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Dec 23, 2009 - a well-established target of drugs against gout and hyperuricemia and exists in two forms: oxidase and deshydrogenase. In some patholog...
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J. Phys. Chem. B 2010, 114, 921–928

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Theoretical Study of the Mechanism of Inhibition of Xanthine Oxydase by Flavonoids and Gallic Acid Derivatives Laure Lespade*,† and Sylvie Bercion‡ Institut des Sciences Mole´culaires, UniVersite´ de Bordeaux 1, 351 cours de la Libe´ration, 33405 Talence, France, and UMR QUALITROP 1270, Faculte´ des Sciences Exactes et Naturelles, UniVersite´ des Antilles et de la Guyane, BP 250, 97159 Pointe a` Pitre Cedex, Guadeloupe, France ReceiVed: May 5, 2009; ReVised Manuscript ReceiVed: September 23, 2009

Xanthine oxidase is a flavoprotein enzyme which catalyzes the oxidative hydroxylation of purine substrates. Because of its availability, it has become a model for structural molybdoenzymes in general. The enzyme is a well-established target of drugs against gout and hyperuricemia and exists in two forms: oxidase and deshydrogenase. In some pathologies, its level increases in oxidase form, being the source of free radicals which can cause damage to surrounding tissues. It is important to understand the mechanisms of the enzyme inhibition to help in the search of new inhibitors. The main active center is a molybdopterin buried in a cavity. Theoretical calculations can be of some help for distinguishing the important aspects in the inhibition: attraction inside the cavity and anchorage. In this paper, the molybdopterin molecule geometry has been optimized by ab initio with the DFT method and the results have been shown to be very similar to the X-ray coordinates. In order to evaluate the attraction inside the cavity, the electrostatic potential between the charged molybdopterin molecule and two series of inhibitors, some flavonoids, and some gallic acid derivatives have been calculated using the multipolar development supplied by the Gaussian package. The good concordance between the electrostatic force and IC50 indicates that the attraction is an important factor in the inhibition and must be taken into account in the designing of new drugs. I. Introduction Xanthine oxidoreductase (XOR) is a complex molybdoflavoenzyme, which is abundant in cow’s milk. It has been known for more than a century and studied in its pure form for over 60 years.1,2 XOR catalyzes the hydroxylation of hypoxanthine to xanthine and of xanthine to urate. It appears in two interconvertible forms of the same gene product:3-5 xanthine deshydrogenase (XDH), which predominates in vivo in nonpathological conditions, and xanthine oxidase (XO). These enzymes are composed of two identical subunits of approximately 145 kDa. Each subunit contains one molybdenum center, one flavin (FAD), and two nonidentical [2Fe-2S] iron-sulfur centers.6,7 The oxidative hydroxylation takes place at the molybdenum center with a concomitant reduction of NAD+ for XDH or molecular oxygen for XO at the flavin center. The reduction of molecular oxygen produces free radicals which can cause damage on tissues. Granger et al.8-10 proposed that the enzyme plays an important role in the pathogenesis of ischemia-reperfusion injury since the elevated concentration of calcium induces a conversion of XDH in XO. Concomitantly, ATP is catabolized to hypoxanthine. On reperfusion, the activation of XO generates superoxide and hydrogen peroxide. Other pathological conditions show enhanced plasma XO levels: hepatic, acute viral infection, hemorrhagic shock, thermal stress, and hypercholesterolemia.11 Even if the hypothesis of Granger is still controversial, XO is generally seen as a potentially destructive agent in the vasculature. But the system is very * To whom correspondence should be addressed. E-mail: l.lespade@ ism.u-bordeaux1.fr. † Universite´ de Bordeaux 1. ‡ Universite´ des Antilles et de la Guyane.

complex, since uric acid is also an effective scavenger of peroxynitrite.12 The most known XOR inhibitor is allopurinol (1,5-dihydro4H-pyrazolo[3,4-d]pyrimidin-4-one). It was approved by the FDA in 1966 for the treatment of gout.13 Allopurinol is a substrate for the enzyme.14 Its oxidation product, oxypurinol, is also a good inhibitor. However, allopurinol may induce hypersensivity reactions in patients with renal insufficiency and concomitant administration of thiazide diuretics.15 These undesirable effects have prompted efforts to isolate other types of XO inhibitors. In particular, ethnobotanical research has provided XO inhibitors of natural origin. This paper is devoted to the study of one of the possible mechanisms of inhibition: the attraction of the molecule inside the cavity. For that purpose, the electrostatic potential interactions of two classes of polyphenolic molecules of natural origin with the charges inside the cavity have been studied theoretically. Two main classes of molecules have been selected. Flavonoids are natural compounds present in a large variety of plants, fruits, and vegetables.16 They are known to possess diverse pharmacological activities such as antioxidative effects. Their ability to inhibit xanthine oxidase has been largely studied.17,19 The other studied class has been extracted from a Neo-Caledonian plant, Cunonia macrophylla. Among the gallic acid derivatives extracted from the plant, three of them have been tested in vitro toward xanthine oxidase: gallic acid, ellagic acid, and ellagic acid-4-O-β-D-xylopyranoside.20 The last has been shown to present the best activity toward xanthine oxidase. The relatively different structure of the two types of compounds permits a better comprehension of the mechanism. In the first part of the paper, the crystallographic data of the molybdopterin cavity will be analyzed and compared to the ab initio modeling of the molybdopterin moiety. Then the equations giving the electrostatic interactions between the

10.1021/jp9041809  2010 American Chemical Society Published on Web 12/23/2009

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Lespade and Bercion

TABLE 1: List of Some Geometric Parameters of the Different Models of Molybdpterina

ModO (apical) Mo-O (equatorial) MoS ModS PO β (CCOP) β (COPO) β (COPO) β (COPO) µx (D) µy (D) µz (D) Θxx (D Å) Θxy (D Å) Θyy (D Å) Θzz (D Å)

1FIQ

3B9J

Molybd1

Molybd2

Molybd3

Molybd4

model 1

model 2

model 3

model 4

model 5

model 6

1.96 2.51 2.19 2.51 1.94 1.52 1.30 1.45 -22 112 92 -139 -10 6 -6 -57 81 47 10

1.73 2.0 2.55 2.01 2.11 1.52 1.51 1.51 66 -179 -63 60 -11 -14 -3 -65 33 41 24

1.70 2.52 2.39 2.35 2.17 1.65 1.52 1.50

1.70 1.94 2.53 2.53 2.17 1.65 1.52 1.50

1.71 2.46 2.41 2.38 2.24 1.53 1.55 1.54

1.71 1.97 2.51 2.47 2.2 1.51 1.55 1.56

-188 -76 58 -11 0 -0 -84 37 54 30

-190 -78 56 -14 -7 0 -62 51 26 36

-184 -65 54 -16 0 0 -88 75 16 72

-186 -61 48 -12 -6 0 -57 64 -17 74

a The dipole and quadrupole moments have been calculated by DFT keeping constant all the heavy atoms and optimizing only the hydrogens. The two first columns correspond to the X-ray data of the two enzymes deposited in protein data bank. The next columns correspond to fully optimized models (except β (CCOP)) with one negative charge and water or hydroxyl group. The last ones correspond to a molybdopterin with two negative charges.

molybdopterin moiety and the inhibitor in front of the cavity will be developed. The last part will be devoted to the results and discussion. II. Analysis of the Catalytic Center 1. Structural Description of the Molybdopterin Cavity. The crystal structure of bovine enzyme has been determined21-23 and deposited in the Protein Data Bank (codes 1FIQ and 3B9J).24 The genes of all the mammalian enzymes are highly conserved.2 The two crystallographic data confirm that the active centers are the molybdopterin moieties which have approximately the same structure, with the exception of the position of one of the sulfur bound to the molybdenum. A further study of the enzyme in complex with a slow substrate FYX-50122 has confirmed that the ModO group occupies the apical position. In the first study, the enzyme forms a complex with the salicylate inhibitor approaching the equatorial Mo-H2O oxygen atom of the molybdenum center at a distance of 3.6 Å. The distance between the molybdenum atom and the equatorial oxygen (2.51 Å, Table 1) is compatible with the existence of a water molecule bound to the molybdopterin moiety rather than a hydroxide group. On the contrary, the crystallographic data of the complex of xanthine oxidase with a slow substrate, 2-hydroxy-6-methylpurine, give a distance of 2 Å for Mo-O, which is characteristic of Mo-OH group. There are some discrepancies between the coordinates of the two molybdopterin moieties, in particular for the phosphate which is embedded in the enzyme cavity (Table 1). The dihedral angle between the phosphate group and the first ring of the molybdenum cofactor (Moco cofactor) is very different in the two studies. However, in the two cases, the distances of the PO bonds are relatively short. From the crystallographic data, it cannot be excluded that the phosphate has two negative charges. In the side chains there is only one positive residue inside the cavity, the arginine 880 in bovine xanthine deshydrogenase. This residue is scarcely visible at the main entrance of the cavity (Figure 1a) which is situated in front of the molybdenum center and for almost all the positions; its charge is hindered or canceled by the glutamates’ ones. Thus the Moco cofactor is a negatively charged molecule embedded

Figure 1. (a) Image of the molybdopterin moiety inside the cavity of bovine xanthine oxidase (PDB accession code 1FIQ). The molybdopterin is in red with the active center accessible at the bottom of a cavity approximately 15-20 Å long. The phosphate is scarcely visible on the left. (b) View of the second channel leading to the cavity. The inhibitor salycilate and the arginine 880 are indicated in yellow. At the top of the image, the molybdenum center is noticeable in yellow.

in the cavity. It creates an important electrostatic potential which can attract polar molecules inside the cavity from the main entrance.

Inhibition of Xanthine Oxydase by Flavonoids There is another channel perpendicular to the main entrance. It also leads to the interior of the cavity and has been described in ref 22. Figure 1b gives a view of the corresponding part of the enzyme. One can observe the salycilate inhibitor inside the cavity and, at the bottom, the residue arginine 880 whose positive charge attracts the anionic inhibitors. They are first attracted by two lysines (771 and 778) which are situated at the top of the slot. From outside the channel, the negative charges of the glutamates and of the molybdopterin moiety are hindered. The narrowness of this channel prevents nonplanar or wide molecules from having access to the cavity. Thus, two kinds of molecules can be attracted in the cavity. The planar and narrow anions can be attracted by the arginine residue through the perpendicular channel. Neutral molecules and substrates enter the cavity in front of the molybdenum moiety. 2. Modelization of the Molybdopterin Moiety. The aim of this paper is to calculate the electrostatic interactions between the molybdopterin moiety and two series of inhibitors situated at the main entry, where the molybdenum center is visible, in order to evaluate the dependence of the electrostatic potential with the inhibition force. For that purpose, the molybdopterin moiety has been modelized with the entire possible hypothesis. The calculations have been made keeping constant the X-ray coordinates given by the two available studies and optimizing the coordinates of the hydrogen atoms (two first columns of Table 1, respectively, for 1FIQ and 3B9J). In the first case, it has been supposed that a water molecule was coordinated to the molybdenum. In the second case, the molybdopterin moiety has been optimized with a hydroxyl group. For the other models, the whole Moco cofactor has been fully optimized with the exception of two dihedral angles of the phosphate in order to mimic the steric hindrance of the side chains. Models 3 and 4 correspond to the cases with only one negative charge on the phosphate and, respectively, the Mo-OH or Mo-OH2 groups. Models 5 and 6 possess two negative charges on the phosphate. All calculations were carried out with the density functional method of B3LYP25,26 using the Gaussian 03 package.27 The following basis sets have been used: Mo atom has been described by DGDZVP basis with an f polarization function;28 6-31+G(d,p) has been used for the others elements. The crystallographic data have been read with Hyperchem package. For all the calculated models the internal coordinates displayed in Table 1 match reasonably well with the experimental ones. The discrepancies between the different models are not sufficiently important to make a choice, in particular if one considerate that the complexation of the enzyme with substrates change the distances in the Moco cofactor.29-32 As a consequence, the electrostatic interactions between the inhibitors and the molybdopterin moiety have been calculated for the whole models. As the cavity is approximately 15 Å long, the interactions have been calculated with a distance of 20 Å between the centers of mass. III. Theoretical Analysis of Inhibition Mechanism 1. Electrostatic Forces. Long-range attractive component of the intermolecular force between two molecules or ions has three possible contributions:33 the electrostatic force arises from the interactions between the multipole components; the induction contribution comes from the distortion of the electron charge distribution induced by the other molecule; and the dispersion contribution energy is a result of the correlations between the electron density fluctuations in the two molecules. When the molecules are distanced by 20 Å, one has only to consider the first contributions. The usual perturbation treatment of intermolecular forces leads to a central-multipole representation

J. Phys. Chem. B, Vol. 114, No. 2, 2010 923 of the electrostatic energy. For a pair of molecules A and B, whose center of mass is separated by a vector R, the electrostatic energy ∆Eelec can be written:34,35

∆Eelec ) 1 (1)n ξnA ξn′B T 4πε0 n,n′ (2n - 1)!!(2n′ - 1)!! Rβγ...υR′β′γ′...υ′ Rβγ...υ R′β′γ′...υ′ (1)

∑

nA where ξRβγ...υ is an nth rank multipole tensor:

nA ξRβγ...υ )

(1)n n!

∑ eiAri2n+1 ∂r∂iR ∂r∂iβ ∂r∂iγ ... ∂r∂iυ i

() 1 ri

(2)

eAi is the charge of the ith atom of the molecule A and ri its Cartesian coordinates vector. These multipole tensors are calculated in the Gaussian package up to the quadrupole (traceless quadrupole). The tensor TRβλ...υ is a function of the geometry and in particular of the intermolecular separation vector R which links the center of mass of the two molecules:

TRβγ...υ ) ∇R∇β∇γ...∇υ |R| -1

(3)

(2n - 1)!! indicates (2n - 1)!/2n-1(n - 1)!. If one considers only the first terms of the central-multipole representation, up to quadrupole, the electrostatic energy can be simplified to

∆Eelec )

∑ ∑[

1 TqAqB + TR(qAµBR - qBµAR ) + 4πε0 Rβγδ Rβγδ 1 B A + qBΘRβ - 3µAR µβB) + T (qAΘRβ 3 Rβ 1 1 B A B ) + TRβγδΘRβ Θγδ (4) T (µBΘA - µAR Θβγ 3 Rβγ R βγ 9

]

where q, µ, and Θ are respectively the charge, dipole moment, and traceless quadrupole moments of the two A and B molecules. Figure 1a shows a frontal view of the cavity. The active center is accessible via a path which corresponds roughly to the y axis of the molydopterin moiety (Figure 2). Thus, the electrostatic energy, ∆Eelec has been computed with a distance vector R in the XY plane, with an angle of 0 to 20° with respect to the Y axis. The different terms are given in Appendix. It has also been supposed that the inhibitor can rotate around R, as can be seen in the X-ray studies. 2. Choice of the Inhibitors. To evaluate the dependence of the electrostatic intermolecular force in the inhibition force, it was important to study inhibitors with a broad range of activity. Flavonoids are molecules that have been largely studied for their numerous biochemical and physiological activities.16,36,37 Their antiradical and antioxidant as well pro-oxidant potencies have been put forward. Indeed, they are involved in reactive oxygen species (ROS) direct trapping but can also inhibit enzymes responsible for superoxide anion production, in particular xanthine oxidase.18,38 Cos et al.18 have studied the structureactivity relationship of a large series of flavonoids and evidenced the importance of hydroxyl substituents on C-5 and C-7 and their absence on C-3 (Figure 3) in the inhibition. The presence

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Figure 2. Modelization of the molybdopterin moiety keeping constant the Cartesian coordinates of the heavy atoms of the crystallographic data of bovine xanthine oxidase (PDB accession code 1FIQ, model 1).

Figure 3. Template of flavonoids.

of a hydroxyl group and its conformation can radically change the electrostatic multipoles of the molecule. In the present study, the geometry optimization and the calculations of the multipoles have been performed for eight compounds. They exhibit IC50 values ranging from 0.55 µM for luteolin to 10.1 µM for morin (Table 2). Each compound possesses at least two conformers, (eight for luteolin, Figure 4) whose energy ranges within 1 kcal/ mol. These different energies have been computed with Gaussian package27 and the same DFT method and basis as the molybdopterin moiety. The calculations of the geometry are in accordance with other publications.39,40 In particular, the dihedral angles O1C1C1′C2′ of quercetin, luteolin, and chrysin are in good agreement with the previous calculated values. From the Table 2, one can notice that the hydroxyl on position 3 stabilizes the molecule in a planar configuration except for the morin where the hydroxyl on position 2′ has strong interactions with the C ring. As B3LYP functional is lacking in any dispersion terms, the energies of the conformations have also been calculated with MP2 method and the same basis set 6-31+G(d,p). In Figure 4, the enthalpy differences for the eight most stable conformations of luteolin are indicated. The results with the two methods are not very different, indicating that the dispersion terms are not crucial in the energy of the studied flavonoids. The analysis of the different electrostatic forces (Appendix) indicates that, for a neutral molecule, the main component is the interaction between the molybdopterin charge and the longitudinal dipole moment of the inhibitor. In Table 3 the longitudinal dipole moments of all the conformations of luteolin are displayed, proving the diversity of this component with the molecular conformation. For the other molecules, only the average dipole is given. One can observe a general trend: the more powerful inhibitors possess the larger longitudinal dipole moments. The calculated longitudinal dipole moments are very similar in DFT or MP2 methods. However, they are calculated very differently with molecular mechanical methods because of the large electronic delocalization which is not taken into

Lespade and Bercion account by these methods. Thus, it is not possible to consider the whole cavity in the calculation of the electrostatic forces but rather to stress the most important features. The first term in the development of the electrostatic forces corresponds to the interactions between the charges in the bottom of the cavity and the longitudinal dipole moment of the inhibitor. It can be of the same order of magnitude as the dipole-dipole interactions of the inhibitor with residues situated at approximately 6-7 Å from the center of mass of the inhibitor, that is to say, at the entrance of the cavity which is relatively large. The residues situated at the entrance of the cavity are essentially leucins, valins, or phenylalamines, which are not particularly polar. The only polar residue is a serin with a hydroxyl group pointing outside the cavity. The electrostatic potential due to its dipole moment does not annihilate the electrostatic potential created by the charges at the bottom of the cavity when the inhibitor is in vicinity of the residue but, on the contrary, it reinforces it. Thus, it is justified to consider the effect of the molybdopterin charges to outline the characteristics of good inhibitors. The analysis of the electrostatic forces also evidence that only the neutral forms can enter into the cavity by the entrance in front of the molybdenum center, the anionic species being repulsed by the charge of the molybdopterin moiety. So, the pKa has to be taken into account in the modelization of the inhibition mechanism. This study has been completed with another class of polyphonic molecules extracted from a New Caledonian plant, Cunonia macrophylla. Among the ellagitannins extracted from the plant, three of them have been tested toward xanthine oxidase: gallic acid, ellagic acid, and ellagic acid-4-O-β-Dxylopyranoside.20 They are all planar molecules (Figure 5). Contrary to the flavonoids, these compounds have only one stable conformation at room temperature. Because of its low pKa,4 the gallic acid is principally in its anionic form.41 Ellagic acid has no dipole moment: the first two electrostatic interactions (Appendix) are zero. 3. Calculation of pKa. It is important to know the concentration of neutral forms of the inhibitors since they are the only ones susceptible to enter the enzyme cavity by the frontal channel. The pKa of ellagic acid has been experimentally measured42 and found to be 11 at 20 °C. Since xylose is not deprotonated at physiological pH, one can guess that ellagic acid-4-O-β-D-xylopyranoside also has a high pKa. Several studies have been devoted to the measurement or calculations of the pKa of polyhydroxyflavones.43-47 It has been shown that the deprotonation is dependent on the position of the single hydroxyl moiety. Hydrogen bounding of the C3-OH or C5-OH with the C4dO carbonyl group hampers deprotonation. On the contrary, the hydroxyl moiety on C4′ is more easily deprotonated if there is a hydroxyl group in position C3′ which stabilizes the anion. However, the measurement of the pKa is rather difficult since these compounds have a very limited solubility in water and the addition of organic solvent drastically changes the value of the pKa. Theoretical calculation can help in its determination. Leman´ska et al.47 have demonstrated that there was an empirical linear dependence between the calculated deprotonation energy in gas and the experimental pKa values inside a series of hydroxyflavones. The quantum mechanical procedure is as follow: all geometries are optimized with DFT (density functional theory) method by using a 6-31+G(d) basis set as implemented in Gaussian 03 computational package. Then single-point energies are evaluated with a larger basis set, 6-311+G(2d,2p). The deprotonation energy is calculated as the difference between the electronic energy of the anion minus

Inhibition of Xanthine Oxydase by Flavonoids

J. Phys. Chem. B, Vol. 114, No. 2, 2010 925

TABLE 2: Characteristics of the Inhibitorsa

luteolin apigenin chrysin kaempferol galanguin myricetin quercetin morin allopurinol

β(O1C2C1′C2′) (deg)

longitudinal dipole moment (D)

IC50 (from refs 18 and 20) (µM)

17 16.8 19.8 0 0 0 0 30

3.5 3.8 3.2 1.8 1.2 2.4 2 0.9 4

0.55 0.7 0.84 1.06 1.8 2.38 2.62 10.1 0.24

1.8 0 2.4

10 2.5 1.25

gallic acid ellagic acid ellagic acid-4-O-β-D-xylopyranoside

pKa (expt)

pKa (estd) 7

8.5 8.4 8.2 6.8

(ref (ref (ref (ref

47) 47) 47) 47)

7.5 7

7 (ref 47) 7.5 4 (ref 41) 11 (ref 51)

a

The dihedral angles and the longitudinal dipole moment correspond to averages on all the possible conformations. The IC50 of the gallic acid derivatives have been scaled to the value of quercetin indicated in ref 18.

Figure 4. Some conformations of luteolin. The enthalpy difference with the most stable conformation is indicated when calculated with DFT method. In parentheses are given the corresponding values calculated with MP2 (see text).

TABLE 3: Dihedral Angle between the B and C Rings of Luteolin and Dipole Moment Components for All the Most Stable Conformationsa

luteolin 1 luteolin 2 luteolin 3 luteolin 4 luteolin 5 luteolin 6 luteolin 7 luteolin 8

β(O1C2C1′C2′) (deg)

longitudinal dipole moment (D)

lateral dipole moment (D)

respective concn

19.5 161.5 18.8 161.3 16.5 162.2 18.9 163.0

7.3 5.9 4.3 4.7 1.9 0.9 4.8 3.7

2 -7 5.8 -2.4 4.6 -2.3 0.8 -5.5

0.049 (0.073) 0.048 (0.057) 0.07 (0.086) 0.071 (0.091) 0.288 (0.245) 0.244 (0.181) 0.112 (0.132) 0.116 (0.134)

a The concentration of each conformation is indicated in the last column when calculated with DFT method and in parentheses for the MP2 value (see text).

the electronic energy of the molecule. In the present study, all the studied flavonoids have pKa values around 7 and 8.5. To give more precision on the dependency between the deprotonation energy and the pKa, two hydroxyflavones with pKa of 10 and 11.5, respectively, have been included in the calculations. The result is given in Figure 6. One can see that, when the deprotonation energy is between 331 and 334 kcal/mol, the pKa is around 8; that is to say, that more than the two-third of the

Figure 5. The most stable conformation of ellagitanins.

molecules are in neutral form at physiological pH (7.5). The corresponding compounds (apigenin, chrysin, and kaempferol) have at most one hydroxyl group on the B ring. Morin and gualanguin possess deprotonation energy of 229 kcal/mol. Their pKa can be evaluated at 7.5. All the other compounds exhibit deprotonation energies less than 225 kcal/mol: their pKa can be evaluated around 7. IV. Results The electrostatic energy (eq 4) has been calculated for all the conformations of all the studied inhibitors. The concentrations ci of the different forms have been estimated at room temperature with Boltzmann law with the enthalpy calculated by MP2 method. The interaction between the inhibitor and the molybdopterin is

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Uelec ) c′

∑ ci∆Eielec

Lespade and Bercion

(5)

i

where c′ is the concentration in neutral form at the physiological pH of 7.5. The interaction has been calculated for the different models of molybdopterin. Indeed, as displayed in Table 1, the multipoles depend on the geometry of the model. The greatest discrepancies concern the µy dipole moment component. It is strongly dependent on the geometry of the phosphate, which has been found different in the two sets of studied crystallographic data. However, the electrostatic results are comparable for the whole models. The greatest discrepancy is found between the models with one or two negative charges on the phosphate. This is due to the fact that the main contribution in the electrostatic potential comes from the first component (E1 in the appendix) which does not depend on the dipole and quadrupole moments of the molybdopterin moiety. This component has a maximum value when the dipole moment of the inhibitor lies along R. Figures 7 and 8 display the results for models 1 and 5. In the two cases one can observe a good correspondence between the magnitude of the electrostatic potential and the inhibition force IC50. There is only one aberration for luteolin. For this compound, the electrostatic potential is calculated of the same magnitude as for apigenin but its low calculated pKa drastically lessens the average of the potential. Thus, the mechanism of inhibition for flavonoids molecules is largely dependent on the attraction of the molecule at the main entry of the cavity. The polar molecule firmly stays in front of the molybdopterin moiety because of the electrostatic interactions and prevents xanthine from attaining the catalytic site. The position inside the cavity does not seem important. One can observe the same phenomenon for the gallic acid derivatives. Gallic acid is a bad inhibitor because it is principally in anionic form. It enters the cavity by the second channel like salycilate. Inside the cavity, its position is destabilized by the repulsive forces from molybdopterin moiety and glutamates. Ellagic acid is a symmetric molecule with no dipole moment. However, it possesses a high quadrupole moment which maximizes the second electrostatic potential E22. The calculations give electrostatic potentials of the same order of magnitude as the quercetin ones for all the models, which is consistent

Figure 7. Calculated electrostatic interaction potential (in mdyn Å) as a function of log(IC50). It has been calculated for all the possible configurations with a distance vector R between the molybdopterin (model 1) and the inhibitor lying in the x,y plane (see Figure 2) and making an angle of 0-20° with the y axis. The distance between the two centers of masses is 20 Å, and the inhibitor has the possibility to rotate freely around its longitudinal axis. Its longitudinal axis is along the y axis of the molybdopterin moiety. (a) Flavonoids with allopurinol as in ref 18. (b) Ellagitannins with quercetin as in ref 20.

with the inhibition forces. The dipole moment of ellagic acid4-O-β-D-xylopyranoside enhances the electrostatic interaction potential. V. Conclusion

Figure 6. Plot of experimental pKa values for some hydroxyflavones (3-OH, 5-OH, apigenin, chrysin, kaempferol, quercetin, galanguin) against the calculated deprotonation energy DE.

This paper has pointed out that there are two kinds of inhibition of the enzyme. If the inhibitor is in anionic form, it enters the cavity by a narrow channel and anchors near the arginine 880 which is situated at approximately 10 Å from the catalytic center. The inhibitor must be sufficiently long as TEI672048 to block the main entry of the cavity and narrow to access the cavity. The inhibition by neutral molecules has been more thoroughly studied. The calculations of the electrostatic interaction potential between the molybdopterin active center and two series of

Inhibition of Xanthine Oxydase by Flavonoids

Figure 8. Calculated electrostatic interaction potential (in mdyn Å) as a function of log(IC50). It has been calculated for all the possible configurations with a distance vector R between the molybdopterin (model 5) and the inhibitor lying in the x,y plane (see Figure 2) and making an angle of 0-20° with the y axis. The distance between the two centers of masses is 20 Å, and the inhibitor has the possibility to rotate freely around its longitudinal axis. Its longitudinal axis is along the y axis of the molybdopterin moiety. (a) Flavonoids with allopurinol as in ref 18. (b) Ellagitannins with quercetin as in ref 20.

inhibitors at the entering of the main cavity have been shown to be nicely correlated with the force of inhibition except for one compound: luteolin. To be an inhibitor, a molecule has to enter the cavity and then firmly stay inside. In this calculation, the residues around the active center generally can be neglected because the main potential is induced by the charge of the molybdopterin moiety. The only polar residue situated at the entrance is a serin which locally reinforces the attraction potential. As a result, the most potent inhibitors in these classes of polyphenolic compounds, flavonoids and gallic acid derivatives, are the molecules which have the largest longitudinal dipole moments and a pKa above 8 (except for luteolin). Effectively, the analysis of Table 2 clearly indicates that the good inhibitors have an important longitudinal dipole moment. However, molecules with no or weak longitudinal dipole moments like ellagic acid and galanguin can inhibit the enzyme if they have a sufficiently important quadrupole moment. So, the main conclusion of this paper is that the inhibition potency

J. Phys. Chem. B, Vol. 114, No. 2, 2010 927 of neutral molecules is correlated to the attraction of the molecule at the main entrance of the cavity. The inhibitor blocks the approach of substrates toward the metal complex but its position inside the cavity does not seem so important. When the molecule is buried in the bottom of the cavity, the present calculations are no more valid; other interactions become important as the dispersive and induction forces. And other amino acids whose charge is not visible at the entry of the cavity may induce important interactions in the vicinity of the molybdenum center. As a consequence, it is not evident that the most potent inhibitors correspond to the most stable complexes with the amino acids of the cavity. The bad correlation between the electrostatic force and the inhibition potency of luteolin may result from a bad calculation of the pKa and the resulting bad estimation of the dissociation constant. One can notice that the pKa is a property of the molecule in aqueous solution: calculations of the isolated molecule are too crude to lead to a good precision. The simulation of the aqueous solution with the PCM method27 does not improve the dispersion of the curve. Good calculations of pKa must explicitly involve water molecules and employ larger basis sets.49 Such calculations are time consuming for molecules of the size of luteolin and beyond the scope of this study. Another explanation would be to suppose that the anionic form of luteolin can enter the cavity by the other channel. The anionic form of luteolin is planar. The good correlation between the inhibition potency and the electrostatic forces indicates that this is not the case for the other flavonoids with a low pKa, that is to say myricetin, galanguin, and quercetin. All these compounds possess a hydroxyl group on the position 3 which increases the width of the molecule. In a recent study,50 four naturally occurring compounds luteolin, quercetin, and two other somewhat larger molecules, silibinin and curcumin, have been measured for their in vitro potency of inhibition. It has been found that silibinin inhibits XO but less than the two flavonoids, luteolin and quercetin. This molecule has an important longitudinal dipole moment but its nonplanar structure prevents it from going inside the cavity. Curcumin is not an inhibitor certainly because its most stable conformation is the most symmetric one and has only lateral dipole moment. In conclusion, this study has shown that two properties are important in the design of new inhibitors of medium size derived from flavonoids: the molecule must be polar, with a longitudinal dipole moment, and must be weakly dissociated at physiological pH. Acknowledgment. The calculations have been made with an SGI computer and a cluster IBM P5-575 purchased with the funds of the Re´gion Aquitaine, France. Appendix Interaction between the molybdopterin moiety (M) and the inhibitor (I) when the distance vector R is lying in the (x,y) plane. The first component is proportional to 1/R2 and is the major contribution at the distance R ) 20 Å. It is maximum when the dipole moment of the inhibitor is parallel to R. However, the second contributions (E12 and E22) have to be taken into account in molecule with low or zero longitudinal dipole moment.

E1 ) -

qM (µI R + µIy Ry) 3 x x 4πε0R

928

J. Phys. Chem. B, Vol. 114, No. 2, 2010

E21 )

1 I M I M µIx µM x + µy µy + µz µz 4πε0R3

[

3

E22 )

E3 )

(

Lespade and Bercion

2 I M I M I M R2x µIx µM x + Ry µyµy + RxRy(µx µy + µx µy )

R2

[ (

R2x ΘIxx + R2y ΘIyy + 2RxRyΘIxy 1 M 3q 12πε0R3 R2

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]

)]

Rx3 1 M I 3Rx - 5 2 (µxI Θxx - µxMΘxx )+ 5 4πε0R R

3Ry - 5

Ry3 R2

]

M I (µyI Θyy - µyMΘyy ) +

1 M I [2(µxI Θxy - µxMΘxy )+ 4πε0R5

M I M I - µyMΘxx ) + (µyI Θzz - µyMΘzz )]Ry + (µyI Θxx 1 M I M I [2(µyI Θxy - µyMΘxy ) + (µxI Θxx - µxMΘxx )+ 4πε0R5 5 M I M I (µxI Θzz - µxMΘzz )]Rx [2(µxI Θxy - µxMΘxy )+ 4πε0R5 M I - µyMΘxx )] (µyI Θxx

RyRx2 R2

-

5 M I [2(µyI Θxy - µyMΘxy )+ 4πε0R5 M I - µxMΘyy )] (µxI Θyy

RxRy2 R2

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