![]() Two peptides (Met-enkephalin and the C-peptide fragment consisting of the 1–13 residues of ribonuclease A) and two proteins (protein G and barnase) are treated and a number of different conformations are considered. ), an elaborate statistical-mechanical approach, which allows us to calculate the density structure of the solvent near a protein molecule in a prescribed conformation and its solvation free energy (SFE). For these reasons, the TE gain occurring in this particular system is expected to be quite substantial. The solvent in the biological system is water whose molecular size is exceptionally small. ![]() The geometric features of the side chains lead to a much larger overlapped volume than in the case of simple spheres (compare Fig. The gain in the TE of the solvent arising from the contact is dependent not on the absolute value of the overlapped volume but on the overlapped volume scaled by the size of the solvent molecules. The excluded volume for the solvent molecules and the overlapped volume are represented in the same manner as in Fig. 2 B, three side chains are considered to illustrate an example of intramolecular contacts. In our application, the small particles are from the solvent and the large particles correspond to protein subunits. We apply the concept to protein folding occurring in a dense solvent where the solvent molecules energetically move round. ![]() Besides the highly specific interactions of steric and chemical nature, this entropic effect is omnipresent in a biological system. ![]() Within the framework of the Asakura and Oosawa (AO) theory, the free-energy change is given as −(Δ V/ V S) η S k B T = −3( d L/ d S) η S k B T/2 (Īn important point of the concept described above is that the large particles are driven to contact each other for increasing the TE and decreasing the free energy of the small particles. We remark that the resultant free-energy change takes the same value in both of the isochoric and isobaric processes. The increase leads to a gain in the translational entropy (TE) of the small particles. When two large particles contact each other, the excluded volumes overlap (the overlapped volume is shadowed), and the total volume available to the translational movement of the small particles increases by this amount. The excluded volume is the spherical volume with diameter ( d L + d S) that is the sum of the volumes of the large particle and of the envelope colored in blue. The presence of a large particle generates the volume from which the centers of the small particles are excluded. In such a system, all allowed configurations have the same energy and the system behavior is purely entropic in origin. The small and large particles are hard spheres with diameter d S and those with diameter d L, respectively, and there are no soft interactions (e.g., van der Waals and electrostatic interactions) among the particles at all. Suppose that large particles are immersed in small particles and the number density of the small particles is much higher than that of the large particles. These results are true only when the solvent is water whose molecular size is the smallest among the ordinary liquids in nature. The translational movement of water molecules is quite effective in achieving the tight packing in the interior of a natural protein. A significant finding is that the largest TE is attained in the native structure. For protein G we have tested over 100 compact conformations generated by a computer simulation with the all-atom potentials as well as the native structure. ![]() It is shown that if the number of residues is sufficiently large, the TE gain is powerful enough to compete with the conformational-entropy loss upon folding. An elaborate statistical-mechanical theory is employed to analyze the TE of water in which a protein or peptide with a prescribed conformation is immersed. It is a gain in the translational entropy (TE) of water originating from the translational movement of water molecules. We show that even in the complete absence of potential energies among the atoms in a protein-aqueous solution system, there is a physical factor that favors the folded state of the protein. ![]()
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