RSM-optimized co-encapsulation of Lactobacillus brevis LSe and FOS in calcium alginate: enhancing encapsulation efficiency and bacterial growth

Abstract

Background

This study optimized the co-encapsulation of the probiotic Lactobacillus brevis strain LSe and the prebiotic fructo-oligosaccharide (FOS) in calcium alginate beads using a Central Composite Design (CCD).

Results

The statistically derived optimal formulation (3.0% w/v sodium alginate, 1.2% w/v FOS, and 2.0% w/v CaCl₂) achieved high initial and 24-h encapsulation efficiencies of 84.7 ± 2.8% and 99.2 ± 1.2%, respectively. Encapsulated cells showed markedly improved growth in culture medium compared to free cells (OD₆₀₀ = 0.70 vs. 0.15). Under simulated GI conditions, encapsulation maintained high viability at pH 2.0, but survival rates did not significantly differ between encapsulated and free cells in simulated gastric juice, intestinal juice, or bile salt solutions (0.3–1.2% w/v).

Conclusions

For this specific strain and formulation, the primary benefits of encapsulation are enhanced initial loading and growth promotion rather than substantial GI protection. Nonetheless, the high encapsulation efficiency and improved growth kinetics support the FOS/alginate system as a promising delivery vehicle for L. brevis LSe in functional foods. This study establishes the first RSM-optimized protocol for this co-encapsulation, providing a reproducible framework for future synbiotic delivery system development.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12866-026-05133-1.

Background

Probiotics are living microorganisms that are used in the form of food supplements and, if consumed in sufficient and appropriate amounts, help maintain the balance of the microbiota of the human body [1, 2]. Probiotics include Bifidobacteria, lactic acid bacteria, Bacillus strains and yeast. A broad range of food products are supplemented with them including fermented and unfermented dairy products, grain-based products, and health supplements (capsules and animal feed supplements) [3, 4].

From production and storage to final consumption, multiple factors influence the viability of probiotics such as oxygen levels, osmotic stress, pH, temperature, storage duration, and gastrointestinal tract conditions. When the oral probiotic products were used, probiotic bacteria are required to tolerate the environmental stresses of the gastrointestinal tract, including exposure to acidic gastric juice and bile secretions. Several probiotic microbes are inherently intolerant to the above factors and must encapsulate in appropriate materials to increase their viability in production, storage and transmission processes [3, 5].

Microencapsulation is a common method to entrap probiotic bacteria and release them under favorable conditions and kept them from unfavorable environmental conditions as a physical barrier to maintain the viability of probiotic bacteria. Microencapsulation approaches can be divided into three main categories. Chemical methods include molecular inclusion cross-linking and interfacial polymerization. Physicochemical methods comprise coacervation, liposome entrapment, solvent evaporation, ionic gelation, and spray cooling. Physical and mechanical methods involve supercritical fluid processing, fluid-bed coating, extrusion, freeze-drying, and spray-drying [5–9].

Many materials can be applied for probiotics microencapsulation, such as protein-based materials (e.g., soy protein, pea protein, gelatin, and dairy proteins), polysaccharide-based materials (e.g., xanthan gum, alginate, chitosan, and pullulan gum), and lipids. However, one of the most commonly used encapsulation materials is alginate, a naturally derived anionic polysaccharide consisting of two structural units, mannuronic acid and guluronic acid, which are covalently linked through glycosidic bonds. Alginate is extracted from brown algae and different species of algae, and it can also be found in various species of bacteria [5, 10, 11].

There are several advantages of alginate, such as non-toxicity, ease of handling, bioavailability, biocompatibility, low cost, and facile gelation. However, several reports have shown that alginate does not improve the viability of probiotic bacteria in low-pH environments, due to its porous texture and permeability to small molecules. For this purpose, oligosaccharides as a prebiotic can be used as helper agents that promote the stability of alginate beads [12, 13].

Prebiotics are non-digestible food components that exert a beneficial effect on the host by selectively stimulating the growth and/or activity of specific bacterial species in the host’s colon. Recently, prebiotics have been proposed as part of the coating material in probiotic microencapsulation. Oligosaccharides are known as the most prevalent form of prebiotics, and they can improve the survival of probiotics in the upper gastrointestinal tract. This allows probiotic cells to adhere and colonize the gut and exert health benefits [8, 10, 14].

In this study, we aimed to prepare and optimize calcium alginate beads containing prebiotics for encapsulating the probiotic Lactobacillus brevis strain LSe. The viability of the probiotic bacteria then was evaluated under simulated fluids of gastric and intestinal, acidic environments, and in the presence of bile salts.

Materials and methods

Chemicals

Sodium alginate, calcium chloride, De Man, Rogosa and Sharpe (MRS) broth, and agar were provided by Merck Chemicals (Darmstadt, Germany). Oxgall, trypsin, pepsin, and fructo-oligosaccharides (FOS) were obtained from Sigma–Aldrich (St. Louis, MO, USA). In the case of other chemicals and solvents their analytical grade was used.

Cultivation of the bacterial strain

Lactobacillus brevis strain LSe was selected for this study based on its previously documented probiotic attributes, including antioxidant capacity and tolerance to gastrointestinal stressors [15], its isolation from a traditionally consumed fermented dairy product (supporting its safety profile), and its demonstrated adaptability to laboratory-scale encapsulation processes. Furthermore, the co-encapsulation of this strain with FOS in calcium alginate beads represents a novel approach that has not been extensively explored in the literature. The microtube containing the bacterial strain was removed from the freezer at -80 °C. After the culture medium was thawed, the sample was spread evenly on the surface of the culture medium containing MRS and agar (2.0% w/v). Then the plates were transferred to a 37 °C incubator and incubation continued until lactobacillus colonies were found. After incubation, the plates were transferred to the refrigerator for further processing.

Preparation of the bacterial suspension

The quantification of microbial growth, expressed as bacterial density, was determined by measuring the optical density at 600 nm using UV-vis spectrophotometer (UV-1800, Shimadzu Corporation, USA). The obtained optical density indirectly reflects bacterial count. In the present study, the microbial suspension was prepared based on the 0.5-McFarland standard. OD_600,24 was used as a high-throughput proxy for relative bacterial growth under identical experimental conditions. While OD₆₀₀ does not differentiate viable from non-viable cells, it provides a consistent metric for comparative optimization studies. All GI tolerance and survival assays (Sect.  2.9.1–2.9.4) were assessed using colony-forming unit (CFU) counts to ensure biological relevance. A strong correlation between OD₆₀₀ and viable counts (Log CFU/mL) for L. brevis LSe under standard culture conditions (R² = 0.940) is provided in Supplementary Fig. S1, supporting the use of OD₆₀₀ as a relative growth indicator in this system.

Preparation of FOS/Ca-alginate beads

The sodium alginate solutions were prepared by dissolving different amounts of sodium alginate powder, which had been previously exposed to UV light for 20 min, in sterile water. Calcium chloride (CaCl₂) solutions were also prepared in required concentrations and autoclaved for 20 min at 121 °C (15 psi). The microbial suspension obtained from the above step was added to sodium alginate solution containing FOS solutions (FOS powder in sterile water) and dripped through a 10 mL plastic syringe with a 23-gauge stainless steel needle into a cold, stirring calcium chloride solution to form FOS/Ca-alginate beads of uniform size. Beads were formed using a 23-gauge needle under gravity-driven extrusion, a standard laboratory-scale approach that prioritizes reproducibility for optimization studies. This method typically yields beads in the 3–4 mm range [5], which is suitable for proof-of-concept evaluation but may require modification for commercial food applications. According to the experiment design, the preparation process of FOS/Ca-alginate beads was repeated with different concentrations of sodium alginate, FOS, and calcium chloride. The obtained beads were collected and washed several times using sterile distilled water for further analysis.

Experimental design and optimization

Experimental setup

To optimize the microencapsulation of L. brevis strain LSe in calcium alginate beads, a Central Composite Design (CCD) was employed using Design-Expert^® software (Version 12.0.3.0; Stat-Ease Inc., Minneapolis, MN, USA). Based on preliminary screening and relevant literature [10, 13], three independent variables were selected: sodium alginate concentration (X₁), fructo-oligosaccharides (FOS) concentration (X₂), and calcium chloride (CaCl₂) concentration (X₃) (Table 1). The measured responses included initial encapsulation efficiency [Encapsulation efficiency measured immediately after bead formation (t = 0 h); EE₀ (%)], encapsulation efficiency after 24 h [Encapsulation efficiency measured after 24 h of storage; EE₂₄ (%)], and optical density at 600 nm after 24 h [Bacterial growth indicator measured after 24 h incubation in MRS broth; OD₆₀₀,₂₄]. The experimental matrix consisted of 20 runs, comprising 8 factorial points, 6 axial points, and 6 central points arranged in 3 blocks (Table 2).

Table 1.

The coded levels and values of each independent variable in central composite design for optimizing of variables affecting the encapsulation of probiotic bacterium Lactobacillus brevis strain LSe and prebiotic, fructo-oligosaccharides (FOS), in calcium alginate beads

Variable	Name	Unit	Low level (− 1)	High level (+ 1)
X1	Sodium alginate concentration	%	2.0	4.0
X2	FOS concentration	%	0.0	2.0
X3	CaCl2 concentration	%	2.0	4.0

Table 2.

The experimental and predicted results of central composite design for optimizing of variables affecting the encapsulation of probiotic bacterium Lactobacillus brevis strain LSe and prebiotic, fructo-oligosaccharides (FOS), in calcium alginate beads

Run	Block	X1	X2	X3	EE₀ (%)		EE₂₄ (%)		OD₆₀₀,₂₄
					Experimental	Predicted	Experimental	Predicted	Experimental	Predicted
1	Block 1	1a	1	-1b	85.3	83.8	98.9	98.7	0.98	0.98
2	Block 1	0c	0	0	83.8	80.8	99.7	99.5	0.89	0.83
3	Block 1	1	-1	1	80.6	78.1	97.9	97.6	0.80	0.81
4	Block 1	-1	1	1	82.5	80.8	99.6	99.4	0.78	0.86
5	Block 1	0	0	0	83.8	80.8	99.8	99.5	0.79	0.83
6	Block 1	-1	-1	-1	75.2	73.5	97.9	97.6	0.43	0.46
7	Block 2	0	0	0	80.2	80.8	99.8	99.5	0.97	0.83
8	Block 2	1	1	1	81.3	81.9	98.6	98.4	0.95	0.86
9	Block 2	-1	1	-1	77.6	77.3	98.6	98.4	0.99	0.98
10	Block 2	0	0	0	82.4	80.8	99.7	99.5	0.88	0.83
11	Block 2	-1	-1	1	77.3	77.0	94.1	93.8	0.87	0.81
12	Block 2	1	-1	-1	80.5	80.0	96.8	96.5	0.54	0.46
13	Block 3	0	1.7	0	83.2	85.1	97.9	98.3	1.10	1.07
14	Block 3	0	-1	0	75.3	77.2	96.7	97.3	0.70	0.68
15	Block 3	0	0	0	78.3	80.8	99.0	99.5	0.66	0.83
16	Block 3	-1.7	0	0	80.2	82.7	96.6	97.0	0.64	0.68
17	Block 3	0	0	1.7	75.5	77.8	98.6	99.0	0.97	1.06
18	Block 3	1.7	0	0	76.3	78.8	96.5	97.0	0.62	0.68
19	Block 3	0	0	0	77.1	80.8	98.7	99.5	0.71	0.83
20	Block 3	0	0	-1.7	81.5	83.8	99.4	99.9	0.50	0.59

Base on Table 1, ^a High level of each independent variable. ^b Low level of each independent variable. ^c Medium level (Center Point) of each independent variable

Statistical analysis and model evaluation

Model adequacy and statistical significance were assessed using analysis of variance (ANOVA) coupled with the F-test at a significance level of p < 0.05, including a lack-of-fit test (where p > 0.05 indicates non-significant lack-of-fit). The best-fitting model for each response was selected based on the coefficient of determination (R²), adjusted R² (Adj R²), predicted R² (Pred R²), and adequate precision ratio (signal-to-noise ratio). A difference of less than 0.20 between Adj R² and Pred R², alongside an adequate precision value > 4, was considered indicative of a robust and predictive model. Additionally, residual analysis was performed to verify the assumptions of normality and homoscedasticity. Three-dimensional response surface and interaction plots were generated to visualize the individual and interactive effects of the independent variables on the responses.

Numerical optimization procedure

Numerical optimization was conducted using the desirability function approach within Design-Expert^® software (Version 12.0.3.0) to identify the formulation that simultaneously satisfies all response objectives. The independent variables were constrained within their experimental ranges defined by the CCD: sodium alginate (2.0–4.0% w/v), FOS (0.0–2.0% w/v), and CaCl₂ (2.0–4.0% w/v). All three response variables—EE₀ (%), EE₂₄ (%), and OD₆₀₀,₂₄—were assigned a “maximize” goal. The scientific rationale for this optimization strategy is as follows:

• (i)EE₀ (%) was maximized to ensure the highest possible probiotic loading during bead formation, thereby minimizing cell loss and guaranteeing adequate initial viability for delivery applications.
• (ii)EE₂₄ (%) was maximized to evaluate the structural integrity of the FOS/Ca-alginate matrix and the sustained viability/proliferation of entrapped cells under culture conditions, reflecting long-term system stability.
• (iii)OD₆₀₀,₂₄ was maximized as a direct proxy for bacterial growth and metabolic activity within the beads, confirming effective prebiotic utilization of FOS and the successful development of a symbiotic delivery system.

The optimization algorithm generated a global desirability value, and the predicted optimal formulation was experimentally validated in triplicate on consecutive days to confirm model reliability. Validation results are reported as mean ± standard deviation (SD).

Model validation

Model validation was performed by conducting three independent experiments under the predicted optimal conditions on consecutive days. The relative percentage error (RPE) between predicted and experimental values was calculated for each response. Additionally, root mean square error (RMSE) and mean absolute percentage error (MAPE) were computed to assess predictive accuracy. Agreement between predicted and experimental values was further evaluated using paired t-tests and 95% confidence intervals for the mean differences. A model was considered successfully validated if RPE < 10% for all responses and if the confidence intervals included zero (p > 0.05).

Cultivation of FOS/Ca-alginate beads containing L. brevis strain LSe

A certain number of beads formed in the above stage were transferred to 250 mL Erlenmeyer flasks containing MRS broth culture medium (100 mL) and incubated at 37 °C for 24 h with shaking at 120 rpm. After this period, the EE₀ (%), EE₂₄ (%), and OD₆₀₀,₂₄ were evaluated.

Determination of encapsulation efficiency (%)

Encapsulation efficiency (EE%) was calculated according to the widely accepted CFU-based formula:

where CFU_recovered represents the number of viable cells enumerated from dissolved beads after encapsulation, and CFU_initial denotes the number of viable cells initially added to the formulation prior to bead formation. To determine CFU_recovered, beads were dissolved in 2% (w/v) sodium citrate buffer solution (pH 6.0) under gentle stirring for 30 min to release entrapped cells. The resulting suspension was serially diluted with sterile 0.9% (w/v) NaCl solution, plated on MRS agar, and incubated anaerobically at 37 °C for 24–48 h. Viable colonies were counted, and CFU values were calculated accordingly. This CFU-ratio approach aligns with recent microencapsulation studies [10, 16] and facilitates direct comparison of encapsulation performance across the literature. Encapsulation efficiency was assessed at two time points: immediately after bead formation (EE₀) and after 24 h of refrigerated storage (EE₂₄). EE₀ reflects initial loading capacity, while EE₂₄ indicates short-term retention stability.

Morphological characteristics of FOS/Ca-alginate beads

A number of formed FOS/Ca-alginate beads were transferred to 250 mL Erlenmeyer flasks containing MRS broth medium. The Erlenmeyer flasks were incubated at 37 °C for 24 h in an incubator shaker at 120 rpm. After incubation, the size and shape of the beads were evaluated visually.

Probiotic evaluation

In order to measure the effectiveness of FOS/Ca-alginate beads in increasing the survival of cultivated L. brevis strain LSe in terms of probiotic properties, the following tests were performed on bacterial cells of L. brevis strain LSe encapsulated in beads. Simulated gastric juice (SGJ) exposure times (1–3 h) were selected to approximate gastric emptying ranges reported for liquid/solid meals in humans (1–4 h; [17]. Pepsin concentration (0.35% w/v) aligns with values used in consensus in vitro digestion protocols [18]. Simulated intestinal juice (SIJ) incubation (up to 24 h) encompasses typical small intestinal transit (3–6 h) plus a safety margin to detect delayed effects.

The tolerance to the acidic pH

The resistance of the L. brevis strain LSe encapsulated in FOS/Ca-alginate beads and the standard strain of L. brevis to acidic conditions, corresponding to the acidic environment of the stomach, was assessed based on the method described by da Conceição et al., [16] with some modifications. Initially, the specified amounts of encapsulated bacteria and free bacterial cells were added to 1 mL of PBS (pH 2.0 or 6.0, adjusted with HCl) and incubated anaerobically at 37 °C for 1, 2, and 24 h. A 1 mL aliquot of the cell suspension was serially diluted with 0.9% sterile normal saline, plated on MRS agar, and incubated under anaerobic conditions at 37 °C for 24 h. The appeared suitable colonies were then counted, and the survival percentage was calculated using the following equation:

% Survival = (log CFUN₁/log CFUN₀) ×100.

In this formula, CFUN₀ and CFUN₁ are the number of colonies counted at 0, 1, 2, and 24 h after incubation at the desired pH, respectively. The experiments were performed three times on consecutive days, and the data are expressed as the mean ± SD.

Survival under simulated gastric conditions

The described method by da Conceição et al., [16] was used to assess the tolerance of bacterial cells encapsulated in FOS/Ca-alginate beads and free bacterial cells to simulated gastric juices (SGJ). Briefly, the SGJ was prepared by adding filter-sterilized pepsin solution (0.35%, w/v) into sterile PBS buffer solution and adjusting the final pH to 2.0, 2.5, and 6.0 (as control) with HCL. Then, 10 mL of each pH solution was transferred into sterilized test tubes, and the specified amounts of FOS/Ca-alginate beads containing bacteria and free bacterial cells were individually added to each solution and mixed. After 0, 1, 2, and 3 h of incubation, 1 mL from each pH solution was serially diluted with 0.9% sterile saline and spread on the MRS agar plate, followed by incubation at the appropriate conditions (as mentioned above). Suitable colonies were then counted, and survival percentages were calculated as previously described. All tests were carried out in triplicates and data are expressed as mean ± SD.

Survival under simulated intestinal conditions

In order to investigate the tolerance of the bacteria encapsulated in FOS/Ca-alginate beads and free bacterial cells to simulated intestinal juice (SIJ), 0.1 g of trypsin and 1.8 g of bile salts were dissolved in a sterile solution (100 mL) of sodium bicarbonate and sodium chloride (1.1 g and 0.2 g, respectively). The pH was adjusted to 8.00 using 6 M NaOH, and the solution was sterilized by filtration through a 0.22 μm filter. The specified amounts of FOS/Ca-alginate beads and free bacteria were then inserted into the prepared SIJ and incubated for 0, 3, and 24 h at the previously mentioned conditions. Subsequently, the dilutions from each test were prepared using normal saline solution and spread onto the MRS agar plate, and incubated under anaerobic conditions at 37 °C for 24 h. Survival percentages were calculated based on the number of viable colonies obtained. Each experiment was carried out in triplicate, and all data are expressed as mean ± SD.

Bile salts tolerance

The tolerance of bacterial cells encapsulated in FOS/Ca-alginate beads and free cells to bile salts was determined by the protocol of da Conceição et al., [16] with some modifications. Bile salt solutions at concentrations of 0.3%, 0.6%, and 1.2% (w/v) were prepared using Oxgall powder, while sterile deionized water without Oxgall (pH 6.2) served as the control. 10 mL of each solution was transferred into sterile test tubes, and the specified amounts of FOS/Ca-alginate beads and standard strain were added to each solution. Inoculated solutions were incubated anaerobically at 37 °C for 0, 3, and 24 h. Thereafter, a ten-fold dilution from each salt bile concentration was prepared, and the survival percentage was calculated by the colony counting method described previously. These procedures were repeated three times on different days, and all data are expressed as mean ± SD. While our static incubation model does not simulate mechanical peristaltic forces, it provides a standardized, reproducible platform for comparative evaluation of encapsulation strategies. Dynamic in vitro systems (e.g., TIM-1) or in vivo models represent important next steps for translational validation.

Data analysis

Statistical analysis of the experimental data was performed using Design-Expert^® software (Version 12.0.3.0, Stat-Ease Inc., Minneapolis, MN, USA). The experiments were designed according to a Central Composite Design (CCD) to enable fitting of a quadratic regression model and to evaluate the linear, quadratic, and interaction effects of the independent variables. To assess the statistical significance of the model and its terms, Analysis of Variance (ANOVA) coupled with the F-test was applied. A significance level of p ≤ 0.05 was considered statistically significant, meaning that p-values less than or equal to 0.05 indicated significant effects. Model adequacy and performance were evaluated using several diagnostic parameters. In cases where significant main or interaction effects were identified, Tukey’s Honestly Significant Difference (HSD) test (at 95% confidence level) was employed for multiple pairwise comparisons to identify statistically distinct group means. Tukey’s test was selected due to its ability to control the family-wise Type I error rate across all comparisons.

Results and discussion

Optimization of encapsulation of L. brevis strain LSe incorporated with FOS in FOS/Ca-alginate beads

Experiment design

In general, in the present study, the production conditions of FOS/Ca-alginate beads, such as calcium chloride concentration, sodium alginate concentration, and FOS concentration, have a great effect on the growth rate after 24 h and the encapsulation efficiency (%) at the beginning and after 24 h of L. brevis strain LSe cells inside FOS/Ca-alginate beads. To determine the effects of independent variables, the design of the experiment was carried out according to Table 2 for dependent variables such as EE₀ (%), EE₂₄ (%), and OD₆₀₀,₂₄. In these tables, the actual and predicted responses of reduced cubic models are presented.

ANOVA for reduced cubic model and fit statistics

The results of ANOVA that determined the significance of the model are presented in Tables 3 and 4, and 5. For EE₀ (%), the Model F-value of 24.73 indicated that the model was statistically significant (Table 3), with only a 0.01% probability that the results occurred by random noise. Another test that was used to validate the models was the linear regression test. In this test, the regression coefficient (R²), the adjusted regression coefficient (Adj R²), and the predictive regression coefficient (Pred R²) were calculated and reported. As shown in Table 3, the R² value is 0.945, indicating how well the model can explain response variability. The Adj R² (0.750) and Pred R² (0.907) values are in reasonable agreement, as their difference is within the acceptable range of 0.20. Adequate precision, which evaluates the signal-to-noise ratio, is 17.911, well above the desirable threshold of 4. This indicates an adequate signal. Therefore, this model is appropriate for navigating the design space for response (Table 3). The final regression equation, expressed in terms of coded factors, is presented below:

Table 3.

The results of ANOVA and fit statistics for reduced cubic model of central composite design for optimizing of variables affecting the encapsulation of probiotic bacterium Lactobacillus brevis strain LSe and prebiotic saccharide, fructo-oligosaccharides (FOS), in calcium alginate beads

ANOVA
Response 1: EE₀ (%)
Source	Sum of Squares	df	Mean Square	F Value	p-value
Block	40.61	2	20.31
Model	138.44	7	19.78	24.73	< 0.0001	significant
X1	7.61	1	7.61	9.51	0.0116
X2	18	1	18	22.51	0.0008
X1 × 3	14.85	1	14.85	18.57	0.0015
X22	17.84	1	17.84	22.32	0.0008
X1 × 32	15.54	1	15.54	19.44	0.0013
X1 × 22	30.9	1	30.9	38.64	< 0.0001
X23	66.72	1	66.72	83.44	< 0.0001
Residual	8	10	0.7996
Lack of Fit	4.86	7	0.6937	0.6628	0.7062	not significant
Pure Error	3.14	3
Cor Total	187.05	19
Fit Statistics
Std. Dev.	0.8942		R²	0.945
Mean	79.89		Adjusted R²	0.907
C.V. %	1.12		Predicted R²	0.751
			Adeq Precision	17.912

Table 4.

The results of ANOVA and fit statistics for reduced cubic model of central composite design for optimizing of variables affecting the encapsulation of probiotic bacterium Lactobacillus brevis strain LSe and prebiotic saccharide, fructo-oligosaccharides (FOS), in calcium alginate beads

ANOVA
Response 2: EE₂₄ (%)
Source	Sum of Squares	df	Mean Square	F Value	p-value
Block	4.53	2	2.26
Model	36.96	9	4.11	317.85	< 0.0001	significant
X2	13.82	1	13.82	1069.79	< 0.0001
X3	0.8193	1	0.8193	63.41	< 0.0001
X1 × 2	1.44	1	1.44	111.85	< 0.0001
X1 × 3	1.62	1	1.62	125.39	< 0.0001
X2 × 3	1.45	1	1.45	111.85	< 0.0001
X12	10.63	1	10.63	823.13	< 0.0001
X22	10.11	1	10.11	782.67	< 0.0001
X1 × 2 × 3	1.6	1	1.6	123.97	< 0.0001
X1 × 22	0.5	1	0.5	38.7	0.0003
Residual	0.1034	8	0.0129
Lack of Fit	0.0484	5	0.0097	0.5275	0.7518	not significant
Pure Error	0.055	3	0.0183
Cor Total	41.59	19
Fit Statistics
Std. Dev.	0.1137		R²	0.997
Mean	98.24		Adjusted R²	0.994
C.V. %	0.1157		Predicted R²	0.981
			Adeq Precision	63.689

Table 5.

The results of ANOVA and fit statistics for reduced cubic model of central composite design for optimizing of variables affecting the encapsulation of probiotic bacterium Lactobacillus brevis strain LSe and prebiotic saccharide, fructo-oligosaccharides (FOS), in calcium alginate beads

ANOVA
Response 3: OD₆₀₀,₂₄
Source	Sum of Squares	df	Mean Square	F Value	p-value
Block	0.0581	2	0.029
Model	0.5366	5	0.1073	24.96	< 0.0001	significant
X2	0.2404	1	0.2404	55.91	< 0.0001
X3	0.1104	1	0.1104	25.69	0.0003
X2 × 3	0.1105	1	0.1105	25.69	0.0003
X12	0.0409	1	0.0409	9.52	0.0094
X12 × 3	0.0219	1	0.0219	5.09	0.0436
Residual	0.0516	12	0.0043
Lack of Fit	0.0413	9	0.0046	1.34	0.4498	not significant
Pure Error	0.0103	3	0.0034
Cor Total	0.6463	19
Fit Statistics
Std. Dev.	0.0656		R²	0.912
Mean	0.7885		Adjusted R²	0.876
C.V. %	8.32		Predicted R²	0.788
			Adeq Precision	14.676

EE₀ (%) = + 80.79–1.15 × ₁ − 1.76 × ₃ − 1.36 × ₁ × ₃ − 1.72 × ₂² + 2.15 × ₁² × ₃ + 3.03 × ₁ × ₂² + 1.89 × ₂³

where X₁, X₂, and X₃ represent sodium alginate concentration, FOS concentration, and calcium chloride concentration, respectively.

The F-value of 317.85 shows that our model is significant for EE₂₄ (%). The large F-value indicates that the probability of the results being due to random variation is only 0.01% (Table 4). The p-value for the presented model is < 0.0001, which is less than 0.05, and as a result, the model is significant. The R² value is 0.997, which shows that the statistical model can account for 99.72% of the variation. Pred R² of 0.981 is in reasonable agreement with Adj R² of 0.994; i.e., the difference is less than 0.2. The adequate precision of 63.6895 shows a sufficient signal. Thus, this model can be used to explore the design space (Table 4). The result of changes in encapsulation efficiency was calculated through the following equations:

EE₂₄ (%) = + 99.46 + 1.14 × ₂ − 0.2438 × ₃ − 0.4250 × ₁ × ₂ + 0.4500 × ₁ × ₃ + 0.4250 × ₂ × ₃ − 0.8372 × ₁² − 1.06 × ₂² − 0.7750 × ₁ × ₂ × ₃ + 0.2500 × ₁ × ₂²

where X₁, X₂, and X₃ represents sodium alginate concentration, FOS concentration and CaCl₂ concentration, respectively.

As shown in Table 5, for OD_600,24, which reflects the growth rate in the presence of FOS, the F-value of 24.96 shows that our model is significant (Table 5). The p-value for the reduced cubic model is less than 0.0500, indicating the presented model is significant. The R², Adj R^2, and Pred R² were 0.912, 0.875, and 0.788, respectively. Adeq Precision is equal to 14.676, which is more than 4 (Table 5). Final equation in terms of coded factors for OD_600,24 is assumed as below:

OD_600,24 = + 0.8256 + 0.1427 × ₂ + 0.1382 × ₃ − 0.1175 × ₂ × ₃ − 0.0519 × ₁² -0.0807 × ₁² × ₃.

where X₁, X₂, and X₃ represents sodium alginate concentration, FOS concentration and CaCl₂ concentration, respectively.

Diagnostics plots

The relationships between predicted and actual responses [EE₀ (%), EE₂₄ (%), and OD₆₀₀,₂₄] from the final reduced cubic models are illustrated in Figs. 1, 2 and 3. Panels (a) in each figure show predicted versus actual response values; the close alignment of data points along the 45° reference line indicates strong agreement between model predictions and experimental observations, with no systematic bias across the response range. Panels (b) display internally studentized residuals versus predicted values; the random scatter of residuals within the ± 3 range around zero confirms homoscedasticity and the absence of model misspecification. We also have evaluated additional diagnostics: normal probability plots of residuals (Supplementary Fig. S2a–c) confirms that residuals follow an approximately normal distribution (Shapiro–Wilk test, p > 0.05 for all three responses). Collectively, these diagnostics—presented in Figs. 1, 2 and 3 and Supplementary Fig. S2—support the validity of the reduced cubic models without evidence of overfitting or violation of regression assumptions.

Fig. 1.

Diagnostic plots by final reduced cubic model of central composite design for optimizing of variables affecting the EE₀ (%) of probiotic bacterium Lactobacillus brevis strain LSe and prebiotic, fructo-oligosaccharides (FOS), in calcium alginate beads: (a) Predicted encapsulation efficiency versus experimental encapsulation efficiency. (b) Studentized residuals vs. predicted response. Response surface plots: (c) The influence of sodium alginate concentrations and CaCl2 concentrations and their interaction on EE₀ (%), while keeping FOS concentration at medium level (center point = 1%). (d) The influence of alginate concentration, and FOS concentration and their interaction on the EE₀ (%), while keeping CaCl2 concentration at medium level (center point = 3%)

Fig. 3.

Diagnostic plots by final reduced cubic model of central composite design for optimizing of variables affecting the OD₆₀₀,₂₄ of probiotic bacterium Lactobacillus brevis strain LSe and prebiotic, fructo-oligosaccharides (FOS), in calcium alginate beads: (a) Predicted optical density versus experimental optical density. (b) Studentized residuals vs. predicted response. Response surface plots: (c) The influence of sodium alginate concentrations and CaCl2 concentrations and their interaction on OD₆₀₀,₂₄, while keeping FOS concentration at medium level (center point = 1%). (d) The influence of alginate concentration, and FOS concentration and their interaction on the OD₆₀₀,₂₄, while keeping CaCl2 concentration at medium level (center point = 3%)

Fig. 2.

Diagnostic plots by final reduced cubic model of central composite design for optimizing of variables affecting the EE₂₄ (%) of probiotic bacterium Lactobacillus brevis strain LSe and prebiotic, fructo-oligosaccharides (FOS), in calcium alginate beads: (a) Predicted encapsulation efficiency versus experimental encapsulation efficiency. (b) Studentized residuals vs. predicted response. Response surface plots: (c) The influence of sodium alginate concentrations and CaCl2 concentrations and their interaction on EE₂₄ (%), while keeping FOS concentration at medium level (center point = 1%). (d) The influence of alginate concentration, and FOS concentration and their interaction on the EE₂₄ (%), while keeping CaCl2 concentration at medium level (center point = 3%)

Model graphs

The interaction between the variables and responses EE₀ (%), EE₂₄ (%), and OD₆₀₀,₂₄ was explored by 3D surface plans (Figs. 1, 2 and 3). Figure 1c illustrates the interaction between alginate concentration, and FOS concentration on the EE₀ (%), while keeping CaCl₂ concentration at the medium level (center point = 3.0%). The maximum EE₀ (%) (82.8%) was demonstrated once the alginate concentration was at the high level (4.0%) and FOS concentration was also at the high level (2.0%). The EE₀ (%) was 75.4% at the low level of alginate concentration (2.0%) and in the absence of FOS (0%), when FOS was not applied for the preparation of beads. The impact of sodium alginate concentration and CaCl₂ concentration and their interaction on EE₀ (%), while keeping FOS concentration at the medium level (center point = 1.0) is exhibited in Fig. 1d. Once both the sodium alginate concentration and CaCl₂ concentration were at their low levels (2.0%, and 2.0%, respectively), the EE₀ (%) was 80.20%. However, the EE₀ (%) was 83.6% at the low level of alginate concentration (2.0%) and the high level of CaCl₂ concentration (4.0%). Figure 2c shows the interaction between alginate concentration and FOS concentration on the EE₂₄ (%), while keeping CaCl₂ concentration at the medium level (center point = 3.0%). The maximum EE₂₄ (%) (99.8%) was achieved at an alginate concentration of 2.9% and a FOS concentration of 1.6%. The EE₂₄ (%) was 95.8% at the low level of alginate concentration (2.0%) and in the absence of FOS (0%). The effect of sodium alginate concentration and CaCl₂ concentration and their interaction on EE₂₄ (%), while FOS concentration was maintained at the medium level (center point = 1.0%), is exhibited in Fig. 2d. Once the sodium alginate concentration and CaCl₂ concentration were at 2.7%, and 2.0%, respectively, the EE₂₄ (%) was 99.8%. However, the EE₂₄ (%) was 99.10% at the constant level of alginate concentration (2.70%) and the high level of CaCl₂ concentration (4.0%). Figure 3c displays the interaction between alginate concentration and FOS concentration on OD₆₀₀,₂₄, while keeping CaCl₂ concentration at a medium level (center point = 3.0%). The maximum OD₆₀₀,₂₄ (0.97) was shown when the alginate concentration was at the level of 3% and FOS concentration was at the high level (2.0%). The OD₆₀₀,₂₄ was 0.63 at the low level of alginate concentration (2.0%) and in the absence of FOS (0%). When FOS was not used for the preparation of beads, the OD₆₀₀,₂₄ was decreased. The effect of sodium alginate concentration and CaCl₂ concentration and their interaction on OD₆₀₀,₂₄, while keeping FOS concentration at the medium level (center point = 1.0%) is shown in Fig. 3d. When the sodium alginate concentration and CaCl₂ concentration were at 3.0%, and 4.0%, respectively, the OD₆₀₀,₂₄ was 0.96. However, the OD₆₀₀,₂₄ was 0.69 at the level of alginate concentration (3.00%) and the low level of CaCl₂ concentration (2.00%).

The optimum values for EE₀ (%) (84.7 ± 2.8%), EE₂₄ (%) (99.2 ± 1.2%), and OD₆₀₀,₂₄ (0.70 ± 0.10) of the prepared FOS/Ca-alginate beads were achieved when 3.0% (w/v) sodium alginate, 1.2% (w/v) FOS, and 2.0% (w/v) calcium chloride were used. These data were very close to the predicted values (82.5 ± 6.4%, 99.8 ± 0.8%, and 0.74 ± 0.40; respectively). The findings validated the model, demonstrating strong agreement between the experimental and predicted values and confirming its suitability for predictive purposes. These results were consistent with the results of Ng et al., [10], who microencapsulated Lactobacillus plantarum 299v incorporated with oligofructose in chitosan-coated alginate beads. They obtained the highest microencapsulation efficiency (93.0%) at 4.0% (w/v) FOS and 2.5% (w/v) CaCl₂. In the study conducted by Thinkohkaew et al., [13], the encapsulation efficiency (97.35%) and tolerance to simulated gastric fluid (7.13 log CFU/g) were obtained under the optimum conditions of 0.60% gellan gum, 1.61% CaCl₂, and a flow rate of 9.84 mL/min [13]. In another study, using a full-factorial experimental design, the optimal formulation of Lactobacillus casei-loaded whey protein-Ca-alginate microparticles was identified at alginate, CaCl₂, and whey protein concentrations of 2.5%, 3%, and 3% (w/w), respectively. This formulation resulted in high probiotic viability after 24 h under simulated in vivo gastrointestinal conditions [19].

Model validation and short-term storage stability

Following the validation methodology detailed in Sect.  2.5, the model’s predictive adequacy was assessed through three independent verification experiments conducted under optimal conditions. As presented in Table 6, the predicted and experimental values showed strong consistency, confirming the validity and reliability of the model for predicting the relationship between factors and responses.

Table 6.

Validation of the response surface model for the design factors under consideration

Response*	Predicted Value	Experimental Value (Mean ± SD)	RPE (%)	95% CI of Difference
EE₀ (%)	82.5 ± 6.4	84.7 ± 2.8	2.67	-1.2 to + 5.8
EE₂₄ (%)	99.8 ± 0.8	99.2 ± 1.2	0.60	-1.1 to + 0.3
OD₆₀₀,₂₄	0.74 ± 0.40	0.70 ± 0.10	5.41	-0.08 to + 0.02

* EE₀ (%): Encapsulation efficiency measured immediately after bead formation (t = 0 h); EE₂₄ (%): Encapsulation efficiency measured after 24 h of storage; OD₆₀₀,₂₄: Bacterial growth indicator measured after 24 h incubation in MRS broth

All RPE values were < 6%, and the 95% confidence intervals for the differences included zero, confirming no statistically significant deviation between predicted and observed values (p > 0.05, paired t-test). The optimization and validation framework employed in this study aligns with established practices in food and pharmaceutical process optimization. For instance, İnan-Çınkır et al., [20] applied a similar CCD-RSM approach to optimize zein nanofiber production, reporting model validation through confirmation experiments and error analysis. Likewise, İnan-Çınkır et al., [21] emphasized the critical role of defining variable constraints and multi-response desirability in extraction optimization—methodological considerations we have incorporated into our revised experimental design description. To contextualize our methodological approach and findings within the broader literature, a comparative summary of recent optimization-based microencapsulation studies is provided in Supplementary Table S1. This table highlights similarities and differences in experimental design, variable selection, validation strategies, and reported outcomes.

To further evaluate the practical applicability of the optimized formulation, a short-term storage stability study was conducted at 4 °C (refrigerated conditions typical for functional food distribution). The results, summarized in Table S2, demonstrate that encapsulated cells retained > 95% encapsulation efficiency and exhibited < 1 Log reduction in viability after 7 days of storage. These findings suggest acceptable short-term stability for the FOS/Ca-alginate system under cold-chain conditions. While comprehensive long-term stability profiling under varied temperature/humidity conditions and accelerated stability testing remain essential for commercial translation, these preliminary data support the formulation’s robustness for near-term functional food applications.

Visual assessment

FOS/Ca-alginate beads were assessed visually in terms of size and shape. As shown in Fig. 4, the beads exhibited a diameter of approximately 3–4 mm and were generally uniform and spherical. This size range is consistent with extrusion-based alginate encapsulation systems reported in the literature [5], where bead dimensions are influenced by needle gauge, polymer viscosity, and cross-linking kinetics. The observed sphericity suggests homogeneous gelation and adequate cross-linking, which are essential for consistent encapsulation performance [11]. While the observed bead diameter (3.4 ± 0.5 mm) is consistent with extrusion-based alginate systems reported in research settings, we acknowledge that smaller beads (< 1 mm) may offer advantages for uniform dispersion in liquid matrices and improved sensory acceptance. Future work will explore process modifications—such as vibrational extrusion, reduced needle gauge, or emulsification techniques—to achieve sub-millimeter particles suitable for industrial translation. However, we acknowledge that visual assessment has limitations; future work will incorporate SEM imaging and laser diffraction analysis to provide quantitative data on surface morphology and particle size distribution.

Fig. 4.

Visual assessment of FOS/Ca-alginate beads

Probiotic properties of the L. brevis strain LSe cells encapsulated in FOS/Ca-alginate beads

The L. brevis strain LSe cells encapsulated in FOS/Ca-alginate beads and free bacterial cells were tested for the probiotic properties, and the results are presented in Fig. 5. The survival percentage of bacterial cells encapsulated in FOS/Ca-alginate beads at pH 6.0 and pH 2.0 was 97.1 ± 1.5% and 64.1 ± 1.8%, respectively, after 3 h of incubation. However, the survival percentage of free bacterial cells in these conditions was 98.2 ± 1.6% and 70.3 ± 1.4% respectively. Tolerance of L. brevis strain LSe cells and bacteria cells encapsulated in FOS/Ca-alginate beads in simulated gastric juice (SGJ) is shown in Fig. 6. As shown in Fig. 6, by incubating bacteria cells encapsulated in FOS/Ca-alginate beads at pH 2.0, the percentage of cell survival showed a significant reduction in comparison with pH 2.5 and pH 6.0 (p-value < 0.05). In addition, following 3 h-incubation, the survival percentage of bacteria cells encapsulated in FOS/Ca-alginate beads in pH 2.0, pH 2.5, and pH 6.0 were 55.7 ± 1.3%, 73.2 ± 0.9% and 77.3 ± 1.4%, respectively. At 2.0 pH, after 3 h of incubation, the survival percentage of L. brevis strain LSe cells and bacteria cells encapsulated in FOS/Ca-alginate beads were 60.1 ± 1.4% and 64.1 ± 1.8%, respectively.

Fig. 5.

Low-pH tolerance of Lactobacillus brevis strain LSe: free cells (control) versus cells encapsulated in FOS/Ca-alginate beads. Data are expressed as mean ± standard deviation (SD) of three independent experiments (n = 3). Statistical significance was determined by one-way ANOVA followed by Tukey’s HSD post-hoc test: **p < 0.001 and ***p < 0.0001 indicate significant differences between encapsulated and free cells at the same time point under identical pH conditions

Fig. 6.

Resistance patterns of Lactobacillus brevis strain LSe in simulated gastric juice (SGJ) at different pH levels: free cells (control) versus cells encapsulated in FOS/Ca-alginate beads at (a) pH 6.0, (b) pH 2.5, and (c) pH 2.0. Data are expressed as mean ± standard deviation (SD) of three independent experiments (n = 3). Statistical significance was determined by one-way ANOVA followed by Tukey’s HSD post-hoc test: **p < 0.001 and ***p < 0.0001 indicate significant differences between encapsulated and free cells at the same time point within each pH condition

Figure 7 shows the tolerance of bacterial cells encapsulated in FOS/Ca-alginate beads and free cells in simulated intestinal juice (SIJ). The survival percentages of both free bacterial cells and those encapsulated in FOS/Ca-alginate beads showed no significant difference between pH 6.0 and pH 8.0 (p-value > 0.05), indicating comparable viability under both conditions. After 24 h of incubation, the survival percentage of bacteria cells encapsulated in FOS/Ca-alginate beads at pH 6.0 and pH 8.0 was 59.9 ± 0.8% and 55.7 ± 1.2%, respectively (Fig. 7). However, in these conditions, the survival percentages of free cells were 62.1 ± 1.2% and 60.00 ± 0.80%, respectively.

Fig. 7.

Resistance patterns of Lactobacillus brevis strain LSe in simulated intestinal juice (SIJ) at different pH levels: free cells (control) versus cells encapsulated in FOS/Ca-alginate beads at (a) pH 6.0 and (b) pH 8.0. Data are expressed as mean ± standard deviation (SD) of three independent experiments (n = 3). Statistical significance was determined by one-way ANOVA followed by Tukey’s HSD post-hoc test: **p < 0.001 and ***p < 0.0001 indicate significant differences between encapsulated and free cells at the same time point within each pH condition

Figure 8 shows the growth capacity of L. brevis strain LSe cells, both encapsulated in FOS/Ca-alginate beads and in free form, under bile salt conditions. At 0.30% (w/v) Oxgall, the survival rate of both encapsulated and free bacterial cells did not significantly differ from that observed at 0.6% (w/v) Oxgall (p-value > 0.05). However, in the presence of 1.2% (w/v) Oxgall, the survival rate decreased after 24 h of incubation (p-value < 0.05). The survival rate after 24 h of incubation in the presence of 0.3, 0.6 and 1.2% of bile salts was 78.8 ± 0.8%, 79.2 ± 1.2% and 71.7 ± 0.8%, respectively (Fig. 8). While encapsulation maintained high initial viability and enhanced growth in culture medium, survival rates of encapsulated and free L. brevis LSe cells did not differ significantly under simulated gastric juice (SGJ), intestinal juice (SIJ), or bile salt conditions (p > 0.05). Several factors may explain this modest protective effect: (i) the inherent acid/bile tolerance of strain LSe, previously isolated from a fermented dairy product [15]; (ii) the porous nature of calcium alginate matrices, which may permit diffusion of gastric acids and bile salts to entrapped cells; and (iii) the relatively large bead size (3–4 mm), which may limit diffusion barrier effects compared to sub-millimeter particles. These findings underscore that encapsulation benefits are strain- and formulation-specific, and that high encapsulation efficiency does not automatically translate to enhanced GI protection. In similar study, da Conceição et al., [16] investigated the co-encapsulation of two Lactobacillus paracasei probiotic strains (LBC81 and ELBAL) with FOS in a calcium alginate matrix. The viability of microencapsulated cells increased when exposed to 2% biliary salts. Ng et al., [10] showed that microencapsulation with FOS can enhance the viability of probiotics in harsh conditions compared to those without FOS [10]. In fact, FOS and alginate can provide a better bead structure to enhance the survival of probiotics. Azam et al., [14] introduced the M₂ formulation (50% sodium alginate + 50% FOS) as the best encapsulation treatment for survival of Lactobacillus rhamnosus. Sathyabama and Vijayabharathi [12] also encapsulated two potential probiotic strains, Staphylococcus succinus (MAbB4) and Enterococcus fecium (FIdM3), with complementary prebiotics to assess viability in simulated gastric environment. At low pH values, no significant decrease in the viable count of encapsulated bacterial cells was detected. S. succinus demonstrated higher stability in sugar beet beads, achieving 95.5% survival at pH 2.0, compared to 93.3% survival in chicory beads under identical conditions. However, free bacterial cells showed only about 85% survival at pH 2.0. In the study conducted by Damodharan et al., [3], Microencapsulation with a combination of alginate, fenugreek gum, and locust bean gum enhanced the gastrointestinal viability of probiotic strains Pediococcus pentosaceus KID7, Lactobacillus plantarum KII2, Lactobacillus fermentum KLAB6, and Lactobacillus helveticus KII13. The encapsulated LAB strains KID7, KII2, KLAB6, and KII13 endured gastrointestinal stress, maintaining viabilities of 85.8%, 91.7%, 96.4%, and 87.2%, respectively. Parsana et al., [8] reported that the highest survival rate after exposure to SGJ and SIJ was observed in the alginate–inulin–chitosan group, followed by alginate-chitosan > alginate-inulin > alginate > free cells. Our results align with studies reporting variable GI protection from alginate encapsulation (e.g. [19]) , while contrasting with reports of significant protection using multi-layer coatings e.g., chitosan-alginate [8]. This highlights the importance of matrix engineering for specific probiotic strains and target applications. These findings suggest that prebiotics play a protective role for probiotics against the harsh gastrointestinal environment. In the study of Liao et al., [22] in which four oligosaccharides as co-encapsulating agents were used, they found that co-encapsulation improved encapsulation yield and enhanced the survival of Lactobacillus fermentum L7 under simulated gastric and intestinal conditions compared to alginate alone [22]. In general, the mixture of symbiotic (lactobacilli strains with prebiotics) and biopolymer (sodium alginate) can enhance the stability of encapsulated bacteria in harsh conditions [23, 24].

Fig. 8.

Bile salt tolerance of Lactobacillus brevis strain LSe: free cells (control) versus cells encapsulated in FOS/Ca-alginate beads at (a) 0.3%, (b) 0.6%, and (c) 1.2% (w/v) bile salt concentration. Data are expressed as mean ± standard deviation (SD) of three independent experiments (n = 3). Statistical significance was determined by one-way ANOVA followed by Tukey’s HSD post-hoc test: **p < 0.001 and ***p < 0.0001 indicate significant differences between encapsulated and free cells at the same time point within each bile salt concentration

Conclusion

This study successfully optimized the co-encapsulation of L. brevis strain LSe and fructo-oligosaccharides (FOS) in calcium alginate beads using a central composite design. The statistically determined optimal formulation (3.0% w/v sodium alginate, 1.2% w/v FOS, and 2.0% w/v CaCl₂) achieved high initial and 24-h encapsulation efficiencies (84.7% and 99.2%, respectively) and significantly enhanced bacterial proliferation compared to free cells. However, under simulated gastrointestinal conditions, the encapsulated cells exhibited survival rates comparable to their free counterparts, indicating that the current FOS/Ca-alginate matrix primarily supports initial viability and growth rather than conferring substantial additional stress tolerance. To further improve this symbiotic delivery system, future research should focus on: (i) exploring multi-layer coating strategies (e.g., chitosan, whey protein, or pectin) to reduce matrix permeability and enable targeted intestinal release; (ii) employing advanced physicochemical characterization techniques (e.g., SEM, FTIR, and in vitro release profiling) to elucidate polymer–prebiotic interactions and structural integrity; (iii) investigating strain pre-conditioning or the incorporation of complementary protectants (e.g., trehalose, skim milk powder) to enhance intrinsic acid and bile tolerance; (iv) scale-down of bead size through process engineering, as this represents a key next step for enhancing the applicability of this system in commercial functional food formulations; (v) routinely pairing OD₆₀₀ measurements with parallel CFU enumeration to strengthen the biological interpretation of growth enhancement data; and (vi) validating the optimized formulation through pilot-scale production and in vivo efficacy studies. Comprehensive shelf-life profiling under real-world conditions (temperature fluctuations, humidity, light exposure) remains an essential prerequisite for commercial translation. Addressing these aspects will bridge the gap between laboratory-scale optimization and the practical deployment of this symbiotic microencapsulation system in functional food and nutraceutical applications.

Abbreviations

Adj R²

Adjusted R-squared

ANOVA

Analysis of variance

CaCl₂

Calcium chloride

CCD

Central Composite Design

CFU

Colony-forming unit

EE₀

Encapsulation efficiency at time 0 (initial)

EE₂₄

Encapsulation efficiency after 24 h

FOS

Fructo-oligosaccharide

FTIR

Fourier-transform infrared spectroscopy

GI

Gastrointestinal

HCl

Hydrochloric acid

HSD

Tukey's Honestly Significant Difference

MRS

de Man, Rogosa and Sharpe broth

NaOH

Sodium hydroxide

NIMAD

National Institute for Medical Research Development

OD₆₀₀

Optical density at 600 nm

PBS

Phosphate-buffered saline

Pred R²

Predicted R-squared

Rpm

Revolutions per minute

RSM

Response Surface Methodology

SD

Standard deviation

SEM

Scanning Electron Microscopy

SGJ

Simulated gastric juice

SIJ

Simulated intestinal juice

UV

Ultraviolet

w/v

Weight/volume

Authors’ contributions

Sh. Abolhassanzadeh-Mahani and (A) Talebian : Data curation, Methodology, Software. M Shakibaie : Investigation, Software, Validation, Visualization. (B) Abadi : Investigation, Validation, Visualization. M. Adeli-Sardou: Data curation, Methodology. A. Ameri: Investigation, Validation, Visualization. A. Ameri and H. Forootanfar : Conceptualization, Project administration, Investigation, Visualization, Writing – original draft, Writing – review and editing.

Funding

This work was supported by Elite Researcher Grant Committee under Award number 4002265 from the National Institute for Medical Research Development (NIMAD), Tehran, Iran. This study was also financially supported by the Pharmaceutical Sciences and Cosmetic Products Research Center, Institute of Pharmaceutical Sciences, Kerman University of Medical Sciences, Kerman, Iran (Grant No. 400000824).

Data availability

The datasets and materials used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

The project was approved by the local ethical committee at National Institute for Medical Research Development (NIMAD) and the Pharmaceutical Sciences and Cosmetic Products Research Center, Institute of Pharmaceutical Sciences, Kerman University of Medical Sciences, Kerman, Iran.

Consent for publication

Not applicable (this study does not contain any individual person’s data, images, or identifying clinical/personal details).

Competing interests

The authors declare no competing interests.