The Study of Zinc Ions Binding to αS1-, β- and κ-Casein

The presented studies focused on the specificity binding of particular casein fractions: αS1-, β- and κ-casein (αS1CN, βCN, κCN), with zinc ions. The binding mechanism was determined by kinetic modeling using results of batch sorption. For this goal, models of zero-order kinetics, pseudo-first-order, pseudo-second-order and Weber–Morris intraparticle diffusion were used. The formation of Zn-αS1CN, Zn-βCN and Zn-κCN complexes was additionally monitored using spectroscopic methods such as Fourier transform infrared spectroscopy (FT-IR) and Raman spectroscopy, characterizing active functional groups involved in the binding process. Additionally, a mass spectrometry technique—matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS)—was used to characterize respective protein fractions and obtained complexes. Spectroscopic and spectrometric studies were carried out both before and after binding the protein with zinc ions. The obtained results showed the difference in Zn-αS1CN, Zn-βCN and Zn-κCN complexes created at separate kinetic stages. On the basis of instrumental studies, a significant influence of acidic (glutamic acid (Glu), aspartic acid (Asp)) and aromatic (tryptophan (Trp), phenylalanine (Phe), tyrosine (Tyr)) amino acids on the formation of metal complexes was proven. In turn, spectrometric studies allowed determining the molecular masses of casein isoforms before and after binding to zinc ions.


Introduction
Casein is recognized as the main cow's milk protein, accounting for about 80% of the total milk protein content [1]. It is not a homogeneous protein but consists of several fractions. The main fractions are α (α S1 , α S2 )-, βand κ-casein (αCN, βCN and κCN). They form colloidal aggregates called micelles in combination with calcium phosphate [2]. The primary role of caseins in milk is to ensure the effective transport of calcium and phosphate from the mammary gland directly to the newborn baby [3]. The main components of casein (αCN, βCN and κCN) form a strong micellar complex stabilized by van der Waals forces, hydrophobic effects, hydrogen bonding and electrostatic and steric stabilization [2]. In addition, micelles are stabilized by physicochemical properties such as the ability of phosphorylated serine residues to bind to calcium ions and the amphiphilic nature of κCN, which is a fraction that is glycosylated and responsible for stabilizing micelles on the surface [4]. The size of micelles varies depending on the amount of specific fractions-mainly κCN-cow feed and season (in summer, the micelles are smaller, and in winter, the opposite is true) [5]. The amount of calcium ions is also mechanism of binding zinc to casein can be a tool in their medical application [28]. Pomastowski and co-authors studied the interaction of zinc ions with casein [9], however, the distribution of the zinc ion binding in various casein fractions was not known.
Hence, the main goal of this study was to explain the binding process of zinc ions to individual casein fractions. Therefore, models of zero-order kinetics, pseudo-first-order, pseudo-second-order and Weber-Morris intraparticle diffusion were applied. This objective has been achieved by previous characterization of individual casein fractions (α S1 CN, βCN, κCN) isolated from cow's milk, and the study of their dispersion stability, isoelectric point and molecular masses. In addition, spectroscopic (FT-IR, Raman) and spectrometric (MALDI-TOF MS) studies were carried out to determine the contribution of the active functional group in the binding process of zinc ions to casein fractions.

Results and Discussion
2.1. Characteristics of α S1 CN, βCN, κCN In order to determine the isoelectric point and to examine protein stability, the zeta potential value was measured for the initial time (t = 1 min), after one hour (t = 1 h) and after five hours (t = 5 h). The zeta potential results of α S1 CN, βCN and κCN as a function of pH (2)(3)(4)(5)(6)(7)(8)(9)(10)(11) are presented in Figure 1. Isoelectric points (pI) for α S1 CN, βCN and κCN were found to be 4.80 ± 0.72, 4.55 ± 2.15 and 4.40 ± 0.28, respectively. The surface charges of all investigated proteins are in the range of −35-+32 mV. In addition, it was observed that with increasing time, the zeta potential values changed and protein stability was noticed after t = 1 h and t = 5 h. At low pH values, the surface charge of proteins was positive and the zeta potentials became more negative with increasing pH. The results show that the more stable proteins are βCN and κCN and the least stable is α S1 CN. The potential values of α S1 CN, βCN and κCN at pH = 2 and pH = 3 were found between +15 and +32 mV, except t = 1 min for α S1 CN, for which the zeta potential was noticed between +3 and +14 mV. Above pH = 3, a decrease in the zeta potential to −20/−30 mV at pH = 5 for each protein was observed. In the case of t = 1 min for α S1 CN, the decrease in the zeta potential occurred from pH = 4 to pH = 6.
The zeta potential provides an indicative measure of dispersion stability. The chemical properties of the surface of the particles affect the zeta potential of each dispersion. The surface chemistry can be modified by changing the pH, surfactant concentration and salt concentration. Therefore, it is important to determine the effect of pH on the zeta dispersion potential [29].
The protein charge is mainly controlled by two processes: (de)protonation of functional surface groups and counter-ions condensation on the protein surface [30]. Farrel et al., 2004 [31], indicated that pI for α S1 CN, βCN and κCN were 4.92-5.05, 5.41 and 5.77, respectively, while according to Egito et al., 2002 [32], the pI values for α S1 CN, βCN and κCN were 4.4-6.3, 4.4-5.9 and 3.5-5.5, respectively. The pI depend on the origin of the sample, the method of determination and the used electrolyte [23]. The zeta potential provides an indicative measure of dispersion stability. The chemical properties of the surface of the particles affect the zeta potential of each dispersion. The surface chemistry can be modified by changing the pH, surfactant concentration and salt concentration. Therefore, it is important to determine the effect of pH on the zeta dispersion potential [29].
The protein charge is mainly controlled by two processes: (de)protonation of functional surface groups and counter-ions condensation on the protein surface [30]. Farrel et al., 2004 [31], indicated that pI for αS1CN, βCN and κCN were 4.92-5.05, 5.41 and 5.77, respectively, while according to Egito et al., 2002 [32], the pI values for αS1CN, βCN and κCN were 4.4-6.3, 4.4-5.9 and 3.5-5.5, respectively. The pI depend on the origin of the sample, the method of determination and the used electrolyte [23].

Kinetic Study of the Zinc Binding Process
Kinetic studies contribute to the understanding of the mechanism of binding casein isoforms (αS1CN, βCN and κCN) with zinc ions. The obtained experimental kinetic data were examined with

Kinetic Study of the Zinc Binding Process
Kinetic studies contribute to the understanding of the mechanism of binding casein isoforms (α S1 CN, βCN and κCN) with zinc ions. The obtained experimental kinetic data were examined with reference to zero-, pseudo-first-and pseudo-second-order kinetic models and the Weber-Morris intraparticle diffusion model. Matching the experimental kinetic data to the models allowed for explaining the rate of the binding of zinc ions to proteins, but also for determining the degree of adsorption of zinc ions on the protein adsorbent. Figure 2A shows the kinetics of the binding process of zinc ions to casein fractions in the form of a plot of concentration of zinc ions in solution per unit of time. For α S1 CN, three steps were identified, while for βCN and κCN, two steps were identified.
Step I in α S1 CN, βCN and κCN is associated with rapid initial sorption. Meanwhile, Step II for βCN and κCN is related to slower sorption and gradual achievement of the sorption equilibrium. A different situation is observed in the case of α S1 CN. Namely, Step II is also associated with gradual sorption, after which Step III appears with an even slower sorption compared to Step II without achieving a state of equilibrium. However, Step II in the case of βCN and κCN is significantly faster compared to α S1 CN. The obtained results indicate that the process of zinc ion sorption for all three proteins: α S1 CN, βCN and κCN, is not linear and several separate steps can be identified. adsorption of zinc ions on the protein adsorbent. Figure 2A shows the kinetics of the binding process of zinc ions to casein fractions in the form of a plot of concentration of zinc ions in solution per unit of time. For αS1CN, three steps were identified, while for βCN and κCN, two steps were identified.
Step I in αS1CN, βCN and κCN is associated with rapid initial sorption. Meanwhile, Step II for βCN and κCN is related to slower sorption and gradual achievement of the sorption equilibrium. A different situation is observed in the case of αS1CN. Namely, Step II is also associated with gradual sorption, after which Step III appears with an even slower sorption compared to Step II without achieving a state of equilibrium. However, Step II in the case of βCN and κCN is significantly faster compared to αS1CN. The obtained results indicate that the process of zinc ion sorption for all three proteins: αS1CN, βCN and κCN, is not linear and several separate steps can be identified. In order to calculate the rate constants of the sorption kinetics of zinc ions for linear segments of the obtained steps, a zero-order kinetics model was used, which describes in detail the successive steps of sorption. The values of the rate constants for Step I in the case of αS1CN, βCN and κCN were noticed to be equal to 3.02, 0.54 and 7.0 (mg/L)/min, whereas they were 0.026, 0,030 and 0.085 (mg/L)/min for Step II, respectively. For Step III in the case of αS1CN, the rate constant was found to be 0.0033 (mg/L)/min. The results are summarized in Table 1, and in Figure 3, the sorption effectiveness per time unit is shown. In order to calculate the rate constants of the sorption kinetics of zinc ions for linear segments of the obtained steps, a zero-order kinetics model was used, which describes in detail the successive steps of sorption. The values of the rate constants for Step I in the case of α S1 CN, βCN and κCN were noticed to be equal to 3.02, 0.54 and 7.0 (mg/L)/min, whereas they were 0.026, 0.030 and 0.085 (mg/L)/min for Step II, respectively. For Step III in the case of α S1 CN, the rate constant was found to be 0.0033 (mg/L)/min. The results are summarized in Table 1, and in Figure 3, the sorption effectiveness per time unit is shown.
A pseudo-first-and pseudo-second-order kinetic model was applied to the experimental data as well ( Figure 2B). The calculated values of the determination coefficient (R 2 ) and standard deviation (S) indicated a more accurate description of the kinetics of the sorption of zinc ions to casein proteins by means of a pseudo-second-order kinetics model. The obtained values of the determination coefficient for α S1 CN and βCN, in comparison to κCN, in the case of both pseudo-second-order kinetics models, indicate low values of the determination coefficient to the obtained experimental results. The not accurate fitting of α S1 CN and βCN to the classical kinetics model determines the contradictory nature of metal ions sorption in comparison to the glycosylated form of κCN. The calculated kinetic constants are summarized in Table 1. The fast sorption step (Step I) for the two proteins: α S1 CN and κCN, occurs during the first 2 min of the process, in which 23.88 ± 0.21% of zinc ions were bound to α S1 CN and the sorption capacity of the protein was 2.41 ± 0.02 mg/g, while for κCN, these values increased slightly and amounted to 55.41 ± 0.13% and 5.60 ± 0.00 mg/g, respectively. For Step I, in the case of βCN, the effectiveness of binding to protein was 42.88 ± 0.20% and the amount of zinc ions absorbed on the protein was 4.33 ± 0.02 mg/g. The sorption process in Step II in the case of α S1 CN, βCN and κCN ends after 180, 60 and 20 minutes, respectively. The sorption effectiveness of zinc ions by casein isoforms for this step was 42.08 ± 1.31%, 47.62 ± 0.72% and 61.48 ± 0.32%; the sorption capacity was found to be 4.25 ± 0.14, 4.81 ± 0.08 and 6.21 ± 0.05 mg/g. In the last step, Step III, the sorption process for αCN is completed after an incubation period of 1440 min, with a sorption effectiveness of 58.31 ± 1.31% and a sorption capacity of 5.89 ± 0.12 mg/g. The maximum sorption effectiveness and sorption capacity of α S1 CN, βCN and κCN were 58.31 ± 1.31% and 5.89 ± 0.12 mg/g (α S1 CN), 51.05 ± 0.97% and 5.16 ± 0.11 mg/g (βCN) and 67.81 ± 0.30% and 6.85 ± 0.05 mg/g (κCN). Table 1. Kinetic model parameters for the zinc ions sorption by α S1 CN, βCN and κCN and values of the distribution coefficient and the Gibbs' free energy change of the metal ions sorption.

Zn-α S1 CN Zn-βCN
Zn-κCN  A pseudo-first-and pseudo-second-order kinetic model was applied to the experimental data as well ( Figure 2B). The calculated values of the determination coefficient (R 2 ) and standard deviation (S) indicated a more accurate description of the kinetics of the sorption of zinc ions to casein proteins by means of a pseudo-second-order kinetics model. The obtained values of the determination coefficient for αS1CN and βCN, in comparison to κCN, in the case of both pseudo-second-order kinetics models, indicate low values of the determination coefficient to the obtained experimental results. The not accurate fitting of αS1CN and βCN to the classical kinetics model determines the contradictory nature of metal ions sorption in comparison to the glycosylated In order to determine the mechanism involved in the process of binding zinc ions to casein isoforms, experimental data were also subjected to the Weber-Morris intraparticle diffusion model ( Figure 2C). The Weber-Morris model revealed two steps of sorption.
Step I was attributed to adsorption on the external surface of proteins or diffusion of zinc ions through the boundary layer as well as a sharp drop in zinc ion concentration. In turn, Step II corresponds to intraparticle diffusion that limits the speed of the process, thus indicating the absorption of zinc ions into the protein structure. In the final step, a sorption equilibrium was noticed. The Weber-Morris model revealed that zinc ions are mainly adsorbed on the external surface of casein isoforms. Then, gradual sorption of zinc ions causes their further diffusion inside the proteins structure.
In addition, the values of the change of Gibbs' free energy (∆G 0 ) and the distribution coefficient (K d ) of sorption of zinc ions to α S1 CN, βCN and κCN were calculated, which were found to be −15.52 kJ/mol and 559.49, −14.80 kJ/mol and 417.25 and −16.52 kJ/mol and 842.62, respectively. Negative values of Gibbs' free energy for α S1 CN, βCN and κCN confirm that the process of zinc ion binding to these proteins is spontaneous. The obtained values are presented in Table 1.
The obtained results indicate that at the initial stage of rapid sorption, 1 mole of α S1 CN, βCN and κCN sorbed 0.86 (α S1 CN), 1.59 (βCN) and 1.63 (κCN) mole of zinc ions. It turns out that according to the Weber-Morris model, most zinc ions are surface-bound to κCN and the least to α S1 CN. The situation changes rapidly in a second, slower stage, namely, per one mole of α S1 CN, βCN and κCN, 2.12, 1.76 and 1.81 mole of zinc ions is sorbed, respectively. This shows that zinc ions are further diffused and absorbed to the greatest extent into the internal structure of α S1 CN. These results are consistent with the assumptions of the models characterizing casein micelles, where κCN constitutes the outer shell of the micelles, and α S1 CN is localized in the interior of the casein micelle [14]. Assuming that the synthesis of the binding of zinc ions with individual casein fractions is completed with a state of equilibrium (except for α S1 CN) after external adsorption steps and penetration of zinc ions into the internal structure of proteins, κCN binding zinc ions on the external surface is the most spontaneous reaction (∆G 0 = −16.52 kJ/mol).

Spectroscopic Analysis
Spectral characteristics of unmodified (control) α S1 CN, βCN and κCN as well as the zinc ion-modified ones were determined to establish active chemical groups involved in the zinc ion binding process. The resulting FT-IR spectrum is shown in Figure 4. The obtained FT-IR spectra prove that zinc binding influences the spectrum of individual caseins in infrared. It was observed that after binding zinc to casein, the intensity of selected bands was significantly reduced and the appearance of the spectra changed.
As a result of NH stretching vibrations, the amide band A was observed in the range of 3429-3100 cm −1 . Its frequency depends on the strength of the hydrogen bond. The amide A band is usually part of Fermi's resonance double [33]. For unmodified proteins, a shift appeared from 3301 (α S1 CN) to 3289 cm −1 (βCN and κCN). On the other hand, comparing the unmodified proteins ( Figure 4A) with Zn-protein complexes (modified, Figure 4B), the shift occurred from the bands of about 3289 to 3429 cm −1 , respectively.
The spectral range between 3000 and 2840 cm −1 is dominated by the absorption of hydrophobic hydrocarbons residue [34]. After binding proteins with zinc ions, bands in the respective region are visible only for the Zn-κCN complex.
The FT-IR spectrum is dominated by the protein amide I (~1650 cm −1 ) and amide II (~1550 cm −1 ) bands, mainly due to the C=O stretching and the NH bending of the peptide bond. The amide I band is extremely sensitive to secondary protein structures (α-helix, β-sheets, random coils) and to the presence of intermolecular β-sheets in protein aggregates [34]. According to Herskovits and co-authors' [35] studies, the percentage of α-helix in α S1 CN is estimated at 5-15%, and comparable values of α-helix occur in βCN-7-25%, and κCN-10-20% [4,35]. The percentage of β-sheet in α S1 CN is between 18 and 20% [36] and 34 and 46% for β-sheet-like [37]. Both α S1 CN and βCN have around 20-30% turns. The turns are clearly distinguishable from what are commonly called undefined, random or structureless [36]. For βCN, the presence of 15-33% β-sheet has been reported and in the case of κCN, 20-30% of β-structure has been reported [36]. Comparison of the unmodified (control) proteins and zinc-protein complexes for amide I resulted in a shift from the bands of 1650 (control, Figure 4A) to 1633, 1632 and 1635 cm −1 (α S1 CN, βCN and κCN, respectively, Figure 4B). In addition, amide I vibrations, absorbing nearly 1650 cm −1 , also originate from the stretching vibrations of C=O with a small proportion of CN out-of-phase stretching vibrations, CN deformation and bending in the NH plane. Amide I vibrations are slightly dependent on the nature of the side chain [33]. In amide II, there is an out-of-phase NH in the bend flat, CN stretching vibrations and CN stretching vibrations with less CO in the plane bend and CC and NC stretching vibrations [34]. For amides II, shifts between control proteins and Zn-protein complexes were observed from 1540 (α S1 CN,), 1539 (βCN) and 1544 (κCN) ( Figure 4A) to 1548 (Zn-α S1 CN), 1549 (Zn-βCN) and 1546 (Zn-κCN) cm −1 ( Figure 4B). Signals at 1400 cm −1 from amino acid side chains in peptides and proteins are related to CH 3 asymmetrical and symmetrical bending vibrations [38].The band in this range corresponds to proline (Pro), the amino acid most commonly found both in βCN and κCN, representing 16.7% and 11.8%, respectively, which can make a significant contribution to the binding with zinc ions [33]. However, the bands at~1540 and 1400 cm −1 may also be assigned to the deprotonated carboxylic groups COO − asparagine (Asp) and glutamine (Glu) residues [39]. The most Glu is contributed by α S1 CN representing 12.6% of total amino acid residues, being the most common amino acid, followed by βCN at 9.1%, and κCN at 7.1%. Therefore, the binding of zinc ions to α S1 CN, βCN and κCN can be carried out by coordinating with the oxygen of the side chain Asp and Glu [40,41].  As a result of NH stretching vibrations, the amide band A was observed in the range of 3429-3100 cm −1 . Its frequency depends on the strength of the hydrogen bond. The amide A band is usually part of Fermi's resonance double [33]. For unmodified proteins, a shift appeared from 3301 (αS1CN) to 3289 cm −1 (βCN and κCN). On the other hand, comparing the unmodified proteins ( Figure 4A) with Zn-protein complexes (modified, Figure 4B), the shift occurred from the bands of about 3289 to 3429 cm −1 , respectively.
The spectral range between 3000 and 2840 cm −1 is dominated by the absorption of hydrophobic hydrocarbons residue [34]. After binding proteins with zinc ions, bands in the respective region are visible only for the Zn-κCN complex. The spectral area 1500-1200 cm −1 also includes the area of amide III bands, resulting from bending NH and stretching CN [34]. For the band at about 1401 cm −1 corresponding to unmodified βCN, a slight change was observed as opposed to unmodified α S1 CN and κCN (1398 and 1399 cm −1 , respectively). However, the bands 1398, 1399 and 1401 cm −1 , corresponding to unmodified α S1 CN, κCN and βCN, respectively, after binding to zinc ions are shifted to 1402 cm −1 for all proteins. Moreover, for unmodified βCN and κCN, a new band at 1369 cm −1 (not see in α S1 CN) appeared with a slight shift of κCN to 1379 cm −1 . After binding of proteins to zinc ions, a shift in the 1369 to 1362 cm −1 band for βCN was observed and a new 1362 cm −1 band for α S1 CN and κCN was noticed. The bands occurring at~1240 and~1079 cm −1 are caused by the asymmetrical and symmetrical stretching of ionized PO 2-, respectively [38]. The control protein bands 1241 (α S1 CN) and 1240 cm −1 (βCN, κCN) were slightly shifted in complexes to 1240 cm −1 for α S1 CN, 1236 cm −1 for βCN and 1232 cm −1 for κCN. In turn, the bands 1079 (βCN, κCN) and 1077 cm −1 (α S1 CN) were shifted to 1051 (α S1 CN, κCN) and 1081 cm −1 (βCN) after binding to zinc ions. For βCN (unmodified, Figure 4A), a new 1207 cm −1 signal was registered, while for α S1 CN (unmodified) at 1173 cm −1 , a shift to 1163 cm −1 for βCN and κCN (unmodified) was observed. However, comparing these signals (1173, 1163 cm −1 ) with the signals obtained after binding with zinc ions (1136 cm −1 for α S1 CN and κCN, 1139 cm −1 for βCN), a shift occurs. For the Zn-βCN complex ( Figure 4B), two new 1108 and 1100 cm −1 bands were observed. In the case of control proteins ( Figure 4A), the bands 975, 978 and 978 cm −1 (α S1 CN, βCN and κCN, respectively) corresponding to the −PO 3 2− moiety of the serine phosphate residue were observed. For complexes ( Figure 4B), there was a shift in the bands to a value of about 998 (Zn-α S1 CN, Zn-κCN) and 981 cm −1 (Zn-βCN) to assign the phosphate ions HPO 4 2-. The presence of the 978 cm −1 band means that CCP (colloidal calcium phosphate) molecules are released from the phosphate residues, causing an increase in the negative charge of casein particles. The appearance of the first band (~978 cm −1 ) suggests that the CCP particle dissociates into Ca 2+ and HPO 4 2− when the serine phosphate residue is released [42].
In α S1 CN, there are two phosphorylation centers containing serine (Ser), which is 8.0% and crucial for stabilizing calcium phosphate nanoclusters in casein micelles [4]. These changes may indicate the binding of zinc ions to casein fractions with phosphate ions. All shifts and appearances of new signals, especially in the range of 1650-978 cm −1 , occurring in the obtained complexes are correlated with metal-protein binding.
Moreover, the use of Raman spectroscopy allowed the observation of vibrational spectra. The Raman spectra provided complementary information to that obtained by IR spectroscopy that showed that apart from carboxylic and phosphate groups, aromatic amino acids also play an important role in metal-protein interaction. The Raman spectra were registered in the 400-4000 cm −1 frequency range and are shown in Figure 5.
The Raman protein spectra are dominated by bands associated with the main peptide chain, aromatic side chains and sulphur-containing side chains, and therefore are group vibrations that are either multiple related or electron-rich such as C=O, C=N, C=C, S-S, S-C and S-H. Therefore, changes may result in βCN being similar to complexes rather than to other control proteins [43]. Polar functional groups are characterized by stronger signals in the infrared spectrum, while non-polar functional groups are associated with more intense Raman bands [44]. Figure 5A represents the Raman spectra of unmodified protein fractions. Comparing the spectra for unmodified proteins fractions (α S1 CN, βCN, κCN), similarities were observed in the case of α S1 CN and κCN, while βCN indicated large differences in the shape of the registered bands. Raman bands in the range 2428-3381 cm −1 were assigned to bond CH (CH 2 , CH 3 ), -C-H or =C-H stretch [44]. For the bands 3380 (α S1 CN) and 3381 cm −1 (κCN), a shift was observed for βCN to 3293 cm −1 (Figure 5A), while after binding to zinc ions ( Figure 5B), a shift was observed to 3260, 3255 and 3258 cm −1 for α S1 CN, βCN and κCN, respectively. For unmodified βCN, the 3058 cm −1 band was observed, which is not found in unmodified α S1 CN and κCN. However, after binding to zinc ions, this band (3058 cm −1 ) is present in all complexes. Shifts were also observed between bands for unmodified proteins-2971 (κCN), 2966 (α S1 CN) and 2930 cm −1 (βCN). After binding of proteins to zinc ions, the absorbance of those bands was similar to unmodified βCN (2929 cm −1 for Zn-βCN and Zn-κCN, 2932 cm −1 for Zn-α S1 CN). Similarly, it was observed in the case of bands 2818 and 2718 cm −1 (α S1 CN), 2820 and 2718 cm −1 (κCN) and 2876 and 2725 cm −1 (βCN) that, after binding, they corresponded to the value of unmodified βCN bands (2875, 2723 cm −1 for complexes). The Raman protein spectra are dominated by bands associated with the main peptide chain, aromatic side chains and sulphur-containing side chains, and therefore are group vibrations that are either multiple related or electron-rich such as C=O, C=N, C=C, S-S, S-C and S-H. Therefore, changes may result in βCN being similar to complexes rather than to other control proteins [43]. Polar functional groups are characterized by stronger signals in the infrared spectrum, while non-polar functional groups are associated with more intense Raman bands [44]. Figure 5A represents the Raman spectra of unmodified protein fractions. Comparing the spectra for unmodified proteins fractions (αS1CN, βCN, κCN), similarities were observed in the case of αS1CN and κCN, while βCN indicated large differences in the shape of the registered bands. Raman bands in the range 2428-3381cm −1 were assigned to bond CH (CH2, CH3), -C-H or =C-H stretch [44]. For the bands 3380 (αS1CN) and 3381 cm −1 (κCN), a shift was observed for βCN to 3293cm −1 (Figure 5A), while after binding to zinc ions ( Figure 5B), a shift was observed to 3260, 3255 and 3258 cm −1 for αS1CN, βCN and κCN, respectively. For unmodified βCN, the 3058 cm −1 band was observed, which is not found in unmodified αS1CN and κCN. However, after binding to zinc ions, this band (3058 cm −1 ) is present in all complexes. Shifts were also observed between bands for unmodified proteins-2971 (κCN), 2966 (αS1CN) and 2930 cm −1 (βCN). After binding of proteins to zinc ions, the absorbance of those bands was similar to unmodified βCN (2929 cm −1 for Zn-βCN and Zn-κCN, 2932 cm −1 for Zn-αS1CN). Similarly, it was observed in the case of bands 2818 and 2718 cm −1 (αS1CN), 2820 and 2718cm −1 (κCN) and 2876 and 2725 cm −1 (βCN) that, after binding, they corresponded to the value of unmodified βCN bands (2875, 2723 cm −1 for complexes).
The spectra registered at amide and amino acids region 500-1655 cm −1 illustrate the changes between the modified samples and unmodified. The signals noticed at 1663/1665 cm −1 correspond to the C=O stretching mode associated with the CONH protein group (amide I) [45,46], but the bands registered at 1600 and at 1613/1616 cm −1 are generated by Tyr-OH [45]. In turn, the 1455 cm −1 band is The spectra registered at amide and amino acids region 500-1655 cm −1 illustrate the changes between the modified samples and unmodified. The signals noticed at 1663/1665 cm −1 correspond to the C=O stretching mode associated with the CONH protein group (amide I) [45,46], but the bands registered at 1600 and at 1613/1616 cm −1 are generated by Tyr-OH [45]. In turn, the 1455 cm −1 band is assigned to the NH deformation and CN stretching [46] in amide II. The common bands (1663/1665, 1613/1616, 1550, 1445/1446, 1315/1317, 1244, 1120 and 1002 cm −1 ) have been also noticed for the modified α S1 CN and βCN protein samples. The bands 1665, 1616, 1446, 1315 and 1002 cm −1 were also observed for modified κCN, while bands 1550 and 1244 cm −1 for modified κCN disappeared. The 1120 cm −1 band corresponding to modified α S1 CN and βCN for modified κCN has been shifted to 1098 cm −1 . Disappearance of the band also occurred for unmodified α S1 CN and κCN at 1665 cm −1 and βCN at 1600, 1565 and 1123 cm −1 . However, the 1411 cm −1 band for unmodified α S1 CN and κCN for unmodified βCN disappeared, and after binding with zinc ions, this band with a shift to 1420 cm −1 occurred only for κCN. The mentioned bands, 1002 cm −1 for Zn-α S1 CN, Zn-βCN and Zn-κCN for unmodified proteins, are shifted to 986 (α S1 CN), 987 (κCN) and 1001 cm −1 (βCN). The 1002 cm −1 band ( Figure 5B) corresponds to phenylalanine (Phe) [47]. This amino acid constitutes about 4.0% of the total of residues in α S1 CN, 4.3% in βCN and 2.4% in κCN and may be responsible for protein binding with zinc ions. The new signals were observed at 1206 and 852 cm −1 only for the modified α S1 CN.
The Raman's spectra illustrate the amide region III (1200-1340 cm −1 ), including C-N tension and N-H bending [48]. The signal observed at 1306/1315 cm −1 is assigned to the alanine (Ala) bands. The band registered at 1235/1244 cm −1 corresponds to the CH 2 carbohydrate twisting mode. The most important current vibration modes have been assigned to CO stretching and deformation of CC and COH (1120-1064 cm −1 ), as well as deformation of COC (950-870 cm −1 ) [46]. What is more, the bands at 852, 830 and 642 cm −1 can correspond to the tyrosine (Tyr) vibration [45] and the bands 758 and 556 cm −1 to the tryptophan (Trp) [45]. The regions 630-670 cm −1 and 700-745 cm −1 found in α S1 CN and κCN control and Zn-α S1 CN complex originate from C-S stretch cysteine and methionine [44]. The occurrence of residues of Cys11 and Cys88 results in the formation of a complex disulphide bond pattern among κ-CN molecules, with all possible combinations being observed (Cys11-Cys11, Cys11-Cys88 and Cys88-Cys88). There is also a certain amount of monomeric κCN associated with an intramolecular disulphide bond, but it is no more than 10% κCN [49]. In turn, the 564 and 755 cm −1 bands are assigned to the tryptophan (Trp) residues [45], which occupy about 1% [4]. Signal shifts in complexes may indicate their participation in the bond with zinc ions.
Similarly, kinetic and spectroscopic studies on the binding of zinc ions to casein carried out by Pomastowski et al. indicate the dominant presence of carboxyl groups Asp and Glu and phosphate groups involved in the binding [9]. In turn, studies on the binding of zinc ions to αCN carried out by Srinivas and Prakash [10] indicate the initial binding to serine phosphates. The binding process is fast, while the affinity of the binding is weak and does not cause any structural changes. However, further reaction with zinc ions leads to binding with aromatic amino acids, including Trp [10]. Zinc binding causes the rearrangement of the secondary protein structure and increases orderliness. It was also observed in the quenching of intrinsic αCN fluorescence by zinc interacting with histidine (His), glutamic acid (Glu), aspartic acid (Asp) and cysteine (Cys) [10]. The presence of Asp and Glu carboxylic groups has also been found in the case of silver to lactoferrin (LTF) binding [23]. The potential binding sites were determined by means of molecular dynamics simulations, which were consistent with and complemented the instrumental studies carried out. For caseins, which are non-crystalline proteins, their total primary and partially secondary structures are known, but homologous proteins with a known crystallographic structure are unavailable. In Kumosiński et al., 1991 [50], an attempt was made to construct a three-dimensional κCN structure using molecular modeling, and the structures obtained were preliminary models. Additionally, despite the fact that the computational approach allows for studying the processes and properties of proteins, there are limitations to the possibility of obtaining accurate parameters that would allow for studying posttranslational modifications (PTMs), which are crucial in caseins' structure [51]. The proposed casein models require additional validation using other approaches and deserve further investigation, which will be our goal in future studies.

Spectrometric Analysis
Studies on control proteins (unmodified) before binding with zinc ions were performed for three casein fractions obtained during chromatographic separation in our previous studies [52]. To determine the masses of casein isoforms both before and after binding of zinc ions, the analysis of intact proteins was carried out using MALDI-TOF MS ( Figure 6).
The masses of intact casein isoforms were found to be 23,985.874 ± 0.326 and 19,032.393 ± 0.326 m/z for βCN and κCN, respectively. In the case of α S1 CN, two overlapping signals were observed. These signals correspond to values 23,530.363 ± 0.326 and 23,604.819 ± 0.326 m/z. According to the literature data, the registered signals are coming from different genetic forms of α S1 CN [53,54].
The respective signals appeared in the sample after zinc ions binding (Zn-α S1 CN complex) at 23,507.614 and 23,597.329 m/z. This difference is connected to the degradation of some parts of the protein structure during the zinc ions binding process. Compared to the unmodified protein (control), in the case of the Zn-α S1 CN complex, a new signal has been observed (8661.218 and 9257.008 m/z). This observation is the result of protein decay to the more hydrophobic fragments, e.g., 8661.218 and 9257.008 m/z ( Figure 6). A different situation was observed in the case of the βCN protein.
The characteristic signal registered at 23,985.874 ± 0.326/23 and 982.382 ± 0.326 m/z was noticed in both the unmodified and modified βCN protein. Moreover, in the case of the Zn-βCN complex, a new signal with the m/z ratio of 8025.292 m/z has been noticed. This signal indicates that hydrophilic zinc ions bind to the hydrophobic protein through indirect interaction with oxygen from water. βCN is more hydrophobic than other casein isoforms. This is due to a negative net charge in the N-terminal with five phosphoserylic and hydrophobic C-terminal residues [55]. In the case of the κCN protein, which is the smallest of the caseins, the signal is suppressed (in comparison with the control signal 19,032.393 m/z) after binding to the zinc ions. Perhaps it is an effect of glocosylation occurring only in κCN. The κCN is a glycoprotein sensitive to the proteinase (chymosin) site, which causes cleavage of the glycoprotein into two parts: the N-terminal para-κ-casein domain and the C-terminal domain of κ-casein with macroglyceride, which is highly heterogeneous in terms of oligosaccharide content [56]. determine the masses of casein isoforms both before and after binding of zinc ions, the analysis of intact proteins was carried out using MALDI-TOF MS ( Figure 6). The masses of intact casein isoforms were found to be 23,985.874 ± 0.326 and 19,032.393 ± 0.326 m/z for βCN and κCN, respectively. In the case of αS1CN, two overlapping signals were observed. These signals correspond to values 23,530.363 ± 0.326 and 23,604.819 ± 0.326 m/z. According to the literature data, the registered signals are coming from different genetic forms of αS1CN [53,54].
The respective signals appeared in the sample after zinc ions binding (Zn-αS1CN complex) at 23,507.614 and 23,597.329 m/z. This difference is connected to the degradation of some parts of the protein structure during the zinc ions binding process. Compared to the unmodified protein (control), in the case of the Zn-αS1CN complex, a new signal has been observed (8661.218 and 9257.008 m/z). This observation is the result of protein decay to the more hydrophobic fragments, e.g., 8661.218 and 9257.008 m/z ( Figure 6). A different situation was observed in the case of the βCN protein. The characteristic signal registered at 23,985.874 ± 0.326/23 and 982.382 ± 0.326 m/z was noticed in both the unmodified and modified βCN protein. Moreover, in the case of the Zn-βCN complex, a new signal with the m/z ratio of 8025.292 m/z has been noticed. This signal indicates that hydrophilic zinc ions bind to the hydrophobic protein through indirect interaction with oxygen from water. βCN is more hydrophobic than other casein isoforms. This is due to a negative net charge in the N-terminal with five phosphoserylic and hydrophobic C-terminal residues [55]. In the case of the κCN protein, which is the smallest of the caseins, the signal is suppressed (in comparison with the control signal 19,032.393 m/z) after binding to the zinc ions. Perhaps it is an effect of glocosylation occurring only in κCN. The κCN is a glycoprotein sensitive to the proteinase (chymosin) site, which causes cleavage of the glycoprotein into two parts: the N-terminal para-κ-casein domain and the C-terminal domain of κ-casein with macroglyceride, which is highly heterogeneous in terms of Figure 6. Mass spectra of intact standard solutions of α S1 CN, βCN, κCN and their complexes with zinc ions (Zn-α S1 CN, Zn-βCN, Zn-κCN). The casein fractions (α S1 CN, βCN, κCN) used in present study have been previously separated and identified by our research group according to Pomastowski et al. [52] using high-performance liquid chromatography (HPLC) and MALDI-TOF MS techniques, respectively. In the current research, the isolated fractions were used to continue the study by the investigation of the mechanism of binding zinc ions with the obtained casein fractions.

Isoelectric Point Determination
The isoelectric point of casein isolated from milk was determined by the diffraction light scattering technique (Zetasizer, Malvern Instruments, Malvern, UK). The protein was suspended in 0.09% sodium chloride solution (Sigma-Aldrich, Warszawa, Poland) in the range of pH 2-11, sonicated for 10 s and analyzed using the DTS1070 cuvette (Malvern Panalitycal). All the measurements were performed in three repetitions.

Kinetic Study of Zinc Ions Binding to α S1 CN, βCN and κCN
For the kinetic studies, the samples were prepared by mixing α S1 CN, βCN, κCN and zinc nitrate (V) (Sigma-Aldrich, Warszawa, Poland) solutions at a ration of 1:1 (v/v) with the final concentration of 5000 and 25 mg/L. The protein samples were suspended in 0.09% sodium chloride at pH = pI. Then, the samples were incubated at 4 • C and analyzed after a certain period of time: 2, 5, 10, 20, 30, 45, 60, 80, 140, 180 and 1440 min, and centrifuged (12,000 rpm, 10 min). Part of the supernatant was mineralized in aqua regia and diluted to 1% nitric acid (V) (Sigma Aldrich, Poland). The concentration of zinc ions was determined by inductively coupled plasma-mass spectrometry ICP-MS (7900 ICP-MS, Agilent Technologies).
To explain the mechanism of zinc ion sorption by casein isoforms, zero kinetics, pseudo-firstand pseudo-second-order kinetics models, and intraparticle diffusion models were used to analyze the results.
The kinetic models were expressed with the following formulas: • The zero-order kinetics model: • The pseudo-first-order kinetics model: where: q t -the amount of zinc ions sorbed for a certain period of time [mg/g], q e -the amount of zinc sorbed at equilibrium [mg/g], and k 1 -the rate constant of the pseudo-first-order sorption kinetics [1/min].

•
The pseudo-second-order kinetics model: where: k 2 -the rate constant of the pseudo-second-order sorption kinetics [(g/mg)/min].
• The Weber-Morris intraparticle diffusion model: where: A-a constant indicating the thickness of the boundary layer diffusion or external surface adsorption [mg/g], and K ip -the intraparticle diffusion rate constant [(mg/g)/min 0.5 ] The amount of zinc sorption by casein isoforms from an aqueous solution (for experimental data) was determined as follows: where: V-the volume of solution from which sorption occurs [L], and m-the sorbent mass [g].
Additionally, the distribution coefficient (K d ) of zinc ions sorption by α S1 CN, βCN and κCN and Gibbs' free energy for zinc adsorption were calculated.
The following equations were used: where: q e -the amount of zinc sorbed by casein isoforms at equilibrium time [mg/g], and C e -the equilibrium concentrations of zinc in solution [mg/L].
where: ∆G 0 -the energy of adsorption [kJ/mol], R-the gas constant (8.314 J/mol·K), T-the adsorption absolute temperature (295 K), and K d -the distribution coefficient.

Spectroscopic and Spectrometric Analysis
For the FT-IR, Raman and MALDI-TOF MS studies, the complexes were prepared by mixing α S1 CN, βCN, κCN and zinc nitrate (V) (Sigma-Aldrich, Warszawa, Poland) solutions at a ration of 1:1 (v/v) with the final concentrations of 5000 and 25 mg/L. The protein samples were suspended in 0.09% sodium chloride at pH = pI. Then, the samples were incubated at 4 • C for 24 h (because, after this time, we are sure that the metal-protein binding will take place). After the incubation time, the samples were centrifuged (12,000 rpm, 10 min). The supernatant was removed and the resulting sediment was lyophilized and submitted to further spectroscopic and spectrometric analyses. In turn, isolated CN (control) was prepared by dissolving in distilled water.
3.3.1. Fourier Transform Infrared Spectroscopic (FT-IR) and Raman Spectroscopy (Raman) Analysis of α S1 CN, βCN and κCN Spectroscopic methods (FT-IR, Raman) have been used as techniques for analyzing the changes of the active functional group and the secondary structure of the protein system. Spectra in FT-IR analysis were recorded by using a Spectrum 2000 from Perkin-Elmer, Waltham, MA, and were recorded in the MIR range from 400 to 4000 cm −1 , and 15 scans were averaged at a resolution of 4. The samples were prepared in three repetitions by grinding them with potassium bromide powder (KBr) and pressed into a disc.
The Raman signals were recorded with the Raman Spectrometer (Senterra, Bruker Optik) in a spectral range of 400-4000 cm −1 with an integration time of 3 × 30 s using a 532 nm laser excitation, at 20 × 5 mW power, in combination with 10 fM accumulation. The samples were prepared in three repetitions by direct application of the sample on a microscope slide.
All spectra were processed using ORIGIN software.

Matrix-Assisted Laser Desorption Ionization−Time of Flight Mass Spectrometry
(MALDI-TOF/TOF-MS) Analysis before and after Zing Binding to Isoforms of Casein MALDI mass spectra were acquired using a Bruker UltrafleXtreme II mass spectrometer provided with 2 kHz speed in TOF mode and 1 kHz speed in TOF/TOF mode equipment with a modified Nd:YAG laser operating at the wavelength of 355 nm. For MALDI-TOF MS analysis of the intact proteins before and after binding of zinc to isoforms of casein, samples were prepared according to the dried droplet method using sinapinic acid (SA) as matrix, and next, the samples were applied to ground steel. In turn, Protein Calibration Standards II was selected for calibration. Spectra were obtained in linear positive ion mode over an m/z range of 5000-100,000.

Conclusions
This study describes for the first time the mechanism of binding zinc ions to individual casein fractions, causing the formation of complexes, and thus indicating the precise contribution of individual fractions to the binding. The performed kinetic studies of the binding of zinc ions with α S1 CN, βCN and κCN indicate a heterogeneous kinetic process carried out in three steps for Zn-α S1 CN, Zn-βCN and Zn-κCN. The initial stage is associated with rapid initial sorption, the second stage with moderate sorption and the third stage with gradual achievement of the sorption equilibrium. Experimental data subjected to the Weber-Morris model indicated two stages of sorption ending in a sorption equilibrium step. The first step was related to adsorption occurring on the external surface of proteins, while the second step was related to intraparticle diffusion of zinc ions.
Spectroscopic studies (FT-IR) have proven that the main role in the binding of zinc ions to α S1 CN, βCN and κCN complexes is played phosphate groups and carboxylic groups of Glu and Asp. Raman's spectroscopy supplemented the information from the gap in the information obtained from FT-IR analysis and indicates that the presence of aromatic amino acids such as Tyr, Trp and Phe was involved in the binding with zinc ions.
The use of mass spectrometry allows the accurate determination of masses and thus the identification of α S1 CN, βCN and κCN. The mass spectra obtained after binding the protein with zinc ions indicate that in the case of α S1 CN, the carboxylic groups Asp and Glu play a key role. βCN binds to zinc ions through indirect interactions with oxygen ions, whereas in κCN, the binding of zinc ions takes place probably through weak electrostatic interactions with deprotonated functional groups. However, the proposed binding mechanism requires additional validation using complementary approaches, especially molecular modeling methods.