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We propose a method to calculate the size of the cooperatively rearranging region (CRR), NCRR, from the free energy landscape. In the free energy landscape picture, the particles in the CRR correspond to those involved in determinig the saddle point between two adjacent basins. By using this method, we estimate NCRR of the 3‐D random configuration of hard spheres. We also find that the system can transit to the adjacent basin via the lower height of the saddle point by the string motion.

We have recently proposed a novel picture of the rotation mechanism for F(1)-ATPase [T. Yoshidome, Y. Ito, M. Ikeguchi, and M. Kinoshita, J. Am. Chem. Soc. 133, 4030 (2011)]. In the picture, the asymmetric packing in F(1)-ATPase, originating from the water-entropy effect, plays the key role in the rotation. Here, we analyze the differences between the experimentally determined structures of yeast F(1)-ATPase before and after 16° rotation of the γ subunit with the emphasis on the water-entropy effect. For each of these structures, we calculate the hydration entropies of three sub-complexes comprising the γ subunit, one of the β subunits, and two α subunits adjacent to them. The β(E), β(TP), and β(DP) subunits are involved in sub-complexes I, II, and III, respectively. The calculation is performed using a hybrid of the angle-dependent integral equation theory combined with the molecular model for water and the morphometric approach. The absolute value of the hydration entropy is in the following order: sub-complex Isub-complex IIsub-complex III. The packing efficiency of the sub-complex follows the opposite order. The rotation gives rise to less efficient packing in sub-complex III and a corresponding water-entropy loss. However, the other two sub-complexes, accompanying water-entropy gains, become more efficiently packed. These results are consistent with our picture of the rotation mechanism, supporting its validity. The water-entropy analysis shows that the interfaces of α(DP)-β(DP) and α(E)-β(E) become more open after the rotation, which is in accord with the experimental observation.

Yeast frataxin is a protein exhibiting cold denaturation at an exceptionally high temperature (280 K). We show that the microscopic mechanism of cold denaturation, which has recently been suggested by us [Yoshidome and Kinoshita, Phys. Rev. E 79, 030905(R) (2009)], is also applicable to yeast frataxin. The hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach is employed for calculating hydration thermodynamic quantities of the protein with a prescribed structure. In order to investigate the characteristics of the cold-denatured structures of yeast frataxin, we consider the entropy change upon denaturation comprising the loss of the water entropy and the gain in the protein conformational entropy. The minimum and maximum values of the conformational-entropy gain (i.e., the range within which the exact value lies) are estimated via two routes. The range of the water-entropy loss is then determined from the entropy change experimentally obtained [Pastore et al., J. Am. Chem. Soc. 129, 5374 (2007)]. We calculate the water-entropy loss upon the transition from the native structure to a variety of unfolded structures. We then select the unfolded structures for which the water-entropy loss falls within the determined range. The selection is performed at cold and heat denaturation temperatures of yeast frataxin. The structures characterizing cold and heat denaturations are thus obtained. It is found that the average values of the radius of gyration, excluded volume, and water-accessible surface area for the cold-denatured structures are almost the same as those for the heat-denatured ones. We theoretically estimate the cold denaturation temperature of yeast frataxin from the experimental data for the enthalpy, entropy, and heat-capacity changes upon denaturation. The finding is that the temperature is considerably higher than 273 K. These results are in qualitatively good accord with the experimental observations.

The hydrophobic and hydrophilic hydrations are analyzed with the emphasis on the sign of the heat capacity of hydration (HCH). The angle-dependent integral equation theory combined with a multipolar water model is employed in the analysis. The hydration entropy (HE) is decomposed into the translational and orientational parts. It is found that the orientational part governs the temperature dependence of the HE. The orientational part is further decomposed into the solute-water pair correlation component (component 1) and the water reorganization component (component 2). For hydrophilic solutes, components 1 and 2 are negative and positive, respectively. As the temperature becomes higher, component 1 increases while component 2 decreases: They make positive and negative contributions to the HCH, respectively. The strong solute-water electrostatic attractive interactions induce the distortion of water structure near the solute and the break of hydrogen bonds. As the temperature increases, the effect of the attractive interactions becomes smaller and the distortion of water structure is reduced (i.e., more hydrogen bonds are recovered with increasing temperature). The latter effect dominates, leading to negative HCH. During the heat addition the formation of hydrogen bonds, which accompanies heat generation, occurs near the solute. Consequently, the addition of the same amount of heat leads to a larger increase in the thermal energy (or equivalently, in the temperature) than in the case of pure water. The hydrophobic hydration, which is opposite to the hydrophilic hydration in many respects, is also discussed in detail.

On the basis of the density functional theory, we give a clear definition of the free energy landscape. To show the usefulness of the definition, we construct the free energy landscape for rearrangement of atoms in an FCC crystal of hard spheres. In this description, the cooperatively rearranging region (CRR) is clealy related to the hard spheres involved in the saddle between two adjacent basins. A new concept of the simultaneously rearranging region (SRR) emerges naturally as spheres defined by the difference between two adjacent basins. We show that the SRR and the CRR can be determined explicitly from the free energylandscape., 11 pages, 3 figures, submitted to J. Chem. Phys