Modelling the Reactions Catalyzed by Coenzyme B12 Dependent

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Modelling the Reactions Catalyzed by Coenzyme B Dependent Enzymes: Accuracy and Cost-Quality Balance Christian Rainer Wick, and David Matthew Smith J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b11798 • Publication Date (Web): 01 Feb 2018 Downloaded from http://pubs.acs.org on February 2, 2018

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The Journal of Physical Chemistry

Modelling the Reactions Catalyzed by Coenzyme B12 Dependent Enzymes: Accuracy and CostQuality Balance Christian R. Wick†,* and David M. Smith†,‡,* †

Division of Physical Chemistry, Group for Computational Life Sciences, Ruđer Bošković

Institute, Bijenička cesta 54, 10000 Zagreb, Croatia ‡

Center for Computational Chemistry, FAU Erlangen-Nürnberg, Nägelsbachstrasse 25, 91052

Erlangen, Germany

ABSTRACT. The reactions catalyzed by coenzyme B12 dependent enzymes are formally initiated by the homolytic cleavage of a Carbon-Cobalt bond and a subsequent or concerted Hatom-transfer reaction. A reasonable model chemistry for describing those reactions should, therefore, account for an accurate description of both reactions. The inherent limitation due to the necessary system size renders the coenzyme B12 system a suitable candidate for DFT or hybrid QM/MM methods, however, the accurate description of both homolytic Co-C cleavage and Hatom-transfer reactions within this framework is challenging and can lead to controversial results with varying accuracy. We present an assessment study of 16 common density functionals applied to prototypical model systems for both reactions. H-abstraction reactions were modeled based on 4 reference reactions designed to resemble a broad range of coenzyme B12 reactions.

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The Co-C cleavage reaction is treated by an ONIOM(QM/MM) setup that is in excellent agreement with solution phase experimental data and is as accurate as full DFT calculations on the complete model system. We find that the meta-GGAs TPSS-D3 and M06L-D3 and the metahybrid M06-D3 give the best overall performance with MUEs for both types of reactions below 10 kJ mol-1. Our recommended model chemistry allows for a fast and accurate description of coenzyme B12 chemistry that is readily applicable to study the reactions in an enzymatic framework.

INTRODUCTION Coenzyme B12 dependent enzymes utilize coenzyme B12 (5’-deoxyadenosylcobalamin, dAdoCbl) to facilitate a broad range of controlled radical reactions. The different classes of these enzymes, however, show subtle differences in coenzyme binding, substrate selectivity and tolerance to structural variations of the coenzyme.1 Nevertheless, the reactions of coenzyme B12 enzymes (with exception of the ribonucleotide reductases) can be described by a general mechanism (Scheme 1).2,3 Formally, the initial step is the generation of a 5’-deoxyadenosylradical (dAdo·) and a Co(II) containing Cob(II)alamin (Cbl) after homolytic cleavage of the Carbon-Cobalt bond of coenzyme B12. The dAdo· radical readily abstracts a hydrogen atom from the substrate to form a substrate-radical and dAdo. The substrate itself can be located some 6 Å from the Co atom of dAdoCbl, as in Methylmalonyl Co-A Mutase (MCM, Figure 1),4 an example of the carbon-skeleton mutases, or slightly further removed (with a Co-substrate distance of ca. 8 Å) as in the case in the eliminases, such as diol dehydratase (DDH).1,5,6 The


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substrate-radical then undergoes a 1,2-rearrangement before the hydrogen atom is transferred back from dAdo (H-recombination) to give dAdo· and the reaction product.

Scheme 1. Generalized mechanism of coenzyme B12 dependent enzymes. The question as to whether the Co-C cleavage and the subsequent H-abstraction reaction proceed via a concerted or a stepwise mechanism remains still controversial (for a very good summary on this topic, the interested reader is encouraged to consult Refs 7–13 and the citations therein). From a theoretical perspective, the reactions involved are challenging and the size of the molecules renders them suitable candidates for DFT or hybrid methods. The homolytic cleavage of the Co-C bond of dAdoCbl and related species has been intensively investigated previously at various levels of theory including DFT,10,11,14–19 Empirical Valence Bond (EVB)8,9 and hybrid QM/MM methods,7,13,20–23 the results of which have also been summarized in several excellent reviews (e.g. Refs. 24–26). While most of the earlier work on isolated dAdoCbl (i.e. without an enzymatic framework in the gas-phase or a dielectric continuum) has been based on truncated model systems of dAdoCbl, which exclude the sidechains of dAdoCbl, recent work has shown that the inclusion of dispersion corrections and the interactions of the side chains are crucial for the reproduction of the experimental Bond Dissociation Enthalpy (BDE). Regardless of the model system, the DFT based studies showed that hybrid DFs such as B3LYP(-D3) clearly underestimate the Co-C bond strength, while


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dispersion corrected pure functionals, such as BP86-D3 and TPSS-D3 are able to reproduce the experimental BDE. The experimental exploration of radical hydrogen atom transfer reactions is often a very difficult task and, as a result, theoretical studies play a major role in this field.27,28 The radical reactions initiated after homolytic cleavage of the Co-C bond occurring in several classes of coenzyme B12 dependent enzymes have been investigated by small prototypical model reactions with high level compound ab initio methods,3,29 which were specially designed for the treatment of radical species.30–33 Based on the findings with high level reference calculations, it was also possible to estimate the applicability of e.g. DFT methodologies to radical H-atom transfer reactions, which allows the inclusion of large molecules such as the corrin ring for the estimation of their impact on the following radical reactions.10,11,13 It was found that hybrid functionals such as B3LYP can produce results of acceptable accuracy and that their performance is superior to non-hybrid pure functionals such as BP86.3,10,34

Figure 1. Active site of human Methylmalonyl-CoA mutase (MCM, PDB-ID: 2XIQ4) in complex with Cobalamin (Cbl, orange), 5’-deoxyadenosyl (dAdo, green) and Malonyl Co-A (purple) in a state where the Co-C bond is broken.


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The conclusion that emerges from this previous work is that local GGAs such as BP86 give consistent results for the Co-C bond breaking step,10,14 but are less than ideal for describing Hatom transfer. On the other hand, hybrid functionals, such as B3LYP, ensure an accurate description of the thermodynamics and kinetics of the H-atom transfer reactions3 but fail to describe the Co-C bond breaking step.10,14,18,19,35 However, to the best of our knowledge, the performance of a broader range of density functionals (DFs) on both types of reaction was never assessed in a rigorous manner. Thus, the goal of this study is to find a suitable model chemistry for a balanced and accurate description of the initial bond breaking and H-atom-transfer reactions of coenzyme B12 dependent enzymes. This will help us to answer the remaining open questions regarding the mechanism of different types of coenzyme B12 dependent enzymes and their interesting chemistry.

METHODS All computations (if not otherwise noted) were carried out with Gaussian 09.36 The following set of density functionals (DFs) was considered: APFD37, B3LYP38–40, BP8641,42, B97D43, BLYP41,39, BMK44, M0645, M06L45, M06-2X45, MN12L46, PBE47, PBE048, TPSS49, and wB97XD50. The inclusion of atom-pair-wise dispersion corrections51 is denoted by the addition of “–D3” after the name of the functional. Geometry optimizations, Zero-Point Energy (ZPE) corrections and thermal corrections to Enthalpy (H298) and Free Energy (G298) at 298 K were calculated at the TPSS-D3/def2-SVP52 level of theory. The nature of all energy optimized structures (minima and transition states) was verified by vibrational analysis. Single-Point (SP) energy calculations


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were carried out with def2-TZVP basis sets. The spin-unrestricted formalism was used to describe open shell systems if not otherwise noted. Co-C Bond Dissociation Enthalpy. The BDE was calculated with fully optimized structures for both a truncated model and a full model of coenzyme B12 (Figure 2; 71 and 209 atoms, respectively). For the treatment of the full model system, we applied a ONIOM(QM:MM) scheme as indicated in Figure 2 and Figure S1 (120 atoms in the high layer). The ONIOM(QM:MM) calculations utilize the AMBER force field parameters for coenzyme B1253 including the modifications from Bucher et al.7 The atomic charges for the dAdo-radical were generated with the R.E.D. tools54 using a procedure, which is compatible to the Duan et al. force field.55 A total of 8 conformations with 4 orientations were considered. Geometry optimizations were carried out at the ONIOM(TPSS-D3/def2-SVP:AMBER) level of theory with mechanical embedding.56 SP energy calculations were carried out with the def2-TZVP basis set and the ONIOM electrostatic embedding scheme.57 Solvation free energy corrections were estimated with the Polarizable Continuum Model58 using the integral equation formalism59 (IEFPCM), utilizing UFF atomic radii scaled by 1.1 (as implemented in Gaussian 09) and a dielectric constant of 78.3553 for water. Only the electrostatic contributions were considered in the calculation of the solvation free energy. Within the ONIOM framework, the solvation free energy corrections were estimated with the ONIOMPCM/A version of the IEFPCM methodology, as described by Vreven et al.60 In ONIOMPCM/A, the reaction field is self-consistently derived from the integrated ONIOM density and no further approximations are introduced, as in PCM/B, PCM/C or PCM/X. The Bond dissociation Enthalpy (BDEgas, 0K) includes ZPE corrections and is calculated as 𝐵𝐷𝐸𝑔𝑎𝑠, 0𝐾 = 𝐸(𝐶𝑏𝑙(𝐼𝐼)) + 𝐸(𝑑𝐴𝑑𝑜 ·) − 𝐸(𝑑𝐴𝑑𝑜𝐶𝑏𝑙) + ΔZPE

(1)


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The computed BDEs were compared to back corrected18 experimental BDEs taken from Ref 61. Additional (RO-)DLPNO-CCSD(T)62–64 and (RO-)RI-MP2 calculations were performed with ORCA 4.0.1.65 The RI-MP2 calculations were carried out with def2-TZVPP, def2-QZVPP and the corresponding def2-TZVPP/C and def2-QZVPP/C auxiliary basis sets.66 Extrapolation to the MP2 complete basis set limit followed the two point schemes for SCF67 and correlation energies,68 utilizing the optimized exponents for 3/4 extrapolation.69 The final DLPNOCCSD(T)/CBS energy was obtained as 𝐶𝐶𝑆𝐷(𝑇)𝐶𝐵𝑆 = 𝐶𝐶𝑆𝐷(𝑇)𝑑𝑒𝑓2−𝑇𝑍𝑉𝑃𝑃 + 𝑀𝑃2𝐶𝐵𝑆 − MP2𝑑𝑒𝑓2−𝑇𝑍𝑉𝑃𝑃

(2)

In addition to an analysis of the fractional occupation number weighted electron density (FOD),70 we determined the T1 diagnostics71 to estimate the amount of static electron correlation (SEC) inherent in the transition-metal containing species and to prove the reliability and applicability of these single reference post-HF methods (Figure S2, Table S1). H-atom-transfer reactions. In absence of high quality experimental data for the reaction enthalpies and enthalpies of reaction for the model systems studied, higher level reference calculations were carried out at the G3(MP2)-RAD32 level of theory. G3(MP2)-RAD is a highlevel composite method designed for radical thermochemistry, which approximates the URCCSD(T)/G3MP2Large level of theory by URCCSD(T)/6-31G(d), RMP2/6-31G(d) and RMP2/G3MP2Large single point calculations on B3LYP/6-31G(d) geometries together with scaled (by 0.9806) B3LYP/6-31G(d) computed ZPE corrections. In this study, we slightly modified the procedure by using TPSS-D3/def2-SVP geometries and (unscaled) ZPE corrections for both the homolytic Co-C cleavage and the H-atom transfer reactions. The necessary URCCSD(T)72 calculations were carried out with Gaussian 09.


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RESULTS AND DISCUSSION The following section is structured in three parts, for the sake of clarity. First, we will discuss the homolytic cleavage of the Co-C bond of coenzyme B12, including a few remarks regarding the model system selection. This discussion will include an investigation of the accuracy of different DFs spanning the range from local-GGA and meta-GGA, to hybrid and meta-hybrid in comparison to the experimental BDE. In part two, we concentrate on the model reactions for the H-abstraction of two classes of coenzyme B12 dependent enzymes, namely the carbon-skeleton mutases and the eliminases, and discuss the accuracy of the different DFs with regard to the thermodynamics and kinetics of the model reactions. In the final part, we will combine our findings for both Co-C cleavage and H-abstraction to identify the DFs with the best overall performance. 1. Homolytic Co-C Cleavage. The size of coenzyme B12 is undoubtedly a limiting factor regarding the choice of the level of theory to describe the homolytic cleavage of the Co-C bond. Therefore, it would be very advantageous to use a truncated model system (such as delineated in Figure 2) to decrease the computational cost. However, it was found by Kepp19 and Qu. et al.18 that the inclusion of the side chains (together with a decent correction for dispersion effects) is crucial in order to reproduce the experimental BDE. Unfortunately, the quality of the results strongly depends on the DF used and their findings are in agreement with earlier results that e.g. B3LYP(-D3) underestimates the Co-C bond strength, while BP86-D3 is in good agreement with the experimental data. Since TPSS-D3 performed even slightly better in the calculations on the full model system,18 we choose this model chemistry as reference for a hybrid ONIOM(QM/MM) setup that includes the side chain interactions based on the AMBER force field for coenzyme B12.7,53 We find that this setup is in full accordance with the complete DFT


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model regarding the calculated BDEs (Table 1.) and energy corrections to the BDE (Table 2.). Thus, we decided to use the ONIOM(QM/MM) setup instead of pure DFT as the basis for our assessment of different DFs, because, (I), it tremendously reduces the computational costs, and, (II), represents a model chemistry that will allow us to study the reactions within an enzymatic environment, where several amino acid residues and not only the side chains of Cbl establish important interactions with dAdo and the whole coenzyme. The ONIOM setup, therefore, achieves a balanced treatment of the important non-covalent effects keeping the same QM/MM layering in the gas phase and in the enzyme.

Figure 2. Different model systems of coenzyme B12. A) Full model system and ONIOM(QM/MM) layering. QM atoms are shown as balls and sticks, while the MM layer extends as wireframe (purple, see also Figure S1). B) Truncated model system. The Cobalt ion is represented by a brown sphere. Hydrogen atoms are omitted for clarity.


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Table 1. TPSS-D3 Co-C Bond Dissociation Enthalpies (BDE) at 0 K calculated with different model systems (kJ mol-1). BDEgas, 0Ka

ΔD3b

DFTtrunc.c

166.7

61.0

DFTfullc,d

210.0

140.6

ONIOMfullc

217.9

104.2

Exp.e

215.5

a

BDE calculated in the gas phase including ZPE corrections; bΔD3: Calculated contribution from D3-dispersion corrections to the total BDE; ctruncated and full model systems are specified in Figure 2.; dTPSS-D3/def2-TZVP full DFT values taken from Qu et al.18; eexperimental BDE61 back corrected from solution data (taken from Qu et al.18). The experimental error bar is ±8 kJ mol-1. Table 2. Comparison of the TPSS-D3 / ONIOM computed corrections to the electronic bond dissociation energies (kJ mol-1). ONIOMa DFTb ΔD3c 104.2 140.6 d ΔZPE -21.8 -24.7 e ΔH298 -18.3 -18.4 f ΔG298 -94.9 -104.2 g ΔGsol -33.0 -32.6 a ONIOM(TPSS-D3/def2-SVP:AMBER) computed corrections. bTPSS-D3/def2-TZVP full DFT values taken from Qu et al.18. cΔD3: Calculated contribution from D3-dispersion corrections to the total BDE. dΔZPE: contributions from Zero Point Energy corrections. eΔH298: Contributions from thermal corrections to Enthalpy at 298 K. fΔG298: Contributions from Free Energy corrections at 298 K. gΔGsol: Contribution from solvation free energy corrections in water computed with PCM/A (ONIOM(TPSS-D3/def2-TZVP:AMBER)) and COSMO-RS (DFT)

To further leverage the clear advantages of our defined ONIOM(DFT:MM) setup, we also investigated its general quality and the balance of the QM/MM layering by switching from DFT


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to high level DLNPO-CCSD(T)/CBS calculations for the QM part (Table 3). The accuracy and the general applicability of single-reference CC calculations strongly depends on the amount of SEC inherent in the model system and thus it is important to explore the potential multireference character of the systems investigated.70,73–75 The calculated T1 diagnostics (Table S1) are all below 0.02, which is in the acceptable range for 3d transition metal complexes.73 However, the FOD analysis shows that at least the Cbl(II) species exhibits a degree of SEC (Table S2, Figure S2), which indicates a potential borderline case for the applicability of singlereference post-HF methods.70 Nevertheless, in such cases, it has been previously noted that CCSD(T) can still produce results of excellent quality without multi-reference corrections, especially if the energies are extrapolated to the complete basis set limit.75 In this regard, we found that the DLPNO-CCSD(T)/CBS computed BDEs are again in very good agreement with the experimental values, justifying the accurate QM/MM layering and allowing us to better understand the accuracy of other DFs within the established framework. Table 3 shows that not only TPSS-D3, but also 5 out of 16 different DFs predict gas-phase and solution-phase BDEs in excellent agreement with the experimental data. Among the best DFs are a hybrid functional (APFD), a meta-hybrid (M06-D3), two meta-GGAs (M06L-D3, TPSS-D3) and two GGAs (PBE-D3 and BLYP-D3), with deviations that fall within the experimental error of ±8 kJ mol-1. In contrast to the findings with full DFT calculations, BP86-D3 overestimates the BDEs, whereas B3LYP-D3 still underestimates (as expected) the strength of the Co-C bond. The highest deviation from the experimental data is observed for M062X-D3, which also underestimates the Co-C bond strength. Generally, we find that the inclusion of an appropriate dispersion correction is also crucial in the ONIOM calculations (Table S2). For example, the hybrid functionals (without dispersion corrections) show a weak correlation regarding the


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amount of exact exchange and the Co-C bond strength (Table S3), which is completely lost when dispersion corrections are added. Overall, it is difficult to definitively assign the exact reason for the poor performance of the majority of functionals in the context of the ONIOM calculations. Namely, the ONIOM setup certainly includes a favorable cancellation of errors, some of which arise because a significant proportion of the non-covalent and dispersion interactions are included via the MM layer.

Table 3. ONIOM computed Co-C BDE in the gas phase and in water (kJ mol-1). BDEgas, 0Ka BDEaq, 298Kb APFD 216.6 123.4 B3LYP-D3 174.0 80.8 B97D 232.2 139.0 BLYP-D3 214.8 121.6 BMK-D3 201.7 108.5 BP86-D3 246.7 153.5 M06-D3 210.0 116.8 M06 172.3 79.1 M062X-D3 129.0 35.8 M06L-D3 214.8 121.6 M06L 194.2 101.0 MN12L 249.6 156.3 PBE-D3 215.2 122.0 PBE0-D3 165.2 72.0 TPSS-D3 217.9 124.7 ωB97XD 187.5 94.3 CCSD(T)/CBSc 216.2 123.0 d Exp. 215.5 125.5 a BDE calculated with ONIOM(QM/def2-TZVP:AMBER) in the gas phase including ONIOM(TPSS-D3/def2-SVP:AMBER) ZPE corrections. bBDE at 298 K including ONIOM(TPSS-D3/def2-SVP:AMBER) enthalpy corrections and COSMO-RS TPSSD3/def2-TZVP computed solvation enthalpy corrections (taken from Qu et al.18). cDLPNOCCSD(T) extrapolated as described in the methods section dexperimental BDE61 back corrected from solution data (taken from Qu et al.18). The experimental error bar is ±8 kJ mol-1.


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2. H-atom-transfer. The performance of different DFs on the hydrogen abstraction reactions was studied based on four model reactions (Scheme 2.), which directly resemble the two Habstraction reactions of MCM (class I, carbon-skeleton mutases) and DDH (class II, eliminases). The reference energies were computed with a slightly modified version of G3(MP2)-RAD (details are given in the Methods section). G3(MP2)-RAD was shown to reproduce experimental Heats of Formation32,33, Radical Stabilization Energies27,28 and Barrier Heights3 of radical reactions with high accuracy, rendering it a perfectly suited reference method for our comparison. Following the reactions in Scheme 2, we are able to assess the accuracy of the DFs based on the thermodynamics and the kinetics separately.

Scheme 2. Model reactions for the H-atom-abstractions (a) and recombinations (r) in Class I and II coenzyme B12 dependent enzymes. Enthalpies of Reaction. Our reference calculations (Table 4) indicate that only the initial Habstraction reaction in the model for MCM (I.a) is thermoneutral. The final H-recombination step is slightly endothermic (I.r, 24.8 kJ mol-1). The model reaction for DDH starts with a slightly exothermic H-abstraction reaction (II.a, -25.1 kJ mol-1), while the final recombination reaction (II.r, 11.4 kJ mol-1) is again endothermic. In general, all investigated DFs are able to reproduce the thermodynamics of our model reactions with mean unsigned errors (MUE) below


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8 kJ mol-1. M06L with and without atom-pair-wise dispersion corrections shows the worst agreement with the reference enthalpies (MUE = 7.7 kJ mol-1). The best functional is M06-2XD3, with a MUE of 1.6 kJ mol-1 and a mean signed error (MSE) of only 0.4 kJ mol-1, which is in line with previous findings involving a broad range of different radicals.30,76–78

Table 4. Computed Enthalpies of Reaction in the gas phase at 0 K (ΔHgas, 0K) and the resulting total mean-errors and largest absolute deviations (LAD) for all four reactions (kJ mol-1). I.a

I.r

II.a

II.r

MSE

MUE

LAD

APFD

-0.1

30.2

-31.9

15.3

0.5

4.2

6.8

B3LYP-D3

-0.1

32.0

-29.9

15.4

1.4

4.2

7.2

B97D

-1.3

38.7

-31.4

18.3

3.1

7.2

13.9

BLYP-D3

-0.4

37.4

-32.9

17.5

2.5

6.9

12.6

BMK-D3

-0.8

27.5

-30.2

10.9

-1.1

2.4

5.1

BP86-D3

-0.3

35.6

-33.9

17.5

1.8

6.6

10.8

M062X-D3

0.0

26.7

-27.1

13.5

0.4

1.6

2.1

M06-D3

-1.4

33.0

-29.4

18.4

2.2

5.4

8.2

M06

-1.5

32.9

-29.3

18.2

2.2

5.3

8.1

M06L-D3

-1.4

37.9

-31.6

20.9

3.5

7.7

13.1

M06L

-1.4

37.8

-31.5

20.7

3.5

7.7

13.0

MN12L

-0.6

34.9

-29.3

16.3

2.4

5.1

10.1

PBE0-D3

0.0

29.2

-31.1

15.5

0.5

3.8

6.0

PBE-D3

-0.2

35.7

-35.7

19.1

1.8

7.5

10.9

TPSS-D3

-0.4

34.8

-32.0

16.9

1.9

5.8

10.0

ωB97XD

0.1

30.5

-32.4

16.0

0.6

4.5

7.4

Ref.

0.5

24.8

-25.1

11.4

0.0

0.0

0.0


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Barrier Heights. The reference reactions for our comparison involving the thioesters (I.a and I.r) show very similar Enthalpies of Activation (Table 5.), amounting to about 47 kJ mol-1. The Barriers of the class II reactions are much smaller with values of 25 kJ mol-1 and 36 kJ mol-1 for II.a and II.r, respectively. We again use these reference values as the basis for the further assessment of the performance of our set of DFs. In general, we observe a much higher diversity among the different DFs compared to the performance based on the reaction energies, with MUEs for barriers ranging from 2.6 kJ mol-1 (M06-2X-D3) to 27.8 kJ mol-1 (BP86-D3). The lowest MUEs are obtained by the two hybrid functionals M06-2X-D3 and M06(-D3) closely followed by M06L(-D3). M06L(-D3) is the only local DF with an MUE below 10 kJ mol-1, while B3LYP-D3, PBE0, BMK-D3 and ωB97XD are the only remaining DFs with MUEs below 10 kJ mol-1. The two meta GGAs, TPSS-D3 and MN12L are in the next rank with MUEs below 15 kJ mol-1. One interesting aspect is that, even for the small model reactions, the inclusion of longrange D3 corrections to the M06 suite of DFs, which already implicitly cover medium-range dispersion effects due to their parameterization, increase the overall accuracy.


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Table 5. Computed Enthalpies of Activation in the gas phase at 0 K (Δ‡Hgas, 0K) and the resulting total mean errors and LADs for all four elementary reactions (kJ mol-1). I.a

I.r

II.a

II.r

MSE

MUE

LAD

APFD

32.8

33.2

5.9

20.3

-15.5

15.5

18.5

B3LYP-D3

41.2

48.5

12.4

29.9

-5.5

6.6

12.0

B97D

27.8

41.1

-1.0

18.6

-16.9

16.9

25.4

BLYP-D3

30.1

40.4

-0.4

19.6

-16.1

16.1

24.8

BMK-D3

41.0

35.7

16.3

26.0

-8.8

8.8

10.6

BP86-D3

20.2

25.1

-10.7

8.2

-27.8

27.8

35.2

M062X-D3

50.7

49.1

24.6

38.3

2.1

2.1

3.8

M06-D3

43.9

45.9

17.3

34.6

-3.1

3.1

7.1

M06

52.1

56.0

23.1

41.6

4.7

5.3

9.7

M06L-D3

45.9

50.2

15.7

38.7

-0.9

4.0

8.7

M06L

49.8

54.6

18.4

41.7

2.6

5.6

8.3

MN12L

63.1

60.2

34.7

53.0

14.2

14.2

16.5

PBE0-D3

38.9

43.7

9.8

27.4

-8.6

8.6

14.6

PBE-D3

24.1

33.0

-8.3

14.3

-22.8

22.8

32.8

TPSS-D3

33.8

43.3

4.8

23.7

-12.1

12.1

19.7

ωB97XD

42.8

50.3

16.1

31.9

-3.3

5.2

8.4

Ref.

47.0

46.3

24.4

36.5

0.0

0.0

0.0

3. A compromise of accuracy. Up to this point, we strictly separated the discussion of the CoC cleavage and the kinetics and thermodynamics of the H-atom transfer reactions to delineate the apparent performance of our test set of DFs on a transparent basis. The remaining question we have to answer is: What is the overall performance? We seek a functional, which ensures a wellbalanced and accurate treatment of both reactions, preferably with low computational expense. Therefore, we combined and clustered all of our thermodynamic and kinetic data based on the functional type (Figure 3). As it can be seen, there is no clear trend as to which class of


16

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functional is the best for our purpose. Local GGA functionals give the highest MUEs for the Habstraction reactions, which renders them a poor choice for the description of both reactions, although half of the pure GGAs predict accurate BDEs for the Co-C cleavage. Meta-GGAs, however, are able to give accurate BDEs as long as atom-pair-wise (long-range) dispersion corrections are included, while producing MUEs for the H-abstraction reactions below 10 kJ mol-1. Such performance is only of intermediate accuracy with regard to the best performing DFs for the H-Abstraction reactions. Nevertheless, keeping in mind that the experimental error bar for the Co-C BDE is about ±8 kJ mol-1, the Meta-GGAs can certainly be considered as promising. The hybrids, except APFD and M06-D3, are not able to reproduce the experimental BDE of the Co-C cleavage. Since APFD performs slightly worse for the H-atom transfers, M06-D3 is the best hybrid DF for our purposes based on the raw statistics. In summary, M06-D3, M06L-D3 and TPSS-D3, as well as APFD can all be recommended in terms of providing a well-balanced and accurate treatment of both reaction types. Nevertheless, if the computational cost is also taken into account, M06L-D3 and TPSS-D3 are the best choices.


17


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Figure 3. Summary of Errors for both Co-C cleavage and H-abstraction reactions. The plotted errors include the difference between the computed BDEgas,0K and the experimental value (𝛥𝐵𝐷𝐸𝑔𝑎𝑠,0𝐾 = 𝑐𝑜𝑚𝑝 − 𝑒𝑥𝑝.), the total MSE and the total MUE including ΔHgas, Δ‡Hgas,

0K

0K

and

for the H-abstraction reactions I.a, I.r, II.a and II.r, (MSEH,tot and MUEH,tot,

respectively).

CONCLUSIONS TPSS-D3 reproduces the experimental Co-C BDE of dAdoCbl in the gas phase and in water, when a full model of dAdoCbl is considered. It was shown that the good agreement with the reference values is retained, when the secondary non-covalent interactions between the side chains of Cbl and dAdo are treated by a molecular mechanics force field within an ONIOM(QM/MM) framework. The Co-C BDE can be reproduced not only with various other


18

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meta-GGAs and GGAs, but also with the meta-hybrid M06-D3, as long as atom-pair-wise dispersion corrections are added, and with the hybrid APFD. All DFs are able to correctly describe the thermodynamics of the H-abstraction reactions, nevertheless, many DFs show high MUEs regarding the kinetics. Finally, we can recommend M06L-D3 and TPSS-D3 for the accurate and efficient description of the key reactions of coenzyme B12 dependent enzymes. A slightly better description of the H-abstraction reactions can be achieved with M06-D3, with the associated expense of moving from meta-GGAs to a meta-hybrid.

ASSOCIATED CONTENT Supporting Information. The following files are available free of charge. Supporting Information containing: The ONIOM setup (Figure S1), the FOD Analysis (Figure S2), SEC diagnostics (Table S1), Dispersion corrections to the Co-C BDE (Table S2), Correlation between exact exchange and computed BDE (Table S3), All mean errors (Table S4), A summary of key geometrical data (Table S5), Coordinates of all energy minimized structures (Table S6), refined MM charges (Table S7), (Word Document).

AUTHOR INFORMATION Corresponding Author *Christian R. Wick; E-mail: [email protected]. David M. Smith; E-mail: [email protected]


19


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Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors thank the Croatian Science Foundation (project number IP11-2013-8238) and the EAM Cluster of Excellence at the Friedrich-Alexander University Erlangen-Nürnberg for financial support. We also thank the University of Zagreb Computing Centre (SRCE) for granting computational time on the ISABELLA cluster and CRO-NGI infrastructure. ABBREVIATIONS BDE, Bond Dissociation Enthalpy; Cbl, Cobalamnin; dAdo, 5’-deoxyadenosyl; dAdoCbl, 5’deoxyadenosylcobalamin; DDH, diol dehydratase; DF, Density Functional; DFT, Density Functional Theory; DLPNO, Domain based local pair natural orbital; GGA, Generalized Gradient Approximation; LAD, Largest Absolute Deviation; MCM, methylmalonyl Co-A Mutase; MM, molecular mechanics; MSE, Mean Signed Error; MUE, Mean Unsigned Error; SEC, static electron correlation; SP, Single-Point; ZPE, Zero-Point Energy

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TOC Graphic


31


Scheme 1. Generalized mechanism of coenzyme B12 dependent enzymes. 36x15mm (600 x 600 DPI)


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Scheme 2. Model reactions for the H-atom-abstractions (a) and recombinations (r) in Class I and II coenzyme B12 dependent enzymes. 52x33mm (600 x 600 DPI)



Figure 1. Active site of human Methylmalonyl-CoA mutase (MCM, PDB-ID: 2XIQ4) in complex with Cobalamin (Cbl, orange), 5’-deoxyadenosyl (dAdo, green) and Malonyl Co-A (purple) in a state where the Co-C bond is broken. 62x48mm (300 x 300 DPI)


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Different model systems of coenzyme B12. A) Full model system and ONIOM(QM/MM) layering. QM atoms are shown as balls and sticks, while the MM layer extends as wireframe (purple, see also Figure S1). B) Truncated model system. The Cobalt ion is represented by a brown sphere. Hydrogen atoms are omitted for clarity. 82x44mm (300 x 300 DPI)



Figure 3. Summary of Errors for both Co-C cleavage and H-abstraction reactions. The plotted errors include the difference between the computed BDEgas,0K and the experimental value (∆BDEgas, 0K = comp - exp.), the total MSE and the total MUE including ∆Hgas, 0K and ∆‡Hgas, 0K for the H-abstraction reactions I.a, I.r, II.a and II.r, (MSEH,tot and MUEH,tot, respectively). 94x52mm (600 x 600 DPI)


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Modelling the Reactions Catalyzed by Coenzyme B12 Dependent

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