J. Phys. Chem. B 2007, 111, 3251-3257
3251
First Principles Study of Coenzyme B12. Crystal Packing Forces Effect on Axial Bond Lengths Carme Rovira*,† and Pawel M. Kozlowski*,‡ Centre de Recerca en Quı´mica Teo` rica, Parc Cientı´fic de Barcelona, Josep Samitier 1-5, 08028 Barcelona, Spain, and Department of Chemistry, UniVersity of LouisVille, LouisVille, Kentucky 40292 ReceiVed: September 14, 2006; In Final Form: January 5, 2007
In this work we analyze the structure of coenzyme B12 (AdoCbl) by means of periodic density functional theory (DFT) in order to elucidate the influence of the corrin side chains and the crystalline environment on the properties of axial bonds. The Co-Nax axial bond is very weak and its strength of less than 8 kcal/mol is four times smaller than Co-C which in solution is ∼31 kcal/mol. The proper description of the Co-Nax distance has been problematic in previous DFT calculations and the source of disagreement between experiment and theory remained unexplained. To resolve this discrepancy, periodic DFT calculations within the CarParrinello molecular dynamics (CPMD) framework were carried out on three different structural models of increased complexity. The simplest model (DBI-Ado+) contains the naked corrin ring with a total of 96 atoms. The second model is the full coenzyme B12 (AdoCbl) with 209 atoms which has been taken from crystallographic analysis. To understand the extent to which the crystal packing forces influence the structural properties of AdoCbl the complete crystal consisting of four AdoCbl molecules plus 48 water molecules periodically repeated in space was analyzed (1008 atoms). The results show that the properties associated with the Co-C bond can be well reproduced using truncated models. This does not apply to the Co-Nax axial bond and the presence of the local environment appears to be essential for the correct prediction of its bond length. The most interesting outcome of the present analysis is the finding that the actual length of the Co-Nax bond (2.262 Å) is largely influenced by crystal packing forces.
Introduction Coenzyme B12, also called adenosylcobalamin (AdoCbl), serves as a cofactor in about a dozen enzymatic reactions in which a hydrogen atom is interchanged with a functional group such as alkyl fragment, -OH or -NH2 on an adjacent carbon atom.1-8 It is the most complex tetrapyrrolic cofactor in which the central cobalt atom is coordinated by four equatorial nitrogen ligands donated by pyrroles A-D of the corrin ring (Figure 1). Axially, the cobalt ion is coordinated on the “lower” face by a nitrogen from the intramolecular base 5,6-dimethylbenzimidazole (DBI) and on the “upper” face by 5′-deoxyadenosyl (Ado) moiety. The cobalt-carbon bond is one of few metal-carbon bonds known in biology and is the key to the reactivity of this coenzyme. During enzymatic catalysis the Co-C bond is cleaved homolytically, leading to the formation of the 5′deoxyadenosyl radical and cob(II)alamin.9 The energy required to cleave this bond has been measured to be quite low ∼31 kcal/ mol10-13 and undergoes homolysis with a rate constant of ∼9 × 10-9 s-1 at 37 °C.14-16 In contrast, the kcat for some AdoCbl-dependent enzymes is on the order of 102 s-1.17 The rate of enzymatically accelerated cleavage of cobalt-carbon in AdoCbl-dependent enzymes exceeds the rate observed in aqueous solution by about 12 orders of magnitude as a consequence of the coenzyme interaction with the substrate in the presence of an apoenzyme. Although rather low, the Co-C * Corresponding authors. C.R.: tel.; +34 93 4037112; fax, +34 93 4037225; e-mail,
[email protected]. P.M.K.: tel.; +1 502 852-609; fax, +1 502 852-8149; e-mail,
[email protected]. † Parc Cientı´fic de Barcelona. ‡ University of Louisville.
Figure 1. Molecular structure of 5′-deoxy-5′adenosyl-cobalamin (AdoCbl or coenzyme B12).
strength must be substantially lowered in enzymatic catalysis. In order to achieve a reaction acceleration of ca. 12 orders of
10.1021/jp0660029 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/06/2007
3252 J. Phys. Chem. B, Vol. 111, No. 12, 2007 magnitude, the Co-C bond dissociation energy must be further reduced by about ∼15-17 kcal/mol. The details of how such destabilization is achieved have proven elusive. Effects from corrin distortion, displacement of axial base ligand, or angular distortion of the alkyl group have been suggested to play an important role in the Co-C labilization. However, no single factor (or factors) has been recognized as responsible for the significant lowering of energy dissociation. While many aspects of enzymatic catalysis involving coenzyme B12 as cofactor remain elusive, our understanding of AdoCbl-dependent enzymes has been greatly enhanced over the past few years. The X-ray crystallographic analyses of several B12-dependent enzymes18-21 have been performed, and many problems concerning the mechanism of action are now being solved on the basis of the X-ray structures. In addition, the structure of the AdoCbl22 and several related cobalamins23,24 have been accurately re-determined using synchrotron radiation. While this body of experimental work has established the essential structure of the coenzyme B12 and several B12dependent enzymes, further progress toward achieving a better understanding of these complex bioinorganic systems requires more sophisticated approaches for interpretation of this, yet sometimes conflicting, body of experimental data. With that respect methods of computational chemistry, in particular density functional theory (DFT), are promising techniques capable to elucidate properties of enzymatic active sites from an atomistic and electronic point of view. The potential of DFT to study tetrapyrrolic bioinorganic molecules25 and models of enzymatic radical reactions has been recognized and many applications are documented in literature.26,27 However, due to size and complexity application of DFT to study structural and electronic properties of the B12 cofactors has been hampered for a long time.28 Only recently calculations employing realistic structural models including the full corrin ring have been reported (see ref 29 for details). Particular emphasis has been placed on structure,30-34 factors influencing strength of the Co-C bond35-38 and spectroscopic properties.39,40 Studies using the combined QM/MM approach, where one part of the cofactor is described by DFT while rest of the molecule by molecular mechanics, have been recently reported.41 QM/MM approaches have also been applied to study the interaction between the cofactor and the protein42 and to model the enzymatic mechanism of homolytic Co-C bond cleavage.43,44 While these computational studies provided valuable insights into the structure and electronic properties of the cofactor, skepticism has been expressed by experimentalist about applicability of DFT to study B12-dependent systems.45,46 The underestimation of the Co-C bond dissociation energy and the overestimation of the Co-Nax bond length have been among topics of intense scrutiny and critique. Due to the large size of the cofactor, simplified model systems in which all side-chain groups were replaced by hydrogen atoms (referred as naked corrin model), have been used in nearly every DFT study (see refs 30-44). Since the structure does not include the negative phosphate-containing side chain, the model is a singly positive charged species, the consequences of which have not been systematically investigated at DFT level. The first attempt to perform the calculation in the full cofactor was done by Ching, Randaccio and co-workers,47,48 who employed structure of full cobalamins using the orthogonalized linear combination of atomic orbitals (OLCAO) method, which is based on the local density approximation. However, geometries were taken from high-resolution crystallographic data and not optimized. To date, only in one study was the full cofactor of methylcobalamin
Rovira and Kozlowski (MeCbl) analyzed by first principles method and the full structure was optimized.49 In this work the Co-Nax bond distance in MeCbl cofactor was correctly reproduced by DFT calculations for the first time, showing that the use of the complete molecule is crucial to reproduce these structural properties. In the case of coenzyme B12, the situation is more complex because of the larger size of the coenzyme, which has roughly a globular shape with numerous hydrogen bonds located on its surface. The influence of packing effects in the Co- Nax bond has been attributed to crystal packing forces but never quantified.50,51 In fact, the crystal structure of the cofactor shows a dense network of intermolecular interactions among the closely packet molecules,22 mediated by a number of solvent molecules. Therefore, it is expected that the cofactor structure in the crystal is different than the structure of an isolated cofactor. Moreover, the truncated gas-phase models often used to study the properties of B12 might not capture essential structural details of the coenzyme such as metal-ligand bond distances and angles. Inspired by the recent work on MeCbl,49 the aim of the present study is to apply the same DFT analysis within to coenzyme B12 (Figure 1). In addition, we analyze the structure and electronic properties of the cofactor in the solid state by means of periodic DFT, moving our computational study to a different level of complexity and reliability. Furthermore, in order to elucidate the influence of each constituent of the system (cofactor side chains, crystal water molecules, neighboring molecules in the crystal) the calculations will be carried out in different steps of complexity, adding sequentially all these factors. The calculation of the B12 crystal represents one of the largest calculations done with DFT and will allow us to better compare our results with the experimental data, as well as assess the reliability of using small models. In addition, our calculations will give a quantitative description of the network of hydrogen bonds involving water and the AdoCbl molecules, complementing the information obtained in the X-ray structure.22 Computational Details All calculations reported in this work have been carried out using the BP86 functional52 within the DFT-based first principles Car-Parrinello molecular dynamics (CPMD) framework.53,54 A detailed description of the CPMD methodology is well documented in literature,55 while its application to study related biological systems can be found in several reviews.56,57 As pointed out in the Introduction, of particular relevance to this work is a recent CPMD analysis of methylcobalamin (MeCbl)49 where the computational analysis was focused on the structureenergy relationship for MeCbl with and without axial base. In our calculations the Kohn-Sham orbitals are expanded in a plane waves (PW) with specific cutoff for the kinetic energy. Previous calculations on cobalt containing macrocycles49,58 have demonstrated that a cutoff value of 70 Ry is sufficient to achieve a good convergence of energies and structural properties of cobalt complexes and consequently the same value was applied in the present studies. In order to elucidate the electronic and structural properties of coenzyme B12, three different models of increased complexity have been investigated in detail. The simplest model contains the naked corrin ring with total of 96 atoms. The truncated model of coenzyme, DBI-[CoIII(corrin)]-Ado+, denoted throughout the paper as DBI-Ado+, is the same as structural models employed in most DFT calculations up to date (see for example refs 30-44). The second model is full coenzyme B12 with 209 atoms and denoted as AdoCbl, which has been taken from
Coenzyme B12
Figure 2. Optimized structure of the truncated DBI-Ado+ cofactor.
crystallographic analysis without any structural simplifications. To understand the extent to which the crystal packing forces influence the structural properties of AdoCbl, the complete crystal consisting of four AdoCbl molecules plus 48 water molecules periodically repeated in space was analyzed. This is the largest model and consists of total 1008 atoms. Additional calculations were also performed in the absence of crystalline waters. The recently determined crystal structure of AdoCbl22 using synchrotron radiation was the source of Cartesian coordinates and the initial structure for each system under consideration was build based on these X-ray data. Each system was enclosed in orthorhombic cell of sizes 14 × 21 × 14 × Å3 (for DBI-Ado+), 20 × 20 × 20 Å3 (for AdoCbl), and 15.19 × 21.32 × 27.55 × Å3 (for [4AdoCbl + nH2O]cryst and [4AdoCbl]cryst), respectively. Periodic boundary conditions (PBC) were used in all cases except for the truncated model which bear a positive charge. In this case the calculations were performed in an isolated box. Only valence electrons were explicitly included in computations, and their interaction with the ionic cores was described by norm-conserving, ab initio pseudopotentials generated by means of the scheme developed by Troullier and Martins.59 The pseudopotential for Co was supplemented with nonlinear core corrections to improve its transferability with respect to spin state energies.60 Structure optimizations were performed by means of molecular dynamics with scaling of the nuclear velocities, using a time step of 3 au and a fictitious mass of the CP Lagrangian of 900 a.u. Room-temperature molecular dynamics of the adenosyl radical were performed using a time step of 5 au. The Cartesian coordinates of the optimized structures generated by the study are collected in the Supporting Information (SI) document. Results and Discussion 1. Strength of the Co-C Bond. The relatively weak Co-C bond, which is reversibly cleaved and formed during enzymatic catalysis, is the central feature of the coenzyme B12. Therefore, the computational modeling of the enzymatic activity of B12dependent enzymes requires a detailed understanding of the factors that influence its strength and limits associated with particular level of theory. Any reliable calculations should be capable to provide an accurate estimate of Co-C strength and correctly predict its bond dissociation energy (BDE). The BDEs for coenzyme B12 have been accurately measured in solution and estimated at 31 kcal/mol10-13 while DFT calculations have
J. Phys. Chem. B, Vol. 111, No. 12, 2007 3253
Figure 3. Optimized structure of the full AdoCbl cofactor (hydrogen atoms are omitted for clarity).
TABLE 1: Comparison of Experimental and Computed BDEs Based on the BP86 Functional system AdoCbl AdoCbl DBI-Rib+,a AdoCblb DBI-Ado+ DBI-Ado+ AdoCbl
BDE (kcal/mol) 30.9 ( 4.1 31.5 ( 1.3 36.5 35.2 31.9 29.7 31.5
method
ref
calorimetry thermolysis BP86/6-31g(d) BP86/LANL2DZ/6-31g(d) BP86/6-31g(d) BP86/PW BP86/PW
13 11,51 36 41 38 present work present work
a The Ado has been simplified to Rib. b The presence of the side chains were included via QM/MM.
been systematically applied to reproduce this energy.35-38,41 Early DFT applications were not fully successful because the commonly used hybrid B3LYP functional significantly underestimates the strength of the Co-C bond.31,32,35,37 Recently, it was established that the non-hybrid BP86 functional produces very consistent results in comparison to experiment in terms of BDE and axial bond lengths.36,38 In addition, factors like basis set quality, zero point vibrational energy (ZPE), basis set superposition error (BSSE), relativistic or solvent effects were also analyzed and quantified.36 However, one of the most fundamental questions related to structural simplifications with respect to side chains has not been systematically investigated. In fact, Randaccio and co-workers47 emphasized that side chains must be included in modeling cobalamins, based on calculations of the electronic spectrum while other investigations using semiempirical methods have found no important role of side chains.61 To understand the influence of side chains on the Co-C strength energy, we computed the dissociation energy for a naked corrin ring model DBI-Ado+ (Figure 2) and the full AdoCbl molecule (Figure 3). The dissociation energy of the Co-C bond was computed for both systems by subtracting the energy of the optimized isolated fragments form the full optimized structure as in previously reported computational studies. The results of the present study along with experimental values together with relevant theoretical and experimental data are summarized in Table 1. For comparison we selected only results based on the BP86 functional and models which contain the DBI as axial base and the Ado as axial ligand. The BDE obtained for DBI-Ado+ (29.7 kcal/mol) is within the range of reported energies (31.9-36.5 kcal/mol), although
3254 J. Phys. Chem. B, Vol. 111, No. 12, 2007
Rovira and Kozlowski
Figure 4. Structure of the 5′-deoxyadenosyl radical during the CPMD simulation at 300 K.
slightly lower than the values previously obtained for the same model with the BP86 functional. This could be due to the lack of BSSE in our approach since calculations were based on PW’s. The energy comparison with AdoCbl shows that the inclusion of the side chains increases the BDE from 29.7 to 31.5 kcal/ mol. This is most likely a consequence of cancellations of two opposite effects. The strength of the Co-C bond scales with its length and previous studies have established that the dependence is approximately linear.35 Consequently, the BDE should be energetically higher for truncated DBI-Ado+ model because it has slightly shorter Co-C bond length in comparison to full cofactor (see Figures 2 and 3 for details). At the same time, the AdoCbl structure (Figure 3) has one intramolecular H-bond between the Ado and corrin side chains which is not present in the truncated model (Figure 3). Apparently, the H-bond compensates for the Co-C bond weakening, and the net result is that it takes more energy to separate Ado ligand and corrin moiety apart in case of full cofactor. Although the dissociation energy of the Co-C bond for AdoCbl obtained in this work matches experimental values, results require further elaboration. All reported calculations were carried out for single molecule in gas phase without explicit inclusion of solvent effects and the final results were compared to experimental data in solution. Two previous studies took into account explicitly solvent effects, but they reached somehow opposite conclusions. Jensen and Ryde36 concluded that solvent effects are not so important for correct prediction of dissociation energies, but they used naked corrin models in their analysis similar to DBI-Ado+. Contrary, analysis of solvation effect based on the Miertus-Scrocco-Tomasi model carried out by Maseras and co-workers41 have demonstrated that solvent effects are critical for correct prediction of Co-C bond strength in cobalamins. In their work the presence of the side chains were included via a QM/MM scheme, and it was shown that solvent effects are necessary for the correct reproduction of experimental trends in bond dissociation energies in solution for MeCbl and AdoCbl cofactors. Clearly, the issue of solvation has to be further investigated. Besides the lack of solvent effect the reported values in Table 1 were not corrected for zero point vibrational energy (ZPE) while from previous works it is know that this correction is in order of 4 kcal/ mol. Inclusion of the ZPVE lowers dissociation energy to ∼27.5 kcal/mol which is now lower that one obtained via thermolysis but still in range
within experimental error measured by laser-induced photoacustic calorimetric technique. The Ado radical itself is a complex molecule with complicated conformational properties as revealed by a recent DFT analysis which located 34 minima and 36 transition states.62 Consequently, is not obvious which minimum should be used to compute the dissociation energy. Furthermore, it is possible that the Ado radical does not fully dissociate from the corrin ring when measurements are carried out in solution (cage effects). Therefore, the global minimum might not be correct because the stabilization is due to presence of internal H-bonds which may not be present in solution. To illustrate this point the conformational freedom of the Ado radical at room temperature was explored by means of CPMD, starting from the Ado conformation present in the optimized structure of AdoCbl. The simulation shows that the Ado molecule goes spontaneously to a new configuration that is 4.4 kcal/ mol lower in energy (Figure 4) and closely resembles the 3gg minimum found in ref 62. Only by knowing the structure and dynamics in solution, as for example in ethylene glycol, could solve this problem. This would require carrying out CPMD simulations in solution, but this is out of the reach of our present computational capabilities. 2. Axial Bond Lengths in Coenzyme B12. The cobalt corrinoids have been subject of many structural studies since the historical solution of the vitamin B12 crystal structure by Hodgkin.63 The structure of coenzyme B12 (Figure 1) has been characterized by X-ray crystallography, by neutron diffraction, and by 2D-NMR spectroscopy, while recently several cobalamins have been accurately re-determined using synchrotron radiation.4,22 Despite this large body of structural data accumulated over years, only recently have calculations employing realistic structural models using full corrin macrocycle been carried out. The earlier applications based on the B3LYP functional have shown that DFT calculations predict quite well the structural parameters associated with corrin ring and that the length of the Co-C bond could be reasonably well reproduced. The most difficult structural parameter turned to be the Co-Nax bond length associated with axial base which was found to be longer by more than 0.1 Å in comparison to experiment.30,31,32 This difficulty may be partially attributed to the fact that the Co-Nax bond is very weak and its strength of less than 8 kcal/mol49 is about four times smaller than Co-C
Coenzyme B12
J. Phys. Chem. B, Vol. 111, No. 12, 2007 3255
TABLE 2: Selected Structural Parameters of the Truncated Model, the Full Coenzyme, and the Periodic Models Compared with X-Ray Data parameter
DBI-Ado+
AdoCbl
[4AdoCbl]cryst
Co-C Co-NDBI Co-Nc (aver)b Nc-C ∠ Co-C-C ∠ C-Co-NDBI ∠ Nc-Co-NDBI ∠ C-Co-Nc δ Nc-C1-C2-Nc Fold angle (R)
2.027 2.154 1.859, 1.923 1.314-1.490 122.8 175.2 89.5-91.6 84.0-93.13 37.2 10.3
2.024 2.155 1.855, 1.932 1.314-1.509 126.4 170.9 86.3-95.2 82.5-90.5 41.0 13.5
2.034 2.211 1.853, 1.923 1.316, 1.508 123.8 172.5 86.4-95.5 85.2-92.1 34.9 15.4
[4AdoCbl + nH2O]cryst 2.034 2.262 1.851, 1.920 1.316, 1.509 123.0 173.7 86.8-94.4 85.8-91.6 35.9 14.5
X-raya 2.032(3) 2.237(3) 1.871, 1.911 1.308-1.498 123.4(2) 171.3 86.1-94.8 84.0-93.2 38.4 14.3
a X-ray data were taken from the work of Randaccio and co-workers, ref 22. b Average values corresponding to the short and long equatorial Co-N bond lengths.
which in solution is ∼31 kcal/mol. Additionally, a recent systematic analysis revealed that part of the problem is related to the B3LYP functional and that the BP86 functional produces much more accurate description of axial bond lengths in comparison to experimental data.36,38 While the use of the BP86 functional gives overall better performance and provides better estimation of the Co-Nax bond the agreement with experiment is still not fully satisfactory in case of truncated models.38 To further investigate the source of this discrepancy calculations have been carried out for (i) small model of the isolated cofactor, i.e., truncated with respect to side chains, (ii) the isolated cofactor, (iii) and the cofactor in the solid-phase using periodic boundary conditions and the crystallographic cell. The most relevant structural parameters obtained from these calculations for DBI-Ado+, AdoCbl, and finally [4AdoCbl + nH2O]cryst are summarized in Table 2. From analysis of the optimized bond lengths, it is apparent that the truncated model reproduces well the Co-C bond but underestimates the Co-Nax length. The increase of the cutoff value in the PW expansion (data not shown) leads to monotonic increase of the Co-Nax but does not bring this distance even close to what is observed experimentally. To explore the axial bond lengths behavior in full coenzyme B12, its structure was optimized for direct comparison with X-ray data (Table 2). The analysis of the optimized cofactor revealed a few new intramolecular H-bonds, not only among the corrin side chains, but also between the Ado group and the corrin side chains (Figure 3). For instance, an intramolecular hydrogen bond is formed between one of the corrin amide substituents and the OH of the ribose ring of Ado. The same interaction was also found in previous QM/MM calculations by Maseras et al.41 There is a slight increase of the Co-Nax bond but its value of 2.155 Å is still far from X-ray of 2.237(3) Å. It appears that in case of AdoCbl the length of the Co-NDBI converges nearly to the value of ∼2.16 Å which was previously reported for MeCbl.49 To verify that the length of 2.155 Å is indeed a true minimum in case of AdoCbl and not local two different initial starting points for geometry optimization were used: one based on modified structure of MeCbl while second on X-ray coordinates. In both cases the geometry optimization converged to the same structure. To further understand the optimized structure of AdoCbl, it is useful to connect the present results (Table 2) with the ones previously obtained for the closely related MeCbl cofactor.49 The optimized axial Co-NDBI (2.150 Å) and Co-CMe (1.992 Å) bond lengths in MeCbl are already in excellent agreement with X-ray data of 2.162 Å and 1.979 Å, respectively. This comparison illustrates that the inclusion of side chains is sufficient for MeCbl but not for AdoCbl and does not bring the axial bond lengths closer to experiment. To rationalize this
observation, the importance of both electronic and steric effects needs to be taken into account. While in the truncated models, DBI-Me+ and DBI-Ado+ electronic effects are dominant, in the case of the full cofactors the steric interactions with the corrin side chains apparently starts to play an important role. The relatively weak Co-NDBI bond to large extend is controlled by the local environment and this is why in both cases the length approaches the same value. Nevertheless, the Co-Nax bond in AdoCbl is still shorter than the experimental value in the crystalline phase, suggesting that crystal packing forces appear to have a critical role for the correct prediction of the CoNDBI bond length. 3. Structure of Coenzyme B12 in Presence of Crystal Packing Forces. As ultimate solution of the problem related to accurate description of the Co-NDBI bond in case of coenzyme B12, the CPMD calculations were performed on the complete coenzyme crystal structure. In addition to the four AdoCbl molecules of the crystallographic unit cell, the 48 water molecules were also explicitly taken into account. The final structure consists of total 1008 atoms per unit cell. The optimized structure of the full coenzyme B12 reveals that the axial NDBI-Co-CAdo bond lengths cannot be correctly reproduced even when all side chains were properly included (Table 2). In contrast, the axial NDBI-Co-CMe bond lengths in the case of MeCbl, are in very good agreement with X-ray data. The key difference between AdoCbl and MeCbl lies in the complex Ado ligand which interacts with the nucleotide loop of another molecule while such interaction is not present when the cofactor has a small Me group. To quantify this effect the full crystal structure (4 AdoCbl + 48 water molecules per unit cell) was optimized using periodic boundary conditions and the crystallographic unit cell dimensions. The optimized structure of one of the four equivalent AdoCbl molecules of the unit cell is shown in Figure 5, where the complex H-bond network present between the upper face of coenzyme and the nucleotide loop of the nearest neighbor molecule is highlighted. The most important outcome of these complex calculations is the optimized Co-C bond of 2.034 Å and Co-NDBI which is now 2.262 Å, fully consistent with X-ray data (Table 2). This observation implies that intermolecular interactions exerted by neighboring molecules are critical, and that 2.240(3) Å bond length is due to intermolecular interactions in the crystal (i.e.; packing effects). It should be further emphasize that when the calculations were carried out without crystalline waters the cobalt-nitrogen distance was somewhere in between what is observed for isolated cofactor and that of the crystal plus solvent (Table 2). Therefore, when the computational model approaches reality the computed results converge to the experimental values. Each piece taken out like packing forces, corrin
3256 J. Phys. Chem. B, Vol. 111, No. 12, 2007
Rovira and Kozlowski crystal packing forces. However, the substantial effect of packing forces on the Co-Nax bond does not seem to translate into changes in the Co-C bond strength responsible for reactivity of the cofactor. Further comparison of present results for AdoCbl with previous analysis for MeCbl reveals that for MeCbl a single cofactor molecule is sufficient for a correct description of key structural parameters. This is not the case for AdoCbl, where, in addition to using the full structure, the presence of crystal packing forces is critical to obtain quantitative results. The key to understand these critical differences between MeCbl and AdoCbl cofactors lies in their crystal structures. While the small methyl is isolated in MeCbl, there are many interactions between the Ado group and neighboring atoms in case of AdoCbl. Most noticeable is a series of hydrogen bonds between the Ado ligand and nucleotide loop which is the main reason for an additional lengthening of the Co-NDBI bond. Without proper inclusion of environmental factors only semiquantitative description of cobalt-axial base bonding can be obtained based on DFT calculations. This appears particularly critical when extension will be made to study coenzyme B12 embedded in the enzyme environment. Our study suggest that to reproduce changes in the Co-Nax distance it would be very critical to describe well all hydrogen bond interactions between the axial ligand and the protein.
Figure 5. Optimized structure of the coenzyme B12 in the crystal. The network of interactions between the upper face of the coenzyme and its neighboring molecule is shown. Water molecules act as a bridge between the two molecules. Only hydrogen bond interactions shorter than 2 Å are shown.
loop, side chain is not for free and has a noticeable effect on the structure of the coenzyme. Summary and Conclusion The computational studies presented here on the electronic structure of coenzyme B12 were aimed to clarify the influence of the corrin side chains and the crystalline environment on the properties of the axial Co-C and Co-Nax bonds. Due to the large size of the cofactor, simplified models with respect to sidechains have been applied in nearly every DFT studies. In the present work, the structure of the full coenzyme was analyzed (209 atoms), and furthermore, to take explicitly into account the effect of crystal packing forces, the complete crystal structure (consisting of four molecules plus 48 crystalline waters) was constructed and optimized (1008 atoms). These are the most extensive and complex calculations carried out for B12-containing systems up today. The results obtained using periodic DFT and the BP86/PW framework place the computational study of coenzyme B12 at the different level of complexity and reliability. The present study allows further address several fundamental issues as well as critically asses the reliability of simplifications used in previous computational studies. Three different levels of complexity were applied in the computational analysis: the truncated model with respect to side-chains, the isolated cofactor and the cofactor in the crystalline phase. The results show that the properties associated with the Co-C bond can be well reproduced using truncated models. This does not apply to the Co-Nax axial bond and the presence of the local environment appears to be essential for correct prediction of its bond length. The most interesting outcome of the present analysis is the finding that the actual length of the Co-Nax bond (2.262 Å) is largely influenced by
Supporting Information Available: The Cartesian coordinates of the optimized structures generated by this study. This material is available free of charge via the Internet at http:// pubs.cas.org. References and Notes (1) Dolphin, D. Ed. In B12; Wiley-Interscience: New York, 1982. (2) Marzilli, L. G. In Bioinorganic Catalysis; Reedijk, J.; Ed.;, Marcel Dekker: New York, 1993, pp 227-259. (3) Kra¨utler, B.; Arigoni, D.; Golding, B. T.; Eds. Vitamin B12 and B12 Proteins; Wiley-VCH: New York, 1998. (4) Banerjee, R. Chemistry and Biochemistry of B12; John Wiley & Sons: New York, 1999. (5) Banerjee, R. Chem. Biol. 1997, 4, 175-186. (6) Banerjee, R. Biochem. 2001, 40, 6191-6198. (7) (a) Toraya, T. Chem. ReV. 2003, 103, 2095-2127. (b) Toraya, T. Cell. Mol. Life Sci. 2000, 57, 106-127. (8) Banerjee, R. Chem. ReV. 2003, 103, 2083-2094. (9) Halpern, J. Science 1985, 227, 869-875. (10) Hay, B. P.; Finke, R. G. J. Am. Chem. Soc. 1986, 108, 48204829. (11) Hay, B. P.; Finke, R. G. Polyhedron. 1988, 7, 1469-1481. (12) Finke, R. G.; Hay, B. P. J. Inorg. Biochem. 1990, 40, 19-22. (13) Luo, L. B.; Li, G.; Chen, H. L.; Fu, S. W.; Zhang, S. Y. J. Chem. Soc. Dalton Trans. 1998, 2103-2107. (14) Finke, R. G.; Hay, B. P. Inorg. Chem. 1984, 23, 3041-3043. (15) Waddington, M. D.; Finke, R. G. J. Am. Chem. Soc. 1993, 115, 4629-4640. (16) Brown, K. L.; Zou, X. J. Inorg. Biochem. 1999, 77, 185-195. (17) Hay, B. P.; Finke, R. G. J. Am. Chem. Soc. 1987, 108, 80128018. (18) (a) Mancia, F.; Keep, N. H.; Nakagawa, A.; Leadlay, P. F.; McSweeney, S.; Rasmussen, B.; Bosecke, P.; Diat, O.; Evans, P. R. Structure 1996, 4, 339-350. (b) Mancia, F.; Evans, P. R. Structure 1998, 6, 711720. (c) Mancia, F.; Smith, G. A.; Evans, P. R. Biochemistry 1999, 38, 7999-8005. (19) (a) Reitzer, R.; Gruber, K.; Jogl, G.; Wagner, U. G.; Bothe, H.; Buckel, W.; Kratky, C. Structure 1999, 7, 891-902. (b) Gruber, K.; Reitzer, R.; Kratky, C. Angew. Chem.; Int. Ed. 2001, 40, 3377-3380. (20) (a) Shibata, N.; Masuda, J.; Tobimatsu, T.; Toraya, T.; Suto, K.; Morimoto, Y.; Yasuoka, N. Structure 1999, 7, 997-1008. (b) Shibata, N.; Masuda, J.; Tobimatsu, T.; Toraya, T.; Suto, K.; Morimoto, Y.; Yasuoka, N. Structure 1999, 7, 997-1008. (c) Masuda, J.; Shibata, N.; Morimoto, Y.; Toraya, T.; Yasuoka, N. Structure. 1999, 8, 775-788. (d) Shibata, N.; Masuda, J.; Morimoto, Y.; Yasuoka, N.; Toraya, T. Biochemistry 2002, 41, 12607-12617. (e) Shibata, N.; Nakanishi, Y.; Fukuoka, M.; Yamanishi, M.; Yasuoka, N.; Toraya, T. J. Biol. Chem. 2003, 278, 22717-22725. (21) (a) Yamanishi, Μ.; Yunoki, M.; Tobimatsu, T.; Sato, H.; Matsui, J.; Dokiya, A.; Iuchi, Y.; Oe, K.; Suto, K.; Shibata, N.; Morimoto, Y.; Yasuoka, N.; Toraya, T. Eur. J. Biochem. 2002, 269, 4484-4494. (b) Liao,
Coenzyme B12 D-I.; Dotson, G.; Turner, Jr. I.; Reiss, L.; Emptage, M. J. Inorg. Biochem. 2003, 93, 84-91. (22) Ouyang, L.; Rulis, P.; Ching, W. Y.; Nardin, G.; Randaccio, L. Inorg. Chem. 2004, 43, 1235-1241. (23) Ouyang, L.; Furlan, M.; Geremia, S.; Slouf, M.; Srnova, I. Toffoli, D. Inorg. Chem. 2000, 39, 3403-3413. (24) Ouyang, L.; Rulis, P.; Ching, W-Y.; Slouf, M.; Nardin, G.; Randaccio, L. Spectochim. Acta A. 2005, 61, 1647-1652. (25) (a) Ghosh, A. Acc. Chem. Res.; 1998, 31, 189-198. (b) Ghosh, A. In The Porphyrin Handbook; Kadish, K. M.; Guilard, R.; Smith, K. M.; Eds.; Academic Press: New York, 1999; Vol. 7, pp 1-38. (26) Himo, F.; Siegbahn, P. E. M. Chem. ReV. 2003, 103, 2421-2456. (27) Kamachi, T.; Toraya, T.; Yoshizawa, K. J. Am. Chem. Soc. 2004, 126, 16207-16216. (28) (a) Salem, L.; Eisenstein, Ο.; Anh, N. T.; Burgi, H. B.; Devaquet, A.; Segal, G; Veillard, A. NouV. J. Chim. 1977, 1, 335-348. (b) Christianson, D. W.; Lipscomb, W. N. J. Am. Chem. Soc. 1985, 107, 26822686. (c) Mealli, C.; Sabat, M.; Marzilli, L. G. J. Am. Chem. Soc. 1987, 109, 1593-1594. (d) Zhu, L.; Kostic, N. M. Inorg. Chem. 1987, 26, 41944197. (e) Hansen, L. M.; Derecskei-Kovacs, A.; Marynick, D. S. J. Mol. Struc. (THEOCHEM) 1998, 431, 53-57. (29) Kozlowski, P. M. Curr. Opin. Chem. Biol. 2001, 5, 736-743. (30) (a) Andruniow, Τ.; Zgierski, Μ. Ζ.; Kozlowski, P. Μ. Chem. Phys. Lett. 2000, 331, 500-515. (b) Andruniow, T.; Zgierski, M. Z.; Kozlowski, P. M. J. Phys. Chem. Β. 2000, 104, 10921-10927. (c) Andruniow, Τ.; Kuta, J.; Zgierski, M. Z.; Kozlowski, P. M. Chem. Phys. Lett. 2005, 410, 410-416. (31) Do¨lker, N.; Maseras, F.; Lledo´s, A. J. Phys. Chem. B. 2001, 105, 7564-7571. (32) Jensen, K. P.; Ryde, U. J. Mol. Struct. (THEOCHEM) 2002, 585, 239-255. (33) Randaccio, L.; Geremia, Geremia, S.; Stener, M.; Toffoli, D.; Sangrando, E. Eur. J. Inorg. Chem. 2002, 93-103. (34) Pratt, D. A.; van der Donk, W. J. Am. Chem. Soc. 2005, 127, 384396. (35) (a) Andruniow, T.; Zgierski, M. Z.; Kozlowski, P. M. J. Am. Chem. Soc. 2001, 123, 2679-2680. (b) Kozlowski, P. M.; Zgierski, M. Z. J. Phys. Chem. Β. 2004, 108, 14163-14170. (36) Jensen, K. P.; Ryde, U. J. Phys. Chem. A 2003, 107, 7539-7545. (37) Do¨lker, N.; Maseras, F.; Siegbahn, P. E. M. Chem. Phys. Lett. 2004, 386, 174-178. (38) Kuta, J.; Patchkovskii, S.; Zgierski, M. Z.; Kozlowski, P. M. J. Compt. Chem. 2006, 27, 1429-1437. (39) (a) Andruniow, T.; Zgierski, M. Z.; Kozlowski, P. M. Chem. Phys. Lett. 2000, 331, 502-508. (b) Andruniow, T.; Zgierski, M. Z.; Kozlowski, P. M. J. Phys. Chem. A. 2002, 106, 1365-1373. (c) Kozlowski, P. M.; Andruniow, T.; Jarzecki, A. A.; Zgierski, M. Z.; Spiro, T. G. Inorg. Chem. 2006, 45, 5585-5590. (40) (a) Andruniow, T.; Kozlowski, P. M.; Zgierski, M. Z. J. Chem. Phys. 2001, 115, 7522-7533. (b) Stich, T. R.; Brooks, A. J.; Buan, N. R.; Brunold, T. C. J. Am. Chem. Soc. 2003, 125, 5897-5914.
J. Phys. Chem. B, Vol. 111, No. 12, 2007 3257 (41) Do¨lker, N.; Morreale, A.; Maseras, F. J. Biol. Inorg. Chem. 2005, 10, 509-517. (42) Freindorf, M.; Kozlowski, P. M. J. Am. Chem. Soc. 2004, 126, 1928-1929. (43) Jensen, K. P.; Ryde, U. J. Am. Chem. Soc. 2005, 127, 9117-9128. (44) Kwiecien, R. A.; Khavrutskii, I. V.; Musaev, D. G.; Morokuma, K.; Banerjee, R.; Paneth, P. J. Am. Chem. Soc. 2006, 128, 1287-1292. (45) Finke, R. G. Private communication (March 2003). (46) Brown, K. L. Chem. ReV. 2005, 105, 2075-2149. (47) Ouyang, L.; Randaccio, L.; Rulis, P.; Kurmaev, E. Z.; Moewes, A.; Ching, W. Y. J. Mol. Struct. (THEOCHEM) 2003, 622, 221-227. (48) Kurmaev, E. Z.; Moewes, A.; Ouyang, L.; Randaccio, L.; Rulis, P.; Ching, W-Y.; Bach, M.; Neumann, M.; Europhys. Lett. 2003, 62, 582587. (49) Rovira, C.; Biarnes, X.; Kunc, K. Inorg. Chem. 2004, 43, 66286632. (50) Finke, R. G. In Vitamin B12 and B12 Proteins; lectures presented at the 4th European Symposium on Vitamin B12 and B12 Proteins; Krau¨tler B., Arigoni, D., Golding B.T., Eds.; Wiley-VCH: Weinheim, Germany, 1998; Chapter 25. (51) Randaccio, L.; Geremia, S.; Nardin, G.; Wuerges, J. Coord. Chem. ReV. 2006, 250, 1332-1350. (52) (a) Becke, A. D. J. Chem. Phys. 1986, 84, 4524-4529. (b) Perdew, J. P. Phys. ReV. B 1986, 33, 8822-8824. (53) Car, R.; Parrinello, M. Phys. ReV. Lett. 1985, 55, 2471-2474. (54) Computations were performed using the CPMD program. Copyright IBM Corp. 1990-2003. Copyright MPI fu¨r Fesrko¨rperforschung, Stuttgart, Germany, 1997-2001. (55) (a) Tse, J. S. Annu. ReV. Phys. Chem. 2003, 53, 24-290. (b) Marx, D.; Hutter, J. Ab initio molecular dynamics. In Modern Methods and Algorithms of Quantum Chemistry; Grotendorst, J., Ed.; John von Neumann Institute for Computing: Julich, Germany, 2000; pp 301-409. (56) Carloni, P.; Rothlisberger, U.; Parrinello, M.; Acc. Chem. Res. 2002, 35, 455-464. (57) Rovira, C. In Methods in Molecular Biology, Vol 305, ProteinLigand Interactions: Methods and Applications; Nienhaus, G. U., Ed.; Humana Press: Totowa. NJ, 2005; pp 527-566. (58) (a) Rovira, C.; Kunc, K.; Hutter, J.; Parrinello, M. Inorg. Chem. 2001, 40, 11-17. (b) Rovira, C.; Kunc, K.; Parrinello, M. Inorg. Chem. 2002, 41, 4810-4814. (59) Troullier, N.; Martins, J. L. Phys. ReV. B. 1991, 43, 1993-2006. (60) Louie, G.; Froyen, S.; Cohen, M. L.; Phys. ReV. B 1982, 26, 17381742. (61) Jensen, Κ. P.; Mikkelsen, K. V. Inorg. Chim. Acta. 2001, 323, 5-15. (62) Khoroshun, D. V. , Warncke, K.; Ke S.-C.; Musaev, D. G.; Morokuma, K.; J. Am. Chem. Soc. 2003, 125, 570-579. (63) Hodgkim, D. C. Science. 1965, 150, 979-988.
