Characterization of experimentally determined native-structure models of a protein using energetic and entropic components of free-energy function

Structural stability of proteins in aqueous and nonpolar environments

A protein folds into its native structure with the α-helix and∕or β-sheet in aqueous solution under the physiological condition. The relative content of these secondary structures largely varies from protein to protein. However, such structural variability is not exhibited in nonaqueous environment. For example, there is a strong trend that alcohol induces a protein to form α-helices, and many of the membrane proteins within the lipid bilayer consists of α-helices. Here we investigate the structural stability of proteins in aqueous and nonpolar environments using our recently developed free-energy function F = (Λ - TS)∕(k(B)T(0)) = Λ∕(k(B)T(0)) - S∕k(B) (T(0) = 298 K and the absolute temperature T is set at T(0)) which is based on statistical thermodynamics. Λ∕(k(B)T(0)) and S∕k(B) are the energetic and entropic components, respectively, and k(B) is Boltzmann's constant. A smaller value of the positive quantity, -S, represents higher efficiency of the backbone and side-chain packing promoted by the entropic effect arising from the translational displacement of solvent molecules or the CH(2), CH(3), and CH groups which constitute nonpolar chains of lipid molecules. As for Λ, in aqueous solution, a transition to a more compact structure of a protein accompanies the break of protein-solvent hydrogen bonds: As the number of donors and acceptors buried without protein intramolecular hydrogen bonding increases, Λ becomes higher. In nonpolar solvent, lower Λ simply implies more intramolecular hydrogen bonds formed. We find the following. The α-helix and β-sheet are advantageous with respect to -S as well as Λ and to be formed as much as possible. In aqueous solution, the solvent-entropy effect on the structural stability is so strong that the close packing of side chains is dominantly important, and the α-helix and β-sheet contents are judiciously adjusted to accomplish it. In nonpolar solvent, the solvent-entropy effect is substantially weaker than in aqueous solution. Λ is crucial and the α-helix is more stable than the β-sheet in terms of Λ, which develops a tendency that α-helices are exclusively chosen. For a membrane protein, α-helices are stabilized as fundamental structural units for the same reason, but their arrangement is performed through the entropic effect mentioned above.

A new theoretical approach to biological self-assembly

Upon biological self-assembly, the number of accessible translational configurations of water in the system increases considerably, leading to a large gain in water entropy. It is important to calculate the solvation entropy of a biomolecule with a prescribed structure by accounting for the change in water-water correlations caused by solute insertion. Modeling water as a dielectric continuum is not capable of capturing the physical essence of the water entropy effect. As a reliable tool, we propose a hybrid of the angle-dependent integral equation theory combined with a multipolar water model and a morphometric approach. Using our methods wherein the water entropy effect is treated as the key factor, we can elucidate a variety of processes such as protein folding, cold, pressure, and heat denaturating of a protein, molecular recognition, ordered association of proteins such as amyloid fibril formation, and functioning of ATP-driven proteins.