*4.6. Determination of Kinetic Parameters*

All kinetic studies were performed in 0.1 M sodium phosphate buffer, pH 7.0, at 20 ◦C. The Michaelis–Menthen constants, *K*<sup>m</sup> and *V*max, were determined from the coefficients of linear regression of the Lineweaver–Burk plot. The substrate concentrations (mM) were 3.24, 2.59, 1.62, 1.29, 0.81, 0.65, 0.40, and 0.32 for wild α-PsGal and 2.50, 2.0, 1.25, 1.0, 0.62, 0.50, 0.31, and 0.25 for the C494N mutant.

#### *4.7. Transglycosylation*

#### 4.7.1. Acceptor Specificity of Transglycosylation

For preliminary determination of acceptor specificity of transglycosylation, the synthesis reactions were performed at 20 ◦C for 24 h in a mixture (10 μL) containing 0.01 U of an enzyme, 10 mM of pNP-α-Gal or melibiose as the substrate, and 20 mM of glucose, galactose, fructose, fucose, or xylose as acceptor in 0.05 M sodium phosphate buffer (pH 7.0). The reaction was stopped by heating at 100 ◦C for 5 min and the reaction mixture was centrifuged at 14,000 rpm. Sugars were analyzed by TLC, mass spectrometry, and NMR spectroscopy methods.

#### 4.7.2. Transglycosylation Using Heavy-Oxygen Water (H2 18O)

An experiment using mass spectrometry and heavy-oxygen water was prepared similarly as described in Section 4.7.1. above; but the concentrations were significantly lowered. Seven identical reaction mixtures were created. Each mixture contained 1.4 mg melibiose, 10 μL enzyme (1 U), and 70 μL H2O18 (0.02 M sodium phosphate buffer, 0.05 M NaCl, pH 7.0). The mixtures were incubated for 1, 2, 4, 6, 8, 12, and 24 h. Each reaction mixture was dissolved in 1 mL methanol and introduced into the mass spectrometer. For ESIMS and ESIMS-MS experiments, direct injection was performed using a syringe pump (KD Scientific, Hollison City, MA, USA) at a flow rate 5 μL/min. For LC-ESIMS experiments, samples were further diluted 10 times in methanol.

#### 4.7.3. Identification of Transglycosylation Products

The recombinant α-PsGal or D451A and C494N mutants, in an aqueous solution of 0.05 M sodium phosphate buffer (pH 7.0), were added to the preweighed dry samples of substrates melibiose or pNP-α-Gal or their mixture and were incubated for a certain time (Table 3) at 20 ◦C or 8 ◦C. The standard units of activity (U) or milligrams enzyme added (mg), the incubation time (τ) and reaction temperature are shown in Table 2. The reaction was stopped by heating at 100 ◦C for 5 min. The samples were centrifuged to remove the denatured protein and dried on Refrigerated CentriVap Concentrater (Labconco, Kansas City, MO, USA). The qualitative composition of the hydrolysis and transglycosylation products were analyzed by TLC and MALDI-MS without their separation from the reaction mixtures. Identification of oligosaccharides in the mixture and their output was performed via NMR spectroscopy.

#### 4.7.4. Thin-Layer Chromatography Analysis

Mono- and oligosaccharide composition of the hydrolysis and transglycosylation products were analyzed on silica gel TLC plates on aluminum foil (Sigma-Aldrich, St. Louis, MO, USA) with a 254 nm fluorescent indicator. The pore diameter was 60 A. Rf was calculated for every stain.

Weighed freeze-dried reaction product mixtures were placed in 0.5 mL Eppendorf, dissolved in distilled water to a concentration of 5 mg/mL, and centrifuged at 10,000 rpm to remove the denatured protein. A small spot of the analyzed mixture and standard compounds were applied at the start line of the TLC plate and chromatographed over 30 minutes in a sealed chamber Latch-Lid ChromatoTank (General Glass Blowing Co. Inc., Richmond, CA, USA), containing 100 mL of the mobile phase butanol/acetic acid/water (3:1:1; *v*/*v*/*v*). For visualization of stains, the plate was treated three times with 5% sulfuric acid solution, drying by warm air after each spraying.

#### 4.7.5. Mass Spectrometry Analysis

The molecular weights of the oligosaccharide ions were recorded as sodium adducts [M + Na]<sup>+</sup> using MALDI time-of-flight mass spectrometer, Ultra Flex III (Bruker BioSpin GmbH, Rheinstetten/Karlsruhe, Germany) equipped with a smartbeam laser (355 nm, Bruker Daltonik GmbH, Bremen, Germany) in reflector mode at an accelerating voltage of 21 kV, using the saturated solution (acetonitrile-water, 1:1) of 2,5-dihydroxybenzoynoic acid as a matrix.

The composition of the oligosaccharide mixture after enzymatic transformation was performed using an Ultimate 3000 rapid separation liquid chromatography (RSLC) nano system (Dionex, Thermo Fisher Scientific, Waltham City, MA, USA) connected to a Bruker Impact II quadrupole time-of-flight (Q-TOF) mass spectrometer (Bruker Daltonics, Bremen, Germany). An Acclaim (Thermo Fisher Scientific, Waltham City, MA, USA) PepMap RSLC column (75 μm × 150 mm, C18, 2 μm, 100 A) was used for chromatographic separation. The mobile phases were 0.1% formic acid in H2O (eluent A) and 0.1% formic acid in acetonitrile (eluent B). The gradient program was: isocratic at 1% of eluent B from start to 5 min, from 1% to 10% eluent B from 5 to 10 min, from 10% to 95% eluent B from 10 to 11 min, and isocratic at 95% of eluent B to 15 min. After returning to the initial conditions, equilibration was achieved after 10 min. Chromatographic separation was performed at a 0.4 μL/min flow rate at 40 ◦C. Injection volume was 0.2 μL. The mass spectrometry detection was performed using CaptiveSpray (Bruker Daltonics, Bremen, Germany) ionization source at a capillary voltage of 1.3 kV. Collision induced dissociation (CID)-produced ion mass spectra were recorded in auto-MS/MS mode with collision energy 43 eV. The precursor ions were isolated with an isolation width of 1 mass unit.

The mass spectrometer was calibrated using the ESI-L Low Concentration Tuning Mix (Agilent Technologies, Santa Clara, CA, USA). The instrument was operated using the OTOFControl software (version 4.0, Bruker Daltonics, Bremen, Germany) and data were analyzed using Data Analysis software (version 4.3, Bruker Daltonics, Bremen, Germany).

#### 4.7.6. NMR Spectroscopy Analysis

The structure of disaccharides was characterized by NMR spectroscopy. Signals in the NMR spectra of sugars were assigned by two-dimensional correlated spectroscopy (H,H-COSY) and two-dimensional heteronuclear multiple bond correlation spectroscopy (HSQC) experiments. One-dimensional 1H-NMR and 13C-NMR, and two-dimensional H,H-COSY and HSQC spectra were recorded with a Bruker Avance III 500 HD (Bruker BioSpin GmbH, Rheinstetten/Karlsruhe, Germany) spectrometer in D2O at 50 ◦C with acetone as internal standard (δ = 31.45 and 2.20 ppm for 13C NMR and 1H NMR spectra, respectively). 1H NMR anomer signals of α-pNP-galactopyranose, β-galactopyranose, melibiose, and bigalactosides, as well as proton signals of the free 4-nitrophenol ring were analyzed and integrated by the standard software TopSpin 3.2.

The depth of the pNP-α-Gal conversion (HpNPαGal, %) was calculated by

$$\rm{H}\_{\rm pNPacGal} = \langle \rm{I}\_{\rm Cal} / (\rm{I}\_{\rm pNPacGal} + \rm{I}\_{\rm Cal2pNP} + \rm{I}\_{\rm Cal2}) \rangle \times 100 \tag{1}$$

where IGal is integrated intensities of all 1H signals of liberated Galα,β, IpNP<sup>α</sup>Gal is the integrated intensity of 1H proton signals in substrate pNP-α-Gal, and IGal2pNP and IGal2 are the integrated intensity of 1H proton signals in transglycosylation products.

The depth of melibiose conversion (HMel, %) was calculated by

$$\text{pH}\_{\text{Mel}} = (\text{I}\_{\text{Gal}} / \text{I}\_{\text{Mel}}) \times 100 \tag{2}$$

where IMel is the integrated intensities of signals 1H of initial mixture of melibiose.

Yield of oligosaccharides in the total reaction mixture (Y, %) was calculated by

$$\text{Y} = \left\{ \mathbf{I}\_{\text{product}} \;/\ \left( \mathbf{I}\_{\text{Call}} + \mathbf{I}\_{\text{Glc}} + \mathbf{I}\_{\text{Call2}} + \mathbf{I}\_{\text{Gal2pNP}} \right) \right\} \times 100 \tag{3}$$

where Iproduct is the integrated intensity of all 1H signals of a particular oligosaccharide.
