Exploration on self-equilibrium rule and adsorption-desorption model between pine nut (Pinus koraiensis) peptide molecules and environmental moisture molecules

Journal Pre-proofs Exploration on self-equilibrium rule and adsorption-desorption model between pine nut (Pinus koraiensis) peptide molecules and environmental moisture molecules Ruiwen Yang, Huapeng Ju, Liyan Yuan, Haiqing Ye, Songyi Lin PII: DOI: Reference:

S0963-9969(20)30107-1 https://doi.org/10.1016/j.foodres.2020.109082 FRIN 109082

To appear in:

Food Research International

Received Date: Revised Date: Accepted Date:

22 October 2019 9 January 2020 4 February 2020

Please cite this article as: Yang, R., Ju, H., Yuan, L., Ye, H., Lin, S., Exploration on self-equilibrium rule and adsorption-desorption model between pine nut (Pinus koraiensis) peptide molecules and environmental moisture molecules, Food Research International (2020), doi: https://doi.org/10.1016/j.foodres.2020.109082

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Exploration on self-equilibrium rule and adsorption-desorption model between pine nut (Pinus koraiensis) peptide molecules and environmental moisture molecules

Ruiwen Yang 1, Huapeng Ju 2, Liyan Yuan2, Haiqing Ye 1, Songyi Lin 1, 2,*

1:

College of Food Science and Engineering, Jilin University, Changchun, 130062, P.R.

China 2:

National Engineering Research Center of Seafood, School of Food Science and

Technology, Dalian Polytechnic University, Dalian 116034, P.R. China

Running title: Model analysis of adsorption and desorption in PNP powder during storage

*To the Corresponding author Professor Songyi Lin College of Food Science and Engineering, Jilin University Changchun, 130062, P.R. China Tel.: +86 18840821971 Fax: +86 411 86318655 E-mail: [email protected]

1

Abstract The storage of pine nut (Pinus koraiensis) peptide (PNP) powder involves hygroscopic phenomena. To investigate the adsorption and self-equilibrium rules between these peptides and the environmental moisture molecules, several studies such as low-field nuclear magnetic resonance (LF-NMR), dynamic vapor sorption (DVS) and adsorption-desorption models were done. The results showed that the outward moisture migration occurred during storage as 7.80% and 16.68% moisture were respectively constrained by the original sample and 90 days after lyophilization, by chemical bonding. Additionally, 1.79% moisture was lost in PNP powder at day 90. The optimized adsorption model for PNP powder was changed from Henderson’s to Oswin’s model during the 90 days’ storage whereas the optimized desorption model was changed from Halsey’s to GAB’s model. The PNP powder at day 90 presented smaller particles with an average diameter and height of 15.645 nm and 50 nm, respectively, and it contained more molecular moisture which cannot be removed. The free thiol of the PNP powder at day 0 and day 90 was 1.75 ± 0.16 μM SH/g and 1.95 ± 0.16 μM SH/g, respectively, and the total sulfhydryl was 101.46 ± 1.06 μM SH/g and 118.44 ± 1.27 μM SH/g. The registered increased sulfhydryl content contributed to the generation of off-flavor. Keywords: Adsorption-desorption models; Moisture self-equilibrium; Hygrothermal parameters; Quality deterioration

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1. Introduction Pine nut (Pinus koraiensis) peptide (PNP) powder, a by-product of the Korean pine seed oil, has been often considered as a waste disposal for the food industry. PNP powder ranging 3-10 kDa presents interesting biological activities such as immunocompetence and antioxidant (Lin, Liu, Liu, & Yu, 2017 a; Yang, Li, Lin, Zhang, & Chen, 2017). During the process of production, the PNP powder undergoes through liquification to become sticky, nubby and smelly. This influences crucially the quality of the product including its bioactivities, existence form and flavor. Therefore, the study of the process of PNP powder storage is imperative. Several previous studies focused on food storage stability: Amaral et al. investigated the microbiological, physicochemical and sensory characteristics of lamb pâté during 90 days of storage and Todaro et al. described the effects of refrigerated storage up to 180 days (Amaral et al., 2015; Todaro et al., 2017). The detecting times were 15, 30, 60, 90, 120, and 180 day. In our previous studies, the PNP powder was stored for 30 days with 75% relative humidity (RH), at 25 °C. The results showed that Maillard reaction, lipids oxidation and microbial fermentation occurred during this time (Lin, Yang, Cheng, Wang, & Qin, 2017 b). However, more research will be needed in order to study the moisture absorption behavior during the storage, to build mathematical isotherm models of the PNP powder, and calculate sorption characteristics and adsorption-desorption kinetic parameters. This aids the comprehension on how moisture influences the PNP powder and specially its deterioration. In the terms of the method selection, the low-field nuclear magnetic resonance (LF3

NMR) was used to determine the water dynamics of Asp-His-Thr-Lys-Glu peptide and of water content in sea cucumber peptide powders during storage (Yang et al., 2016; Wang et al., 2019). These studies indicated that LF-NMR has extensive applications in the detection of moisture migration. Additionally, this method can be used to reveal the form of interactions between moisture molecules and food. The dynamic vapor sorption (DVS) was used before to investigate the water dynamics in the egg white peptide AspHis-Thr-Lys-Glu during storage and the moisture absorption of soybean peptide SerHis-Glu-Cys-Asn (Yang et al., 2016; Lin et al., 2016 a). It was concluded that DVS is an effective tool for obtaining information about the sorption kinetics of foods. The measurement of moisture sorption isotherms is important in agricultural engineering, as the inherent relationship between moisture and relative humidity during the drying and storage processes can affect food (Mulet, García-Pascual, Sanjuán, & García-Reverter, 2002). Mathematical models to describe moisture sorption isotherms are being used for predicting water sorption properties of food, and can be divided into several categories, kinetic models based on a mono-layer film, kinetic models based on a multi-layer and condensed film, kinetic models based on a multi-layer, and condensed film and empirical models (Teunou, Fitzpatrick, & Synnott, 1999). So that includes many models: Brunauer-Emmett-Teller (BET), Smith, Langmuir, Ferro Fontan, Peleg, Guggenheim-Anderson-de Boer (GAB), modified GAB, Timmermann GAB, Oswin, modified Oswin, Henderson, modified Henderson, Chung-pfost, modified Chung-pfost, Halsey and modified Halsey and others (Basu, Shivhare, & Mujumdar, 2006; AlMuhtaseb, Mcminn, & Magee, 2002). The characteristic parameters of hygroscopicity 4

can be obtained by mathematical model and the quantitative of hygroscopicity process to guide the production and storage of terminal products. In this present study, the PNP products were stored in extreme conditions (75% RH and 25 °C) with the aim to create an environment set to be as severe as possible. This setting made visible the majority of the degradation products. Also, this environment can provide sufficient moisture molecules to be bound to peptide molecules. As far as we know, there is no research on combining LF-NMR, DVS and adsorption-desorption model to explore the adsorption and self-equilibrium rules between the PNP powder and environmental moisture molecules at home and abroad. Hence, in terms of food industry, the impact of our methods can be regarded as fully innovative and meaningful. The objectives of this work were to: (1) determine moisture migration from and to PNP powder by LF-NMR to find the adsorption rule between environmental moisture molecules and the peptide molecules; (2) measure PNP powder sorption isotherms by DVS, to study the sorption isotherms’ type and water self-equilibrium rule; (3) calculate the hygrothermal parameters of the PNP powder, including the equilibrium moisture content (EMC) and critical relative humidity (CRH); (4) build the optimal adsorptiondesorption model of the PNP powder by nonlinear regression method; (5) measure the surface morphologies of the PNP powder by atomic force microscopy (AFM), and (6) to determine the sulfhydryl and disulfide contents to assess the deterioration levels of the peptide powder.

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2. Materials and methods 2.1. Materials and regents The PNP powder was obtained from the Good Manufacturing Practice (GMP) production department at College of Food Science and Engineering, Jilin University (Changchun, China). The GMP’s production is up to the standard of class 100000, and the information of GMP regulations was primarily sourced from the government website China Food and Drug Administration. 5, 5’-Dithiobis (2-nitrobenzoic acid) (DTNB), ethylene diamine tetraacetic acid (EDTA), sodium dodecyl sulfate (SDS), βmercaptoethanol, urea, guanidine hydrochloride and trichloroacetic acid (TCA) were purchased from Beijing Chemical Plant (China) and all reagents were of analytical grade. 2.2. Preparation of PNP powder The PNP powder was prepared as reported by Lin et al., with additional sterilization steps in the pilot scale test expansion at the GMP production department (Lin et al., 2017 b). The PNP powder was weighed into 20 mL glass vials and stored in a temperature and humidity controlled chamber (STIK Co., Ltd., Shanghai, China) at 75 % RH and 25 °C. Storage interval times were set at 0, 6, 15, 30 and 90 days. 2.3. Exploration of the adsorption rule of PNP powder The exploration of the adsorption rule was achieved by LF-NMR. Three vials from each monitoring point were collected to be further analyzed. Samples for each storage interval were tightly sealed with polytetrafluoroethylene (PTFE) caps and placed into the NMR glass tubes. The water migration of the PNP powder was analyzed using a 6

NMI-20 NMR analyzer (Niumag Co., Ltd., Shanghai, China) by the method already described with some alterations (Wang et al., 2019). The time constant that measures how fast the signal decays is called spin - spin relaxation time or transverse relaxation time (T2). This was measured using the Carr-Purcell-Meiboom-Gill (CPMG) sequence. The MesoMR-60-40 mm was used as the magnet probe and the duration between successive scans (TW) was 2000 ms. The receiver gain (RG) represents the amplification of the nuclear magnetic signal before it is received by the receiver and the settings were RG1=20 dB, DRG1=1; PRG=1. The number of the scans (NS) was 3000 while SW is the receiver bandwidth frequency at 200 kHz. The parameter to control the first data point acquired (RFD) was 0.02 ms and the iterations of the inversion process was set up to 1×106. A linear distribution of exponential decays was defined by the following equation (Lin, Yang, Li, Chen, & Zhang, 2016 b):

M(t) 

 t M 2iexp  T2i   e(t) i 1  



n

(1)

Where M(t) is the residual magnetization at a given time t, n is the number of exponential components in the samples, M2i is relaxation amplitude of the ith component, T2i is transverse relaxation time of the ith component, and e(t) is the residual error. The signal per mass of total water was the sum of each signal per mass component. The contents of different water fractions were calculated by the following equations. They represent the moisture absorption ability of samples.

Total signal per mass(/g) 

7



n i 1

m

A2i (2)

Water content(%) 

A2i



n i 1

A2i

 100% (3)

Where A2i is the area of different water fraction, and m is the mass of the PNP powder. 2.4. Study of the water self-equilibrium rule of PNP powder Water sorption and desorption kinetics of the PNP powder at day 0, day 90 and day 90 after lyophilization were measured by a method previously described, with some modifications (Yang et al., 2016). Controlled atmosphere microbalance (DVS apparatus, Surface Measurement System Ltd, London, UK) was used to obtain the water vapor sorption and isotherm plot. The EMC of the each sample was calculated at each RH. The PNP powder at day 0 and day 90 after lyophilization were placed on the aluminum holder in the DVS chamber. The RH of the chamber was controlled by dry nitrogen mixed with water vapor (0.5 L/min). In the initial step of this method, the drying, the RH was to set to 0% for 3 h. The RH increased from 0% to 90% with gradient steps of 10% to finally reach the maximum of 95%. Afterwards, the RH was decreased in the reverse order to 0%. As for the samples of PNP powder at day 90, the RH firstly decreased from 75% to 0%. Afterwards, the RH was increased from 0% to 90% and then decreased in reverse order to 0%. When the change of dm/dt was lower than 0.002% during 5 min or when the running time reached 360 min, this meant that the equilibrium was reached. Afterwards, the target RH was automatically changed to the next preset value. 2.5. Calculation of hygrothermal parameters The humidity of ambient air is one of the external causes for hygroscopicity of powders. Critical relative humidity (CRH) is an index to measure the moisture 8

absorption of a powder (Fan, 1997). It is when the RH reaches a certain value-the CRH value-that the moisture absorption rate increases sharply. If powders are stored and prepared in RH levels lower than its CRH, this can reduce its hygroscopic speed. For the sorption isotherm curves, if the curve points at both ends of the curve as tangent lines are taking into account, the horizontal value that corresponds to the intersection of the two tangents is the CRH of a powder. 2.6. Mathematical modeling and comparison of adsorption and desorption isotherms Because of the different combination of water fractions in powders, it is difficult to figure out the theoretical isothermal adsorption equation. There are several mathematical models to describe water sorption isotherms of agricultural materials. In this paper, eleven commonly used models were used to calculate the sorption and desorption isotherms. They were BET, GAB, modified GAB, Oswin, modified Oswin, Henderson, modified Henderson, Chung-pfost, modified Chung-pfost, Halsey and modified Halsey. Brunauer, Emmett and Teller presented the multi-molecular layer theory (BET) based on the single molecular layer adsorption theory (Brunauer, Emmet, & Teller, 1938). The BET equation is a fundamental milestone in the Type II and III interpretation of multilayer sorption isotherms. The two constant equation of BET was summarized. M 

abaw (1  aw)[1  (b  1)aw]

(4)

Where M is equilibrium of moisture content (%, dry basis), a is the monolayer saturation adsorption (%), b is the BET constant and aw is the water activity. The following equation, developed by Van den Berg, refined the BET theories and 9

proposed the equation with three constants (Van den Berg, 1984) whereas Jayas and Mazza introduced the temperature factor into the equation (Jayas, & Mazza, 1993). This modified GAB model is below: M 

M 

abcaw (1  caw)(1  bcaw  caw)

(5)

ab(c/T)aw (1  baw)[1  baw  b(c/T)aw]

(6)

Where M is the equilibrium moisture content (%, dry basis), a, b and c are the specific constants in equations, T is the absolute temperature (K) and aw is the water activity. Oswin presented an equation of the form as a series expansion, in a sigmoid-shaped curve (Oswin, 1946). Chen revised the model because he found out the linear relationship between the parameters and temperature (Chen, 1988): aw b M  a( ) 1  aw

(7)

aw 1/c M  (a  bT)( ) 1  aw

(8)

Where M is the equilibrium moisture content (%, dry basis), a, b and c are the specific constants in equations, T is the absolute temperature (K) and aw is the water activity. Henderson equation is regarded as the most widely used model to correlate the water activity and the amount of water absorbed. Thompson, Peart and Foster added a constant to the temperature to revise the equation (Thompson, Peart, & Foster, 1968). aw  1  exp(  aT M b )

(9) aw  1  exp[  a (T  b ) M ] c

(10) Where M is the equilibrium moisture content (%, dry basis), a, b and c are the specific 10

constants in equations, T is the absolute temperature (K) and aw is the water activity. Chung and Pfost studied the evaporation energy of moisture in the adsorption of grain, and concluded that the change of adsorption free energy correlates with the water content (Chung, & Pfost, 1967 a; Chung, & Pfost, 1967 b). In order to make the equation has better fitting, Pfost et al. added a constant to the temperature to modify the equation (Pfost, Mourer, Chung, & Milliken, 1976). a exp(cM )] bT

(11)

a exp(cM )] bT

(12)

aw  exp[

aw  exp[

Where M is the equilibrium moisture content (%, dry basis), a, b and c are the specific constants in equations, T is the absolute temperature (K) and aw is the water activity. Halsey described the multilayer molecular adsorption model (Halsey, 1948), in which the potential energy of a molecule varies inversely as the Cth power distances from the surface. Iglesias and Chirife proposed a modified Halsey equation by expressing the parameter with an empirical exponential function (Iglesias, & Chirife, 1976 b). aw  exp(

 a c M ) bT

aw  exp[-exp( a  b T) M  c )]

(13) (14)

Where M is the equilibrium moisture content (%, dry basis), a, b and c are the specific constants in equations, T is the absolute temperature (K) and aw is the water activity. 2.7. Surface morphologies of PNP powder by atomic force microscopy The microstructure and topography of the original PNP powder and PNP powder at 11

day 90 were obtained with Park AFM (Park NX10; Park Systems Corporate, Gwanggyo, Korea) at room temperature. The 10 μL of samples in Milli-Q water (10 μg/mL) were immediately deposited on a fresh mica surface (Agar Scientific, Beijing, China), and naturally air-dried in a fume hood. Samples were scanned on true noncontact mode. The sample thickness and scan range were 2 mm and 5μm, respectively. Data was processed and analyzed with NanoScope Analysis (Bruker Co., Karlsruhe, Germany). 2.8. Contents of sulfhydryl and disulfide in PNP powder The sulfhydryl (free SH-) and total sulfhydryl (SH- and reduced SS-) of the PNP were measured according to the procedure of Ellman and Beveridge, Toma and Nakai with some modification (Ellman, 1959; Beveridge, Toma, & Nakai, 1974). 75 mg of PNP powder was dissolved in 10 mL PBS (0.1 mol/L, pH 8.0), which contained EDTA (1 mmol/L) and 1% SDS. The mixture was stirred for 30 min at 25 °C. From this solution, 3 mL were added to 3 mL PBS (0.1 mol/L, pH 8.0), which contained EDTA (1 mmol/L) and 1% SDS. Then to this solution, 0.1 mL DTNB (39.6 mg DTNB dissolved in 10 mL PBS) were added and submerged in a water bath for 1 h at 25 °C. After, the solution was centrifuged at 10000 g for 30 min and the supernatant was collected and its absorbance measured at 412 nm to calculate the free thiol with the extinction coefficient of 13600 M-1. The control group was designed without DTNB. As for the total sulfhydryl, 1 mL of PNP solution was added to 0.05 mL βmercaptoethanol and 4 mL urea-guanidine hydrochloride solution (8 mol/L urea and 5 mol/L guanidine hydrochloride). The solution was submerged in a water bath for 1 h at 25 °C. After that, 10 mL of 12% TCA were added to the solution and let to stand in the 12

water bath for another 1 h at 25 °C. The mixture was then centrifuged at 5000 g for 10 min. After, the precipitate was dispersed in 5 mL of 12% TCA, and the βmercaptoethanol was removed by centrifugation. This last step was repeated twice. Finally, the precipitate was dispersed in 10 mL PBS (0.1 mol/L, pH 8.0), which contained EDTA (1 mmol/L) and 1% SDS, and 0.08 mL DTNB were added. The mixture was kept in the water bath for 1 h at 25 °C, and then centrifuged at 10000 g for 30 min. The supernatant was collected and its absorbance measured at 412 nm to calculate the total sulfhydryl with the extinction coefficient of 13600 M-1: μM SH/g 

73.53  A412  D C

(15)

Where A412 is the absorbance of solution at 412 nm, C was the concentration of sample (mg/mL), D is the dilution factor (2.03 and 10.08 for sulfhydryl and total sulfhydryl, respectively). 2.9. Statistical analysis Data analysis was carried out with SPSS 13.0 software (SPSS Inc., Chicago, IL, USA). The significant analysis of the LF-NMR results was calculated using analysis of variance (ANOVA) and the least significant difference (LSD) test (P < 0.05). All experiments were performed three times and the data expressed as the mean ± standard deviation (SD). The mathematical modeling of eleven commonly used models was achieved with the basis of regression analysis. Auto2Fit 5.5 (7D-Soft High Technology Inc.) was used to execute the curve fitting and regression analysis. This algorithm solved the problem of the initial value that must be given for numerical optimization calculation. The convergence tolerance was 1×e-10. The maximum of iterations was 13

1000 and the screen update rate was 20. The goodness of fit of each model was assessed with error sum of squares (SSE), root mean square error (RMSE), coefficient of determination (R2) and chi square (χ2), and were calculated using following equations (Xie, 2010; Mehta, & Singh, 2006; Bonner, & Kenney, 2013):

SSE 

n

 ( yi 



2

yi)

(16)

i 1

  1 RMSE   n  

1



n

  yi  i 1 n



 yi 

 yi   

yi

i 1



2

2

2     100  

2

     yi yi    i 1  2  R  1 n 2  yi  yi n

i 1

2



     yi  yi   i 1    n  N n

(17)



(18)

2

(19)

Where yi is the experimental value, ŷi is the predicted value, yi is the average value. n is the number of observations and N is the number of constants.

14

3. Results and discussion 3.1. Adsorption rule between environmental moisture molecules and peptide molecules The LF-NMR has extensive applications in the detection of moisture migration. Transverse relaxation T2 from a CPMG pulse experiment is shown in Figure 1 (A). The signal amplitude decreased with the extension of the time and the results showed that the free decay highly depended on the storage time. This way the shorter the storage time, the faster the decay was. The Figure 1 (B) showed the distributions of T2 relaxation time of PNP powder at 75% RH and 25 °C at 0 days, 6 days, 15 days, 30 days and 90 days. The T2 relaxation time represents the distribution of the water fractions. Four proton fractions were found in the PNP powder. The fastest fraction, with the relaxation time of 0.1~1 ms, was regarded as the combined water (T21) and the next fraction, with the relaxation time of about 10~100 ms, was considered as immobilized water (T22). Double hump was observed with the relaxation time of approximately 10~100 ms. T22 was the fraction with a relaxation time of approximately 9~25 ms followed by T2b with a relaxation time of about 35~55 ms. This was possibly caused by two types of hydrogen protons that had a similar form and experienced a dynamic exchange, which meant that the signal could not be separated by LF-NMR (Li et al., 2015). T2b had more degrees of freedom and binding sites than T22, however both considered to be immobilized water. The final fraction T23, had a relaxation time of approximately 100~300 ms, and was identified as free water. Thus, the process of storage during 90 days, the amplitude of four proton fractions was dynamic changed. 15

The changes of signal per mass of total water on PNP powder are illustrated in Figure 1 (C). The total signal per mass showed the tendency to increase slowly, achieving the maximum of 701.91±5.25 (au.ms)/g at day 30, and reaching 694.42±4.90 (au.ms)/g at day 90. Furthermore, in order to investigate the decreased quality of the PNP powder, the contents of water distribution were analyzed (Figure 1 C). The content of combined water achieved a maximum at day 6, gradually decreasing until day 90. Accordingly, the content of immobilized water gradually increased at the subsequent storage process. Wu et al. proposed that the decreased of the content of T2 reflected in the loss of water and vice-versa (Wu et al., 2006). The results indicated that PNP powder had significant moisture migration during the storage as the combined water and moisture accumulated at day 6, migrated to immobilized water from day 15. In order to analyze the migration of water fractions, the changes of T2 relaxation times are shown in Figure 1 D. T2 is the time it takes the excited spin-spin proton to achieve dynamic equilibrium after energy exchange with the adjacent protons and it reflects the difference in the degrees of freedom of water. The longer transverse relaxation time is, the higher the degrees of freedom, and vice-versa (Pitombo, & Lima, 2003). The results showed that the degrees of freedom of T22 have reduced, whereas the degrees of freedom of T2b and T23 increased gradually. These results proved that the outward moisture migration occurred during the storage. The obtained results confirmed the moisture migration rule that states that, with increased storage times, the combine water gradually transforms into the immobilized water that is simultaneously converted into free water. The simplified model of adsorption rule between environmental moisture molecules and peptide 16

molecules is illustrated in Figure 2, which can be used to interpret the proton dynamics of PNP powder during the storage. [Figure 1] [Figure 2] 3.2. Sorption isotherms type and water self-equilibrium rule of PNP powder The kinetic curve and moisture sorption isotherms of PNP powder at day 0, PNP powder at day 90 and PNP powder at day 90 after lyophilization are shown in Figure 3. In the continuous sorption 70%-95% RH stage, the rate of mass increased sharply for PNP powder at day 0 (Figure 3A). The registered rates were 6.69% at 70-80% RH, 10.44% at 80-90% RH and 16.62% at 90-95% RH. Therefore, the 70% RH could be set as a characteristic point, which can be related to the CRH of the sample. In the desorption processing, the rate of mass reached a minimum value of -18.56% at 80%70% RH. This can also be related to the CRH of the sample. The PNP powder absorbed water slightly when the RH of storage environment was less than 70% and the change of mass reached maximum value of 79.93% at 95% RH. The equilibrium time of desorption was approximately the same as the equilibrium time of sorption and the hysteresis values can be obtained from desorption values subtract sorption values. As shown in Figure 3B, the sorption curve of PNP powder at day 0 was lower than that of the desorption curve. In general, the desorption curve lies above sorption curve and a closed hysteresis loop is formed (Al-Muhtaseb et al., 2002), however, moisture desorption ultimately failed to reach its initial mass as 7.80% moisture was constrained by the PNP powder by chemical bonding. The sorption hysteresis value was close to 17

zero at 60% RH and the hysteresis reached maximum value of 14.32 % at 90% RH. It is known that the capillary porous structure of adsorbent are elastic and swell in the sorption process (Rao, 1941) and the loss of moisture causes the capillary porous structure to shrink and collapse. This way, structural alteration leads to the disappearance of the hysteresis because of the absence of capillary condensation. As shown in Figure 3C, the rate of mass increase of PNP powder at day 90 went up slightly. Only in the continuous sorption 80%-95% RH stage, the rate of mass increase of PNP powder at day 90 augmented steeply. The rates were 1.53% at 80-90% RH and 7.15% at 90-95% RH. The level of 80% RH was the characteristic point. During the desorption process, the rate of mass increase decreased significantly from 9.13% to 0.54% and this was because of CRH of the sample. The change of mass reached a maximum of 17.83% at 95% RH and the equilibrium time of desorption was longer than the equilibrium time of sorption as the sorption process took 410.71 min at and the desorption process 1098.03 min. As shown in Figure 3D, the desorption curve was above sorption curve between 50%-95% RH, and the intersections were seen between 40% and 50% RH. Overall, the desorption curve was lower than sorption curve. Furthermore, moisture desorption ultimately failed to reach its initial mass as 1.79% moisture was lost. The hysteresis reached maximum value 17.71 % at 80% RH and the sorption and desorption isotherms of PNP powder at day 90 were complex and could be classified as of an undefined structure type. The undefined structure makes PNP powder to lose its structure as the sample contains capillary water, however, when the content of moisture increases to a characteristic point, the undefined structure of the sample will collapse. 18

If the collapse is fast, the mass of moisture loss is greater than that of moisture absorption (Hancock, & Zografi, 1997). As shown in Figure 3E, the rate of mass increase of the PNP powder at day 90 after lyophilization increased slightly and only in the continuous sorption 70%-95% RH stage, the rate of mass increase increased relatively faster. The rates were of 2.78% at 70-80% RH, 9.45% at 80-90% RH and 12.46% at 90-95% RH, being 70% RH the characteristic point. The change of mass reached a maximum value of 51.36% at 95% RH and the equilibrium time of desorption (1487.36 min) was longer than the equilibrium time of sorption (1233.86 min). As shown in Figure 3F, the desorption curve was higher than the sorption curve. The moisture desorption ultimately failed to reach its initial mass as 16.68% moisture was constrained by the PNP powder. The hysteresis reached maximum value of 25.35 % at 80% RH. Generally, desorption curve of amorphous materials above the sorption curve during the moisture absorption process. As for crystalline materials, the sorption curve is above (Lin et al., 2016 a). This means that the structure of PNP powder at day 90 had definitely changed. The result of the change of mass indicated that the hydroscopicity of the PNP powder at day 90 reduced significantly as more moisture was constrained. The lyophilization could improve the quality of the stored PNP powder, as there was still a significant difference between the original sample and stored sample. These results showed that the structure of PNP powder was changed during the storage, and it cannot be reversed because new products might be generated during the moisture absorption process. [Figure 3] 19

3.3. Hygrothermal parameters of PNP powder CRH is a characteristic parameter of hygroscopic substances important for controlling storage conditions. The CRH of PNP samples were calculated (Figure 4). The linear equations for PNP powder at day 0 were y = 4.0935x - 308.95 and y = 0.034x and the CRH was 76.11%. The linear equations for PNP powder at day 90 were y = 1.9701x - 169.33 and y = -0.0122x + 0.0082 and the CRH was 85.43%. The linear equations for PNP powder at day 90 after lyophilization were y = 2.9299x - 226.98 and y = 0.0123x + 0.0007 and the CRH was 77.80%. The results were consistent with the DVS results, indicating that the RH of the PNP powder and its storage environment should be controlled at no more than 70%. Teunou and Fitzpatrick (1999) observed that the CRH decreased with the increased temperature, meaning that caking problems were greater at higher temperatures. In addition, Teunou, Fitzpatrick and Synnott (1999) concluded that materials with low humidity were relatively more sensitive to molecular moisture and to higher CRH. In the present study, the original sample had lower CRH, which means it had greater potential to be agglomerated and to be more sensitive to moisture. The results also showed that the hygroscopicity of the PNP powder significant decreased after storage because of the non-removable bound water within it. Finally, lyophilization improved the quality of the stored PNP powder, although visible changes in the structure. [Figure 4] 3.4. Optimization model of adsorption-desorption in PNP powder The fitted curves of PNP powder are shown in Figure 5 (A-K). Parameters and fitting index values obtained by the regression of 11 models are demonstrated in Table 1. The accuracy of fit of aforementioned models was evaluated by RMSE and the residual 20

values are located in a horizontal band centered on zero, meanings the model is considered acceptable. The suitability of the models was evaluated by the χ2. Therefore, a model was considered acceptable when R2 is high and SSE, RMSE and χ2 were low. The results of adsorption isotherm models showed that GAB and modified GAB models had the highest R2 (0.9994), followed by the Henderson and modified Henderson model (0.9917), and then Halsey and modified Halsey model (0.9618). Parallelly, the SSE, RMSE and χ2 of GAB and modified GAB model were higher than those of Henderson and modified Henderson model. A comprehensive analysis of various indicators indicated that Henderson and modified Henderson model were the best adsorption model for the PNP powder. The results of desorption isotherm models showed that the GAB and modified GAB model had the highest R2 (0.9756), followed by the Oswin and modified Oswin (0.9343), and then Halsey and modified Halsey model (0.9322). Also, the SSE of GAB and modified GAB model and Oswin and modified Oswin model were too high at 237.013 and 479.4822, respectively. Thus, the optimized desorption model for PNP powder was the Halsey and modified Halsey model. Solving the formulas by substituting the data from values from the table, it is possible to calculate the adsorption isotherm model and desorption isotherm model (Table 2). After a storage of 90 days, the optimized adsorption model for the PNP powder was the Oswin and modified Oswin model with a R2 of 0.9766 and the optimized desorption model was GAB and modified GAB model at the R2 of 0.8794. The optimized adsorption model for PNP powder at day 90 after lyophilization was the Henderson and modified Henderson model with a R2 of 0.9707 and the optimized desorption model was Halsey 21

and modified Halsey model with the R2 of 0.8753. By solving the formulas, the adsorption isotherm and desorption isotherm models can be obtained (Table 2). Generally, the optimized adsorption model for the PNP powder was changed from the Henderson model to the Oswin model for a storage of 90 days whereas the optimized desorption model was changed from the Halsey model to the GAB model. Also, the lyophilization could restore the adsorption and desorption isotherm models, but the effect of model fitting had decreased. This meant the moisture absorption behavior and structure of the PNP powder were changed during the storage. There are five classifications for adsorption isotherms: Type Ⅰ, Type Ⅱ, Type Ⅲ, Type Ⅳ and Type Ⅴ (Sing, 1985). In this paper, the adsorption isotherms were of the Type Ⅲ and the adsorption and desorption curves of the PNP powder have similar change rates. The reversible Type Ⅲ isotherm, which is not common, is convex to aw axis, where the adsorbate-adsorbate interactions play an important role (Sing, 1985). Foods rich in soluble components have been found to show Type Ⅲ behavior (AlMuhtaseb et al., 2002). Al-Muhtaseb, Mcminn and Magee (2002) summarized aw range of different models: the Henderson model ranged from 0.05-0.8, the Halsey model from 0.05-0.8, the Oswin model from 0.05-0.9 and the GAB model from 0.05-0.95. The Henderson model has been applied to many foods, but compared to the Halsey equation, its feasibility is limited (Basu et al., 2006). The modified Henderson has been selected by the American Society of Agricultural Engineers (ASAE, 1996) to describe the moisture absorption behavior of cereals and oil seeds. Halsey equation, by its turn, is a good representation of adsorption data that conform to the type Ⅰ, Ⅱ, or Ⅲ shapes 22

(Gregg & Sing, 1967). Iglesias & Chirife (1976 a) stated that the modified Halsey equation is simpler than the models with four parameters. Different too, the Oswin equation was adopted to fit the water sorption isotherms of marjoram, dill, granulated garlic, semolina, skim milk powder, ground coffee and fish oil (Furmaniak, Terzyk, Gołembiewski, Gauden, & Czepirski, 2009; Botrel, Fernandes, Borges, & Yoshida, 2014). Igathinathane, Womac, Sokhansanj and Pordesimo (2005) observed that the modified Oswin was the best model for all corn stover components. Finally, the GAB model is regarded as the most widely sorption model and has been adopted by a group of West European food researchers (Van den Berg, & Bruin, 1981). In our study, the results confirmed that these models can also be used to fit the moisture sorption isotherms of the PNP powder. [Figure 5] [Table 1] [Table 2] 3.5. Surface features changes of PNP powder AFM is often used to obtain surface morphologies of samples as the diameter and height distribution of particles can be clearly shown. The single particles of original samples could be exhibited with an average diameter of 34.3626 nm, and an average height of 50 nm, as calculated by NanoScope Analysis (Figure 6 A-B). The particles were irregular in shape but were aggregated. As for the PNP powder at day 90, the single particles showed an average diameter of 15.645 nm, and an average height of 50 nm (Figure 6 C-D). The particles’ shape looked like water droplets, round and dispersed. 23

Stoklosa et al. observed that samples with smaller particles gained more weight in higher RH conditions than larger particle (Stoklosa, Lipasek, Taylor, & Mauer, 2012). In our study, the PNP powder at day 90 presented smaller particles and, therefore, it contained more molecular moisture that cannot be removed. Finally, a rounded spherical structure was formed. 3.6. Quality deterioration of PNP powder by sulfhydryl and disulfide content The contents of sulfhydryl and total sulfhydryl groups are described in Figure 6 (E). The free thiol of the PNP powder at day 0 and day 90 were 1.75 ± 0.16 μM SH/g and 1.95 ± 0.16 μM SH/g, respectively, whereas the total sulfhydryl of PNP powder at day 0 and day 90 were 101.46 ± 1.06 μM SH/g and 118.44 ± 1.27 μM SH/g, respectively. These results indicate that the sulfhydryl content of PNP powder increased during the storage. The content of disulfide has great effect on the structure of protein and sulfhydryl is also an important group in proteins. Ai et al. found that the hydrolysate of an egg white possessed high sulfhydryl content because of the exposure of the sulfhydryl and disulfide bonds (Ai et al., 2019). Also, protein’s denaturation could lead to the exposure of sulfhydryl groups which release SH2, influencing the generated offflavor (Lamb, Payne, Xiong, & Castillo, 2013). The results indicated that the structure of the PNP powder has changed during the storage. Thus, the increased sulfhydryl contents contributed to the generation of off-flavors. [Figure 6]

24

4. Conclusions In this study, the adsorption and self-equilibrium rules between peptides and environmental moisture molecules were investigated by LF-NMR, DVS and adsorption-desorption model. During the interaction between the PNP powder and environmental moisture molecules, moisture molecules are adsorbed by the peptide powder, which leads to the rapid increase of combined water and total water contents. The outward moisture migration occurred during the storage. With the increase of storage time, the combined water was gradually transformed into immobilized water which was simultaneously converted into free water. During the process of water selfequilibrium rule, it was concluded that the sorption isotherms type changed as undefined structure after storage. The optimized adsorption model for PNP powder changed from the Henderson model to the Oswin model with 90 days of storage, while the optimized desorption model for PNP powder changed from the Halsey model to the GAB model. Lyophilization can restore the adsorption and desorption isotherm models, although the effect of model fitting has decreased. The results of AFM showed that the moisture was bonded with the PNP powder during the storage. Additionally, the increased sulfhydryl contents contributed to the generation of off-flavor. Further studies can be used to determine the flavor fingerprint of PNP powder during the storage and also modify the drying technique to slow down moisture absorption. The characteristic parameters of hygroscopicity were obtained by mathematical models during a quantitative hygroscopicity process. In the future, we aim to combine the mathematical models and flavor fingerprint to guide and inform the production and 25

storage of terminal products.

Acknowledgements The authors acknowledge the financial support provided by the National Natural Science Foundation of China (31772018).

26

References Amaral, D. S., Silva, F. A. P., Bezerra, T. K. A., Arcanjo, N. M. O., Guerra, I. C. D., Dalmás, P. S., & Madruga, M. S. (2015). Effect of storage time and packaging on the quality of lamb pâté prepared with ‘variety meat’. Food Packaging and Shelf Life, 3, 39-46. https://doi.org/10.1016/j.fpsl.2014.10.004. Al-Muhtaseb, A. H., Mcminn, W. A. M., & Magee, T. R. A. (2002). Moisture sorption isotherm characteristics of food products: a review. Food and Bioproducts Processing, 80 (2), 118-128. https://doi.org/10.1205/09603080252938753. ASAE. (1996). ASAE Standards, (43rd Edn.) American Society of Agricultural Engineers, St Joseph, MI. Ai, M. M., Tang, T., Zhou, L. D., Ling, Z. T., Guo, S. G., & Jiang, A. M. (2019). Effects of different proteases on the emulsifying capacity, rheological and structure characteristics of preserved egg white hydrolysates. Food Hydrocolloids, 87, 933– 942. https://doi.org/10.1016/j.foodhyd.2018.09.023. Bonner, I. J., & Kenney, K. L. (2013). Moisture sorption characteristics and modeling of energy sorghum (Sorgum bicolor (L.) Moench). Journal of Stored Products Research, 52, 128-136. https://doi.org/10.1016/j.jspr.2012.11.002. Beveridge, T., Toma S. J., & Nakai, S. (1974). Determination of SH- and SS-groups in some food proteins using Ellman's reagent. Journal of food science, 39, 49-51. https://doi.org/10.1111/j.1365-2621.1974.tb00984.x. Brunauer, S., Emmet, P. H., & Teller, E. (1938). Adsorption of gases in multimolecular layers.

Journal

of

the

American 27

Chemical

Society,

60,

309-319.

https://doi.org/10.1021/ja01269a023. Basu, S., Shivhare, U. S., & Mujumdar, A. S. (2006). Models for sorption isotherms for foods:

a

review.

Drying

Technology,

24,

917–930.

https://doi.org/10.1080/07373930600775979. Botrel, D. A., Fernandes, R. V., Borges, S. V., Yoshida, M. I. (2014). Influence of wall matrix systems on the properties of spray-dried microparticles containing fish oil. Food

Research

International,

62,

344–352.

https://doi.org/10.1016/j.foodres.2014.02.003 Chen, C. (1988). A study of equilibrium relative humidity for yellow-dent corn kernels. Ph.D. thesis, University of Minnesota: St. Paul. Chung, D. S., & Pfost, H. B. (1967 a). Adsorption and desorption of water vapour by cereal grains and their products. Part I. Heat and free energy changes of adsorption and

desorption.

Transactions

of

the

ASAE,

10,

549-551,

555.

https://doi.org/10.13031/2013.39726. Chung, D. S., & Pfost, H. B. (1967 b). Adsorption and desorption of water vapour by cereal grains and their products. Part II. Hypothesis for explaining the hysteresis effect.

Transactions

of

the

ASAE,

10,

552–555.

https://doi.org/10.13031/2013.39727. Ellman, G. L. (1959). Tissue sulfhydryl groups. Archives of biochemistry and biophysics, 82, 70-77. https://doi.org/10.1016/0003-9861(59)90090-6. Fan. B. T. (1997). Chinese Drugs Pharmaceutics. pp. 553-554. Shanghai: Shanghai Science and Technology Publishing Company, China. 28

Furmaniak, S., Terzyk, A. P., Gołembiewski, R., Gauden, P. A., Czepirski, L. (2009). Searching the most optimal model of water sorption on foodstuffs in the whole range of relative humidity. Food Research International, 42, 1203–1214. https://doi.org/10.1016/j.foodres.2009.06.004 Gregg, S.J., & Sing, K.S.W. (1967). Adsorption, Surface Area and Porosity. Academic Press, London and New York. Hancock, B. C., & Zografi, G. (1997). Characteristics and significance of the amorphous state in pharmaceutical systems. Journal of pharmaceutical sciences, 86(1), 1-12. https://doi.org/10.1021/js9601896. Halsey, G. (1948). Physical adsorption on non-uniform surfaces. Journal of Chemical Physics, 16, 931–937. https://doi.org/10.1063/1.1746689. Iglesias, H.A., & Chirife, J. (1976 a). Prediction of the effect of temperature on water sorption isotherms of food material. International Journal of Food Science & Technology, 11 (2), 109-116. https://doi.org/10.1111/j.1365-2621.1976.tb00707.x Iglesias, H.A., & Chirife, J. (1976 b). Equilibrium moisture content of air dried beef: Dependence on drying temperature. International Journal of Food Science & Technology, 11, 567–573. https://doi.org/10.1111/j.1365-2621.1976.tb00759.x. Igathinathane, C., Womac, A. R., Sokhansanj, S., & Pordesimo, L.O. (2005). Sorption equilibrium moisture characteristics of selected corn stover components. American Society of Agricultural Engineers, 48(4), 1449−1460. doi: 10.13031/2013.19170 Jayas D. S., & Mazza G. (1993). Comparison of five, three-parameter equations for the description of adsorption data of oats. Transactions of the ASAE, 36(1), 119–125. 29

https://doi.org/10.13031/2013.28322. Lin, S. Y., Liu, X. T., Liu, B. L., & Yu, Y. L. (2017 a). Optimization of pine nut (Pinus koraiensis) meal protein peptides on immunocompetence in innate and adaptive immunity response aspects. Food and Agricultural Immunology, 28, 109-120. https://doi.org/10.1080/09540105.2016.1228835. Lin, S. Y., Yang, R. W., Cheng, S., Wang, K., & Qin, L. (2017 b). Decreased quality and off-flavour compound accumulation of 3-10 kDa fraction of pine nut (Pinus koraiensis) peptide during storage. LWT-Food Science and Technology, 84, 2333. https://doi.org/10.1016/j.lwt.2017.05.032. Lin, S. Y., Xue, P. Y., Yang, S. L., Li, X. F., Dong, X. P., & Chen, F. (2016 a). Water dynamics of Ser-His-Glu-Cys-Asn powder and effects of moisture absorption on its chemical properties. Journal of the Science of Food and Agriculture, 97 (10), 3124-3132. https://doi.org/10.1002/jsfa.8154. Lin, S., Yang, S., Li, X., Chen, F., & Zhang, M. (2016 b). Dynamics of water mobility and distribution in soybean antioxidant peptide powders monitored by LF-NMR. Food Chemistry, 199, 280–286. https://doi.org/10.1016/j.foodchem.2015.12.024. Li, T., Tu, C., Rui, X., Gao, Y., Li, W., Wang, K., Xiao, Y., & Dong, M. (2015). Study of water dynamics in the soaking, steaming and solid-state fermentation of glutinous rice by LF-NMR: A novel monitoring approach. Journal of Agricultural and Food Chemistry, 63(12), 3261-3270. https://doi.org/10.1021/acs.jafc.5b00769. Lamb, A., Payne, F., Xiong, Y. L., & Castillo, M. (2013). Optical backscatter method for determining thermal denaturation of β-lactoglobulin and other whey proteins 30

in

milk.

Journal

of

dairy

science,

96,

1356–1365.

https://doi.org/10.3168/jds.2012-5791. Mehta, S., & Singh, A. (2006). Adsorption isotherm for red chilli (Capsicum annum L.).

European

Food

Research

and

Technology,

223,

849-852.

https://doi.org/10.1007/s00217-006-0279-z. Mulet, A., García-Pascual, P., Sanjuán, N. & García-Reverter, J. (2002). Equilibrium isotherms and isosteric heats of morel (Morchella esculenta). Journal of Food Engineering, 53, 75-81. https://doi.org/10.1016/S0260-8774(01)00142-X. Oswin, C. R. (1946). The kinetics of package life. III. Isotherm. Journal of Society Chemical Industry, 65, 419-421. https://doi.org/10.1002/jctb.5000651216. Pfost, H. B., Mourer, S. G., Chung, D. S., & Milliken, G. A. (1976). Summarizing and reporting equilibrium moisture data for grains. ASAE Paper No. 76–3520; ASAE: St. Joseph, MI. Pitombo, R. N. M., & Lima, G. A. M. R. (2003). Nuclear magnetic resonance and water activity in measuring the water mobility in Pintado (Pseudoplatystoma corruscans) fish. Journal of Food Engineering, 58(1), 59-66. https://doi.org/10.1016/s02608774(02)00334-5. Rao, K. S. (1941). Disapperance of the hysteresis loop. The role of elasticity of organogels in hysteresis in sorption. Sorption of water on some cereals. Journal of physical chemistry, 45, 531-539. https://doi.org/10.1021/j150408a021. Stoklosa, A. M., Lipasek, R. A., Taylor, L. S., & Mauer, L. J. (2012). Effects of storage conditions, formulation, and particle size on moisture sorption and flowability of 31

powders: A study of deliquescent ingredient blends. Food Research International, 49, 783–791. https://doi.org/10.1016/j.foodres.2012.09.034. Sing, K. S. W. (1985). Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity. Pure and Applied Chemistry, 57 (4), 603-619. https://doi.org/10.1351/pac198254112201. Teunou, E., Fitzpatrick, J. J., & Synnott, E.C. (1999). Characterisation of food powder flowability.

Journal

of

Food

Engineering,

39,

31-37.

https://doi.org/10.1016/S0260-8774(98)00140-X Teunou, E., & Fitzpatrick, J. J. (1999). Effect of relative humidity and temperature on food powder flowability. Journal of Food Engineering, 42, 109-116. https://doi.org/10.1016/S0260-8774(99)00087-4 Todaro, M., Palmeri, M., Settanni, L., Scatassa, M. L., Mazza, F., Bonanno, A., & Grigoli, A. D. (2017). Effect of refrigerated storage on microbiological, chemical and sensory characteristics of a ewes’ raw milk stretched cheese. Food Packaging and Shelf Life, 11, 67–73. https://doi.org/10.1016/j.fpsl.2017.01.005. Thompson, T. L., Peart, R. M., & Foster, G. H. (1968). Mathematical simulation of corn drying-a

new

model.

Transactions

of

the

ASAE,

24

(3),

582-586.

https://doi.org/10.13031/2013.39473. Van den Berg, C., & Bruin, S. (1981). Water activity and its estimation in food systems. Rockland, L. B. & Stewart, G. F. (Eds.), pp. 147-177. NewYork: Academic Press, USA. Van den Berg, C. (1984). Desorption of water activity of foods for engineering purposes 32

by means of the GAB model of sorption. In Engineering and Foods. In B. M. Mckenna (Ed.), pp. 311-321. London: Elsevier, U. K. Wang, K., Yang, R. W., Sun, N., Dong, Y. F., Cheng, S., & Lin, S. Y. (2019). The formation pattern of off-flavor compounds induced by water migration during the storage of sea cucumber peptide powders (SCPPs). Food Chemistry, 274, 100109. https://doi.org/10.1016/j.foodchem.2018.08.123. Wu, Z., Bertram, H. C., Kohler, A., Bocker, U., Ofstad, R., & Andersen, H. J. (2006). Influence of aging and salting on protein secondary structures and water distribution in uncooked and cooked pork. A combined FT-IR microspectroscopy and 1H NMR relaxometry study. Journal of Agricultural and Food Chemistry, 54(22), 8589-8597. https://doi.org/10.1021/jf061576w. Xie, Z. H. (2010). MATLAB Statistical Analysis and Application: 40 Cases Analysis studies 2nd Edition. Beijing: Beijing University of Aeronautics and Astronautics Press, China. Yang, R. W., Li, X. F., Lin, S. Y., Zhang, Z. M., & Chen, F. (2017). Identification of novel peptides from 3 to 10 kDa pine nut (Pinus koraiensis) meal protein, with an exploration of the relationship between their antioxidant activities and secondary structure.

Food

Chemistry,

219,

311-320.

https://doi.org/10.1016/j.foodchem.2016.09.163. Yang, S. L., Liu, X. Y., Jin, Y., Li, X. F., Chen, F., Zhang, M. D., & Lin, S. Y. (2016). Water dynamics in egg white peptide, Asp-His-Thr-Lys-Glu, powder monitored by dynamic vapor sorption and LF-NMR. Journal of Agricultural and Food 33

Chemistry, 10, 2153-2161. https://doi.org/10.1021/acs.jafc.6b00056.

34

Appendices Atomic force microscopy (AFM) American Society of Agricultural Engineers (ASAE) Analysis of variance (ANOVA) Brunauer-Emmett-Teller (BET) Critical relative humidity (CRH) Carr-Purcell-Meiboom-Gill (CPMG) Chi square (χ2) Dynamic vapor sorption (DVS) 5, 5’-Dithiobis (2-nitrobenzoic acid) (DTNB) Ethylene Diamine Tetraacetic Acid (EDTA) Equilibrium moisture content (EMC) Guggenheim-Anderson-de Boer (GAB) Good Manufacturing Practice (GMP) Low-field nuclear magnetic resonance (LF-NMR) Least significant difference (LSD) Number of the scans (NS) Poly tetra fluoro ethylene (PTFE) Pine nut (Pinus koraiensis) peptide (PNP) Receiver gain (RG) Root mean square error (RMSE) Relative humidity (RH) 35

Parameter to control the first data point acquired (RFD) Coefficient of determination (R2) Receiver bandwidth frequency (SW) Ethylene Diamine Tetraacetic Acid (SDS) Standard deviation (SD) Error sum of squares (SSE) Trichloroacetic acid (TCA) Transverse relaxation time (T2) Magnet probe and the duration between successive scans (TW) Combined water (T21) Immobilized water (T22)

36

Figure Captions Figure

Caption

No. 1H

NMR relaxation curves at 75% RH and 25°C of PNP powder. (A)

Transverse relaxation T2 from a CPMG pulse experiment. (B) the Figure 1

distributions of T2 relaxation time of PNP powder at 75% RH and 25 °C for 0 day, 6 days, 15 days, 30 days and 90 days. (C) the contents of water distribution in PNP powder for 0 day, 6 days, 15 days, 30 days and 90 days. (D) the changes of T2 relaxation times.

Figure 2

The simplified model for adsorption rule between environmental moisture molecules and peptide molecules in PNP powder. The kinetic curve and moisture sorption isotherms of PNP powder at day 0

Figure 3

(A and B), PNP at day 90 (C and D) and PNP at day 90 after lyophilization (E and F).

Figure 4

Figure 5

The CRH of PNP powder at day 0 (A), day 90 (B) and day 90 after lyophilization (C). The eleven fitted curves of adsorption-desorption model in PNP powder. Atomic force microscopy topographic images of original PNP powder and PNP powder at day 90. (A) Typical top-view AFM images of original PNP

Figure 6

powder. (B) 3D-view AFM images of original PNP powder. (C) Typical topview AFM images of PNP powder at day 90. (D) 3D-view AFM images of PNP powder at day 90. (E) The contents of sulfhydryl and total sulfhydryl groups of PNP powder at day 0 and day 90.

37

Table 1 The parameters and fitting indexes of adsorption-desorption model

a

Sorption of sample at day 0 R b c M SSE R2 SE

BET

4.604 3

34.7 398

GAB

20.18 14

Modified GAB

4.9069

20.5 683

0.9 994

1.874

439799. 7355

3.77 91

4.810 5

0.9 994

1.874

462536 94.5276

0.67 68

-

3.5 855

141.4 146

0.9 824

11.28 55

17.2588

0.55 35

-

6.6 022

1.61 54

3.5 855

141.4 146

0.9 824

11.28 55

0.5495

0.21 7

1.8 06 6

6.6 022

-

0.0 295

0.009 6

0.9 916

0.064 3

0.0002

-

0.1 097

479. 482 2 479. 482 2 0.13 24

0.66 21

0.0 295

0.009 6

0.9 917

0.064 3

0.0002

0.1 097

-

660.0 423

0.9 164

0.59 27

0.85 96

0.6 613

4.810 5

20.18 14

0.85 96

45.6 351

0.6 613

Oswin

13.60 6

0.61 91

Modified Oswin

64.46 12

Henders on Modified Henders on

0.001 9 0.002 1

a

29.08 28

7.7 462

0.66 05 0.66 21 8.03 89

Chisqua re

Desorption of sample at day 0 R ChiSS 2 b c M R squa E SE re

1.33 45 0.03 66

Chungpfost

6.456

0.07 93

0.17 37

0.1 273

0.178 3

0.8 4

0.565 4

0.6034

0.00 45

Modified Chungpfost

104.4 226

22.7 69

0.07 6

0.0 68

0.050 8

0.9 59

0.213 1

249.148 6

8.34 77

Halsey

0.174 8

0.00 05

0.82 01

0.0 735

0.059 4

0.9 618

669.4 9

2.0612

0.00 07

Modified -1.296 Halsey

0.03 66

0.82 02

0.0 735

0.059 4

0.9 618

669.4 903

-0.7126

0.05 64

Sorption of sample at day 90 BET

GAB

1.446 7

0.08 85

-0.499

0.01 55

0.6 76 8 2.7 66 9

1.3 34 5 0.1 35 9 0.1 07 8 1.5 07 2 1.5 07 2

11. 131 7

136 3.06 3

0.85 33

32.46 78

4.6 418

237. 013

0.97 56

45.07 62

4.6 418

237. 013

0.97 56

45.07 62

0.93 43

11.57 14

0.93 43

11.57 14

0.88 31

0.438 8

0.13 24

0.88 31

0.438 8

0.0 865

0.08 23

0.93 16

0.331 4

0.1 116

0.13 71

0.89 13

0.430 8

0.0 816

0.07 32

0.93 22

0.308 6

0.0 815

0.07 32

0.93 22

0.308 6

Desorption of sample at day 90

-

0.93 75

9.668 1

0.9 81

24.20 35

1.06 79

0.50 96

2.856 4

0.9 955

190.2 511

38

0.6548

0.29 66

41303.3 262

0.00 01

-

4.7 581

249. 017

0.72 02

181.9 479

0.6 58 3

3.3 687

124. 83

0.87 94

40.06 22

Modified GAB

0.498 9

1.08 4

1.17 53

0.50 96

2.856 4

0.9 955

190.2 605

324247. 9365

0.65 83

0.0 01 1

3.3 687

Oswin

0.243 8

1.46 52

-

0.99 31

10.84 93

0.9 766

25.68 57

3.8174

0.59 64

-

4.3 79

Modified Oswin

21.02 6

0.27 62

0.68 25

0.99 31

10.84 93

0.9 766

25.68 57

1027.24 28

13.2 912

1.6 76 7

4.3 79

Henders on

0.008 9

0

-

0.30 93

1.052 3

1.7 0E32

2.127 3

Modified Henders on

0.008 9

0.18 72

0

0.30 93

1.052 3

2.9 58

2.123 7

Chungpfost

28.81 84

0.43 91

0.20 05

0.23 66

0.615 9

0.4 147

Modified Chungpfost

67.84 71

2.60 03

0.20 05

0.23 66

0.615 9

Halsey

131.4 284

2.43 11

0

0.30 93

Modified Halsey

0

0

0

0.33 46

BET

2.8885

GAB

59489.3 256

8.11 41

Modified GAB

918932. 6255

0.77 55

Oswin Modified Oswin

0.87 94

40.06 22

0.76 09

44.11 47

0.76 09

44.11 47

1.05 23

1.70 E32

2.127 3

0.0089

0

-

0.3 093

0.0120

20.1 413

0

0.3 093

1.05 23

2.95 8

2.123 4

1.487 1

6.458

0.07 93

0.1 273

0.17 83

0.84

0.565 4

0.4 147

1.487 1

81.5585

0.15 68

0.1 273

0.17 83

0.84

0.565 4

1.052 3

1.7 038

2.123 5

2.199

0

0.3 093

1.05 23

0

2.124 3

1.231 3

1.7 038

3.347

0

0

0.3 098

1.05 59

0

2.211 9

Sorption of sample at day 90 after lyophilization 9.70 77

124. 830 3 210. 936 6 210. 936 6

-

4.1 211

186. 819 6

0.93 82

0.7 755

0.9 882

10.7 41

0.99 64

0.0 004

0.9 882

10.7 41

0.99 64

7.0155

0.69 29

-

2.4 915

68.2 82

0.97 95

163.080 5

2.20 9

1.4 432

2.4 915

68.2 82

0.97 95

14.918 3

3.3498

3.3498

9.5938

9.5938

39

0.04 07 0.00 39

0.1 73 7 0.1 73 7

Desorption of sample at day 90 after lyophilization 3.7045

13.9131

11.5 47 196. 472 6

-

15. 956 3

280 0.63 86

0.62 37

164.7 316

0.7 91 2

6.2 931

435. 638 2

0.83 51

4.597

15 12 8.3 88 1

6.2 931

435. 638 3

0.83 51

4.597

0.79 44

8.506 6

0.79 44

8.506 6

13.9131

0.79 12

24.5929

0.28 62

-

7.0 215

-1.9606

0.34 49

3.4 93 9

7.0 215

542. 321 2 542. 321 2

Henders on Modified Henders on

0.0047

0.0424

0.46 85 68.4 481

-

0.0 536

0.03 16

0.97 07

0.4 685

0.0 536

0.03 16

0.97 07

0.1038

0.0002

0.1038

1.4215

Chungpfost

0.6034

0.00 45

0.1 359

0.0 865

0.08 23

0.93 16

0.3314

-0.0065

Modified Chungpfost

135.927 8

0.71 9

0.1 359

0.0 865

0.08 23

0.93 16

0.3314

529.88

Halsey

7.7116

0.10 2

0.3 976

0.0 853

0.08

0.92 57

0.1505

0.0025

Modified Halsey

-21.465

0.27 85

0.3 976

0.0 853

0.08

0.92 57

0.1505

2.8221

40

1.99 42 70.9 617 1.04 74 11.7 557 7.76 47 0.07 16

1.9 94 2 0.1 03 2 0.1 03 2 2.7 8 2.7 99 8

0.1 323

0.19 27

0.81 86

0.621 2

0.1 323

0.19 27

0.81 86

0.621 2

0.1 267

0.17 66

0.83 97

0.570 4

0.1 267

0.17 66

0.83 97

0.570 4

0.1 107

0.13 48

0.87 53

0.465 6

0.1 107

0.13 48

0.87 53

0.465 6

Table 2 optimized adsorption isotherm model and desorption isotherm model of PNP powder Original PNP powder

PNP powder after 90 days’

PNP powder after 90 days’

storage

storage (Lyophilization treatment)

Adsor

Henderson model

Oswin model

Henderson model

ption

aw  1  exp(0.0019TM 0.6621 ) aw 1.4652 M  0.2438( ) 1  aw

aw  1  exp(0.0047TM 0.4685 )

Modified

Modified Henderson

isother Henderson Modified Oswin model

m model

1  exp[0.0424  (T - 68.4481) M aaww 1/0.6825 ) M  (21.026  0.2762T)( 1  aw 0.6621 ] aw  1  exp[0.0021(T - 8.0389) M

Desor

Halsey model

ption

 0.0025  2.0612 1.5072 M  (1  0.6583aw)(1  0.0001  0.6583aw  0.6583a w) ) M  2.78 ) aw  exp( M aw  exp( 7.7647T 0.0007T

model

GAB model

Halsey model 41303.3262  0.0001  0.6583aw

isother Modified Halsey model m model

Modified GAB model

Modified Halsey model

324247.936 5  0.6583  (0.001/T)a w

M M 1.5072 )] aw  exp[-exp(-0.7126  0.0564T) aw  exp[-exp(2 .8221  0.0716T) M 2.7 (1  0.6583a w)[1  0.6583a w  0.6583(0.0 01/T)a w]

41

(A)

(B) 42

(C)

(D) Figure 1 43

0 day Outside water

15 days

6 days Combined water (T21)

Combined water (T2a)

30 days Immobilized water (T22)

Figure 2

44

Immobilized water (T2b)

90 days Free water (T23)

(A)

(B)

(C)

(D)

45

(E)

(F) Figure 3

46

Change in Mass (%)

90 y = 4.0935x - 308.95

70

50

30

10

y = 0.034x

-10 0

20

40

60

80

100

120

100

120

RH (%) (A) 20 y = 1.9701x - 169.33

Change in Mass (%)

15

10

5 y = -0.0122x + 0.0082 0

-5 0

20

40

60

RH (%) (B)

47

80

60 y = 2.9299x - 226.98

Change in Mass (%)

50 40 30 20

y = 0.0123x + 0.0007

10 0 -10 0

20

40

60

RH (%) (C) Figure 4

48

80

100

120

(A)

49

(B)

(C)

(D)

(E)

(F1)

(F2)

50

(G1)

(G2)

(H1)

(H2)

(I1)

(I2)

51

(J1)

(J2)

(K1)

(K2)

Figure 5

52

5 4 nm

μm

3

50

0

2

1 2

1 0

1

2

3

4

5

3 4

0

5

μm

5

3

4

(A)

0

1

2 μm

(B) 5 nm

4 3

μm

50 0 1

2

2 3

1

4

0

1

2

3

4

5

0

5

μm

(C)

5

3

4

μm

(D)

53

2

1

0

(E) Figure 6

54

Graphical abstract Adsorption rule LF-NMR

90 days

0 day

0 day

PNP powder

Toguide the production and storage of terminal products.

Deterioration Off-flavor

90 days

Self-equilibrium rule DVS

Adsorption-desorption model

5 5

4

μm

3 3

2

2

1

1 0

1

2

3

4

5

0

0

1

3

2 μm

μm

55

4

5

0

μm

4

Henderson model Modified Henderson model Halsey model Modified Halsey model Oswin model Modified Oswin model GAB model Modified GAB model

Highlights 1. Found the adsorption rule between moisture molecules and peptide molecules. 2. Explored the sorption isotherms type and water self-equilibrium rule of peptide. 3. Built the optimal adsorption-desorption model of PNP powder. 4. Optimized adsorption model for PNP powder changed from Henderson to Oswin model. 5. Optimized desorption model for PNP powder changed from Halsey to GAB model.

56

CRediT author statement

Ruiwen Yang：Project design，data analysis, writing- Original draft preparation. Huapeng Ju：Methodology, DVS data analysis. Liyan Yuan：LF-NMR & Surface morphologies analysis. Haiqing Ye：Writing- Validation. Songyi Lin：Editing –Supervision-Reviewing.

57

Declaration of interests ■ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

58