J. Phys. Chem. B 2007, 111, 12883-12887
12883
Reaction Mechanism of the Vitamin K-Dependent Glutamate Carboxylase: A Computational Study Pedro J. Silva† and Maria Joa˜ o Ramos*,‡ REQUIMTE, Faculdade de Cieˆ ncias da Sau´ de, UniVersidade Fernando Pessoa, Rua Carlos da Maia, 296, 4200-150 Porto-Portugal, and REQUIMTE, Faculdade de Cieˆ ncias, UniVersidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto-Portugal ReceiVed: May 17, 2007; In Final Form: August 28, 2007
In the reaction cycle of glutamate carboxylase, vitamin K epoxidation by O2 has been proposed to generate a very strong base able to remove a proton from the γ carbon of a Glu residue, thus yielding a Glu-based carbanion that readily reacts with CO2. We have used hybrid density functional theory to study this appealing mechanism. Our calculations show a very exergonic four-step mechanism with the reaction of (triplet) O2 with the singlet vitamin K anion as the rate-limiting step, with a rate similar to the experimental value. Our study also establishes the need to apply continuum models when performing the optimization of minimumenergy crossing points between potential energy surfaces of different multiplicities for enzyme model systems.
I. Introduction Most blood-clotting proteins are post-translationally modified by a vitamin K-dependent carboxylase which couples vitamin K hydroquinone (KH2) oxidation to the carboxylation of 9-12 glutamate in each of the blood-clotting factors.1 These newly formed γ-carboxylated glutamate (Gla) residues strongly and selectively chelate Ca2+ ions, which trigger conformational changes2,3 that allow the development within the Gla domain of the protein4 of a binding site for exposed phosphatidylserine head groups located on the activated membrane surfaces of blood platelets and endothelial cells. During glutamate carboxylation, vitamin KH2 is converted into vitamin K epoxide, which is then recycled back to the hydroquinone form by a vitamin K reductase. An explanation for the relationship between glutamate carboxylation and vitamin K epoxidation has been proposed by Dowd et al.5 in the socalled base amplification mechanism. According to this mechanism (Figure 1), abstraction of a proton from vitamin KH2 by a protein base allows addition of an O2 molecule to the cofactor, yielding a dioxetane intermediate which then collapses into a strongly alkaline alkoxide. This strong base then abstracts a proton from the γ carbon of the substrate Glu residue, thereby generating a strong carbanion that will be carboxylated by CO2 in the mechanism’s last step. Cysteine residues6 have been proposed to act as bases in the initial hydroquinone deprotonation, but recent reports indicate that this role may be fulfilled by a lysine residue instead.7 In order to test the feasibility of the base amplification mechanism, we carried out DFT calculations in model systems. Our calculations afford a complete description of the epoxidation and carboxylation reactions and allowed us to identify the ratelimiting step of this intriguing enzyme. II. Methods All calculations were performed at the Becke3LYP level of theory.8-10 Autogenerated delocalized coordinates11 were used * Corresponding author. E-mail:
[email protected]. † Universidade Fernando Pessoa. ‡ Universidade do Porto.
for geometry optimizations, using a medium-sized basis set, 6-31G(d), since it is well-known that larger basis sets give very small additional corrections to the geometries, and their use for this end is hence considered unnecessary from a computational point of view.12-14 More accurate energies of the optimized geometries were calculated with several triple ζ quality basis sets: 6-311+G(d,p) , 6-311+G(2d,p), 6-311+G(2d,2p), and 6-311+G(3d,2p) (Table 1). The larger basis set is very close to saturation for this system, and all electronic energies reported were computed at this high level. However, studies of the basis set dependence (Supporting Information) show that the smaller basis sets 6-311+G(2d,p) and 6-311+G (2d,2p) yield errors under 0.8 kcal mol-1 versus 6-311+G(3d,2p). Zero point (ZPE) and thermal effects (T ) 298.15 K, P ) 1 bar) were evaluated using a scaling factor of 0.9804 for the computed frequencies. The structure of the minimum energy crossing point (MECP) between non-interacting singlet and triplet states was located at the B3LYP/6-31G(d) level employing the methodology developed by Harvey et al.15 State-averaged wavefunctions were converged at the CASSCF(12,9) level. The coupling between the two states due to the spin-orbit coupling operator was then computed exactly using the full Breit-Pauli operator.16 The singlet-triplet transition probability (P) was estimated from the Landau-Zener formula:17
P ) 1 - e-2δ δ ) π |Hij|2/pν|∆gij| where Hij is the spin-orbit coupling matrix element between the electronic states and ∆gij is the difference of the gradients calculated for the two states at the crossing point. ν is the velocity with which the system is passing the crossing region and, in our case, cannot be larger than the 418 m s-1 calculated from the kinetic theory of gases. Actual values will be much smaller, and therefore our calculated singlet-triplet transition probabilities (P) are over-estimated. The reactive glutamate side chain was modeled as propionic acid. Vitamin K was modeled as 2,3-dimethyl-naphtoquinone.
10.1021/jp0738208 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/13/2007
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Figure 1. Proposed reaction mechanism for vitamin K-dependent glutamate carboxylase.
TABLE 1: Relative Electronic Energies (kcal mol-1) of the Described Intermediates in the Base Amplification Mechanism, Calculated at the B3LYP/6-311+G(3d,2p)// B3LYP/6-31G(d) Level vitamin K hydroquinone MECP dioxetane intermediate TS1 alkoxide TS2 glutamate carbanion γ-glutamyl glutamate
gas phase
)4
) 20
) 78.3
0.0 23.0a 8.7 15.7 -45.1 -36.3 -34.8 -55.0
0.0 17.3b 3.8 10.2 -49.9 -39.7 -39.9 -63.5
0.0 15.5b 2.7 8.7 -51.3 -40.2 -39.9 -65.1
0.0 15.1b 2.5 8.4 -51.5 -40.1 -40.5 -64.9
a MECP geometry optimized in gas-phase. b MECP geometry optimized with a PCM model. All values except those for the minimum energy crossing points include zero-point and vibrational contributions. MECP values do not include the contribution due to the avoided crossing (estimated as, at most, 4.4 kcal mol-1).
Since the binding site of vitamin K to glutamate carboxylase is not known, no protein aminoacids could be included in our model. Environmental contributions to the stationary points and transition states were computed with the polarizable conductor model (PCM),18-20 as implemented in PcGamess,21 with a wide range of possible dielectric constants ( ) 4, 20, and 78.3). Unless otherwise noted, all energies mentioned in the text are computed by applying the PCM ( ) 4) on gas-phase optimized geometries. Dispersion and repulsion effects were evaluated as described by Amovilli and Mennucci.22Atomic charge and spin density distributions were calculated with a Mulliken population analysis23 based on symmetrically orthogonalized orbitals,24 using the larger basis set. Except for PCM calculations in steps
Figure 2. Structure of the minimum-energy crossing points between the siglet and triplet potential energy surfaces in (a) the gas phase and (b) solution (PCM model, ) 4). Spin populations on the incoming oxygen molecule are depicted in italics.
involving paramagnetic species, which were performed with Gamess-US (February 22, 2006 release), all calculations were performed with the PcGamess software package. Computed singlet-triplet gaps were corrected following the procedure described by Ovchinnikov and Labanowski.25 III. Results In the absence of a three-dimensional structure of glutamate carboxylase, the study of the initial hydroquinone step could not be performed: indeed, the accurate computational deter-
Vitamin K-Dependent Glutamate Carboxylase
J. Phys. Chem. B, Vol. 111, No. 44, 2007 12885
Figure 3. Structures of the reactant, transition state, and product of the alkoxide anion-generating step. Relevant charges in italics.
Figure 4. Structure of the transition state of glutamate γ-deprotonation. Relevant charges in italics.
mination of actual pKa of aminoacid residues in macromolecules is a daunting task even when the full structure is known,26 because of the subtle effects of long-range dipoles and the differential solvation of protonable groups. Our study began therefore with the O2 addition to the vitamin K hydroquinone anion. IIIA. O2 Addition to the Vitamin K Hydroquinone Anion. In Dowd’s model, vitamin KH2 oxidation begins with the addition of a (triplet) O2 molecule to the (singlet) substrate. We investigated the minimum energy crossing point between these two potential energy surfaces both in the gas phase and in a continuum model with ) 4. In both instances, the oxygen molecule was found to attack the substrate hydroquinone at the carbon atom bearing the protonated OH group. The minimumenergy crossing points in the gas phase and in continuum models are otherwise quite different: the inclusion of the dielectric dramatically increases the distance of the O2 molecule to the substrate at the MECP from 1.55 to 1.84 Å (Figure 2) and decreases the electronic energy barrier from 23.0 kcal mol-1 to 17.3 kcal mol-1. The spin-orbit coupling are also quite different in both circumstances (2.16 cm-1 in the gas phase vs 12.72 cm-1 in solvent). These results clearly show that the geometry and properties of minimum-energy crossing points are very sensitive to the presence of solvent: unlike the calculation of relative solution energies of stable intermediates and transition states,27,28 MECP optimization and characterization should not be performed by applying a continuum model on gas-phase optimized geometries. The increase in the electronic barrier due to the avoided crossing may be estimated using the Landau-Zener formula. Using the calculated spin-orbit coupling, the difference of gradients along the C-O bond (17.5 kcal mol-1/Å) and an upper estimate of 418 m s-1 for the velocity of the O2 approach to the substrate; the avoided crossing increases the barrier by, at most, 4.4 kcal mol-1. The total electronic barrier in this case therefore lies between 17.3 and 17.3 + 4.4 ) 21.7 kcal mol-1
Figure 5. Potential energy surface for glutamate deprotonation and carboxylation computed at the B3LYP/3-21G level.
and is compatible with the experimental value of 17.4 kcal mol-1 (calculated from reaction kcat29). The singlet-triplet gap at the computed minimum-energy crossing point is 0 kcal mol-1 at the B3LYP/6-31G(d) level, ) 4. Its value increases slightly to 2.4 kcal mol-1 at the higher B3LYP/6-311+G(3d,2p) level ( ) 4). IIIB. Alkoxide Anion Generation. No stable or meta-stable intermediates were found between the minimum-energy crossing point and the dioxetane intermediate postulated in the baseamplification mechanism. This intermediate is a four-membered cyclic peroxide with highly asymmetrical C-O bonds due to the presence of different substituents in the involved carbon atoms. This species lies only 3.8 kcal mol-1 above the reactants. The dioxetane ring may rapidly and irreversibly open, yielding an alkoxide as postulated by Dowd et al.5 The transition state lies only 6.4 kcal mol-1 above the dioxetane intermediate. The peroxide bond is now 0.53 Å longer than the one in the dioxetane intermediate, and the C3-O bond has become much shorter. As the peroxide bond breaks, a novel epoxide bond forms, yielding the final (very stable) alkoxide product (Figure 3). This reaction step is exergonic by 53.7 kcal mol-1 and effectively irreversible. IIIC. Proton Abstraction from Glutamate γ Carbon and Carboxylation. We have expanded the computational model in order to evaluate the ability of the alkoxide generated in the previous step to deprotonate the γ carbon of a substrate glutamate residue. At the calculated equilibrium geometry, the vitamin K alkoxide lies 1.95 Å away from the glutamate Cγ hydrogen, and the negative charge is almost completely (-0.90) localized in the vitamin K alkoxide. As proton transfer progresses, a transition state is reached 10.2 kcal mol-1 above the reactant state. In this state, the proton lies only 1.166 Å away from vitamin K; the charge in vitamin K is -0.46, and -0.56 net charge has been transferred to the Glu substrate. Then, as the proton approaches to 1.04 Å of vitamin K, the substrate returns to an equilibrium position 1.82 Å away from the proton. Most of the negative charge (-0.76) now lies at the γ-depro-
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Figure 6. Overall reaction energy profile of vitamin K-dependent glutamate carboxylase at the B3LYP/6-311+G(3d,2p) // B3LYP/6-31G(d) level. (Solid line) ) 4; (dashed line) ) 20; (dotted line) ) 78.3.
tonated glutamate (Figure 4). This reaction step is endergonic by 10.0 kcal mol-1. The glutamate carbanion readily reacts with CO2: indeed, no transition state for the carboxylation step could be found in fine scans constraining the CO2-carbanion bond from 3.80 to 1.58 Å. This step is exergonic by 23.6 kcal mol-1 and is clearly not rate-determining. Our failure to locate a transition state for this step prompted us to consider the possibility that proton transfer from Glu and carboxylation might occur in a concerted mechanism. However, the results of two-dimensional fine scans along these coordinates are not compatible with a concerted mechanism (Figure 5). Conclusions This study confirms the basic features of the base amplification mechanism proposed by Dowd et al.5 Whereas both dioxetane conversion into the alkoxide and CO2 addition to the glutamate carbanion were found to proceed very rapidly, the initial O2 addition to vitamin K steps show an activation energy close to the experimental value (Figure 6). As an important side result, this study also establishes the need to apply continuum models when performing MECP optimization for enzyme model systems. Supporting Information Available: Geometries of the reactants, transition states and products of all chemical reactions, as well as correlated orbitals used in CASSCF calculations and spin-orbit evaluation; energetic profiles computed with smaller basis sets: 6-311+G(d,p), 6-311+G(2d,p), and 6-311+G(2d,2p); basis set dependences of repulsion and dispersion energies. This material is available free of charge via the Internet at http:// pubs.acs.org.
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