Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

Abstract

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.

Intramolecular Interactions Overcome Hydration to Drive the Collapse Transition of Gly15

“…Liquid water is both a good solvent for the hydration of the peptide unit 15,41 and also a poor solvent from the perspective of folding, as the hydration effects lose in comparison to intrapeptide interactions.…”

Importance of Hydrophilic Hydration and Intramolecular Interactions in the Thermodynamics of Helix–Coil Transition and Helix–Helix Assembly in a Deca-Alanine Peptide

“…The simulation approach closely followed previous work, 11 and for completeness the details of the implementation of the regularization approach are summarized in the Supporting Information (Sec. S.I).…”

“…2,3,11 In practice, we adjust the range λ such that P (ε|ϕ) is Gaussian. With the introduction of the field, we have 2,3,11 $$\beta {\mu }^{\text{ex}}=\underset{\text{local chemistry}}{\underset{true︸}{\text{ln }{x}_0[\varphi ]}}+\underset{\text{long}-\text{range}}{\underset{true︸}{\beta {\mu }^{\text{ex}}[P(\epsilon |\varphi )]}}-\underset{\text{G packing}}{\underset{true︸}{\text{ln }{p}_0[\varphi ]}}$$ where − k B T ln x 0 [ϕ(λ)] is the work done to apply the field in the presence of the solute, − k B T ln p 0 [ϕ(λ)] is the corresponding quantity in the absence of the solute, and βμ ex [ P (ε|ϕ)] is the contribution to the interaction free energy in the presence of the field. Figure 1 provides a schematic description of eq 1.…”

“…In eq 1 we follow G-packing to the hydrated solute; in eq 2 we follow SE-packing. Figure adapted from ref 11 with permission from Elsevier.…”

Conditional Solvation Thermodynamics of Isoleucine in Model Peptides and the Limitations of the Group-Transfer Model

“…16 In brief, ϕ λ is applied such that λ varies from 0 to 5 Å. For every unit angstrom, a five-point Gauss-Legendre quadrature rule defines the λ points sampled.…”