Uncovering Differences in Hydration Free Energies for Model Compound Mimics of Charged Sidechains of Amino Acids

Free energies of hydration are fundamental quantities that are relevant for modeling and understanding sequence-specific conformational and phase equilibria of intrinsically disordered proteins (IDPs). Of particular importance are accurate values for the free energies of hydration of model compounds that mimic the charged sidechains of Arg, Lys, Asp, and Glu. Direct measurements of these quantities are challenging, and accordingly the values used to date rely on decompositions of measurements of whole salts. This has created considerable uncertainty regarding the desired quantities. Here, we adapt and deploy a Thermodynamic Cycle based Proton Dissociation in conjunction with published data from direct measurements along the relevant thermodynamic cycle to obtain new values for the free energies of hydration for model compounds that mimic the sidechains of Arg, Lys, Asp, and Glu. We obtain independent assessments for these inferred values using direct free energy calculations based on the polarizable AMOEBA forcefield and water model. The TCPD and AMOEBA derived values agree with one another. The new numbers suggest that Arg has the least favorable free energy of solvation, followed by Lys. On average, the sidechains of Asp and Glu have free energies of hydration that are ~1.8 times more favorable than Arg and ~1.5 times more favorable than Lys. Calculations used to extract the temperature dependence of free energies of hydration reveal positive heat capacities of hydration for Arg and Lys and negative heat capacities of hydration for Asp and Glu. We analyze the hydration structures around the different solutes to uncover a structural explanation for the observed differences in free energies of hydration. Although the sidechains of Arg and Lys are both amphiphilic, we find that the Arg sidechain has more of a hydrophobic character. In contrast, both Asp and Glu are hydrophilic both in terms of their solvation thermodynamics and hydration structure. Our results provide a physico-chemical explanation for recent accounts documenting the differences of Arg and Lys with respect to one another and with respect to Asp / Glu as determinants of conformational and phase equilibria of IDPs.