Prediction of Hydrolysis Pathways and Kinetics for Antibiotics under

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Prediction of Hydrolysis Pathways and Kinetics for Antibiotics under Environmental pH Conditions: A Quantum Chemical Study on Cephradine Haiqin Zhang, Hongbin Xie, Jingwen Chen,* and Shushen Zhang Key Laboratory of Industrial Ecology and Environmental Engineering (MOE), School of Environmental Science and Technology, Dalian University of Technology, Dalian 116024, China S Supporting Information *

ABSTRACT: Understanding hydrolysis pathways and kinetics of many antibiotics that have multiple hydrolyzable functional groups is important for their fate assessment. However, experimental determination of hydrolysis encounters difficulties due to time and cost restraint. We employed the density functional theory and transition state theory to predict the hydrolysis pathways and kinetics of cephradine, a model of cephalosporin with two hydrolyzable groups, two ionization states, two isomers and two nucleophilic attack directions. Results showed that the hydrolysis of cephradine at pH = 8.0 proceeds via opening of the β-lactam ring followed by intramolecular amidation. The predicted rate constants at different pH conditions are of the same order of magnitude as the experimental values, and the predicted products are confirmed by experiment. This study identified a catalytic role of the carboxyl group in the hydrolysis, and implies that the carboxyl group also plays a catalytic role in the hydrolysis of other cephalosporin and penicillin antibiotics. This is a first attempt to quantum chemically predict hydrolysis of an antibiotic with complex pathways, and indicates that to predict hydrolysis products under the environmental pH conditions, the variation of the rate constants for different pathways with pH should be evaluated.

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INTRODUCTION Antibiotics have been frequently detected in rivers, lakes, regional discharges and coastal waters.1 The presence of antibiotics in the aquatic environment attracts extensive concern, as antibiotics can induce bacterial resistance even at environmental concentrations.2 The molecular structures of many antibiotics contain hydrolyzable functional groups (e.g., ester, amide, imide, and halogen), rendering antibiotics susceptible to hydrolytic degradation.3 Hydrolysis of some antibiotics may lead to formation of metabolites with higher environmental persistence and some antimicrobial properties.4 Thus, it is of great importance to investigate the hydrolysis kinetics and products of antibiotics for their ecological risk assessment. According to the limited experimental data,5 hydrolysis halflives (t1/2) for organic chemicals can vary from seconds to years. Experimental determination of the hydrolysis kinetics is generally supposed to be time-consuming if the hydrolysis rates are very slow. Amide and ester moieties are known as the functional groups for many drug molecules.6 These hydrolyzable functional groups also appear frequently in many classes of antibiotic molecules (e.g., penicillins, cephalosporins, macrolides, and lincosamides). Thus, the experimental determination alone cannot meet the need of ecological risk © XXXX American Chemical Society

assessment of so many antibiotics as well as other hydrolyzable organic pollutants. Although linear free-energy relationships (LFERs) can be employed to estimate hydrolysis rate constants (kH),5,7 the construction of LFER models relies on experimental databases, and the utility of LFERs is limited by their applicability domains.8,9 Moreover, most LFER models can hardly provide information on reaction pathways. As far as we know, there are no available LFER models that can predict kH of antibiotics. In contrast to LFERs, a combined use of the density functional theory (DFT) and transition state theory may predict kH and hydrolysis pathways. For example, DFT was successfully employed to predict kH of chlorambucil and hexamethylphosphoramide.10,11 However, to the best of our knowledge, few studies employed DFT to predict hydrolysis of antibiotics, especially antibiotics with multiple hydrolyzable functional groups. It became the purpose of this study to test the feasibility of using DFT to predict hydrolysis pathways and kinetics of antibiotics. Cephradine (velosef), a cephalosporin antibiotic Received: November 4, 2014 Revised: January 7, 2015 Accepted: January 15, 2015

A

DOI: 10.1021/es505383b Environ. Sci. Technol. XXXX, XXX, XXX−XXX

Article

Environmental Science & Technology

activation (ΔG‡) to distinguish favorable/unfavorable hydrolysis pathways and to predict the kH values. Then the predicted rate constants were compared with experimental results.

with two hydrolyzable functional groups was selected as a case for the study. The cephalosporin antibiotic has two amide groups (the C8N5 lactam and the C14N13 amide) and an αamino group in the side chain (Figure 1). Cephalosporin

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MATERIALS AND METHODS Computational Details. All the DFT calculations were performed with the Gaussian09 software package.16 All geometries of reactants, transition states (TSs), intermediates, and products were calculated at the B3LYP/6-311++G(d,p) level. To evaluate the effects of functionals and basis sets on the results, different basis sets [6-311++G(d,p), 6-311++G(2d,2p), 6-311++G(2d,2pd), 6-311++G(2df,2pd), 6-311++G(3df,2pd), 6-311++G(3df,3pd)] and functionals [M062X and B3LYP-D3, where “D3” means dispersion correction introduced by Grimme et al.17] were selected to calculate the important species in the rate-determining step of the most likely pathways. The B3LYP and M062X hybrid functionals have been successfully used to predict kH of hexamethylphosphoramide and chlorambucil, respectively.10,11 The integral equation formalism of the polarized continuum model (IEFPCM) based on the self-consistent-reaction-field method was employed to mimic the water solvent effect.18 As definition of solute cavity is an important factor in determining the accuracy of the IEFPCM, we evaluated three different atomic

Figure 1. Molecular structure of cephradine (molecular weight = 349.4) and its hydrolyzable functional groups.

antibiotics (e.g., cephradine, cephalexin, and cephaloglycin) have been frequently detected in environmental waters, with concentrations up to μg·L−1.1,12−15 We calculated the Gibbs free energies of reaction (ΔG) and the Gibbs free energies of

Figure 2. Potential hydrolysis pathways and the corresponding Gibbs free energies (ΔG, kJ/mol) for hydrolysis of cephradine (The pathways marked with green are thermodynamically favorable, and those with red are unfavorable.). B


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9.0). NaN3 (200 mg·L−1) was employed as a biocide to inhibit biodegradation of the target compound. The reaction vessels were triangular bottles wrapped with aluminum foil to prevent photodegradation. To facilitate comparison of the experimental kH with the predicted values, the experimental temperature was kept at 298.15 ± 1 K by using a water bath. Periodically throughout the experiment, 1 mL of the reaction mixture was withdrawn for quantification purpose. A Hitachi HPLC equipped with an Agilent Eclipse XDB−C18 column (4.6 × 150 mm2, 5 μm) was employed for the analysis. The mobile phase consisted of 30% methanol and 70% sodium acetate (0.02 M), running at a flow rate of 0.8 mL·min −1. The injection volume was 20 μL. First-order reaction kinetics was employed to calculate the hydrolysis rate constants.

radii for defining the solute cavity, which is detailed in the Supporting Information (SI). TSs were verified by both intrinsic reaction coordinate (IRC)19 and frequency (i.e., only one imaginary frequency) calculation. To facilitate comparison of the calculated kH with the experimental values, the calculated standard state ΔG and ΔG‡ values (at 298.15 K) were corrected from 1 atm to 1 mol·L−1, by adding 7.9 kJ·mol −1 for the reaction A → B + C, and reducing 7.9 kJ·mol −1 for the reaction A + B → C and left unchanged for the reaction A → B.20 As cephradine has two ionizable sites (pKa1 = 2.6 ± 0.1 for the carboxyl, pKa2 = 7.3 ± 0.1 for the α-amino),21 it exists in two ionic forms at the environmental pH range (6.0−8.5): zwitterion (AH±) and anion (A−). As a result, cephradine has five possible hydrolysis pathways (Figure 2): hydrolysis of the C8N5 lactam of AH± or A−, hydrolysis of the C14N13 amide of AH± or A−, as well as intramolecular nucleophilic attack of the α-amino group toward β-lactam of A−, i.e., intramolecular aminolysis.22 By taking into account the acid-catalyzed, neutral and basecatalyzed reactions, we can express kH at a given pH as kH = kH+·[H+] + kN + kOH‑·[OH−],5 where kH+ (L·mol−1·s−1) is the second-order rate constant for the acid-catalyzed hydrolysis of AH±; kN (s−1) is the sum of the first-order rate constants for the water assisted hydrolysis of AH± and A−, and intramolecular aminolysis of A−; kOH‑ (L·mol−1·s−1) is the second-order rate constant for the base-catalyzed hydrolysis of AH± and A−. Yamana and Tsuji observed that cephradine is fairly acid stable at pH < 5,22 which was also confirmed by our preliminary experiments (SI Figure S3). Schwarzenbach et al. also noted that for all the hydrolyzable compounds, reactions with OH− (base catalysis) is important even at conditions of pH < 7, and acid catalysis is relevant only for compounds showing rather slow hydrolysis kinetics.5 Thus, it is reasonable to assume that kH+ ≈ 0 for cephradine, and the kH expression can be simplified to kH = kN + kOH‑·[OH−]. ΔG values for all the possible hydrolysis pathways were calculated from the free energy differences between the products and reactants, and employed to distinguish thermodynamically favorable/unfavorable pathways. For the thermodynamically favorable pathways, the ΔG‡ values were calculated to distinguish kinetically favorable/unfavorable pathways. Nucleophilic attack of H2O, OH−, or −NH2 on the reaction sites can take place from either the exo α side (where the lone pair of electrons on the β-lactam nitrogen is located) or from the endo β side.21 Therefore, the different directions of nucleophilic attack were considered in the calculation (Figure 1). The rate constants for the attack from the preferential directions were calculated by applying the pseudo steady state approximation (detailed in the SI). Experimental Methods. Cephradine (purity ≥99%) was purchased from Zhejiang Anglikang Pharmaceutical Co., Ltd. Methanol, acetic acid, phosphate, boric acid, sodium hydroxide, sodium chloride, and hydrochloric acid were purchased from Tianjin Kemiou Chemical Reagent Company. All the other chemicals are of analytical or HPLC grade of purity. Ultrapure water (18 MΩ) was obtained with an OKP ultrapure water system of Shanghai Lakecore. Hydrolysis of cephradine was measured in buffer solutions with a constant ionic strength (0.06 mol·L−1) adjusted by sodium chloride. The buffers used were acetic acid/acetate (pH 5.0), phosphate (pH 6.3, 7.0, 8.0), and boric acid/borate (pH

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RESULTS AND DISCUSSION Thermodynamics. As intramolecular hydrogen bonds can be formed between the H atom of the α-amino group and the O atom in the amide, cephradine (A− and AH±) can isomerize between cis- (Ac− and AHc±) and trans-configurations (At− and AHt±). If the energy difference is sufficiently large, then the less stable isomer can isomerize to the more stable isomer.22 We calculated the ΔG values for the isomerism (SI Figure S4). On the basis of the ΔG values, the equilibrium constants (K) for the interconversion were calculated. According to the calculated K values, At− is more stable than Ac−, with At− accounting for 99.98% of the anions (A−). While for the zwitterions (AH±), AHc± (>99.99%) is more stable. Thus, At− and AHc± were selected for the further calculations. The calculated ΔG values for all the hydrolysis pathways are shown in Figure 2. On the basis of the ΔG values, we identified the thermodynamically favorable pathways that are marked with green in Figure 2. Hydrolysis of the C8N5 lactam. We identified two nucleophilic attack processes from either the α or β side. One is a direct hydrolysis process, in which H and −OH of H2O are concertedly added to the N5 and C8 sites, respectively. The other is an indirect hydrolysis process, in which −OH of H2O is added to the C8 site, while H of H2O first transfers to the O12 position of the carboxyl group and then further transfers to the N5 site. As can be seen from Figure 3(a,b), for both At− and AHc±, the overall ΔG‡ values for the α side attack are lower than those for the β side attack. Thus, the attack of H2O on the C8N5 lactam occurs preferentially from the α side. More importantly, the overall ΔG‡ values in the direct hydrolysis processes of At− and AHc± are much higher than those in the corresponding indirect hydrolysis processes for the nucleophilic attack from either the α or β side, indicating that the indirect hydrolysis process is more favorable. Thus, the carboxyl group can accelerate water assisted hydrolysis of cephradine. According to Pliego Jr.,23,24 explicit water molecules may have impacts on the DFT calculated ΔG‡. We further considered the effects of explicit water molecules on the catalytic role of the carboxyl group. The results show that the involvement of explicit water molecules does not have a great impact on the process (as detailed in the SI). To the best of our knowledge, this is the first time that the role of the carboxyl group in the hydrolysis of cephradine is pointed out. As all the cephalosporins and penicillins have a common parent structure, it can be inferred that the carboxyl group also plays a catalytic role in the hydrolysis of other cephalosporin and penicillin antibiotics. The base-catalyzed hydrolysis also involves the direct and indirect processes. For both the direct and indirect processes, C


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Figure 3. Schematic free energy surfaces for the nucleophilic attack of OH−/H2O to At−/AHc± species calculated at the B3LYP/6-311++G(d,p) level (The total energy of the reactants is set as zero. The symbols RCs, IMs and TSs stand for reactant complexes, intermediates and transition states, respectively. The corresponding geometric structures are shown in SI Figures S5−S14).

OH− attacks on the C8 site in the initial step. Subsequently, H of OH− transfers directly to the N5 site in the direct process; while in the indirect process, H first transfers to the carboxyl group and then further to the N5 site. According to Figure 3(c,d), the addition of OH− to the C8 site is a rate-determining step, and the overall ΔG‡ values for OH− attack from the α side are lower than those from the β side. This indicates that OH− also prefers to attack the C8N5 bond from the α side. In addition, the ΔG‡ values of the direct processes are slightly higher than those of the indirect processes, demonstrating that the carboxyl group also participates in the base-catalyzed hydrolysis processes. Intramolecular Aminolysis. Our calculation showed that the intramolecular aminolysis is initiated by the attack of −NH2 on the C8 site, and can occur from either the α or β side. The schematic free energy surfaces and geometries for the intermediates and transition states are presented in SI Figures S15−S17. The overall ΔG‡ value for the intramolecular aminolysis from the β side (127.8 kJ/mol) is lower than that from the α side (219.4 kJ/mol). Llinás et al. investigated intramolecular aminolysis of cephaloglycin by a semiempirical AM1 method, and also found that the intramolecular aminolysis from the β side is more favorable than from the α side.21 However, the overall ΔG‡ value for intramolecular aminolysis is slightly higher than that of the indirect hydrolysis processes, although some previous studies purposely investigated the intramolecular aminolysis of cephaloglycin.21 Hydrolysis of the C14N13 Amide Bond. As shown in Figure 2, water assisted hydrolysis of the C14N13 amide bond is thermodynamically unfeasible (ΔG > 0). Therefore, only the base-catalyzed hydrolysis of the C14N13 amide bond was considered. The attack of OH− on the C14 site can also occur

from either the α or β side. According to Smith,25 the basecatalyzed hydrolysis of the amide bond follows a BAC2 mechanism. The schematic free energy surfaces and geometries for the intermediates and transition states involved in the BAC2 mechanism are presented in SI Figures S19−S21. The overall ΔG‡ value for the α side attack (136.5 kJ/mol) is lower than that for the β side (152.4 kJ/mol). More importantly, the overall ΔG‡ value for the base-catalyzed hydrolysis of the C14 N13 amide bond is much higher than that for the base-catalyzed hydrolysis of the C8N5 lactam bond (70.7 kJ/mol), revealing that the base-catalyzed hydrolysis most likely occurs via OH− attacks on the C8N5 lactam bond. Thus, in the subsequent rate constants calculation, we did not consider the hydrolysis of the C14N13 amide bond. Prediction of kH at Different pH Values. On the basis of the identified pathways, the different rate constants for OH−/ H2O attack on the At−/AHc± species from the α side and -NH2 attack on At− from the β side were calculated (SI Table S1). On the basis of these rate constants, pseudo-first-order rate constants (kA−H2O, kAH±H2O, kA−OH−, kAH±OH−, and kA−NH2) for the hydrolysis and intramolecular aminolysis were calculated at different pH levels by the following formulas: k A−H2O = kAtα ,H2O·

[A−] [A all]

(1)

k A−OH− = kAtα ,OH·

[A−]·[OH−] [A all]

(2)

k AH±OH− = kAHcα ,OH· D

[AH±]· [OH−] [A all]

(3)


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Environmental Science & Technology k AH±H2O = kAHcα ,H2O· k A−NH2 = k tβ NH2·

−

[AH±] [A all]

kH = kAH±H O + kAH±OH + kA −OH− + kA −H O + kA −NH 2

2

(4)

[A−] [A all]

2

(6)

The predicted logkH values from the different DFT methods are listed in Table 1 and SI Table S11, together with the corresponding values determined experimentally. It can be deduced that the calculated logkH values are highly sensitive to the different functionals and the atomic radii for defining solute cavity. The combined use of the B3LYP functional with the UFF atomic radii26 yields logkH values that are the closest to the experimental ones. The selection of basis sets also influences the calculated logkH values, and the logkH values from the 6-311++G(2d,2p) basis set are closer to the experimental ones. More importantly, the predicted logkH values at the B3LYP/6-311++G(2d,2p) level with the UFF atomic radii 26 are in reasonable agreement with the experimental ones. Subsequent Reactions for the Primary Intermediates. As shown in Figure 4, the contribution of kAH±H2O, kAH±OH− and kA−OH− to kH is more evident than the other pathways. A main product from these hydrolysis pathways of the C8−N5 lactam is 2H-1−3-Thiazine-2-acetic acid (HTA, pKa2 = 7.28), which has two ionic forms in the environmental pH range: HTA− and HTA2−. We further investigated the subsequent transformation of HTA. As shown in Figure 2, only intramolecular amidation of HTA− and base-catalyzed hydrolysis of HTA2− are thermodynamically favorable. On the basis of the schematic free energy surfaces and geometries for the intermediates and transition states (SI Figures S22−S25), the overall ΔG‡ value for the intramolecular amidation of HTA− to form 2H-1,3thiazine-carboxylic acid (HTCA) is 82.1 kJ/mol, implying the amidation of HTA− is kinetically feasible. However, it is kinetically unfeasible for the base-catalyzed hydrolysis of HTA2− to produce 1,4-cyclohexadiene-1-acetic acid (CAA) and 2H-1,3-thiazine-2-acetic acid (HTAA) due to the corresponding high ΔG‡ value (157.9 kJ/mol). Thus, the final product for hydrolysis of cephradine is HTCA. Previous experiments on hydrolysis products identification of cephradine have detected HTCA as the only product.27,28 Yamana and Tsuji investigated the hydrolysis of cephaloglycin in dioxane-water solutions (pH = 8.0), and observed that the hydrolysis rate increased with the proportion of dioxane (an aprotic solvent that can form H-bonds with water), and concluded that water did not play a significant role in the hydrolysis and intramolecular aminolysis.22 However, the experimental observation cannot preclude the base-catalyzed hydrolysis pathway of cephaloglycin. In the current study, we found that the hydrolysis of cephradine at basic conditions proceeds via the opening of the β-lactam ring followed by intramolecular amidation between the α-amino and carboxylate groups, and the process leads to HTCA that can also be formed from intramolecular aminolysis of cephradine. As the reaction rate of intramolecular aminolysis is much lower than that of the

(5)

where kAtα,H2O and kAHcα,H2O are the rate constants for the attack of H2O on At− and AHc± from the α side, respectively; kAtα,OH and kAHcα,OH are the second-order rate constants for the attack of OH− on At− and AHc± from the α side, respectively; ktβNH2 is the rate constant for the attack of −NH2 on At− from the β side; and Aall stands for the total cephradine. The variations of these pseudo-first-order rate constants with pH are shown in Figure 4.

Figure 4. Variations of logarithms of the pseudo-first-order rate constants for water-assisted hydrolysis of At− (kAH±H2O) and AHc± (kAH±H2O), base-catalyzed hydrolysis of At− (kA−OH−) and AHc± (kAH±OH−), and intramolecular aminolysis of At− (kA−NH2) at different pH levels.

At acidic conditions, the kAH±H2O value is higher than those of other pathways, indicating that H2O attack on the C8N5 lactam of AH± is a predominant hydrolysis pathway. Under neutral and basic conditions, the predominant pathway is the base-catalyzed hydrolysis, as the kAH±OH− and kA−OH− values are greater than those of the other pathways, and the kA−NH2 value is the smallest. This study indicates that it is necessary to calculate the pH dependence of pseudo-first-order rate constants corresponding with different pathways, so as to evaluate the hydrolysis pathways of organic pollutants, as was also pointed out by Blotevogel et al.11 As far as we know, this is the first attempt to quantum chemically calculate the variation of pseudo-first-order hydrolysis rate constants of an antibiotic with pH. The kH value was predicted by the following equation:

Table 1. Experimental Hydrolysis Rate Constants (s−1) of Cephradine at 298.15 K Compared with Those Calculated by the B3LYP Method with the UFF Atomic Radii

a

pH

5.0

6.3

7.0

8.0

9.0

logkH (experimental)a logkH [6-311++G(2d,2p)] logkH [6-311++G(d,p)]

−6.96 −7.22 −6.72

−6.44 −6.63 −6.05

−6.09 −6.13 −5.53

−5.95 −5.70 −5.03

−5.92 −5.28 −4.44

According to the experimental kH values, the hydrolysis half-lives of cephradine can vary from 7 (pH = 9.0) to 72 days (pH = 5.0). E



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ACKNOWLEDGMENTS We thank Prof. W. Peijnenburg (Leiden University) for constructive suggestions. This study was supported by the National Basic Research Program (2013CB430403) and the National Natural Science Foundation of China (21137001, 21325729).

other pathways in the considered pH range (Figure 4), the intramolecular aminolysis does not contribute much to the hydrolysis of cephradine. Since both cephaloglycin and cephradine contain the α-amino groups in their side chains and have similar molecular structures, it can be concluded that hydrolysis of cephaloglycin may proceed via the same pathways as cephradine, i.e., opening of the β-lactam ring followed by intramolecular amidation between the α-amino and carboxylate groups. It must be emphasized that a sound understanding of the hydrolysis pathways of cephaloglycin and other cephalosporins is of great importance, as the overall rate constant kH is mainly determined by the pseudo-first order rate constants for the main pathways. Environmental Implications. Herein, we employed the DFT calculation to predict the hydrolysis pathways and kinetics of cephradine, a model of cephalosporin that has two hydrolyzable groups, two ionization states, two isomers, three general-hydrolysis pathways and two directions of OH−, H2O, and −NH2 nucleophilic attack. The predicted rate constants are of the same order of magnitude as the experimental values, and the predicted products were also confirmed by experimental findings. There are no previous quantum chemical calculation studies dealing with hydrolysis of antibiotics with so many hydrolysis pathways. Many organic pollutants have only one hydrolyzable functional group with a hydrolysis pathway that is less complicated than those of cephradine. Thus, this study implies that the DFT calculation method can be extended to predicting hydrolysis rate constants and pathways of >100 species of cephalosporins29 as well as other hydrolyzable organic pollutants. This study also indicates that in order to assess hydrolysis rates of organic pollutants, the variations of the second-order rate constants (ki) for the different hydrolysis pathways with pH should be evaluated, so as to identify the main hydrolysis pathways/products under environmental pH conditions, as kH is mainly determined by the pseudo-first order rate constants for the main pathways. As far as we know, there are no previous quantum chemical calculations that evaluate the contribution of different hydrolysis pathways of antibiotics under environmental pH conditions. Only by experiment, the dominant hydrolysis pathways can hardly be identified. Thus, the DFT calculation in this study shows superiority in this regard. This study also identified the role of the carboxyl group in the hydrolysis of cephradine. We infer that the carboxyl group also plays a catalytic role in the hydrolysis of other cephalosporin and penicillin antibiotics.

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ASSOCIATED CONTENT

* Supporting Information S

Details on selection of atomic radii, calculation of rate constants, effects of explicit water molecules, experimental data, main geometric structures and schematic free energy surfaces; Figures S1−S25 and Tables S1−S12, as mentioned. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone/fax: +86-411-84706269; e-mail: [email protected]. Notes

The authors declare no competing financial interest. F


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