Effects of ultrasound on the kinetics and thermodynamics properties of papain entrapped in modified gelatin

Journal Pre-proof Effects of Ultrasound on the Kinetics and Thermodynamics Properties of Papain Entrapped in Modified Gelatin

Zeyu Zhang, Ge Bai, Duoxia Xu, Yanping Cao PII:

S0268-005X(19)32525-1

DOI:

https://doi.org/10.1016/j.foodhyd.2020.105757

Reference:

FOOHYD 105757

To appear in:

Food Hydrocolloids

Received Date:

09 November 2019

Accepted Date:

10 February 2020

Please cite this article as: Zeyu Zhang, Ge Bai, Duoxia Xu, Yanping Cao, Effects of Ultrasound on the Kinetics and Thermodynamics Properties of Papain Entrapped in Modified Gelatin, Food Hydrocolloids (2020), https://doi.org/10.1016/j.foodhyd.2020.105757

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Journal Pre-proof Graphical Abstract

Journal Pre-proof Effects of Ultrasound on the Kinetics and Thermodynamics Properties of Papain Entrapped in Modified Gelatin Zeyu Zhang, Ge Bai, Duoxia Xu*, Yanping Cao* Beijing Advanced Innovation Center for Food Nutrition and Human Health (BTBU), School of Food and Health, Beijing Higher Institution Engineering Research Center of Food Additives and Ingredients, Beijing Technology & Business University (BTBU), Beijing, China *Corresponding author (Duoxia Xu) E-mail: [email protected] Address: No.11, Fucheng Road, Beijing 100048, China *Corresponding author (Yanping Cao) E-mail: [email protected] Address: No.11, Fucheng Road, Beijing 100048, China

Journal Pre-proof Abstract: Papain is one of the most promising proteases for hydrolysis and the immobilized papain is widely used in the food industry. The aim of the study was to investigate the effect of different ultrasound conditions on the kinetics and thermodynamics of enzymatic reactions of papain entrapped in modified gelatin. The diffusion of methyl orange pigment in modified gelatin gel was explored to establish the diffusion kinetics of modified gelatin. Results showed that the temperature and ultrasonic had significant effects on the catalytic reaction between papain entrapped in modified gelatin and casein. Kinetics analysis proved that the catalytic reaction of immobilized papain and the release of methyl orange pigment from modified gelatin followed the first order kinetics. The thermodynamic analysis showed that the apparent activation energy, enthalpy and activation free energy were the lowest at 135 kHz and 0.15 W/cm2, which proved that the optimal conditions for the enzymatic hydrolysis of immobilized papain entrapped in modified gelatin gel were 135 kHz and 0.15 W/cm2. The impact of ultrasound on the diffusion showed that the effect of ultrasonic-assisted treatment on the diffusion coefficient (De) of methyl orange pigment in modified gelatin gel was greater than that of ultrasonic pretreatment. In addition, the influence of ultrasonic power on the De was greater than that of ultrasonic frequency. This study reveals ultrasound treatment could accelerate the spontaneous reaction of the enzymatic reaction. This study is important to explain the hydrolysis reaction of immobilized papain to control the progress of the hydrolysis during ultrasound treatment. Keyword: Ultrasound; Papain; Gelatin; Kinetics; Thermodynamics; Diffusion

Journal Pre-proof coefficient 1. Introduction Papain is a pure natural cysteine protease. It has many advantages of high enzyme activity, good thermal stability, non-toxic side effects, and has tremendous prospects for development in food, medicine, biology, feed and textile industries (FernándezLucas et al., 2017; Kang et al., 2018; Rostika et al., 2018; Shariat et al., 2018). Papain can not only be used for protein structure research, peptide localization, solubilization of membrane protein, but also catalyze the hydrolysis of various peptides, amide and ester bonds (Sahoo et al., 2013). Poor recovery and low reusability of free papain limit its application (Lei et al., 2004; Onoja et al., 2018). It can be overcome by immobilizing the enzyme on porous and inert support to offer rigidity and reusability (Onoja et al., 2018; Lei et al., 2004). Many different methods exist for enzymatic immobilization (physical adsorption, embedding, and copolymerization) were able to meet more practical needs (Enayati et al., 2018; Mardani et al., 2018; Muthuvelu et al., 2018). Cellulose, sodium alginate, gelatin and other natural non-toxic polymer materials are often used as carriers of immobilized enzymes to improve their recovery and reusability (Dai et al., 2017; Huang et al., 2015; Sangeetha and Abraham, 2006). In addition to the natural carrier, the new carrier structure makes the application of papain more potential. Gu and coworkers (2018) have prepared a new type of magnetic metal-chelating carrier (PCMM-IDACu2+) for the immobilization of papain. It is worth mentioning that papain immobilized by the novel carriers could improve the automation of industrial production,

Journal Pre-proof microcomputer and continuous, and it is facile to control the enzymatic reaction processes. The papain immobilized by novel magnetic cellulose nanocrystals (MCNCs) could be recovered and renewable by its magnetic properties as efficient carriers for enzymes, drugs, and other biomaterials (Zhang et al., 2016). Other interesting uses of the immobilized papain include water treatment for the removal of heavy metals, adding to the antibacterial package as an antibacterial agent, or preventing yeast flocculation in the bioethanol industry (Cynthya et al., 2014; Metin & Alver, 2016; Silva et al., 2015). It can be seen that the immobilized papain attracted much attention and had strong application potential. However, the immobilized carrier could affect the surrounding environment of the immobilized enzyme and modify the diffusion coefficient of solutes, making a loss of enzyme activity compared with the free enzyme (SáRinger et al., 2019). The kinetic properties of the immobilized enzyme were quite different from those of the free enzyme from a micro perspective (Homaei & Samari, 2017). Homaei and Samari (2017) discovered that the steric hindrance of the active site or substrate diffusion resistance of the immobilized papain increased resulted that the immobilized papain had the negative effect of the lower affinity and the reaction rate. Sheng and coworkers (2018) found that the maximum reaction rate (Vmax) of papain immobilized by porous magnetic nanoparticles was 4.95 mg/I·min which was much larger than its free papain, while, the substrate had a low affinity with papain encapsulated by the carrier resulting in a larger Michaelis-constant values (Km) than its free papain. However, Wang and Zhang (2018) found the opposite conclusion that the Km of the immobilized transglutaminase (TG)

Journal Pre-proof decreased after TG immobilized by polyethersulfone (PES) and methacrylic acid (MA). This may be due to the -NH2 group of the TG molecule was attached to the - COOH group from the PES-MA surface by an amide bond, which caused that the TG was regularly distributed on the PES-MA surface making the higher affinity. Thermodynamics mainly explores the thermodynamic properties of matter form for energy conversion. Thermodynamic parameters include enthalpy (ΔH), entropy (ΔS) and activation free energy (ΔG) of enzymes. Fan and coworkers (2013) found that the thermodynamic parameters of papain were negative, this result indicated that the binding process of papain to an amino-functionalized ionic liquid was spontaneous, and Van der Waals interaction and hydrogen bond played major roles in the process. Tripathi, Noetzel and Marx (2019) have concluded that the catalytic activity of enzymes was usually attributed to the active site, which was revealed by site-directed mutation studies combined with thermodynamic and structural analysis. Ultrasound, as a green and novel physical processing technology, is contributed to not only substance extraction, release and diffuse of solute (Falcão et al., 2018; Gallo, Ferrara, & Naviglio, 2018), also increased the enzyme activity and affected the activation energy of the immobilized enzyme. Nevertheless, ultrasound could change the structure of the carrier and affect the environment surrounding of the immobilized enzyme, which would affect the specificity of the immobilized enzyme to the substrate. This paper aimed to deeply understand the effects of ultrasound power and frequency on the catalytic reaction, the kinetic, thermodynamic parameters and the diffusion coefficient of immobilized papain. Combined with the diffusion of methyl

Journal Pre-proof orange pigment in modified gelatin gel with the kinetic and thermodynamic parameters of the immobilized papain was to better understand the kinetic mechanism of immobilized papain hydrolysis. It would provide a basis for the enzymatic hydrolysis of the immobilized enzymes to control the progress of the hydrolysis. 2. Materials and methods 2.1 Materials Papain (4.96×105 U/g) was procured from Sigma Chemicals (St Louis, MO, USA). Casein was acquired from Beijing Ao Bo Xing Bio-Tech. Co., Ltd. (Beijing, China). Lglutathione was obtained from Beijing Biodi Biotechnology Co., Ltd. (Beijing, China). Gelatin, glutaraldehyde, sodium carbonate (Na2CO3), trichloroacetic acid (TCA) and nbutyl acetate were the products of Sinopharm Group Chemical Reagent Co., Ltd. (Beijing, China). Folin phenol reagent was purchased from Shanghai Yuanye Biotechnology Co., Ltd. (Shanghai, China). All the other chemicals used arose out of analytical grade. 2.2 Preparation of Immobilized Papain Papain solutions (10 mg/mL, 1% (w/v)) were prepared by dissolving in 0.1 M phosphate buffer solution at pH 7.0. The solution could be stored for 3 days at 4 ℃. Gelatin solutions (0.2 g/mL) were prepared by dissolving in 0.1 M phosphate buffer solution at pH 8.0. The gelatin solutions were kept at 50 ℃ and dissolved in the constant temperature water bath (HH-2, Guohua Electric Appliance Co., Ltd., Beijing, China). When gelatin was completely dissolved, glutaraldehyde solutions (0.5%, 1 mL) were added in two portions at 25 min intervals. After uniformly stirring for 10 min, papain

Journal Pre-proof solutions (10 mg/mL, 1% (w/v), 0.5 mL) were slowly added dropwise for 1 min at 40 °C. The solutions were placed on a magnetic stirrer immediately (85-2, Guohua Electric Appliance Co., Ltd., Beijing, China), and glutaraldehyde solutions (4%, 0.5 mL) were slowly added and then mixed for 30 min. Afterwards, slowly dropping the mixed gelatin solutions into butyl acetate at 4 ℃ ensured that the immobilized papain was prevented from accumulating. It was stored in glutaraldehyde solutions (0.5%, 100 mL) at 4 ℃ until immobilized enzymes were washed with deionized water remained without residue. Immobilized enzymes were refrigerated at 4 ℃ for 30 min, washed with pure water three times, and placed on a clean filter paper for use. 2.3 Ultrasound equipment Ultrasonic instruments were assembled from the JXD-02 multi-frequency processing system (JXD-02, Beijing Jinxing Ultrasonic Equipment Technology Co., Ltd., Beijing, China) and the low-temperature circulating water tank (DC-2006, Ningbo Xinzhi Biotechnology Co., Ltd., Zhejiang, China). The volume of the ultrasonic bath was 6×10-3 cm3, and the length, width and depth were 20, 20 and 15 cm, respectively. Ultrasonic instruments were equipped with four different frequencies (28, 40, 50, 135 kHz) and powers (0.05, 0.15, 0.25, 0.35 0.45 W/cm2). The maximum power delivered by the ultrasound generator probe was 0.45 W/cm2. Feng and coworkers (2017) presented the working principle of ultrasonic instruments in detail. A simple schematic diagram of an ultrasound instrument is shown in Fig. 1. 2.4 Enzyme activity measurement The immobilized enzymes were mixed with glutathione solutions (0.1573%, pH

Journal Pre-proof 6.5) and casein solution in a volume ratio of 1:3:10. The activity of papain was evaluated using the Folin-phenol method described by Feng et al. (2016) with a UVvisible spectrophotometer (UV-1240, Shimadzu, Co., Ltd., Tokyo, Japan) at 680 nm. One unit of enzyme activity was referred to as the amount of enzyme required to release the product of casein within 1 min, which was expressed as the rate of conversion of a certain chemical reaction catalyzed. For each set of assays, the control group was used as a blank control without enzyme. 2.5 Determination of the reaction order of immobilized papain 20 g of immobilized papain gels mixed with different concentrations of casein solutions and glutathione solutions (0.1573%, pH 6.5) were placed in a constant temperature water bath at 40 °C. The concentration of casein solution was 0.2, 0.4, 0.6, 0.8, 1.0 g/mL respectively. The sample taken every 5 min was immediately added with 1.92 mL, 0.4 mol/L of TCA to suspend. The enzyme activity was monitored using the Folin-phenol method. The reaction rate formula was: r = 𝑘 ⋅ [𝐴]𝛼 ⋅ [𝐵]𝛽…

(1)

the value of k, the apparent reaction rate constant, was dependent on the concentration of the reactants, the reaction temperature and the catalyst used. α and b indicated the reaction orders of the components A, B, respectively. The sum of each index was the overall reaction level. Equation (1) followed the law of conservation of mass and the reaction was analyzed by integration and construction. The functional relationship between the time and the concentrations of casein was calculated by integrating. The general model of

Journal Pre-proof zero order reaction, the first order reaction, and the second order reaction can be respectively expressed as the equation (2), (3) and (4) (Fu et al., 2019): C=k0 ⋅ t

（2）

𝐶0

ln𝐶0 ― 𝐶 = 𝑘1 ⋅ 𝑡

（3）

1 (𝑎 ― 𝑥)

（4）

1

― 𝑎 = 𝑘2 ⋅ 𝑡

Regression analysis based on data statistics was calculated the relative standard deviation of the curves of C vs time, ln(C0/C) vs time and (1/C-1/C0) vs time. The line with the maximum correlation coefficient was the reaction rate characteristic equation curve. 2.6 Kinetics of enzymatic reaction of the immobilized papain Different concentrations of casein solution were diluted. Immobilized papain gels mixed with different concentration of casein solutions (0.05, 0.1, 0.15, 0.2, 0.4, 0.6, 0.8, 1.0 g/mL) were reacted for 20 min at different frequencies (28, 40, 50 and 135 kHz) and various powers (0.05, 0.15, 0.25, 0.35 and 0.45 W/cm2). The Km and the Vmax were obtained according to the graphical method of a generalized Michaelis-Menten mechanism. 2.7 Thermodynamic parameters of the enzyme reaction 20 g of immobilized enzymes mixed with casein solutions (1.0 g/mL, 200 mL) and glutathione solutions (0.1573%, pH 6.5, 60 mL) were carried out at different temperatures (30, 35, 40, 45, 50 ℃), frequencies (28, 40, 50 and 135 kHz) and powers (0.05, 0.15, 0.25, 0.35 and 0.45 W/cm2). The results of chemical kinetics from different ultrasonic frequencies and power conditions were deduced based on the reaction

Journal Pre-proof characteristic equation curve. Non-ultrasound conditions were considered as blank controls. Arrhenius equations (5) and (6) were used to find the activation energy (Ea) and the pre-exponential factor (A) (Aalaei, Rayner, & Sjoholm, 2018; Fu et al., 2019). 𝐸𝑎

ln𝑘 = ― 𝑅 ⋅ 𝑇 +B

（5）

𝑘 = 𝐴 ⋅ 𝑒 ― 𝐸𝑎/𝑅 ⋅ 𝑇

（6）

where k is the hydrolysis reaction rate constant (min-1), Ea is the experimental activation energy (J/mol or kJ/mol), A is "pre-exponential factor" or "frequency factor" and the temperature-independent factor (mg/g·min), R is the ideal gas constant (8.314 J/mol·K) and T is the absolute temperature (K). The smaller the value of the Ea the easier the reaction, and the larger the value of A, the more active molecule collisions. Ea and A of enzymatic reactions of immobilized papain were determined by intercept and slope of lnk against 1/T curves, of which the slope was -Ea/R. ΔH, ΔS and ΔG indicated the chemical thermodynamics of enzyme reaction (Meziane & Kadi, 2008; Yang et al., 2019). They were calculated by the equations: (7)

△ 𝐻 = 𝐸𝑎 ―R ⋅ T △𝑆=

( △ 𝐻 ―△ 𝐺) T

△ 𝐺 = ―R ⋅ T ⋅ ln

(8)

(

)

𝑘𝑐𝑎𝑡 ⋅ ℎ 𝑘𝑏 ⋅ 𝑇

(9)

where the catalytic constant (kcat) is determined by the ratio of the Vmax and the total concentration of the enzyme. h is the Planck constant and kb is the Boltzmann one. 2.8 Ultrasonic-assisted treatment of diffusion of methyl orange pigment in modified gelatin gel

Journal Pre-proof The concentration of methyl orange pigments was 2×10-3 g/mL gelatin solution. The preparation process of gelatin gel was the same as that of 2.2. The modified gelatin gel beads with methyl orange pigment (5 g) were placed in 300 mL deionized water. The solution was treated at different frequencies (28, 40, 50, 135 kHz), 0.45 W/cm2, and at different powers (0.05, 0.15, 0.25, 0.35, 0.45 W/cm2), 28 kHz, at 40 ℃. The concentration of methyl orange pigment was determined every 10 min by ultraviolet spectrophotometry at 463 nm until the solution concentration reached dynamic equilibrium. 2.9 Ultrasonic pretreatment of diffusion of methyl orange pigment in modified gelatin gel Gelatin gel beads embedded with methyl orange pigment were ultrasonic pretreated for 20 min. The ultrasonic pretreatment and the determination of the concentration of methyl orange were the same with 2.8. 2.10 Calculation of diffusion coefficient If the resistance of liquid film on the surface of particles is neglected, the change of the cumulative concentration of solute can be expressed by the following equation according to Žerajić et al. (2008): 𝐶(𝑡) 𝐶∞

=1―

∑

∞

6 ⋅ 𝛼 ⋅ (1 + 𝛼)

9 + 9 ⋅ 𝛼 + 𝛼2 𝑛=1

⋅𝑒

―

𝐷𝑒 ⋅ 𝑞2 𝑛⋅𝑡 𝑅2

(10)

where C(t) is the concentration of methyl orange in solution at different times (mol/L). C∞ is the concentration of methyl orange in solution (mol/L). R is the radius of the gel particle. De is an effective diffusion coefficient. α means the ratio of solution volume V to gel particle volume:

Journal Pre-proof α=4

V

3πR

(11)

3

n

qn is the non-zero positive solution of the following equation: 3 ⋅ 𝑞𝑛

(12)

tan𝑞𝑛 = 3 + 𝛼 ⋅ 𝑞 2 𝑛

the equation (10) is simplified to (13):

[

ln 1 ―

] = ―0.0016 ⋅ 𝐷 ⋅ 𝑡 + 3.4

𝐶(𝑡) 𝐶∞

𝑒

(13)

2.11 Statistical analysis All of the above experiments were evaluated three times in parallel. Data were subjected to analysis of variance using SPSS, version 22.0 (IBM Corp., Armonk, NY, USA). Unless otherwise specified in the text, p<0.05 was regarded as significant and p<0.01 was more significant. 3. Results and discussion 3.1 Determination of the reaction order of immobilized papain The apparent reaction rate constant was obtained by linear regression (Fu et al., 2019). Table 1 showed that the average slope of the curves of ln(C0/C) vs time of the hydrolysis reaction of casein by the immobilized enzyme was 2.44×10-4, and the RSD value was 0.14. The RSD value and the deviation of the curves of ln(C0/C) vs time were smaller than that of the curves of C vs time and (1/C-1/C0) vs time which meant that the reliability of the experimental data was higher than that of others. This phenomenon indicated that the first order reaction kinetics would be more clearly and accurately to describe the hydrolysis reaction of casein by the immobilized enzyme, compared with the zero order and second order reactions. Therefore, the enzymatic reaction of the immobilized papain with casein was the first order reaction. Huang and coworkers

Journal Pre-proof (2015) studied the diffusion of casein in the alginate-chitosan gel beads by the ultrasound-assisted treatment and they found the result was in accordance with Ding (2018) that the kinetics of the immobilized papain agreed with first order kinetics. These results can be compared with those of Saikia and coworkers (2019), who discovered that the adsorption capacity for substrates of immobilized papain with cubic mesoporous silica nanoparticles (MSNs) as the carrier material followed pseudosecond-order kinetics. Pan and coworkers (2016) found that the hydrolysis of free papain was more consistent with the pseudo-second-order kinetic model by the response surface methodology (RSM) and kinetic model analysis. Therefore, the kinetics model of immobilized papain hydrolysis reaction was influenced by the embedding inflection of carrier materials, substrates and the existing state of papain. 3.2 Kinetics of the immobilized papain with ultrasound assisted-treatment 3.2.1 Reaction rate constant The enzyme-catalyzed reaction that immobilized papain hydrolyzed casein was intended to be promoted range from 30 to 50 ℃ with ultrasound assisted-treatment. Compared with non-ultrasound conditions, the relative enzyme activity was increased by 64% at 40 ℃ with ultrasound assisted-treatment (135 kHz, 0.05 W/cm2). The optimal ultrasound assisted-treatment temperature for immobilized papain was 40 ℃. The result was in accordance with our team's previous results (Bai et al., 2017). Saikia and coworkers (2019) showed that the immobilized papain had good heat resistance and the optimal temperature to achieve the highest activity of 0.6 U/mg was 45 °C, which was 10 ℃ higher than the free papain. A similar observation was also reported by Lei et al.,

Journal Pre-proof (2004). The curve of ln(C0/C) vs time was used to infer the law of chemical kinetics of immobilized papain under different ultrasonic frequencies and power conditions, as shown in Fig. 2 and Fig. 3. Compared with the non-ultrasonic treatment, the catalytic effect of immobilized papain was enhanced significantly under different ultrasonic conditions. The immobilized papain hydrolysis rate constant was increased obviously and regularly with increasing temperature regardless of reaction conditions. Furthermore, modified gelatin, a series of cross-linked water-soluble polymer chain networks of hydrogels, could be expanded and collapsed sharply in response to external stimuli such as temperature, pH, organic solvent, and others (Park, 1993). Both the rate of movement of casein molecules in the solution reaction system and the chances of the contact between casein and gelatin microsphere-encapsulated papain increased which promoted dramatically the process of enzymatic hydrolysis during the ultrasound assisted-treatment process (Lei et al., 2004). 3.2.2 Vmax The cavitation generated by appropriate ultrasonic frequency and power could increase the Vmax of the immobilized enzyme. It could be seen from Fig. 4 that the Vmax was first increased and then decreased as the ultrasonic power increases, and the maximum value of that was taken at 0.15 W/cm2. The Vmax was decreased at 135, 40 and 50 kHz in turn, except for 28 kHz. That was because the cavitation became more and more obvious with the ultrasonic frequency increases, which effectively reduced the resistance of the substrate to inward diffusion and the resistance of the product to

Journal Pre-proof outward diffusion, thereby promoting diffusion (Huang et al., 2015). Besides, the cavitation of ultrasound produced high temperature, high pressure, and strong shear force, which could change the structure of the carrier, exposing the active center of papain, and could make the enzyme and substrate more easily combined, leading to increase the Vmax (Bashari et al., 2014). However, the shear force and the shock wave outside the collapsing cavitation bubble formed a barrier between the substrate and the enzyme with increasing the power of the ultrasound, reducing the Vmax (Zhong et al., 2004). In previous studies, our research team has shown that the enzyme activity and the Vmax value of immobilized papain were lower than that of the free papain without ultrasonic treatment, however, they were increased significantly with ultrasonic treatment (28 kHz, 0.05 W/cm2) (Wu et al., 2011). Zhang and coworkers (2016) found the result was in accordance with Wu (2011) and Saikia (2019). Sáringer (2019) has indicated that the activity of papain decreased upon immobilization. It was most likely attributed to that the conformation of the enzyme was changed and the steric hindrance and diffusion resistance was increased. Ultrasound played a very important role, it could enhance the collision and the interaction between the active center of immobilized papain and the substrate, bring about reducing the blocking force, resulting in the activity and the Vmax value increase significantly. 3.2.3 Km The study found that different ultrasonic conditions could impact the Km of the immobilized papain, except for the Vmax. It was known from the data in Fig. 5 that the Km value of the immobilized papain exhibited different laws under different ultrasonic

Journal Pre-proof powers and frequencies. When the ultrasound power was fixed at 0.05 W/cm2 and 0.45 W/cm2, the Km value of the immobilized papain decreased slightly with increasing the ultrasonic frequencies, and the minimum Km value arrived at 135 kHz. When the ultrasound power was fixed at 0.15 W/cm2 and 0.25 W/cm2, the Km value increased slightly with increasing the ultrasonic frequencies, and the minimum Km value arrived at 28 kHz. While, the Km value of the immobilized papain exhibited spiral reduction with increasing the ultrasonic frequencies when the ultrasound power was fixed at 0.35 W/cm2. That the Km value of the immobilized papain exhibited different laws might because that the interaction of ultrasonic frequency and ultrasonic power changed the structure of the immobilized enzyme and impacted the affinity between enzyme and substrate (Wei et al., 2010). The smaller the Km, the higher the specificity of the enzyme is (Sheng et al., 2018). Wu and coworkers (2011) found that the Km value of immobilized papain decreased to 1.8835 mg/mL after ultrasonic treatment (28 kHz, 0.05 W/cm2), compared with that of immobilized papain without ultrasonic treatment, even close to that of the free (1.8528 mg/mL). This may be the result that the secondary structure of the protein exposing to the cleavage site was altered with ultrasonic frequency and power, which led to the decrease of the Km (Bashari et al., 2013a; Wei et al., 2010). 3.3 Effect of ultrasound assisted-treatment on thermodynamic parameters of the enzymatic reaction 3.3.1 Apparent activation energy It is common to know that the requirement to overcome the energy barrier is

Journal Pre-proof lowered and product formation occurs at a faster rate (Armenise et al., 2018; Ye & Li, 2018). The Ea was obtained through the calculation of the formula (5) and (6) to further explore the mechanism of the catalytic reaction of immobilized papain. When the ultrasound power was fixed at 0.05 W/cm2, the Ea of the immobilized papain with different ultrasonic frequencies (28, 40, 50, 135 kHz) was shown in Table 2. The Ea of the immobilized papain decreased slowly with the increase of frequency and exhibited a significant difference between the different ultrasonic frequency groups (p<0.05). The Ea of the immobilized papain was 34879.47±427.41 J/mol and decreased by 20.4% with ultrasound assisted-treatment at 135 kHz, 0.05 W/cm2, which was smaller than other samples with treatment at ultrasound frequencies (28, 40 and 50 kHz). It was agreed with the report of Qu and coworkers (2018) that the Ea of corn gluten meal with immobilized enzyme was reduced by 17.1% under triple-frequency ultrasound. The decrease of Ea indicated that the energy gap between unexcited state and transition state decreased with the increase of ultrasonic frequency. Furthermore, ultrasound was beneficial to enzymatic hydrolysis and this promotion was related to the cavitation effect produced by the frequency of ultrasound (Qin et al., 2018). Owing to ultrasonic oscillations increased, numbers of shock waves were greatly increased with cavitation nucleus increasing linearly under high frequency and lowpower ultrasound conditions (135 kHz, 0.05 W/cm2). That the resulting shock waves had access to the small gap of the immobilized enzyme at high frequency of 135 kHz not only further increased the chance of collision between papain and casein and also increased the direct effect of the activated molecule (Wang et al., 2018a). Studies had

Journal Pre-proof shown that ultrasound with high frequency (≥2 MHz) even could produce negative pressure and change the physicochemical properties of the medium in solutions, the phenomenon that promoted accessibility between substrates (Nguyen et al., 2017; Xie et al., 2019). Besides, the mesh structure of the gelatin carrier could be changed depending on the instantaneous destructive force generated by the ultrasonic waves. The collision resistances between casein and product molecules were reduced which resulted that the catalytic reactions of immobilized papain were accelerated. It produced the diffusion suppression effect and the stereoscopic shielding effect which affected the microenvironment and distribution effects. Hence, the cavitation intensity by ultrasonic waves produced for the ultrasonic frequency at 135 kHz was strong, which caused to the Ea of the catalytic reactions between the immobilized papain and casein decreased. Table 2 shows that the Ea of the immobilized papain decreased at first and then increased with the increase of ultrasonic power at the same ultrasonic frequency (135 kHz). It was reported that power had a greater influence on cavitation structures than frequency (Li et al., 2018). When the ultrasonic power increased from 0.05 W/cm2 to 0.15 W/cm2, the Ea of the immobilized papain decreased continuously to 33191.14±448.41 J/mol. It was markedly decreased by 24.3% (p<0.05) compared with

the non-ultrasonic treatment. It indicated that the catalytic reaction of modified gelatin immobilized papain was prone to occur at 135 kHz, 0.15 W/cm2. The decrease in activation energy and the accelerating of the catalytic reaction of immobilized papain were due to the obvious effect of cavitation. The shear forces generated by ultrasonic waves might change structures of the immobilized enzymes and

Journal Pre-proof modify both enzyme and substrate macromolecules (Wang et al., 2018b). The repeated shaking of ultrasonic waves accelerated contacts between casein and papain, increased mass transfer power and heat transfer performance, and provided excellent conditions for catalytic reactions (Fei et al., 2018; Tizazu, Roy, & Moholkar, 2018). Awadallak and coworkers (2017) discovered that the synergistic effect of ultrasound and enzymes helped enhance the penetration of casein and various substances and increasing catalytic rates. It might be due to that the network structure of the gelatin carrier became loose and active sites of papain were exposed. However, when the ultrasonic power was increased from 0.25 W/cm2 to 0.45 W/cm2, the value of Ea of the immobilized papain increased. It could be explained by the followings. First, at high ultrasonic frequencies, the amount of cavitation nucleus tended to saturate when the ultrasound intensity reached a certain value. A large amount of ineffective cavitation nucleus generated was shrunk and collapsed quickly as the consequence of ultrasonic power increased, which produced a large amount of scattering intensity, formed instantaneous pressure, and impeded the release of the product, caused blockage of the reaction channels and resulted in the reaction channel blocked, instantaneously. Therefore, the cavitation intensity and the reaction rate were reduced. Second, high-intensity ultrasound caused the structure of the gelatin carrier to be disordered or destroyed excessively, and formed larger pores on their surfaces, affecting the binding of the substrate to the active site of the enzyme directly (Bashari et al., 2013b; Wang et al., 2018a). Third, the high intensity and power ultrasonic waves caused the solution system to produce heat, increase in the vapor pressure and weaken

Journal Pre-proof the cavitation, and hinder the instantaneous blasting of the cavitation nucleus (Li & Lin, 2008; Tian, Yang, & Liao, 2008). Studies showed that the strong collapse of the bubble led to the temperature up to 20000 K instantaneously, and higher temperatures produced by ultrasonic power, which could slow down the progress of the enzyme catalysis (Nazari-Mahroo et al., 2018; Suslick & Flannigan, 2008). Therefore, the generated shock wave energy was reduced, the catalytic reaction was slowed down, and the enzymatic reaction was not performed easily. Fourth, glutaraldehyde solutions as a crosslinking agent and a gelatin-modifying solvent were added to the immobilized papain microspheres. It resulted in the tighter structure of gelatin and lower the molecular diffusion performance and the reduction of the enzymatic reaction rate. 3.3.2 Thermodynamic parameters In general, papain-like proteases have broad specificity and have a conserved core structure which is composed of two differentiated interacting domains (α-helix and βbarrel-like) (Fernández-Lucas et al., 2017). The papain connected with the gelatin carrier by covalent bonds would form a network structure inside, which led to the active sites of papain exposed or hidden. Theoretically, the collision coefficient needed to be taken into account the spatial orientation in the collision as well as the barrier function of a large atomic group in the enzymatic reaction. The model parameters, such as ΔH, ΔS and ΔG could be explained directly collisions of the immobilized enzyme with substrates. The enthalpy change is one of the important factors that restrict the occurrence of an enzymatic reaction. The value of the ΔH was estimated with temperature increasing

Journal Pre-proof from 30 to 50 °C in Table 3, which was decreased clearly as the temperature increased. It reported that the value of the ΔH was positive indicating that the enzymatic reaction was endothermic (Silva et al., 2018). Bansode and Rathod (2018) found that the ΔH value of enzymatic reaction of immobilized lipase decreased by 0.166 kJ/mol when the temperature of ultrasound assisted-treatment increased by 20 °C. Golly and coworkers (2019) found that there was a drastic decline in the ΔH value of the enzymatic reaction of trypsin with the temperature ranging from 20 to 50 °C, and it had a significant improvement in the reaction rate. The influence of ultrasonic power and frequency on the ΔH is as important as that of temperature. It can be seen from Table 4 that the value of the ΔH of the immobilized papain decreased gradually with increasing ultrasonic frequency when ultrasonic power was fixed at 0.05 W/cm2. When ultrasonic frequency fixed at 135 kHz, the value of ΔH of the immobilized papain was the lowest at 0.15 W/cm2. That result was extremely similar to the tendency of the value of Ea. The lower ΔH value indicated that the energy required for the elongation and compression of the chemical bond between the immobilized enzyme and substrate to reach the transition state was small, which was confirmed by Gawas & Rathod’s research (2018). The lower ΔH value is indicative of less unfolding effects in the immobilized enzyme-catalyzed processes. Likewise, the greater the directional complexity of ΔH and the smaller the activation enthalpy (H) in the formation of enzyme-substrate complexes, the easier the formation of enzymesubstrate complexes could be (Bansode & Rathod, 2018). For the effect of ultrasound (20 kHz) on free lipases, it was shown by Jadhav and Gogate (2014) that hydrogen bond

Journal Pre-proof breakage destroyed the hydrophobic nucleus of the enzyme exposing more active sites, and the ΔH value decreased by nearly 35% compared with non-ultrasound treatment. However, high ultrasound power led to the disorder of the carrier structure of the immobilized enzyme, which directly impacted the exposure of the active site and the combination of the substrate with the active site of the immobilized enzyme. It caused an increase in the value of ΔH and a decrease in the reaction rate of the immobilized papain. Hence, the lower ΔH value is beneficial to the enzymatic reaction. ΔS is another important parameter of restricting the occurrence of an enzymatic reaction, which is correlated to the order (rigidity) degree of the enzyme-substrate activated complex (Schirmann et al., 2019; Torabizadeh & Mikani, 2018). Table 4 shows that the absolute value of ΔS at 135 kHz and 0.15 W/cm2 was higher than other ultrasound assisted-treatments. That could be attributed to cavitation bubbles generated by ultrasound instantaneously broken. It oscillated between the solution and the carrier with high intensity, resulting in intense compression and expansion (Chemat et al., 2017; Wen et al., 2018). The shearing force generated caused to break the chemical bond of the material, which affected the particle dispersion and enhanced mass transfer in the carrier (Li et al., 2016; Wang et al., 2018a). Shearing force accelerated the exposure of the active site of an enzyme, increased the contact frequency between substrate and enzyme, and changed the substrate configuration, thereby accelerated the reaction process (Wang, Lei, & Zhou, 2019). The higher ΔS value (in absolute value) of the immobilized papain system confirms the more disordered structure of its transition state. The negative values of ΔS indicated a high spontaneity of reacting molecules (Silva et

Journal Pre-proof al., 2018). Therefore, the structure of enzyme-substrate at transition state was more ordered than in the reacting system, the collisions of the molecules were raised, which increased the reaction rate of the enzymatic reaction of the immobilized papain at 135 kHz and 0.15 W/cm2. ΔG is a measure of feasibility and ease of any reaction. It can be seen from Table 4 that the value of the ΔG presents a law of fluctuation with the increase of ultrasonic frequency when the ultrasonic power fixed at 0.05 W/cm2. However, when the ultrasonic frequency fixed at 135KHz, ΔG first decreased and then gradually increased and reached the minimum value at 0.15 W/cm2, which was 53100.66 J/mol. Under ultrasound condition (135 kHz, 0.15 W/cm2), the immobilized papain system corresponded to lower ΔG, which pointed out an increasing spontaneity of immobilized enzyme-substrate binding. It was in accordance with the reports that ultrasound treatment could alter the structures of an enzyme, which make it more accessible for substrates and to enhance the rate of reaction, accompanied by decreases in ΔG, ΔH, and Ea values (Haile et al., 2011; Jadhav & Gogate, 2014). Consequently, the lower ΔH and ΔG and higher ΔS (in absolute value) elucidated that the enzymatic reaction of the immobilized papain overcomes the lower energy barrier and occurs at a faster rate through enzyme-substrates transition state at 135 kHz and 0.15 W/cm2. 3.4 Effect of ultrasound on the diffusion of methyl orange in glutaraldehyde modified gelatin gel 3.4.1 Effect of glutaraldehyde modification on the diffusion of methyl orange

Journal Pre-proof pigment in gelatin gel The effect of glutaraldehyde modification on the diffusion of methyl orange in gelatin gel was studied under non-ultrasonic conditions. According to equation (13), t 𝐶(𝑡)

was plotted by ln [1 ― 𝐶∞] and the diffusion coefficient (De) was obtained by the slope. The results of the effect of glutaraldehyde on the De of methyl orange in modified gelatin are shown in Table 5. The linear relationships can be seen in both the unmodified gelatin and the modified gelatin samples as determined by the R2 values (0.9674 and 0.9405 respectively). This result demonstrated that the diffusion process was followed by the first order kinetics. The De of methyl orange pigments embedded in unmodified gelatin and glutaraldehyde modified gelatin had a significant difference (p<0.05), and the value of the De were 11.52×10-4 and 11.20×10-4 m2/s, respectively in Table 5. It indicated that gelatin modified by glutaraldehyde affected the diffusion of pigment molecules in a gel. Fourier transform infrared spectroscopy confirmed the formation of amide bonds between glutaraldehyde and primary amino groups in gelatin (Chen & Chang, 2012). Glutaraldehyde modified gelatin gel had a smaller pore size, stronger mechanical properties, and compact structure (Farris et al., 2011). Therefore, the diffusion of low molecular weight solutes in the membrane was hindered by glutaraldehyde modified gelatin gel. Zhu and coworkers (2019) found that there was a significant difference in the diffusion coefficients between modified gelatin and nonmodified gelatin during the controlled release process of methylene blue, which was confirmed by the results of infrared spectroscopy (FT-IR) and scanning electron microscopy (SEM). It indicated that the structure of the glutaraldehyde modified gelatin

Journal Pre-proof carrier could be more compact and the diffusion coefficient was smaller than that of unmodified gelatin. 3.4.2 Effect of ultrasound assisted-treatment on the diffusion of methyl orange pigment in modified gelatin gel The frequency and power of ultrasound are important factors in ultrasound assisted-treatment. Table 6 shows that the equations of the versus the time during the ultrasonic assisted-treatment at different frequency has a linear relationship. It is manifestly seen from Table 6 that the De of methyl orange in modified gelatin processed at 28, 40, 50 and 135 kHz were 18.44×10-4, 28.69×10-4, 23.94×10-4 and 15.88×10-4 m2/s, respectively. The De of methyl orange pigments increased first and then decreased with the increase of frequency of ultrasound-assisted treatment. The cavitation bubbles produced by low-frequency ultrasound were not easy to collapse and would occupy the gel pores in a relatively short time, which impeded the diffusion of methyl orange. However, the De of methyl orange pigments decreased gradually with high frequency treatment. The decrease of De mainly results from the collapsion of cavitation bubbles accompanied by local high temperature, high pressure, strong shear force and strong micro-jet production with high frequency treatment, which led to the changes of the structure of the gel (Gogate & Kabadi, 2009; Wang et al., 2018b). The higher the frequency of ultrasound, the longer the time of ultrasound-assisted treatment, the more destructive the structure of the gel and the lower De value(Marquez et al., 2013). Besides, strong oxidizing free radicals generated by heating decomposition of the medium at the interface of gas and solution in cavitation bubbles, which could degrade methyl orange

Journal Pre-proof pigments and reduce their diffusion coefficients in extreme circumstances (Li, Li, & Gao, 2019; Zhang et al., 2019). It could be seen that proper ultrasonic treatment promoted the diffusion of methyl orange in gel effectively. The effect of ultrasonic power on the De of methyl orange in modified gelatin during the ultrasound-assisted treatment process is shown in Table 7. The results indicated that the equation of De followed linear relationships, as determined by the R2 values from 0.9744 to 0.9971. According to Table 7, the De increased first and then decreased with the increase of ultrasonic power, however, the De of methyl orange in modified gelatin increased when the ultrasonic assisted-treatment power reaches 0.35 W/cm2. The De of methyl orange in modified gelatin with ultrasound power ranging from 0.05, 0.15, 0.25, 0.35 and to 0.45 W/cm2 at 40 kHz were 26.56×10-4, 29.25×10-4, 21.50×10-4, 25.06×10-4 and 28.69×10-4 m2/s, respectively. For about 60 min, the maximum De of methyl orange was 29.25×10-4 m2/s with ultrasound-assisted treatment (40 kHz, 0.15 W/cm2), which was 161.39% higher than that of non-ultrasonic treatment. Under the condition of ultrasound-assisted treatment, it was easier to form cavitation bubbles with the increase of ultrasound power, and the bubble collapse was more intense, and the cavitation effect was more obvious. The improvement of the cavitation effect led to the increase of the methyl orange transfer. Cavitation bubbles generated by high power were not easy to collapse which caused that the effect of cavitation was weak and the diffusion coefficient was reduced (Qiao et al., 2013). It was interesting to find that the De of methyl orange in modified gelatin increased when the ultrasonic power reached at 0.35 W/cm2 and 0.45 W/cm2. It might be due to the heat generated by

Journal Pre-proof cavitation promoted the swelling of the gels at 40 kHz with high ultrasonic power under ultrasound assisted-treatment. Biological materials normally have softer textures and are more liable to be affected by ultrasound than polymeric materials. These results were similar to the findings reported by Tao et al. (2020), who found that the size of macroporous resin particles exhibited a decreasing trend in the ultrasonic field, and the De of anthocyanin in macroporous resin with high ultrasonic power (279 W/L) was 41.65% higher than that of low ultrasonic power treatment (106 W/L). 3.4.3 Effect of ultrasonic pretreatment on the diffusion of methyl orange pigment in modified gelatin gel In addition to ultrasound-assisted processing, ultrasound pretreatment is also commonly used in the industry. Table 8 shows that the effect of ultrasonic frequency on the De in modified gelatin during the ultrasound pretreatment processing. When the ultrasonic power was fixed at 0.45 W/cm2, the De of methyl orange pigment in modified gelatin conforms to the linear equation of first-order dynamics. It was found that the diffusion coefficients of De at 28, 40, 50 and 135 kHz were 9.44×10-4, 7.50×10-4, 9.38×10-4 and 12.96×10-4 m2/s, respectively. It can be seen that with the increase of the frequency of ultrasonic pretreatment, the De of methyl orange pigment in modified gelatin first decreased and then increased, and reached the maximum at 135 kHz, which was different from the results of ultrasound assisted-treatment. Under the condition of short-time ultrasonic pretreatment, the higher the frequency, the shorter the time for the generation and collapse of cavitation bubbles. This may because the number of collapsed cavitation bubbles was far greater than that of the low frequency and the

Journal Pre-proof effect of cavitation was better than that, so the diffusion coefficient was the largest in a short time at high frequencies. Besides, the mesh structure of the gelatin carrier could become loose by the instantaneous destructive force of cavitation bubbles with high frequency ultrasound in a short time. The looser structure of modified gelatin promoted the diffusion of methyl orange pigment from modified gelatin with high frequency ultrasound. The results of exploring the effect of the ultrasonic power on the diffusion of methyl orange pigment in modified gelatin gel with ultrasound pretreatment are shown in Table 9. It can be seen that the equation of De follows linear relationships and agrees with the first order kinetics. The De with ultrasound pretreatment at different powers of 0.05, 0.15, 0.25, 0.35 and 0.45 W/cm2 were 7.19×10-4, 18.13×10-4, 18.31×10-4, 9.75×10-4 and 7.50×10-4 m2/s, respectively. With the increase of ultrasound power, the De of methyl orange pigments in modified gelatin increased first and then decreased, and arrived at the largest was at 0.25 W/cm2 and 40 kHz. Ultrasound with appropriate intensity could promote the diffusion of small molecule pigments, which was due to the cavitation effect of ultrasound (Huang et al., 2015). Instantaneous high temperature, high pressure and strong shear force would occur, which promoted the diffusion when the cavitation bubble collapsed. However, the ultrasonic pretreatment with high ultrasonic power might lead to the aggregation of modified gelatin gels and the reduction of the area ratio, which hindered the diffusion of methyl orange. That result was confirmed by Huang and coworkers’ research (2015) that the area ratio of alginatechitosan gel increased initially and decreased with the increase of ultrasonic power and

Journal Pre-proof the area ratio showed the maximum of 37.22% at 0.25 W/cm2. It was interesting that the law of the area ratio of the alginate-chitosan gel was in good agreement with the diffusion results with ultrasonic pretreatment. 4 Conclusion It was found that ultrasound conditions affected the specificity of immobilized papain to the substrate, which was directly reflected by the Km, Vmax, thermodynamic parameters and De. When the ultrasound assisted-treatment fixed at 135 kHz and 0.15 W/cm2, the reaction rate and the absolute value of ΔS were larger than that of other ultrasound conditions, and the values of Ea, ΔH and ΔG were the smallest. It proved that the optimal ultrasonic condition (135 kHz and 0.15 W/cm2) was conducive to the spontaneous enzymatic hydrolysis of immobilized papain during the ultrasound assisted-treatment process. Meanwhile, ultrasonic treatment could improve the diffusion ability of methyl orange pigment in modified gelatin gel. It indicated that the effect of ultrasonic-assisted treatment on the De was more obvious than ultrasonic pretreatment, and the impact of ultrasonic power on the De was more effective than that of ultrasonic frequency. In the viewpoint of energy saving, adjusting the ultrasonic power with ultrasonic pretreatment to control the progress of the enzymatic reaction of the immobilized papain, which could have broader application prospects in industrial production. Acknowledgements This research was supported by the National Natural Science Foundation of China (31371722),

the

13th

Five‐Year

the

State

Key

Development

Program

Journal Pre-proof (2016YFD0400802), Support Project of High-level Teachers in Beijing Municipal Universities in the Period of 13th Five-year Plan (CIT & TCD201804018), Construction of Service Capability of Scientific and Technological Innovation (PXM2019_014213_000010, PXM2018_014213_000033, PXM2018_014213_000014,

PXM2018_014213_000041,

19005857058)

and

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Journal Pre-proof Conflict of interest The authors declared that they have no conflicts of interest to this work.

Journal Pre-proof Author statement Manuscript ID: FOODHYD_2019_2411 Title: Effects of ultrasound on the kinetics and thermodynamic properties of papain entrapped in modified gelatin

We have made substantial contributions to the research and the manuscript and the acquisition and analysis of date for the manuscript. We have drafted and revised the manuscript for important intellectual content. We have approved the final version of the manuscript to be published and agree to be accountable for all aspects of the work. The authors of the manuscript who have made substantial contributes to the research in the work and manuscript, are named in the manuscript. Zeyu Zhang: Data curation, Writing - Original draft preparation, Investigation, Validation Ge Bai: Methodology, Investigation, Validation Duoxia Xu: Writing - Review & Editing, Project administration, Funding acquisition Yanping Cao: Conceptualization, Supervision, Project administration, Funding acquisition

Zeyu Zhang, Ge Bai, Duoxia Xu, Yanping Cao

Journal Pre-proof Fig. 1 Plane graph of assemble ultrasonic bath system equipment (1, ultrasonic power supply; 2 and 3, regulator for frequency and power of ultrasound; 4, ultrasonic bath; 5, sample flask; 6, thermostatic water). Fig. 2 Effect of ultrasonic frequency (28, 40, 50 and 135 kHz ） on the apparent reaction rate constant of immobilized papain with constant power at 0.05 W/cm2 during the ultrasound assisted-treatment process. Fig. 3 Effect of ultrasonic power (0.05, 0.15, 0.25, 0.35 and 0.45 W/cm2) on apparent reaction rate constant of immobilized papain with constant frequency at 135 kHz during the ultrasound assisted-treatment process. Fig. 4 Effect of ultrasonic power (0.05, 0.15, 0.25, 0.35 and 0.45 W/cm2) on the Vmax of immobilized papain at different ultrasonic frequencies (28, 40, 50 and 135 kHz) during the ultrasound assisted-treatment process. Fig. 5 Effect of ultrasonic power (0.05, 0.15, 0.25, 0.35 and 0.45 W/cm2) on the Km of immobilized papain at different ultrasonic frequencies (28, 40, 50 and 135 kHz) during the ultrasound assisted-treatment process.

Journal Pre-proof Figure 1

Journal Pre-proof

Figure 2

Journal Pre-proof Figure 3

Journal Pre-proof Figure 4

Journal Pre-proof Figure 5

Journal Pre-proof Highlights > The enzymatic hydrolysis of casein immobilized papain accorded with the first-order kinetics. > The cavitation generated by ultrasound could increase the reaction rate of enzymatic reaction. > Rapid formation of papain-casein complexes depended on lower apparent activation energy, activation free energy, enthalpy and bigger entropy. > The diffusion coefficient of glutaraldehyde modified gelatin carrier was lower than that of unmodified gelatin. > Ultrasound could improve the diffusion ability of methyl orange pigment in modified gelatin gels.

Journal Pre-proof Table 1 Kinetic equation of casein hydrolysis by immobilized papain at the non-ultrasonic field. Table 2 The variety of the apparent activation energy of immobilized papain with non-ultrasonic treatment and with different ultrasound assisted-treatments. Table 3 The ΔH of immobilized papain with different ultrasound assisted-treatments (the frequencies of 28, 40, 50 and 135 kHz, and the powers of 0.05, 0.15, 0.25, 0.35 and 0.45 W/cm2), and different temperatures (30, 35, 40, 45 and 50℃). Table 4 The influence of ultrasound assisted-treatment on the ΔH, ΔG and ΔS of the enzymatic reaction of the immobilized papain. Table 5 Effect of glutaraldehyde on the diffusion coefficient of methyl orange in modified gelatin. Table 6 Effect of ultrasonic power at 0.45 W/cm2 on the diffusion coefficient in glutaraldehyde modified gelatin during the ultrasound-assisted treatment process. Table 7 Effect of ultrasonic frequency at 40 kHz on the diffusion coefficient in glutaraldehyde modified gelatin during the ultrasound-assisted treatment process. Table 8 Effect of ultrasonic power at 0.45 W/cm2 on the diffusion coefficient in glutaraldehyde modified gelatin during the ultrasound pretreatment process. Table 9 Effect of ultrasonic frequency at 40 kHz on the diffusion coefficient in glutaraldehyde modified gelatin during the ultrasound pretreatment process.

Journal Pre-proof Table 1 Reaction order Zero order reaction

First order reaction

Second order reaction

Initial concentration (mg/mL)

Equation

R2

k (min-1)

Average of the k (min-1)

RSD

10 8 6 4 2

y = -1.80×10-3 x + 10 y = -2.07×10-3 x + 8 y = -1.53×10-3 x + 6 y = -1.10×10-3 x + 4 y = -4.88×10-4 x + 2

0.98 0.94 0.97 0.91 0.92

-1.80×10-3 -2.07×10-3 -1.53×10-3 -1.10×10-3 -4.88×10-4

-1.71×10-3

58

10 8 6 4 2

y = 1.83×10-4 x y = 2.59×10-4 x y = 2.55×10-4 x y = 2.78×10-4 x y = 2.45×10-4 x

0.98 0.94 0.97 0.91 0.92

1.83×10-4 2.59×10-4 2.55×10-4 2.78×10-4 2.45×10-4

2.44×10-4

14

10 8 6 4 2

y = 1.83×10-5 x y = 3.25×10-5 x y = 4.26×10-5 x y = 6.97×10-5 x y = 1.28×10-4 x

0.97 0.94 0.97 0.91 0.92

1.83×10-5 3.25×10-5 4.26×10-5 6.97×10-5 1.28×10-4

5.72×10-5

72

Journal Pre-proof Table 2 Ultrasound conditions Non-ultrasound

lnk-1/T equation

Ea (J/mol)

y = -5271.12 x + 8.21

43824.11±610.52a

0.05 W/cm2

28 kHz 40 kHz 50 kHz 135 kHz

y = -4381.68 x + 3.81 y = -4385.70 x + 6.32 y = -4259.38 x + 5.71 y = -4195.27x + 5.40

36429.27±698.70b 36462.72±692.40b 35412.52±472.22bc 34879.47±427.41c

135 kHz

0.05 W/cm2 0.15 W/cm2 0.25 W/cm2 0.35 W/cm2 0.45 W/cm2

y = -4195.27x + 5.40 y = -3992.20 x + 5.07 y = -4344.64 x + 6.25 y = -4698.90 x + 7.30 y = -5230.56 x + 9.10

34879.47±427.41cd 33191.14±448.41d 36126.73±804.89c 39066.65±316.28b 43486.89±554.33a

t=0.05 p<0.05

Journal Pre-proof Table 3 ΔH (J/mol) Ultrasound conditions

0.05 W/cm2

135 kHz

Temperature（℃） 30

35

40

45

50

28 kHz 40 kHz 50 kHz 135 kHz

33908.88 33942.33 32892.13 32359.08

33867.31 33900.76 32850.56 32317.51

33825.74 33859.19 32808.99 32275.94

33784.17 33817.62 32767.42 32234.37

33742.60 33776.05 32725.85 32192.80

0.05 W/cm2

32359.08

32317.51

32275.94

32234.37

32192.80

0.15 W/cm2

30670.75

30629.18

30587.61

30546.04

30504.47

0.25

W/cm2

33600.93

33559.36

33517.79

33476.22

33434.65

0.35

W/cm2

36546.26

36504.69

36463.12

36421.55

36379.98

0.45 W/cm2

40966.50

40924.93

40883.36

40841.79

40800.22

Journal Pre-proof Table 4 Ultrasound conditions

0.05 W/cm2

135 kHz

ΔH (J/mol)

ΔG (J/mol)

ΔS (J/mol·K)

28 kHz 40 kHz 50 kHz 135 kHz

33825.74 33859.19 32808.99 32275.94

55040.31 54021.23 55873.13 54578.87

-67.75 -64.38 -73.65 -71.22

0.05 W/cm2

32275.94

54578.87

-71.22

0.15 W/cm2

30587.61

53100.66

-71.89

0.25 W/cm2

33517.79

54433.74

-66.79

0.35 W/cm2

36463.12

55458.20

-60.66

0.45 W/cm2

40883.36

55564.97

-46.88

Journal Pre-proof Table 5 Non-ultrasonic conditions

Equation

De（10-4 m2/s）

R2

Unmodified Gelatin

y=-0.0184 x+0.0874

11.52±0.14a

0.9671

Modified Gelatin

y=-0.0179 x+0.0810

11.20±0.05b

0.9405

t=0.05 p＜0.05

Journal Pre-proof Table 6 Frequency of ultrasound-assisted processing （kHz）

Equation

De（10-4 m2/s）

R2

28

y=-0.0295x-0.0429

18.44

0.9386

40

y=-0.0459x-0.1686

28.69

0.9853

50

y=-0.0383x-0.0235

23.94

0.9709

135

y=-0.0254x-0.0183

15.88

0.9627

Journal Pre-proof Table 7 Power of ultrasound-assisted

Equation

De（10-4 m2/s）

R2

0.05

y=-0.0425x+0.1122

26.56

0.9971

0.15

y=-0.0468x+0.0623

29.25

0.9922

0.25

y=-0.0344x+0.1156

21.50

0.9951

0.35

y=-0.0401x+0.1535

25.06

0.9744

0.45

y=-0.0459x-0.1686

28.69

0.9853

processing（W/cm2）

Journal Pre-proof Table 8 Frequency of ultrasound pretreatment (kHz)

Equation

De（10-4 m2/s）

R2

28

y=-0.0151x-0.7522

9.44

0.8777

40

y=-0.0120x-1.1122

7.50

0.8672

50

y=-0.0150x-0.8344

9.38

0.8829

135

y=-0.0203x-0.7559

12.69

0.9805

Journal Pre-proof Table 9 Power of ultrasound pretreatment (W/cm2)

Equation

De（10-4 m2/s）

R2

0.05

y=-0.0115x-0.8650

7.19

0.9512

0.15

y=-0.0293x-1.0352

18.31

0.8894

0.25

y=-0.0290x+0.8226

18.13

0.9515

0.35

y=-0.0156x-1.2024

9.75

0.7817

0.45

y=-0.0120x-1.1122

7.50

0.8672