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 molten-globule-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 free-energy 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^-1 due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 ± 84) kJ mol^-1. Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.

Figure 1

Ribbon-style visualization of Crambin in its native fold (A) and in a molten-globule-like conformation (B). Images were rendered using VMD (44). To see this figure in color, go online.

Figure 2

Spatially resolved hydration free-energy decomposition of Crambin in its native fold (A) and the molten-globule-like conformation (B) relative to bulk water, visualized on a representative two-dimensional slice through the center of the molecules. The total interaction energy ΔU (top row, left) is split into protein-solvent interactions ΔU_PS (top row, center), and solvent-solvent interactions ΔU_SS (top row, right). In a similar manner, the translational and rotational entropy contributions −TΔS (center rows) are split into the single-molecule entropy −TΔS₁ and multibody correlations −TΔS_≥2. The entropy contribution from the translation-rotation correlation is shown in the bottom left. The spatially resolved free-energy change (sum of the first column) is shown in the bottom right. All numerical values are given in kJ mol⁻¹, and important residues are marked by arrows. To see this figure in color, go online.

Figure 3

Changes in interaction energy (ΔU), entropy (−TΔS), and free energy (ΔF) of the water molecules around each residue of the eight replicas, relative to bulk water. The free-energy change and its energetic and entropic contributions are shown relative to the local convexity and relative to the amino acid hydrophobicity. Results for the native fold are shown in (A), and results for the molten-globule-like conformation are shown in (B). Charged amino acids are depicted as orange circles, and polar amino acids are shown in cyan. Apolar amino acids are colored gray. Pearson correlation coefficients are stated in the corners of each plot. To see this figure in color, go online.

Figure 4

Decomposition of the folding free energy (green) into enthalpy (red) and entropy terms (blue). Positive values favor the native fold, negative values favor the molten-globule-like conformation. Values in kJ mol⁻¹. Error bars denote errors of the mean of the 2 × 4 replicas. To see this figure in color, go online.