The Influence of the Hydrogen Isotope Effect on the Kinetics of Amoxicillin and Essential Elements Interaction

Abstract

Chemical incompatibility between active pharmaceutical ingredients (APIs) and mineral supplements may affect their bioavailability and effectiveness. Water, as the main component of physiological fluids, plays a crucial role in these interactions. Natural waters vary in the deuterium. Estimation of the kinetic isotope effect (KIE) provides valuable information on reaction mechanisms in solvents with different D/H ratios and with the replacement of protium with deuterium in API molecules. Studies of the kinetics of interactions between zinc ions and amoxicillin in water with a natural isotopic composition (D/H = 145 ppm) and in heavy water (99.9% D₂O) offer a model for predicting similar interactions in vivo. The presence of chiral centers in the amoxicillin molecule allowed the use of polarimetry to study the influence of the solvent isotopic composition, temperature, and pH on the rate of interaction. In heavy water, a twofold decrease in the rate of amoxicillin binding to hydrated zinc ions was observed compared to natural water at 20 °C. Arrhenius kinetics confirmed the observed KIE: Ea = 112.5 ± 1.3 kJ/mol for D₂O and 96.0 ± 2.1 kJ/mol for H₂O. For the first time, kinetic polarimetric studies demonstrated differences in the mechanisms of binding of d- and s-element cations to amoxicillin.

1. Introduction

A significant proportion of adverse drug reactions are caused by drug–drug interactions [1,2]. The widespread global use of antibiotics highlights the critical importance of studying their drug interactions [3]. Amoxicillin ((2S,5R,6R)-6-{(E)-[(2R)-2-Amino-1-hydroxy-2-(4-hydroxyphenyl)ethylidene]amino}-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo [3.2.0]heptane-2-carboxylic acid) is particularly significant in this context, as it is one of the most commonly prescribed beta-lactam antibiotics. According to World Health Organization (WHO) recommendations, amoxicillin is included in more than 70% of treatment regimens for infectious diseases [4].

Considerable attention has been given in the scientific literature to the synergy or antagonism of pharmacological effects in interactions between active pharmaceutical ingredients (APIs) [5], as well as to the incompatibility of pharmaceutical substances with excipients [6,7]. The equally important interactions between APIs and multivitamin supplements are rarely addressed. Meanwhile, the long-term use of mineral supplements often continues during the treatment of bacterial infections.

On the other hand, oral administration of drugs containing ligand groups can reduce the absorption of essential microelements. For example, zinc, unlike iron, has no storage sites in the body, and its average daily oral dose is 15 mg [8]. The effective daily dose of amoxicillin is 1500 mg. Their combined use at a molar ratio n_AMX:n_Zn²⁺ = 15:1 leads to complete zinc binding.

Therefore, studies focusing on the interactions of amoxicillin with salts of essential elements, particularly those containing Zn²⁺ ions, warrant special attention. In the human body, zinc acts as a cofactor for more than 300 enzymes. Since the body lacks a reservoir of zinc, its deficiency is compensated by oral intake through food or mineral supplements [9].

To assess the chemical and physical incompatibility of substances in vitro, methods such as Fourier Transform Infrared Spectroscopy, thermogravimetric analysis, differential scanning calorimetry, isothermal stress testing, X-ray diffraction, and other approaches are commonly used [10,11,12,13,14].

The presence of chiral centers in the amoxicillin molecule has enabled the use of polarimetric control to study its interactions with cations of essential elements found in biological supplements (Figure 1). Previously, comparative polarimetric studies of the mechanisms of interaction between s- and d-elements with amoxicillin and other beta-lactam antibiotics had not been conducted.

Changes in the steric configuration of a molecule upon binding with metal ions may disrupt stereoselective interactions with biological receptors and alter the pharmacokinetic and pharmacodynamic parameters that determine pharmaceutical efficacy and safety [15].

To predict and assess the potential clinical severity of drug incompatibilities, it is essential to study the kinetic characteristics of these processes. Evaluating the kinetic isotope effect (KIE) provides valuable insights into the rate-determining steps of these interactions. Water, as a major component of physiological fluids, plays a crucial role in in vitro model studies. Water’s unique physicochemical and biological properties depend on the deuterium/protium (D/H) ratio [16,17,18]. Thus, the pharmacological properties of drugs, along with the pharmacokinetic parameters of processes involving dissolved substances, depend on the isotopic composition of the water [19]. Notably, the isotopes protium (${}_1{}^1\mathrm{H}$) and deuterium (${}_1{}^2\mathrm{D}$) exhibit the largest atomic mass difference observed among isotopes of other elements. The difference in bond length between the O–H bond in H₂O and the O–D bond in D₂O is approximately ~3% [20]. The formation of water clusters through hydrogen bonding directly influences their chemical, electronic, and dielectric properties [21]. Because the isotopic heterogeneity of water decreases from H₂O to D₂O, the structure and properties of the resulting clusters depend on the D/H ratio. The formation of deuterium-stabilized water clusters modifies the optical activity of API solutions, stabilizes intermediates and transition states, and alters the rate of reactions [22]. The influence of the isotopic composition of water on the kinetic characteristics of processes is expressed by the kinetic isotope effect (KIE) = k_H/k_D, where k_H and k_D represent the rate constants of reactions in natural and heavy water, respectively. Thus, KIE reflects the extent to which the reaction rate decreases when a protium atom (H) is replaced by its heavier isotope, deuterium (D) [23].

The aim of this study is to investigate the kinetics of the interaction between amoxicillin trihydrate and ions of essential elements in solutions of water isotopologues.

2. Materials and Methods

2.1. Materials

2.1.1. Chemical Substances

This study used the following substances: amoxicillin trihydrate (Ph.Eur. Reference Standard, EDQM, Strasbourg, France, 99.9%); ZnCl₂, CaCl₂, MgCl₂ (Sigma-Aldrich, Saint Louis, MO, USA, 99.9%). For preparation of buffer solutions, ammonium acetate (Sigma-Aldrich, 99.99%), sodium acetate trihydrate (Sigma-Aldrich, Saint Louis, MO, USA, 99.0%), Tris (Sigma-Aldrich, 99.9%), NaOH (Sigma-Aldrich, Saint Louis, MO, USA, 97.0%), citric acid (Sigma-Aldrich, Saint Louis, MO, USA, 99.5%), and glacial acetic acid (Sigma-Aldrich, Saint Louis, MO, USA, 99.0%) were used.

2.1.2. Water Samples

Deionized, high-resistance water (18.2 MΩ·cm at 25 °C; Milli-Q, Merck Millipore, Darmstadt, Germany) with natural isotopic composition (D/H = 145 ppm) − H₂O, as well as heavy water D₂O with 99.9% deuterium content (Cambridge Isotope Laboratories, Andover, MA, USA), were used for solution preparation.

2.1.3. Sample Preparation

The accurately weighed AMX was dissolved in buffer solutions with the specified D/H ratio. Immediately, the required amount of salt (Sigma-Aldrich^®, puriss.), previously dried at 110 °C, was added. Prepared solutions (n = 5) were filtered through membrane filters with a pore size of 0.22 μm. The pH of solutions was measured using a potentiometer, PH400F (MT Measurement, Shanghai, China).

2.2. Methods

2.2.1. Polarimetry

Optical activity of solutions was measured using an automatic polarimeter POL-1/2 (Atago, Tokyo, Japan) in the 100 mm cell with measurement accuracy of ±0.002° and the resolution of 0.0001°. A Peltier electronic module was employed to control the temperature in the range of 20–32 °C with 2 °C increments.

2.2.2. Fluorimetry

Fluorescence spectra were obtained using a Cary Eclipse spectrofluorimeter (Agilent Technologies, Inc., Santa Clara, CA, USA) with two ultrafast scanning monochromators. Measurements were performed with 1 cm thick quartz cells at 25 °C. The width of the excitation and emission slit was adjusted to 5 nm. An excitation wavelength of 350 nm was selected by considering the results of the analysis of the test compounds by the method of absorption spectroscopy.

2.2.3. UV-Vis Spectroscopy

Spectrometric data were collected using a UV spectrophotometer Cary 300 (Agilent Technologies, Inc., Santa Clara, CA, USA). Measurements were performed with 1 cm thick quartz cells at 25 °C.

2.2.4. Statistical Data Processing

Experimental data processing and plotting was performed using the OriginPro 2021 software package (OriginLab, Northampton, MA, USA). Results are presented as the mean ± standard deviation (SD).

3. Results and Discussion

The presence of four chiral centers in the amoxicillin (AMX) molecule provided the basis for using polarimetry to study the kinetics of the antibiotic’s interactions with essential metal ions. The effects of zinc, calcium, and magnesium chlorides on aqueous amoxicillin solutions were investigated in both acidic and neutral media. Calcium (Ca²⁺) and magnesium (Mg²⁺) ions did not affect the optical activity of the antibiotic (Figure 2). In contrast, kinetic plots of optical rotation versus time (α°–t) showed that upon the addition of zinc chloride, the angle of plane-polarized light rotation gradually decreased, indicating different interaction mechanisms of s- and d-block elements [24,25,26,27].

Fluorescence studies of these solutions demonstrate that a decrease in acidity within the pH range of 3.7 to 7.0 results in an increase in emission intensity (Figure 3a).

Based on the acid–base equilibrium constants of amoxicillin [28], the fluorescence of the aqueous amoxicillin solution at pH 3.7 is primarily attributed to the predominance of the zwitterionic form (II) in the solution. In contrast, at pH 7.0, the content of the fully deprotonated form of the antibiotic increases (Figure 4). The involvement of form III in complex formation—through the conjugation of the lone pair of electrons on the amino nitrogen with the benzene ring’s double bond system and the electron pair on the carbonyl oxygen—enhances the antibiotic’s fluorescence intensity.

Salts of s-block elements, when added to an aqueous solution of amoxicillin, decrease the emission intensity of solutions by forming stable fluorescent products. In the case of introducing d-block element ions (Zn²⁺), a sharp quenching of fluorescence occurs within the first 10 min, followed by a gradual decay until a constant intensity level is reached. It should be noted that the formation of the “AMX:Zinc” complex in methanol differs from that in aqueous solution and occurs so rapidly that measuring the reaction rate is not possible [29]. This suggests the possible involvement of H₂O molecules in the formation of complexes within aqueous solutions [30].

Comparison of polarimetry and fluorimetry results suggests that the initial stage of the investigated process involves the formation of salts via the carboxyl group of amoxicillin:

$${\mathrm{M}}^{2+} + 2 {\mathrm{RCOO}}^{-} \to \mathrm{M}{\left({\mathrm{RCOO}}^{-}\right)}_2$$

For s-block element cations, this stage is the only one observed and is characterized by a rapid attainment of stable fluorescence values, with no effect on the optical activity of the antibiotic solution. The second stage, which occurs exclusively with Zn²⁺, involves the formation of donor–acceptor bonds with the amino group and the carbonyl oxygen [31]. The presence of this second stage results in changes to both fluorescence intensity and optical activity. It should be emphasized that the first-order reaction rate constants (k₁) determined by two different methods are close in value: k₁(fluorimetry) = 1.6 × 10⁻⁴ s⁻¹; k₁ (polarimetry) = 1.8 × 10⁻⁴ s⁻¹.

To explain the differences in the complexation of s- and d-block elements, one can apply the theory of hard and soft acids and bases (HSAB), along with the law of mass action for equilibria. This approach involves considering the formation constants of coordination compounds of magnesium, calcium, and zinc with amoxicillin or its analogs containing amino and carboxyl groups.

According to the HSAB theory, magnesium (Mg²⁺) and calcium (Ca²⁺) ions are classified as hard acids because they have small ionic radii, high positive charges, and high charge densities. Consequently, they form strong chemical bonds with hard bases, such as the carboxylate anion (RCOO⁻), during interionic interactions.

According to the same theory, the d-element cation Zn²⁺ is a borderline acid with relatively softer properties, especially when compared to typical hard acids such as Mg²⁺, Ca²⁺, Fe³⁺, and Al³⁺. Therefore, the chemical bond between the Zn²⁺ ion and a hard base—specifically, the carboxyl oxygen of amoxicillin—may be weaker than the bonds formed by s-element cations from the second and third periods of the periodic table, such as Mg²⁺ and Ca²⁺. However, the zinc cation also exhibits a preference for borderline or soft bases—electron-pair donors such as nitrogen (N) or sulfur (S) atoms. The electron-deficient Zn²⁺ ion, with its unfilled orbitals, can participate not only in ionic interactions with the carboxyl group but also in the formation of coordination bonds via a donor–acceptor mechanism. In these cases, the base is primarily the nitrogen atom of the amino group and, to a lesser extent, the nitrogen atom of the imino group, sulfur atoms, and the nitrogen atom of the thiazolidine ring.

Reference data on the formation constants of coordination complexes containing both carboxyl and amino groups are available in the literature. Notably, IUPAC Technical Reports [24,25] provide valuable information. Of particular interest are the formation constants involving amino acids, which, like amoxicillin, function as bidentate ligands [24]. Similar data are also available for complexones used in medicine—polydentate ligands that contain several of the functional groups under consideration [25].

To analyze numerous publications, including IUPAC technical reports, it is necessary to introduce standardized notations. Let us assume that L represents an amino acid or amoxicillin with fully deprotonated carboxyl (–COO⁻) and amino (–NH₂) groups. M denotes a metal cation (Mg²⁺, Ca²⁺, Zn²⁺). The equilibrium for metal complex formation and its corresponding formation constants are then expressed as follows:

$$\mathrm{M} + \mathrm{L} = \mathrm{ML} \mathrm{and} \mathrm{K} = \left[\mathrm{ML}\right]/\left[\mathrm{M}\right]\left[\mathrm{L}\right]$$

In the case of amoxicillin, this equilibrium is established at a pH above 7.8 (see Figure 4), and for glycine at pH values greater than its pKa of 9.6. At such high pH levels, Mg²⁺ and Ca²⁺ ions form cations of poorly soluble basic salts, such as MOH⁺ and hydroxides M(OH)₂. The reported formation constants should be attributed solely to ionic interactions at the carboxyl group (

Table 1. Formation constants of the complexes ML, MHL, and ML₂ (L denotes fully deprotonated glycine), according to [24].

Metal	M + L = ML lg K = [ML]/[M][L]	M + HL = MHL lg K = [MHL]/[M][HL]	M + 2L = ML2 lg K = [ML2]/[M][L]2
Mg2+	1.3–3.5	2.7	-
Ca2+	1.4	2.4	-
Zn2+	4.8–5.5	8.7–11.6	9.1–9.9

).

When the pH shifts to a more acidic range, the L ligands are protonated at the amino group to form –NH3⁺, which does not interfere with the interaction of d-element cations, resulting in the complex M + HL = MHL. The corresponding equilibrium constants for zinc K (M + HL) are 6–9 orders of magnitude higher than the binding constants of s-element cations at carboxyl groups, as demonstrated for glycine (see Table 1). Moreover, the d-element ion, possessing unfilled internal d-orbitals, can additionally coordinate a second deprotonated L ligand to form the coordination compound ML₂. In more acidic solutions, at approximately pH 5.5, Zn(II) forms ternary complexes with amoxicillin, with stability constants (log β) ranging from 4.62 to 5.32, indicating that the metal bridges the antibiotic and the amino acid [32]. For s-elements, such interactions are not possible, as evidenced by the absence of equilibrium constant values (see Table 1).

The ability of amoxicillin to bind Mg²⁺ and Ca²⁺ ions under various experimental conditions (pH, ionic strength, temperature) was quantitatively assessed using the pL_0.5 parameter [26,27]. These values reflect the low stability constants of the resulting carboxylate complexes. For Mg²⁺, at an ionic strength of I = 0.15 mol·kg⁻¹, pH = 7.4, and T = 298.15 K, pL_0.5 = 2.52. A similar value was obtained for Ca²⁺. At an ionic strength range of I = 0.15–1 mol·kg⁻¹ and a temperature range of T = 288.15–310.15 K, pL_0.5 (Ca²⁺) = 2.88. The low pL_0.5 values and formation constants of calcium and magnesium compounds with amino acids further emphasize the difference in the interactions of s- and d-block elements.

The influence of solution acidity on optical rotation was investigated within the physiological pH range of 3 to 7 (Figure 5). As the antibiotic molecule deprotonated with increasing pH (see Figure 4), an increase was observed in the “rate constant–pH” curve, characteristic of both amoxicillin alone and its mixture with zinc salt. The slight change in the specific rotation of the amoxicillin solution over time is accounted for in the pharmacopoeia, which specifies the rotation angle range as 290–315 [33].

Due to the protonation of both functional groups at pH 1–3 and the inability to form a coordination compound, the optical activity of the solution was very low, making it impossible to monitor the behavior of the components in solutions with pH values corresponding to gastric contents. A significant increase in the rate of interaction was observed in the pH range of 5–7, which was associated with changes in both the degree of protonation of the amoxicillin molecule and the hydration state of the zinc ion [34]. Since amoxicillin absorption occurs in the duodenum and small intestine, where the pH is approximately 5.6 [35], this pH value was selected for further in vitro studies.

The reaction orders with respect to each reagent—amoxicillin and ZnCl₂—were determined using Van’t Hoff’s Differential Method [36]. Increasing the concentration of ZnCl₂ from 1 mmol/L to 4 mmol/L, while maintaining a constant amoxicillin concentration of 1 mmol/L, resulted in an increased reaction rate. In logarithmic coordinates, the slope of the line relative to the abscissa was 1.16, indicating a first-order reaction with respect to the zinc salt. Similar experimental and graphical analyses confirmed that the reaction is zero-order with respect to amoxicillin (Figure 6).

For further kinetic studies, a reagent molar ratio of 1:10 was selected to ensure a high reaction rate. Long-term polarimetric monitoring of combined AMX and ZnCl₂ solutions (1:10) in H₂O and D₂O revealed an exponential decrease in optical activity, regardless of the solvent’s isotopic composition (Figure 7). Plotting the kinetic curves on semilogarithmic coordinates allowed the identification of two stages in the chiral transformations. In the first stage, a coordination compound is formed. According to first-order kinetics, this corresponds to a straight line when plotting ln αº versus time (t). In the second stage, racemization of the formed complex occurs, causing the optical activity to decrease to zero.

The complete loss of optical activity may be connected with the formation of a coordination compound of the composition 2AMX:Zn²⁺ [31,37]. In this case, the antiparallel arrangement of chiral centers in the complex can lead to chirality cancellation, similar to meso compounds that possess an internal plane of symmetry (Figure 8).

The observed complete loss of optical activity in combined solutions over time may reduce the ability for stereoselective binding to the active site of the target protein, consequently diminishing its efficacy [32].

It is well established that the isotopic composition of water influences the rates of processes involving pharmaceutical substances dissolved in it [38]. Furthermore, the vitality parameters of biological objects significantly depend on the D/H ratio, which supports considering deuterium an essential element [16]. Data on deuterated drugs indicate that the D/H ratio in water affects the rates of absorption, distribution, biotransformation, and excretion of medications [39,40].

Replacing water with a natural isotopic composition (D/H = 145 ppm) by heavy water (99.9% D₂O) leads to a decrease in the rate of coordination compound formation. The time required to reach zero optical activity of the solutions (α°) increases from 340 to 500 min. The formation of hydrated intermediates, stabilized by replacing the H₂O with D₂O, results in a 1.5-fold slowdown in reaching zero optical activity during complex formation. Regardless of the solvent’s isotopic composition, the shape of the curves in both arithmetic “α°–t” and semilogarithmic coordinates remains unchanged (see Figure 7).

Differences in reaction rates in waters with different D/H ratios were quantitatively assessed by evaluating the magnitude of kinetic isotope effects (KIE = k_H/k_D) over the temperature range of 20–38 °C (

Table 2. Kinetic isotope effect (KIE) for the reaction of amoxicillin with Zn²⁺ in water with isotopic composition D/H = 145 ppm (k_H) and heavy water D₂O (k_D); acetate buffer (pH = 5.6).

T °C	kH,×·104, s−1	kD,×·104, s−1	KIE = kH/kD
20	0.9 ± 0.007	0.47 ± 0.007	2.0
24	1.8 ± 0.018	0.95 ± 0.006	1.9
28	2.8 ± 0.013	1.67 ± 0.023	1.7
32	4.5 ± 0.034	3.07 ± 0.021	1.5
38	8.8 ± 0.118	6.90 ± 0.108	1.3

). As the temperature increases, the differences in reaction rates diminish, with the KIE decreasing from 2.0 to 1.3 within the studied range.

The activation energy values for the reaction of AMX with zinc ions, determined from Arrhenius plots, also reveal differences in the energy barriers for H₂O and D₂O—96.0 ± 2.1 kJ/mol and 112.5 ± 1.3 kJ/mol, respectively (Figure 9).

Thus, the chemical incompatibility of amoxicillin trihydrate with the essential element ion Zn²⁺ has been experimentally confirmed. Using polarimetric method and electronic spectrometry, differences in the interaction mechanisms of amoxicillin with cations of essential s- and d-block elements were demonstrated. It was established that the formation of intermolecular complexes with the zinc ion as the central atom is pH-dependent and occurs in weakly acidic to neutral media through two stages: first, ionic interaction with the deprotonated carboxyl group; second, donor–acceptor bonding involving the amino group and carbonyl oxygen. The formation of coordination compounds between Zn²⁺ ions and the amoxicillin molecule can result in a reduction in its efficacy.

4. Conclusions

In this study, optical methods—polarimetry, fluorimetry, and UV-visible spectrophotometry—were employed to investigate the chemical incompatibility of amoxicillin with components of mineral supplements, specifically zinc, magnesium, and calcium salts. Polarimetry was used for the first time to determine the rate constants for the formation of AMX-Zn(II) complexes, considering factors such as pH, temperature, and the isotopic composition of the solvent. Changes in optical rotation over time (α°–t) revealed distinct mechanisms of interaction between AMX with elements of the s- and d-blocks of the periodic table. All studied cations exhibited ionic interactions with the deprotonated carboxyl group. However, unlike calcium and magnesium ions, the zinc ion forms donor–acceptor bonds with the amino group and carbonyl oxygen, resulting in changes in both optical activity and fluorescence intensity. The first-order rate constants determined by the two methods were nearly identical: k₁ (polarimetry) = 1.8 × 10⁻⁴ s⁻¹; k₁ (fluorimetry) = 1.6 × 10⁻⁴ s⁻¹.

A significant kinetic isotope effect of k_H/k_D = 2.0 (20 °C) was observed for natural water (H₂O, D/H = 145 ppm) and heavy D₂O (99.9%), indicating the involvement of water molecules in the complexation reaction. These findings were confirmed by Arrhenius kinetics over the temperature range of 20–38 °C. The kinetic isotope effect was reflected in the activation energy barriers for the complexation process in H₂O and D₂O, which were 96.0 ± 2.1 kJ/mol and 112.5 ± 1.3 kJ/mol, respectively.

Because more than 50% of all FDA-approved active pharmaceutical ingredients (APIs) are chiral molecules [41], the results of this study open new possibilities for highly sensitive polarimetric monitoring of the kinetics of interactions between optically active pharmaceutical ingredients and ions of both essential and toxic elements.