Spatially resolved free-energy contributions of native fold and molten-globule-like Crambin

Abstract

The folding stability of a protein is governed by the free-energy difference between its folded and unfolded states, which results from a delicate balance of much larger but almost compensating enthalpic and entropic contributions. The balance can therefore easily be shifted by an external disturbance, such as a mutation of a single amino acid or a change of temperature, in which case the protein unfolds. Effects such as cold denaturation, in which a protein unfolds because of cooling, provide evidence that proteins are strongly stabilized by the solvent entropy contribution to the free-energy balance. However, the molecular mechanisms behind this solvent-driven stability, their quantitative contribution in relation to other free-energy contributions, and how the involved solvent thermodynamics is affected by individual amino acids are largely unclear. Therefore, we addressed these questions using atomistic molecular dynamics simulations of the small protein Crambin in its native fold and a moltenglobule-like conformation, which here served as a model for the unfolded state. The free-energy difference between these conformations was decomposed into enthalpic and entropic contributions from the protein and spatially resolved solvent contributions using the nonparametric method Per|Mut. From the spatial resolution, we quantified the local effects on the solvent freeenergy difference at each amino acid and identified dependencies of the local enthalpy and entropy on the protein curvature. We identified a strong stabilization of the native fold by almost 500 kJ mol À1 due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 5 84) kJ mol À1 . Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.

Spatially Resolved Hydration Thermodynamics in Biomolecular Systems

“…To obtain a complete free energy bill, Heinz and Grubmüller also analyzed the differences between native fold and molten-globule Crambin in the protein–protein interaction energy and protein conformational entropy, in addition to the solvent energies and entropies discussed above. The results ( Figure 7 ) demonstrate the tug of war between the different thermodynamic contributions, 41 which by themselves can be large but almost cancel each other, such that the total free energy of folding is relatively small (−53 kJ/mol in the present case). A striking observation is that the solvent entropy favors the native fold by as much as 498 kJ/mol.…”

“…The hydrophobicity of the individual amino acids is by itself not a very good predictor of the hydration entropy of the water in its surrounding, a result that was also found by others. 41 , 60 , 74 , 75 Thus, instead of single residues, one should think in terms of somewhat more extended protein surface patches or regions with a particular polarity and topology (concave/convex surfaces).…”

“…In a first application to a biomolecular system, Heinz and Grubmüller used Crambin as a case example for a small globular protein and studied the differential solvation of the folded state and an unfolded (molten-globule-like) state. 41 Figure 6 visualizes the spatially resolved decomposition of the hydration free energy of Crambin in the native fold (A) and a molten-globule-like conformation (B), which served as a model for the unfolded state. From the interaction energy perspective, Δ U = Δ U SW + Δ U WW of water near the protein surface is more negative than in bulk ( Figure 6 , first row), with particularly favorable interactions with charged and polar protein residues.…”

“…The translation–rotation two-water correlation is shown in the bottom row. The figure was adopted from ref ( 41 ), where it was published under the Creative Commons Attribution License (CC BY 4.0).…”

“…Positive values favor the native fold and negative values favor the unfolded state. The figure was taken from ref ( 41 ), where it was published under the Creative Commons Attribution License (CC BY 4.0).…”