**4. Conclusions**

In this work, diffusion (Figures 1, 2 and 4), thermodynamic (Figure 5 and Table 2), and relaxation properties (Table 1 and Figure 3) of HA and Gd-DTPA mixtures have been presented and discussed.

Following the previous studies on the binding between drugs and GAGs [73] and similarly to what is shown about polyelectrolyte-protein interactions [81], our results suggest that the interaction between HA and Gd-DTPA is mainly mediated by the role played by the water and determined by two factors: (i) non-covalent processes (hydrogen bonding and electrostatic forces); (ii) conformational changes of the polymer. While the former is endothermic and characterized by negative enthalpy gain, the latter is exothermic and brings a positive entropy gain. Since they occur simultaneously, the overall interaction can be described as the combination of the two above-mentioned factors with one predominating on the others during the mixing. Indeed, both HA and Gd-DTPA have the capacity of forming hydrogen bonds and coordinate water molecules, which not only produces conformational changes but also affect the relaxometric properties of the contrast agent.

In conclusion, our results show a representative picture on GAGs interaction with MRI contrast agents and contribute to build a useful framework for the interpretation of their behavior in solution and for the understanding of the fundamental phenomena underlying the MRI relaxation enhancement. Moreover, we also expect that our results can be extended to other liner Gd-based contrast agents since they present analogous chemistry and relaxation mechanisms. Further potential applications extended also to macrocyclic Gd-based contrast agents could be explored in future works. This knowledge could provide insights into the fields of nanomedicine and precision medicine, where the proper choice

and combination of GAGs with imaging or therapeutic agents is the key factor for the formulation of effective targeted drug delivery systems.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2218-273X/10/12/1612/s1, Figure S1: Fitting of ITC data for Gd-DTPA titrated into 0.1%*w*/*v* HA, Table S1: Values of water self-diffusion coefficient at different DVS concentrations measured at 20 MHz after 8 h and 24 h from DVS addition, Table S2: Longitudinal relaxation times of the crosslinked and non-crosslinked samples without Gd-DTPA measured with Saturation and Inversion Recovery sequences, Table S3: Relaxivity of the crosslinked and non-crosslinked samples without Gd-DTPA measured with Saturation and Inversion Recovery sequences.

**Author Contributions:** Conceptualization, A.M.P. and E.T.; Methodology, A.M.P. and E.T.; Validation, A.M.P. and E.T.; Formal Analysis, A.M.P. and M.R.; Investigation, A.M.P. and M.R.; Resources, E.T.; Data Curation, A.M.P.; Writing-Original Draft Preparation, A.M.P.; Writing-Review & Editing, A.M.P., M.R. and E.T.; Visualization, A.M.P.; Supervision, E.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has been supported by the project "NANOPARTICLES BASED ON A THERANOSTIC APPROACH FOR THE DELIVERY OF A MICRORNA SET TO BE USED FOR BREAST AND THYROID CANCERS RESISTANT TO DRUGS" funded by the MIUR Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2017—grant 2017 MHJJ55.

**Conflicts of Interest:** The authors declare no conflict of interest.
