## 3 Results and Discussion
### Evolution of VOC Profiles During Successive Kefir Grain Passages
In contrast, the coefficients for the quadratic term of the SR and for the interaction between the SR and PMKG were not statistically significant in any of the models. The coefficient for the quadratic term of the PMKG, however, was negative in all cases. Consequently, the optimal value for the SR was consistently at its minimum (25 rpm), while the optimal values for the PMKG fell within the tested experimental range (Tables S22-S24): 3.52%, 3.29%, and 3.20% for the first, second, and third kefir grain passages, respectively (Figure 2). At these optimal conditions, the maximum total volatile organic compound (TVOC) concentrations predicted by the models were 18.55, 17.70, and 27.22 mg/L for the first, second, and third passages, respectively. While shaking rates above 25 rpm may enhance mass transfer into the substrate, they can also promote the loss of volatile compounds from the fermented beverage to the surrounding air, thereby reducing their concentration in the final product. Moreover, excessive agitation may damage the kefir grains, negatively impacting their growth and metabolite production [11]. The observed increase in total VOC concentration with rising PMKG levels--up to the optimal point--could be attributed to a greater number of microbial cells introduced into the substrate [11]. In contrast, the decline in VOC concentrations beyond the optimal PMKG level may result from the increased competition among microbial cells for nutrients or from the production of inhibitory compounds [11], both of which can limit microbial growth and VOC synthesis. Given the complex microbiota of kefir grains--comprising various species from three major microbial groups (lactic acid bacteria [LAB], acetic acid bacteria [AAB], and yeasts)--and the intricate interactions among them, it is difficult to attribute the production of a specific volatile compound to a particular species or microbial group. Consequently, the effects of the two independent variables (SR and PMKG) on the total concentration of volatile compounds cannot be directly linked to their influence on the growth of LAB, AAB, or yeasts. For instance, [PERSON] et al. [11] reported that increasing the shaking rate above 25 rpm promoted the growth of AAB and yeasts and enhanced the total sugar consumption, while inhibiting LAB growth and differentially affecting the production of organic acids and alcohols. The large number of volatile organic compounds (VOCs) detected (82 in total) in the unfermented kiwifruit juice (UKJ) and the 27 fermented beverages produced across three kefir grain passages (Tables S1-S3) made it difficult to detect the similarities and differences among these drinks. For this reason, a principal component analysis (PCA) was performed to reduce the dimensionality of the dataset. The analysis identified 21 principal components with eigenvalues greater than 1.0, collectively explaining 95.73% of the total variance (Table S25). The 21 principal factor values obtained from this analysis were then used in a cluster analysis to identify the similarities and differences among the samples. As shown in Figure 3, a distinct subcluster of seven beverages emerged from the analysis of the 21 principal factor values used as classification variables. This subcluster initially grouped Bev7-24 h (SR = 86 rpm, PMKG = 4.68%, \(w/v\)) and Bev8-48 h (SR = 86 rpm, PMKG = 1.32%, \(w/v\)) at the smallest distance, indicating that these two beverages had the most similar volatile profiles. Notably, the kefir-like beverages Bev7-24 h and Bev8-48 h contained 25 (Table S1) and 24 (Table S2) volatile compounds, respectively, but at relatively low concentrations. Figure 2: Response surface plots generated from empirical models 1, 2, and 3, illustrating the effects of shaking rate (SR) and the proportion of milk kefir grains (PMKG) on the total concentration of volatile compounds ([TVOCs]) in 27 kefir-like beverages during the first, second, and third kefir grain (KG) passages.