A study of the nucleophilic attack of the beta-lactamic bond of antibiotics in water solution

A study of the nucleophilic attack of the beta-lactamic bond of antibiotics in water solution

L. Bounaim ^a,b , N.J. Smeyers ^a , R.H. Gonzalez-Jonte ^a , J.R. Alvarez-Idaboy ^a,c , A. Ezzamarty ^b , Y.G. Smeyers ^a, *

a

Instituto de Estructura de la Materia, CSIC, Serrano, 123, 28006 Madrid, Spain

b

Faculte des Sciences, Universite Hassan II, Ain Chock, Casablanca, Morocco

c

Facultad de QuIÂmicas, Universidad de la Habana, Havana, Cuba

Abstract

The nucleophilic attack of a series of 19 b-lactamic antibiotics (13 penicillins and six cephalosporins), as well as that of the clavulanic acid (CLA), by a hydroxylic anion, is considered in water solution and in gas phase. It is found that the tetrahedral intermediate formation does not occur spontaneously anymore in water solution, but the reaction has to overpass an energy barrier due to the desolvation of the reactants. The desolvation energy barriers, as well as the tetrahedral complex formation energy in water solution are calculated into the PM3 semi-empirical approach and the supermolecule model. In the same way, the energy barriers for the b-lactamic bond breaking and the ®nal product formation energies are determined. The results are compared with those obtained previously for the same molecules in the gas phase.

The energy barrier heights as well as the formation energies found in water solution for the tetrahedral intermediates are seen to exhibit similar behavior in the gas phase and in water solution, except in the case of CLA. This feature could perhaps explain the different behavior of CLA with respect to the d-alanyl-d-alanine-transferase and some b-lactamases. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: Antibiotics; b-Lactamic chemistry; PM3 calculations

1. Introduction

In previous papers, the nucleophilic attack of some penicillins by a hydroxylic anion was considered in gas phase. This reaction takes place essentially in two steps. In the ®rst step, the hydroxylic anion is added to the carbonyl carbon atom of the b-lactamic bond to form the so-called tetrahedral complex. In the gas phase, this reaction occurs spontaneously without any energy barrier. In the second step, the b-lactamic bond is broken to form the ®nal product. This second

reaction needs to overcome a certain energy barrier depending on the enzyme active site. Some corre- lation, however, between the formation energy of the tetrahedral complex and the biological activity was detected [1,2].

This description is not very realistic, the antibiotic in physiologic medium is seen to be in water solution.

Solvent molecules are known to be able to alter potential barriers and even chemical reactions, par- ticularly those involving charged species. Up to now, the solvent effect studies existing in the literature for the alkaline hydrolysis of b-lactamic bond were limited to a single b-lactamic ring (azetidine-2-one ring). During the reaction a signi®cant energy barrier

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* Corresponding author. Fax: 1349-1-585-5413.

E-mail address: smeyers@iem.cfmac.csic.es (Y.G. Smeyers).

due to the hydroxylic anion and b-lactamic moiety desolvation was encountered [3±6].

The purpose of this paper is twofold. The ®rst consists in determining the desolvation barrier height, and the energy formation of the tetrahedral complex in water solution. The second is to determine, always in water solution, the barrier heights for the b-lacta- mic bond breaking and the formation energies of the

®nal products. A series of 19 b-lactamic antibiotics, i.e. 13 penicillins, six cephalosporins, and clavulanic acid (CLA), will be considered. In the same way, any possible correlation between the antibiotic activity and the desolvation or bond breaking barrier heights will be studied. In the same way, the tetrahedral complex and ®nal product formation energies will also be considered.

In the following, the critical points of the reaction path for the tetrahedral complex and ®nal product formation in water solution will be determined, and the results compared with those obtained previously in the gas phase.

2. Historical background

Long time ago Woodward pointed out that the amidic resonance of a b-lactamic peptidic bond would be signi®cantly weakened due to ring constraints [7]. Later, Herman, using a very simple model for cephalosporins (D

-cefem, D

-cefem and cefam), and elementary EHT and CNDO/2 calcu- lations, showed that the structural changes that weaken the b-lactamic bond increase the antibiotic activity [8]. Simultaneously, Boyd compared the EHT the b-lactamic bond orders of various cephalos- porins (Fig. 1), and remarked that the weaker the bond order, the stronger the antibiotic activity in cephalos- porins [9]. On the other hand, Topp and Christensen [10] using a better model, in which the amine group (in position 6 or 7 for penicillins or cephalosporins,

respectively) is taken into account, studied the sulfhydryl anion addition on the carbonyl carbon atom by means of the CNDO/2 approach. These authors related the formation energy of the adducts of different models for penicillins and cephalos- porins with their biological activities. They found that cephalosporins were theoretically more active than penicillins.

In 1975, Boyd et al., using the same adduct model, although with the hydroxylic anion, studied the CNDO/2 approach, the addition reaction assuming a reaction path in which the hydroxylic anion approaches, vertically with respect to the b-lactamic ring, the carbonylic carbon atom from below or from above (a or b faces). They found that the formation energy of the adduct decreases as the anion approaches the carbon atom without any energy barrier, to reach a minimum at 1.50 AÊ. Furthermore, since the CNDO/2 method does not allow to optimize the molecular geometry, they assumed the formation of a second structure, in which the carbonyl carbon atom adopted a tetrahedral structure, which was still more stable [11].

In order to establish the reactivity of a series of cephalosporins, Boyd de®ned a reactivity index called transition energy:

DE _IT ˆ E _IT 2 E _b-Lactam 2 E _OH

…1†

where E

, E

and E

are the formation energy of the tetrahedral complex of b-lactam and the

Fig. 1. Boyd's model for describing penicillins (R ˆ ±CH

) and

cephalosporins (R ˆ ±CHyCH

). Fig. 3. Model for mimicking penicillins and cephalosporins.

Fig. 2. Cephalosporin model for the addition of the hydroxylic

moiety.

Fig. 4. (a) Penicillins; (b) cephalosporins; and (c) clavulanic acid.

Fig. 4. (continued)

hydroxylic anion, respectively. These authors concluded that the more negative the reactivity index, the weaker the b-lactamic bond.

In the same way, Boyd studied three N-substituted monocyclic b-lactamic models using the MINDO/3 approach in order to determine their conformational preference [12].

The second and third structures were supposed to mimic penicillin (R ˆ ±CH

) and cephalosporin (R ˆ ±CHyCH

), while the ®rst one is called the reference structure. These authors found, in all the three cases, that the substituting group was in the b- lactamic ring plane. Later, Boyd et al., using a more satisfactory model for describing cephalosporins (Fig. 2) with different substituting groups in position 3, again studied the addition reaction of the hydro- xylic ion using the CNDO/2 approach [13].

These authors found a parabolic relationship between reactivity index (1) and the antibiotic activity, and this result was interpreted in the follow- ing way: although the b-lactamic bond needs to be weakened to be reactive, it should not be weakened

too much as to be broken through other mechanisms, in particular by the b-lactamases.

Finally, Smeyers et al. [2] considered the nucleophilic attack of the b-lactamic bond by a hydroxylic anion using the MNDO-PM3 method, which allows a full optimization of the molecular geometry. With this aim, these authors adopted the Boyd model for penicil- lins and cephalosporins, but taking into account the exis- tence of the amidic group in position 3, (see Fig. 3). They found that the penicillin, and especially cephalosporin, are more sensitive to the b-lactamic bond breaking than the ªreferenceº model for two reasons: a lower forma- tion energy for the tetrahedral complexes, and a lower formation energy for the reaction products.

Recently Frau et al. [3] showed that the attack of N-methylazetidine-2-one by a hydroxylic anion in water solution does not occur spontaneously without an activation energy to yield the tetrahedral inter- mediate, because of the desolvation of the reactants.

This feature was observed in the continuum model and in the supermolecule model at the semi-empirical level, and later at the ab initio level using the

Table 1

Energy barriers and formation energies ( D E

) of the tetrahedral complex (IT) (in kcal/mol) in water solution and in the gas phase, R being the initial reactants

Molecules, b-lactams Barriers Formation energies ( D E

)

R ! IT R Ã IT In water In gas phase

PK 10.43 229.59 219.16 29.65

PF 10.48 230.41 219.93 210.31

PG 10.75 226.34 215.58 218.33

PAM 9.68 228.73 219.06 212.76

PAMCl 9.78 229.27 219.48 214.34

PAMOH 9.73 228.73 219.00 213.49

PV 10.30 232.39 221.64 215.91

PFE 12.12 230.43 218.31 214.42

PP 9.56 226.29 216.73 213.70

PON 15.13 234.12 218.98 218.63

PClM 13.52 232.93 219.38 218.99

PDN 13.96 233.18 219.22 219.38

PFL 12.47 233.14 220.67 219.63

CEF 11.19 227.53 216.33 216.95

CED 11.02 226.52 215.49 214.60

CEX 13.20 235.74 222.54 222.09

CEM 9.49 232.93 223.45 223.02

CEZ 9.93 227.02 217.09 216.95

CET 8.95 227.26 218.31 217.50

CLA 14.01 228.41 214.39 21.89

self-consistent reaction ®eld model (SCRF) [4,5].

Such a barrier rises up to 20.7, 17.5 and 13.6 kcal/

mol into the PM3-SM3 continuum model, the super- molecule approach (with 20 water molecules) and the ab initio calculations (6-31 1 G

1 SCRF), respec- tively [4,5]. These values agree satisfactorily with the experimental data of 16.1 kcal/mol given for this compound [17].

In the same way, J. Pitarch et al., reported calcu- lations for the neutral and alkaline hydrolyses performed in aqueous solution on N-methylazeti- dione, as a model for b-lactamic antibiotics, at the ab initio levels, using a polarizable continuum model, [18], considering in addition one water molecule, [19], combining molecular mechanics and molecular dynamics, [20,21]. These authors reported a relative low desolvation barrier (5 kcal/mol).

3. Calculations

In this paper, the supermolecule model is adopted by explicitly considering three water molecules associated to the free electron pairs of the b-lactamic moiety and the nucleophilic agent, here the hydro- xylic anion, involved in the reaction. Furthermore, the b-lactamic molecule was considered in its neutral form in order to avoid the possible migration of water molecules on the carboxilate moiety.

When the tetrahedral complex was formed, the b-lactamic bond was broken by arti®cially enlarging the b-lactamic bond.

The semi-empirical MNDO/PM3 method at RHF level was used with full optimization of the geometry for the addition reaction calculations [14]. For the bond breaking reaction the same semi-empirical

Fig. 5. (a) The PAM transition state; (b) the PAM tetrahedral complex; and (c) the PAM ®nal product found in the nucleophilic attack by a

hydroxylic anion in the presence of three water molecules.

procedure was used, but at UHF level, in order to obtain the proper open shell fragments.

The following critical points of the reaction were considered:

1. The formation energy corresponding to the initial products separated by a 5 AÊ distance, in the presence of three water molecules.

2. The desolvation transition state in the presence of three water molecules.

3. The formation energy of the tetrahedral complex corresponding to the energy minimum of the reac- tion path, always with three water molecules ( D E

).

4. The energy barrier found by enlarging the b-lac- tamic bond ( D E

).

5. The formation energy of the ®nal product ( D E

).

In order to determine the energy minima the BFGS optimization procedure (option: analytic gradient precise), completed by an extrapolation procedure EF (option: eigenvalues following), was used to reach a mean gradient lower than 0.01 kcal/

mol AÊ or degree. Several minima were sometimes found depending of the choice of the starting coor- dinates. In these cases, the lowest energy structure was selected.

To determine the transition states, an extension of the iterative procedure LST (linear synchronous transit) was used for the addition reaction [15]. In this procedure, an approximate transition state is

Fig. 5. (continued)

®rst determined on a restricted hypersurface limited to the coordinates that are more involved in the reaction.

With this aim the option TS was used. In a second stage, the usual minimization procedure was applied on all the remaining coordinates. The procedure is repeated up to convergence. Here also various differ- ent structures were sometimes found. As in the mini- mization procedure only the lowest transition state was retained. These transition states were character- ized by calculating the Hessian matrix eigenvalues, which furnished only one negative root.

This procedure, however, does not work for the bond breaking step carried out into the UHF scheme.

In this case, a numerical procedure was resorted to by calculating the formation energy for small interatomic increments of the b-lactamic bond.

In this paper, four groups of penicillins were

considered (see Fig. 4). (a) The precursors: F and K penicillins (PF and PK); (b) penicillins of clinical use: G penicillin (PG), ampicillin (PAM), p-chloro- ampicillin (PAMCl) and amoxicilline (PAMOH);

(c) resistant penicillins to chloric acid (aryloxialkyl- penicillins): V penicillin (PV), feneticillin (PFE) and propicillin (PP); and (d) resistant penicillins to b-lactamases of Class A: oxacillin (PON), chloxa- cillin (PClM), ¯uochloxacille (PFL) and dichloxacilin (PDN).

In the same way, three sets of cephalosporins were considered (Fig. 4b): (a) two of the ®rst generation:

cefalotin (CEF) and cefadroxyl (CED); (b) two of the second generation: cefoxitin (CEX) and cefamandol (CEM); (c) and two of the third generation: ceftisoxim (CEZ) and cefotaxim (CET). Finally, the ®ve critical points for CLA were also determined (Fig. 4c).

Fig. 5. (continued)

4. Results

In Table 1, the energy barrier to reach the desol- vation transition state from the initial products and from the tetrahedral complex are gathered in columns 1 and 2, respectively, for all the b-lactams under study.

In Fig. 5a, the plot of the transition state, found during the nucleophilic attack of PAM by a hydro- xylic anion in the presence of three water molecules, is given as an example of the ®rst step of the reaction.

It is seen how the still partially solvated hydroxylic anion approaches the carbon atom in position 7 of the carbonylic group.

In column 3, the tetrahedral complex formation energies, relative with respect to the initial products, found in water solution are given. Finally, in column 4, the same tetrahedral complex formation energies obtained in the gas phase are shown [16].

In Fig. 5b, the plot of the tetrahedral complex of PAM, found in presence of three water molecules, is given as an example of the second step of the reaction.

It is seen that b-lactamic ring is not yet broken. The hydroxylic anion is now bounded to the carbonylic carbon atom, whereas the hydrogen bond between the water molecules and the amine group in position 29 stabilizes the complex.

When the desolvation barriers or the energy for- mation for the tetrahedral complex formation are examined, the same trend is seen as in the gas phase. The penicillin resistant to the b-lactamases exhibit the largest values (in absolute value).

There is, however, a signi®cant exception to this trend, the CLA shows an important desolvation barrier or formation energy, but a very small tetra- hedral complex formation in the gas phase.

In Table 2, the energy barrier to reach the bond breaking transition state from the tetrahedral complex, obtained in water solution, is shown in column 1. In column 2, the ®nal product formation energies in water solution are given. Finally, the energy barrier and energy formation calculated in the gas phase are shown in columns 3 and 4 [16].

In Fig. 5c, the plot of the ®nal product found in the attack of PAM by a hydroxylic anion in the presence of three water molecules, is given as the last example.

It is seen that the b-lactamic ring is now broken, whereas a hydrogen bond is established between the hydroxylic moiety and the nitrogen atom in position 4 (before belonging to the ring). This hydrogen atom could migrate to form eventually an amide. The three water molecules and the amine group 29 still stabilize the product through hydrogen bonds.

Cephalosporins CEF and CED are seen to exhibit a very low bond breaking barrier, and very strong forma- tion energy for the ®nal product in water solution. CEM presents a low barrier, but a very weak formation energy, and CEX, CEZ and CET even present a repul- sive ®nal product formation energy with respect to the b-lactamic bond enlargement. This result suggests a different bond breaking mechanism for CEM, CEX, CEZ and CET, in which the enzyme has to play an important role. All these cephalosporins were also found to have low barriers in the gas phase, and very strong formation energy for the ®nal products.

In order to verify this last result in water solution, calculations were performed for large values of the b- lactamic bond with full optimization of the geometry, always encountering the initial tetrahedral complexes.

In this case, the b-lactamic receptor presence would

Table 2

Energy barriers and formation energies ( D E

) of the ®nal products (P) (in kcal/mol) in water solution and in the gas phase, with respect to the tetrahedral complex energies (IT)

Molecules, b-lactams In water solution In gas phase IT ! P ( D E

) IT ! P ( D E

) PK 8.83 28.79 13.23 247.23 PF 9.38 22.39 12.78 242.32 PG 7.55 27.10 14.98 259.14 PAM 7.09 210.60 11.50 233.54

PAMCl 7.63 24.30 11.27 241.91

PAMOH 7.65 24.62 11.75 239.33

PV 9.02 25.74 14.76 238.65 PFE 8.92 22.90 11.52 241.33 PP 8.10 210.52 11.84 240.24 PON 8.36 23.84 14.62 244.72 PClM 9.03 24.42 14.68 242.11 PDN 8.09 25.40 15.16 260.96 PFL 8.25 24.49 15.09 242.48 CEF 0.10 218.85 0.86 247.16 CED 1.97 217.77 2.58 235.89

CEX ± 2 1.95 243.03

CEM 3.35 21.63 1.87 242.32

CEZ ± ± 1.73 245.33

CET ± ± 1.45 240.24

CLA 4.30 211.07 7.73 252.56

probably play an important role. To solve this dif®culty, the receptor should explicitly be taken into account.

In all the calculations of the ®nal product formation energy, the hydrogen atom of the attacking hydroxylic anion is seen to point towards the now-free electronic lone pair of the nitrogen atom at a hydrogenic bond distance 2.7 AÊ, reaching the b-lactamic bond with a breaking value of 2.9 AÊ (see Fig. 5c).

5. Discussions

In this paper, the solvent effects are considered in the calculations by introducing only three water molecules located on the free electron pairs of the b-lactamic moiety and the hydroxylic anion. This approach is surely insuf®cient, but when the results are examined, a signi®cant desolvation energy barrier of 10±15 kcal/mol is found, in good agreement with experimental value of 16.1 kcal/mol obtained for N-methylazetidine-2-one [17].

This barrier is probably overestimated, since only the free electron pairs affected by the reaction are taken into account. A large number of solvation water molecules should smooth the desolvation process. Nevertheless, the results obtained here could give the trend of the barrier for the different b-lactams considered.

When the tetrahedral complex formation energy values ( D E

) obtained in water solution are exam- ined, they are seen to follow the same trend as that found in the gas phase, of about 20 kcal/mol.

In particular, penicillins resistant to Class A peni- cillinases present the largest values, as well as the cephalosporins CEX and CEM. This result is not surprising since various authors had detected a relationship between the biological activity and the tetrahedral complex formation energy [11,12].

A signi®cative exception, however, has to be mentioned. The CLA, (as well as the precursors PK and PF) presents a relatively large tetrahedral complex formation energy in water solution, and a very small one in the gas phase. On the other hand, CLA is seen to be biologically inactive as an antibiotic on d-alanyl-d-alanine-transferase, although it acts strongly on b-lactamases of Class A (TEM1 and TEM2). Perhaps this different behavior could be investigated from this point of view.

The bond breaking barrier in water solution exhibits smaller values than in the gas phase, especially in the cases of CLA and cephalosporins, the barriers of which are signi®cantly smaller. The ®nal product formation energies are much smaller than those in the gas phase. This result, however, is not very sig- ni®cant in the absence of a receptor. The total stabilization energy, however, with respect to the initial product is similar in both water solution and in the gas phase, 30±50 kcal/mol, in accordance with the value given for N-methylazetidine-2-one [6].

6. Conclusions

The main difference between the results in the gas phase and water solution is the existence of a maximum in the reaction path due to the desolvation of the reactants. The tetrahedral intermediates, however, exhibit similar stabilization energy in the gas phase and in solution with respect to the initial products, except in the case of CLA. This feature could perhaps explain the different behavior of CLA with respect to the d-alanyl-d-alanine-transferases and the b-lactamases of Class A.

Three water molecules seem to be insuf®cient to simulate the solvent effects. More calculations with more water molecules seem to be necessary.

However, the calculations presented here furnish a signi®cant desolvation energy barrier of 10±15 kcal/

mol, in good agreement with experimental value of 16.1 kcal/mol obtained for N-methylazetidine-2-one [17]. The presence of the active site of the receptor should also be considered to obtain a de®nitive answer [22].

Acknowledgements

Two of us (L.B. and Y.G.S.) wish to thank the authorities of the CSIC of Spain and those of the CNCPRST of Morocco for the economical help received. Similarly, J.R.A.-I. is grateful to the Spanish Ministry of Education and Sciences for the post-graduate grant which allowed him to

®nish this work.

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