms somewhat artificial interactions which result in this disagreement. Finally, it is interesting to monitor some geometric parameters which can be used as indicators of the amount of steric hindrance put on the substrate during the attack. For example, in the case of the WT enzyme the nucleophilic ∡O-C-O angles are 150.1° and 150.3° for attacks on C1 and C2, respectively, thus showing that the two TSs are very similar (see Figure 3 and the Supporting Information for other geometric parameters). In the R1 variant, these angles are 148.9° and 150.5°, respectively, showing that the substrate in the C2 attack which leads to the R,R-configured product is slightly less constrained. In the S1 variant, the opposite trend is observed; the angles are namely 150.2° and 147.5°, respectively. To conclude, the calculations presented herein provide convincing results showing that the quantum chemical cluster methodology for modeling enzyme active sites can reproduce and rationalize enantioselectivity quite well. However, although the absolute R,R or S,S enantioselectivities are well reproduced by the model, the trends within each branch are not accurately captured. One source of error could be that the mutations introduce larger conformational changes of the active site, changes which are not properly represented in our calculations because we use the WT crystal structure as a starting point for the mutant calculations. Other sources of error could be the usual limitations associated with the cluster approach, such as the use of homogenous solvation instead of the specific field provided by the enzyme surrounding, the coordinate-locking scheme, and the use of enthalpy rather than free energies. It should be emphasized that the current calculations have followed the standard cluster approach described in many previous reports, with the aim of investigating how well it performs in this kind of situation. That is, the aim has not been to reproduce the particular experimental results at hand, as might be achieved with enough alterations of active-site models or the underlying quantum chemical methods. In that respect, the results are indeed very promising and show that the cluster approach can be a very economic alternative to the more elaborate schemes currently available in the computational chemistry toolbox and can thus be valuable in the field of biocatalysis. More test cases have of course to be investigated to properly evaluate the strengths and limitations. Future studies on the LEH enzyme include assessment of the role of the starting structure on the selectivity. For example, molecular dynamics simulations can be performed first to equilibrate the mutant structures before the cluster model is cut out. These studies are currently underway in our laboratory as well as investigations of more complicated enzymes with enantiomeric substrates which bind differently to the active site.

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          Rapid planetesimal formation in turbulent circumstellar discs

          The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies (Safronov 1969). How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick together poorly (Benz 2000), and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas (Weidenschilling 1977). Gravitational collapse of the solid component has been suggested to overcome this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin & Shu 2002). Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer (Weidenschilling & Cuzzi 1993, Dominik et al. 2007), but turbulence must be present to explain observed gas accretion in protostellar discs (Hartmann 1998). Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas (Johansen, Klahr, & Henning 2006), and these concentrations are augmented a further order of magnitude by a streaming instability (Youdin & Goodman 2005, Johansen, Henning, & Klahr 2006, Johansen & Youdin 2007) driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar discs.
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            The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity

            A phase transition describes the sudden change of state in a physical system, such as the transition between a fluid and a solid. Quantum gases provide the opportunity to establish a direct link between experiment and generic models which capture the underlying physics. A fundamental concept to describe the collective matter-light interaction is the Dicke model which has been predicted to show an intriguing quantum phase transition. Here we realize the Dicke quantum phase transition in an open system formed by a Bose-Einstein condensate coupled to an optical cavity, and observe the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-ranged interactions between the condensed atoms. These are induced by two-photon processes involving the cavity mode and a pump field. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model. The work opens the field of quantum gases with long-ranged interactions, and provides access to novel quantum phases.
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              QM/MM methods for biomolecular systems.

              Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

                Author and article information

                Angew Chem Int Ed Engl
                Angew. Chem. Int. Ed. Engl
                Angewandte Chemie (International Ed. in English)
                WILEY-VCH Verlag (Weinheim )
                22 April 2013
                19 March 2013
                : 52
                : 17
                : 4563-4567
                Department of Organic Chemistry, Arrhenius Laboratory, Stockholm University 10691 Stockholm (Sweden) E-mail: himo@ 123456organ.su.se
                Author notes

                We acknowledge financial support from the Swedish Research Council, the Göran Gustafsson Foundation, and the Knut and Alice Wallenberg Foundation. Computer time was generously provided by the Swedish National Infrastructure for Computing.

                Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/anie.201300594.

                Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://angewandte.org/open.

                Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

                Re-use of this article is permitted in accordance with the Creative Commons Deed, Attribution 2.5, which does not permit commercial exploitation.



                quantum chemistry, enzymes, enantioselectivity, biocatalysis, transition states


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