Multivariate analysis of the interactive effects of thermosonication and coagulant type on tofu quality characteristics and yield

1 Introduction

Tofu is a traditional Chinese food obtained by coagulation of proteins from soymilk. It is a nutritious food that also provides bioactive compounds such as isoflavones, saponins, and sterols (Wang X. et al., 2023). Tofu, as part of a balanced diet, can potentially reduce the risk of cardiovascular disease, hypertension, diabetes, and hyperlipidemia (Zheng et al., 2020). The typical process of tofu generally includes three steps: soaking, grinding, and boiling soymilk. The soaking time and water-soybean ratio determine the degree of softening and the protein concentration in raw soymilk, respectively. Boiling soymilk denatures proteins, sterilizes it, and coagulates it; it is directly associated with tofu yield and quality (Wang X. et al., 2023). The gel structure of tofu is determined by protein content, hardness, and water-holding capacity (WHC), which is directly related to yield. During heating, soymilk proteins denature and form a protein matrix. Afterward, the addition of coagulant, a key step in the formation of tofu gel, affects the texture and flavor of tofu (Ali et al., 2021). Common coagulants include salts (calcium sulfate, calcium chloride, calcium acetate, calcium lactate, magnesium sulfate, magnesium chloride, trimagnesium citrate), acids (glucono-δ-lactone (GDL), citric acid, lactic acid, tartaric acid), enzymes (chymosin, pepsin, papain, microbial transglutaminase (MTG)), and mixtures of calcium sulfate–magnesium chloride/sulfate and MTG plus brine or GDL are used (Zheng et al., 2020).

The application of high-intensity, low-frequency ultrasound (10–1000 W/cm², 16 kHz–100 kHz) represents an emerging processing technology in the food industry. When power ultrasound is combined with conventional heat, the process is called thermosonication, a multi-hurdle technique that leverages acoustic-thermal synergism to optimize molecular modification and microbial inactivation while minimizing severe, adverse thermal effects (Olaniran et al., 2025). The primary mechanical factor in thermosonication in liquid systems is acoustic cavitation. The violent collapse of cavitation bubbles generates localized, transient pressure-temperature spikes known as ‘hotspots’ (Paniwnyk, 2014). This intense, localized energy generates micro-streaming and severe micro-shear forces that can disrupt the native, compact quaternary and tertiary interactions of globular proteins (Wang X. et al., 2023). Recent investigations have demonstrated that this combined thermal-acoustic stress triggers profound conformational shifts in milk and vegetable protein networks, significantly reducing particle size, increasing surface negative charges, and enhancing intrinsic fluorescence, which collectively indicates an altered protein microenvironment and an increased exposure of hidden hydrophobic domains (Zhang et al., 2026; Wu et al., 2025). This structural deconstruction directly affects gelation during tofu manufacturing. During soymilk boiling or pasteurization, thermosonication forces the spatial unfolding of soy globulins, breaking traditional structural constraints and driving a major transition in the secondary structure (Wu et al., 2025; Zhang et al., 2026). So, previously hidden reactive sites—such as hydrophobic amino acid residues and free sulfhydryl (–SH) groups—become highly accessible on the protein surface (Wang X. et al., 2023; Wu et al., 2025). When these exposed domains interact with single coagulating agents, they may form dense covalent disulfide bonds and stable divalent ionic salt bridges (Geng et al., 2024; Li et al., 2025). This enhanced cross-linking promotes a stronger, more homogeneous, and mechanically robust matrix (Gao et al., 2021). Thus, thermosonication is a highly efficient tool for optimizing tofu yield, water-holding capacity, and instrumental strength (Jooyandeh et al., 2023). Furthermore, this structural reorganization and enzyme denaturation simultaneously inactivate lipoxygenase, successfully suppressing volatile carbonyl compounds (such as hexanal) responsible for the characteristic undesirable ‘beany’ off-flavors in soy matrices (Xie et al., 2023).

Efenberger-Szmechtyk et al. (2018) noted that traditional food quality assessment—using chemical or microbiological analyses and univariate statistics such as ANOVA—may be ineffective in some cases. Advanced techniques combined with multivariate analysis—chemometrics—are more effective for evaluating food safety and quality. Researchers use both linear and non-linear multivariate methods, with non-linear techniques gaining prominence (Rocha et al., 2020). Globalization and consumer demand for safe, healthy food drive the development of new methods to identify and assess food quality markers (Andre and Soukoulis, 2020). Despite numerous analytical tools for quantifying quality markers, chemometrics, including multivariate analysis, experimental design, and regression models, remain key to food process optimization and quality assessment (Andre and Soukoulis, 2020).

Tofu consumption is growing because of its nutritional value and plant-based nature, which aligns with vegetarian and hypocaloric diets. Moreover, as noted above, ultrasound affects tofu yield, texture, and sensory properties. In addition, coagulation is the most critical step in the tofu production process and involves selecting the coagulant(s). The coagulant also affects the tofu’s final quality. Some studies evaluated the effects of ultrasound on the tofu composition (Olaniran et al., 2025; Jooyandeh et al., 2023), microbial stability (Olaniran et al., 2025), microstructure and texture (Gao et al., 2021; Xin et al., 2025), protein modifications (Gao et al., 2021; Xin et al., 2025), and yield using a single coagulant. Previous studies have scarcely evaluated the effects of ultrasound treatment of soymilk and different coagulants on the physicochemical and sensory properties, as well as the microbial quality, of tofu. Therefore, this study aims to evaluate the effects of three pretreatments (untreated, pasteurized, and thermal ultrasound treatment) on soymilk and three single coagulants (calcium chloride, magnesium chloride, and acetic acid) to compare their effects on the yield, physicochemical, textural, and sensory properties, as well as the microbial quality of tofu. The data were analyzed using principal component analysis (PCA), partial least squares (PLS) regression, and multiple linear regression.

2 Materials and methods

2.1 Soymilk production

Soybeans (Glycine max) supplied by Servicios Alimenticios Avanzados S.A. de C.V. (Huejotzingo, Puebla, Mexico) were used as the raw material for soymilk production. The soymilk was prepared using an automatic soymilk maker (Ionmag IOM-201 B Nature Dream, Ionmag Corp., Paju, South Korea). Prior to processing, 100 g of soybeans were soaked in water for 12 h. The soaked soybeans were then combined with water (1700 mL) in the stainless-steel pitcher. The device operated on a fully automated 25-min cycle that integrated preheating, high-speed intermittent milling, and controlled boiling, reaching temperatures ≈95 °C. Upon completion of the cycle, the resulting mixture was filtered through a fine-mesh strainer to separate the solid residue (okara) from the liquid soymilk. According to the experimental design, the soymilk was either left untreated (control), pasteurized, or subjected to ultrasound treatment prior to physicochemical, microbiological, and tofu production analyses.

2.2 Soymilk pasteurization treatment

Pasteurization was performed using a double-jacketed glass vessel to maintain the soymilk at 60 °C throughout the treatment. Samples (1 mL) were collected every 5 min during the 30-min treatment, serially diluted in sterile peptone water, and microbiologically analyzed to determine the kinetics of microbial inactivation (aerobic mesophilic bacteria and total coliforms). After pasteurization, the soymilk was immediately cooled in an ice bath to approximately 10 °C. For each treatment, three replicates were performed, and each of them was analyzed in triplicate.

2.3 Soymilk ultrasound treatment

Ultrasound processing was carried out using 500 mL of soymilk placed in a sterile 750-mL double-jacketed glass vessel to maintain the treatment temperature at 60 °C. A 13-mm probe connected to an ultrasonic homogenizer (CPX-400, Cole-Parmer, Vernon Hills, IL, USA) was immersed approximately 5 cm below the sample surface. Treatments were performed at 65% amplitude (75 μm) for 30 min. Samples (1 mL) were collected every 5 min, serially diluted in sterile peptone water, and microbiologically analyzed to evaluate the kinetics of microbial inactivation. At the end of the treatment, the soymilk was cooled in an ice bath to approximately 10 °C. For each treatment, three replicates were performed, and each of them was analyzed in triplicate.

2.4 Tofu preparation

Nine tofu formulations were produced according to the experimental design (Table 1), combining three physical soymilk pretreatments and three single chemical coagulants, while excluding ultrasonication at room temperature due to the thermal denaturation threshold required for soy protein gelation; furthermore, in previous preliminary studies (data not shown), ultrasound treatment at room temperature exhibited no significant effect on the microbial load of soymilk and failed to properly produce a cohesive tofu matrix. The manufacturing process was based on the methodology described by Shurtleff and Aoyagi (1987), with modifications to the agitation and pressing conditions, as described by Zhang et al. (2018) and Geng et al. (2024). Following these treatments, soymilk batches were equilibrated to the optimum coagulation temperature (75 °C) (Shih et al., 1997). Curd formation was induced by incorporating the tested coagulants (Table 1) at a concentration of 2%. The resulting protein matrices were transferred to molding blocks, where separation was achieved using the modified pressing conditions (500 g/cm² for 30 min). A schematic representation of the tofu production process is depicted in Figure 1. For each treatment and coagulant agent used, three replicates were performed; the prepared tofu samples were stored in sealed plastic bags under refrigeration (4 °C) until analysis.

TABLE 1. Description of the tofu systems experimentally produced and the nomenclature used.

2.5 Microbial analysis

The microbiological quality of untreated soymilk samples was evaluated by enumerating aerobic mesophilic bacteria, total coliforms, Staphylococcus aureus, and molds and yeasts. Briefly, 1 mL of each sample was serially diluted in sterile peptone water and surface-plated on Tryptic Soy Agar (TSA, Merk KGaA, Darmstadt, Germany), Violet Red Bile agar (VRB, Merk KGaA, Darmstadt, Germany), Baird-Parker agar (Merk KGaA, Darmstadt, Germany), and Potato Dextrose Agar (PDA, Merk KGaA, Darmstadt, Germany) acidified with tartaric acid (14 mL/1,000 mL agar at 10 g/100 mL) for the enumeration of aerobic mesophiles, total coliforms, S. aureus, and molds and yeasts, respectively. Plates were incubated at 35 °C for 24 h for aerobic mesophiles, coliforms, and S. aureus, whereas molds and yeasts were incubated at 25 °C for 72 h before colony counting. For each treatment, three replicates were performed, and each of them was analyzed in triplicate.

The microbiological quality of the nine tofu formulations was evaluated. Briefly, 1 g of each tofu sample was aseptically collected, serially diluted in sterile peptone water, and analyzed for aerobic mesophilic bacteria, total coliforms, S. aureus, and molds and yeasts using the microbiological procedures and incubation conditions described for soymilk. For each treatment and coagulant agent, three replicates were performed, and each replicate was analyzed in triplicate.

2.6 Microbial inactivation kinetics in soymilk

Survival curves for aerobic mesophilic bacteria (AMB) and total coliforms were constructed by plotting the logarithm of the survival ratio (Log N/N) as a function of treatment time. The inactivation kinetics under thermal and thermo-ultrasound treatments were described using the nonlinear Weibull model, expressed in its logarithmic form according to Equation 1:

Log N N O = − b * t n (1)

Where N is the remaining microbial population at time t (min), N _*0* is the initial population at time zero (CFU/mL), b is the scale parameter, and n is the shape parameter that defines the concavity of the curve. From the estimated parameters of the Weibull model, the following statistics were calculated from the survival frequency distribution: mean, mode, variance, and skewness coefficient. Additionally, the D value (decimal reduction time, min) was determined as the time required to achieve a 90% reduction in the initial microbial load using the Weibull approximation under Equation 2:

D = 1 b 1 n (2)

The kinetic parameters (b and n) were estimated using nonlinear regression. The goodness of fit and predictive capacity of the model were statistically evaluated using the coefficient of determination (R²) and the root mean square error (RMSE).

2.7 Physicochemical characterization of tofu

For soymilk (untreated, pasteurized, and ultrasound-treated), the pH was measured by direct immersion of a previously calibrated electrode (pH 4.0 and 7.0 buffer solutions) using a pH meter HI2210 (Hanna Instruments, Woonsocket, RI, USA). Soluble solids (°Bx) were determined using a digital refractometer (PR-1, Atago, Bellevue, WA, USA) previously calibrated with distilled water. Water activity (aw) was measured using an AquaLab Series 3 TE equipment (Decagon Device Inc., Pullman, WA). Protein, fat, and ash were determined following AOAC (2012) methods 991.20, 989.05, and 945.46, respectively. All samples were evaluated in triplicate.

The pH of tofu was analyzed according to method 981.12 AOAC (2012), while for the proximate composition, the methods 926.08, 989.05, and 920.123 (AOAC, 2012) for moisture, fat, and protein were followed, respectively. The soluble solids and aw were analyzed as previously described. A texture analyzer TA. XT2 (Stable Micro Systems, Godalming, UK) was used for compression tests using an acrylic cylinder (d = 20 mm) at 1 mm/s to a depth of 5 mm. The compression force (N) was recorded and used to determine tofu hardness. To evaluate the efficiency of the treatments and coagulants, the tofu yield (Y %) was calculated, which reflects the mass recovery, including water retention, using Equation 3:

Y % = W t o f u W s o y b e a n s (3)

Where W _*tofu* is the final weight of the fresh pressed tofu (g), and W _*soybeans* is the initial weight of the dry soybeans (g).

The color of soymilk and tofu was determined in triplicate using a Gardner Color System 05 (BYKGardner, Inc., Columbia, MD), which was calibrated to measure reflectance using the Hunter scale to evaluate the parameters lightness (Lh), red-green color (ah), and yellow-blue color (bh). Hue and chroma were then calculated.

2.8 Sensory evaluation of tofu

Sensory evaluation was performed using a hedonic scale test with 30 untrained panelists. Informed consent was obtained from all subjects involved in the study. The panelists were informed about the use of soybeans in the tofu formulations. Each participant signed an informed consent by responding affirmatively to the following statement: “I am aware that my responses are confidential, and I agree to participate in this sensory evaluation.” They were informed they could withdraw from the test at any time without giving a reason; we explicitly stated, “The products are safe for consumption,” and that participants’ data would not be disclosed without their knowledge.

The attributes evaluated included color, texture, flavor, acidity, and overall acceptability. To integrate the hedonic panel evaluations (30 judges, 9-point scale) in a multidimensional manner and mitigate the impact of non-discriminatory variables, a Single Sensory Index was developed as a metric of overall quality. Initially, a preliminary analysis of variance (ANOVA) of the individual attributes (color, consistency, flavor, and acidity) was performed to identify variables that did not differ significantly (p > 0.05).

Subsequently, a multiple linear regression analysis was performed using individual data from the 30 consumers, with overall acceptability as the dependent variable (Y) and the significant descriptive attributes as independent variables (Xi). The relative weight (%Wi) of each attribute was calculated by normalizing its respective partial regression coefficients (βi), according to Equation 4:

% W i = β i ∑ i = 1 k β i * 100 (4)

Where k represents the total number of significant attributes included in the model. The Single Sensory Index for each experimental tofu unit was structured using the weighted linear combination expressed in Equation 5:

S i n g l e S e n s o r y I n d e x = % W t e x t u r e t e x t u r e + % W f l a v o r f l a v o r + % W a c i d i t y a c i d i t y + % W c o l o r c o l o r (5)

2.9 Statistical analysis

Statistical analyses were performed using Minitab 19 software, and statistical significance was assessed at the 95% confidence level. To evaluate differences in composition, physicochemical and sensory properties, an analysis of variance (ANOVA) was performed to assess whether treatment type had a statistically significant effect.

2.10 Principal components analysis and partial least squares regression

Principal component analysis (PCA) was applied to explore similarities among soymilk treatments and coagulant agents in tofu formulations. The number of principal components retained was selected based on the cumulative explained variance and the scree plot. Score plots were used to identify clustering patterns among formulations, whereas loading plots were examined to determine the variables contributing most strongly to the observed variability.

Partial least squares (PLS) regression was performed to investigate the relationship between soymilk treatments and coagulant agents in tofu yield and hardness. The predictor matrix (X) consisted of the physicochemical characteristics of each tofu. The response matrix (Y) included either the yield or the hardness. The optimal number of latent variables was determined by maximizing the cross-validated predicted R-squared (R² _pred) using the leave-one-out method. Model performance was evaluated using the coefficient of determination (R²), R² _pred, and the root mean square error (RMSE). XLSTAT (v. 2026), which computes standard deviations for each standardized coefficient (variable importance), was used to identify the experimental factors that exert the strongest influence on tofu.

3 Results and discussion

3.1 Microbiological quality of soymilk

After preparing the soymilk, microbial populations were assessed to determine the initial microbial load. The results show that the hot extraction process effectively reduces the microbial load in soybeans. The AMB count is within the acceptable range; however, total coliforms exceed international guidelines, which set a limit of 100 CFU/mL. The low counts of molds and yeasts indicate that the extraction temperature used was sufficient to control them. The absence of S. aureus confirms the product’s safety. The results (Table 2) demonstrate the necessity for thermal treatments, either pasteurization or thermoultrasonication.

TABLE 2. Microbial load Log₁₀ N (CFU/mL) present in untreated soymilk.

3.2 Microbiological quality of pasteurized and thermo-sonicated soymilk

For the soymilk, which was pasteurized at 60 °C for 30 min and treated with low-frequency ultrasound (65% amplitude, 75 μm, 60 °C, 30 min), microbial populations were subsequently determined to assess their reduction during treatments. Microbial inactivation kinetics were determined for AMB and total coliforms. For pasteurized soymilk, the reduction of AMB (Figure 2) was approximately 2 log CFU/mL, and ultrasound reduced it by approximately 2.5 log CFU/mL. For US treatment, a greater decrease in microbial populations was observed in AMB and coliforms (Figure 3). Compared with pasteurization, ultrasound has a greater effect on bacteria (Figures 2, 3). Traditional pasteurization as a heat treatment inactivates bacterial cells through protein denaturation, membrane disruption, and oxidative stress, leading to bioenergetic failure and cell death (Sun et al., 2025). Acoustic cavitation induced by high-intensity ultrasound generates micro-streaming, localized high pressures and local temperature increases, and shear forces that mechanically weaken microbial cell walls and increase membrane permeability. The resulting membrane damage disrupts cell clusters and exposes microorganisms to sustained physical stress (Akdeniz and Akalın, 2022). Cavitation bubble implosion splits water molecules to generate reactive oxygen species (free radicals), which damage internal cellular components such as DNA and lipids (He et al., 2021; Shet et al., 2026). During thermal sonication, synergistic stress increases microorganisms’ sensitivity to thermal denaturation, accelerating inactivation kinetics and potentially reducing the severe thermal exposure required for soymilk pasteurization.

A Weibull non-linear regression of inactivation curves for pasteurization and thermoultrasonic treatment was performed to obtain model parameters, frequency distributions, and D-values. Table 3 reports Weibull parameters, survival frequency distribution statistics, and D-values for AMB and coliforms in pasteurized and ultrasonicated soymilk. The Weibull mathematical model demonstrated predictive ability in describing the inactivation kinetics of both microbial groups under the two evaluated treatments. The coefficients of determination (R ²) range from 0.987 to 0.991, indicating that the model explains more than 98.7% of the observed variability in microbial survival. This is supported by RMSE values ranging from 0.054 to 0.090. The low standard errors for the kinetic parameters (b and n) and the narrow 95% confidence intervals confirm the significance of the data obtained.

TABLE 3. Weibull parameters, survival frequency distribution statistics, and D value for mesophiles and coliforms in pasteurized and thermoultrasonicated soymilk.

For both microbial groups and under all experimental conditions, n was >1.0, ranging from 2.22 to 2.45. Physiologically, a value of n > 1 describes survival curves with a pronounced downward concavity (shoulder), as shown in Figures 2, 3. This demonstrates that bacterial cells do not inactivate immediately and linearly but instead undergo an initial period of resistance, during which they accumulate sublethal damage before collectively inactivating in response to the physical treatment (van Boekel, 2002; Peleg and Cole, 1998; Albert and Mafart, 2005; Buzrul, 2022). As shown in Table 3, ultrasound-assisted pasteurization exhibited superior lethal efficacy compared with traditional thermal pasteurization. The D-value decreased from 21.1 to 19.4 min, accompanied by an increase in the scaling parameter (b). For total coliforms, the D-value decreased from 25.9 to 24.6 min. Coliforms exhibited slightly higher resistance in the soymilk matrix, possibly attributable to the structural characteristics of their Gram-negative cell wall. For both aerobic mesophiles and coliforms, the lower average D-values observed in the combined thermo-ultrasound treatment do not differ significantly (p > 0.05) from thermal pasteurization. Despite the lack of statistical significance, the numerical reduction in D-values highlights a clear technological advantage of the combined treatment. Previous studies mentioned that ultrasound lowers D values are achieving, by inducing acoustic cavitation, where microbubbles collapse and produce shock waves, pressure, and shear forces (Akdeniz and Akalın, 2022; Raja et al., 2025).

Weibull modeling, treated as a statistical distribution of cell death times (Figure 4), yielded central tendency and dispersion parameters (Table 3) that provide further insight into the process’s behavior (van Boekel, 2002; Bevilacqua et al., 2015; Possas et al., 2018). Ultrasound decreased the mean inactivation time and mode in both microbial groups, with the mode shifting from 16.17 to 14.96 min for AMB, confirming faster population collapse (Akdeniz and Akalın, 2022). Variance (Table 3) also decreased (from 78.97 to 64.46 in AMB, and from 110.76 to 90.63 in coliforms), indicating more uniform resistance. Lower variance statistically indicates greater homogeneity in the population’s resistance, likely due to ultrasound-induced cell disruption (Akdeniz and Akalın, 2022). Positive skewness values indicate right-skewed distributions, common in populations where the maximum inactivation rate occurs after the shoulder phase.

The downward-concave behavior (n > 1) observed in processed soymilk aligns with research on thermal processing and emerging technologies for plant-based matrices. Studies evaluating microbial inactivation in soymilk using the Weibull model report that the shape parameter remains above 1 because matrix components provide a protective effect. Soybean proteins and fats act as colloidal heat shields that prolong the initial shoulder phase and delay the immediate lethality rate (Kwok & Niranjan, 1995; Kwok et al., 2002; Giri and Mangaraj, 2012; Possas et al., 2018; Reyes-Jurado et al., 2023; Irshad et al., 2026). Thermo-ultrasound synergism supports the use of non-thermal and moderate-thermal barrier methods.

3.3 Effect of treatments on the physicochemical characteristics and composition of soymilk

The physicochemical properties and chemical composition of soymilk subjected to different treatments were determined. Table 4 compares untreated soymilk, pasteurized soymilk, and soymilk treated with thermoultrasonic technology. A statistically significant (p < 0.05) variation in chemical composition and physicochemical properties among the different soymilks is observed.

TABLE 4. Comparison of chemical composition and physicochemical properties of untreated, pasteurized, and thermoultrasonically treated soymilk.

For each row, different superscript letters indicate significant differences (p < 0.05). Hue and chroma were calculated from the average of the ah and bh values.

Some authors claim that low-frequency ultrasound treatment does not alter the physicochemical properties of food; however, statistically significant differences are observed among soymilk treatments. These differences are attributed to the effects of low-frequency ultrasound on chemical reactions and enzyme inhibition in soymilk. Thermoultrasonicated soymilk is homogenized because the process breaks down fat globules. Regarding color change, ultrasonicated soymilk is lighter than pasteurized soymilk. Untreated soymilk also shows variations in parameter ah, which are reflected in the hue and chroma of each soymilk.

3.4 Assessment of the composition and physicochemical properties of tofu

Table 5 presents the physicochemical properties and composition of tofu using three coagulants and three pretreatments. Analysis of variance reveals significant differences (p < 0.05) in the chemical composition and physicochemical properties of the tofu varieties influenced by both the types of soymilk and the coagulating agents used. The tofu quality properties depend primarily on the chemical nature of the coagulating agent and are secondarily modulated by physical pretreatment applied to soymilk (pasteurization and thermoultrasound). The chemical nature of the coagulating agents determines the tofu texture and yield to be higher in the following order CaCl₂ > MgCl₂ > acetic acid. The systems exhibiting the most notable changes are those prepared with ultrasonicated soymilk.

TABLE 5. Physicochemical properties and composition of the different types of tofu.

Nomenclature of the systems is shown in Table 1. For each row, different superscript letters indicate significant differences (p < 0.05).

Hue (H) and chroma (C) were calculated from the average of the ah and bh values.

The physical pretreatment of soymilk introduced a secondary, consistent gradient trend: Ultrasonicated > Pasteurized > Untreated for tofu hardness (Table 5). For the three coagulant types, using ultrasonicated soymilk consistently produced the firmest tofu profiles (6.8 N for acetic acid, 11.5 N for MgCl₂, and 15.0 N for CaCl₂). This increase is possibly driven by acoustic cavitation and its associated micro-shear forces, which disrupt the native quaternary and tertiary interactions of globular soy proteins (Wang X. et al., 2023). This physical disruption induces molecular unfolding and reduces overall particle size, exposing hidden internal functional groups such as hydrophobic amino acid residues and free sulfhydryl (–SH) groups while increasing surface hydrophobicity (Gao et al., 2021). Once exposed, these sites become accessible to interact with coagulants, maximizing covalent disulfide bond formation and reinforcing the gel network’s mechanical rigidity (Zheng et al., 2020). This sharp upward trend in ultrasound-induced mechanical hardness operates via a tightly coupled trade-off with matrix yield and native protein retention.

3.4.1 Effect of calcium chloride and magnesium chloride on tofu

The type of coagulant affects macronutrient retention, process yield, and the texture of the final product. Tofu obtained with CaCl₂ exhibits the highest protein content (10.2%–10.6%), yield (14.54%–14.60%), and hardness (12.5 N–15.0 N). While MgCl₂ (the main component of traditional nigari) produced tofu with intermediate profiles, similar protein content (8.5%–8.8%), fat content (4.76%–4.86%), yields (∼12.7%), and moderate hardness (9.5 N–11.5 N). Although magnesium is a divalent cation, its reaction rate differs from calcium, producing a softer gel network appreciated for its traditional organoleptic properties. CaCl₂ and MgCl₂ enhance the tofu texture and yield compared with acetic acid. This behavior is governed by the underlying molecular aggregation mechanisms. Divalent salts neutralize exposed carboxyl groups on soy globulins (7S and 11S), promoting dense, stable divalent ionic bridges and hydrophobic contact zones within the three-dimensional network (Geng et al., 2024; Li et al., 2025). Calcium forms more effective bridges between the negatively charged carboxyl groups of soy globulins, especially glycinin, causing precipitation and forming a homogeneous, compact gel network compared with MgCl₂, which traps soluble solids (Zheng et al., 2020), explaining the highest yield and hardness.

3.4.2 acetic acid effect on tofu properties

Treatments with acetic acid resulted in the lowest values for almost all critical indicators: pH (4.45–4.78), reduced protein (6.6%–6.9%), low yield (11.59%–12.36%), and soft texture (5.8 N–6.8 N). Unlike salts, acetic acid lowers the pH of soymilk to about 4.5, causing proteins to lose charge, precipitate, and form a weaker gel. This gel retains fewer solids, exhibits greater syneresis, and releases soluble proteins into the whey, reducing yield and firmness. Acetic acid induces precipitation by shifting the medium pH to the proteins’ isoelectric point (∼4.5). The acid-induced clumping relies on disordered electrostatic and hydrophobic collapses around neutral surface charges, yielding porous, structurally weaker matrices (Geng et al., 2024; Wang B. et al., 2023). This mechanism explains the low yield, soft textures, and acidic pH (∼4.5) systematically observed across all acetic acid treatments.

3.5 Microbiological quality analysis of tofu

Table 6 shows that pasteurized and ultrasonicated soymilk improved microbiological quality compared with untreated soymilk; ultrasonic treatment shows a significant reduction in AMB and total coliforms. The results of the microbiological analysis of nine tofu varieties (Table 6) indicate that all samples meet international safety and hygiene standards and consistently fall below the risk limits (Soyfoods Association of America, 1986). AMB counts ranged from 2.10 to 2.98 log(CFU/g). Thermoultrasound-treated soymilk reduced the initial AMB load compared with untreated and pasteurized soymilk. The use of acetic acid resulted in slightly lower counts in untreated and pasteurized soymilk, which could be attributed to an inhibitory effect from the decrease in pH. In all samples evaluated, total coliform counts remained <10 CFU/g and S. aureus counts <10 CFU/g. Yeast and mold counts ranged from 1.74 to 1.95 log(CFU/g). The Soyfoods Association of America (1986) reports that at the plant, on the day of production, at 4.4 °C, the standard plate count in tofu shall be less than 2000 CFU/g, and coliforms less than 10 CFU/g, and at the time the tofu is sold, an acceptable product must meet these criteria: coliforms between 11 and 500 CFU/g, and standard plate count less than 100,000 CFU/g (Soyfoods Association of America, 1986). Research on soy derivative processing shows that ultrasound creates acoustic cavitation, which mechanically damages bacterial cell membranes (Olaniran et al., 2025). Tofu frequently has high microbiological counts, often due to cooling failures (Wu et al., 2023). Industrial tofu samples have reported mesophilic counts above 5.0 log CFU/g and common coliform presence, mainly caused by cross-contamination (Rossi et al., 2016).

TABLE 6. Microbial load present in the different types of tofu.

Nomenclature of the systems is shown in Table 1.

3.6 Sensory evaluation of different tofu systems

Sensory analysis using a 9-point hedonic scale showed that the pretreatments applied to the soymilk (pasteurization and thermoultrasound) and the nature of the coagulating agent had a statistically significant effect (p < 0.05) on the overall acceptability and sensory attributes of the tofu, except for color (Table 7). Regarding color, average scores ranged from 5.08 to 6.25 (placing it in the “I like it slightly” category), with no significant differences (p > 0.05) between treatments. This demonstrates that neither the hydrodynamic energy of ultrasound nor the thermal denaturation from pasteurization appreciably modified the soy’s native chromophoric compounds, resulting in a homogeneous and acceptable visual appearance for the consumer panel.

TABLE 7. Sensory scores of the different tofu types.

Nomenclature of the systems is shown in Table 1. For each row, different superscript letters indicate significant differences (p < 0.05).

When evaluating tofu texture (consistency), a significant increase in sensory ratings was observed when using soymilk subjected to high-intensity ultrasound. Tofu made with untreated soymilk showed the lowest acceptance for consistency (2.35, “I moderately dislike it”), with the CMS sample (coagulated with MgCl₂). In contrast, the homologous treatments subjected to ultrasonic treatment, such as MgCl₂ (4.71), acetic acid (4.99), and CaCl₂ (4.91), approached neutral acceptance (∼5.0), statistically better than their thermal and untreated counterparts. This behavior directly correlates with acoustic cavitation breaking down native aggregates and exposing internal functional groups, thus improving molecular crosslinking capacity (Yuan et al., 2025). Thus, the panel perceived gels with a more uniform, cohesive texture and a lack of gritty mouthfeel, a phenomenon supported by Wang B. et al. (2023), who confirmed that the rheology and gel strength of soy proteins improve significantly after controlled sonication.

Flavor and acidity attributes were key in differentiating and rejecting tofu systems. Tofu (untreated soymilk coagulated with acetic acid) received the lower taste rating in the study (2.90) and low acidity acceptance (3.63). This is attributed to acid aggregation around the isoelectric pH (∼4.5), which results in a porous matrix, thereby concentrating free volatile acids and undesirable flavor compounds (Paz-Yépez et al., 2024). However, when acetic acid was combined with ultrasonication, the taste improved significantly to 4.42. This increase is based on the fact that acoustic cavitation and the generated thermal microcurrents not only modify proteins but also facilitate the volatilization and forced extraction of carbonyl compounds such as hexanal and 2-pentylfuran, responsible for the astringent or “bean-like” flavor characteristic of soybeans (Wang X. et al., 2023; Guan et al., 2021). The highest flavor scores were assigned to the use of divalent salts with soymilk treated thermally or by ultrasound (CCP = 6.71; CMU = 6.39), indicating the judges’ intrinsic preference for neutral salt profiles over strongly acidic ones (Geng et al., 2024). Awoyale et al. (2025) studied how chemical composition, texture, and taste acceptance relate in tofu made with different coagulants—vinegar, lime juice, alum, and steeped Ogi water. Vinegar-coagulated tofu had the highest fat, ash, and fiber, while steeped Ogi water had the most protein. Steeped Ogi water improved sensory qualities most, followed by vinegar, making the tofu tastier and more attractive; lime was the least favored.

The overall acceptability parameter for tofu made from untreated soymilk had the lowest hedonic index among the panel (CMS = 3.25; AAS = 3.34), placing it in the rejection zone. The applied technologies improved the finished product quality, with ultrasound + MgCl₂ (6.55) and ultrasound + CaCl₂ (6.56) evaluated as better, in the “moderately liked” class. These results confirm that high-intensity ultrasound acts as a viable tool in the food industry, since, by interacting synergistically with coagulants based on divalent ionic bridges, it suppresses the traditional defects of soft texture and unpleasant flavors of soy, improving the market value and final palatability of tofu (Li et al., 2025; Geng et al., 2024).

To integrate the different sensory attributes into a single quality metric, a Single Sensory Quality Index was developed using a multiple linear regression model. The color attribute was excluded from the preliminary predictive analysis because it showed no statistical variation between samples (p > 0.05). When fitting the model with the remaining attributes and assessing the risk of overfitting given the panel size (30 judges), cross-verification of the model was tested using the adjusted R². The model achieved an ordinary R² of 0.965 and an adjusted R² of 0.944. This variation (2.09%) reveals that despite the sample size, the relative weights driving the Single Sensory Quality Index led predominantly by acidity (49.38%, coefficient = 0.7494, p < 0.05), followed by consistency (25.68%. coefficient = 0.3898) and flavor (24.94%, coefficient = 0.3786), are statistically stable, reliable, and highly representative of the panel’s consensus. The weighted scores were normalized to a standardized scale from 1 to 9. To consolidate the attributes evaluated by the sensory panel into a single quality indicator to facilitate decision-making, a Single Sensory Index was calculated for each of the nine tofu varieties. Figure 5 presents the results of this mathematical integration.

The dominant relative weight assigned to acidity (49.38%), paired with the statistical overlap among top-performing samples (such as CMU and CCU) in Table 7, reflects a classic penalty-driven consumer perception pattern commonly observed in non-dairy matrices (Silva et al., 2026). This perceptual mechanism was mathematically verified by a positive correlation between the panelists’ acidity and flavor scores (R2 = 0.68), indicating a sensory interaction during product evaluation. Within sensory rejection and acceptance dynamics, critical parameters such as acidity do not operate linearly across the evaluative scale; instead, they function as psychophysical threshold switches. In the rejection zone, when the profile shifts toward a sharp, vinegary note (pH < 5.0), panelists penalize the sample sharply, triggering a major drop in overall acceptability because both flavor and acid balance change simultaneously. Within the target acceptance zone, judges perceive neutral-salt tofu samples as properly balanced (Awoyale et al., 2025; Shi et al., 2020). Thus, their hedonic scores are within the same group. Therefore, the multiple linear regression model accurately identifies acidity not as a linear descriptor, but as the primary gating factor for global quality, meaning that maintaining this attribute within the overlapping target zone is a mandatory prerequisite for product viability.

The classification (Table 5) reveals a clear segmentation of perceived quality by pretreatment-coagulant combination, with the neutral acceptance threshold (a score of 5.0 on the hedonic scale) serving as the statistical boundary between technologically viable treatments and those the panel rejected.

3.7 Principal component analysis

Principal Component Analysis of the physicochemical and structural properties of tofu (Figure 6) revealed that the coagulating agent exerts a determining influence on the product’s quality profile. At the same time, the soymilk pretreatments act as secondary modulating factors. The first two principal components explained most of the system’s variability. PC1 is characterized by strongly positive loadings on the variables’ protein (0.455), yield (0.44), ash (0.434), and hardness (0.429). PC2, on the other hand, shows a marked vector opposition between moisture (0.599) and the variables of soluble solids (°Bx, −0.523) and fat content (−0.466).

The samples coagulated with CaCl₂ mostly appeared in the positive quadrant of PC1, suggesting a simultaneous increase in yield, hardness, protein, and mineral content. This pattern aligns with findings reported by Li et al. (2025) and Van et al. (2025), who state that certain saline coagulants support stable hydrophobic interactions and disulfide cross-bridge formation, leading to dense networks without weakening the gel’s mechanical strength.

In contrast, the use of acetic acid drastically shifted the samples toward highly negative values in PC1 (up to −3.31) and positive values in PC2. This indicates the production of tofu with structural deficiencies, low yield, and reduced macronutrient retention. Direct acidification may neutralize the surface charges of soy globular proteins toward their isoelectric points, causing disordered aggregation and gel syneresis, which reduces the matrix’s ability to retain lipids and proteins (Van et al., 2025). Furthermore, the combination of acetic acid with ultrasound pretreatment intensified this decrease in PC1. High-intensity ultrasound disperses protein aggregates and enhances gelation via cavitation (Xin et al., 2025), but acidity hindered homogeneous gel formation, creating a weak matrix.

Although the first two principal components capture a cumulative variance of 63.6%, reflecting the multifactorial complexity and inherent noise of modified food matrices, the Score Plot shows that the spatial grouping of the tofu samples is primarily driven by the coagulating agent. The treatments form three distinct clusters along the PC1 and PC2 axes based on whether acetic acid, calcium chloride, or magnesium chloride was used, whereas the soymilk pretreatments act as secondary modulators within those clusters.

Tofu samples with MgCl₂ clustered near neutral on PC1 but exhibited the most negative PC2 values (−2.36), reflecting low-moisture matrices rich in fat and soluble solids (°Bx). This effect, intensified by thermal treatments (pasteurization and thermal ultrasound), results from protein denaturation exposing hydrophobic regions and increasing ionic release from the coagulant. This process leads to gel contraction and mechanically traps fat globules dispersed in the soymilk whey (Xin et al., 2025; Chen et al., 2023).

3.8 Predictive modeling using PLS

For predictive modeling of tofu quality (hardness) and yield, PLS regression used leave-one-out cross-validation. The optimal number of latent components was chosen based on R² _pred and statistical parsimony. Although the three-component model had a higher R² _pred, the two-component solution (R²pred >90%) was selected to maintain degrees of freedom for nine treatments, reduce overfitting risk, and reliably explain response variability. The final two-component PLS models achieved a robust R² _pred, indicating predictive capability for tofu yield and hardness based on the selected predictors.

Standardized coefficients (Figure 7) indicated that physical processing factors and electrostatic balance mainly influence gel hardness, while yield results from a combined effect of hydration and thermal denaturation. For the tofu hardness model, ultrasound pretreatment (standardized coefficient = 0.231) is significant positive driver (p < 0.05), this phenomenon involves acoustic cavitation disrupting soy globulin aggregates (7S and 11S), exposing hydrophobic regions and free sulfhydryl groups (Zheng et al., 2020; Wang X. et al., 2023); Also, medium pH (standardized coefficient = 0.222) is a significant positive driver (p < 0.05). The system’s pH strongly influences aggregation, with near-neutral pH reducing electrostatic repulsion and promoting compact protein aggregation. This structural change may promote denser crosslinking during gelation. Acetic acid’s effect (−0.199) rapidly lowers pH towards the isoelectric point, causing disordered precipitation and fragile gel formation. Adding calcium-based coagulant (0.178) and higher protein density (0.192) helps form stable divalent ionic bonds, supporting structure.

The PLS model indicates that yield (%) primarily depends on the matrix’s moisture-holding capacity, which interacts with soluble and structural solids such as proteins (standardized coefficient = 0.192) and ash (0.159), significantly affecting product yield (p < 0.05). Thermal pasteurization of soymilk significantly increases yield (0.171) but does not affect hardness. Heat denaturation causes globular soy proteins to unfold, exposing hydrophilic sites that enhance whey and free water retention in the curd capillaries during pressing (Wang X. et al., 2023). Hardness, included as a predictor, was the strongest factor (p < 0.05) influencing yield (standardized coefficient = 0.234). This suggests that a robust gel structure creates an effective mechanical network, reducing syneresis and curd breakage and helping preserve macronutrients in the final tofu.

4 Conclusion

Three types of soymilks (untreated, pasteurized, and thermally ultrasound-treated) were used to prepare tofu using three coagulants (CaCl₂, MgCl₂, and acetic acid). Non-linear inactivation was observed for aerobic mesophilic bacteria and total coliforms during pasteurization and thermal ultrasound treatment. The Weibull model fitted the data well and showed that microbial groups exhibited initial resistance to treatments (n > 1). Thermoultrasound treatment increased tofu hardness regardless of coagulant type. The type of coagulant primarily affects protein content, yield, and hardness, with higher values for the following: CaCl₂ > MgCl₂ > acetic acid. The microbial quality of tofu was satisfactory. Tofu from soymilk treated with high-intensity ultrasound and coagulated with divalent salts improved tofu acceptability. Advanced chemometric and statistical tools enabled systematic interpretation of factors affecting tofu quality. PCA showed the coagulating agent as the main factor in macroscopic and sensory differences, while ultrasound and thermal pretreatments modulated final texture. PLS indicated that hardness depends on ultrasound-induced acoustic cavitation and near-neutral pH, promoting a firm gel. Yield and hardness are key predictors, with a strong protein network. These findings might be a framework reference for industrial improvements in tofu production. However, scaling and reevaluation of these data should be performed at an industrial level.

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Footnotes

Edited by: Daniela Lamas, Institute of Marine and Coastal Research (IIMyC), Argentina

Reviewed by: Guangliang Xing, Changshu Institute of Technology, China

Shengqi Zhang, Jiangsu University, China