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.

Highlights

  • Folding free energies of proteins at room temperature typically range in the order of a few tens of kilojoules per mol [1,2,3,4], which approximately corresponds to the interaction energy of just a few hydrogen bonds [5]

  • Cold denaturation has been attributed to a temperature-induced weakening of the hydrophobic effect [2], which arises from the thermodynamics of the solvation shell

  • We will first address the contribution of individual amino acids and the protein shape to the solvent free-energy contributions for a number of exemplary residues and subsequently provide a more systematic assessment

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Summary

Introduction

Folding free energies of proteins at room temperature typically range in the order of a few tens of kilojoules per mol [1,2,3,4], which approximately corresponds to the interaction energy of just a few hydrogen bonds [5] This small folding free energy results from a delicate balance between competing enthalpy and entropy contributions, each of which are much larger in magnitude but compensate each other almost entirely [2]. Proteins can unfold at low temperatures [2,6,7], the protein-internal interaction energies favor the folded state and the entropic protein free-energy contribution ÀTDS, which favors the unfolded state, should decrease in magnitude This effect, known as cold denaturation, seems paradoxical only if the protein, but not the solvent, contributions are considered for the free-energy difference estimation. The hydrophobic effect is known to be a major driving force for protein folding and stability [2,8,9,10]

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