Oxidases as Oxygen Scavengers in Hypoxic Conditions: A Kinetic Model

A simple kinetic model allowed for the description of the observed decay of the oxygen content in hypoxic aqueous samples with and without headspace, in the presence of glucose oxidase (Glucox) or laccase and their substrates (glucose for Glucox and ABTS for Laccase). The experimental tests involved both the direct measurement of the oxygen content with a fluorescence-based probe and the indirect stopped-flow spectroscopic detection of colored compounds generated from suitable chromogenic reagents. The complete depletion of dissolved oxygen occurred in the no-headspace samples, whereas some residual oxygen remained in a steady state in the samples with headspace. Simple pseudo-first-order kinetics was adequate to describe the behavior of the system, as long as oxygen was the rate-limiting compound, i.e., in the presence of excess substrates. The values of the kinetic constants drawn from best-fit routines of the data from both experimental approaches were quite comparable. The oxygen residues in the samples with headspace seemed related to the low solubility of O2 in the aqueous phase, especially if compared with the large amount of oxygen in the headspace. The extent of such residue decreased by increasing the concentration of the enzyme. The kinetic model proposed in this paper can be of help in assembling suitable sensors to be used for food safety and quality control.


Introduction
Residual oxygen can be seriously detrimental to the shelf life of many perishable products, such as food and pharmaceutical preparations, since it is responsible for enzymatic and non-enzymatic "browning", even under hypoxic conditions [1][2][3]. These occur in packages inflated with inert atmosphere, which can contain residual oxygen or allow some oxygen to infuse from the exterior [4][5][6][7][8].
Oxidases can play the role of oxygen scavengers [3,[9][10][11][12], either when placed in separate oxygen-permeable bags within the package, or when added to the inner layer of the packaging material itself. The flavoenzyme glucose oxidase (Glucox), as a free or immobilized enzyme, has been used in many applications in food packaging [7]. In particular, it was shown that the Glucox immobilized on the film's surface shows tenfold higher activity than the enzyme present within the polymer matrix, although its capacity for total oxygen removal was lower than the enzyme immobilized on the film's surface [7]. Glucox has found broad and satisfactory uses in preserving perishable products, in particular when coupled with enzymes capable of decomposing its hydrogen peroxide byproduct (such as catalase), or using hydrogen peroxide as a reagent for further oxidation steps (such as peroxidases) [4,[13][14][15]. The presence of either of these "secondary" enzymes also minimizes the inhibiting effects of H 2 O 2 on the activity of Glucox [16]. The Glucox/HRP and Glucox/catalase combinations are the subjects of some papers ( [6] and therein quoted works), although, to our knowledge, no direct comparison has been reported. These issues based oxygen sensors, either adherent to the packaging surface or embedded in any of the coating layers.

Results and Discussion
The use of the Oxysense 101 device allowed a direct way to monitor the decrease of O 2 content with both enzymes and under both conditions (presence/absence of headspace) used in this study. According to the experimental evidence, Figure 1 indicates that both enzymes were acting as effective oxygen scavengers even under hypoxic conditions, leaving no residual O 2 in the system, no matter the initial O 2 content, when the sample had no headspace. As explained in the section Section 3, the starting oxygen concentration, [O 2 ] i , was calculated from the value of the partial pressure of oxygen, p(O 2 ), in the (Ar/O 2 ) gas mixture used to condition the environment where the aqueous solution was prepared.
Molecules 2023, 28, x FOR PEER REVIEW 3 of 13 concentration in the system. These conditions are also of interest for the assembly/setup and control/management of active packaging materials/structures that can host enzymebased oxygen sensors, either adherent to the packaging surface or embedded in any of the coating layers.

Results and Discussion
The use of the Oxysense 101 device allowed a direct way to monitor the decrease of O2 content with both enzymes and under both conditions (presence/absence of headspace) used in this study. According to the experimental evidence, Figure 1 indicates that both enzymes were acting as effective oxygen scavengers even under hypoxic conditions, leaving no residual O2 in the system, no matter the initial O2 content, when the sample had no headspace. As explained in the section Section 3, the starting oxygen concentration, [O2]i, was calculated from the value of the partial pressure of oxygen, p(O2), in the (Ar/O2) gas mixture used to condition the environment where the aqueous solution was prepared.  1 also provides graphical evidence that simple exponential decay can fit very well the kinetics of the O2 depletion in the no-headspace samples, regardless of their initial O2 content. The fitting function used was: Figure 1 also provides graphical evidence that simple exponential decay can fit very well the kinetics of the O 2 depletion in the no-headspace samples, regardless of their initial O 2 content. The fitting function used was: where k 1 = k 1G = 0.039 min −1 , and k 1 = k 1L = 0.046 min −1 for Glucox and Laccase, respectively, in fair agreement with the values calculated (as the ratio V max /K M of Michaelis-Menten parameters) from the literature data [21,22]. This interpretation implies that the O 2 depletion is-at least under hypoxic conditions and in the presence of excess co-substrate (glucose and ABTS for Glucox and laccase, respectively)-the rate-limiting step in the overall cycle of both enzymes.
These results are essentially identical to those obtained from stopped-flow spectrophotometric tests where absorbance was the detected variable.
In the case of laccase, the colored compound is ABTS-ox, formed during the reduction of laccase-ox. In other words, the spectrophotometric detection of the absorbance (Abs) related to ABTS-ox at 436 nm wavelength (ε = 29,300 M −1 cm −1 [20], see Figure 2) is indeed equivalent to the direct Oxysense test. The relevant kinetic scheme, therefore, reflects a simple exponential growth, and thus corresponds to the same kinetic model that describes the Oxysense data (see above), namely, (2) where k1 = k1G = 0.039 min −1 , and k1 = k1L = 0.046 min −1 for Glucox and Laccase, respectively, in fair agreement with the values calculated (as the ratio Vmax/KM of Michaelis-Menten parameters) from the literature data [21,22]. This interpretation implies that the O2 depletion is-at least under hypoxic conditions and in the presence of excess co-substrate (glucose and ABTS for Glucox and laccase, respectively)-the rate-limiting step in the overall cycle of both enzymes.
These results are essentially identical to those obtained from stopped-flow spectrophotometric tests where absorbance was the detected variable.
In the case of laccase, the colored compound is ABTS-ox, formed during the reduction of laccase-ox. In other words, the spectrophotometric detection of the absorbance (Abs) related to ABTS-ox at 436 nm wavelength (ε = 29,300 M −1 cm −1 [20], see Figure 2) is indeed equivalent to the direct Oxysense test. The relevant kinetic scheme, therefore, reflects a simple exponential growth, and thus corresponds to the same kinetic model that describes the Oxysense data (see above), namely, (2) In the case of Glucox, the stopped-flow spectrophotometric investigation made use of the coupled process, where guaiacol was oxidized by the H2O2 produced in the Glucox cycle, thanks to the presence of horseradish peroxidase (HRP), to form a colored quinone that showed a broad-shouldered absorbance maximum in the 420-470 nm range [23]. The absorbance at 436 nm [24] was selected for the present work ( Figure 3). In the case of Glucox, the stopped-flow spectrophotometric investigation made use of the coupled process, where guaiacol was oxidized by the H 2 O 2 produced in the Glucox cycle, thanks to the presence of horseradish peroxidase (HRP), to form a colored quinone that showed a broad-shouldered absorbance maximum in the 420-470 nm range [23]. The absorbance at 436 nm [24] was selected for the present work ( Figure 3). The dome-shape trends shown in Figure 3 reveal that, as expected, the quinone decays to form other products [23], which were detected in the present work with HPLC tests. Taking into account the stoichiometry, namely, 1 mole of O 2 yields 4 moles of quinone, a simplified kinetic model allows the fit of the absorbance trend, namely, where k 2 = 0.25 k 1G . This corresponds to the known equation for two consecutive steps, where [Q] is the quinone concentration. The dome-shape trends shown in Figure 3 reveal that, as expected, the quinone decays to form other products [23], which were detected in the present work with HPLC tests. Taking into account the stoichiometry, namely, 1 mole of O2 yields 4 moles of quinone, a simplified kinetic model allows the fit of the absorbance trend, namely, where k2 = 0.25 k1G. This corresponds to the known equation for two consecutive steps, where [Q] is the quinone concentration. From the k2 values determined through the fitting routine, one can calculate the values of k1G reported in Figure 4, which allows the comparison of the values of the kinetic constants, k1G and k1L, determined with the Oxysense (0.039 and 0.046 min −1 , respectively) and the spectrophotometric approach (0.043 and 0.042 min −1 , respectively). From the k 2 values determined through the fitting routine, one can calculate the values of k 1G reported in Figure 4, which allows the comparison of the values of the kinetic constants, k 1G and k 1L , determined with the Oxysense (0.039 and 0.046 min −1 , respectively) and the spectrophotometric approach (0.043 and 0.042 min −1 , respectively).
The presence of a headspace hosting some oxygen substantially modified the picture. For these experiments, the direct monitoring of the oxygen content was the only approach used, since the stopped-flow spectrophotometric approach was not possible.
As shown in Figure 5, the decrease in oxygen content after the enzyme addition was not completed with either enzyme and, in the end, reached a steady concentration, [O 2 ] e , which appeared lower than the initial oxygen content, [O 2 ] i , of the sample. In addition, as exemplified in Figure 6 for glucose oxidase, the [O 2 ] e decreased with the increasing enzyme concentration.
The starting condition (namely, before the injection of the enzyme) reflects a true solubility equilibrium, [O 2 ] i = K H p i (O 2 ), with K H being the Henry constant. The depletion of oxygen from the liquid phase would trigger the transfer of oxygen from the headspace to the liquid phase to re-establish equilibrium. Were the oxygen transfer too slow with respect to the enzymatic scavenging, one would observe a complete oxygen depletion from the liquid phase. However, what actually occurs is competition between the processes, with the scavenging of the oxygen supply from the headspace initially ahead. However, as the oxygen concentration in the liquid phase, [O 2 ], decreases, the scavenging rate also decreases, since it is proportional to [O 2 ]. The system finally reaches a steady condition (for the duration of the experiment); namely, the rate of oxygen supply from the headspace counterbalances the scavenging rate: the oxygen concentration in the liquid phase attains a steady value, [O 2 ] e . The experimental evidence presented in Figures 5 and 6 allowed a simple kinetic interpretation of the observed trends.
where k tr and k 1 are the kinetic constants, with k 1 being proportional to the enzyme concentration.
where k2 = 0.25 k1G. This corresponds to the known equation for two consecutive steps, where [Q] is the quinone concentration. From the k2 values determined through the fitting routine, one can calculate the values of k1G reported in Figure 4, which allows the comparison of the values of the kinetic constants, k1G and k1L, determined with the Oxysense (0.039 and 0.046 min −1 , respectively) and the spectrophotometric approach (0.043 and 0.042 min −1 , respectively).
Molecules 2023, 28, x FOR PEER REVIEW 6 of 13 The presence of a headspace hosting some oxygen substantially modified the picture. For these experiments, the direct monitoring of the oxygen content was the only approach used, since the stopped-flow spectrophotometric approach was not possible.
As shown in Figure 5, the decrease in oxygen content after the enzyme addition was not completed with either enzyme and, in the end, reached a steady concentration, [O2]e, which appeared lower than the initial oxygen content, [O2]i, of the sample. In addition, as exemplified in Figure 6 for glucose oxidase, the [O2]e decreased with the increasing enzyme concentration. In the final steady condition, (d[O 2 ]/dt) = 0, which means that As for the starting condition, one may use the equilibrium constant, namely, The steady condition is long-lasting because of two main reasons: • the solubility of oxygen is very low (see Table 1), and • the amount of oxygen in the headspace (18 mL, about 40 µmoles for p(O 2 ) = 50 hPa) is much larger than in the liquid phase (4 mL, about 0.05 µmoles). This also implies a very small variation in p(O 2 ) in the headspace.
used, since the stopped-flow spectrophotometric approach was not possible. As shown in Figure 5, the decrease in oxygen content after the enzyme addition was not completed with either enzyme and, in the end, reached a steady concentration, [O2]e, which appeared lower than the initial oxygen content, [O2]i, of the sample. In addition, as exemplified in Figure 6 for glucose oxidase, the [O2]e decreased with the increasing enzyme concentration.    For a given enzyme concentration, the ratio between the initial and end values of the oxygen content in the liquid phase therefore is The corresponding fit of the experimental data ( Figures 5 and 6) seems satisfactory for both enzymes, in spite of the underlying naïve kinetic model that is much simpler than the literature reports [15][16][17][18][19]. The model also accounts for the observed larger extent of the [O 2 ] decay for the larger enzyme concentration ( Figure 4) and for the correlation between (Figure 7). From the slope of the straight-line fits reported in Figure 7, one can estimate (k tr /k 1 ) ≈ 0.97 for both enzymes, which reflects the balanced competition between the transfer and scavenging rates.
Molecules 2023, 28, x FOR PEER REVIEW 8 of 13 • the amount of oxygen in the headspace (18 mL, about 40 moles for p(O2) = 50 hPa) is much larger than in the liquid phase (4 mL, about 0.05 moles). This also implies a very small variation in p(O2) in the headspace. For a given enzyme concentration, the ratio between the initial and end values of the oxygen content in the liquid phase therefore is The corresponding fit of the experimental data ( Figures 5 and 6) seems satisfactory for both enzymes, in spite of the underlying naïve kinetic model that is much simpler than the literature reports [15][16][17][18][19]. The model also accounts for the observed larger extent of the [O2] decay for the larger enzyme concentration ( Figure 4) and for the correlation between ([O2]i − [O2]e) and pi(O2) (Figure 7). From the slope of the straight-line fits reported in Figure 7, one can estimate (ktr/k1) ≈ 0.97 for both enzymes, which reflects the balanced competition between the transfer and scavenging rates. The residue of oxygen in real packages that allow some headspace can have adverse consequences for the quality and/or safety of very perishable products. The results of the The residue of oxygen in real packages that allow some headspace can have adverse consequences for the quality and/or safety of very perishable products. The results of the kinetic approach presented above allow the definition of some guidelines for the packaging practice. Relatively stable products can tolerate some residual oxygen for some hours (or days); they do not require vacuum or inert atmosphere packaging in the presence of an oxygen scavenger, such as those considered in this work. The residual oxygen actually does not persist indefinitely, as the apparent steady level does not correspond to a true equilibrium condition, but slowly decays because of the scavenging action of the enzyme. A larger concentration of the enzyme and/or a reduction of the p(O 2 ) in the headspace will accelerate the oxygen depletion, as suggested by the data reported in Figures 6 and 7. Very sensitive products would, instead, require vacuum and/or inert atmosphere packaging. In such cases, the enzyme scavenging action would concern just the oxygen traces coming from the production lines and/or infused from the exterior through the packaging, thereby prolonging the overall shelf life of the product.

Spectrophotometric Measurements
A stopped-flow mixer (Bio Logic MPS-52, Seyssinet-Pariset, France) connected to a circular dichroism spectrometer (JASCO J810, Cremella, LC, Italy) was used for investigating the reaction kinetics. In this particular system, a stepping motor drove gas-tight syringes through a mixing chamber and a cylindrical microcuvette (2 mm optical path, total capacity 0.08 mL), placed in a four-window observation head that allows the simultaneous detection of fluorescence and transmittance/absorbance. Stopped-flow absorbance measurements were carried out from 0 to 10 min at a given wavelength (436 nm for both the Glucox and laccase tests) with a bandwidth of 4 nm. Dedicated software (Bio Logic MPS-52) was used for the data analysis.

Measuring the Oxygen Removal
The tests of enzymatic activity concerned two main situations: (A) a two-phase system, namely, liquid and gas (large headspace); (B) a single liquid phase with a given oxygen initial concentration (no headspace).
(A) Measurements in the presence of a headspace An oxygen sensor (DOT, see below) was glued with a silicon adhesive (RV 118) to the internal wall of a standard 22 mL vial, fitted with a gas-tight, perforable rubber stopper, and sealed with an aluminum lid and a butylenic rubber frame ( Figure 8A). The vials were purged with at least three vacuum/Ar cycles through a standard vacuum line, before being filled with Ar/O 2 mixtures (approximately 5-10-15-20% oxygen, v/v) prepared in a mixer (Map Mix PBI Dansensor) at an overall constant pressure of 0.1 MPa. The actual composition of each gas mixture was checked with a gas chromatograph (Hewlett Packard HP 5870 SERIES II), equipped with a thermo-conductivity sensor and a CTR I stainless steel column (2 m × 6 mm, Alltech Italia Srl, Casalecchio di Reno, Italy).
Molecules 2023, 28, x FOR PEER REVIEW 10 of 13 An oxygen sensor (DOT, see below) was glued with a silicon adhesive (RV 118) to the internal wall of a standard 22 mL vial, fitted with a gas-tight, perforable rubber stopper, and sealed with an aluminum lid and a butylenic rubber frame ( Figure 8A). The vials were purged with at least three vacuum/Ar cycles through a standard vacuum line, before being filled with Ar/O2 mixtures (approximately 5-10-15-20% oxygen, v/v) prepared in a mixer (Map Mix PBI Dansensor) at an overall constant pressure of 0.1 MPa. The actual composition of each gas mixture was checked with a gas chromatograph (Hewlett Packard HP 5870 SERIES II), equipped with a thermo-conductivity sensor and a CTR I stainless steel column (2 m × 6 mm, Alltech Italia Srl, Casalecchio di Reno, Italy). A standard vacuum line was used to prepare the anaerobic reaction mixtures under Ar. gas-tight syringes, which allowed the transfer of a 4 mL solution of a given composition to each vial and achieve equilibration with the adjusted gas phase. The corresponding oxygen concentration in the liquid phase was checked to compare the response of the Oxysense 101 probe (in the absence of enzyme) and the oxygen solubility at various T ( Table 1).
The vials underwent the OxySense 101 tests immediately after the anaerobic addition of the required enzyme (in negligible volumes). The samples for the stopped-flow tests were the same solutions contained in the vials, withdrawn with gas-tight syringes (replacing the withdrawn volume with an identical volume of Ar at 0.1 MPa) and directly injected in the stopped-flow apparatus.

(B) No-headspace measurements
In this case, each vial was completely filled with appropriate mixtures of substrate solutions prepared either anaerobically under Ar or equilibrated with air at atmospheric pressure, that is, at p(O2) = 210 hPa ( Figure 8B) at room temperature. Cooling the airexposed mixtures allowed the attainment of slightly higher oxygen contents. Figure 9 reports a scheme of the sensing Oxysense 101 device that detects the effects of oxygen on the fluorescence of a ruthenium/phenanthroline complex, which is one of several specific biosensors [25][26][27]. The fluorescence decay obeys the law I/I0 = exp(−t/τ), where  is the decay time and I stands for the intensity of the emitted fluorescence. The decay time is related to the partial pressure of oxygen through the Stern-Volmer equation, τ0/τ = 1 + KSV p(O2), often written in the form (1/τ = A p(O2) + B) [27]. Since the parameters A and B in the last equation depend on the temperature and on minor modifications of the composition among individual lots of the sensitive film, a preliminary calibration of A standard vacuum line was used to prepare the anaerobic reaction mixtures under Ar. gas-tight syringes, which allowed the transfer of a 4 mL solution of a given composition to each vial and achieve equilibration with the adjusted gas phase. The corresponding oxygen concentration in the liquid phase was checked to compare the response of the Oxysense 101 probe (in the absence of enzyme) and the oxygen solubility at various T ( Table 1).

Principle and Operation of the Oxysense 101
The vials underwent the OxySense 101 tests immediately after the anaerobic addition of the required enzyme (in negligible volumes). The samples for the stopped-flow tests were the same solutions contained in the vials, withdrawn with gas-tight syringes (replacing the withdrawn volume with an identical volume of Ar at 0.1 MPa) and directly injected in the stopped-flow apparatus.

(B) No-headspace measurements
In this case, each vial was completely filled with appropriate mixtures of substrate solutions prepared either anaerobically under Ar or equilibrated with air at atmospheric pressure, that is, at p(O 2 ) = 210 hPa ( Figure 8B) at room temperature. Cooling the airexposed mixtures allowed the attainment of slightly higher oxygen contents. Figure 9 reports a scheme of the sensing Oxysense 101 device that detects the effects of oxygen on the fluorescence of a ruthenium/phenanthroline complex, which is one of several specific biosensors [25][26][27]. The fluorescence decay obeys the law I/I 0 = exp(−t/τ), where τ is the decay time and I stands for the intensity of the emitted fluorescence. The decay time is related to the partial pressure of oxygen through the Stern-Volmer equation, τ 0 /τ = 1 + K SV p(O 2 ), often written in the form (1/τ = A p(O 2 ) + B) [27]. Since the parameters A and B in the last equation depend on the temperature and on minor modifications of the composition among individual lots of the sensitive film, a preliminary calibration of each lot of film at various temperatures is necessary. Noteworthily, the sensitive film used in this device is stable in the temperature range 0-90 • C, and over the 2-11 pH range. each lot of film at various temperatures is necessary. Noteworthily, the sensitive film used in this device is stable in the temperature range 0-90 °C, and over the 2-11 pH range. In the used vials, illustrated in Figure 8, a hydrophobic polymeric film (100 μm thick) hosting the reactive mixture (4,7 biphenyl 1,10 phenanthroline and ruthenium chloride) is glued onto a glass disc (5 mm diameter and 0.17 mm thick). An external pulsed LED acts as the blue-light source. Using a pulsed light allows computer-assisted measurement of the decay rates of the red fluorescence emitted by the ruthenium complex in the film (1 to 5 μs), in the presence and absence of oxygen, respectively). Dedicated software then converts the fluorescence decay rates into the oxygen content in the gas phase, p(O2), in the % of the 1000 hPa total pressure, whereas the oxygen content of the liquid phase (in μg/mL, ppm) was calculated from tabulated oxygen solubility data (Table 1).

Conclusions
The fluorescent probe and spectrophotometric tests allowed the monitoring of the decay of the oxygen content of the hypoxic samples in the presence of glucose oxidase and laccase. The collected data showed that, in hypoxic conditions and for a given enzyme concentration, the oxygen concentration was the rate-limiting factor of the redox cycles. This evidence justified the use of simple pseudo-first-order kinetics to describe the observed trends. Both enzymes seemed to be efficient oxygen scavengers, both in the presence or in the absence of headspace.
The whole oxygen content of the liquid phase was exhausted in the samples with no headspace. In the presence of some headspace, the oxygen content of the liquid phase attained a residual value that appeared quite steady (for the duration of the experiment). This, presumably, was a consequence of the balance between the transfer of oxygen from the headspace and the scavenging action of the enzyme. In view of the damaging effects of such residues in packaged food, the experimental evidence showing that the residues of oxygen were smaller for larger concentrations of the enzyme could be of some interest.
The simplified kinetic model of the oxygen scavenging activity of these oxidases in hypoxic conditions can be of help not only for monitoring practices of food and pharmaceutical industries, but also for the future developments of biosensors.  In the used vials, illustrated in Figure 8, a hydrophobic polymeric film (100 µm thick) hosting the reactive mixture (4,7 biphenyl 1,10 phenanthroline and ruthenium chloride) is glued onto a glass disc (5 mm diameter and 0.17 mm thick). An external pulsed LED acts as the blue-light source. Using a pulsed light allows computer-assisted measurement of the decay rates of the red fluorescence emitted by the ruthenium complex in the film (1 to 5 µs), in the presence and absence of oxygen, respectively). Dedicated software then converts the fluorescence decay rates into the oxygen content in the gas phase, p(O 2 ), in the % of the 1000 hPa total pressure, whereas the oxygen content of the liquid phase (in µg/mL, ppm) was calculated from tabulated oxygen solubility data (Table 1).

Conclusions
The fluorescent probe and spectrophotometric tests allowed the monitoring of the decay of the oxygen content of the hypoxic samples in the presence of glucose oxidase and laccase. The collected data showed that, in hypoxic conditions and for a given enzyme concentration, the oxygen concentration was the rate-limiting factor of the redox cycles. This evidence justified the use of simple pseudo-first-order kinetics to describe the observed trends. Both enzymes seemed to be efficient oxygen scavengers, both in the presence or in the absence of headspace.
The whole oxygen content of the liquid phase was exhausted in the samples with no headspace. In the presence of some headspace, the oxygen content of the liquid phase attained a residual value that appeared quite steady (for the duration of the experiment). This, presumably, was a consequence of the balance between the transfer of oxygen from the headspace and the scavenging action of the enzyme. In view of the damaging effects of such residues in packaged food, the experimental evidence showing that the residues of oxygen were smaller for larger concentrations of the enzyme could be of some interest. The simplified kinetic model of the oxygen scavenging activity of these oxidases in hypoxic conditions can be of help not only for monitoring practices of food and pharmaceutical industries, but also for the future developments of biosensors.
Author Contributions: P.B., laboratory investigation; S.I., methodology and data curation; D.F., formal analysis; F.B., supervision; A.S., conceptualization of the kinetic interpretation; original draft preparation, review and editing. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: All the detailed data are available on request addressed to the corresponding author, Alberto Schiraldi, at alberto.schiraldi@unimi.it.