Quantum-Mechanical Study on the Catalytic Mechanism of Alkaline ...

Article pubs.acs.org/jcim

Quantum-Mechanical Study on the Catalytic Mechanism of Alkaline Phosphatases Gabriela L. Borosky* INFIQC, CONICET and Departamento de Química Teórica y Computacional, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina S Supporting Information *

ABSTRACT: Alkaline phosphatases (APs) catalyze the hydrolysis and transphosphorylation of phosphate monoesters. The catalytic mechanism was examined by quantummechanical calculations using an active-site model based on the X-ray crystal structure of the human placental AP. Free energies of activation and of reaction for the catalytic steps were evaluated for a series of aryl and alkyl phosphate esters, and the computational results were compared with experimental values available in the literature. Mechanistic observations previously reported in experimental works were rationalized by the present theoretical study, particularly regarding the difference in the rate-determining step between aryl and alkyl phosphates. The formation rate of the covalent phosphoserine intermediate followed a linear free energy relationship (LFER) with the pKa of the leaving group. This LFER, which could be experimentally determined only for less reactive alkyl phosphates, was verified by the present calculations to apply for the entire set of aryl and alkyl phosphate substrates.

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expressed by tumor cells,16 it has been used as a tumor marker in several clinical reports.17−20 In this way, this enzyme is presumed to play an interesting role in cancer diagnosis and therapy. Molecular docking, molecular dynamics, and quantummechanical calculations were previously applied to the study of the catalytic mechanism of PLAP.21,22 Activation barriers and free energy values for each reaction step were computed for methyl phosphate21 and phenyl phosphate22 as substrates. The aim of this work was to achieve a better understanding of the activity of APs by means of additional quantum-chemical calculations on the catalytic mechanism of PLAP as a model AP. Continuing our former studies,21,22 in this instance the reaction steps of the mechanism were evaluated for diverse aryl and alkyl phosphate substrates. The existence of a dependence of the rate of catalysis on the pKa of the leaving group was inspected. The present computational results were validated by comparison with experimental assessments reported in the literature.

INTRODUCTION The alkaline phosphatase (AP) superfamily involves a large group of homodimeric metalloenzymes present in almost all living species.1 The amino acid sequence of APs from different organisms is very well conserved, especially residues in the active site and surrounding regions.2,3 As the sequences of mammalian APs fit the structure of the Escherichia coli bacterial enzyme,2 the catalytic mechanism determined for the latter has been proposed to be similar for eukaryotic APs.4 These enzymes catalyze the hydrolysis and transphosphorylation of a broad range of phosphate monoesters by a mechanism involving the formation of a covalent phosphoserine intermediate and release of inorganic phosphate and an alcohol.5 A two-step reaction mechanism (Scheme 1) has been proposed on the basis of kinetic and biochemical data.6−8 The first chemical step involves the generation of the covalent intermediate E−P (k2, Scheme 1), while in the second chemical step this phosphoserine is hydrolyzed (k3, Scheme 1). Transphosphorylation to a phosphate acceptor (k5, Scheme 1) takes place in nucleophilic buffers (presence of R′OH). The rate-limiting step is pH-dependent for aryl phosphate substrates, as the hydrolysis of the covalent intermediate E−P (k3, Scheme 1) is rate-determining at acidic pH < 7.5, whereas the release of phosphate from the non-covalent enzyme− phosphate complex (E·Pi) (k4, Scheme 1) becomes ratelimiting under basic conditions (pH > 7.5).9−11 In contrast, the phosphorylation of the enzyme (k2) has been proposed to be the rate-determining step for the reaction of alkyl phosphates.12 Human placental AP (PLAP) is one of the four human AP isoenzymes.13 It has been suggested to be a modulator of fetal growth because it increases growth and survival of fetal cells.14,15 Since PLAP is one of the proteins ectopically © 2017 American Chemical Society

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COMPUTATIONAL METHODS General Methodology. Procedures were based on the cluster approach, which has been successfully applied to model enzymatic reactions.23−25 In this technique, a limited part of the enzyme is carefully selected to appropriately represent the active site at a quantum-mechanical level. The protein residues surrounding the active site that are not explicitly included in the calculations may influence the model in two main modes. First, they may cause steric restraints that must be considered in Received: December 13, 2016 Published: February 13, 2017 540

DOI: 10.1021/acs.jcim.6b00755 J. Chem. Inf. Model. 2017, 57, 540−549

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Journal of Chemical Information and Modeling Scheme 1. General Catalytic Mechanism of APs

the dianionic monoesters (charge −2e), since experimental observations had determined that these substrates bind and react as dianions.12 The side chains of arginine, aspartate, and glutamate residues were considered as ionized, and histidines were defined as neutral, singly protonated on Hδ. The complete model system had a net charge of −1, resulting from the sum of seven positive charges (two Zn2+ ions, one Mg2+ ion, and one arginine) and eight negative charges (three aspartates, two glutamates, one hydroxide anion, and the phosphate monoester dianion substrate). Quantum-Mechanical Methods. ONIOM29 calculations employing two quantum-mechanical layers (QM:QM) were carried out with the Gaussian 09 suite of programs.30 Density functional theory (DFT) optimizations with the B3LYP functional31−33 were performed for the high layer, consisting of three metal cations, the phosphate monoester dianions, five water molecules, one hydroxide ion, the carboxylate groups of glutamates and aspartates, the −CH2OH groups of serines, and the −C(NH2)2 group of arginine (around 40 heavy atoms and 25 hydrogens). The 6-31+G* basis set was employed for C, O, N, P, Mg, and H atoms, and the LANL2DZ pseudopotential was applied for Zn atoms. For the low layer (73 heavy atoms and 78 hydrogens), energy minimizations with the semiempirical method PM3MM34 were performed. The ONIOM(B3LYP:PM3MM) methodology has been shown to be appropriate in our prior studies.21,22 The electrostatic effect of the environment was considered via polarized continuum model (IEFPCM)35−38 optimizations, using a dielectric constant ε = 4.0 to simulate the influence of the residues surrounding the active site. The positions of the backbone atoms (involved in peptide bonds) were held fixed to preserve the active-site structure, whereas the coordinates of the rest of the atoms were fully optimized. Minima and transition states (TSs) on the potential energy surfaces were characterized by harmonic vibrational frequency calculations, which also afforded the corresponding zero-point vibrational energies, thermal corrections, enthalpies, entropies, and free energies. ONIOM(B3LYP/6-311+G(2d,p):PM3MM)-IEFPCM singlepoint and frequency computations were performed for all of the optimized stationary points in order to obtain more accurate energy and free energy values.

order to avoid significant artificial repositioning of the model residues because of the absence of the surrounding amino acids. Therefore, certain key coordinates at the boundary of the system are conserved as in the X-ray structures to model the steric interactions. In this way, the positions of the backbone atoms obtained from high-resolution X-ray structures are kept fixed, while the coordinates of all of the other atoms in the model system are relaxed. Second, polarization caused by the enzyme surroundings can affect the computed energies; for this reason, polarizable continuum methods are usually employed to take into account electrostatic effects, using a dielectric constant ε = 4 to represent the protein environment.23−25 It has been proved that relative solvation effects decrease very fast as the model size increase, since more groups providing polarization are explicitly added. This combination of a coordinate-locking procedure and continuum solvation effectively accounts for the residues not included in the model, affording precise calculated energies.23−25 The cluster model is the quantum-mechanicsonly (QM-only) method of the two popular quantum-chemical approaches to address enzymatic reaction mechanisms. The other approach is the quantum mechanics/molecular mechanics (QM/MM) model, in which the entire enzyme is considered, with a small core described quantum-mechanically while the rest is treated by molecular mechanics.26,27 In this work, theoretical calculations were performed with a model of 219 quantum atoms, a size which is expected to yield accurate results by the cluster method.23−25 The starting geometry was built from an X-ray structure with an atomic resolution of 1.8 Å (PDB entry 1EW2).28 Former molecular dynamics simulations had verified the stability of the crystal structure, particularly within the active-site region.21 The coordinates of the backbone atoms were kept fixed to avoid distortion of the active site during geometry optimization of the side chains of all residues, as this procedure had been previously confirmed to be appropriate.21,22 The influence of the environment was considered by using a polarizable implicit continuum solvation model with a dielectric constant ε = 4.0 to represent the rest of the amino acids surrounding the active site; this value is generally considered to be a good representation of the protein environment.24,25 Enzyme Model. The three-dimensional structure of PLAP was obtained from the Protein Data Bank (PDB entry 1EW2).28 The computational model was composed of the catalytic metal triad (two Zn2+ ions (M1 and M2) and one Mg2+ ion (M3)) with their ligands Asp316, His320, His432, His358, Asp357, Asp42, Glu311, Ser155, and the nucleophilic Ser92 as well as the significant residues Arg166 and Glu429 (the hydrophilic pocket). Valences at cut peptide bonds were completed with hydrogen atoms. Six water molecules were conserved: three to complete Mg2+ coordination (one as a hydroxide ion) and three coordinated to Glu429. The phosphate ion in 1EW2 was utilized as a template for building

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RESULTS AND DISCUSSION The reaction steps of the catalytic mechanism of APs were computationally evaluated within the active site of PLAP, which includes the catalytic Ser92, the metal triplet (two Zn2+ and one Mg2+), Arg166, Glu429, and some other relevant proximate amino acids (Figure 1). The hydrophilic pocket formed by Arg166 and Glu429 is presumed to stabilize the hydrophilic moiety of the phosphate monoester ligand. Residue Glu429 also stabilizes the water molecules that bridge the gap to the phosphate group of the phosphoseryl intermediate.39 One of 541


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Journal of Chemical Information and Modeling

contacts with the guanidinium group of Arg166. After energy minimization, the water molecule originally included as a hydroxide ion was protonated by the hydroxyl group of catalytic Ser92, which became ionized. This spontaneous proton transfer, also observed in our previous works,21,22 had been proposed in the literature.4,12,40 After formation of the covalent phosphoserine intermediate (Scheme 2, step 1), the aromatic oxide leaving group is stabilized by coordination to Zn1. This anion is displaced from metal coordination by one water molecule in step 2, and a Zn1coordinated hydroxide ion is formed in step 3 by proton transfer to Glu429. In step 4, the nucleophilic hydroxide attacks the phosphoserine, releasing a hydrogen phosphate dianion and regenerating the nucleophilic serine oxyanion. A proton transfer returns Glu429 to its initial ionized form, generating dihydrogen phosphate ion as the final product in step 5. The structures of selected stationary points are shown in Figure 3, and calculated free energies are presented in Table 1. The mechanism in Scheme 3 was considered for the alkyl phosphate substrates. With these alkyl oxide leaving groups, the difference in pKa values allowed proton transfer from the Zn1coordinated water to generate an alkyl alcohol and hydroxide ion in step 3 (pKa for H2O = 15.7, pKa for MeOH = 15.5, pKa for BuOH = 16.1; on the other hand, pKa for PhOH = 10.0 (Scheme 2)).41 Therefore, hydrogen phosphate dianion was the final product for these substrates. Computed free energies are displayed in Table 1, and the structures of model stationary points are illustrated in Figure 4. The pathways were computed from the respective Michaelis complexes, whose initial coordinates were derived from previous molecular docking calculations.21 The potential energy surfaces calculated for all of the phosphate esters in this study shared some common features. The Michaelis non-covalent complex was converted into the covalent phosphoserine through a small rotation of the side chain of Ser92. The TS for the first chemical step, involving generation of the covalent phosphoserine (step 1 in Schemes 2 and 3), presented a trigonal-bipyramidal configuration corresponding to an in-line displacement reaction, as proposed by Holtz et al.,43 with bond forming/breaking oxygens in an opposite axial disposition. The three nonbridging oxygens of the transferred phosphoryl group bisected the axial plane and formed stabilizing interactions with Arg166, Zn2, and one Mg3-bound water. In all cases, departure of the leaving group was assisted by coordination with Zn1. The nucleophilic attack by a hydroxide anion coordinated to Zn1 on the phosphoseryl intermediate (second chemical step, step 4 in Schemes 2 and 3) also exhibited a trigonal-bipyramidal TS corresponding to another in-line displacement. The stabilizing interactions of the phosphoryl group in this transition structure were similar to those observed in the first TS. In general, the positions of the model residues experienced only minor variations, with negligible modifications in the atomic coordinates during the course of the catalytic mechanism. This observation suggests that the active-site structure presents an optimal configuration to assist the hydrolysis of phosphate monoesters. Keynote theoretical investigations on the mechanism of APs have recently been reviewed.44,45 Comparison with experimental assessments allows validation of computational results. Reproduction of experimental observations is a proper test of the accuracy of theoretical procedures and supports their interpretations and predictions. However, comparison of theoretical and experimental kinetic

Figure 1. Active site of PLAP with relevant adjacent residues. Fixed atoms are indicated with asterisks.

these waters is significantly conserved because it is the nucleophile involved in the hydrolysis of the covalent phosphoserine. In this work, the mechanism of catalysis in the active site of PLAP was modeled for the dianions of several primary phosphate esters: two aryl phosphates and nine alkyl phosphates (Figure 2). These substrates were selected from a previous experimental study in which the corresponding kcat/ KM values for the E. coli AP-catalyzed hydrolysis were reported.12

Figure 2. Dianions of phosphate esters selected as substrates.

For the aryl phosphate substrates 1 and 2, the catalytic mechanism illustrated in Scheme 2 was evaluated inside the active site, starting from the Michaelis complex. The initial coordinates for this structure were determined by previous molecular docking calculations.22 In this complex, the oxygen of the ester leaving group was coordinated to Zn1, one nonbridging oxygen was coordinated to Zn2, and the other two nonbridging oxygen atoms presented hydrogen-bond 542


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Journal of Chemical Information and Modeling Scheme 2. Mechanism for the Hydrolysis of Aryl Phosphate Dianions

computational results yielded barriers of 16.3−18.9 kcal/mol for methyl, ethyl, propyl, butyl, and isobutyl phosphates, in accordance with these observations. The free energy profiles are displayed in Figure 5. The two chemical steps of the catalytic mechanism are step 1 (Schemes 2 and 3, corresponding to k2 in Scheme 1) and step 4 (Schemes 2 and 3, equivalent to k3 in Scheme 1). The activation free energies in Table 1 indicate that the hydrolysis of the covalent intermediate (k3) is the rate-limiting step for aryl phosphate monoesters. On the other hand, for alkyl phosphate substrates the computed values point to the nucleophilic attack of the serine alkoxide to phosphorus (k2) as the rate-determining step. While for aryl phosphates the rate-determining step corresponds to product release (k4 in Scheme 1) at pH > 7.5 and to hydrolysis of the phosphoserine (k3) at pH < 7.5,9−11 phosphorylation of the enzyme (k2) has been hinted as ratelimiting for alkyl phosphates.12 Hence, the present computational results are in accordance with the mechanistic interpretations arising from experimental observations. The more reactive alkyl phosphate substrates 3−6 represent an intermediate case. According to calculations for Scheme 3, the higher barrier corresponds to the serine attack to phosphorus in step 1 (k2 in Scheme 1; Figure 5a). However, if a neutral active site model is considered in the second chemical step (as for aryl phosphates in Scheme 2), the TS for hydrolysis of the phosphoserine is the highest in energy (step 4, k3 in Scheme 1; Figure 5b). Taking into account the fact that trifluoroethyl phosphate (3) and propargyl phosphate (4) have values of kcat/KM that are similar to those for p-nitrophenyl phosphate and phenyl phosphate, these most reactive alkyl phosphates were suspected to be limited by the same process as aryl phosphates; nevertheless, test experiments for 3 did not evidence a change in rate-determining step compared with ethyl phosphate (8).12 By inspection of the potential energy surfaces calculated for both types of substrate (Table 1 and Figure 5), the following factors appear to determine the difference in rate-limiting step for alkyl and aryl phosphates. The basicity of the corresponding leaving group seems to be the major aspect influencing the barrier height of the first chemical step (k2), as departure of a more stable aromatic anion is thermodynamically favored. In

data is not straightforward. Whereas computed barriers correspond to the free energy difference between the TS and the Michaelis complex (ΔG⧧cat) and are related to kcat, the reported experimental values are usually kcat/KM, which provide the free energy barrier as measured from the ground state of the free enzyme and substrate in solution to the TS for the first irreversible reaction step (ΔG⧧obs). These two free energy barriers are related through the binding free energy of the substrate (ΔG⧧obs = ΔG⧧cat − ΔGbinding). Thus, ΔG⧧obs derived from the experimental kcat/KM value is a lower bound for the calculated free energy of activation of a chemical step (ΔG⧧cat). Table 1 presents the free energies of activation afforded by the present computations, along with the corresponding values from experimental studies reported in the literature12 (ΔG⧧obs values were determined from kcat/KM by transition-state theory46). The calculated activation barriers are higher than those derived from kcat/KM values, supporting the reliability of the computational methodology and level of theory employed in this work. Although hydrolysis of the phosphoserine is the same reaction for both type of substrates (step 4 in Schemes 2 and 3), the activation barrier for this step was 4.6 kcal/mol lower for alkyl phosphates than for aryl phosphates. This hydrolysis reaction was exothermic for alkyl phosphates but endothermic for the aromatic substrates (Table 1). Even though the model system was the same for both types of substrate, the total charge was −1e after departure of an alkyl alcohol in Scheme 3, while the system became neutral after removal of an aryl oxide in Scheme 2. It has been suggested that the activation energies for phosphoryl transfer reactions in metalloenzymes are very sensitive to the charge balance around the active center, with neutral models being more suitable for reproducing experimental data.47 An activation free energy of 16.2 kcal/mol was determined for the hydrolysis of the covalent intermediate by measuring the rate constant for breakdown of a radioactive E− P complex (k3 in Scheme 1).48 It is worth noting the very good agreement between this value and the free energy barrier of 15.9 kcal/mol calculated for aryl phosphate substrates (Table 1). Phosphorylation of the enzyme by alkyl phosphates should have a barrier higher than 16.2 kcal/mol, since experimental evidence has indicated that k2 is rate-limiting.12 The present 543


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Figure 3. Model stationary points for p-nitrophenyl phosphate as the substrate (bond distances in Å): (a) Michaelis complex; (b) TS for Ser92 nucleophilic attack; (c) covalent phosphoserine intermediate, with water complexed to Zn1; (d) TS for phosphoserine hydrolysis.

k4 is rate-limiting).9−11 A pKa of 8.0 has been suggested for the zinc-coordinated water.12 Linear Free Energy Relationships. When applied to enzymatic reactions, linear free energy relationships (LFERs) or Brønsted correlations can provide information about the nature of the TS if the chemical step is rate-limiting and substituentspecific effects are negligible.49 For a series of rate constants with different leaving groups, the Brønsted parameter βlg, which is the slope of the plot of log(k) versus pKa of the leaving group, describes the change in effective charge in going from

regard to the second chemical step (k3), the presence of a more basic alkyl oxide anion would help the proton transfer from the Zn1-coordinated water molecule to generate the nucleophilic hydroxide (step 3 in Scheme 3), assisting the hydrolysis of the phosphoserine intermediate; on the other hand, formation of the hydroxide ion would be less facile in the presence of an aryl substrate (step 3 in Scheme 2). Therefore, the second energy barrier becomes the highest for aryl phosphates, with the enzymatic rate-determining step being highly influenced by the pH of the medium (at pH < 7.5, k3 is rate-limiting; at pH > 7.5, 544


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Table 1. Reaction and Activation Free Energies Computed for the Hydrolysis of Phosphate Ester Dianions (in kcal/mol);a Reaction Steps Are Shown in Schemes 2 and 3 step 1 b

substrate (pKa, kcat/KM, 1 2 3 4 5 6 7 8 9 10 11

c

ΔG⧧obsd)

(7.1, 3.3 × 107, 7.2) (10.0, 2.4 × 107, 7.4) (12.4, 2.0 × 107, 7.5) (13.6, 2.8 × 107, 7.3) (14.0, 7.5 × 106, 8.1) (14.2, 2.3 × 106, 8.8) (15.5, 1.2 × 106, 9.2 3.5 × 105,f 9.9) (15.9, 1.5 × 105, 10.4) (16.1, 1.3 × 105, 10.5) (16.1, 8.6 × 104, 10.7) (16.1, 4.2 × 104, 11.1)

⧧

ΔGr

ΔG

−9.7 −1.9 5.9 7.6 9.3 6.7 13.1 14.4 13.9 14.6 15.4

4.8 6.4 14.3 13.5 15.2 13.8 16.3 17.4 18.8 18.0 18.9

step 2

step 3e

ΔGr

ΔGr

−6.1 −8.8 −9.3 −7.9 −10.0 −4.5 −6.6 −10.1 −10.7 −11.0 −12.2

10.8 10.8 1.2 −0.4 0.5 0.2 −2.6 −0.6 −1.7 −0.1 −0.1

(3.5) (0.4) (0.8) (−2.1) (−6.4) (−4.2) (−3.1) (−3.5) (−3.1)

step 4e ΔGr 8.3 8.3 −10.5 −10.5 −10.5 −10.5 −10.5 −10.5 −10.5 −10.5 −10.5

(−4.5) (−4.5) (−4.5) (−4.5) (−4.5) (−4.5) (−4.5) (−4.5) (−4.5)

step 5 ΔG⧧ 15.9 15.9 11.3 11.3 11.3 11.3 11.3 11.3 11.3 11.3 11.3

(15.9) (15.9) (15.9) (15.9) (15.9) (15.9) (15.9) (15.9) (15.9)

ΔGr −12.8 −12.8 − − − − − − − − −

a

At the ONIOM(B3LYP/6-311+G(2d,p):PM3MM//B3LYP/6-31+G(d):PM3MM)-IEFPCM level. bpKa of the alcohol leaving group from ref 41. From ref 12 (in M−1 s−1). dCalculated from kcat/KM values. eValues in parentheses were obtained by using a neutral active site model, similar to that for aryl phosphates (see the text). fFrom ref 42. c

Scheme 3. Mechanism for the Hydrolysis of Alkyl Phosphate Dianions

reactants to the TS. The AP-catalyzed hydrolysis of aryl Ophosphorothioates follows a steep leaving-group dependence (βlg = −0.77),50 whereas for alkyl phosphates βlg = −0.85,12 both values being consistent with a dissociative TS. On the basis of the above experimental observations, log(k2) values (derived from the calculated activation free energies by TS theory;46 Table 2) were plotted against the corresponding pKa values in order to gauge the existence of a LFER. A linear correlation with a coefficient R2 = 0.933 and a slope of −1.15 was determined (Figure 6), which confirms the strong dependence of the rate of formation of the covalent phosphoserine intermediate on stabilization of the leaving group. It is worth of mentioning that as the AP-catalyzed reactions of aryl phosphates are not limited by this chemical step, the relationship between kcat/KM and the leaving group pKa could not be experimentally observed with aromatic substrates.12 As the pKa depends on the electrostatic properties of the local environment,51 the pKa values of the leaving groups within a protein should differ from the values in solution reported in ref 41. However, computational approaches to calculate pKa values in enzymes are very demanding and converge slowly (see, e.g., refs 52 and 53). Nevertheless, a very good correlation

was obtained with the solution values employed in the present work. The TSs for serine attack to trifluoroethyl phosphate (3), fluoroethyl phosphate (6), and cyanoethyl phosphate (5) presented a stabilizing hydrogen-bonding interaction between one of the water molecules and one fluorine or nitrogen atom of the substrate. As these compounds were among the most reactive alkyl phosphates examined, this specific interaction between the active site and these particular leaving groups was taken into account to check any perturbation effect on the observed LFER. It should be noted that consistent deviations for 3 had been detected in experimental LFERs, and exclusion of this phosphate from the analyzed data improved the linear correlation.12 Thus, exclusion of 3 from correlation yielded a coefficient R2 = 0.956 for the linear fit in Figure 6, whereas further excluding 3, 5, and 6 afforded a value of R2 = 0.963. The steep dependence of the AP-catalyzed hydrolysis of organic phosphates on the electron-withdrawing properties of the leaving group suggests substantial buildup of negative charge on this group in the TS. This observation is consistent with a dissociative TS, with significant bond breaking and charge accumulation on the leaving group. Table 2 summarizes the bond distances and Mulliken charge densities in the TSs for step 1 characterized for the 11 substrates considered. The 545


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Figure 4. Model stationary points for ethyl phosphate as the substrate (bond distances in Å): (a) Michaelis complex; (b) TS for Ser92 nucleophilic attack; (c) covalent phosphoserine intermediate, with water complexed to Zn1; (d) TS for phosphoserine hydrolysis.

computations for 11 phosphate esters as substrates. Stationary points on the corresponding potential energy surfaces (intermediates and TSs along the reaction pathway) were optimized and characterized. The computed free energy barriers were in good accordance with experimental results for the AP-catalyzed hydrolysis of these substrates.12 The calculated activation barriers were higher than those derived from kcat/KM assessments and consistent with those derived from kcat values. The correspondence between the activation free energy of 15.9 kcal/mol calculated for the hydrolysis of the

computations indicate that a lower pKa of the leaving group gives rise to a more exothermic reaction with a lower activation barrier and an earlier TS. That is, the general trend shows that bonding between the P atom and the O of the nucleophilic Ser92 (P−OSer92) and cleavage of the leaving group bond (P− Olg) are both less advanced for a lower pKa value.

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CONCLUDING REMARKS The catalytic mechanism of hydrolysis in the active site of PLAP as a model AP was inspected by quantum-mechanical 546


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Figure 5. Free energy profiles for the catalytic mechanism. (a) Free energy barriers for step 4 calculated according to Scheme 3 for alkyl phosphates. (b) Free energy barriers for step 4 computed according to Scheme 2 for all substrates (neutral model).

Table 2. Computed Values Corresponding to Step 1 (Schemes 2 and 3)a bond length (Å) (Mulliken charge density at O) substrate (pKa) 1 2 3 4 5 6 7 8 9 10 11 a

(7.1) (10.0) (12.4) (13.6) (14.0) (14.2) (15.5) (15.9) (16.1) (16.1) (16.1)

b

⧧

ΔGr (kcal/mol)

ΔG (kcal/mol)

log(k)

−9.7 −1.9 5.9 7.6 9.3 6.7 13.1 14.4 13.9 14.6 15.4

4.8 6.4 14.3 13.5 15.2 13.8 16.3 17.4 18.8 18.0 18.9

9.3 8.1 2.3 2.9 1.6 2.7 0.8 0.04 −1.0 −0.4 −1.0

P−OSer92 2.381 2.213 2.159 2.083 2.092 2.068 2.011 2.028 2.024 2.026 2.026

(−0.572) (−0.581) (−0.588) (−0.593) (−0.594) (−0.594) (−0.598) (−0.597) (−0.591) (−0.592) (−0.597)

P−Olg 2.049 2.126 2.154 2.198 2.181 2.206 2.275 2.257 2.225 2.222 2.257

(−0.472) (−0.468) (−0.509) (−0.518) (−0.524) (−0.517) (−0.507) (−0.517) (−0.521) (−0.518) (−0.516)

At the ONIOM(B3LYP/6-311+G(2d,p):PM3MM//B3LYP/6-31+G(d):PM3MM)-IEFPCM level. bpKa of the alcohol leaving group from ref 41.

covalent intermediate (k3 in Scheme 1) and the experimental value of 16.2 kcal/mol determined by measuring the rate constant for breakdown of a radioactive E−P complex48 was especially remarkable.

The calculated results pointed to the hydrolysis of the covalent intermediate (k3) as the rate-limiting step for aryl phosphate monoesters, while the nucleophilic attack of the serine alkoxide to phosphorus (k2) is the rate-determining step 547


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Journal of Chemical Information and Modeling Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author gratefully acknowledges financial support from ́ Consejo Nacional de Investigaciones Cientificas y Técnicas (CONICET) and the Secretariá de Ciencia y Tecnologiá de la Universidad Nacional de Córdoba (Secyt-UNC). Access to computational resources at the Mendieta and Cristina clusters from CCAD-UNC, which is part of SNCAD-MinCyT, Argentina, is also acknowledged.

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(1) McComb, R. B.; Bowers, G. N., Jr.; Posen, S. Measurement of Alkaline Phosphatase Activity. In Alkaline Phosphatases; Plenum Press: New York, 1979; pp 986−989. (2) Kim, E. E.; Wyckoff, H. W. Structure of Alkaline Phosphatases. Clin. Chim. Acta 1990, 186, 175−178. (3) Murphy, J. E.; Tibbitts, T. T.; Kantrowitz, E. R. Mutations at Positions 153 and 328 in Escherichia Coli Alkaline Phosphatase Provide Insight Towards the Structure and Function of Mammalian and Yeast Alkaline Phosphatases. J. Mol. Biol. 1995, 253, 604−617. (4) Kim, E. E.; Wyckoff, H. W. Reaction Mechanism of Alkaline Phosphatase Based on Crystal Structures: Two-metal Ion Catalysis. J. Mol. Biol. 1991, 218, 449−464. (5) Schwartz, J. H.; Lipmann, F. Phosphate Incorporation into Alkaline Phosphatase of E. coli. Proc. Natl. Acad. Sci. U. S. A. 1961, 47, 1996−2005. (6) Holtz, K. M.; Kantrowitz, E. R. The Mechanism of the Alkaline Phosphatase Reaction: Insights from NMR, Crystallography and Sitespecific Mutagenesis. FEBS Lett. 1999, 462, 7−11. (7) Reid, T. W.; Wilson, I. B. Escherichia Coli Alkaline Phosphatase. In The Enzymes; Boyer, P. D., Ed.; Academic Press: New York, 1971; Vol. 4, pp 373−415. (8) Coleman, J. E. Structure and Mechanism of Alkaline Phosphatase. Annu. Rev. Biophys. Biomol. Struct. 1992, 21, 441−483. (9) Bloch, W.; Gorby, M. S. Catalytic Mechanism of Escherichia Coli Alkaline Phosphatase: Resolution of Three Variants of the Acylenzyme Mechanism. Biochemistry 1980, 19, 5008−5018. (10) Gettins, P.; Coleman, J. E. 31P Nuclear Magnetic Resonance of Phosphoenzyme Intermediates of Alkaline Phosphatase. J. Biol. Chem. 1983, 258, 408−416. (11) Hull, W. E.; Halford, S. E.; Gutfreund, H.; Sykes, B. D. Phosphorus-31 Nuclear Magnetic Resonance Study of Alkaline Phosphatase: The Role of Inorganic Phosphate in Limiting the Enzyme Turnover Rate at Alkaline pH. Biochemistry 1976, 15, 1547− 1561. (12) O’Brien, P. J.; Herschlag, D. Alkaline Phosphatase Revisited: Hydrolysis of Alkyl Phosphates. Biochemistry 2002, 41, 3207−3225. (13) Millán, J. L. Mammalian Alkaline Phosphatases: From Biology to Applications in Medicine and Biotechnology; Wiley-VCH: Weinheim, Germany, 2006. (14) She, Q.-B.; Mukherjee, J. J.; Huang, J.; Crilly, K. S.; Kiss, Z. Growth Factor-like Effects of Placental Alkaline Phosphatase in Human Fetus and Mouse Embryo Fibroblasts. FEBS Lett. 2000, 469, 163−167. (15) She, Q.-B.; Mukherjee, J. J.; Chung, T.; Kiss, Z. Placental Alkaline Phosphatase, Insulin, and Adenine Nucleotides or Adenosine Synergistically Promote Long-term Survival of Serum-starved Mouse Embryo and Human Fetus Fibroblasts. Cell. Signalling 2000, 12, 659− 665. (16) Fishman, W. H.; Inglis, N. I.; Stolbach, L. L.; Krant, M. J. A Serum Alkaline Phosphatase Isoenzyme of Human Neoplastic Cell Origin. Cancer Res. 1968, 28, 150−154. (17) Dempo, K.; Elliot, K. A. C.; Desmond, W.; Fishman, W. H. Demonstration of Gamma-glutamyl Transferase, Alkaline Phosphatase, CEA and HCG in Human Lung Cancer. Oncodev. Biol. Med. 1981, 2, 21−37.

Figure 6. Leaving-group dependence for step 1 of the AP-catalyzed hydrolysis of organic phosphates.

proposed for alkyl phosphate substrates. These observations agree with mechanistic interpretations derived from previous experimental studies, which suggest these different rate-limiting steps for aryl and alkyl phosphates.9−12 The difference in ratedetermining step for alkyl and aryl phosphates was ascribed to the basicity of the corresponding leaving groups. In regard to the first chemical step (k2), departure of a more stable aromatic alkoxide is preferred, affording a lower barrier. The presence of a more basic alkyl oxide anion favors the proton transfer from a Zn1-coordinated water to form the nucleophilic hydroxide for the second chemical step (k3, step 3 in Scheme 3) and assists the hydrolysis of the phosphoserine intermediate; on the other hand, generation of the hydroxide ion is more energetically costly for the aryl phosphate substrates. A lower pKa of the leaving group increased the exothermicity of the covalent phosphoserine formation reaction, causing a lower activation barrier with an earlier TS. A linear correlation with a coefficient R2 = 0.933 and a slope of −1.15 was observed, indicating a strong dependence of the rate of formation of the phosphoserine intermediate on the stability of the leaving group. Because the AP-catalyzed reactions of aryl phosphates are not limited by this chemical step, the relationship between kcat/KM and the leaving group pKa could be experimentally determined only for alkyl phosphate substrates.12 Interestingly, the present computational results confirm the existence of this LFER for the complete set of aryl and alkyl phosphates.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jcim.6b00755. Cartesian coordinates for relevant optimized stationary points (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

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Gabriela L. Borosky: 0000-0001-7660-962X 548


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