Semiempirical calculations of the hydrolysis of penicillin G

THEO CHEM ELSEVIER

Journal of Molecular Structure (Theochem) 390 (1997) 255-263

Semiempirical calculations of the hydrolysis of penicillin G J. Fraua, J. Donosoa, F. Mufiozay*, F. Garcia Blancob aDepartament de Qui’mica, Universitat de les Illes Balears. E-07071 Palma de Mallorca, Spain ‘Departamento de Quimica-Fisica. Facultad de Farmacia, Instituto Pluridisciplinar UCM, Universidad Complutense, E-28040 Madrid, Spain

Received 26 September 199.5;accepted 13 November 1995

Abstract A theoretical study of the gas-phase alkaline hydrolysis of penicillin G on the assumption of a BACZmechanism is reported. Various semiempirical methods were used to determine the influence of different parameterizations on the process. Among the most salient results obtained, the standard AM1 method predicted opening of the thiazolidine ring to yield the corresponding imine and enamine structures. Keywords:

Penicillin G; Hydrolysis:

/3-Lactam antibiotics;

Semiempirical

1. Introduction /3-Lactam

antibiotics

are among

the most

widely

used antibacterial agents on account of their broad spectrum and low toxicity. The earliest generation of these compounds was composed of penicillins. All research aimed at designing and synthesizing new /3-lactam antibiotics has so far been based on their mechanism of action. These antibiotics act by inhibiting transpeptidases and carboxypeptidases (two types of enzymes involved in bacterial wall synthesis) via acylation of a serine residue [l-6]. Tipper and Strominger [l] suggested that the antibiotic resembles the D-alanylalanine peptide fragment and the enzyme mistakes it for its substrate. Thus, the three-dimensional shape of an inhibitory molecule can be one of the important factors in determining how well it fits into the active site of each lethal target * Corresponding author. Fax: 3471-173426; e-mail: dqufmiO@ ps.uib.rs.

calculation

enzyme [7]. However, for a homogeneous set of structures, where molecular shape is invariant in the sterically important regions, chemical reactivity becomes a dominant determinant of antibacterial activity [8]. There is evidence that the enzyme acylation mechanism is similar to alkaline hydrolysis [9], so some authors have suggested that the alkaline hydrolysis constant for the fl-lactam carbonyl group may be related to antibacterial activity [ 10,111. Scheme 1 rationalizes such a hypothesis via the enzymatic and non-enzymatic hydrolysis of a penicillin. Following the pioneering theoretical studies of Boyd [12], several groups developed various theoretical approaches (basically semiempirical methods) in order to investigate the geometry and conformational equilibria [13-221, as well as the chemical reactivity [23-291, of this type of compound. In this work we carried out a comprehensive theoretical study of the alkaline hydrolysis of penicillin G by using the MIND0/3, AM1 and PM3 semiempirical calculation

0166-1280/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved PII SO166-1280(96)04781-l

J. Frau et al./Journal of Molecular Structure (Theochem) 390 (1997) 255-263

256

a) Enzimatic hydrolysis b) Alkaline hydrolysis

a)

b-En2

-$ COOH

OH-Em

b)

Tetrahedral

Int. (b)

Enamine

Imine Scheme 1.

J. Frau et al.lJournal of Molecular Structure (Theochem) 390 (1997) 255-263

methods. different process.

We also determined the effects of the substituents of the bicyclic ring on the

251

the vibration to be followed were determined, the geometry being increased by a small amount along the coordinates concerned and reoptimized by gradient minimization.

2. Method 3. Results Fig. 1 shows both the structure of the penicillin G molecule and the numbering scheme used in this paper. The geometry of penicillin G was generated from standard bond length, bond angle and dihedral angle values. The MMP2 method [30] was used in conjunction with the parameters reported by Wolfe et al. [31] for atoms S, and C5 to analyze the orientations of the side-chains, which essentially depended on the CzsN&%C5, C31C2R-C25N10 and N4C3-C14022 dihedrals. The most stable structure was subsequently optimized by using the AM1 [32], PM3 [33] and MIND0/3 [34] semiempirical methods implemented in the AMPAC package [35]. The computations were carried out on Digital VAX 8820 and VAX9000, as well as Silicon Graphics Indigo XZ 4000 computers. The reaction studied was consistent with a BACz mechanism (base-catalyzed, acyl cleavage, bimolecular) involving a hydroxyl ion as the nucleophile. All calculations performed along the reaction coordinate were derived from a single-determinantal restricted Hartree-Fock (RHF) function excluding configurational interactions. As a further control test for diradical character, single-point calculations were done with the unrestricted Hartree-Fock (UHF) formalism on selected RHF-calculated transition states, with essentially zero expectation values for the 6’) operator and enthalpies of formation essentially equal to the RHF ones being recorded in all cases. The geometries and energies of the transition states detected along the reaction coordinates were refined by minimizing the gradient norm using the Powell, NLLSQ or EF/TS algorithms. Subsequently, stationary points were characterized by FORCE frequency analysis. The matrix for the second derivative of the energy with respect to position (i.e. the Hessian matrix) had a single, negative value for all the transition states reported here. In order to exclude spurious negative eigenvalues, the atomic motions making up

Fig. 1 shows the structures of the reaction intermediates obtained with the PM3 method and Table 1 lists their most salient geometric parameters as calculated by using the different semiempirical methods tested. A comparative analysis of the most salient bond lengths for the bicyclic system with reported values (Table 1) reveals that the MIND0/3 method provided the best predictions. On the other hand, the AM1 and PM3 methods overestimated the CT-N4 bond length and slightly underestimated the S-C bond lengths (particularly that for the S ,-C2 bond). The bond angles provided by all the methods tested were quite similar. However, there were some appreciable differences in the predicted angles for the dihedrals that determine the conformations of the side-chains and thiazolidine ring. Dexter and Van der Veen [36] obtained C25NI,,-C6C5 dihedral angles of 123.0 and 169”, respectively, for aqueous procaine penicillin G (APPG) and the potassium salt of penicillin G (KPG) by using the X-ray diffraction technique; the two angles are similar to the value reported by Wolfe et al. [31], namely 165”. As can be seen in Table 1, except for PM3, all the theoretical methods tested predicted C1SNIO-C6C5 dihedral angles that were very similar to those reported by previous authors. The N4C.7-C14Q22 dihedral angle, which determines the orientation of the carboxyl group, was reported to be 15.7 and 40” for APPG and KPG, respectively [36], similar to the value reported by Wolfe et al. [31] and to those provided by the theoretical methods used here. Based on the AM1 and PM3 predictions, the 6/3aminoacyl side-chain adopts a compact conformation where the benzene ring lies at the top, close to the thiazolidine ring. The prevalence of this conformation is favored by the formation of various hydrogen bonds, namely H2h-S1 and Hq, Hz9 and H7,, (hydrogens bonded to Czs) with O?, in the AM1 method. and

J. Frau er al.IJournal of Molecular Structure (Theochem) 390 (1997) 255-263

258

a

C

Fig. 1. Reactants,

products and reaction intermediates

b

d provided by the PM3 method, and numeration

of the bicyclic system

J. Frau et al.lJournal of Molecular Structure (Theochem) 390 (1997) 255-263

e

Fig. 1. Continued.

259

J. Frau et al./Journal of Molecular Structure (Theochem) 390 (1997) 255-263

260

Table 1 Main geometric parameters of penicillin Ga,b b

a

C

d

e

f

g

1.356 2.994 2.909 1.819 1.878 121.6 117.0 96.6 10.8 149.6 -103.3 24.9 19.5 75.8 144.4

1.341 3.029 3.239 1.820 1.875 122.0 118.1 96.6 10.0 149.4 -178.2 -52.1 19.8 82.5 150.8

1.329 2.909 1.611 1.822 1.851 117.5 116.1 96.6 16.3 143.3 -151.3 -2.2 23.6 68.9 149.3

h

MIND013 042-G G-N4

1.396(1.389c/1.38d)

N4-H43 src2 SI-C5 N4GG GW7 CS~ICZ N~CS-SICZ C~SNIO-GG H43042-C708 H4304zrC7N4 N4G-W7 N4C3-C14022 C~~C~E-CZ~NIO

1.844 (1.833c/1.847d) 1.775 (1.79871.818d) 88.4 (87.3c/88.3d) 86.5 (84.4?84.1d) 99.7 (91.8c/95.2d) 22.1 (35.5 ‘/O.l d) 156.9 (123.0c/169d) -1.0 (13.1”/5.4d) 42.4 (15.7140d) 141.4 (-95.6c/5d)

1.388 1.553 2.949 1.828 1.812 91.6 89.4 97.7 20.6 154.8 -15.6 117.8 1.5 65.4 149.2

1.352 1.977 3.073 1.823 1.844 99.6 97.9 96.1 20.9 163.1 -17.8 103.0 2.6 67.1 149.7

1.337 3.011 3.946 1.819 1.881 122.4 117.3 96.5 10.4 152.2 -3.3 120.6 18.1 82.6 146.2

1.424 1.583 2.986 1.818 1.797 110.8 88.0 94.4 -7.0 -167.1 -24.5 107.4 4.6 -156.2 -76.2

1.393 1.916 3.043 1.815 1.817 98.5 94.6 93.9 -7.3 -178.0 -28.9 92.9 8.0 -153.4 -78.3

1.364 2.669 3.628 1.811 1.875’ 113.0 109.0 92.9 0.5 116.4 -11.7 102.6 22.5 -126.3 91.1

1.394 1.624 3.037 1.870 1.830 92.0 90.7 94.4 -3.7 164.9 -5.6 122.0 3.3 -175.7 -101.5

1.363 2.147 3.089 1.864 1.851 102.1 11.4 94.0 -4.8 174.7 -23.5 92.1 -5.2 -170.0 59.4

1.362 3.108 4.410 1.865 1.891 115.9 108.8 92.9 -9.9 111.8 -5.5 116.6 -70.3 -170.3 169.7

1.241 3.143 1.024 1.820 1.813 122.6 119.0 101.8 7.6 125.6 _ 28.9 53.3 151.5

AMI 04z-c7 C7-N4

1.447

N4-H43 s,-c2 s,-G N4W6 GW7 CSSIC2 N4Cd,C2 G.+m-C6G H43042-C708

1.821 1.786 89.7 84.9 95.1 4.1 139.6 -

H43042-C7N4 N4GGC7 N,C3-C14022 C3,C28-C25NI0

6.2 43.0 -35.9

1.264 3.043 1.014 1.802 1.839 114.6 112.2 94.2 -10.8 99.1 55.8 -123.9 47.7

PM3 042-c7 C7-N4

1.481

N4-H43 s,-c2 s,-cs N4GC6 cScOc7 WIG?

N4C5-S&2 CzNto-C&s H43042-C70R H43042-C7N4 N4CS-CbC7 NJC3-C14022 CK2d%N,,

1.875 1.815 88.8 87.6 94.5 6.2 -75.9

4.5 39.8 -54.8

a Bond lengths in Angstroms, bond angles and dihedral angles in degrees h The hydroxyl ion is 042H43. ’ Aqueous procaine penicillin G (equatorial conformation) [36]. d Potassium penicillin G monohydrate salt (axial conformation) [36]. ’ The S ,-C5 bond length has been fixed at 1.875 A in structured.

1.381 2.929 3.189 1.868 1.893 114.8 108.0 92.7 -11.9 110.5 -75.0 49.4 -55.0 -169.9 139.3

1.337 2.921 1.767 1.866 1.870 112.7 108.9 93.3 -10.4 106.3 168.7 4.9 -54.9 -167.5 159.9

1.229 2.863 1.269 1.866 1.859 112.5 109.1 94.2 -12.7 100.1 161.6 1.0 -45.2 -164.7 146.3

1.258 2.964 1.028 1.856 1.867 111.3 113.7 93.9 -7.2 136.3 _ _ 49.0 -125.5 -101.9

J. Frau et al.iJournal of Molecular Structure (Theochem) 390 (1997) 255-263

HI8 (hydrogen of the methyl group in C,), HZ9, HjO with 0Z7 in the PM3 method. Because the MIND0/3 method takes no account of hydrogen bonding, it predicts that the extended conformation of the 6&aminoacyl side-chain is about 2 kcal mol-’ more stable than the compact conformation. The N4C5-SIC2 dihedral angle, which determines the conformation of the thiazolidine ring, ranged from 22.1” for MIND0/3 to 4-5” for the other methods. This suggests that MIND0/3 stabilizes the equatorial conformation, where the sulfur atom lies above the plane formed by the other atoms included in the thiazolidine ring, whereas the other methods stabilize a virtually axial conformation where the C2 atom is the one located above the plane formed by the other atoms. Fig. 2 shows the reaction profiles obtained by using the different semiempirical methods tested. As with other previously studied /3-lactam systems [27-291, the reaction was found to be consistent with a BACz mechanism involving the following steps: 1. nucleophilic attack of the OH- group to yield the tetrahedral intermediate (structure b); 2. opening of the @-lactam ring to yield structure d; 3. rotation of the acid group formed (structure f) and

a

Fig. 2. Reaction (

profiles provided ) MIND0/3; (.

by the semiempirical methods: - -) PM3.

.) AMl; (-

261

subsequent proton transfer to the /3-lactam nitrogen (structure h). Initially, the nucleoRhile (Od2-Hh3) lies normal to the /3-lactam ring, 3.0 A above it on the cx side of the bicyclic system, which is the more energetically favored. As in gas-phase nucleophilic attack, the OH- approach meets no energy barrier until the tetrahedral intermediate (b), which is much more stable than the reactants, is formed. The intermediate exhibits a slightly expanded CT-N4 bond length but preserves a planar four-membered ring (see Table 1). Both the 6-aminoacyl chain and the acid group at C3 in the tetrahedral intermediate were subject to a conformational analysis. According to all the methods tested, except for MIND0/3, the side-chain at Ch undergoes a conformational change since the benzene ring evolves from a coplanar orientation with respect to the bicyclic system (a compact conformation) to an extended conformation. The AM1 and PM3 methods predict a conformational change in the carboxyl group at C3 by which atom HZ4 lies in a pseudo-trans position, thereby facilitating bonding to the /3-lactam nitrogen. This orientation is preserved, with only slight variations, throughout the reaction. Because MIND0/3 cannot detect hydrogen bonding, it predicts a pseudo-cis conformation for HI4 that is about 4 kcal mol-’ more stable than the pseudo-trans conformation. The system evolves to structure d via a saddle point (c) across a low potential barrier. Structure d exhibits a virtually fully open /3-lactam ring and preserves the nucleophile proton bonded to the oxygen atom. The AM1 method does not allow this structure to be stabilized. This method predicts a charge transfer from the /3-lactam nitrogen to the sulfur atom and hence an opening of the thiazolidine ring to yield the corresponding imine and enamine (structures i and j, respectively). On the other hand, the PM3 method predicts a substantially increased length for the S,-C5 bond, which, however, is not broken. As stated above, the last step in the process involves the transfer of Hq3 to the /3-lactam ring. This entails a prior rearrangement of the acid group by rotation about the C6-C, bond (f), which is followed by proton transfer to give the end-product (h). This product exhibits a fully open fl-lactam ring, a slightly rearranged acid group and a virtually axial

262

J. Frau et al.IJournal of Molecular Structure (Theochem) 390 (1997) 255-263

conformation for the thiazolidine ring based on its N4C5-SrC2 dihedral angle value (see Table 1). Based on the MIND0/3 calculations, the rotation and subsequent proton transfer are two distinct steps since the 042-H43 bond length is 0.977 A at the transfer energy maximum (g), after which it starts to increase. Structures d and h have similar energies. The PM3 method provides a rotation potential barrier of 3.4 kcal mol-‘. However, structure f is much more stable relative to the predictions of the other methods; the proton transfer energy barrier is also very high (18.4 kcal mol-‘) and the enthalpies for structures f and h are similar. These results can be ascribed to the formation of two hydrogen bonds (Hz4 and H43 with the /3-lactam nitrogen) that stabilize structure f. As can be seen, the semiempirical methods tested provide significantly different results. Thus, MIND0/3 cannot detect hydrogen bonding, which hinders realization of the last step; it also results in much less marked stabilization of the tetrahedral intermediate and the reaction end-product. On the other hand, AM1 does not allow structure d to be stabilized, so it predicts an end-product with an open thiazolidine ring. The PM3 method is free from this shortcoming, but overstabilizes structure f. A comparison of the results reported for the penicillin bicyclic system [28] with those obtained in this work reveals that the latter are slightly overestimated as regards product stabilization and slightly underestimated in relation to activation energy barriers. This is consistent with the experimental results; in fact, according to Page [37], the secondorder rate constant for the hydroxyl ion-catalyzed hydrolysis of penicillin G is larger than that for the bicyclic system. However, the difference in chemical reactivity between the two types of compounds does not account for the dramatic difference in their antibacterial activity. This suggests that the primary role of the side-chain is of a structural nature (it helps the antibiotic to bind to the target). A comparison of the results obtained with different &lactam systems [12,26-291 shows that the presence of the acid group and the ring fused to the /3-lactam ring (the thiazolidine ring in penicillins and the dihydrothiazine ring in cephalosporins) cause these compounds to have some peculiar properties. A comparison of the reaction pathway for the

hydrolysis of the azetidin-Zone ring [27] with that deduced in this work reveals considerable differences. Thus, the tetrahedral intermediate is much more stable and the energy barrier for its evolution lower, which show penicillins to be more reactive. As regards cephalosporins, the release of the group at position 3’ has a marked stabilizing effect [29]. On the other hand, the sulfur atom in the thiazolidine ring allows the negative charge of the /3-lactam nitrogen in structure d to be delocalized to some extent, thereby increasing the SIC5 bond length. This prevents AM1 from stabilizing such a structure and leads to end-products with an open thiazolidine ring (i and j), which in turn is consistent with the experimentally observed epimerization at C5 above pH 8 [38]. The results obtained by our group in a recent comparative study on the reactivity of penicillins and clavulanic acid (a /3-lactam antibiotic with an 0 atom at position 1) showed the hydrolysis products having an open ring fused to the P-lactam cycle were more stable than those from penicillins [39]. This confirms the significance of the presence of the heteroatom at position 1 on the chemical reactivity of this type of compound.

Acknowledgements The authors are grateful to the Spanish DGICYT for financial support awarded for the realization of this research in the framework of the Project PB93-0422. Credit is also due to Dr L. Montero for kindly providing the program for MMP2 calculations. Time allocation for calculations was generously provided by the Centre de Calcul de la Universitat de les Illes Balears.

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