Optimization of the ultrasonic treatment for Tara gum using response surface methodology

Abstract High-intensity ultrasound irradiation proved to be an effective method for modifying tara gum by generating low molecular weight products and better water solubility. The objectives of this research were to optimize the parameters for the high-intensity ultrasonic treatment with response surface methodology and improve the tara gum solubility. The results demonstrated that after the ultrasound treatment, the solubility of the tara gum had increased (17.7%) as a result of the reduced intrinsic viscosity (70%). The molecular weight of the untreated tara gum was 1.89 x 106 Da, and after ultrasound treatment, it was reduced to 0.47 x 106 Da. Rheological analyses confirmed the reduction in molecular weight for the modified and optimized tara gum and the resulting increase in solubility. This knowledge provides a better understanding of ultrasound treatment technology and increases the scope for use of tara gum in the food industry.


Introduction
Tara gum (TG), also called Peruvian carob, is a polymer obtained by grinding the endosperm of Caesalpinia spinosa tree seeds.Peru is the largest producer of TG, with approximately 80% of the total cultivation.TG is a galactomannan with functionality and structure similar to those of guar and carob gums; however, the mannose/galactose ratios differ, and they are 3/1 for TG, 2/1 for guar gum and 4/1 for carob gum [1] .Due to its similar functional properties, TG has been considered an important alternative with which to relieve the short supply of the two common galactomannan sources (guar gum and carob gum) [2] , and it exhibits other advantages, such as easy availability, nontoxicity, biocompatibility and biodegradability [2] .Galactomannans are neutral hydrophilic polysaccharides with approximate molecular weights (Mw) of 1.0 × 10 6 g•mol −1 , and they contain a linear chain of (1-4)-β-D-mannopyranoses linked to α-D-galactopyranosyl units via (1-6) glycosidic bonds [3] .The galactomannan from TG has a high molecular weight, and like other polysaccharides, its chemical structure, monosaccharide composition, bonding modes and branched structures can compromise the biological activities of the polysaccharide [4] .Various studies have reported that high molecular weight polysaccharides exhibit high viscosity and low solubility in water, which could reduce their biological activity and possibly limit application of the polysaccharides [4][5][6] .Aqueous TG solutions are neutral and highly viscous [6] .To dissolve TG completely, heating is necessary, which can be considered a disadvantage in economic and practical terms.
In this context, high-intensity ultrasound (HIUS) with frequencies between 20-100 kHz and intensities above 1 W/ cm 2 proved to be effective in depolymerization and generation of products exhibiting low molecular weight and better solubility in water [7,8] , and it is a green technology; it does not require or produce unwanted chemical products (that is, it does not produce substances that could contaminate the final product), which allows broader application in the pharmaceutical, cosmetic and the food industries.HIUS is widely used to improve the functionality and change the structures of proteins [9] , as in the ultrasound-assisted extraction of new galactomannans and polysaccharides [10] and in modification of various galactomannans and polysaccharides, including pectin [11,12] , sodium alginate [13] , konjac glucomannan [6] and TG recently studied in our laboratory [14] .Thus, the use of a simple sonication method for reducing and increasing the solubilities of polysaccharides represents an important adaptation of the mechanical properties of TG solutions, enabling more adequate and rational uses of the polysaccharides in various fields.However, these previous studies have only superficially addressed the effects of ultrasound, and the ultrasonic parameters have not been optimized.Furthermore, the effects of HIUS on galactomannans, especially those in tara gum, have been sparsely reported.
In this study, the parameters such as time, amplitude and concentration were optimized by means of response surface methodology after treatment of aqueous solutions of TG with HIUS, and the effects of HIUS on the physicochemical and rheological properties of the TG were evaluated.

Experimental design
In using the response surface methodology (RSM), three independent variables were considered: X 1 is the sonication time (2.84 to 112.15 min), X 2 is the TG concentration (0.19 to 1.20% w/v) and X 3 is the amplitude (26 to 93%), and the dependent variable is the intrinsic viscosity (Y).A control was prepared without the ultrasound treatment.The methodology used was as described by Li et al. [15] .The quadratic polynomial regression model (Equation 1) was employed to correlate these values to their coded variables: A software package (SAS ® 9.0 ADX Interface for Design of Experiments) was used for analyses of the experimental data.The optimal condition for each variable was obtained by applying the numerical optimization procedure.

Ultrasonic treatment
Solutions of TG with the desired concentrations (0.19 to 1.20% w/v) were prepared with ultrapure water and stirred at 300 rpm (SP-160, SP Labor, Brazil) overnight at room temperature (25 °C).Then, the dispersion was transferred to a jacketed beaker connected in a thermoregulated bath with external circulation (Quimis, Q214M2, Brazil) at 25 °C ± 0.01 and stirred with a C-MAG HS 7 magnetic stirrer (IKA, Staufen, Germany) at 200 rpm throughout the process.The samples were subjected to HIUS by employing an ultrasound generator (UP 100H, Hielschier, Germany) containing a titanium sonotrode (MS2, 2 mm diameter); the frequency was 30 kHz and the power was 100 W. The ultrasound probe was submerged in the sample to a depth of 0.5 cm.

Determination of intrinsic viscosities
The intrinsic viscosities were measured with the method of Li et al. [15] .The relative viscosities (ηr) of the untreated tara gum (UTG) and tara gum-treated and optimized (TGTO) samples were measured with capillary viscometers (Schott-Gerate, Germany), and the capillaries were immersed in a thermostatic bath (CT-52, Schott-Gerate, Germany) at 25 °C ± 0.05.The intrinsic viscosities [η] were calculated with Equations 2 and 3: where t s is the flow time of the solution with UTG and TGTO, t 0 is the flow time of the solvent, η r is the relative viscosity, η sp is the incremental viscosity, and c is the concentration of UTG and TGTO (g/mL).

Molecular weight
The molecular weights of UTG and TGTO were determined with an adapted viscosimetric method [16] .In summary, the dynamic viscosity was calculated with data obtained from Cannon-Fenske capillary viscometers (Schott-Gerate, Germany), in which aqueous solutions containing UTG and TGTO were prepared at concentrations from 0.01 to 0.05%.The sample readings were taken in triplicate.The intrinsic viscosity was estimated by extrapolation of Martin's curves to "zero" concentration using Equations 4 and 5: where [η] is the intrinsic viscosity (cm 3 /g), ηsp is the specific viscosity, c is the concentration of the TG (g/mL), η is the solution viscosity of the TG (g/cm.s),η 0 is the solvent viscosity (g/cm.s),and K is Martin's constant.
The molecular weight was estimated with the Mark-Houwink Equation 6: where [η] is the intrinsic viscosity (dL/g), M v is the average viscosimetric molecular weight expressed as g mol -1 and α is a constant related to the structure of galactomannan, which was determined with Equation 7: ( ) where the mannose:galactose (M:G) ratio is the ratio of mannose and galactose in the polysaccharide structure, which was obtained from nuclear magnetic resonance spectroscopy ( 1 H NMR). The decrease in [η] is equivalent to the decrease in the average molecular mass, so it can be considered an indication of TG degradation before and after ultrasound treatment and optimization.

Average particle size determination
The hydrodynamic diameters (d.nm) of the 0.1% (w/v) UTG and TGTO solutions were determined using a Zetasizer (Malvern Instruments, Nano-ZS, UK) at 632.8 nm with a 90° angle at 25 °C, and the experiments were performed in triplicate.

Fourier Transform Infrared (FTIR) Spectra of UTG and TGTO
The spectra were determined with an FTIR spectrometer (Bruker, Vertex 70, Germany) over the range 4000−500 cm -1 .

Solubility of UTG and TGTO
Solubilities were determined according to the method of Rodriguez-Canto et al. [17] .Freeze-dried samples were prepared at 0.1% (w/v) in distilled water and stirred with a magnetic stirrer (C-MAG HS 7, IKA, Germany) at room temperature (25 °C) for 1 h.The samples were centrifuged (Digicen 21R, OrtoAlresa, Spain) at 3500 × g for 30 min at 25 °C to remove the insoluble material.Then, the supernatant was collected and dried in an oven (SX 1.3, Sterilifer, Brazil) at 105 °C for 24 h.

Measurements of constant shear
All rheological properties, including the flow behavior with increasing shear rate and frequency sweep tests of the UTG and TGTO, were measured at a constant temperature of 25 °C with a MARS II rotational rheometer (Thermo Fisher Scientific, Karlsruhe, Germany) equipped with a plate-and-plate geometry (PP 60Ti, 60 mm diameter).The UTG and TGTO solutions were prepared in deionized water with concentrations of 1.0%, 3.0% and 4.0% (w/v), and constant shear rate tests were performed over the range 0.01 to 300 s -1 at 25 °C.The flow behavior was analyzed with the rheological models of Newton (Equation 8), the power law (Equation 9), Bingham (Equation 10) and Herschel-Bulkley (Equation 11): where τ is the shear stress (Pa), γ ̇ is the shear rate (s -1 ), η is the Newtonian viscosity (Pa • s), K is the consistency coefficient n Pa s ⋅ , n is the flow behavior index (dimensionless), 0 τ is the initial yield stress (Pa), and pl η is the Bingham plastic viscosity (Pa • s).The quality of the fit was evaluated from the coefficient of determination (R 2 ).

Dynamic shear measurements
Dynamic oscillatory measurements were performed to ensure linear viscoelastic conditions with frequency sweep tests performed over the range 0.1 to 100 Hz for UTG and TGTO (1%) and over the range 0.1 to 10 Hz for TGTO (3% and 4%) by applying a constant shear stress for analyses of the storage modulus (G') and loss modulus (G'') as a function of the oscillation frequency.

Statistical analyses
One-way analysis of variance (ANOVA) and Tukey's test were used to establish the significance of differences between mean values at the 0.05 significance level.The statistical analyses were performed with Origin ® 8.5 software (OriginLab Corporation, USA).

Optimization of the experimental design
The effects of different HIUS treatments on the intrinsic viscosity are presented in Table S1, and the regression analysis and ANOVA are presented in Table S2.This table shows that only the linear model was significant (p< 0.05), and the value of the coefficient of determination (R 2 ) was 79.39, suggesting that the regression equation obtained with the RSM was viable.The analysis suggested that the linear effects of the time and concentration variables were significant (p < 0.05), and there was no significant effect (p < 0.05) for the amplitude variable.Using the linear model, the decoded Equation 12was developed for the intrinsic viscosity: where η is the intrinsic viscosity, t is the time and C is the gum concentration.Based on the predicted model, the optimal conditions for the experiment in which the variables were tested included a time of 112 min, a concentration of 0.19% (w/v) and an amplitude of 60%.
With these optimized conditions, the intrinsic viscosity was 5.97 (dL/g) according to the SAS program.This result was attributed to the greater exposure (112 min) of the TG to the HIUS, which increased the number of cavitational events, generated free radicals, enabled depolymerization of the TG and, consequently, generated TG with a low intrinsic viscosity [15,18] .These results agreed with the response surface plot shown in Figure 1.

Intrinsic viscosity, molecular weight and particle size
The ultrasonic treatments caused substantial decreases in the intrinsic viscosity of TG due to reductions in the molecular weight and chain length of the gum.The intrinsic viscosities of UTG and TGTO were 12.31 dL/g and 3.14 dL/g, respectively.The degradation rate of TG was estimated to be 59%.The average molecular weight (Mw) was higher for UTG (1.89 x 10 6 Da) than for TGTO (0.47 x 106 Da), which was consistent with the reductions in the intrinsic viscosity, indicating that ultrasound was an effective method for TG depolymerization.The average hydrodynamic diameter (Z-average) of UTG was 147.1 ± 4.90 nm, while that of TGTO was 139.7 ± 2.4 nm. Figure 2 shows the distributions of the UTG and TGTO particle sizes.For UTG (Figure 2A), we observed that the size distribution was wide and contained 3 uneven peaks, whereas TGTO (Figure 2B) showed 2 narrower and more uniform peaks.
The reductions and uniformity of the particle sizes observed in this study may have been related to cavitation in the aqueous TG solution caused by the HIUS treatment.According to Li et al. [15] , shear forces alter the structures of polysaccharides after explosion of the cavitation bubbles generated by the ultrasonic treatment, disperse the polysaccharide aggregates and cause reductions in the molecular weights and particle sizes.Our results agree with other studies in which polysaccharides were degraded with ultrasonic irradiation [4,6] .

Analysis of the FTIR spectra
Figure 3 shows that both UTG and TGTO showed broad absorption bands at 3319 and 3368 cm -1 , respectively.These could be due to hydrogen bonding involving the hydroxyl groups in the gum molecules and correspond to O-H stretching vibrations.The band at 2918 cm -1 was attributed to symmetric CH stretching vibrations [14,19] .The absorption band at approximately 1638 cm -1 corresponded to the asymmetric stretching vibrations of C-O bonds [4] .The peaks at 1023 cm -1 for TGTO and 1014 cm -1 for UTG indicated bending vibrations of H 2 C-O-CH 2 bonds [14,19] .The spectra of UTG and TGTO showed absorption bands at 810 cm -1 characteristic of α-linked D-galactopyranose units, and at 871 cm -1 characteristic of β-linked D-mannopyranose.The infrared spectra of UTG and TGTO clearly that there were no major changes in the functional groups or chemical structures caused by the treatments and that ultrasound-induced chain scissions only broke the polymer structures and resulted in viscosity reductions without any changes in the primary structures  or in the functional properties of the tara gum, as reported previously [4,6,12] .

Effects of ultrasound on the solubilities of UTG and GTTO
The solubilities of TGTO and UTG were 99.67 and 84.67%, respectively.TGTO showed a more significant increase in the water solubility, approximately 17.5%, compared to UTG.The ultrasonic waves caused cavitation due to the expansion and contraction cycles experienced by material, and these cycles disrupted the cell walls of the solid matrix [20] .These ruptures enabled solvent penetration, which explains the increase seen in the TG solubility after the ultrasound treatment.Furthermore, this result may be related to destruction of intra-and intermolecular noncovalent bonds, which would expose more hydrophilic polysaccharide groups to water and increase the solubility [21] .The current study achieved a better result than the study carried out by Santos, Isabel and Garcia-Rojas [14] , in which the solubility of TG was 83% after sonication for 60 min at 25 °C.The higher solubility found in this study is consistent with the results described above (Item 3.2.1), in which prolonged exposure to sonication contributed to a greater reduction in the molecular weight and, consequently, an increase in the solubility.Ultrasound-induced increases in the solubilities of polysaccharides have already been reported [21] , but studies with galactomannans are still scarce.
The development of new technologically sophisticated products via nonthermal processing is one of the major trends for the coming years [22] .In this sense, it should be noted that the solubility achieved in this research was possible only with application of the optimized ultrasonic treatment method, and prior thermal processing was not required.There is global demand for new products similar to unprocessed and made with nonthermal technologies.Thus, the food industry could apply an adapted form of TGTO [23] .Consumers are demanding foods with innovative ingredients, and in the future, TGTO can be used to prepare functional foods and beverages from ingredients that are easily soluble at room temperature, such as with instant foods.In addition, the modified TGTO can be used in packages with edible films that require a material with low water resistance that is biodegradable and safe for human consumption.

Rheological Properties of the UTG and TGTO
Table 1 summarizes the parameters of the Newtonian, power law, Bingham and Herschel-Bulkley models obtained by fitting the rheological data of the UTG (1%, w/v) and TGTO (1, 3 and 4%, w/v) solutions.Thus, the flow behaviors of the UTG and TGTO solutions were best described by the power law model, which presented R 2 values close to 1 (R 2 = 0.99 and 0.97).An increase in the concentration of TGTO from 1 to 4% resulted in an increase in the consistency coefficient K and a decrease in the flow behavior index n (Table 1).This indicated that the solutions became more resistant to flow and were increasingly pseudoplastic as the concentration of TGTO was increased.According to Wei et al. [24] , gums with low n values and improved pseudoplasticities are advantageous because they provide a less viscous mouthfeel with easier mixing and serve as thickeners in nutritional formulations used for the management of dysphagia.When comparing UTG and TGTO, we observed a reduction in the consistency coefficient K from 6.806 ± 1.336 to 0.029 ± 0.001 at a 1% concentration.The modifications in the rheological properties are useful, as they confirm a reduction in the molecular weight of TG and consequently the increased solubility.
The flow and apparent viscosity curves of UTG and TGTO are shown in Figure 4A and B. Non-Newtonian behavior was observed for the UTG with decreasing viscosity and increasing strain rate.The TGTO presented as a Newtonian fluid with a very low viscosity close to that of water.This behavior was attributed to breaking of the polymeric network and orientation or alignment of the microstructures along the direction of shear flow, which reduced the flow resistance [25] .This indicated that the ultrasound treatment caused strong changes in the rheological properties due to a reduction of the molecular mass of the TGTO and was consistent with other studies that treated polysaccharides with ultrasound [6,13] .τ is the initial yield stress (Pa), pl η is the Bingham plastic viscosity (Pa•s)and coefficient of determination (R 2 ).
The plots of ' G and '' G as a function of frequency for the UTG solution presented crossover points ( ) G G ′ = ′′ at low frequencies (1 to 10 Hz).Initially, the solutions behaved as liquids with '' G higher than G′, and after the crossing point, elastic behavior was established with ' G higher than '' G Figure 4C and D, as in other studies [6,16] .At frequencies above 10 Hz, ' G and '' G showed nonlinearity corresponding to disentanglement and irreversible flow of the UTG and TGTO molecules as a result of the shear force [6] .In Figure 4E and F, in which TGTO has higher concentrations of 3% and 4%, the solutions behaved as liquids with '' G higher than G′.Furthermore, both the ' G and '' G for TGTO decreased, possibly due to breaking of the polymer chain [6] .In water, the UTG formed a relatively elastic dispersion (solid property) that became a viscous dispersion (fluid property) after ultrasound treatment.These results corroborated the results of Li et al. [6] , who studied the ultrasonic degradation and rheological profiles of konjac glucomannan (KGM) and observed that ultrasound weakened the intermolecular interactions.

Conclusion
A high-intensity ultrasound treatment significantly affected the physicochemical, functional, and rheological properties of TG, depending on the ultrasound treatment time and polymer concentration.After the ultrasound treatment, the TG showed a reduction in the intrinsic viscosity and particle sizes.These changes positively influenced the functional properties of the TG, as shown by the increased solubility.In addition, the TGTO solution behaved as a Newtonian fluid with low viscosity and consistency; this indicated that the ultrasound treatment caused strong changes in the rheological properties of the TG solution and confirmed the effectiveness of the treatment.The increased solubility of galactomannan, the reduced viscosity, and the reduction in molecular mass, will enable future technological applications, such as with functional beverages, instant foods and edible film packaging.In addition to biological applications involving the antioxidant activity and bioaccessibility of TG, it meets the various demands of the food processing industry.Therefore, advances in ultrasonication treatments of natural polymers are expected to provide new applications in various industrial fields.

Where b 0
(constant term); b 1 , b 2 and b 3 (linear effects); b 11 , b 22 and b 33 (quadratic effects); and b 12 , b 13 and b 23 (interaction effects) represent the coefficients of the polynomial model.

Figure 1 .
Figure 1.Influence of treatment parameters on the viscosity.Effects of time and concentration (A), time and amplitude (B) and concentration and amplitude (C) on the intrinsic viscosity of the TG.

Figure 4 .
Figure 4. Rheological measurements of the UTG and TGTO solutions.Flow curves (A), apparent viscosity curves for the UTG and TGTO solutions (B); storage and loss moduli (G', G'') for UTG at a 1% concentration (C) and TGTO at a 1% concentration (D) and at 3% (E) and 4% (F) at 25 °C.

Table 1 .
Rheological parameters obtained from the Newton, Power Law, Bingham, and Herschel-Bulkley models for UTG and TGTO solutions at 25 °C.
where τ is the shear stress (Pa), γ ̇ is the shear rate (s -1 ), η is the Newtonian viscosity (mPa•s), K is the consistency coeficiente n Pa s ⋅ , n is the flow behavior index (dimensionless), 0