Introduction

Poly(γ-glutamic acid) (γ-pga) exists in the typical Japanese foods, e.g., natto (fermented soybeans), which is generated by Bacillus natto, as a component of natto mucilage (sticky substance). It is believed that γ-pga has been used as a safe food ingredient. The γ-pga is made of d- and l-glutamic acid units connected by amide linkages between α-amino and γ-carboxylic acid groups (Fig. 1). It is water soluble, non-toxic toward humans and the environment. It has broad applications in the food, chemical, biological, and medical industries [1,2,3]. Moreover, γ-pga was used as a natural adsorbent to remove mutagenic heterocyclic amines and organic dyes from aqueous solution [4,5,6,7].

It is reported that γ-pga is a potential biosorbent for the removal and recovery of heavy metals from wastewaters due to its ability to bind metal ions. For example, Jamiu et al. [8] synthesized a γ-pga-based resin as a sorbent for sequestering Co2+ ions from aqueous solution. Hu et al. [9] developed a biocomposite sorbent incorporating γ-pga for binding and recovery of Cu2+ ions. Bodnar et al. [10] described the preparation of biodegradable nanoparticles based on the complexation of γ-pga with Pb2+ ions, demonstrating that γ-pga was a promising sorbent for the removal of heavy metals in polluted water. Zhang et al. [11] produced palladium-doped zero-valent iron nanoparticles using poly(γ-glutamic acid) (Fe–Pd@PGA NPs) for dechlorination of p-chlorophenol.

Fig. 1
figure 1

Structure of poly(γ-glutamic acid), γ-pga

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Previously, we reported that the vanadyl ion (VO2+) strongly coordinated to the oxygen atom of the carboxyl group of γ-pga to form VO(γ-pga) complex in aqueous solution (pH 2–5) with a VO(O4) coordination sphere [12]. The VO(γ-pga) complex exhibited higher insulin-mimetic activity than that of vanadyl sulfate (VOSO4) as observed in both the in vitro and in vivo experiments using streptozotocin (STZ)-induced type-1 diabetic and type-2 diabetic KKAy mice [13, 14]. We also found that the zinc(II)-poly(γ-glutamic acid), Zn(γ-pga), complex normalized the hyperglycemia in type-2 diabetic KKAy mice within 21 days when administrated orally at doses of 10–20 mg (0.15–0.31 mmol) Zn per kg body mass for 30 days [15]. In addition, the impaired glucose tolerance, elevated HbA1c levels, and metabolic syndromes were significantly improved in Zn(γ-pga)-treated KKAy mice compared to those administrated with saline and ZnSO4 [15]. In 2015, Sirelkhatim et al. [16] reported that the zinc oxide nanoparticles (ZnO–NPs) exhibit attractive antibacterial properties due to the increased specific surface area as the reduced particle size leads to enhanced particle surface reactivity. However, the antimicrobial activity of Zn(γ-pga) complex was not described in the literature.

In this study, the kinetics of Zn(γ-pga) complex formation was examined in aqueous as a function of contact time, solution pH, initial concentration of zinc ion, and solution temperature. The formation equilibrium of Zn(γ-pga) complex in aqueous solution was observed at four different temperatures. The formation of Zn(γ-pga) complex was confirmed by FTIR and 13C NMR spectroscopy. The kinetics and mechanism involved in the formation of Zn(γ-pga) complex were analyzed by several model equations (i.e., pseudo-first-order, pseudo-second-order equations, Elovich, film diffusion, and intraparticle diffusion models). Freundlich, Temkin, and Langmuir isotherm models were applied to compute the equilibrium data. Apparent thermodynamic parameters were evaluated for the formation of Zn(γ-pga) complex in aqueous solution. Moreover, the antimicrobial efficacy of Zn(γ-pga) complex was examined against a gram-negative bacteria (i.e., Escherichia coli) and a gram-positive bacteria (i.e., Bacillus subtilis).

Materials and methods

Materials

The sample of γ-pga with a d/l-enantiomeric mixture having the average molecular weight 5 × 105 Da was obtained from Bioleaders Japan Corporation (Osaka, Japan). The polymer was used without further purification. Zinc(II) sulfate seven hydrate, ZnSO4·7H2O, was obtained from Wako Pure Chemical Industries, Ltd. (Osaka, Japan). All other reagents were commercially available in the highest grade of purity and were used without further purification. Two strains of bacteria were used for this study, namely Escherichia coli DH5α (i.e., gram-negative) and Bacillus subtilis RBW (i.e., gram-positive).

Preparation of Zn(γ-pga) complex in solid state

The Zn(γ-pga) complex was prepared by mixing excess amounts of ZnSO4 (1 mol/L) and 10 mL of γ-pga (1% w/v) solutions under magnetic stirring overnight at room temperature. The solution was then evaporated to approximately 2 mL and cooled in an ice bath. A large amount of acetone was added to the remaining solution to complete the precipitation of Zn(γ-pga) complex. The resulting precipitate was washed with distilled water and acetone and dried on silica gel under a vacuum condition at room temperature.

Preparation of Zn(γ-pga) complex in solution

Typically, 10 mL of γ-pga (1% w/v) solution was prepared in deionized water (or in D2O) by adding 0.7 mL of 1 mol/L NaOH or NaOD. The Zn(γ-pga) complex was prepared in aqueous solution (pH 2–9) by mixing ZnSO4 (1 mol/L) and γ-pga (1% w/v) under magnetic stirring. The final concentration of ZnSO4 was 0.05–3.50 mmol/L and that of γ-pga was (0.1–1.0% w/v) in solution depending on the observed experiments. The pH of the samples was adjusted by adding micro-liter amount of 1 mol/L HCl or NaOH. The pH of the reaction mixtures was determined by using a pH meter (Adwa AD8000). The concentration of ZnSO4 in 0.1% (w/v) of γ-pga was considered as the concentration of Zn(γ-pga) complex in solution which was used in antimicrobial studies.

Spectroscopic measurements

UV–visible absorption spectra of γ-pga and Zn(γ-pga) complex were measured by using a Shimadzu UV-1800 Spectrophotometer (Shimadzu, Japan) in the wavelength region of 200–800 nm at room temperature; the quartz cell had a path length of 1.0 cm. Before each measurement, the base line of spectrophotometer was calibrated against the solvent of the respective solution. The Fourier transformation infrared (FTIR) spectra of the γ-pga and solid Zn(γ-pga) complex were measured with the samples in compressed KBr disks at the frequency range of 400–4000 cm−1 using FTIR spectrometer (IRPrestige-21 FTIR Spectrophotometer, Shimadzu, Japan). The 13C NMR spectra of γ-pga and Zn(γ-pga) complex in D2O were measured with an NMR spectrometer (Varian UNITY INOVA 400NB) at 400 MHz. The 13C chemical shifts were recorded relative to tetramethylsilane (TMS) as an internal reference. A small amount (5 μL) of 0.1 mol/L NaOD and 20 μL of 0.1 mol/L DCl in the D2O solution were used in the adjustment of the sample (60 mL) pH 5. The value of pD 5 here is a direct meter reading from the pH meter without correction of deuterium effects.

Preparation of membrane

The dialysis membrane was of 8-cm strips and 2.5 cm width of Visking dialysis flat membranes (Medicell International Ltd., London, SE8 3FD) with a molecular weight cutoff not greater than 14,000 daltons. These membranes were treated with hot water at 70 °C. At every 1-h interval, the water was changed by fresh deionized water for efficient removal of sulfur and other soluble materials. This process was carried out for 24 h. The membranes were then stirred for 1 h to cool and to bring at room temperature. The membranes were continuously stirred with 70% methanol for 30 min. Finally, the membranes were stored overnight in 50% methanol.

Batch binding experiments

In order to evaluate the binding features of zinc(II) ion onto γ-pga, batch binding experiments were conducted in 125-mL stoppered bottles containing 57 mL of ZnSO4 (1.05 mmol/L) solution and 3 mL of γ-pga (0.1% w/v) solution in a dialysis membrane. Zinc(II) ions can easily enter into the dialysis membrane and form Zn(γ-pga) complex, which remained inside of the membrane. The pH of the metal solution was adjusted with 1 mol/L HCl or NaOH solution, by using a pH meter (Adwa AD8000). The stoppered bottles were shaken in a thermostated shaker at room temperature (30 ± 0.2 °C), with a speed of 120 r/min, until reaching equilibrium. Each bottle was capped to avoid evaporation at high temperature. Sample bottles were withdrawn at desired time intervals for analyzing the concentration of metal ion in the outer solution of dialysis membrane. The amount of Zn2+ bound to γ-pga was determined from the difference in zinc concentration in aqueous solution before and after treatment with γ-pga. The zinc concentration in the solution was measured by atomic absorption spectrometry (AA-7000 Shimadzu, Japan). The concentration of zinc was calculated using a calibration curve at a concentration range of 0.1000–0.4000 ppm for the standard zinc solutions (Wako Pure Chemical Industries Ltd., Osaka, Japan). The detection limit of zinc concentration was approximately 0.011 ppm. The correlation coefficient of linear regression was r = 0.999 for a total of three metal concentrations. The measurement conditions are as follows: current: 8 mA/0 mA; burner height: 7 mm; wavelength: 213.9 nm; burner angle: 0 deg; slit width: 0.5 nm; fuel gas flow: 2.0 l/min; lighting mode: BGC-D2; type of oxidant: air.

The amount of zinc(II) ion bound per unit γ-pga at time t, qt (mmol/g), is determined by

$$ q_{t} = \frac{{V\left( {C_{0} - C_{t} } \right)}}{m}, $$
(1)

where C0 (mmol/L) and Ct (mmol/L) are the concentrations of zinc in out solution at initial and any time t, respectively, V (L) is the volume of metal solution, and m (g) is the amount of dry γ-pga used.

The binding kinetics was also performed varying initial concentration of metal solutions (0.05–1.0 mmol/L) and temperatures (30, 35, 40, and 45 °C), respectively. The equilibrium binding was carried out at four different temperatures (30, 35, 40, and 45 °C) and at pH 5.

The amount of zinc(II) bound to γ-pga at equilibrium time, qe (mmol/g), was determined by

$$ q_{\text{e}} = \frac{{V\left( {C_{0} - C_{\text{e}} } \right)}}{m}, $$
(2)

where Ce (μmol/L) is the concentrations of zinc in outer solution at equilibrium time and C0, V, and m remain the same as described above. All kinetics and binding equilibrium data presented in this paper are the average of double measurements.

Preparation of bacterial subculture and test plate

The test organisms were transferred from the pure cultures to the Luria-Bertani (LB) broth using a sterile transfer loop and incubated overnight in a shaker at 37 °C for their optimal growth. Bacteria were then transferred to the subculture containing about 20–25 mL of semisolid LB agar medium. Finally, 100 µL of bacteria culture was transferred to the petri plate and spread uniformly with the help of a sterile spreader [17].

Preparation of diffusion disks

Sterile blank antimicrobial disks (6 mm in diameter, Oxoid Ltd. Hampshire, England) were used to investigate the antimicrobial activity of the test samples. The antimicrobial disks were dipped into test samples at various concentrations. The disks were then taken in a sterile petri plate and dried. Finally, the disks containing the desired tested samples were placed in test plates to examine the antimicrobial activity. Chloramphenicol was used as positive control to compare the antimicrobial activity of the test samples, and deionized water was used as negative control [18].

Determination of antimicrobial activity of Zn(γ-pga) complex by disk diffusion method

The standard disk diffusion method was used to investigate the antimicrobial activity of Zn(γ-pga) complex against a gram-negative bacteria (i.e., E. coli) and a gram-positive bacteria (i.e., B. subtilis) [19].

Steric filter disks containing different amounts of test sample were placed on LB agar plate containing uniformly seeded bacteria. The plates were then incubated for 16 h at 37 °C for the growth of the bacteria. The antimicrobial potency of the Zn(γ-pga) complex was measured by their ability to prevent the growth of the microorganisms surrounding the disks which gives a clear zone of inhibition. After incubation, the antimicrobial activity of Zn(γ-pga) complex was determined by measuring the diameter of the zone of inhibition with a slide calipers.

Determination of the inhibitory concentration 50 (IC50) value

The IC50 values of all samples were determined through serial solution method [20]. Briefly, γ-pga (0.1% w/v), ZnSO4 solution alone at different concentrations (i.e., 0.00, 0.20, 0.40, 0.60, 0.80, and 1.00 mmol/L) and various concentrations of ZnSO4 (i.e., 0.00, 0.20, 0.40, 0.60, 0.80, and 1.00 mmol/L) in 0.1% w/v of γ-pga considered as the concentration of Zn(γ-pga) complex in solution were added to the bacterial cultures, and the final volume was made up to 2 mL. The samples were incubated overnight at 37 °C with gentle shaking. For each batch of IC50 determination, a blank tube as negative control (i.e., 2-mL LB broth without any bacterial strains) and a positive control (10 µg chloramphenicol antibiotic was added to bacterial cultures) were also incubated. The absorbance of all samples was measured at 600 nm, using a Shimadzu UV-1800 Spectrophotometer (Shimadzu, Japan). The experiment was performed multiple times, and data were expressed as a mean of several replications (n = 3) with standard deviations. The data were plotted into the graph, and the values of IC50 were determined by using following equation:

$$ Y = ax + b, $$
(3)

where Y is the 50% inhibition, x is the concentration of samples in which 50% inhibition occurs, b is a constant, and a is the coefficient.

Results and discussion

Preparation and characterization of Zn(γ-pga) complex

Zn(γ-pga) complex was synthesized in aqueous solution (pH 5) at the ratio of 1:0.02 of ZnSO4 and γ-pga (final concentration of ZnSO4 1 mmol/L and γ-pga 1.0% w/v). The structure of synthesized Zn(γ-pga) complex was characterized by UV–visible absorption, FTIR, and 13C NMR spectra. The same complex was synthesized in solid state to confirm its structure in aqueous solution. The UV–visible absorption, FTIR, and 13C NMR spectra of γ-pga and Zn(γ-pga) complex are shown in Figs. S1–S3. The spectroscopic data are shown in Table S1.

It is noticed that the absorption maxima of Zn(γ-pga) complex in aqueous solution (pH 5) appeared at 258 and 340 nm, whereas an aqueous solution of free γ-pga (1% w/v) showed absorption peak at 265 nm (Fig. S1). Thus, the blueshift (7 nm) of the absorption band at 258 nm and a new band around at 340 nm in the UV region must be ascribed to the transition of electrons associated with the complex formation [15]. Similar phenomenon was also observed in previously reported zinc(II)-ciprofloxacin complex in aqueous solution [21].

The FTIR spectrum of γ-pga (Fig. S2a) revealed strong peaks at 3295 cm−1 for N–H stretching, at 1734 cm−1 for stretching vibration due to the C=O in –COOH group, at 1620–1660 cm−1 for amide I (C=O stretch), and at 1540–1560 cm−1 for amide II (N–H bend) (Table S1). It is noted that the FTIR spectrum of the Zn(γ-pga) complex (Fig. S2b) showed no peak at 1734 cm−1 for the C=O vibration of the carboxylic acid group, indicating that the –COOH group has been deprotonated and coordinated to the metal center. The strong absorption bands of the asymmetrical and symmetrical valency vibrations due to the –COO− group were observed at around 1640 and 1404 cm−1, respectively (Table S1). The relatively large value of ∆[υas(COO−) − υs(COO−)] = 236 cm−1 indicates that the carboxylate anion coordinated to Zn(II) as a monodentate ligand [22]. Similar phenomena were observed in the case of VO(γ-pga) complex in which the carboxylic acid groups of γ-pga were coordinated to the vanadyl ion (VO2+) [13].

Figure S3 shows the 13C NMR spectra of γ-pga and Zn(γ-pga) complex. The 13C NMR spectrum of γ-pga in aqueous solution (pD 5) showed five typical signals at 181.5 ppm for carboxyl carbon, 178.1 ppm for carbonyl carbon, 57.5 ppm for α-carbon, 30.5 ppm for β-carbon, and 35.1 ppm for γ-carbon, respectively (Fig. S3a). On the other hand, the 13C NMR spectrum of Zn(γ-pga) complex in aqueous solution (pD 5) showed five signals at 180.9 ppm for carboxyl carbon, 178 ppm for carbonyl carbon, 57.4 ppm for α-carbon, 30.5 ppm for β-carbon, and 35.2 ppm for γ-carbon, respectively, when the complex was also prepared at the ratio of 1:0.02 of ZnSO4 and γ-pga (final concentration of ZnSO4 1 mmol/L and γ-pga 1.0% w/v). The up-field shift for carboxyl carbon ∆[δ(Zn(γ-pga)) − δ(γ-pga)] = − 0.6 ppm in the complex also suggests coordination of zinc(II) metal ion through the side chain carboxylate groups of the γ-pga although the shift is small. This result can be justified by the fact that the blueshift (7 nm) of the absorption band at 258 nm and a new band at 340 nm (Fig. S1; Table S1) were observed when the Zn(γ-pga) complex was prepared at the ratio of 1:0.02 of ZnSO4 and γ-pga (final concentration of ZnSO4 1 mmol/L and γ-pga 1.0% w/v). Therefore, the spectroscopic data confirm the formation of Zn(γ-pga) in solution as well as in solid state.

Effect of contact time on the binding of zinc(II) ions onto γ-pga in aqueous solution

In order to determine the equilibrium time, the binding of zinc(II) metal ions onto γ-pga was studied as a function of time in aqueous solution at pH 5. The plot of qt versus t is shown in Fig. 2. It is observed that the zinc(II) ions rapidly bound to γ-pga within the first 30–60 min, and thereafter, the rate of binding decreased gradually and reached equilibrium within 300 min. The rapid binding may be due to strong attractive forces between the metal ions and carboxylic groups of γ-pga. When the binding of metal ions on the surface of γ-pga reached saturation, the rate slowed down, and zinc(II) ions started penetrating into the pores of the γ-pga with a slower rate. Therefore, the 360-min duration was maintained as the optimum equilibrium time for further studies.

Fig. 2
figure 2

Plot of binding capacity (qt) versus contact time (t) for the binding of ZnSO4 (1.00 mmol/L) onto γ-pga (0.1% w/v) in aqueous solution pH 5 and temperature 30 °C. Solid line was numerically generated by using pseudo-second-order adsorption kinetic Eq. (5) and the values of qe(cal) and k2 listed in Table 1

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Effect of solution pH on the binding of zinc(II) ions onto γ-pga in aqueous solution

From the physiological point of view, the effect of pH on metal binding is imperative, as the gastrointestinal pH varies widely from 2.5 in the stomach to 7 in the small intestine, due to the presence of a complex mixture of different varieties of minerals and secretions [23]. In addition, the pH of aqueous solution plays a significant role in the binding of zinc(II) onto γ-pga as well as the formation of Zn(γ-pga) complex. At present study, the effect of pH on the binding of zinc(II) ions onto γ-pga was performed in aqueous solution at varying pH 2–9 with 1.00 mmol/L fixed concentration of zinc(II) ions and γ-pga dosage of 0.1% w/v for 360 min. The results are shown in Fig. 3a. The initial rate of metal ion binding, h (mmol/g min) increased significantly with increasing solution pH up to pH 5 (Table 1), and then, it decreased with increasing solution pH 6–8 (Table 1). After 360 min, the extent of equilibrium metal ions binding (qe) onto γ-pga versus solution pH is shown in Fig. 3b. The equilibrium binding capacities of γ-pga were considerably low at pH 2.0 which is less than pKa of γ-pga (~ 4) [24]. The carboxyl groups of γ-pga remained mostly in the non-ionized form, and the binding of Zn2+ onto γ-pga was largely inhibited at pH < 4.0 [23, 25]. The metal ions binding capacity at equilibrium of γ-pga steeply increased from 2.36 to 6.52 mmol/g with increasing pH 2–5 and then decreased in the region of pH 6–8. The maximum amount of Zn2+ ions bound to γ-pga was found to be 6.52 mmol/g in aqueous solution at pH 5. The γ-pga is an anionic polymer possessing numerous carboxyl groups, and a chemical reaction via electrostatic interaction might occur between carboxylate ion (‒COO−) of γ-pga and cationic ion Zn2+. The pKa value of glutamic acid is around 4 [5, 24]. At lower pH (pH < pKa) in which surface sites on the adsorbent were positively charged and unfavorable to the binding of cations due to electrostatic repulsion, the carboxylic acid groups primarily remained in the protonated form and as a result binding of Zn2+ was largely inhibited. Furthermore, the tendency of γ-pga to form intermolecular hydrogen bonds at low pH might cause a more compact α-helical conformation, resulting in a decrease in functional groups available for Zn2+ binding [26, 27].

Fig. 3
figure 3

a The effects of pH on the binding kinetics of zinc(II) ion onto γ-pga in aqueous solution at 30 °C (solution volume: 60 mL; γ-pga: 0.10% w/v; [Zn2+]: 1.00 mmol/L; solution pHs: filled square box: pH 2; open circle: pH 3; filled circle: pH 4; open diamond: pH 5; filled diamond: pH 6; open triangle: pH 7; filled triangle: pH 8). All solid lines were numerically generated by using pseudo-second-order adsorption kinetic Eq. (5) and the values of qe(cal) and k2 listed in Table 1. b The plot of qe versus pH

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Table 1 Comparison of experimental and calculated qe values, and kinetic parameters obtained from various kinetic models applied for the batch binding of zinc(II) ions onto γ-pga in aqueous solution
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At higher pH (pH > pKa), surface sites on the adsorbent were negatively charged and favorable to the binding of cations due to electrostatic interaction. The binding of Zn2+ was largely enhanced due to deprotonation of carboxyl groups on γ-pga accompanied with a conformation transition from a helix to a random coil at the pH 5 [27]. The transition of a helical conformation to random coil conformation might contribute to the increase in the site on γ-pga surface available for Zn2+ binding. The midpoint of the helix–coil transition is around pH 5.1–6.0 [25]. The metal ions binding capacity of γ-pga decreased at equilibrium in the region of pH 6–8 due to the change in coordination mode of zinc(II) ion or due to the formation of Zn(OH)2, where it does not deposit, but remains in solution by hydrophobic interaction. On reaching pH 9, a copious quantity of white precipitate was found due to the formation of Zn(OH)2. Similar phenomenon was observed in the case of zinc complex with poly(α-l-glutamic acid), Zn(α-pga), in aqueous solution studied by polarographic and circular dichroism spectroscopic methods [28]. The author concluded that Zn(II) ions do not bind with α-pga in aqueous solution at pH lower than 3. When pH increases from 5.5 to 7.0, the interaction between α-pga and Zn(II) ions was found more effective, and finally, Zn(OH)2 was formed above pH 7. Thus, the complexation reaction between zinc(II) ion and γ-pga is favorable in aqueous solution at pH 5, and all further studies were performed at solution pH 5.

Effect of initial concentration of metal ions on the binding of zinc(II) ions onto γ-pga in aqueous solution

The effect of initial metal ion concentration on the binding kinetics of zinc(II) ions onto γ-pga was investigated in aqueous solution (pH 5) at room temperature (30 °C). The results are shown in Fig. 4. It is observed that the zinc(II) ion binding was fast for the initial 30 min, and thereafter, it proceeded at a slower rate and finally reached equilibrium. The metal uptake reached equilibrium within 60 min for 0.05 mmol/L and 240 min for 1.00 mmol/L zinc(II) ion solutions, respectively. However, the data were taken for 360 min to ensure that complete equilibrium was established. As the initial concentration of the metal solution was increased from 0.05 to 1.00 mmol/L, the equilibrium binding zinc(II) ions (qe) were increased from 0.74 to 6.65 mmol/g (Table 1). Similar results were also observed in the binding of lead and cadmium onto γ-pga in aqueous solution [24].

Fig. 4
figure 4

The effects of initial metal ion concentration on the binding kinetics of zinc(II) onto γ-pga in aqueous solution (pH 5) at 30 °C (solution volume: 60 mL; γ-pga: 0.10% w/v; [zinc(II)]0: open triangle: 0.05 mmol/L; filled diamond: 0.10 mmol/L; open diamond: 0.25 mmol/L; filled circle: 0.50 mmol/L; open circle: 1.00 mmol/L). All solid lines were numerically generated by using pseudo-second-order adsorption kinetic Eq. (5) and the values of qe(cal) and k2 listed in Table 1

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Effect of temperature on binding of zinc(II) ions onto γ-pga in aqueous solution

Temperature is an important parameter that can influence the equilibrium and rates of binding processes. The kinetics of metal ions binding onto γ-pga was investigated in aqueous solution (pH 5) at four different temperatures, 30, 35, 40, and 45 °C, and the results are depicted in Fig. 5, where the initial concentration of metal solution was 1.00 mmol/L. These results indicate that the initial rate of metal ion binding, h (mmol/g min), and the amount of equilibrium zinc(II) ion binding, qe (mmol/g), increased with increasing the solution temperature from 30 to 45 °C (Table 1). Therefore, the zinc(II) ions interact more efficiently with functional groups of γ-pga at higher temperatures because the mobility of the metal ions increased with rising solution temperature. Mu et al. [29] reported similar phenomena as observed in binding of Pb2+ ion onto γ-pga in aqueous solution.

Fig. 5
figure 5

The effects of temperatures on the binding kinetics of zinc(II) onto γ-pga in aqueous solution (pH 5) (solution volume: 60 mL; γ-pga: 0.10% w/v; [zinc(II)]0: 1.00 mmol/L; temperature: open circle: 30 °C; filled circle: 35 °C; open diamond: 40 °C; filled diamond: 45 °C). All solid lines were numerically generated by using pseudo-second-order adsorption kinetic Eq. (5) and the values of qe(cal) and k2 listed in Table 1

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Modeling of binding kinetics

The binding kinetics illustrates the metal uptake rate onto the γ-pga in binding reaction. This is an essential feature in expressing the efficacy of binding. Various kinetic models have been utilized to investigate the metal ions binding mechanisms in aqueous solutions. Here, pseudo-first-order [30], pseudo-second-order [31], Elovich [32], film diffusion [33], and intraparticle diffusion [34] kinetic models were employed to analyze the binding kinetic data obtained from batch experiments. The pseudo-first-order binding kinetics is usually stated by Eq. (4):

$$ \log \left( {q_{\text{e}} - q_{t} } \right) = \log q_{\text{e}} - \frac{{k_{1} }}{2.303}t, $$
(4)

where k1 (1/min) is the pseudo-first-order sorption rate constant estimated from the slope of a plot log(qe − qt) versus t.

The pseudo-second-order kinetic model is expressed as:

$$ q_{t} = \frac{{k_{2} q_{\text{e}}^{2} t}}{{\left( {1 + k_{2} q_{\text{e}} t} \right)}}, $$
(5)

where k2 (g/mmol min) is the pseudo-second-order binding rate constant calculated from a linearized form of this equation, represented by Eq. (6):

$$ \frac{t}{{q_{t} }} = \frac{1}{{k_{2} q_{\text{e}}^{2} }} + \frac{1}{{q_{\text{e}} }}t. $$
(6)

The plot of t/qt versus t would exhibit a straight line if pseudo-second-order kinetics is applicable. The values of k2 and qe were obtained from intercept and slope of the straight line. The initial rate of binding, h (mmol/g min), is given by Eq. (7):

$$ h = k_{2} q_{\text{e}}^{2} . $$
(7)

The Elovich model is generally expressed as:

$$ q_{t} = \frac{1}{\beta }\ln \left( {\alpha \beta } \right) + \frac{1}{\beta }\ln t, $$
(8)

where α (mmol/g min) is the initial rate of metal binding and β (g/mmol) is associated with the degree of surface coverage and the activation energy for chemisorption. The Elovich coefficients can be estimated from the plot of qt versus ln t.

The values of correlation coefficients (R2) and kinetic parameters obtained from various applied kinetic models are presented in Table 1. The values of R2 obtained from pseudo-first-order (≤ 0.981) and Elovich (≤ 0.990) kinetic models are insignificant compared to the values of R2 (≥ 0.999) found in the cases of pseudo-second-order kinetic model. Moreover, the calculated qe(cal) values from pseudo-second-order kinetic model and the experimental qe(exp) values are comparable (Table 1), suggesting a promising condition for pseudo-second-order binding kinetics, and the carboxylate and amide groups of γ-pga may be predominantly involved in Zn(γ-pga) complex. Similar results were also noted in the binding of lead and cadmium ions onto γ-pga in aqueous solution [23].

The film diffusion model is expressed as:

$$ \ln \left( {1 - F} \right) = - \,k_{\text{fd}} t $$
(9)
$$ F = \frac{{q_{t} }}{{q_{\infty } }}, $$
(10)

where kfd (1/min) is the diffusion rate parameter in film diffusion model, F is the fractional attainment of the equilibrium, and qt (mmol/g) and q∝ (mmol/g) are the amounts of zinc(II) ion adsorbed after t time and infinite time, respectively. Typical plots of ln(1 − F) versus t for zinc(II) adsorption onto γ-pga in aqueous solution are not shown in this paper. The values of film diffusion kinetic parameter (kfd) and R2 obtained from applied model are presented in Table 2.

Table 2 Diffusion rate parameters (kfd, kid1, kid2, and kid3) for the binding of zinc(II) ion onto γ-pga in aqueous solution at various condition
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The intraparticle diffusion model equation can be written as:

$$ q_{t} = k_{\text{id}} t^{0.5} + I, $$
(11)

where kid (mmol/g min0.5) is the intraparticle diffusion rate constant and I (mmol/g) is the intercept. The typical intraparticle diffusion plots for the binding of zinc(II) ions onto γ-pga at various initial metal ion concentrations are shown in Fig. 6. From this figure, it is observed that there were three linear portions. The intraparticle diffusion rate constants, kid1 (mmol/g min0.5), kid2 (mmol/g min0.5), and kid3 (mmol/g min0.5), were calculated from the slope of the corresponding linear regions in Fig. 6. The values of kid1 (mmol/g min0.5), kid2 (mmol/g min0.5), and kid3 (mmol/g min0.5) express diffusion rates of the different stages in the binding (Table 2). The changes of kid1 (mmol/g min0.5), kid2 (mmol/g min0.5) and kid3 (mmol/g min0.5) represent the binding levels of the exterior and interior surfaces of γ-pga [33]. The metal ion binding rate was very fast at the early stage because the zinc(II) ion was adsorbed by the exterior surface of γ-pga. When exterior surface of γ-pga was saturated, then metal ions entered into γ-pga and were adsorbed by the interior surface of the γ-pga with slow diffusion rate. From Fig. 6, it is also be noticed that none of the straight lines at any concentration of metal ion solution passed through the origin, which suggests that the zinc(II) ions binding mechanism was complex and both surface binding as well as intraparticle diffusion contributed to the actual binding process.

Fig. 6
figure 6

Typical intraparticle diffusion model plots for the binding of zinc(II) ions onto γ-pga in aqueous solution (pH 5) at various initial metal ion concentrations (solution volume: 60 mL; γ-pga: 0.10% w/v; temperature: 30 °C; [Zn(II)]0: concentration (filled square box: 0.05 mmol/L; filled diamond: 0.10 mmol/L; filled triangle: 0.25 mmol/L; filled circle: 0.50 mmol/L; asterisk: 1.00 mmol/L). The values of kid1 (mmol/g min0.5), kid2 (mmol/g min0.5) and kid3 (mmol/g min0.5) are listed in Table 2

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Binding isotherm

The analysis of the binding isotherm data is important to know the nature of the interaction between metal ions and the adsorbent used in this study. A plot of qe versus Ce at various temperatures is presented in Fig. 7. The values of qe increased with increasing solution temperature from 30 to 45 °C, indicating that the present binding reaction is an endothermic process.

Fig. 7
figure 7

Binding isotherm of zinc(II) ion onto γ-pga in aqueous solution (pH 5) at various temperatures ([zinc(II)]0: 1–3.5 mmol/L; solution volume: 60 mL; γ-pga: 0.10% w/v; Temperature: open circle: 30 °C; filled circle: 35 °C; open diamond: 40 °C; filled diamond: 45 °C). All solid lines were numerically generated by using the Langmuir model in Eq. (16) and the Langmuir isotherm constants listed in Table 3

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The binding isotherm data were examined by using three isotherm models such as Freundlich [35], Temkin [36], and Langmuir [37]. Nonlinear and linear forms of all the applied models are presented as follows:

Freundlich model:

$$ {\text{Nonlinear form}}\quad q_{\text{e}} = K_{\text{F}} C_{\text{e}}^{{\frac{1}{n}}} $$
(12)
$$ {\text{Linear form}}\quad \ln q_{\text{e}} = \frac{1}{n}\ln C_{\text{e}} + \ln K_{\text{F}} , $$
(13)

Temkin model:

$$ {\text{Nonlinear form}}\quad q_{\text{e}} = \frac{RT}{{b_{\text{T}} }}\ln (K_{\text{T}} C_{\text{e}} ) $$
(14)
$$ {\text{Linear form}}\quad q_{\text{e}} = \frac{RT}{{b_{\text{T}} }}\ln K_{\text{T}} + \frac{RT}{{b_{\text{T}} }}\ln C_{\text{e}} , $$
(15)

Langmuir model:

$$ {\text{Nonlinear form}}\quad q_{e} = \frac{{K_{\text{L}} C_{\text{e}} }}{{\left( {1 + a_{\text{L}} C_{\text{e}} } \right)}} $$
(16)
$$ {\text{Linear form}}\quad \frac{{C_{\text{e}} }}{{q_{\text{e}} }} = \frac{1}{{K_{\text{L}} }} + \frac{{a_{\text{L}} }}{{K_{\text{L}} }}C_{\text{e}} , $$
(17)

where Ce (mmol/L) is the equilibrium metal ion concentration in solution, KF ((mmol/g)(mmol/L)−1/n) and n are the Freundlich isotherm constants indicating the capacity and intensity of the binding, respectively. KT (mmol/L) is the Temkin isotherm constant, bT (J/mol) is a constant related to heat of binding, R (8.314 J/mol K) is an ideal gas constant, and T is the absolute temperature (K). The qe (mmol/g) is the amount of equilibrium metal ions adsorbed per unit weight of adsorbent, KL (L/g), and aL (L/mmol) are the characteristic constants of the Langmuir equation, and the ratio of KL/aL gives the maximum metal ions binding capacity qm (mmol/g) of γ-pga. The values of isotherm parameters are given in Table 3. In all cases, Langmuir isotherm has highest correlation coefficients (R2), which is considerably a better fit compared to Freundlich and Temkin binding isotherms. According to Langmuir, the maximum metal binding capacity of γ-pga was found to be 13.97 mmol/g at 30 °C and 20.58 mmol/g at 45 °C, respectively.

Table 3 Comparison of the binding isotherm parameters obtained from various isotherm models for the Zn(γ-pga) complex
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Activation energy and thermodynamic parameters

The values of k2 at various temperatures recorded in Table 1 were used to estimate the activation energy of the Zn(γ-pga) complex. Assume that the correlation among the rate constant (k2), temperature (T), and activation energy (Ea) follows the Arrhenius equation, which induces the following expression [33]:

$$ \ln k_{2} = - \frac{{E_{\text{a}} }}{RT} + {\text{Constant,}} $$
(18)

where R is the gas constant. The slope of plot of lnk2 versus 1/T (figure not shown; correlation coefficient, R2 = 0.951) was used to evaluate Ea, which was estimated to be 18.23 kJ/mol in temperature range of 30–45 °C. Chemisorption or physisorption mechanisms are often an important indicator to describe the type of interaction between adsorbate and adsorbent. The physisorption processes usually have energies in the range of 4–40 kJ/mol, while higher activation energies (40–400 kJ/mol) suggest chemisorption [33]. Ion exchange and chelation are the mechanisms that govern the zinc adsorption from aqueous solution onto γ-pga. Beside these, the value of Ea (18.23 kJ/mol) indicates that it might be possible a physisorption mechanism to be present, but its importance to be rather low, as suggested by the aforementioned analyses [38].

Thermodynamic parameters related to the binding process, i.e., Gibb’s free energy change (∆G°, kJ/mol), enthalpy change (∆H°, kJ/mol), and entropy change (∆S°, J/mol K), are determined by using the values of Langmuir binding constant (aL, L/mol) and the following equations [39]:

$$ \Delta G^{ \circ } = - \,RT\ln a_{\text{L}} $$
(19)
$$ \ln a_{\text{L}} = \frac{{\Delta S^{ \circ } }}{R} - \frac{{\Delta H^{ \circ } }}{RT}, $$
(20)

where R (8.314 J/mol K) is the universal gas constant and T is the absolute temperature (K). The values of ∆H° and ∆S° can be calculated from the slope and y-intercept of the linear plot of lnaL versus 1/T (R2 = 0.985). The thermodynamic results are presented in Table 4. The enthalpy change (∆H°) indicates that the present binding followed endothermic processes. The positive value of ∆S° confirms the higher translational entropy developed by the displaced water molecules as compared to that lost as a result of metal ions uptake [40]. Negative values of ∆G° indicate that the metal ions binding by γ-pga adsorbent is a spontaneous process and more favorable process at higher temperature. The increase in the binding capacities of γ-pga at higher temperatures may be attributed to the enhanced mobility and penetration of metal ions within the adsorbent porous structures by overcoming the activation energy barrier and enhancing the rate of intraparticle diffusion [40].

Table 4 Thermodynamic parameters (ΔG°, ΔH°, and ΔS°) for the Zn(γ-pga) complex
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Antimicrobial activity of Zn(γ-pga) complex

All the test samples were investigated for their antimicrobial activity against both the gram-negative (i.e., E. coli) and gram-positive (i.e., B. subtilis) bacteria by simple disk diffusion method. Different concentrations of the test sample were used in the antimicrobial analyses. The typical zone of inhibition for each bacteria due to the Zn(γ-pga) complex is shown in Fig. 8. It is noticed that Zn(γ-pga) complex inhibited the growth of both gram-negative (i.e., E. coli) and gram-positive (i.e., B. subtilis) bacteria. The antimicrobial activity of γ-pga, ZnSO4, and Zn(γ-pga) complex against a gram-negative (i.e., E. coli) and a gram-positive (i.e., B. subtilis) is depicted in Fig. 9. The experimental data reveal that ZnSO4 (1.0 mmol/L) and Zn(γ-pga) (0.5 and 1.0 mmol/L) complex showed antimicrobial activity against a gram-negative (i.e., E. coli) and a gram-positive (i.e., B. subtilis) bacteria. However, ZnSO4 (0.5 mmol/L) and γ-pga (0.1% w/v) did not show any antimicrobial activity against a gram-negative (i.e., E. coli) and gram-positive (i.e., B. subtilis) bacteria (Fig. 9). It might be due to the insufficient concentration of ZnSO4 and γ-pga to inhibit the growth of these model bacterial strains [41, 42]. As a result, ZnSO4 (0.5 mmol/L) and the polymer γ-pga (0.1% w/v) have not shown any antibacterial property alone. The maximum antimicrobial activity was observed in Zn(γ-pga) (1.00 mmol/L) complex against a gram-negative (i.e., E. coli) and a gram-positive (i.e., B. subtilis) bacteria.

Fig. 8
figure 8

Determination of antimicrobial of Zn(γ-pga) (0.5 and 1.0 mmol/L) complex against, a gram-negative bacteria (i.e., Escherichia coli), b gram-positive bacteria (i.e., Bacillus subtilis)

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Fig. 9
figure 9

Antimicrobial activity of γ-pga, ZnSO4 and Zn(γ-pga) complex against open square box: gram-negative bacteria (i.e., Escherichia coli), filled square box: gram-positive bacteria (i.e., Bacillus subtilis)

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Determination of MIC (minimum inhibitory concentration) and IC50 (inhibitory concentration 50) value

In order to determine the maximum wavelength (λmax) of bacterial culture, the absorbance of bacterial culture grown overnight was measured at different wavelengths ranging from 560 to 620 nm. Here, the λmax value of bacterial culture was found to be 600 nm. The inhibitory concentration 50 (IC50) value of ZnSO4 and Zn(γ-pga) complex was estimated to be (0.92 ± 0.05) and (0.76 ± 0.03) mmol/L for gram-negative bacteria (i.e., E. coli) (Fig. 10) and (1.17 ± 0.04) and (0.94 ± 0.02) mmol/L for gram-positive bacteria (i.e., B. subtilis) (Fig. 11), respectively.

Fig. 10
figure 10

Absorbance at 600 nm for gram-negative bacteria grown overnight (i.e., Escherichia coli) in the presence of different concentration of ZnSO4 (open circle) and Zn(γ-pga) (filled circle)

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Fig. 11
figure 11

Absorbance at 600 nm for gram-positive bacteria grown overnight (i.e., Bacillus subtilis) in the presence of different concentration of ZnSO4 (open circle) and Zn(γ-pga) (filled circle)

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The IC50 values explain the bacteriostatic as well as the bactericidal activity of the test samples, which is required to inhibit the bacterial growth and multiplication by 50%. It is well known that the absorbance of bacterial culture increased with the increase in concentration of bacteria. Since the samples possess both bacteriostatic and bactericidal activity, the absorbance of bacterial culture was decreased with increasing the sample concentrations (Figs. 10, 11). Therefore, the IC50 values of Zn(γ-pga) in case of gram-negative bacteria (i.e., E. coli) and gram-positive bacteria (i.e., B. subtilis) were the lowest among all other samples, and consequently, it requires less amount of the sample to inhibit the growth of bacteria by 50% to achieve bacteriostatic and bactericidal effects.

Moreover, in the disk diffusion method, it also shows that the antimicrobial activity of the test samples in terms of their zone of inhibition was found up to a certain distance around the disk of placement (Fig. 8), which actually explains the ability of the sample to inhibit the growth of bacteria.

Conclusions

In conclusion, γ-pga is a hydrophilic, biodegradable, non-immunogenic, and naturally available biopolymer which strongly interacts with ZnSO4 to form Zn(γ-pga) complex. A multi-site interaction by complexation mechanism involving carboxylate anion and amide functional groups is proposed for the formation of Zn(γ-pga) complex. The binding kinetics follows pseudo-second-order kinetics. The binding equilibrium follows the Langmuir isotherm model. The maximum amount of zinc(II) ions bound to γ-pga in aqueous solution (pH 5) was estimated to be 20.58 mmol/g at 45 °C. The freshly prepared Zn(γ-pga) complex is found to have potent antimicrobial activity against a gram-negative bacteria (i.e., E. coli) and a gram-positive bacteria (i.e., B. subtilis), respectively. The IC50 value of Zn(γ-pga) complex was found to be (0.76 ± 0.03) mmol/L for gram-negative bacteria (i.e., E. coli) and (0.94 ± 0.02) mmol/L for gram-positive bacteria (i.e., B. subtilis), respectively. Hence, it is proposed that γ-pga can be used as an important carrier for developing Zn(γ-pga) complex as an antimicrobial agent, which can be a potential source of chemical and biologically important drug candidates.