## 2 Results and Discussion
### Enzyme Kinetics Using RNase B  
To gain more quantitative insight into the mechanistic changes of the enzymatic deglycosylation upon immobilization, the kinetic parameters (V\({}_{\text{max}}\), K\({}_{\text{m}}\)) were estimated using linearized plotting techniques (Lineweaver-Burk and Hanes Woolf) to reduce the error of non-linear estimation (Figure 5). V\({}_{\text{max}}\), the maximum forward velocity of the reaction, decreased from 0.551 glycan/min to 0.076 glycan/min (Lineweaver Burk estimation) upon immobilization of Endo BI-1 as calculated on RNase B (Figure 6). The Michaelis constant (K\({}_{\text{m}}\), a measure of substrate affinity) also decreased upon immobilization from 2.27 mg/mL for the free enzyme to 0.299 mg/mL once Endo BI-1 was immobilized on the amino-activated methacrylate resin. The goodness-of-fit for the Lineweaver Burk linear model (R\({}^{2}\)) for free and immobilized enzyme was 0.89 and 0.96 respectively. Hanes Woolf linear estimation revealed similar trends (0.333 and 0.081 V\({}_{\text{max}}\) values, 1.17 and 0.345 K\({}_{\text{m}}\) values for free and immobilized enzymes, respectively) to Lineweaver Burk. Decreased V\({}_{\text{max}}\) is typical of enzyme immobilization [32; 36], wherein lower maximum velocity is likely due to limited access of the large, macromolecular substrate to the active site of the immobilized enzyme. The immobilized enzyme is on a molecular tether, and steric hindrances limit access to more occluded glycan sites on the substrate with respect to the three-dimensional structure. As a point of comparison, \(\beta\)-1.4-galactosidase, with a molecular weight of approximately 465 kDa in its tetrameric form, with lactose as substrate at 360 Da has an overall substrate/enzyme size ratio of 0.0008:1, whereas for RNase B and Endo BI-1, the substrate/enzyme size ratio is approximately 0.32:1. This suggests a more limited diffusion and increased steric challenge with respect to active site availability.  
Figure 4: Mean relative activity of free and immobilized enzyme at different (**a**) temperature and (**b**) pH values using RNase B. Error bars represent one standard deviation and means, within the same chart, followed by different letters (a, b, c, d, e, and f) are statistically different at \(p<0.05\).  
Increased apparent affinity accompanied by decreased Vmax is consistent with uncompetitive inhibition. Possible explanations of this phenomenon are the formation of a more stable enzyme-substrate complex between Endo BI-1 and RNase B upon immobilization, or simply deglycosylated RNase B may have difficulty diffusing away from immobilized Endo BI-1 upon interaction with the active site. Both stable enzyme-substrate complexes and diffusional challenges would increase apparent affinity and inhibit forward reaction progress and are documented phenomena [36; 37].  
Enzymes with diverse, macromolecular substrates may exhibit substrate-dependent kinetic behavior. For example, when Endo BI-1 was tested on different glycoproteins, Vmax and Km also varied. The Michaelis constants for RNase B, lactoferrin, and concentrated whey proteins were 0.25, 0.43, and 0.90 mg/mL respectively, potentially due to different sizes, purities, and physicochemical properties of the glycoproteins [20]. The overall increase in Km for Endo BI-1 in this study (0.33 vs. 025 mg/mL) is likely related to differences in reaction conditions and analytical methods used in both studies. While this study utilized MALDI-ToF MS to measure the hydrolytic efficiency of Endo BI-1, previous studies utilized a spectrophotometric phenol-sulfuric assay, wherein the diverse array of monosaccharides present in \(N\)-glycans from lactoferrin and other whey proteins could have yielded different responses.