Thermal Stability of Fructooligosaccharides Extracted from Defatted Rice Bran: A Kinetic Study Using Liquid Chromatography-Tandem Mass Spectrometry

Thermal degradation kinetics of fructooligosaccharides (FOS) in defatted rice bran were studied at temperatures of 90, 100, and 110 °C. FOS extracted from rice bran and dissolved in buffers at pH values of 5.0, 6.0, and 7.0 were prepared for the thermal treatments. The residual FOS (including 1-kestose (GF2), nystose (GF3), and 1F-fructofuranosylnystose (GF4)) contents were determined using the ultra-performance liquid chromatography-electrospray ionization-tandem mass spectrometry (UPLC-ESI-MS/MS) method. The results showed that the thermal degradation kinetics of GF2, GF3, and GF4 followed a first-order kinetic model. Thermal degradation rate constants (k values) of GF2, GF3, and GF4 at different temperature and pH values were estimated using the first-order kinetic equation and SAS 9.1. As a result, these k values decreased gradually as the pH of the sample increased from 5.0 to 7.0. The Arrhenius model was applied to describe the heat dependence of the k-values. The activation energy (Ea) was calculated for each case of GF2, GF3, and GF4 degradation at pH values of 5.0, 6.0, and 7.0. The result showed that rice bran FOS is very thermostable at neutral pH while more labile at acidic pH.


Analysis of FOS by UPLC-ESI-MS/MS
The rice bran-extracted samples thermally treated were analyzed for the residual GF2, GF3, and GF4 contents using an ultra-performance liquid chromatography system equipped with an ESI (Waters Corporation, Milford, MA, USA) coupled to an MS/MS system (Xevo TQS Micro, (Waters Corporation, Milford, MA, USA). The chromatographic separation was performed on a Luna amino-NH 2 column (150 mm × 2 mm × 5 µm) (Phenomenex, Torrance, Los Angeles, CA, USA) [30]. The elution was performed at a constant flow rate of 0.45 mL/min following the program presented in Table 1, with an injection volume of 10 µL and an overall run time of 5 min per sample injection. The Xevo TQS Micro MS/MS system runs in negative ionization mode. The initial optimization parameters are as follows: ionization potential (capillary) of 2.5 kV, source temperature of 150 • C, desolvation temperature of 500 • C, and nitrogen gas rate of 800 mL/h. The fragmentation conditions for measurement of GF2, GF3, and GF4 are also reported in Table 1.

Kinetic Data Analysis
Degradation of GF2, GF3, and GF4 can be described by a first-order kinetic model [2] (Equation (1)): where A 0 and A are respectively initial-and remaining concentrations at time t (min); and k is the degradation rate constant (min −1 ). Equation (1) is valid under isothermal conditions, whereby the degradation rate constant k can be determined from a linear regression analysis of ln(A/A 0 ) versus time.
The temperature dependence of the degradation rate constants can be estimated using the Arrhenius equation (Equation (2)): where T is absolute temperature (K); T 0 is reference absolute temperature (K); k 0 is k at T 0 (min −1 ); E a is activation energy (kJ mol −1 ), and R T (8.314 J mol −1 K −1 ) is the universal gas constant. The activation energy can be estimated by linear regression analysis of the natural logarithm of the rate constant versus the inverse of absolute temperature.
Many empirical polynomial models describing the relationship between the predicted response (i.e., k value in the present case) and the independent variables (i.e., temperature and pH) have been formulated [31][32][33][34][35]. Among those, the second-order polynomial model for two factors can be addressed in this study (Equation (3)).

Development of Standard Curves for GF2, GF3, and GF4 Analysis
The UPLC-ESI-MS/MS analysis of the standard FOS solutions (consisting of GF2, GF3, and GF4) was performed with analytical data presented in Tables 2-4, and the corresponding chromatograms for GF2, GF3, and GF4 are plotted in Figures 1-3. Based on the data obtained, standard curves with good correlation coefficients (r 2 equals 0.9997, 0.9992, and 0.9999 for GF2, GF3, and GF4, respectively) were constructed using regression analysis.

Thermal Degradation Kinetics of the Rice Bran FOS at Different pH Values
The effect of combined temperature and pH on the thermal degradation of rice branextracted GF2, GF3, and GF4 dissolved in buffered solutions was studied at 90, 100, and 110 °C and pH values of 5.0, 6.0, and 7.0. As observed, the combined temperature-pH

Thermal Degradation Kinetics of the Rice Bran FOS at Different pH Values
The effect of combined temperature and pH on the thermal degradation of rice branextracted GF2, GF3, and GF4 dissolved in buffered solutions was studied at 90, 100, and 110 • C and pH values of 5.0, 6.0, and 7.0. As observed, the combined temperature-pH degradation of the rice bran GF2, GF3, and GF4 samples could be adequately described by a first-order model (Equation (1)) in the temperature range of 90-110 • C (Figure 4). Degradation rate constants, k values, estimated using linear regression analysis of ln(A/A 0 ) versus t, are reported in Table 5. As expected, the degradation rate constants increase with increasing temperatures at different pH values; however, the degradation rate constants decrease with increasing pH values. These findings are well in line with the data reported by L'homme et al. [2] for the study on pH-temperature hydrolysis of standard FOS dissolved in buffers, as those authors mentioned that the hydrolysis of standard FOS obeyed pseudofirst-order kinetics and took place much more easily at acidic pH than at neutral or basic pH values. As discussed and analytically proved by those authors [2], the stability of FOS is associated with the protonation of the breaking group. When the oxygen of the C-O osidic bond is protonated, the protonated oligosaccharides are more rapidly degradated at acidic pH than at neutral or basic pH values. Blecker et al. [27] reported that pseudofirst-order kinetics were found for the acid hydrolysis of five commercially available mixes of oligofructose samples. For a better view of the estimated rate constants of first-order degradation of rice bran GF2, GF3, and GF4 as a function of different combinations of temperature and pH, a three-dimension graph was constructed ( Figure 5). As shown in Figure 5, the thermal degradation of rice bran-extracted GF2, GF3, and GF4 took place more easily at acidic pH than at neutral pH values. For each combination of temperature and pH, GF3 showed a faster degradation compared to GF2 and GF4. As mentioned by L'homme et al. [2], the concentration and water activity of FOS have an effect on their stability during treatments. In our experiments, the initial concentrations of GF2, GF3, and GF4 prepared from the rice bran crude extract were 669.32, 78.68, and 12.53 µg/L, respectively. The large difference in concentration of GF2, GF3, and GF4 might be one reason, among others, for the profound heat-pH sensitivity of GF3. On the other hand, the ionic strength of the buffers of pH 5.0 to 7.0 used for the dissolution of FOS during the experiments might interfere with the protonation of oxygen of the C-O osidic bond, leading to fast degradation of GF3. GF4 prepared from the rice bran crude extract were 669.32, 78.68, and 12.53 µ g/L, respectively. The large difference in concentration of GF2, GF3, and GF4 might be one reason, among others, for the profound heat-pH sensitivity of GF3. On the other hand, the ionic strength of the buffers of pH 5.0 to 7.0 used for the dissolution of FOS during the experiments might interfere with the protonation of oxygen of the C-O osidic bond, leading to fast degradation of GF3.         As graphing ln(k) versus 1/T formed a linear line with a good correlation coefficient (Figure 6), the temperature dependence of the k-values, expressed in terms of activation energy (Ea), in the temperature range studied, could be estimated using the Arrhenius equation (Equation (2)), with an activation energy range of 61.8-77.7 kJ.mol −1 obtained for GF2, 67.5-92.3 kJ.mol −1 for GF3, and 49.2-72.6 kJ.mol −1 for GF4 (Table 5). These findings are comparable with the data reported by L'homme et al. [2] for the study on pH-temperature hydrolysis of standard fructooligosaccharides dissolved in buffer at pH 7.0 with the activation energy ranging from 56.7 to 75.4 kJ.mol −1 for GF2, GF3, and GF4 being reported. As graphing ln(k) versus 1/T formed a linear line with a good correlation coefficient (Figure 6), the temperature dependence of the k-values, expressed in terms of activation energy (E a ), in the temperature range studied, could be estimated using the Arrhenius equation (Equation (2)), with an activation energy range of 61.8-77.7 kJ·mol −1 obtained for GF2, 67.5-92.3 kJ·mol −1 for GF3, and 49.2-72.6 kJ·mol −1 for GF4 (Table 5). These findings are comparable with the data reported by L'homme et al. [2] for the study on pH-temperature hydrolysis of standard fructooligosaccharides dissolved in buffer at pH 7.0 with the activation energy ranging from 56.7 to 75.4 kJ·mol −1 for GF2, GF3, and GF4 being reported. Figure 5. Estimated rate constants (min −1 ) of first-order degradation of rice bran GF2, GF3, and GF4 at different combinations of temperature and pH.
As graphing ln(k) versus 1/T formed a linear line with a good correlation coefficient (Figure 6), the temperature dependence of the k-values, expressed in terms of activation energy (Ea), in the temperature range studied, could be estimated using the Arrhenius equation (Equation (2)), with an activation energy range of 61.8-77.7 kJ.mol −1 obtained for GF2, 67.5-92.3 kJ.mol −1 for GF3, and 49.2-72.6 kJ.mol −1 for GF4 (Table 5). These findings are comparable with the data reported by L'homme et al. [2] for the study on pH-temperature hydrolysis of standard fructooligosaccharides dissolved in buffer at pH 7.0 with the activation energy ranging from 56.7 to 75.4 kJ.mol −1 for GF2, GF3, and GF4 being reported.   Table 6 shows the half-life time obtained for GF2, GF3, and GF4 dissolved in buffered solutions at pH 5.0, 6.0, and 7.0 through isothermal treatments at increasing temperatures from 90 to 110 • C. A 20-degree increase in the incubation temperature at pH 5.0 resulted in comparable decreases in the observed half-life values of GF2, GF3, and GF4 (3.9-fold, 3.2-fold, and 3.5-fold, respectively), while at pH 6.0 the decreases were 2.9-fold, 4.9-fold, and 3.2-fold, respectively, and at pH 7.0 those were 3.1-fold, 4.1-fold, and 2.3-fold, respectively.

Modeling of Combined Temperature and pH Dependence of Degradation Rate Constants
By fitting Equation (3) with X 1 as the temperature variable and X 2 as the pH variable on the experimental data, the model parameters were estimated using nonlinear regression analysis (proc NLIN, SAS). Based on the model parameters estimated, however, it was shown that the terms β 0 and β 22 were redundant, as indicated by the large standard error (~100%). As a consequence, these terms were omitted, and a reduced version of Equation (3) was used (i.e., Equation (4)). Model parameters estimated based on Equation (4) are shown in Table 7. For the re-constructed second-degree polynomial model (Equation (4)), no tendency was found by graphing residuals (differences between experimental and predicted k values, respectively) as a function of temperature, pH, experimental k value, and estimated k value (data not shown). In addition, the parity plots of the predicted k values based on Equation (4) versus the experimental k values were established for GF2, GF3, and GF4 ( Figure 7). The deviation from the bisector can be considered an indicator of the inaccuracy of the models. The less the experimental and predicted k values mutually differ, the more successful the models are. Good agreements between the estimated k values and the experimental k values were observed for the aforementioned model version [31,35]. By inserting all model parameters of Table 7 into Equation (4), heat-pH combinations resulting in specific preset degradation rate constants k of 0.016676, 0.021072, and 0.025567 min −1 corresponding to 8, 10, and 12% loss, respectively, of rice bran GF2, GF3, and GF4 for a total process time of 5 min were simulated and represented in isorate contour plots (Figure 8). By inserting all model parameters of Table 7 into Equation (4), heat-pH combinations resulting in specific preset degradation rate constants k of 0.016676, 0.021072, and 0.025567 min −1 corresponding to 8, 10, and 12% loss, respectively, of rice bran GF2, GF3, and GF4 for a total process time of 5 min were simulated and represented in isorate contour plots (Figure 8).

Conclusions
Rice bran-extracted GF2, GF3, and GF4 were rather thermally stable compounds at neutral pH while more labile at acidic pH. Among these, GF3 was more heat sensitive compared to GF2 and GF4. A mathematical equation was suggested for a description of the temperature-pH behavior of rice bran-extracted GF2, GF3, and GF4 during the processing of rice bran-based foods. This equation could be useful in designing alternative processing conditions for temperature-pH processing of rice bran-based products. Degradation kinetic studies of rice bran FOS in real food products would be interesting for food processors to evaluate the potential of temperature-pH processing of these products. Similar works can be applied for process stability studies of many other food quality attributes. This type of research is a good approach for the calculation and optimal design of processes for the food processing industry.