## 2 Materials and Methods
### Baby-M-SHIME(r) Study  
The SHIME(r) model was initially described by [PERSON] et al. and was developed as an in vitro representation of the gastrointestinal tract of adult humans [17]. The model was later adapted to allow modeling of both the luminal and mucosal microbial communities (M-SHIME(r)) [22; 23]. The Baby-M-SHIME(r) model was adapted from an adult model as described in [PERSON] et al. [24] to represent the gastrointestinal tract of weaned infants [25]. Adapations included the use of medium to simulate both the intake of solid food and digested infant formula, and the use of optimized retention times and pH ranges to represent the infant gut (described in detail below). This study used the Baby-M-SHIME(r) model to assess the effects of the test product compared to an untreated control using the microbiota of four healthy 6-24-month-old babies. Therefore, two parallel Quad-Baby-M-SHIME(r) configurations were implemented, with each Quad-Baby-M-SHIME(r) assessing the effect of the test product versus the untreated control for two donors. Each arm of the Quad-Baby-M-SHIME(r) consisted of three reactors simulating the stomach/small intestine, proximal colon (PC), and distal colon (DC). The stomach/small intestine reactor operated using a fill-and-draw principle; peristalic pumps added a defined amount of nutritional medium (140 mL) to the stomach (pH 3) for an incubation time of 1.5 h after which pancreatic and bile liquid (60 mL, 2.5 g/L NaHCO\({}_{3}\), 0.9 g/L pancreatic, 4 g/L oxgall) were added for the small intestine simulation (pH 6; 1.5 h incubation). The intestinal suspension was then pumped to the PC (pH 5.8-6.0, volume 300 mL, retention time 12 h) and then the DC (pH 6.0-6.5, volume 500 mL, retention time 20 h); both were under constant stirring. A total retention time of 32 h was used in this study to mimic the short transit of the infant gastrointestinal tract. Each colonic reactor was inoculated with fecal microbiota (5% [\(v/v\)]) of 6-24-month-old babies (4 individual donors) and included a simulation of the mucosal environment by the inclusion of mucin-coated microcosms ([PERSON] et al. [22]). Medium simulating both the intake of solid food and digested infant formula was used and contained both carbohydrates and digested milk compounds (4 g/L mucin, 1 g/L yeast extract, 0.2 g/L cysteine, and approximately 10 g/L digested milk fragments (4.8 g/L lactose, 0.5 g/L casein, and 4.6 g/L lactalbumin)) as described by [PERSON] et al. [24]. Once initiated, the SHIME(r) cabinet and integrated software were run according to the manufacturer's instructions (ProDigest, Ghent, Belgium).  
The experimental timeline included a two-week stabilization period (d-14 to d0), allowing the fecal microbiota to differentiate into communities representative of each colon region; a subsequent two-week control period (d1 to d14), which provided reference values for the microbial community and composition in each of the colonic compartments; a 5-day antibiotic treatment period (d15 to d19); and a two-week follow-up period (d20 to d33). During the antibiotic treatment period, reactors were treated with 75 mg/day amoxicillin and clavulanic acid (2:1) administered in 3 doses of 25 mg each which corresponded with the reactor feeding schedule. During the follow-up period, the reactors were supplemented with 2 \(\times\) 10\({}^{9}\) CFU MegaSporeBiotic(tm) each day.