Animal Performance

All piglets were housed in individual pens with free access to feed and fresh potable water. They were kept in a 12 h light/12 h dark regimen with housing temperature maintained at 25 ◦C. Health monitoring of all piglets was performed daily. Individual performance of feed intake and body weight were measured weekly. At the end of the 28-day feeding period, final body weight and total feed intake were used to calculate feed conversion ratio for each dietary treatment.

Apparent Digestibility

Ten days before the end of the experiment, Cr2O3 was included in the diets (3 g/kg diet) as an ingestible marker for estimation of the apparent digestibility of TEs. After five days of adaptation, excreta samples were collected for five days and pooled from each animal and stored at −20 ◦C until freeze-drying. At the end of the feeding period, the piglets were stunned with an electric shock and exsanguinated, followed by the collection of the small intestinal content. pH values in the digesta of duodenum, jejunum, and ileum were measured using a digital pH meter. The collected digesta samples from the duodenum, the middle part of the jejunum, and ileum and pooled excreta samples were freeze-dried, ground, and stored until further analysis. Dry matter (DM) total apparent digestibility was estimated from collected pooled excreta samples. The apparent digestibility of TEs and DM was calculated using the following formula (1):

Apparent digestibility of TEs/DM, % = 100 − [(Cr2O3 in diet × TEs/DM in digesta and/or faeces)/(Cr2O3 in digesta and/or faeces × TEs/DM in diet) × 100]

> (1)

#### 2.1.2. Experiment In Situ

After slaughtering the piglets from each dietary treatment group (in vivo experiment), we collected the digesta from their duodenum, jejunum, and ileum to investigate the effects of Zn and fibre source on in situ solubility of Zn, Cu, Fe, and Mn in the small intestine. Measuring the solubility of these trace elements (TEs) from the digesta samples was done using the technique of centrifugation and a method based on Kleinman et al. [25]. Briefly, 0.5 g of digesta sample from each small intestinal segmen<sup>t</sup> was put into a bottle together with 25 mL ultra-pure water (EASYpure II UV/UF, Werner Reinst-wassersysteme, Leverkusen, Germany). Then, the samples were shaken at 180 rpm for 60 min. After centrifugation at 6000 rpm for 10 min, the supernatants were filtered through filter papers (Whatman 541), and the soluble content of TEs in the supernatants was analysed directly by atomic absorption spectrophotometry (AAS). The in situ soluble content of TEs was calculated according to the following Equation (2):

In situ soluble TEs, % = (soluble TEs in digesta supernatant/total TEs in the diet) × 100 (2)

### 2.1.3. Experiment In Vitro

#### In Vitro Solubility of Zn Sources

We estimated the effect of pH of buffers simulating the GIT environment on in vitro Zn solubility from both Zn supplements (zinc sulphate, zinc glycinate) at three concentrations 20, 100, and 150 mg Zn/L of buffer. Aliquot amounts of ZnSO4 and ZnGly were placed into bottles with magnetic stirring and dissolved in 0.2 M glycine-HCl buffer at pH 2.0 to simulate gastric digestion and in 0.2 M sodium acetate simulating pH in the small intestine at pH 4.5 and 6.5 [26]. The mixtures were incubated in a shaking bath at 39 ◦C for 4 h to simulate digestion, and filtered through 541 Whatman papers for Zn analysis using AAS. All incubations were done in duplicate, and in vitro solubility of ZnSO4 and ZnGly infiltrates was calculated according to Equation (3):

In vitro solubility of Zn source, % = (soluble Zn content/total Zn content) × 100 (3)

#### In Vitro Simulated Solubility of TEs

In vitro simulated solubility of Zn, Cu, Fe, and Mn from four experimental diets differing in Zn and fibre source (see detailed description of in vivo study, Table 1) were estimated using a three-step in vitro simulated digestion assay applying the method of Boisen and Fernández [27]. This assay procedure investigated the solubility of the trace elements in the simulated stomach, small and large intestine digestion.

From each experimental diet (Table 1), nine dried and ground sub-samples (500 ± 0.1 mg) were weighed into pre-weighed bottles, then 25 mL of 0.1 M phosphate buffer (pH 6.0) and 10 mL of 0.2 M HCl were added, and the mixture was stirred with a magnetic bar. To mimic the gastric phase (GP), the pH of the mixture was adjusted to pH 2.0 with 1 M HCl and 1 mL of freshly-prepared pepsin solution (25 mg of pepsin/mL; P7000, Sigma Aldrich, St. Louis, MO, USA). Then, 0.5 mL chloramphenicol (0.5 g/100 mL ethanol, C-0378, Sigma Aldrich, St. Louis, MO, USA) was added to the mixture before incubating at 39 ◦C for 60 min in a water bath with shaking (150 rpm).

After the gastric phase incubation, the bottles were taken out of the water bath, and to mimic the small intestinal phase (SIP), 10 mL of 0.2 M phosphate buffer (pH 6.8) and 5 mL of NaOH (0.6 M) were added to the mixture and magnetic stirring was resumed. After pH was adjusted to 6.8 (with 1 M HCl or 1 M NaOH), 1 mL of pancreatin solution (100 mg of pancreatin/mL; P1750, Sigma Aldrich, St. Louis, MO, USA) was added, and then closed bottles were incubated for 4 h at 39 ◦C in a water bath.

The small intestine phase incubation was followed by the last process of simulated digestion phase in the large intestine (LIP) with 10 mL EDTA (0.2 M) added and pH adjusted to 4.8 with 30% glacial acetic acid. The mixture was carefully stirred with 0.5 mL of Viscozyme multi-enzyme complex (Viscozyme L V2010, Sigma-Aldrich, St. Louis, MO, USA) to simulate microbial fermentation in the large intestine, and incubated at 39 ◦C for 18 h in a water bath with shaking.

During all incubation periods, the bottles were closed and mixtures were stirred slowly and constantly to simulate feed digestion. At the end of each simulated phase, the pH of the mixtures was measured and 2 mL of samples were collected for centrifuging at 4000× *g* for 20 min. The supernatants from each digestion phase were filtered through 0.22 μm filter membranes (Millex GS, Merck Millipore, Tullagreen, County Cork, Carrigtwohill, Ireland) and diluted with ultrapure water for subsequent analysis directly by means of AAS. The solubility of TEs in the filtrates was calculated according to the following Equation (4):

In vitro simulated solubility of TEs, % = (soluble TEs in the GP, SIP, LIP/total TEs in the diet) × 100, (4)

> TEs = trace elements, GP = gastric phase, SIP = small intestinal phase, LIP = large intestinal phase.

In Vitro Dry Matter Digestibility and pH

After the large intestinal phase, undigested residues from the incubated bottles were filtered in dried and pre-weighed glass filter crucibles containing Celite (Celite 545, Sigma Aldrich, St. Louis, MO, USA), then washed twice with 10 mL of 96% ethanol and 10 mL of 99.5% acetone, and the crucibles were finally oven-dried for 48 h at 105 ◦C. After cooling, the crucibles were weighed to estimate in vitro dry matter digestibility (IVDMD) calculated using the following Equation (5):

In vitro digestibility of DM, % = [DM in diet − (DM in residue - DM blank)] /DM in diet × 100 (5)

> At the end of each in vitro simulated phase, pH values in buffers with undigested residues were measured with the pH electrode of a digital pH meter.
