Modeling of Isotope Effects on Binding Oxamate to Lactic

Aug 28, 2009 - The independent unit of this structure contains two tetramers, each of them with a unique constitution of two active sites with the ope...
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J. Phys. Chem. B 2009, 113, 12782–12789

Modeling of Isotope Effects on Binding Oxamate to Lactic Dehydrogenase Katarzyna S´widerek,† Artur Panczakiewicz,‡ Anna Bujacz,§ Grzegorz Bujacz,§ and Piotr Paneth*,† Institute of Applied Radiation Chemistry, Technical UniVersity of Lodz, ul. Zeromskiego 116, 90-924 Lodz, Poland, FQS Poland, ul. Parkowa 11, 30-538 Krakow, Poland, and Institute of Technical Biochemistry, Technical UniVersity of Lodz, ul. Stefanowskiego 4/10, 90-924 Lodz, Poland ReceiVed: April 19, 2009; ReVised Manuscript ReceiVed: July 21, 2009

A new crystal structure of the rabbit muscle L-lactic dehydrogenase (PDB code 3H3F) has been determined. The independent unit of this structure contains two tetramers, each of them with a unique constitution of two active sites with the open loop conformation and two with the loops closed over the actives sites. On the basis of this structure, interactions of an inhibitor, oxamate anion, with the protein have been modeled using different hybrid schemes that involved B3LYP/6-31++G(d,p) DFT theory level in the QM layer. In ONIOM calculations, either Amber (QM:MM) or one of the three semiempirical parametrizations, AM1, PM3, and RM1 (QM:QM) was used, while in the traditional QM/MM scheme, the OPLS-AA force field was used for the outer layer. Normal modes of vibrations of oxamate in aqueous solution and in the active site of the enzyme were used to calculate binding isotope effects. On the basis of the comparison of the values obtained theoretically with those experimentally determined for the oxygen atoms of the carboxylic group of oxamate it was concluded that the DFT/OPLS-AA scheme, applied to the dimer consisting of two chains, one with the open loop and the other with the closed loop conformation, provides the best description of the active site. Calculations of the binding isotope effects of the other atoms of oxamate suggest that nitrogen isotope effect may be useful for the experimental differentiation between open and closed loop conformations. Introduction Lactic dehydrogenase (LDH) is an enzyme present in a wide variety of organisms, including plants and animals.1,2 It catalyzes the interconversion of pyruvate and lactate with concomitant interconversion of NADH and NAD+.3 The major isozyme of skeletal muscle and liver, LDH-5, has four muscle M subunits, while LDH-1 is the main isozyme for heart muscle containing four H units. Usually LDH-2 is the predominant form in the serum. The difference between isozymes such as molecular structure, specificity of tissue, affinity to substrates, and inhibitors and electrophoretic mobility are fundamental factors in using LDH as an indicator in clinical diagnostics.4-8 Disorders indicated by an elevated level of LDH in serum indicate, e.g., cancer,5,9-13 heart failure,8-10,14,15 liver damage,14,15 pneumonia,16,17 etc. Thus, details of binding of the reactant and/or inhibitor in the active site of different isoforms of this enzyme are of interest and timely. In the mid 90s, we studied the oxygen isotope effect of oxamate carboxylic oxygen atoms on its binding to lactic dehydrogenase both experimentally18 and theoretically.19 These studies showed that changes in the hydrogen bonding network between the aqueous solution and LDH enzyme active site can lead to significant binding isotope effects (BIEs). With the above-mentioned applications of LDH in diagnostics, BIEs may prove to be very useful means of determinations of the conformation and type of different LDH isozymes. We have, therefore, initiated studies to (i) evaluate which QM/MM methods are the most reliable in description of LDH-coenzyme* Corresponding author. Phone: +48 42 631-3199. E-mail: paneth@ p.lodz.pl. † Institute of Applied Radiation Chemistry, Technical University of Lodz. ‡ FQS Poland. § Institute of Technical Biochemistry, Technical University of Lodz.

inhibitor ternary complexes and (ii) to learn at which positions binding isotope effects are the most useful in identifying the conformations and isozymes. X-ray crystallography provides information about the tertiary structure of macromolecules and can create an excellent model for theoretical calculations of ligand-protein interactions. The crystal structure of the studied protein, determined with highresolution and good statistical parameters, provides a starting point for computational analysis. Herein we report a new tetrameric LDH structure that contains simultaneously two different environments with the loop open or closed over the active site. For both these structures of the active site, we have carried out theoretical calculations at different QM/MM and QM/QM levels and calculated values of BIEs. The fact that the asymmetric part of the unit cell possesses a few copies of protein molecules differing in conformation in the active sites allowed us to study the conformational changes occurring upon complex formation. Experimental Methods X-ray Details. Rabbit muscle lactic dehydrogenase was purchased from Sigma in the form of an ammonium sulfate crystalline suspension. A 0.5 mL portion (containing approximately 5 mg of protein) was dissolved in 4.5 mL of buffer containing 10 mM Hepes pH 7.5 and 150 mM NaCl. The solution was concentrated 10 times using Viva-spin concentrators with 10 kDa cutoff (Vivascience, Lincoln, U.K.). The buffer exchange was repeated 5 times to remove the ammonium sulfate. The final volume, 250 µL of the exchanged buffer, was concentrated giving 10 mg/mL of protein. Before crystallization, protein was mixed with 2 molar excess of NADH at concentration 100 mM and 5 molar excess of oxamate at 200 mM concentration and afterward was incubated for 4 h.

10.1021/jp903579x CCC: $40.75  2009 American Chemical Society Published on Web 08/28/2009

Isotope Effects on Binding Oxamate to LDH

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TABLE 1: Data Collection and Structure Refinement Statistics Data Collection radiation source X11, EMBL Hamburg wavelength (Å) 0.8162 temperature of measurements (K) 100 space group P1 cell parameters (Å and °) a ) 65.495, b ) 85.279, c ) 138.526 R ) 98.49, β ) 91.67, γ ) 111.59 resolution range (Å) 60.0-2.38(2.47-2.38)a reflections collected 234 352 unique reflections 98 703(6121) completeness (%) 89.9 (55.6) redundancy 2.4 (1.6) / 10.5 (2.0) Rintb 0.077 (0.337) Refinement number of reflections in 93 816/4887 the working/test sets c R/Rfree (%) 15.97/20.67 number of atoms 20 530/1196/352/48/92 (protein/HOH/OXM/NAI/ACT) bond lengths (Å) bond angles (°) (Å2)

rms Deviations from Ideal 0.019 2.09 20.5

Residues in Ramachandran Plot (%) most favored regions 89.1 allowed regions 10.9 PDB code 3H3F

Figure 1. Tetramer ABCD from crystal structure of rabit muscle LDH (half of independent unit) with oxamate and cofactor bonded in all four active sites.

a Values in parentheses correspond to the last resolution shell. Rint ) Ph Pj|Ihj)|/Ph Pj Ihj, where Ihj is the intensity of observation j of reflection h. c R ) Ph||Fo|)|Fc||/Ph|Fo| for all reflections, where Fo and Fc are observed and calculated structure factors, respectively. Rfree is calculated analogously for the test reflections, randomly selected, and excluded from the refinement. b

The investigated protein is a large molecule, and the obtained crystals crystallized in the form of thin plates that require a strong beam to produce high-quality data. To obtain the complexes of LDH with an oxamate inhibitor, we used the cocrystallization in hanging drop method. The crystals have a tendency to grow in clusters, so to prevent cluster formation we used seeding. All crystallization experiments were performed at 21 °C. The initial crystals were obtained from Hampton Research Crystal Screens I, II and PEG/Ion Screen (Aliso Viejo, CA, USA). After optimization of the crystallization conditions, the crystals used for diffraction experiments were grown from 16% PEG 8K, 100 mM Tris buffer pH 7.5, and 100 mM sodium acetate. Single crystals of the complex in the form of thin plates at dimensions 0.1 × 0.2 × 0.03 mm appeared in approximately 10 days. A mixture of the well solution with 50% v/v PEG 400 in the ratio 1:1 was used as a cryoprotectant during the diffraction experiment. X-ray diffraction experiments were performed at 100 K using the X11 EMBL beamlines of the DESY synchrotron (Hamburg, Germany). Diffraction data were indexed, integrated, and scaled using Denzo and Scalepack from the HKL2000 program package.20 Table 1 shows the data collection and processing statistics. The structure of the complex was solved by molecular replacement. An initial molecular-replacement solution was obtained using the LDH-human complex (PDB code 1i10) as the search model in MolRep.21 Manual model rebuilding was subsequently performed using Coot.22 Refmac523 was used for structure refinement with TLS.24 Water molecules were introduced manually using Coot. Rfree25 was monitored using a randomly chosen subset of reflections comprising 5% of the unique data set. Side chains of a number of residues were

Figure 2. Superposition of two monomers with the loop open (A shown in blue) and closed (B shown in cyan).

modeled in two conformations. The quality of the final structure was assessed using PROCHECK.26 The final refinement statistics are shown in Table 1. All crystallographic calculations were performed using the CCP4 suite of programs.27 The tetramer diagrams and superposed monomers A and B with open and closed conformation in Figures 1 and 2 were prepared using Pymol.28 Rabbit muscle dehydrogenase in complex with NADH and oxamate crystallized in the form of a cluster of thin plates. The diffraction data were processed in two space groups, P1 and C2, but only the triclinic resulted in proper statistics during integration and scaling. The unit cell contains two tetramers, which is typical for mammalian dehydrogenase.29,30 Each monomer binds one NADH molecule and one oxamate ion. In each tetramer, we can distinguish two monomers (A, D and E, H) with open and two monomers (B, C and F, G) with closed conformation of the loop A97-N107, which create “lids” of the enzyme’s active sites. The resolution of diffraction data, 2.38 Å, allowed us to model all eight protein chains, each containing

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331 amino acids, in a well-defined electron density map contoured at the 1σ of 2Fo-Fc map level, except the loop regions A97-R105 in monomers with open conformation and a few site chains, which required the 0.7σ map contouring level. The short N-terminal helix created by residues L3-I8 is located on the neighboring monomer surface and has polar contacts with its amino acids. This secondary structure element is connected to the main globular part by a stretch linker H9-Q19. The central part has mixed alpha-beta architecture described as the Rossman fold and is created by two β-sheets: the six-stranded parallel one and the second containing four antiparallel chains. The β-sheets are surrounded by helixes: four are located on the eternal surface of each monomer, and five create the interface of dimers in both tetramers. Four monomers, creating tetramer, are related by two perpendicular 2-fold axes. Two tetramers belong to the asymmetric unit, and each of them can be treated as a dimer of dimers. The pair of monomers in one dimer is related by two 2-fold axes approximately parallel to the longest helixes, creating the dimer interface. The describing dimer interacts with the analogical one by the second 2-fold axis perpendicular to the first one. The second interface is created by loops region. The thermal vibration of the NADH molecule and oxamate located in the active site of monomers is much lower for monomers with closed conformation (B, C, E, F) than in monomers with open loops A97-N107 (A, D, E, H). Computational Details The X-ray structures of the LDH are used as starting points for modeling. All missing hydrogen atoms are added using the Maestro ver. 8.5 module of the Schrodinger software package.31 Additionally, His192 is protonated manually. Geometry optimization is subsequently performed using two QM/MM and QM/QM schemes to model interactions of the inhibitor in the active site of monomers of LDH. First, the molecular mechanics force field OPLS-AA 200532-34 in combination with the B3LYP35-37 DFT functional expressed in the 6-31++G(d,p) basis set, as implemented in the QSite ver. 5.0 program,38 is used. Second, ONIOM39,40 with the same DFT level in combination with either AMBER41 molecular mechanics force field or with the AM1,42-44 PM3,45,46 or RM147 semiempirical method is used. The calculations at the semiempirical level are performed by using the LocalSCF program,48,49 which provides very fast, linearly scaling algorithms specially designed for protein modeling. We have modified revision d01 of the Gaussian03 program50 to accept calculated externally LocalSCF geometries, energies, and gradients for the description of the lower layer within two-layer ONIOM calculations. The microiteration mechanism is employed to reduce the number of geometry optimization steps. Vibrational frequencies of oxamate when the ONIOM protocol is used are calculated by using field of point charges of the remaining atoms. Theoretical values of binding isotope effects (BIEs) are subsequently calculated using the Isoeff program51 from frequencies of normal modes of vibrations according to eq 1

BIE )

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KL ) KH

3nS-6

∏ i

E S S E E uiH · sinh(uiL /2) 3n -6 uiH · sinh(uiL /2)

S S uiL · sinh(uiH /2)

/∏ i

E E uiL · sinh(uiH /2) (1)

where u ) hVi/(kT); Vi are isotopic frequencies for oxamate in water, S, and in the active site of the enzyme, E; subscripts

L and H denote the light and heavy isotope, respectively; T is temperature fixed at 300 K; and h and k are Planck’s and Boltzmann’s constants, respectively. To obtain BIE values, oxamate in aqueous solution is modeled by placing the oxamate ion in the sphere of 516 water molecules. Using the HyperChem program,52 from a cubic box of 20 × 20 × 20 Å of water molecules centered at the carboxylic carbon atom of oxamate, with the minimum distance between solvent and solute of 2.3 Å, a sphere with the radius of about 15 Å is prepared. Geometry optimization of this system is subsequently performed using the same QM/MM and QM/QM schemes as in the case of the enzymatic system. Results and Discussion Analysis of the Active Site Geometry. The obtained unique structure of the rabbit muscle LDH provides a highly interesting model for comparison of interactions between the inhibitor (oxamate), the cofactor (NADH), and important amino acid residues in the open and closed loop conformations of the active site of the enzyme because both forms are present simultaneously in the single tetrameric structure. From this crystal structure, we have chosen for theoretical calculations two monomers, named Chain A and Chain B, and the dimer that contains both of these chains as representative examples. In the monomer called Chain A, the loop is open, while in Chain B, it is closed over the active site thus allowing for studies of interactions in two different active site environments. Even the system of the monomer with the cofactor and the inhibitor is, however, too large to be treated within the quantum mechanical framework. Therefore, we have treated only oxamate at the DFT level and the remaining atoms using semiempirical or force field description. We have found five amino acids, i.e., Gln99, Arg105, Arg168, His192, and Thr247, that are in the proximity of oxamate, i.e., in the 5 Å distance from oxamate in Chain B. We start the discussion with presenting the geometry of active sites in monomeric chains A and B and the energetics of interactions of these aminoacids with oxamate obtained at different theory levels. For clarity, selected atoms of the abovementioned residues as well as atoms of oxamate have been labeled consecutively, and this numbering is provided in Figure 3 (heavy atoms) and Figure 4 (hydrogen atoms). The most important hydrogen bond contacts of Gln99, Arg105, Arg168, His192, and Thr247 amino acids and NADH with oxamate within the active site are illustrated in Figure 4. Two of these amino acids, Gln99 and Arg105, reside in the mobile loop and interact directly with the inhibitor only in the closed conformation of Chain B. Gln99 forms a hydrogen bond with the nitrogen atom (N6) from oxamate, while Arg105 forms hydrogen bonds with one of the carboxylic oxygen atoms (O1) and the carbonyl oxygen (O5) of the inhibitor. Other residues that interact with the inhibitor are not part of the loop. Arg168 by forming hydrogen bonds with two carboxyl oxygen atoms (O1 and O2) orients oxamate in the proper position which is required for the substrate for accepting the proton and hydride ion from His192 and NADH, respectively. Thr247 forms the hydrogen bond with one of the carboxylic oxygen atoms (O2) of oxamate. In one case, i.e., for Chain B with RM1, the calculated active site geometry is a bit different than in the remaining cases. This difference is important because it involves the hydrogen atom from histidine (His192), the source of proton that participates in the catalytic reaction. In this case, the hydrogen atom (H3) bonded to the imidazole ring of histidine (His192) migrates to the carboxylic group of asparagine (Asp165) during optimization.

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Figure 3. Scheme of Chain A active site of LDH with numeration of proper atoms of residues and oxamate molecules used to define the size of the active site.

Figure 4. Interactions of oxamate with the active site of LDH and NADH. Selected distances [Å] for Chain A and Chain B are indicated using color scheme representing different methods of the lower level of the ONIOM calculations (green, OPLS; orange, AMBER; red, AM1; gray, PM3; purple, RM1).

Strong hydrogen bonds for both monomers are formed between carboxyl oxygen atoms (O1 and O2) from oxamate and hydrogen atoms from Arg168 (H4 and H5). In the case of H4-O1 for both monomers, the shortest hydrogen bond is obtained for the AMBER force field and the longest for RM1. In Chain A and Chain B, the shortest hydrogen bond is 1.682 and 1.765 Å, respectively, while the longest bond is 2.673 and 2.320 Å, respectively. The valence angle N4-H4-O1 changes from 117.3° for RM1 to 173.5° for OPLS in Chain A and from 138.1° for RM1 to 174.5° for PM3 in Chain B, respectively. In Chain A, the shortest hydrogen bond labeled H5-O2 is equal to 1.781 Å for PM3, and the longest is 2.127 Å for AM1. In Chain B, the corresponding values are 1.550 Å for RM1 and 2.060 Å for AM1. The angle N5-H5-O2 ranges from 116.6° for RM1 to 177.3° for PM3 in Chain A and from 151.1° for

AM1 to 178.3° for PM3 and OPLS in Chain B. The Thr247 residue does not form hydrogen bonds with oxamate; the distance between H6 and O2 significantly exceeds the sum of their van der Waals radii,53 and the O6-H6-O2 angle does not exceed 47° in both monomers. In the case of Arg105 and Gln99 amino acid residues, geometric analysis presents considerable similarity in descriptions of their interactions with the oxamate molecule in the active site of both chains. While for Chain A distances between inhibitor molecule and Arg105 and Gln99 are close to 10 Å (open loop), for Chain B distances are not only shorter (Gln99) but also within the hydrogen bond contact (Arg105). The shortest H8-N6 distance in Chain B is equal to 2.446 Å for AMBER, and the longest, obtained for OPLS, is longer by 1.197 Å. Hydrogen bonds are formed between Arg105 and oxamate

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Figure 5. Interactions of oxamate with water molecules in the active site of LDH. Distances [Å] and valence angles [°] for Chain A and Chain B are indicated using a color scheme representing different methods of the lower level of ONIOM calculations (green, OPLS; orange, AMBER; red, AM1; gray, PM3; purple, RM1).

(H1-O5 and H2-O1) in the active site with closed loop conformation in the range between 1.776 for RM1 and 2.346 Å for AMBER and between 1.690 Å for AMBER and 2.096 Å for AM1, respectively. In the case of the His192 residue and NADH cofactor which participates in the catalytic reaction in the active site, the majority of distances between the oxygen atom O5 of oxamate and hydrogen atoms from His192 and the carbon atom C of oxamate and the hydrogen atom from NADH do not exceed 4 Å. In Chain B, results obtained with the OPLS force field exhibit slightly longer distances between oxamate and either NADH or His192 than in the other used approaches. A few water molecules are observed in the vicinity of the LDH active site in the crystal structure. Upon optimization of the monomers, only one of these water molecules appears close enough to the inhibitor to create a hydrogen bond with the oxygen atom of oxamate. Distances between oxygen atom O2 and the hydrogen atom of the water molecule and angles between O2, the hydrogen atom H, and the oxygen atom of the water molecule obtained with different theory levels applied to the outer sphere are presented in Figure 5. A strong hydrogen bond is obtained only with the AMBER force field. No detectable influence of water molecules on the calculated BIEs has been observed. Energetics of the Hydrogen Bond Interactions. To assess the strength of hydrogen bonds,54 we have carried of analysis of interaction energy on all found hydrogen bonds according to eq 2

Einter ) Eoxa+residue - Eoxa - Eresidue

(2)

In this equation, Einter is the energy of interaction between oxamate and the specific residue or cofactor; Eoxa+residue is the total energy of oxamate with specific residue or cofactor; Eoxa is the energy of oxamate; and Eresidue is the energy of a specific residue or cofactor. Results are illustrated in Figure 6. Interaction energies are computed in the gas phase from geometries obtained in QM/MM calculation. As can be seen in both LDH monomer models, His192 and Arg168 fragments are responsible for the largest contributions to the stabilization of oxamate in the active site because of the formation of hydrogen bonding between carboxyl oxygen atoms of inhibitor and Arg168 and the carbonyl oxygen atom of the inhibitor and His192. Negligible stabilization is observed for Thr247 and Gln99 for which obtained values are almost 10fold lower.

The contribution from Arg105 is different for Chain A and B due to its localization in the mobile loop, while the presence of NADH in the active site leads to destabilization of the enzyme-inhibitor complex. The significantly different interaction energy observed in the results obtained from calculations for Chain B using RM1 parametrization comes from the previously mentioned fact of the proton transfer to Asp165 during optimization. One of the goals of our calculations is to identify the best method for accounting for the interactions in the active site of the enzyme. We have, therefore, compared optimized structures with the crystallographic image of the active site. Two criteria are used. First, the size of the crystallographic active site is compared with the size of the active site obtained from calculations. We have defined the size of the active site using five distances between selected atoms (C1 to C5) of amino acid residues and the cofactor. The scheme of the active site with designated atoms is presented in Figure 3. Table 2 presents deviations of calculated distances from those observed in crystallographic data together with the mean unsigned errors (MUE) for used methods. Second, we have compared hydrogen bond contacts available for oxamate within the active site. Analysis of the size of the active site shows that the biggest deviation from the crystallographic data is observed for the longest distances between residues in the active site as C1-C4 (Arg105-Thr247), C3-C6 (Arg168-Gln99), and C2-C6 (His192Gln99). In some cases, their values exceed even 6 Å. Crystallographic distances shorter than 10 Å give deviation values smaller than 1 Å in the majority of used theory levels. Obtained distances between residues or cofactor and atom of oxamate show satisfactory agreement with the crystallographic data. It is not surprising that the biggest deviation is observed for distances between oxamate and Arg105 and Gln99 in Chain A because of the open loop conformation. The lowest MUE value is obtained for AM1 (2.01 Å) and RM1 (1.92 Å) for Chain A and AM1 (0.52 Å) and OPLS-AA (0.50 Å) for Chain B. The worst result is obtained in the case of PM3 for both chains (2.53 and 0.62 Å for Chain A and Chain B, respectively). Formally, AM1 represents the lowest MUE value of 1.26 Å, while 1.58 Å obtained with PM3 is the largest. However, these MUE values are not very far apart, and in fact the performance of all tested methods is quite similar. It is thus not possible to choose the best method on the basis of geometry optimization. Binding Isotope Effects. We have calculated four BIEs values of heavy atoms of oxamate: nitrogen (N6), carbon (C), carbonyl oxygen atom (O5), and multiple isotope effect of both carboxyl oxygen atoms (O1 and O2). All calculations were done for oxamate in the active site of both Chain A and Chain B of LDH vs oxamate in the aqueous solution. The results are shown in Figure 7. Additionally, multiple BIEs of both hydrogen atoms of the amino group of oxamate have been calculated, and these results are presented in Figure 8. BIEs provide information about the changes in ligand environment, thus allowing for elucidation of details of macromolecular interactions. Consequently, calculated isotope effect values of the nitrogen atom (N6) should depend on the hydrogen bond with Gln99, those of the carbon atom (C) on interaction with the hydride from NADH, and those of the carbonyl oxygen atom (O5) on the hydrogen bonds with Arg105 and His192. Carboxyl oxygen atom (O1 and O2) BIEs, on the other hand, should reflect hydrogen bonds with Arg105, Arg168, and Thr247.

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Figure 6. Interaction energy of oxamate with specific amino acid residues and cofactor in the active site of LDH. (A) Chain A. (B) Chain B. Energies calculated at the B3LYP/6-31G++(d,p) level.

TABLE 2: Experimental Distances [Å] and Deviation of Calculated Distances [Å] from Those Observed in Crystallographic Data Chain A

Chain B

distances

Exp

AM1

PM3

RM1

OPLS-AA

AMBER

Exp

AM1

PM3

RM1

OPLS-AA

AMBER

C1-C4 C3-C6 C3-C5 C2-C4 C2-C6 N1-O5 N2-O1 N3-O5 N4-O1 N5-O2 O6-O2 C5-C N8-C6 MUE

17.51 21.10 7.24 8.98 18.10 13.32 14.59 3.76 2.79 3.45 2.53 3.12 12.87

3.09 5.56 0.58 0.03 4.55 3.39 3.87 0.84 0.13 0.47 1.20 0.28 2.10 2.01

3.48 6.69 0.78 0.00 5.89 4.44 4.59 0.59 0.00 0.64 1.63 0.91 3.28 2.53

2.96 4.89 0.48 0.14 3.72 3.92 4.07 0.77 0.48 0.50 1.17 0.39 1.45 1.92

3.94 6.01 0.85 0.01 5.11 4.51 4.82 0.37 0.04 0.49 1.27 0.58 2.76 2.37

3.75 5.20 0.80 0.51 3.90 5.06 5.09 0.18 0.10 0.58 1.77 0.56 3.25 2.37

8.74 9.95 6.61 8.61 8.47 3.13 5.34 3.07 2.87 3.25 3.29 3.35 3.40

0.03 1.16 0.81 0.04 0.99 0.07 2.25 0.05 0.16 0.27 0.43 0.32 0.21 0.52

0.08 1.30 0.90 0.18 0.45 0.31 2.59 0.25 0.05 0.46 0.32 0.76 0.41 0.62

0.12 0.99 0.93 0.45 0.52 0.35 2.61 0.16 0.28 0.64 0.48 0.35 0.11 0.61

0.11 1.41 0.52 0.10 0.57 0.09 2.49 0.14 0.04 0.38 0.19 0.27 0.24 0.50

0.29 1.53 0.54 0.22 1.23 0.00 2.65 0.30 0.10 0.51 0.20 0.13 0.02 0.59

Normal values of BIE are obtained when the interactions with the isotopic atom are weaker in the active site than in the solution, while they are inverse, smaller than unity BIEs in the opposite cases.55 Thorough analysis of the obtained results shows meaningful differences in the absolute values of BIEs and thus in the character of interactions. In the case of Chain A, which is characterized by the open loop, some contradictory results between used theory levels are observed. The BIE of the carbonyl oxygen O5 is inverse when the OPLS-AA, AM1, or RM1 theory level is used, while AMBER and PM3 give normal values. Similarly, in the case of Chain B, normal BIEs are obtained with AM1, PM3, and RM1 and inverse BIEs with AMBER and OPLS-AA. Analysis of these results is not simple. First of all, it is very difficult to find any trends in results obtained from different

approaches for open and closed loops. Second, there is no statement about which kind of interaction with Arg105 or with His192 is more important for BIE values of O5. The lack of this information makes it impossible to draw conclusions about the influence of the protonation state of the nitrogen atom of His192 on BIEs. Similar values for the protonated and deprotonated forms indicate that the other hydrogen atom attached to the nitrogen atom in the imidazole ring can play the same role as the proton in the protonated histidine. Nevertheless, differences between the smallest and largest values of BIE for O5 are equal to 0.0074 and 0.0088 for Chain A and Chain B, respectively. These values are comparable with errors and thus cannot be used as a mechanistic tool. Similar conclusions can be drawn from inspection of BIEs of nitrogen atom labeled N6 and carbon atom labeled C; differences of N6 are equal to

Figure 7. Binding isotope effect values of heavy atoms of oxamate. (A) Chain A. (B) Chain B.

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Figure 8. Binding isotope effect values of hydrogen atoms of the amino group of oxamate.

0.0059 and 0.0039 for Chain A and Chain B, respectively, and 0.0047 for C. An advantageous case provide BIEs of carboxyl oxygen atoms of oxamate O1 and O2. First, differences of the smallest and largest values of 0.0139 for Chain A and 0.0182 for Chain B are well above the experimental uncertainty. Furthermore, the experimental value of singly labeled oxamate has been determined as 0.9840 ( 0.0027.18 Applying the rule of geometric mean56 this value corresponds to a BIE of about 0.968 if both oxygen atoms are simultaneously substituted isotopically. Comparison of the experimental result with those obtained computationally shows that the best, although still not perfect, agreement is obtained for the OPLS-AA force field for which the calculated BIE value is equal to 0.9877 and 0.9816 for Chain A and Chain B, respectively. As can be seen also from hydrogen, H1 and H2 BIEs should provide a good criterion for the selection of the appropriate theory level because of the significant differences between values obtained with use of different methods. Unfortunately, these isotope effects are not easily amenable to experimental scrutiny due to isotopic exchange with solvent. DFT/OPLS Calculations of the Dimer. Following the suggestion obtained in MD calculations57 that to include all nonbonded interactions a model that contains only a single chain is not sufficient and at least a part of the other chain should be included in calculations, we have decided to test if simultaneous inclusion of both monomeric chains improves the agreement between theoretical and experimental values of carboxylic oxygen atom BIE. As discussed in the previous section, only results obtained with the OPLS force field are in reasonable agreement with the experimentally available value of this BIE, and thus only the DFT/OPLS theory level is considered here. The O1 and O2 oxygen atom BIE values for the dimer that contains chains A and B are noticeably different from those obtained with single chains as can be seen from the comparison presented by the third group of values in Figure 9. Carboxylic oxygen atom BIEs deserve special attention, as they exhibit the largest differences between results obtained for the dimer and monomeric chains. For the dimer, its value is more inverse by 0.0110 for Chain A, while in Chain B, this difference is equal to 0.0043. These results show that the presence of both chains significantly influences interactions in active sites of LDH, especially in the case of the chain with open loop conformation. Similar values obtained for both active sites within the dimer exclude the possibility of using this BIE to identify the position of the loop. They are, however, closer to the experimental result as compared with either monomer

Figure 9. Binding isotope effect values of heavy atoms of oxamate in dimer and monomeric chains.

Chain A or Chain B. This suggests that results of other BIEs obtained for the dimer model are more reliable. BIEs of carbonyl oxygen atom (O5), carbonyl atom (C4), and the nitrogen atom (N6) are also more inverse for the dimer than in the case of monomers. Carbonyl oxygen atom BIEs are very close for both active sites, 0.9911 and 0.9920 for open and close loop conformation, respectively. Also, the difference between carbonyl carbon BIEs in the active sites of the dimer is within the same range, and thus it is also not useful for loop conformation analysis. In this respect, much more promising is the nitrogen BIE. Its values for two active sites are 1.0020 and 0.9969 for open and closed conformation, respectively. Both nearly 0.5% difference, well above the experimental error, and difference in the direction (positive for open and inverse for closed conformation) of this BIE render it as the best candidate for the detection of the LDH active site conformation. These studies are underway now in our laboratory. Conclusions On the basis of the new crystal structure of the lactic dehydrogenase tetramer with a unique constitution of two active sites with the open loop conformation and two with the loop closed over the actives sites, we have modeled interactions of an inhibitor of this enzyme, oxamate anion, using different QM/ MM schemes. All schemes involved the B3LYP/6-31++G(d,p) DFT theory level in the QM layer that contained the oxamate. In ONIOM calculations, either Amber or one of the three semiempirical parametrizations, AM1, PM3, and RM1, while in the traditional QM/MM scheme OPLS-AA force field were used for the MM layer. Normal modes of vibrations in aqueous solution and in the active site of the enzyme were used to calculate binding isotope effects. By the comparison with the value obtained experimentally for the oxygen atoms of the carboxylic group of oxamate, we show that the DFT/OPLSAA scheme, applied to the dimer consisting of two chains, one with the open loop and the other with the closed loop conformation, provides the best description of the active site. Our finding that an MM method may perform better that a QM one (in particular, semiempirical) in hybrid calculations supports similar recent findings by Roitberg and co-workers.58 Calculations of the binding isotope effects of the other atoms of oxamate suggest that the nitrogen isotope effect may be useful for the experimental differentiation between open and closed loop conformations. Acknowledgment. This work was supported by the grant NN204/1579/33 from the Ministry of Science and Higher

Isotope Effects on Binding Oxamate to LDH Education, Poland. Access to national computation facilities at Cyfronet, Cracow, PSSC, Poznan, and ICM, Warsaw, is acknowledged. Supporting Information Available: Main geometric features of the active site with open and closed loop active (Table S1), interaction energies (Table S2), and binding isotope effects (Table S3) calculated at different QM/MM levels of theory. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Prahoveanu, E.; Bronitki, A.; Barbu, C. ReV. Roum. Virol. 1973, 10, 217–226. (2) Nagler, R. M.; Lischinsky, S.; Diamond, E.; Klein, I.; Reznick, A. J. Lab. Clin. Med. 2001, 137, 363–369. (3) Robergs, R. A.; Ghiasvand, F.; Parker, D. Am. J. Physiol.: Regul. Integ. Comp. Physiol. 2004, 287, 502–516. (4) Drent, M.; Cobben, N. A. M.; Henderson, R. F.; Wouters, E. F. M.; Dieijen-Visser, M. Eur. Respir. J. 1996, 9, 1736–1742. (5) Langvad, E. Eur. J. Cancer 1968, 4, 107–115. (6) Lossos, I. S.; Breuer, R.; Intrator, O.; Sonenblick, M. Chest 1997, 111, 648–651. (7) Stangg, B. H.; Whyley, G. A. Clin. Chim. Acta 1968, 22, 521– 530. (8) Wro´blewski, F.; Gregory, K. F.; Ann, N. Y. Acad. Sci. 1961, 94, 912–932. (9) Jothy, S.; Slezak, B.; Harlozinska, A.; Lapinska, J.; Adamiak, J.; Rabczynski, J. Tumor Biol. 1996, 17, 58–64. (10) Sliber, D.; Checinska, E.; Rabczynski, J.; Kochman, M. J. Cancer 1975, 16, 675–681. (11) Kawamoto, M. Cancer 1994, 73, 1836–1841. (12) Carda-Abella, P.; Perez-Cuadrado, S.; Lara-Bauque, S.; Gil-Grande, L.; Nunez-Puertas, A. Cancer 1982, 49, 80–83. (13) Rotenberg, Z.; Weinberger, I.; Sagle, A.; Fuchs, J.; Davidson, E.; Sperling, O.; Agmon, J. Clin. Chem. 1988, 34, 668–670. (14) Lossos, I. S.; Breuer, R.; Intrator, O.; Sonenblick, M. Chest 1997, 111, 648–651. (15) Pandian, S. S.; McClinton, S.; Bisset, D.; Ewen, S. W. B. Br. J. Urol. 1997, 80, 670–671. (16) Quist, J.; Hill, A. R. Chest 1995, 108, 415–418. (17) Garay, S. M.; Greene, J. Chest 1989, 95, 769–772. (18) Gawlita, E.; Paneth, P.; Anderson, V. E. Biochemistry 1995, 34, 6050–6058. (19) Gawlita, E.; Anderson, V. E.; Paneth, P. Eur. Biophys. J. 1994, 23, 353–360. (20) Otwinowski, Z.; Minor, W. Methods Enzymol. 1997, 276, 307– 326. (21) Vagin, A. A.; Teplyakov, A. J. Appl. Crystallogr. 1997, 30, 1022– 1025. (22) Emsley, P.; Cowtan, K. Acta Crystallogr. D 2004, 60, 2126–2132. (23) Murshudov, G. N.; Vagin, A.; Dodson, E. Acta Crystallogr. D 1997, 53, 240–255. (24) Winn, M. D.; Isupov, M. N.; Murshudov, G. N. Acta Crystallogr. D 2001, 57, 122–133. (25) Brunger, A. T. Nature 1992, 355, 472–474. (26) Laskowski, R. A.; MacArthur, M. W.; Moss, D. S.; Thornton, J. M. J. Appl. Crystallogr. 1993, 26, 283–291. (27) Potterton, E.; Briggs, P.; Turkenburg, M.; Dodson, E. Acta Crystallogr. D 2003, 59, 1131–1137. (28) DeLano, W. L. The PyMOL Molecular Graphics System; DeLano Scientific: San Carlos, CA, 2002.

J. Phys. Chem. B, Vol. 113, No. 38, 2009 12789 (29) Dunn, C. R.; Wilks, H. M.; Halsall, D. J.; Atkinson, T.; Clarke, A. R.; Muirhead, H.; Holbrook, J. J. Philos. Trans. R. Soc. London, Ser. B 1991, 332, 177–184. (30) Read, J. A.; Winter, V. J.; Eszes, C. M.; Sessions, R. B.; Brady, R. L. Proteins 2001, 43, 175–185. (31) Maestro, version 8.5; Schro¨dinger, LLC: New York, NY, 2007. (32) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225–11236. (33) Jorgensen, W. L.; McDonald, N. A. THEOCHEM 1998, 424, 145– 155. (34) Jorgensen, W. L. BOSS, Version 4.3; Yale University: New Haven, CT, 2001. (35) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (36) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785–789. (37) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200–206. (38) QSite, version 5.0, Schro¨dinger, LLC: New York, NY, 2007. (39) Maseras, F.; Morokuma, K. J. Comput. Chem. 1995, 16, 1170– 1179. (40) Vreven, T.; Morokuma, K. J. Comput. Chem. 2000, 21, 1419–1432. (41) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M., Jr.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179–1597. (42) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902–3909. (43) Dewar, M. J. S.; Jie, C. J. Mol. Struct. (Theochem.) 1989, 187, 1–13. (44) Dewar, M. J. S.; Yuan, Y. C. Inorg. Chem. 1990, 29, 3881–3890. (45) Stewart, J. J. P. J. Comput. Chem., 1989, 10, 209–220; 221-264. (46) Stewart, J. J. P. J. Comput.-Aided Mol. Des. 1990, 4, 1–105. (47) Rocha, G. B.; Freire, R. O.; Simas, A. M.; Stewart, J. J. P. J. Comput. Chem., 2006, 27, 1101–1111. (48) Anikin, N. A.; Anisimov, V. M.; Bugaenko, V. L.; Bobrikov, V. V.; Andreyev, A. M. J. Chem. Phys. 2004, 12, 1266–1270. (49) Bugaenko, V. L.; Bobrikov V. V.; Andreyev A. M.; Anikin, N. A.; Anisimov, V. M. LocalSCF2; Fujitsu Limited: Tokyo, Japan, 2008. (50) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchain, H.P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J., Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (51) Anisimov, V.; Paneth, P. J. Math. Chem. 1999, 26, 75–86. (52) HyperChem, Release 7.0; Hypercube, Inc.: Gainesville, FL, 2001. (53) Bondi, A. J. J. Phys. Chem. 1964, 68, 441–451. (54) Sobczyk, L.; Grabowski, S. J.; Krygowski, T. M. Chem. ReV. 2005, 105, 3513–3560. (55) Schramm, V. L. Curr. Opin. Chem. Biol. 2007, 11, 529–536. (56) Bigeleisen, J. J. Chem. Phys. 1995, 23, 2264–2267. (57) Schmidt, R. K.; Gready, J. E. J. Mol. Model. 1999, 5, 153–168. (58) Seabra, G. M.; Walker, R. C.; Roitberg, A. E. J. Phys. Chem. A 2009, ASAP.

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