## 4 Conclusions  
The immobilization of ASNase onto pristine and f-MWCNTs with different size diameters proved to affect the properties of the ASNase bioconjugate. The hydrothermal treatment with nitric acid promoted a higher specific surface area of the material due to \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**MWCNT**} & \multicolumn{2}{c}{**f-MWCNT**} \\ \cline{2-5}  & **Free ASNase** & **Im immobilized** & **Free ASNase** & **Im immobilized** \\  & **(0.3 mg/mL)** & **ASNase** & **(0.4 mg/mL)** & **ASNase** \\ \hline \(v_{max}\) (mM min\({}^{-1}\)) & 0.044 & 0.017 & 0.043 & 0.010 \\ \(S_{50}\) (mM) & 258.0 & 113.6 & 288.3 & 73.8 \\ \(h\) & 1.7 & 1.6 & 1.6 & 2.1 \\ \(k_{cat}/S_{50}\) (mM\({}^{-1}\) min\({}^{-1}\)) & 4.65 & 1.83 & 3.40 & 0.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Kinetic parameters for free and immobilized L-asparaginase (ASNase) onto pristine and functionalized multi-walled carbon nanotubes (f-MWCNTs). the creation of defect sites and holes on the sidewalls of the tubes, improving the support capacity to bind more enzyme particles and, consequently, to achieve higher enzyme \(RRA\). In turn, the best \(RRA\) results of adsorbed ASNase were obtained with f-MWCNTs-1020 and f-MWCNTs-2040, showing the importance of the nanomaterial diameter size for the enzyme binding. MWCNTs with diameters smaller than 10 nm showed to be too small for total enzyme binding, even presenting larger specific surface areas. MWCNTs with diameters larger than 40 nm revealed lower ASNase activity after immobilization, probably due to the smaller surface areas and, consequently, fewer ASNase molecules adsorbed. The optimization of the immobilization conditions made it possible to attain \(RRA\) and \(IY\) values of 100 and 99%, respectively, when immobilizing 0.4 mg/mL of ASNase onto 2 mg of f-MWCNTs-1020 during 30 min of contact time, at pH 8. The calculation of the ASNase \(pl\) (5.2) together with the determination of the \(pH_{\text{PZC}}\) of the f-MWCNTs (3-4) showed that under the optimal conditions, the primary binding forces responsible for the ASNase adsorption onto f-MWCNTs are most likely \(\pi\)-\(\pi\), CH-\(\pi\) and hydrophobic interactions. Exceptional operational stability was achieved when immobilizing the ASNase onto f-MWCNTs, allowing its reuse for six reaction cycles with a retained activity of 74 \(\pm\) 2%, value 1.3 times higher than when immobilized onto pristine MWCNTs (57 \(\pm\) 8%). Determining the kinetic parameters for this allosteric enzyme also proved that the immobilization onto MWCNTs improved the ASNase affinity for the substrate, especially when using the functionalized materials. This work demonstrates the impact of MWCNTs diameter and surface functionalization on the binding of ASNase and biocompatibility of the bioconjugate, maximizing their potential application in the pharmaceutical, food or biosensing industries. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12178924/s1](https://www.mdpi.com/article/10.3390/app12178924/s1)]([https://www.mdpi.com/article/10.3390/app12178924/s1](https://www.mdpi.com/article/10.3390/app12178924/s1)), Figure S1. Effect of pH and diameter of multiwalled carbon nanotubes (MWCNTs) on the immobilization yield (\(IY\)). Immobilization of 0.086 mg/mL of L-asparaginase (ASNase) onto 2 mg of pristine (MWCNTs) and functionalized MWCNTs (f-MWCNTs) for 60 min of contact time. Error bars correspond to the standard deviation between replicates. Figure S2. Effect of immobilization time and diameter of multi-walled carbon nanotubes (MWCNTs) on the immobilization yield (\(IY\)). Immobilization of 0.086 mg/mL of L-asparaginase (ASNase) onto 2 mg of pristine (MWCNTs) and functionalized MWCNTs (f-MWCNTs) at pH 8. Error bars correspond to the standard deviation between replicates. R.O.C., J.G.P., L.S.T. and M.C.N. : methodology, investigation. R.O.C. and R.A.M.B. : writing--original draft. M.G.F., J.L.F., V.C.S.-E., A.P.M.T. and C.G.S.