## 3 Results and Discussion
### Boronate Ester Formation  
The development of a system like the one here proposed requires knowledge of the binding affinity between boronic acid and diol moieties. To this scope, an analytical method based on UV-Vis spectroscopy was used. Alizarin Red S (ARS) was chosen as reporter model diol to study the MeO-PEG\({}_{2000}\)-PBA complexation according with the scheme reported below (Scheme 3). ARS shows a drastic shift of the spectral band at around 500 nm in response to the formation of a covalent reversible boronic ester. Since MeO-PEG-PBA lack a significant overlapping absorption in the 400-600 nm spectral region, the only absorbing species are free ARS and the ARS-boronic ester. The amount of complex formed ([AB]) can be expressed as a function of the constant of the equilibrium between ARS and MeO-PEG\({}_{2000}\)-PBA (\(K_{ars}\)) and of the initial concentrations of the reactants, \(C_{ars}\) and \(C_{PEG-PBA}\). The assay was conducted at two different pH: 7.4 and 10.0. Note that the absorption of ARS and ARS-boronic ester at pH 7.4 are almost overlapped (511 and 457 nm, respectively), and the increase in the complex appears as a shift of the absorption band (Figure 4a) instead of a balancing of two bands around an isosbestic point. Differently, at pH 10, the complex absorption maximum is shifted to 413 nm, thus revealing, upon the change of free ARS/ARS-boronic ester ratio, an isosbestic point at 451 nm (Figure 4c). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Polymer** & **a** **DD\({}_{\text{mol}}\)** & **b** **DD\({}_{\text{mol/wt}}\)** & **c** **Mw (Da)** & **c** **Mn (Da)** & **c** **D** & **d** **MnNMR (Da)** \\ \hline MeO-PEG\({}_{2000}\) & / & / & 2800 & 2700 & 1.03 & 2353 \\ MeO-PEG\({}_{2000}\)-PBAPin & 53.2 \(\pm\) 4.9 & 1.88 \(\times\) 10\({}^{-4}\) & 3000 & 2900 & 1.05 & 2918 \\ MeO-PEG\({}_{2000}\)-PBA & 56.2 \(\pm\) 3.2 & 1.68 \(\times\) 10\({}^{-2}\) & 3000 & 2900 & 1.05 & 2945 \\ PLA1–5k d & / & / & 2100 & 1000 & 2.00 & 871 \\ PLA5–10k d & / & / & 6800 & 5000 & 1.35 & 4226 \\ PLA-ALk1–5k & 72.1 \(\pm\) 0.2 & 1.91 \(\times\) 10\({}^{-4}\) & 2500 & 1700 & 1.47 & 3237 \\ PLA-ALk5–10k & 67.2 \(\pm\) 2.7 & 1.73 \(\times\) 10\({}^{-4}\) & 12,200 & 8100 & 1.51 & 5431 \\ PLA-Gal 1–5 kDa & 32.1 \(\pm\) 1.8 & 1.20 \(\times\) 10\({}^{-2}\) & **e**/ & **e**/ & **e**/ & 2457 \\ PLA-Gal 5–10 kDa & 28.3 \(\pm\) 0.6 & 1.01 \(\times\) 10\({}^{-2}\) & **e**/ & **e**/ & **e**/ & 3889 \\ \hline \hline \end{tabular}  
* Derivatization degree defined as the moles of functionalized chains%. b Derivatization degree defined as mmoles of functionalization moiety (PBAPin, PBA, alkine, or Gal) per 100 mg of product. c obtained by GPC in THF. d obtained by 1H NMR in DMSO-\(d_{6}\). e not soluble in under GPC conditions.  
\end{table} 
Table 1: Molecular characteristics of PEG and PLA derivatives object of this study and of their precursors: average degree of derivatization (DD\({}_{\text{mol}}\)% and DD\({}_{\text{mol/wt}}\)%), weight average molecular weight (Mw), number average molecular weight (Mn), and dispersity index (D) of polymeric materials used in this study. **Scheme 3. ** Competitive binding in three components assay to determine spectrophotometrically the binding constants of galactose with MeO-PEG-PBA. Kars: binding constant between Ars and MeO-PEG2000-PBA; Kexc: constant which governs the competitive equilibrium ARS/MeO-PEG2000-PBA + Gal Gal/MeO-PEG2000-PBA + ARS. The binding constant between Gal and MeO-PEG2000-PBA is calculated as the product of Kars and Kexc. In the insert, the molar extinction coefficients (c) for free and complexed ARS are reported at pH 7.4 and 10. Detailed information on the analytical methods used for the calculation of binding constants is reported in Supplementary material. Figure 4: The 200–600 nm spectral changes during competitive binding in three components assay at two different pH. **(a)** Absorption of ARS and ARS/PEG2000-PBA boronic ester at pH 7.4.