First-Principles Interaction Analysis Assessment of the Manganese

Article pubs.acs.org/JPCB

First-Principles Interaction Analysis Assessment of the Manganese Cation in the Catalytic Activity of Glycosyltransferases Vladimir Sladek†,‡ and Igor Tvaroška*,† †

Institute of Chemistry, Centre for Glycomics, Slovak Academy of Sciences, 84538 Bratislava, Slovakia Department of Chemistry, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Tokyo 171-8501, Japan

‡

ABSTRACT: The energetic effect of water substitution reactions in hexacoordinated [Mn(H2O)6−nLzn]2+nz complexes with L = methanol, formic acid, formamide, formate, imidazole, and diphosphate is quantitatively analyzed at the MP2/triple-ζ level of theory. Subsequently, the state-of-the-art open shell symmetryadapted perturbation theory (SAPT) analysis of the interaction energies of Mn2+···ligand dimers with selected O-, S-, and Nbinding ligands is presented and compared to similar interactions of Mg2+ and Zn2+ ions. We find that the induction energies in the dimers with manganese are almost twice as large as in dimers with magnesium. The total interaction energies rise in the order Mn2+ < Mg2+ < Zn2+. The calculations of the Mn2+ → Mg2+ replacement reaction suggest that metal-dependent glycosyltransferases influence the binding preference of Mn2+ over Mg2+ by inserting amino acids that coordinate the metal via nitrogen or sulfur into their active site.

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Nevertheless, the role of Mn2+ is currently experimentally examined for its biological effect and binding motif in enzymes.12 Glycosyltransferases together with glycosyl hydrolases (GH) constitute the backbone of complex carbohydrate biosynthesis pathways in cells.13,14 The mechanism of GTs involves the transfer of a sugar unit from a sugar donor molecule, most commonly nucleotide diphosphate sugars, to a specific sugar acceptor. Divalent metal cations (usually Mn2+ or Mg2+) are present in the active site of many retaining glycosyltransferases.15 The manganese cation (Mn2+) plays an especially important role in this respect being the optimal metal for GTs (e.g., SpsA, Gal-T1, GnT1, Mfng, GlcAT-1, GlcAT-P), while other cations are less efficient.15 In the active site of GTs, the Mn2+ ion is anchored via noncovalent interactions with amino acids. Part of the Mn2+ role is to interact with the nucleotide diphosphate sugars and “lock” the donor in a way to facilitate the catalytic mechanism of the GT enzyme. A divalent manganese cation also contributes to a scission of the glycosidic linkage of the donor by stabilizing the developing charge on the leaving nucleoside diphosphate. Thus, the interaction partners of Mn2+ in glycosyltransferases (GTs) are always the diphosphate parts of the nucleotide diphosphate sugar, the alternating partners being amino acids and water molecules. The most common shape of the coordination shell of Mn2+ is a (bipyramidal) octahedron containing six ligands. Amino acids that hold Mn2+ in the active site vary for each enzyme. Though

INTRODUCTION Divalent metal cations (Me) are present in the active site of many enzymes and often are an absolute requirement for their full catalytic activity. Among biologically active metal cations, manganese is the second most widely distributed element from the first-row transition metals in living organisms and is surpassed only by iron.1 Other biogenic divalent ions, for example, Mg2+, Zn2+, Ca2+, Ni2+, Co2+, and Cu2+ are also very common cofactors in many enzymes. It has been observed that the replacement of magnesium by manganese does not necessarily cause a reduction in the catalytic activity of enzymes.2 On the other hand, magnesium is less often a catalytically competent replacement for manganese.3 Glycosyltransferases (GT), in particular, show a clear decrease in the catalytic activity when manganese is replaced by magnesium.4 There are a few notable exceptions such as the glucosyl-3phosphoglycerate synthase (GpgS), which prefers Mg2+ for maximal activity in vitro.5 While the biologically active ions Mg2+, Zn2+, and Ca2+ have been studied numerous times for many different aspects such as benchmark calculations for force field development to solvation shell analysis, manganese remains an odd case in that respect.6−10 This is probably caused by the complex electronic structure of manganese ions with a sextet ground state configuration as opposed to the remaining ones, which are closed shell singlets. Bock et al. presented the first step toward a comparative analysis of the difference between these ions.11 The computational possibilities were however limited to ground state calculations with highly correlated approaches such as Møller−Plesset perturbation theory (MP2) and Couple Cluster with Single, Double and Triple excitations (CCSDT). © XXXX American Chemical Society

Received: April 20, 2017 Revised: June 2, 2017

A

DOI: 10.1021/acs.jpcb.7b03714 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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the importance of the Mn2+ cation is well recognized in the biosynthesis of glycans, the function of the metal in the catalytic mechanism of GTs is not clearly understood. Therefore, understanding of the interactions between the Mn2+ cation and amino acids in the active site of the enzyme may be very useful in the rational design of GT inhibitors and the development of artificial metalloenzymes.16−19 In this study, we attempt to shed some light on the role of Mn2+ cation on the catalytic activity of GTs using another approach, symmetry-adapted perturbation theory (SAPT). SAPT calculations offer deeper insight into the nature of the interactions by allowing the decomposition of the interaction energy into physically interpretable contributions.20−22 A specific code, SAPTos (open shell SAPT) was used to analyze the interaction in the Mn2+ clusters.23,24 These calculations are known to yield results close to CCSD(T) qualitative level.25,26 The individual energy terms constitute in sum the whole interaction energy and are usually grouped as follows

COMPUTATIONAL DETAILS All structures were optimized at the DFT level using the Becke’s three-parameter hybrid functional, B3LYP.32 The augmented, correlation consistent, valence polarizable double and triple ζ basis sets, aug-cc-pV{D,T}Z (short notation AV{D,T}Z), were used for geometry optimization and single point calculations, respectively.33 Minima on the potential energy surfaces were verified by vibrational normal-mode analysis. The same methodology was applied to the larger systems, which to some extent approximate the ions coordination in the enzyme. Such level of calculation is not uncommon for enzyme modeling.34 Also, this way, consistency of the small and larger models is maintained throughout this work. Separate single point energies upon the B3LYP/aug-ccpVDZ geometries were obtained by second-order Møller− Plesset perturbation theory MP2, thus with full designation as MP2/AVTZ//B3LYP/AVDZ.35 DFT and MP2 calculations were carried out in the Gaussian 09 and ORCA packages.36,37 The manganese cation was modeled in its high spin−sextet state, as it is its most abundant electron configuration in biological systems.38 SAPT calculations with a monomer treatment at DFT or many-body perturbation theory level, commonly designated as SAPT(DFT) and MBSAPT, respectively, were carried out in the SAPT2012 package.22,24,39 SAPT(DFT) and MBSAPT calculations on systems including Mn2+ were performed using the open shell version as implemented by Ż uchowski et al.23,24 All SAPT calculations utilized the full dimer integral transformation in dimer centered basis set (DC+BS).40 The (mid)bond centered basis functions (3s,3p,2d,2f) were placed between the metal atom and the closest atom of the other monomer.40−42 The exponents were 0.9, 0.3, and 0.1 for s and p and 0.6 and 0.2 for d and f functions.40 SAPT(DFT) uses an asymptotic correction (AC) of the exchange-correlation functional in the DFT calculations. For that purpose ionization potentials (IP) were calculated at the PBE0/AVTZ level of theory. SAPT(DFT) is not particularly susceptible to the accuracy of the IP, but it should not be completely neglected.24,43,44 The PBE0 functional was used in all SAPT(DFT) calculations.45,46 SAPT(DFT) or its density fitted variant DF-SAPT(DFT) are known to be close to CCSD(T) accuracy for organic molecule dimers although not always meeting the spectroscopic accuracy.25,26 For comparison, also many-body SAPT (MBSAPT) calculations have been carried, which allowed the calculation of the Hartree−Fock correction, δEHF int,resp for third and higher order induction and exchangeinduction terms. Finally, these results, sometimes termed as SAPT(3), are comparable to supermolecular interaction energies calculated approximately at the fourth order of perturbation theory (MBPT4).21,47,48

(10) (20) (20) (20) (10) E int = Eels + Eexch + E ind,resp + Eex ‐ ind,resp + Edisp (20) + Eex ‐ disp

(1)

The electrostatic (Coulombic) energy, Eels, and the exchange energy, Eexch, are so-called first order terms (as indicated by the superscript indices, which will be dropped from now on) because they can be extracted from the first order perturbation in the intermolecular (interaction) potential. Eels originates from Coulombic interactions. The exchange term, Eexch, originates from quantum mechanical electron tunneling between the interacting monomers. This term is sometimes called the Pauli repulsion and is the dominant repulsive term at short distances. The induction energy, Eind, originates from interactions of the permanent dipole (multipole) moments of the monomers and hence is large for molecules that are naturally polarized and easily polarizable. The dispersion energy, Edisp, on the other hand, results from the interactions of instantaneous dynamic fluctuations of the electron density, that is, nonpermanent dipoles (multipoles). The Eex‑ind and Eex‑disp terms are additional repulsion energies due to the coupling of electron exchange and the induction and dispersion interactions.20,22 The SAPT(CCSD) method provides the opportunity to calculate these energies from coupled cluster monomer wave functions.27−31 Although very accurate, the SAPT(CCSD) method is seldom used in applications due to extreme computational costs. The aims of this work can be summarized as follows: (i) provide benchmark SAPT analysis of the Me···Lz dimers and [Me(H2O)5]+2···Lz complexes for selected O, S, and N binding ligands; (ii) characterize the energetic effects of water substitution reaction 2 by ligands of biological interest in the hexacoordinated complexes,

HF HF (10) (20) (20) (10) δE int ,resp = E int − (Eels + Eexch + E ind,resp + Eex ‐ ind,resp)

(3)

[Mn(H 2O)6 − n Lz n]2 + nz + Lz → [Mn(H 2O)6 − n − 1Lz n + 1]2 + (n + 1)z + H 2O

Article

Only the two smallest dimers, that is, Mg ···H2O and Mg2+···H2S, were recalculated using the SAPT(CCSD). This limitation to the small systems stems from the extreme computational costs of this method in the evaluation of the dispersion contribution. The Eels, Eexch, Eind, and Eex‑ind terms in SAPT(CCSD) were evaluated in the DCBS setup, and the Edisp and Eex‑disp in the DC+BS setup (i.e., with midbond functions). Also, the dispersion terms were evaluated from density-fitted density susceptibilities to reduce the computational costs. 2+

(2)

the selected ligands, L, are methanol (CH3OH), formic acid (HCOOH), formamide (HCONH2), formate (HCOO−), hydrogen sulfide (H2S), imidazole (IMZ), and diphosphate (DP); (iii) characterize the energetic effects in Mn2+ and Mg2+ complexes representing the catalytic site of selected glycosyltransferases. B

DOI: 10.1021/acs.jpcb.7b03714 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Table 1. SAPT(DFT) Interaction Energies of the Mn+2···L and Mg+2···L Dimers Optimized at the B3LYP/AVTZ Level of Theorya L = H2O Mn

2+

Mg

−74.26 48.19 −164.58 116.15 −7.56 1.69 −80.37 −76.94 3.34 −77.51

Eels Eexch Eind Eex−ind Edisp Eex−disp SAPT(DFT) δEHF int,resp MBSAPT

L = CH3OH 2+

Mn

−64.43 26.18 −95.03 48.06 −1.43 0.34 −86.31 −80.60 5.71 −83.03

Mn

δEHF int,resp MBSAPT

2+

−72.33 31.14 −120.58 59.61 −1.67 0.41 −103.42 −96.32 7.10 −100.80

2+

2+

2+

Mn

−348.87 64.94 −242.49 141.45 −1.75 0.61 −386.10 −371.33 14.77 −380.85

−112.60 72.29 −241.47 160.65 −10.28 2.21 −129.19 −126.04 3.15 −131.95

Mg2+

Mn

−90.59 64.98 −213.71 142.53 −9.52 1.98 −104.32 −102.10 2.22 −107.42

L = HCONH2 Mg

−372.29 112.80 −460.77 351.54 −15.77 5.02 −379.48 −369.20 10.28 −364.39

Eels Eexch Eind Eex−ind Edisp Eex−disp SAPT(DFT)

Mg

−86.54 60.42 −218.22 153.01 −9.02 2.10 −98.25 −92.97 5.28 −96.14

L = HCOO 2+

L = HCOOH

2+

−74.62 32.25 −121.59 53.96 −1.81 0.41 −111.39 −105.69 5.70 −111.62 L = IMZ

Mg

2+

−94.89 35.58 −135.76 60.00 −1.96 0.46 −136.57 −129.64 6.93 −137.41

Mn

2+

Mg2+

−127.88 85.80 −382.42 280.56 −11.67 3.16 −152.44 −134.79 17.65 −133.21

−101.53 42.40 −181.49 96.83 −1.93 0.57 −145.14 −134.09 11.05 −140.47

a

The second line of the SAPT(DFT) data and all MBSAPT data (entries in bold) are approximate 3rd order SAPT(3) energies with the third order terms accounted via the Hartree−Fock approximate correction. All data are in kcal/mol.

Table 2. SAPT Interaction Energies of the Me···H2O (Me = Mn+2, Mg+2, Zn+2) Dimers Optimized at the B3LYP/AVTZ Level of Theorya Me = Mn2+ Eels Eexch Eind Eex−ind Edisp Eex−disp c δEHF int,resp SAPT SAPT(3)

Me = Mg2+

Me = Zn2+

SAPT(DFT)

MBSAPT

SAPT(DFT)

MBSAPT

SAPT(CCSD)

SAPT(DFT)

MBSAPT

−74.26 48.19 −164.58 116.15 −7.56 1.69

−76.42 45.45 −147.13 102.29 −6.93 1.79 3.43 −80.94 −77.51

−64.43 26.18 −95.03 48.06 −1.43 0.34

−68.05 24.48 −87.26 42.72 −1.26 0.30 5.71 −88.74 −83.03

−68.00 24.44 −80.39 36.86 −1.49 (−1.48b) 0.36 (0.37b)

−85.91 52.93 −238.98 171.93 −8.50 1.63

−88.22

−106.89 −96.69

−88.01 49.63 −214.99 153.59 −8.41 1.81 10.20 −108.18 −97.98

−80.37 −76.94

−86.31 −80.60

a The last row contains approximate 3rd order SAPT(3) energies with the third order terms accounted via the Hartree−Fock approximate correction. SAPT(CCSD) energies are provided for Me = Mg+2. All data are in kcal/mol. bEvaluated from density susceptibilities (not density fitted). cThe δEHF int,resp correction was evaluated only in the MBSAPT calculations, which use HF wave functions as a reference.

correction is more accurate for systems dominated by induction energy compared to systems where the monomers have permanent dipole moments or, at least, high polarizabilities. For nonpolar and nonpolarizable systems, the direct calculation of the third order terms brings more accurate results.51 This is probably the reason why in some cases the SAPT(DFT) energy agrees well with the MBSAPT, and the inclusion of δEHF int,resp in the SAPT(DFT) energy causes a larger difference between these two results. This seems to be in particular the case of the dimers with the magnesium ion, which has significantly smaller static polarizability than the manganese ion as discussed later. The selected set of ligands represents the side chains of amino acids interacting with the metal ion via oxygen, nitrogen, and sulfur. The nitrogen coordinating atom of histidine side

The SAPT code was linked to Dalton 2.0, which was used to calculate the monomer wave functions and molecular integrals.49 SAPT(CCSD) calculations were done in Molpro 2012.50

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RESULTS AND DISCUSSION SAPT Binding Energy Components for Me2+···L Dimers. Looking at the SAPT data in Table 1, one sees that the absolute values of the Mn2+···L interaction energies are somewhat smaller for all studied ligands compared to those for Mg2+. An exception is the N-bonded IMZ ligand where the values for Mn2+ are slightly larger. The δEHF int,resp correction accounts approximately for the third (and higher) order induction and exchange-induction terms. However, this C

DOI: 10.1021/acs.jpcb.7b03714 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Table 3. SAPT Interaction Energies of the Me···H2S (Me = Mn+2, Mg+2, Zn+2) Dimers Optimized at the B3LYP/AVTZ Level of Theorya Me = Mn2+ Eels Eexch Eind Eex−ind Edisp Eex−disp b δEHF int,resp SAPT SAPT(3)

Me = Mg2+

Me = Zn2+

SAPT(DFT)

MBSAPT

SAPT(DFT)

MBSAPT

SAPT(CCSD)

SAPT(DFT)

MBSAPT

−45.04 38.24 −228.11 158.45 −6.60 1.32

−46.93 39.25 −224.03 156.14 −6.24 1.62 8.89 −80.19 −71.30

−33.24 19.64 −120.19 57.04 −0.83 0.23

−35.11 19.91 −118.30 55.65 −0.84 0.22 3.67 −76.49 −80.16

−35.61 19.98 −110.33 48.34 −0.83 0.23

−53.36 40.63 −317.80 220.67 −7.35 1.05

−78.22

−116.16 −105.42

−55.12 41.43 −311.82 217.74 −8.09 1.55 10.74 −117.19 −107.20

−81.74 −72.85

−77.35 −73.68

a

The last row contains approximate 3rd order SAPT(3) energies with the third order terms accounted via the Hartree−Fock approximate correction. SAPT(CCSD) energies are provided for Me = Mg+2. All data are in kcal/mol. bThe δEHF int,resp correction was evaluated only in the MBSAPT calculations, which use HF wave functions as a reference.

Table 4. SAPT Interaction Energies of the Me···IMZ (Me = Mn+2, Mg+2, Zn+2) Dimers Optimized at the B3LYP/AVTZ Level of Theorya Me = Mn2+ Eels Eexch Eind Eex−ind Edisp Eex−disp b δEHF int,resp SAPT SAPT(3)

Me = Mg2+

Me = Zn2+

SAPT(DFT)

MBSAPT

SAPT(DFT)

MBSAPT

SAPT(DFT)

MBSAPT

−127.88 85.80 −382.42 280.56 −11.67 3.16

−131.48 85.21 −289.22 262.62 −10.98 3.72 17.65 −150.85 −133.21

−101.53 42.40 −181.49 96.83 −1.93 0.57

−105.93 41.38 −172.57 90.09 −1.99 0.51 11.05 −151.52 −140.47

−137.88 77.47 −473.42 346.68 −11.44 2.65

−141.45 76.43 −446.72 326.77 −12.97 3.13 24.42 −203.08 −178.66

−152.44 −134.79

−145.14 −134.09

−195.95 −171.53

a

The last row contains approximate 3rd order SAPT(3) energies with the third order terms accounted via the Hartree−Fock approximate correction. All data in kcal/mol. bThe δEHF int,resp correction was evaluated only in the MBSAPT calculations, which use HF wave functions as a reference.

different in the hexacoordinated complex, which will be shown later. The obtained results are in very good agreement with the SAPT analysis of the Zn2+···L analysis by Rayón et al. (for L = H2O, H2S, and IMZ among others).9 Therefore, both data can be mutually compared. For Zn2+···H2O (Table 2), the total HF included is SAPT(DFT) interaction energy with δEint,resp −1 −96.69 kcal mol as compared to their −96.5 kcal mol−1. For Zn2+···H2S (Table 3), we obtain −105.42 kcal mol−1 with SAPT(DFT) including δEHF int,resp, and they get −107.9 kcal mol−1. Here the MBSAPT value of −107.20 kcal mol−1 is somewhat closer to their data. The use of the computationally much more expensive SAPT(CCSD) does not result in significant discrepancies of the evaluated energy terms. The Eels, Eexch, Eind, and Eex‑ind terms from SAPT(CCSD) are closer to the MBSAPT values. On the other hand, SAPT(DFT) seems to reproduce the Edisp and Eex‑disp terms very well. The use of density fitting in the approximation of the density susceptibilities shows negligible difference in Mg2+···H2S. Hence, we are quite confident that SAPT(DFT) yields reasonable interaction energies for the purpose of this work. To trace any possible difference in the behavior of the Mn2+···L and Mg2+···L complexes, we calculated the static polarizabilities of the two ions. For Mn2+, we obtained 3.06 au, and for Mg+2, the value is 0.26 au, both calculated with relaxed MP2 densities in the AVTZ basis set. This rather large difference can be explained by a comparison of the electron configuration of the ions. Mg2+ has a singlet configuration with

chain is modeled by imidazole (IMZ), and the sulfur coordinating atom of methionine side chain is modeled by hydrogen sulfide. Recently, a detailed analysis of interactions between Zn2+ and selected small molecules was published9 and was used for a comparison with our calculations on Mn2+ and Mg2+ ions. Water shall be chosen to represent a common interaction through oxygen, and a more detailed analysis of this interaction is presented in Table 2. In Tables 3 and 4, similar analyses are given for hydrogen sulfide, and imidazole, respectively. We were able to calculate SAPT(CCSD) interaction energies for two of the three model systems. The three representative O-, S-, and N-binding systems correspond to atoms by which substrates and amino acids bind to the metal ions most commonly in enzymes.7,11 According to the findings of Bock et al., Mg2+ binds almost exclusively via oxygen, especially when it has a fully occupied hexacoordination.11 The binding situation for Mn2+ is similar to that for Mg2+, although coordination via nitrogen or sulfur is more common. The binding of manganese via the S atom is rare but not as improbable as for magnesium. Zinc, on the other hand, binds via nitrogen almost as often as via oxygen, and binding through sulfur is quite common too.11 The interaction in the [Me(H2O)] complexes was identified as “predominantly electrostatic”, based on natural population analysis (NPA).11 Data in Table 2 show that the induction contribution in the Me···H2O dimers is at least as important as the electrostatic (Coulombic) interaction, and there is little reason for this to be D

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The Journal of Physical Chemistry B fully closed valence shell with 2s2 and 2p6 electrons, whereas Mn2+ has a 4s0, 3d5 open shell configuration. The polarizability of Zn2+ with its valence electron configuration being 4s0 and 3d10 is 1.97 au. From this follows that Mg2+ is a harder ion than Mn2+, which implies that Mn2+ is more polarizable than Mg2+. Therefore, the induction, Eind, and exchange-induction, Eex‑ind, interactions of Mg2+ are significantly smaller than those for the Mn2+. This fact may also be the main reason responsible for the much lower dispersion contribution, Edisp, in Mg2+···L complexes as this originates from instantaneous fluctuations of the electron (charge) density. The fact that Mg2+ is a hard ion is probably also the reason for the systematically smaller exchange energies, Eexch, as there is likely a low penetration of the Mg2+ and the ligand electron shells. The electrostatic Coulombic interactions, Eels, together with the induction energies, Eind, are the dominant stabilizing contributions in both magnesium and manganese complexes. Therefore, the relative importance of the induction energy as the most stabilizing contribution is not to be underestimated. Especially, though Mg2+ is less polarizable, a higher polarizability of the second interacting partner might influence the induction energies, Eind, of the complex. This assumption is supported by an analysis of the mutual contributions to Eind. For example, in the Mg2+···IMZ interaction, we can identify the two monomer contributions to Eind being −181.40 and −0.09 kcal mol−1. Their sum gives the interaction contribution (Table 1 and Table 3), Eind = −181.49 kcal mol−1, so evidently almost the whole term originates from the polarization and dipole moment of one monomer. Of course, the fact is that the metal ion has no net dipole moment while the second partner does contribute significantly to the asymmetry in the E ind contributions. Quite similar numbers are in the least stable dimer Mg2+···H2O with monomer Eind contributions being −94.96 and −0.07 kcal mol−1, the sum of which gives the interaction term −95.03 kcal mol−1 as found in Tables 1 and 2. Contrary to this, the monomer contributions to Eind in Zn2+··· H2O are −234.90 and −4.08 kcal mol−1 summing up to the interaction term of −238.08 kcal mol−1 (Table 2). The larger polarizability of Zn2+ than that of Mg2+ results in an increase in the metal ion monomer contribution to Eind by 2 orders of magnitude. Such nature of the interaction can, therefore, cause problems in the classical molecular dynamics simulations of receptor···ligand interactions if a nonpolarizable force field is applied as was discussed recently.52,53 By analyzing the SAPT(DFT) interaction energy decomposition of the Mn2+···L dimers, we find that the dominant stabilizing contribution is the induction energy Eind in all cases, being roughly twice as large as the Coulombic interactions Eels. As discussed above, this is probably a consequence of the significantly greater polarizability of the manganese and zinc ions than that of magnesium. From this also follows the extensive dispersion interaction as well as the significant increase of the major destabilizing interactions Eexch and Eex-ind. However, in total, the Mn2+···L dimers are about 5−10% less strongly bound than the Mg2+···L dimers. Another small difference is in the shorter Mg2+···L equilibrium separations compared to the Mn2+ counterparts. As an example, we mention the Me···H2O dimer, where the Mn2+···O distance is 1.977 Å, and the Mg2+···O distance is 1.915. Å. In the Mn2+··· IMZ dimer, the difference is minimal with the Mn2+···N distance being 1.958 Å and the Mg2+···N distance is 1.952 Å. The larger size of the manganese atom and its different electron

structure give rise to larger Pauli repulsion represented in the Eexch and Eex‑ind terms. Comparison of the magnitude of the interaction energies with the three ligands leads to the conclusion that for Mn2+ and Zn2+ the interaction with water is somewhat stronger than that with hydrogen sulfide for both manganese and magnesium. On the other hand, the interaction of Mg2+ with water is weaker than that with H2S. The larger natural polarization of H2O results in larger Coulombic interactions as opposed to the H2S complexes. However, the induction and exchange-induction interactions are more dominant in the H2S complexes as a consequence of its larger polarizability (see Table 5). The Table 5. Dipole Moments (μ) and Polarizabilities (α) Calculated at the MP2/AVTZ//B3LYP/AVDZ Level of the Theory with Relaxed MP2 Densities and Ionization Potentials (IP) Calculated at the PBE0/AVTZ//B3LYP/ AVDZ Level of the Theory for Various Metals and Ligands 2+

Mn Mg2+ Zn2+ H2O H2S CH3OH HCOOH HCONH2 COO− IMZ

μ (au)a

α (au)b

IP (au)

0 0 0 0.72 0.40 0.70 0.96 1.68 0.71d 1.55

3.06 0.26 1.97 9.88 24.88 21.50 23.24 28.50 33.41 49.76

1.25 (2.82)c 2.99 1.46 0.46 0.38 0.39 0.39 0.36 0.12 0.32

Conversion factor to Debye is ×2.54179. bConversion factor to Å3 is ×0.14818 (0.5291773). cIPβ is the first ionization potential of the β electron. dEvaluated at the center of mass.

a

interactions of the metal with IMZ are stronger than those with H2O and H2S for all three studied metal ions due to both Coulombic electrostatic and induction energies being more pronounced. Thus, the interaction energy between the metal cation and ligand for Mn2+···L complex decreases in the order IMZ > H2S > H2O, whereas for the Mg2+···L complex in the order IMZ > H2O > H2S. It has been claimed that the ionization potential (IP) of the acidic ligand is essential for its ability to bind magnesium.8 To verify this hypothesis, we investigate the dependence of the SAPT(DFT) interaction energies in the Mn2+···L and Mg2+···L dimers on the ionization potential of the ligand. This dependence is depicted in Figure 1. Although the SAPT interaction energies are usually not interpreted relating to IPs of the interacting monomers, it is interesting that there appears to be a certain correlation between the IPs of the ligand and the total SAPT(DFT) interaction energy as well as individual energy terms. It seems, however, superfluous at this point to seek a deeper physical interpretation. In SAPT(DFT), the IPs are needed to account for the long-range asymptotic correction of the exchange-correlation potential and do not otherwise enter into the evaluation of the energy terms. SAPT Binding Energy Components for [Me(H2O)5]+2··· L Complexes. The calculations of the Me2+···L complexes provide the basic characteristic of Me2+··L. However, the most common coordination number of the divalent magnesium and manganese cation is six. In such complexes, the separation of the metal ion from the ligand is larger than in the simple Me2+···L dimer, and as a result, the interactions may differ. E

DOI: 10.1021/acs.jpcb.7b03714 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 2. B3LYP/AVDZ optimized structures of [Mn(H2O)6−n(CH3OH)n]+2. The ligands are in either opposite or adjacent positions for n = 2,a and n = 2,b, respectively. Analogically, the two remaining water molecules are in either opposite or adjacent positions for n = 4,a and n = 4,b, respectively.

imidazole (IMZ) and formamide (HCONH2). This is in agreement with the observation that the magnesium and manganese cations preferably bind to oxygen, although divalent manganese is more accessible to nitrogen ligands.10 The lowest interaction energy is predicted for hydrogen sulfide (H2S). In the case of H2S, the interaction energy for Mg2+ (−21.4 kcal/ mol) is lower than that for Mn2+ (−23.8 kcal/mol). In general, we observe a significant drop of the total interaction energy for all ligands as compared to the Me2+···L dimers. The reduction of the interaction energy with respect to the SAPT(DFT) energy (without the δEHF int,resp correction) from Table 1 is about 64% for L = H2O, 65% for CH3OH, 67% for HCOOH, 35% for HCOO−, 62% for HCONH2, 58% for IMZ, and 70% for H2S in the complexes containing manganese. Analogically, in the magnesium containing complexes, the drops are 60% for L = H2O, 62% for CH3OH, 64% for HCOOH, 35% for HCOO−, 57% for HCONH2, 57% for IMZ, and 72% for H2S. Except for formate where electrostatic energy is dominant, the induction energy is the dominant stabilizing energy. However, its relative importance is somewhat smaller at the expense of the electrostatic energy. This is a consequence of the greater separation of the ligand and the metal ion as the two energy components have different asymptotic behavior. The Coulombic electrostatic interaction has a more long-range character. The drop of the interaction energy for the H2S ligand is about 10% larger (in relative numbers) than for the H2O ligand. This is presumably connected to the relatively larger importance of the Coulombic interaction between the H2O and ligand as

Figure 1. Dependence of the total SAPT(DFT) interaction energies and the individual contributions on the first ionization potential (IP) of the ligand L in (a) Mn2+···L and (b) Mg2+···L complexes.

Therefore, next, we examine any possible differences in the binding energy components in the [Me(H2O)5]+2···L complexes. The corresponding structures may be found in Figures 2−5 labeled as n = 1. These complexes represent a more realistic biological situation where the first coordination spheres of the metal ions are fully saturated. The interaction energy terms are compiled in Table 6. Similarly to the simple Me2+···L dimers, the interaction energies of five ligands (HCOO−, HCONH2, HCOOH, CH3OH, and H2O) with the [Me(H2O)5]+2 cluster are about 3−7 kcal mol−1 lower when manganese is in the cluster compared to the situation when magnesium is complexed. In contrast, in two manganese complexes, with IMZ and H2S (Figure 6), the interaction energy is higher compared to magnesium complexes. As expected, the negatively charged ligand formate (HCOO−) has the by far the largest interaction energy with the positively charged metal due to the strong attractive electrostatic interactions. Following are the neutral ligands F

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Figure 3. B3LYP/AVDZ optimized structures of [Mn(H2O)]6−n(HCOOH)n]+2. The ligands are in either opposite or adjacent positions for n = 2,a and n = 2,b, respectively. Analogically, the two remaining water molecules are in either opposite or adjacent positions for n = 4,a and n = 4,b, respectively.

Figure 4. B3LYP/AVDZ optimized structures of [Mn(H2O)]6−n(HCONH2)n]+2. The ligands are in either opposite or adjacent positions for n = 2,a and n = 2,b, respectively. Analogically, the two remaining water molecules are in either opposite or adjacent positions for n = 4,a and n = 4,b, respectively.

opposed to the interaction between the H2S and ligand as seen from Tables 2, 3, and 6. Nevertheless, the results indicate that the non-Coulombic interactions constitute at least half of the total interaction energy for the studied ligands at the equilibrium separations of hexacoordinated metal ions. The straightforward consequence of this finding is that one has to be cautious when modeling and analyzing enzymes with a metalcontaining active site by nonpolarized molecular force field methods. Structure and Energetics of Water Substitution Reactions in Hexacoordinated [Me(H2O)6−nLzn]2+nz Complexes. Having established some basic differences in the binding in small Mn2+···L and Mg2+···L dimers and larger [Me(H2O)5]+2···L complexes, we now proceed to the analysis of the manganese hexacoordinated clusters in connection with the water substitution reaction. The coordination sphere of the hexa-aqua complexes of the Mn2+ ion is of bipyramid octahedron shape (Th). This symmetric shape can be maintained because water molecules are small enough to avoid steric clashes and their oxygen atoms interact with Mn2+, so hydrogen bonding between water molecules is not present. The distance between Mn2+ and oxygen is about 2.211 Å, and the H−O−H angle in water is about 106.20°. The octahedron shape of the first coordination sphere is disturbed when nonaqua ligands are introduced. The Gibbs free energies of the subsequent aqua substitution reactions, eq 2, were evaluated at the B3LYP/AVDZ level to be fairly comparable to the B3LYP/

6-31+G* data for Mg2+ complexes.8 The results are collected in Table 7 together with data calculated at the MP2/AVTZ// B3LYP/AVDZ level. By comparing our results and those of the magnesium clusters,8 one can conclude that the general trends are similar for both Mn2+ and Mg2+ ions.8 For replacements of water with methanol; however, we see a less obvious fluctuation of ΔG for different n. While for n = 0, that is, the substitution of the first water in the originally hexa-aqua complex, a thermodynamically favorable ΔG = −4.3 kcal/mol was calculated; for the second successive substitution ΔG drops to −1.7 kcal/mol.8 Such significant change is not observed in the Mn2+ complexes where ΔGMP2 was −4.88, −4.55, and −4.02 kcal/mol for n = 0, 1, and 2, respectively. We provide two values for n = 1 (and n = 3) since the ligands can occupy either the two opposite sites or adjacent sites. In the study of the Mg2+ complexes, only the first arrangement was considered.8 Similarly, as in the case of magnesium, also in manganese complexes, the first substitution disrupts the original bipyramid symmetry. There seems to be a hydrogen bond interaction of the CH3 group with one of the water molecules, but this interaction is not strong enough to pull that water from the equatorial plane. In general, the Mn2+··· O(H2O) distances in [Mn(H2O)CH3OH]+2 are just slightly larger than those in the hexa-aqua complex and vary from 2.217 to 2.229 Å. The calculations indicate that the substitutions up to [Mn(CH3OH)6]+2 are thermodynamically possible. MoreG

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Figure 6. B3LYP/AVDZ optimized structures of [Mn(H2O)6]+2 (a), [Mn(H2O)5(H2S)]+2 (b), and [Mn(H2O)4DP] (c). The Mgcontaining structures look similar.

over, in contrast to the Mg2+ complexes,8 the last substitution seems to be still favorable. The comparison of the ΔGMP2 values for formic acid (HCOOH) in Table 7 revealed that the manganese clusters behave qualitatively similar to magnesium clusters. Also in the case of Mn2+, the first substitution (n = 0) of water by HCOOH calculated at MP2/AVTZ//B3LYP/AVDZ level is thermodynamically less favorable than that by CH3OH. However, the calculation at the DFT/B3LYP/AVDZ level (ΔGB3LYP) suggests the opposite. Two competing factors probably cause this discrepancy. By looking at the SAPT(DFT) data, we see that the total interaction energy of the Mn2+··· CH3OH dimer is smaller by about 6 kcal mol−1 than in the Mn2+···HCOOH dimer. This would suggest that the exchange of water by HCOOH should be favored over the exchange by CH3OH in the manganese cluster. The second factor is the formation of a hydrogen bridge in the [Mn(H2O)5CH3OH]+2 cluster, which does not occur in the [Mn(H2O)5HCOOH]2+ cluster. It is notoriously known that DFT methods are prone to

Figure 5. B3LYP/AVDZ optimized structures of [Mn(H2O)]6−n(HCOO−)n]2−n. The ligands are in either opposite or adjacent positions for n = 2,a and n = 2,b, respectively. Analogically, the two remaining water molecules are in either opposite or adjacent positions for n = 4,a and n = 4,b, respectively.

Table 6. SAPT(DFT) Interaction Energies of the [Mn(H2O)5]+2···L and [Mg(H2O)5]+2···L Complexes Optimized at the B3LYP/AVDZ Level of Theorya L = H2O Mn

2+

Mg

−39.57 30.85 −59.07 46.17 −9.30 1.93 −29.00

Eels Eexch Eind Eex−ind Edisp Eex−disp SAPT(DFT)

L = CH3OH 2+

−37.61 22.34 −36.64 22.80 −6.45 1.23 −34.34

Mn

2+

Mn Eels Eexch Eind Eex−ind Edisp Eex−disp SAPT(DFT)

−281.03 101.00 −228.56 180.75 −26.17 7.42 −246.59

−40.09 24.50 −44.59 26.81 −7.58 1.35 −39.59

Mn

2+

Mg2+

−42.31 34.65 −72.66 54.06 −10.42 1.99 −34.68

−37.60 22.32 −43.24 23.68 −6.79 1.16 −40.47

L = HCONH2 Mg

2+

−273.13 79.58 −122.08 80.48 −20.20 5.44 −249.91

Eels Eexch Eind Eex−ind Edisp Eex−disp SAPT(DFT) a

Mg

−44.04 36.01 −76.09 58.82 −11.12 2.24 −34.19

L = HCOO 2+

L = HCOOH 2+

Mn

2+

−60.31 42.24 −95.03 71.27 −12.01 2.44 −51.38

L = IMZ Mg

2+

−54.55 26.39 −53.92 29.72 −7.67 1.34 −58.69 L = H2S

Mn

2+

Mg2+

−71.89 54.27 −161.267 127.34 −15.04 3.22 −63.36

−60.34 33.64 −75.81 47.54 −9.48 1.75 −62.69

Mn2+

Mg2+

−24.30 25.64 −80.30 62.83 −9.32 1.65 −23.80

−18.12 16.41 −37.01 22.43 −6.15 1.06 −21.37

δEHF int,resp is not included in SAPT(DFT). All data are in kcal/mol. H

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Table 7. Calculated Electronic and Gibbs Free Energies of the Water Substitution Reaction 2 in the [Mn(H2O)6−nLzn]2+nz Complexesa n

ΔEB3LYP

0 1 2 3 4 5

−3.26 −3.09 (−3.20) −3.11 −2.91 (−2.91) −3.09 −2.61

0 1 2 3 4 5

−2.96 −2.69 (−3.33) −4.14 −1.29 (−2.21) −2.92 −2.36

0 1 2 3 4 5

−16.37 −16.67 (−16.82) −14.90 −11.98 (−11.70) −10.29 −9.87

0 1 2 3

−198.70 −121.14 (−121.06) −40.40 42.91 (42.51)

0 0b 1 1b 2 2b

10.61 12.49 9.06 (8.65) 12.80 (12.22) 9.08 12.43

0 0c

−366.30 −368.28

ΔGB3LYP L = CH3OH −3.58 −3.29 (−2.87) −2.59 −3.23 (−3.23) −2.19 −3.93 L = HCOOH −3.81 −3.56 (−3.47) −3.73 0.07 (−2.45) −4.87 −1.76 L = HCONH2 −17.85 −15.41 (−14.97) −14.08 −11.25 (−10.31) −9.56 −10.27 L = HCOO− −197.02 −117.15 (−116.53) −39.56 43.87 (43.47) L = H2S 9.25 11.36 8.02 (8.31) 11.26 (11.74) 8.21 10.62 L = DP −372.58 −375.39

ΔEMP2

ΔGMP2

−4.57 −4.36 (−4.45) −4.54 −4.43 (−4.43) −4.82 −3.76

−4.88 −4.55 (−4.12) −4.02 −4.75 (−4.75) −3.92 −5.08

−2.91 −2.70 (−3.42) −4.38 −1.82 (−2.47) −3.19 −3.05

−3.76 −3.58 (−3.57) −3.97 −0.46 (−2.70) −5.14 −2.45

−16.61 −17.02 (−17.20) −15.78 −13.00 (−12.50) −11.36 −11.41

−18.09 −15.77 (−15.34) −14.96 −12.27 (−11.10) −10.63 −11.82

−201.28 −123.87 (−123.89) −40.28 40.70 (40.57)

−199.60 −119.88 (−119.37) −39.44 41.67 (41.53)

8.26 11.79 8.57 (8.02) 11.95 (11.34) 8.44 11.55

6.89 10.65 7.54 (7.68) 10.41 (10.86) 7.56 9.74

−369.64 −369.75

−375.92 −376.85

a

Numbers in parentheses are for cases where the ligands are in adjacent positions for n + 1 = 2 (for n + 1 = 4, this number is for complexes where the two remaining water molecules are in adjacent positions). The B3LYP results are in AVDZ basis, and the ones labeled as MP2 are MP2/AVTZ// B3LYP/AVDZ values. ΔG calculated at 298.15 K and 1 atm. All data are in kcal/mol. bValues for the [Mg(H2O)6−n](H2S)n]+2 complex. cValues for the [Mg(H2O)4DP] complex.

failure in the description of hydrogen bonding.54−56 For this reason, we assume the ΔGMP2 values to be more trustworthy than ΔGB3LYP. For the Mg2+···CH3OH dimer, the interaction is by about 9 kcal mol−1 less attractive than in the Mg2+··· HCOOH dimer (SAPT(DFT) + δEHF int,resp data in Table 1). However, one has to bear in mind that the separations in the dimer are different than in the hexacoordinated complexes. Hence, the energetic differences are unlikely to be as large as in the dimer case, as can be seen in Table 6 for the [Me(H2O)5CH3OH]+2 complexes. The Mn2+···O(CH3OH) distance is 1.929 Å in the dimer and 2.174 Å in [Mn(H2O)5CH3OH]+2. The Mg2+···O(CH3OH) distance is 1.884 Å in the dimer and 2.082 Å in [Mg(H2O)5CH3OH]+2. Therefore, however tempting it is to try to quantify the effect of the hydrogen bond more accurately, one is probably predestined to failure, should an additive pairwise-interaction model be used for this analysis. The importance of three-body interactions has been shown in, for example, the (H2O)2HCl

trimer.57−60 There is no theoretical justification why these effects should not be significant also in our hexacoordinated model.60,61 The fact that formic acid has a somewhat larger dipole moment and larger polarizability than methanol has a rather negligible effect on the SAPT(DFT) energy contributions. The slight decrease of Eind and Eex‑ind for the Mn2+···HCOOH dimer on the Mn2+···CH3OH dimer is somewhat unexpected. The trend is opposite in the magnesium dimers. Both dimers with HCOOH exhibit an increase in the dispersion energy Edisp compared to the CH3OH dimers, which is connected to the larger polarizability of HCOOH. The Mn2+···O(HCOOH) distance is 1.874 Å in the dimer and 2.157 Å in [Mn(H2O)5HCOOH]+2. The Mg2+···O(HCOOH) distance is 1.827 Å in the dimer and 2.063 Å in [Mg(H2O)5HCOOH]+2. Formamide (HCONH2) has a larger polarizability as well as a larger permanent dipole moment than methanol. Values in Table 7 show that the substitution of the first water by I

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Figure 7. SpsA (a), GnT1 (b), Gal-T1 (c), and MGal-T1 (d) mimicking complexes. For SpsA methyl-diphosphate was used to distinguish it from GnT1. The DP was substituted by two waters in the SpsA (e), GnT1 (f), Gal-T1 (g), and MGal-T1 (h) mimicking complexes.

replacing a magnesium-bound water by a formate,8 the water− formate substitution in manganese-bound water is characterized by a high free energy gain (−200 kcal mol−1). This is the result of the dominant attractive Coulombic electrostatic interactions (Eels) between the positively charged metal and the negatively charged formate. The second water replacement is also characterized by high free energy gain, −117 and −120 kcal/ mol at the B3LYP and MP2 level, respectively. In contrast to replacing water by a neutral ligand, the complexes with more than three HCOO− molecules are thermodynamically unfavorable similarly as in the case of magnesium.8,62 However, it was shown that when one of the carboxylates is bound as a bidentate ligand, the divalent magnesium ion can bind as many as four carboxylate residues,62 and we may expect the same behavior also for manganese. The Mn2+···O(HCOO−) distance is 2.009 Å in the dimer and 2.085 Å in [Mn(H2O)5HCOO−]+1. The Mg2+···O(HCOO−) distance is slightly smaller. Namely, it is 1.941 Å in the dimer and 2.020 Å in [Mg(H2O)5HCOO−]+1. Interestingly, in the dimer, both the Mn2+ and Mg2+ ion bind to both oxygens of the formate equivalently. In the [Mn(H2O)5HCOO−]+1 complex, one oxygen binds to manganese, and one stabilizes two neighboring water molecules via short hydrogen bonds about 1.82 and 1.79 Å long. Manganese and Divalent Magnesium Cations in the Active Site of Glycosyltransferases. The majority of the inverting glycosyltransferases of GT-A fold are metal-dependent enzymes, that is, they require divalent metal cation (usually Mn2+ or Mg2+) for their catalytic activity. Biochemical analyses indicate an ordered sequential mechanism that begins with the Me2+/donor substrate binding to the active site of the glycosyltransferase, and then the acceptor substrate binds forming the enzyme−substrates ternary complex. After the biosynthesized glycan has been detached, the reaction is completed by a liberation of the Me2+/UDP complex through bulk solvation.63 Thus, the coordination shell of the manganese cation in the active site of metal-dependent glycosyltransferases is very specific; it contains two oxygen atoms from the

HCONH2 in the hexacoordinated manganese complex is energetically much more favorable than replacement by HCOOH or CH3OH. This finding is in agreement with the calculation on magnesium clusters.8 However, similarly, as for HCOOH and CH3OH also for HCONH2, the ΔGMP2 values seem to be quite large up to n = 5. It was suggested that the large electrostatic and polarization contributions could overcome steric repulsion even in the [Mg(HCONH 2 ) 6 ] +2 complex. 8 The Mn2+···O(HCONH 2) distance in [Mn(H2O)5HCONH2]+2 and [Mn(HCONH2)6]+2 complexes is 2.11 and 2.20 Å, respectively. However, there seems to be a hydrogen bond between each formamide and one of its neighboring partners, which can reduce the steric effect by a certain amount. The Mn2+···O(HCONH2) distance in the dimer is 1.851 Å. The Mg2+···O(HCONH2) distance in the dimer is 1.808 Å. By looking at Table 1, one sees that both the Mn2+···HCONH2 and Mg2+···HCONH2 dimer interaction energies are higher than for the CH3OH and HCOOH dimers. This is reflected in the larger ΔG values in Table 7. Another neutral ligand is hydrogen sulfide (H2S), and the results on the [Mn(H2O)5H2S]+2 and [Mg(H2O)5H2S]+2 complexes are given in Table 6. The magnesium-containing complex was calculated for the comparison since this complex was not included in the published study of Mg2+ complexes.8 The SAPT interaction energies of the [Mn(H2O)5]+2 and [Mg(H2O)5]+2 clusters with H2O and H2S are given in Table 6. The data reveal that the interaction with H2S is weaker than that with H2O in the hexacoordinated complexes. This may be the principal reason why already the first substitution of water by H2S is energetically unfavorable. The ΔEMP2 or ΔGMP2 for n = 0 from Table 7 correspond rather well with the difference in the SAPT interaction energies for L = H2O and H2S given in Table 6. Positive energies also characterize all subsequent water substitution reactions by H2S and hence the formation of mixed [Mn(H2O)6−n(H2S)n]+2 complexes is unlikely. The charged ligand, formate (HCOO−), represents deprotonated aspartate or glutamate side chains. In analogy to J

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theoretical geometries and X-ray records redundant. Also, no experimental data for structures with magnesium were available (except for SpsA, which will be addressed later). Conclusions on the relevance of using the same structure with fixed positions of the heavy atoms both for Mn2+ and Mg2+ may be drawn by comparing the gas phase structures of Mn2+···L dimers, [Mn(H2O)6−nLzn]2+nz complexes and the X-ray records. First, the Mn2+···IMZ (histidine analog) distance in the dimer is 1.96 and 2.17 Å in [Mn(H2O)5IMZ]2+. In Gal-T1 it is around 2.23 Å. Second, the distances in the Mg2+ moieties are 1.95 Å in the dimer and 2.13 Å in the penta-aqua complex. The distance in the Mn2+···H2S is 2.47 and 2.72 Å in [Mn(H2O)5(H2S)]2+. The Mn2+···Met distance in Gal-T1 is 2.83 Å. Again, in the Mg2+ containing counterparts, the values are 2.46 and 2.74 Å in the dimer and penta-aqua complex, respectively. In conclusion, the equilibrium separations between the Mn2+ and Mg2+ cations and their ligands are not so exceedingly different that it would render our active site models utterly useless. As stated previously, the metal−ligand position is not determined exclusively by their pair interaction and effects such as ligand bulkiness, protein backbone rigidity and interactions of water and DP with other residues are also influential. These factors are present irrespective of the metal ion. There are two possible paths how the metal cation can encounter the donor; the metal may interact with diphosphate in bulk solution and then together bind into the active site of an enzyme or the donor binds to the metal already located in the active site of the enzyme. We have explored both possibilities. First, we have calculated the energetics of the replacement of the two water molecules by DP in hexacoordinated aqueous complexes. The values in Table 7 show a very high free energy gain at the MP2 level for both divalent metals; −376 kcal/mol for Mn2+ and −377 kcal/mol for Mg2+. The gain for Mn2+ is higher than the replacement of two water by two formate molecules (−314 kcal/mol) and also higher than the published B3LYP value7 on Mg2+ (−313 kcal/mol). A close inspection of the complexes revealed that hydrogen bonding between water molecules and the DP oxygens that are not coordinating metal increase the interaction energy. Since these kinds of interactions are different in the formate complexes, we assume that they contribute to the different energetics of formate and DP complexes. Interestingly, the calculated free energy values imply that divalent metal cations Mn2+ and Mg2+ exhibit similar binding to diphosphate. This finding agrees well with thermodynamic data on binding of Mn2+ and Mg2+ to nucleotide phosphates.70 To provide a basis for comparison, we calculated the substitution of the waters by DP also in the active site models of glycosyltransferases, and the obtained values are given in Table 8. In models containing Mn2+ in the active site, the DFT electronic energy ΔE is −212.4, −226.5, −206.9, and −154.0 kcal/mol for SpsA, GnT1, Gal-T1, and MGal-T1, respectively. The replacement of Mn2+ by Mg2+ resulted in a change of ΔE values. Except for SpsA, the calculated affinities are lower implying that the GnT1 and GalT-1 enzymes prefer Mn2+ over Mg2+. In the GnT1 model, the energy ΔE changed to −222.2 kcal/mol, for the Gal-T1 model the ΔE energy decreased to −194.9 kcal/mol, and for MGal-T1 the energy ΔE changed to −148.3 kcal/mol. Surprisingly, in the SpsA, ΔE increased to −218.0 kcal/mol. This increase was unexpected since in the SpsA and GnT1 glycosyltransferases the first coordination shell is similar containing besides DP one carboxylate and two water molecules. However, the inspection of the crystal structures of

diphosphate group of the uridine diphosphate (UDP) moiety with remaining positions filled by enzyme amino acids and water molecules. Here, we have approximated the Mn2+ and Mg2+ coordination in four different enzymatic environments. To explore how the replacement of Mn2+ by Mg2+ cation influences the catalytic activity of glycosyltransferases, we selected four GTs, namely, SpsA, GnT1, Gal-T1, and the M344H mutant of Gal-T1. The computational models of the first coordination shell are shown in Figure 7. The model of SpsA is based on the X-ray 1qgq structure of the UDP−manganese complex of SpsA from Bacillus subtilis.64 The first coordination sphere of Mn2+ in SpsA contains, besides two coordination positions filled by nucleotide diphosphate sugar, one aspartic acid (Asp99) and three water molecules. The GnT1 model is based on the X-ray structure 1foa.65 In the active site of GnT1, similarly to SpsA, Mn2+ is coordinated by only one charged amino acid, namely, aspartic acid (Asp213), and the remaining ligands are three water molecules. In the case of GnT1, the replacement of Mn2+ by Mg2+ decreases the catalytic activity of GnT1 about 60%.66 In Gal-T1, the enzymatic environment is different; manganese binds to three amino acids (Asp254, Met344, and His347) and only one of them is charged. The remaining ligands are water molecules. The coordination of Gal-T1 is particularly interesting, as all three amino acids interact with Mn2+ via different atoms; oxygen from Asp, sulfur from Met, and nitrogen from His. The X-ray structure 2fyd67 of the bovine β-1,4-galactosyltransferase has been used for the construction of the computational model. This enzyme shows no enzymatic activity in the presence of Mg2+.68 However, when Met344 is replaced with His (MGalT1) the catalytic activity in the presence of Mn2+ decreases by 98%, but the activity in the presence of Mg2+ increases to 25% of its wild-type activity.69 In all computational models, we reduced UDP to a dimethyldiphosphate (DP) molecule. The amino acids were capped according to Figure 7. Initially, we attempted to optimize the structure of the clusters without any constraint. Unfortunately, the conformation of the amino acids and DP position changed significantly from their X-ray geometries. Also, the calculations resulted in a considerable deformation of the cluster structure with one water molecule migrating away from Mn2+ toward DP and the remaining two water molecules (in SpsA and GnT1) formed strong hydrogen bonds with DP. In the real enzyme, the positions of the amino acids are more fixed due to the stability of the backbone, and the position of DP is also partially determined by its interactions with other residues and not just manganese. Therefore, in the next attempt, the positions of the heavy atoms were constrained to the X-ray geometries, and the positions of the hydrogen atoms and waters were optimized. This yielded the structures as shown in Figure 7. The DP molecule was subsequently replaced by two additional water molecules, and their positions were reoptimized. The same approach was used for the complexes containing the magnesium cation. It is certainly disputable as how well this method resembles the X-ray structures. On the other hand, even though the resolutions of the PDB records are relatively good; 1.5, 1.8 and 2.0 Å for SpsA, GnT1, and Gal-T1, respectively, the regions around the manganese ion and the ligand have a quite high B-factor. Especially the SpsA structure seems to suffer from this with B-factors on all Mn 2+ coordinating atoms being above 40 Å2. In Gal-T1, the respective B-factors are roughly from 19 to 30 Å2 and in GnT1 from 13 to 28 Å2. This renders the comparison of the K

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The Journal of Physical Chemistry B Table 8. ΔE/B3LYP/AVDZ Energy Change for the Replacement of Two Water Molecules with the DP Ligand in the Active Site Models of Selected Glycosyltransferasesa enzyme

Mn2+

Mg2+

SpsA GnT1 Gal−T1 MGal−T1

−212.4 −226.5 −206.9 −154.0

−218.0 −222.2 −194.9 −148.3

Table 9. Calculated B3LYP/AVDZ Energy Changes (ΔEtr) for the Mn → Mg Transfer Reaction in the Active Site Models of Selected Glycosyltransferasesa

activityb ↓ ↓ ↓ ↑

to to to to

ΔEtr

enzyme active site models [Mn-SpsA]−1 + [Mg(H2O)6]+2 → [Mg-SpsA]−1 + [Mn(H2O)6]+2 [Mn-GnT1]−1 + [Mg(H2O)6]+2 → [Mg-GnT1]−1 + [Mn(H2O)6]+2 [Mn-Gal-T1]−1 + [Mg(H2O)6]+2 → [Mg-GalT1]−1 + [Mn(H2O)6]+2 [Mn-MGal-T1]−1 + [Mg(H2O)6]+2 → [MgMGalT-1]−1 + [Mn(H2O)6]+2 [Mn(H2O)4DP] + [Mg(H2O)6]+2 →[Mg(H2O)4DP] + [Mn(H2O)6]+2

90%c 40% 0% 25%d (↓ to 2%)e

All data are in kcal/mol. bActivity change upon Mn2+ → Mg2+ substitution. cReference 71; ref 64 identifies Mn2+ as the optimal ion. d MGal−T1 activity with Mg2+ compared to Gal−T1 with Mn2+. e MGal−T1 activity compared to Gal−T1, both with Mn2+. a

−6.11 3.74 17.85 2.85 −1.98,b −0.10,c −0.83d

a

2+

All data are in kcal/mol. bB3LYP/AVDZ. cMP2/AVTZ//B3LYP/ AVDZ. dB3LYP/AVDZ thermal correction to Gibbs Free Energy.

2+

SpsA in the complex with Mn and Mg revealed that both structures differ.64 The noticeable difference between the Mn2+ (1qgq) and Mg2+ (1qgs) structures of SpsA is the interaction with diphosphate. In the Mn2+ complex, cation was found to be coordinated by the two phosphate oxygens, whereas in the Mg2+ complex, the Mg2+ cation does not interact with both phosphate oxygens, and is incompletely coordinated by distal phosphate alone.64 Moreover, the Mg2+ ion in the 1qgs structure of SpsA is not solvated by waters, which to some extent defies our strategy where water molecules were kept at their X-ray positions. The B-factors of magnesium and the coordinating atoms in 1qgs are equally large as in 1qgq. In our calculations, the same coordination of the Mn2+ and Mg2+ to both phosphate oxygens was used. Therefore, we assume that the interaction with Mg2+ is overestimated. Nevertheless, the energies calculated for the glycosyltransferase models are considerably smaller than those for hexacoordinated aqueous complexes. This is in agreement with experimental observations11 that the most likely ligand for both cations, though less so for Mn2+, is oxygen. The manganese cation binds to nitrogen and sulfur more frequently than does magnesium, which is also supported by the calculations that showed the stronger interaction of GTs with the manganese cation. The finding that higher interaction energies are predicted for hexacoordinated aqueous complexes compared to GT models also explains why bulk solvation can dislodge the metal/UDP complex from the enzyme in the last step of the reaction catalyzed by metal-dependent glycosyltransferases. The calculation on GalT-1 and mutant MGal-T1 indicate that such mutation leads to a reduction of the ΔE effect connected to the exchange of DP by two water molecules by approximately onequarter of the original magnitude. Also, ΔE equals −154.0 kcal/ mol for the structure containing Mn2+ and decreases to −148.3 kcal/mol when manganese is replaced by Mg2+. The ΔE difference for MGal-T1 is smaller than in the Gal-T1, however, consistent with the general trend. Reactions in which ligands are transferred from manganese to magnesium ions, that is,

Mg2+ complexes. The transfer reaction Mn2+ → Mg2+ in Gal-T1 seems to be the least favorable within the studied enzymes with a strong endothermic character of 17.85 kcal/mol (see Table 9). Interestingly, the mutation of Met344 to His344 resulting in MGal-T1 causes a rather significant reduction of the transfer energy to 2.85 kcal/mol. This agrees well with experimental observation11 that Mn2+ prefers nitrogen binding ligands over sulfur binding ligands, though Mn2+ can accept both nitrogen and sulfur ligands. A similar preference for divalent manganese (3.74 kcal/mol) is calculated for the GnT1 model, where all ligands are oxygen bound. The calculated data qualitatively correlate with the modulations of enzyme activities when divalent manganese is replaced by divalent magnesium, for example, the wild-type Gal-T1 had no activity in the presence of Mg2+ while for GnT1, the Mg2+ presence resulted in a drop in the activity. Also, the mutation to MGal-T1, which was more active in the presence of Mg2+, is reflected in a significant decline in the Mn2+ → Mg2+ substitution energy.68 However, one must be careful with the interpretation of thermodynamics of the Mn2+ → Mg2+ transfer reaction and its connection to the enzyme activity. We have to keep in mind that in the calculations only the first coordination shell was modeled. Other factors like the role of the second shell ligands, the role of the protein matrix, or the effective dielectric environment were not studied. The important role of the interactions with the amino acids forming the enzyme receptor site on the conformation of the nucleotide diphosphate sugar molecule and interaction with the metal has also been stressed.72 The metal interactions with the enzyme and the donor are influenced by intracellular concentrations of Mn2+ and Mg2+ that are very different. The cytosol concentrations of Mn2+ and Mg2+ are in the nanomolar and micromolar range, respectively. To surmount such a large concentration difference that favors Mg2+, the glycosyltransferase requires a well-defined Mn2+ coordination site by including other than O-linked ligands. Therefore, the presence of a permanent binding site in the metal-dependent GTs was suggested.70 On the other hand, the Golgi apparatus acts as a manganese accumulator, which might influence the Golgi resident GTs.73,74 A deeper analysis of the factors mentioned above would require the use of QM(DFT)/ MM calculations with the optimization of the receptor site containing the metal, the donor substrate, and all necessary amino acids.

[MnGT]−1 + [Mg(H 2O)6 ]+2 → [MgGT]−1 + [Mn(H 2O)6 ]+2

(4)

where GT denotes SpsA, GnT1, Gal-T1, and MGalT1 are all, except that for SpsA, endothermic (see Table 9). The SpsA is the only case where an affinity for magnesium is higher compared to manganese (ΔEtr = −6.11 kcal/mol). We presume that this is the result of the same SpsA complex model used for both metals, as discussed above. In other glycosyltransferase models, Mn2+ complexes are more stable than corresponding L

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The Journal of Physical Chemistry B

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basic principles and physical bases of the Mn2+ and Mg2+ binding with various ligands and their role in metal specificity in glycosyltransferases. Nevertheless, many questions regarding the activity of glycosyltransferases and their role in the catalytic activity of these enzymes still need to be addressed. However, to provide more detailed understanding of the role of the divalent manganese and magnesium cations will require extensive calculations using the QM/MM methods and taking into account the whole enzyme.

SUMMARY AND OUTLOOK In the present study, we attempted to provide a qualitative as well as a quantitative description of the energetics of following substitution of water in hexacoordinated complexes of the divalent manganese ion, Mn2+. The obtained results indicate that manganese behaves in this respect very similarly to magnesium cation, Mg2+. The structures of the Mn2+ complexes appear to be quite similar, and moreover, also the energetic balance of the water substitution reactions seems to copy those of the magnesium complexes fairly well. The main difference is that the formation of complexes with waters replaced by various ligands is thermodynamically more favorable for manganese than in the magnesium counterparts. The charged HCOO− ligand is an exception from this, however, similarly to the Mg2+ complexes, the substitution of water is favored only up to n = 2. The selection of the ligands was to mimic side chains of amino acids commonly entering interactions with either Mg2+ or Mn2+ in receptor sites of different enzymes. Our gas phase optimized structures of simple dimer structures point out the somewhat shorter equilibrium separations in Mg2+···L complexes compared to the Mn2+···L ones, in agreement with a slightly larger ionic radius of Mn2+ (0.83 Å for Mn2+(sextet) and 0.72 Å for Mg2+).75 As to the difference between divalent manganese and magnesium complexes with the small organic molecules, we can say that the differences are somewhat ambiguous. There is a clear difference in the decomposition of the interaction energy components mainly caused by the substantially larger polarizability of manganese. On the other hand, these differences cause only about 5−10% variance in the magnitude of the total interaction energies of the manganese and magnesium dimers with the selected ligands. However, even such a small change may play a crucial role in a specificity of the metal for various nonoxygen ligands. Zn2+ exhibits the strongest interaction of the three metal cations with the chosen model O-, S-, and N-binding partners. The calculated SAPT(DFT) values offer accurate ab initio interaction energies commonly achievable only with highly correlated supermolecular approaches such as CCSD(T). At the same time, these results offer the most state of the art insight into the physical nature of the interactions of selected ligands with the Mg2+ and Mn2+ cations. One has to bear in mind the added difficulty of the analysis of divalent manganese cation, as this presents a high spin state; thus, such analysis has been left desired for several years. Four models of glycosyltransferases, namely, SpsA, GnT1, Gal-T1, and MGal-T1, were studied by a DFT method. The relative interaction energies of Mg2+ and Mn2+ cations for a variety of O-, N-, and S-ligands were evaluated. We found that the active sites containing N- or S-ligands have higher affinity to Mn2+ than to Mg2+. This suggests that some of the metaldependent glycosyltransferases developed during evolution the control over the Mn2+ binding by introducing amino acids that coordinate the metal via nitrogen or sulfur into the active site. The presence of N- and S-binding ligands in the active site should discriminate Mg2+ but accept Mn2+. Of course, the affinity of Mn2+ and Mg2+ for a given ligand is not the sole determinant of the activity of GTs. The larger ionic radius of Mn2+ may contribute to the metal specificity in GTs since the replacement of Mn2+ by Mg2+ in a given enzyme may result in tension in the active site as the amino acids would be pulled by Mg2+ to fit more closely their mutual equilibrium separation. In conclusion, in this study, we have shed some light on some

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support was granted by the Scientific Grand Agency of the Ministry of Education of Slovak Republic and the Slovak Academy of Sciences (VEGA 2/0035/16). The work was also supported by AMED-CREST No. 16gm0910003h0302. V.S. also acknowledges Rikkyo SFR project, 2014-2016, and MEXT Supported Program for the Strategic Research Foundation at Private Universities, 2013−2018. V.S. thanks Rafal Podeszwa for consultations and the help with code modifications of the SAPT program.

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