*Article* **The Melting Diagram of Protein Solutions and Its Thermodynamic Interpretation**

**Kálmán Tompa 1, Mónika Bokor <sup>1</sup> and Péter Tompa 2,3,\***


Received: 25 August 2018; Accepted: 30 October 2018; Published: 12 November 2018

**Abstract:** Here we present a novel method for the characterization of the hydration of protein solutions based on measuring and evaluating two-component wide-line 1H NMR signals. We also provide a description of key elements of the procedure conceived for the thermodynamic interpretation of such results. These interdependent experimental and theoretical treatments provide direct experimental insight into the potential energy surface of proteins. The utility of our approach is demonstrated through the examples of two proteins of distinct structural classes: the globular, structured ubiquitin; and the intrinsically disordered ERD10 (early response to dehydration 10). We provide a detailed analysis and interpretation of data recorded earlier by cooling and slowly warming the protein solutions through thermal equilibrium states. We introduce and use order parameters that can be thus derived to characterize the distribution of potential energy barriers inhibiting the movement of water molecules bound to the surface of the protein. Our results enable a quantitative description of the ratio of ordered and disordered parts of proteins, and of the energy relations of protein–water bonds in aqueous solutions of the proteins.

**Keywords:** protein; hydration; wide-line 1H NMR
