Four-dimensional imaging for cryo-electron microscopy experiments using molecular simulations and manifold learning.

Elucidating protein conformational changes is essential because conformational changes are closely related to the functions of proteins. Cryo-electron microscopy (cryo-EM) experiment can be used to reconstruct protein conformational changes via a method that involves using the experimental data (two-dimensional protein images). In this study, a reconstruction method, referred to as the "four-dimensional imaging," was proposed. In our four-dimensional imaging technique, the protein conformational change was obtained using the two-dimensional protein images (the three-dimensional electron density maps used in previously proposed techniques were not used). The protein conformation for each two-dimensional protein image was obtained using our original protocol with molecular dynamics simulations. Using a manifold-learning technique and two-dimensional protein images, the protein conformations were arranged according to the conformational change of the protein. By arranging the protein conformations according to the arrangement of the protein images, four-dimensional imaging is constructed. A simulation for a cryo-EM experiment demonstrated the validity of our four-dimensional imaging technique.

Elucidating Conformational Dynamics and Thermostability of Designed Aromatic Clusters by Using Protein Cages.

Multiple aromatic residues assemble to form higher ordered structures known as "aromatic clusters" in proteins and play essential roles in biological systems. However, the stabilization mechanism and dynamic behavior of aromatic clusters remain unclear. This study describes designed aromatic interactions confined within a protein cage to reveal how aromatic clusters affect protein stability. The crystal structures and calorimetric measurements indicate that the formation of inter-subunit phenylalanine clusters enhance the interhelix interactions and increase the melting temperature. Theoretical calculations suggest that this is caused by the transformation of the T-shaped geometry into π-π stacking at high temperatures, and the hydration entropic gain. Thus, the isolated nanoenvironment in a protein cage allows reconstruction and detailed analysis of multiple clustering residues for elucidating the mechanisms of various biomolecular interactions in nature which can be applied to design of bionanomaterials.

gr Predictor: A Deep Learning Model for Predicting the Hydration Structures around Proteins.

Among the factors affecting biological processes such as protein folding and ligand binding, hydration, which is represented by a three-dimensional water site distribution function around the protein, is crucial. The typical methods for computing the distribution functions, including molecular dynamics simulations and the three-dimensional reference interaction site model (3D-RISM) theory, require a long computation time ranging from hours to tens of hours. Here, we propose a deep learning (DL) model that rapidly estimates the distribution functions around proteins obtained using the 3D-RISM theory from the protein 3D structure. The distribution functions predicted using our DL model are in good agreement with those obtained using the 3D-RISM theory. Particularly, the coefficient of determination between the distribution function obtained by the DL model and that obtained using the 3D-RISM theory is approximately 0.98. Furthermore, using a graphics processing unit, the prediction by the DL model is completed in less than 1 min, more than 2 orders of magnitude faster than the calculation time of the 3D-RISM theory. The position of water molecules around the protein was estimated based on the distribution function obtained by our DL model, and the position of waters estimated by our DL model was in good agreement with that of water molecules estimated using the 3D-RISM theory and of crystallographic waters. Therefore, our DL model provides a practical and efficient way to calculate the three-dimensional water site distribution functions and to estimate the position of water molecules around the protein. The program called "gr Predictor" is available under the GNU General Public License from https://github.com/YoshidomeGroup-Hydration/gr-predictor.

A measure for the identification of preferred particle orientations in cryo-electron microscopy data: A simulation study.

Cryo-electron microscopy (cryo-EM) is an important experimental technique for the structural analysis of biomolecules that are difficult or impossible to crystallize. The three-dimensional structure of a biomolecule can be reconstructed using two-dimensional electron-density maps, which are experimentally sampled via the electron beam irradiation of vitreous ice in which the target biomolecules are embedded. One assumption required for this reconstruction is that the orientation of the biomolecules in the vitreous ice is isotropic. However, this is not always the case and two-dimensional electron-density maps are often sampled using preferred biomolecular orientations, which can make reconstruction difficult or impossible. Compensation for under-represented views is computationally feasible for the reconstruction of three-dimensional electron density maps, but one must know whether or not there is any missing information in the sampled two-dimensional electron density maps. Thus, a measure to identify whether a cryo-EM data is obtained from the bio-molecules adopting preferred orientations is required. In the present study, we propose a measure for which the geometry of manifold projected onto a low-dimensional space is used. To show the usefulness of the measure, we perform simulations for cryo-EM experiment of a protein. It is found that the geometry of manifold projected onto a two-dimensional space for a protein adopting a preferred biomolecular orientation is significantly different from that for a protein adopting a uniform orientation. This result suggests that the geometry of manifold projected onto a low-dimensional space can be used for the measure for the identification that the biomolecules adopt preferred orientations.

Comprehensive 3D-RISM analysis of the hydration of small molecule binding sites in ligand-free protein structures.

Hydration is a critical factor in the ligand binding process. Herein, to examine the hydration states of ligand binding sites, the three-dimensional distribution function for the water oxygen site, gO (r), is computed for 3,706 ligand-free protein structures based on the corresponding small molecule-protein complexes using the 3D-RISM theory. For crystallographic waters (CWs) close to the ligand, gO (r) reveals that several CWs are stabilized by interaction networks formed between the ligand, CW, and protein. Based on the gO (r) for the crystallographic binding pose of the ligand, hydrogen bond interactions are dominant in the highly hydrated regions while weak interactions such as CH-O are dominant in the moderately hydrated regions. The polar heteroatoms of the ligand occupy the highly hydrated and moderately hydrated regions in the crystallographic (correct) and wrongly docked (incorrect) poses, respectively. Thus, the gO (r) of polar heteroatoms may be used to distinguish the correct binding poses.

Growth of Cuprous Oxide Particles in Liquid-Phase Synthesis Investigated by X-ray Laser Diffraction.

Cuprous oxide (Cu2O) particles obtained by surfactant-assisted liquid-phase synthesis have cuboid shapes but the internal structures are difficult to be visualized by electron microscopy. Herein, we investigated the internal structures of numerous individual Cu2O particles with submicrometer dimensions by X-ray diffraction imaging (XDI) using X-ray free-electron laser (XFEL) pulses. The reconstructed two-dimensional electron density maps, which displayed inhomogeneous internal structures, were divided into five classes characterized by the positions and shapes of high and low electron density areas. Further analysis of the maps in each class by a manifold learning algorithm revealed that the internal structures of Cu2O particles varied in correlation with total electron density while retaining the characteristics within each class. On the basis of the analyses, we proposed a growth mechanism to yield the inhomogeneity in the internal structures of Cu2O particles in surfactant-mediated liquid-phase synthesis.

Computational Methods for Configurational Entropy Using Internal and Cartesian Coordinates.

The configurational entropy of solute molecules is a crucially important quantity to study various biophysical processes. Consequently, it is necessary to establish an efficient quantitative computational method to calculate configurational entropy as accurately as possible. In the present paper, we investigate the quantitative performance of the quasi-harmonic and related computational methods, including widely used methods implemented in popular molecular dynamics (MD) software packages, compared with the Clausius method, which is capable of accurately computing the change of the configurational entropy upon temperature change. Notably, we focused on the choice of the coordinate systems (i.e., internal or Cartesian coordinates). The Boltzmann-quasi-harmonic (BQH) method using internal coordinates outperformed all the six methods examined here. The introduction of improper torsions in the BQH method improves its performance, and anharmonicity of proper torsions in proteins is identified to be the origin of the superior performance of the BQH method. In contrast, widely used methods implemented in MD packages show rather poor performance. In addition, the enhanced sampling of replica-exchange MD simulations was found to be efficient for the convergent behavior of entropy calculations. Also in folding/unfolding transitions of a small protein, Chignolin, the BQH method was reasonably accurate. However, the independent term without the correlation term in the BQH method was most accurate for the folding entropy among the methods considered in this study, because the QH approximation of the correlation term in the BQH method was no longer valid for the divergent unfolded structures.

Classification of projection images of proteins with structural polymorphism by manifold: a simulation study for x-ray free-electron laser diffraction imaging.

Coherent x-ray diffraction imaging (CXDI) enables us to visualize noncrystalline sample particles with micrometer to submicrometer dimensions. Using x-ray free-electron laser (XFEL) sources, two-dimensional diffraction patterns are collected from fresh samples supplied to the irradiation area in the "diffraction-before-destruction" scheme. A recent significant increase in the intensity of the XFEL pulse is promising and will allow us to visualize the three-dimensional structures of proteins using XFEL-CXDI in the future. For the protocol proposed for molecular structure determination using future XFEL-CXDI [T. Oroguchi and M. Nakasako, Phys. Rev. E 87, 022712 (2013)10.1103/PhysRevE.87.022712], we require an algorithm that can classify the data in accordance with the structural polymorphism of proteins arising from their conformational dynamics. However, most of the algorithms proposed primarily require the numbers of conformational classes, and then the results are biased by the numbers. To improve this point, here we examine whether a method based on the manifold concept can classify simulated XFEL-CXDI data with respect to the structural polymorphism of a protein that predominantly adopts two states. After random sampling of the conformations of the two states and in-between states from the trajectories of molecular dynamics simulations, a diffraction pattern is calculated from each conformation. Classification was performed by using our custom-made program suite named enma, in which the diffusion map (DM) method developed based on the manifold concept was implemented. We successfully classify most of the projection electron density maps phase retrieved from diffraction patterns into each of the two states and in-between conformations without the knowledge of the number of conformational classes. We also examined the classification of the projection electron density maps of each of the three states with respect to the Euler angle. The present results suggest that the DM method is imperative for future applications of XFEL-CXDI experiments for proteins, and clarify issues to be taken care of in the future application.

An accurate and efficient computation method of the hydration free energy of a large, complex molecule.

The hydration free energy (HFE) is a crucially important physical quantity to discuss various chemical processes in aqueous solutions. Although an explicit-solvent computation with molecular dynamics (MD) simulations is a preferable treatment of the HFE, huge computational load has been inevitable for large, complex solutes like proteins. In the present paper, we propose an efficient computation method for the HFE. In our method, the HFE is computed as a sum of 〈UUV〉/2 (〈UUV〉 is the ensemble average of the sum of pair interaction energy between solute and water molecule) and the water reorganization term mainly reflecting the excluded volume effect. Since 〈UUV〉 can readily be computed through a MD of the system composed of solute and water, an efficient computation of the latter term leads to a reduction of computational load. We demonstrate that the water reorganization term can quantitatively be calculated using the morphometric approach (MA) which expresses the term as the linear combinations of the four geometric measures of a solute and the corresponding coefficients determined with the energy representation (ER) method. Since the MA enables us to finish the computation of the solvent reorganization term in less than 0.1 s once the coefficients are determined, the use of the MA enables us to provide an efficient computation of the HFE even for large, complex solutes. Through the applications, we find that our method has almost the same quantitative performance as the ER method with substantial reduction of the computational load.

Molecular dynamics simulations of yeast F1-ATPase before and after 16° rotation of the γ subunit.

We have recently proposed the "packing exchange mechanism" for F1-ATPase, wherein the perturbation by a substrate binding/release or an ATP hydrolysis is followed by the reorganization of the asymmetric packing structure of the α3ß3 complex, accompanying the γ subunit rotation. As part of a further investigation of this rotational mechanism, we performed all-atom molecular dynamics simulations for yeast F1-ATPase both before and after a 16° rotation of the γ subunit triggered by a Pi release. We analyzed the structural fluctuations, the subunit interface interactions, and the dynamics of the relative subunit arrangements before and after the rotation. We found that with the Pi release the αEßE subunit interface becomes looser, which also allosterically makes the αDPßDP subunit interface looser. This structural communication between these interfaces takes place through a tightening of the αTPßTP subunit interface. The γ subunit interacts less strongly with αDP and ßDP and more strongly with αTP and ßTP. After the Pi release, the tightly packed interfaces are reorganized from the interfaces around ßDP to those around ßTP, inducing the 16° rotation. These results, which are consistent with the packing exchange mechanism, allow us to deduce a view of the structural change during the 40° rotation.

Physical origin of hydrophobicity studied in terms of cold denaturation of proteins: comparison between water and simple fluids.

A clue to the physical origin of the hydrophobicity is in the experimental observations, which show that it is weakened at low temperatures. By considering a solvophobic model protein immersed in water and three species of simple solvents, we analyze the temperature dependence of the changes in free energy, energy, and entropy of the solvent upon protein unfolding. The angle-dependent and radial-symmetric integral equation theories and the morphometric approach are employed in the analysis. Each of the changes is decomposed into two terms, which depend on the excluded volume and on the area and curvature of the solvent-accessible surface, respectively. The excluded-volume term of the entropy change is further decomposed into two components representing the protein-solvent pair correlation and the protein-solvent-solvent triplet and higher-order correlation, respectively. We show that water crowding in the system becomes more serious upon protein unfolding but this effect becomes weaker as the temperature is lowered. If the hydrophobicity originated from the water structuring near a nonpolar solute, it would be strengthened upon lowering of the temperature. Among the three species of simple solvents, considerable weakening of the solvophobicity at low temperatures is observed only for the solvent where the particles interact through a strong attractive potential and the particle size is as small as that of water. Even in the case of this solvent, however, cold denaturation of a protein cannot be reproduced. It would be reproducible if the attractive potential was substantially enhanced, but such enhancement causes the appearance of the metastability limit for a single liquid phase.

Structural characteristics of yeast F1-ATPase before and after 16-degree rotation of the γ subunit: theoretical analysis focused on the water-entropy effect.

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 ß subunits, and two α subunits adjacent to them. The ß(E), ß(TP), and ß(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 I > sub-complex II > sub-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)-ß(DP) and α(E)-ß(E) become more open after the rotation, which is in accord with the experimental observation.

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

We show how to characterize the native-structure models of a protein using our free-energy function F which is based on hydration thermodynamics. Ubiquitin is adopted as an example protein. We consider models determined by the X-ray crystallography and two types of NMR model sets. A model set of type 1 comprises candidate models for a fixed native structure, and that of type 2 forms an ensemble of structures representing the structural variability of the native state. In general, the X-ray models give lower F than the NMR models. There is a trend that, as a model deviates more from the model with the lowest F among the X-ray models, its F becomes higher. Model sets of type 1 and those of type 2, respectively, exhibit two different characteristics with respect to the correlation between the deviation and F. It is argued that the total amount of constraints such as NOEs effectively taken into account in constructing the NMR models can be examined by analyzing the behavior of F. We investigate structural characteristics of the models in terms of the energetic and entropic components of F which are relevant to intramolecular hydrogen bonding and to backbone and side-chain packing, respectively.

Crucial importance of the water-entropy effect in predicting hot spots in protein-protein complexes.

"Hot spots" are residues accounting for the majority of the protein-protein binding free energy (BFE) despite that they comprise only a small fraction of the protein-protein interface. A hot spot can be found experimentally by measuring the BFE change upon mutating it to alanine: the mutation gives rise to a significantly large increase in the BFE. Theoretical prediction of hot spots is an enthusiastic subject in biophysics, biochemistry, and bioinformatics. For the development of a reliable prediction method, it is essential to understand the physical origin of hot spots. To this end, we calculate the water-entropy gains upon binding both for a wild-type complex and for its mutant complex using a hybrid method of the angle-dependent integral equation theory applied to a molecular model for water and the morphometric approach. We note that this type of calculation has never been employed in the previously reported methods. The BFE change due to alanine mutation is evaluated only from the change in the water-entropy gain with no parameters fitted to the experimental data. It is shown that the overall performance of predicting hot spots in our method is higher than that in Robetta, a standard free-energy-based method using fitting parameters, when the most widely used criterion for defining an actual hot spot is adopted. This result strongly suggests that the water-entropy effect we calculate is the key factor governing basic physics of hot spots.

Free-energy function for discriminating the native fold of a protein from misfolded decoys.

In this study, free-energy function (FEF) for discriminating the native fold of a protein from misfolded decoys was investigated. It is a physics-based function using an all-atom model, which comprises the hydration entropy (HE) and the total dehydration penalty (TDP). The HE is calculated using a hybrid of a statistical-mechanical theory applied to a molecular model for water and the morphometric approach. The energetic component is suitably taken into account in a simple manner as the TDP. On the basis of the results from a careful test of the FEF, which have been performed for 118 proteins in representative decoy sets, we show that its performance is distinctly superior to that of any other function. The FEF varies largely from model to model for the candidate models for the native structure (NS) obtained from nuclear magnetic resonance experiments, but we can find models or a model for which the FEF becomes lower than for any of the decoy structures. A decoy set is not suited to the test of a free-energy or potential function in cases where a protein isolated from a protein complex is considered and the structure in the complex is used as the model NS of the isolated protein without any change or where portions of the terminus sides of a protein are removed and the percentage of the secondary structures lost due to the removal is significantly high. As these findings are made possible, we can assume that our FEF precisely captures the features of the true NS.

Rotation mechanism of F1-ATPase: crucial importance of the water entropy effect.

We propose a novel picture of the rotation mechanism of F(1)-ATPase, a rotary-motor protein complex. Entropy, which originates from the translational displacement of water molecules, is treated as the key factor in the proposal. We calculate the water entropy gains upon formation of the α-ß, α-γ, and ß-γ subunit pairs. The gain is given as the difference between the hydration entropy of a subunit pair and the sum of the hydration entropies of the separate subunits forming the pair. The calculation is made using a hybrid of a statistical-mechanical theory for molecular liquids and morphometric approach. The water entropy gain is considered as a measure of tightness of the packing at each subunit interface. The results are highly correlated with the numbers of stable contacts at the subunit interfaces estimated by a molecular dynamics simulation. We also calculate the hydration entropies of three different subcomplexes comprising the γ subunit, one of the ß subunits, and two α subunits adjacent to them. The major finding is that the packing in F(1)-ATPase is highly asymmetrical, and this asymmetry is ascribed to the water entropy effect. We discuss how the rotation of the γ subunit is induced by such chemical processes as ATP binding, ATP hydrolysis, and release of the products. In our picture, the asymmetrical packing plays crucially important roles, and the rotation is driven by the water entropy effect.

Effects of heme on the thermal stability of mesophilic and thermophilic cytochromes c: comparison between experimental and theoretical results.

We have recently proposed a measure of the thermal stability of a protein: the water-entropy gain at 25 °C upon folding normalized by the number of residues, which is calculated using a hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach. A protein with a larger value of the measure is thermally more stable. Here we extend the study to analyses on the effects of heme on the thermal stability of four cytochromes c (PA c(551), PH c(552), HT c(552), and AA c(555)) whose denaturation temperatures are considerably different from one another despite that they share significantly high sequence homology and similar three-dimensional folds. The major conclusions are as follows. For all the four cytochromes c, the thermal stability is largely enhanced by the heme binding in terms of the water entropy. For the holo states, the measure is the largest for AA c(555). However, AA c(555) has the lowest packing efficiency of heme and the apo polypeptide with hololike structure, which is unfavorable for the water entropy. The highest stability of AA c(555) is ascribed primarily to the highest efficiency of side-chain packing of the apo polypeptide itself. We argue for all the four cytochromes c that due to covalent heme linkages, the number of accessible conformations of the denatured state is decreased by the steric hindrance of heme, and the conformational-entropy loss upon folding becomes smaller, leading to an enhancement of the thermal stability. As for the apo state modeled as the native structure whose heme is removed, AA c(555) has a much larger value of the measure than the other three. Overall, the theoretical results are quite consistent with the experimental observations (e.g., at 25 °C the α-helix content of the apo state of AA c(555) is almost equal to that of the holo state while almost all helices are collapsed in the apo states of PA c(551), PH c(552), and HT c(552)).

Importance of water entropy in rotation mechanism of F1-ATPase.

We briefly review our theoretical study on the rotation scheme of F1-ATPase. In the scheme, the key factor is the water entropy which has been shown to drive a variety of self-assembly processes in biological systems. We decompose the crystal structure of F1-ATPase into three sub-complexes each of which is composed of the γ subunit, one of the ß subunits, and two α subunits adjacent to them. The ßE, ßTP, and ßDP subunits are involved in the sub-complexes I, II, and III, respectively. We calculate the hydration entropy of each sub-complex using a hybrid of the integral equation theory for molecular liquids and the morphometric approach. It is found that the absolute value of the hydration entropy follows the order, sub-complex I > sub-complex II > sub-complex III. Moreover, the differences are quite large, which manifests highly asymmetrical packing of F1-ATPase. In our picture, this asymmetrical packing plays crucially important roles in the rotation of the γ subunit. We discuss how the rotation is induced by the water-entropy effect coupled with such chemical processes as ATP binding, ATP hydrolysis, and release of the products.

Entropic potential field formed for a linear-motor protein near a filament: Statistical-mechanical analyses using simple models.

We report a new progress in elucidating the mechanism of the unidirectional movement of a linear-motor protein (e.g., myosin) along a filament (e.g., F-actin). The basic concept emphasized here is that a potential field is entropically formed for the protein on the filament immersed in solvent due to the effect of the translational displacement of solvent molecules. The entropic potential field is strongly dependent on geometric features of the protein and the filament, their overall shapes as well as details of the polyatomic structures. The features and the corresponding field are judiciously adjusted by the binding of adenosine triphosphate (ATP) to the protein, hydrolysis of ATP into adenosine diphosphate (ADP)+Pi, and release of Pi and ADP. As the first step, we propose the following physical picture: The potential field formed along the filament for the protein without the binding of ATP or ADP+Pi to it is largely different from that for the protein with the binding, and the directed movement is realized by repeated switches from one of the fields to the other. To illustrate the picture, we analyze the spatial distribution of the entropic potential between a large solute and a large body using the three-dimensional integral equation theory. The solute is modeled as a large hard sphere. Two model filaments are considered as the body: model 1 is a set of one-dimensionally connected large hard spheres and model 2 is a double helical structure formed by two sets of connected large hard spheres. The solute and the filament are immersed in small hard spheres forming the solvent. The major findings are as follows. The solute is strongly confined within a narrow space in contact with the filament. Within the space there are locations with sharply deep local potential minima along the filament, and the distance between two adjacent locations is equal to the diameter of the large spheres constituting the filament. The potential minima form a ringlike domain in model 1 while they form a pointlike one in model 2. We then examine the effects of geometric features of the solute on the amplitudes and asymmetry of the entropic potential field acting on the solute along the filament. A large aspherical solute with a cleft near the solute-filament interface, which mimics the myosin motor domain, is considered in the examination. Thus, the two fields in our physical picture described above are qualitatively reproduced. The factors to be taken into account in further studies are also discussed.

Effects of side-chain packing on the formation of secondary structures in protein folding.

We have recently shown that protein folding is driven by the water-entropy gain. When the alpha-helix or beta-sheet is formed, the excluded volumes generated by the backbone and side chains overlap, leading to an increase in the total volume available to the translational displacement of water molecules. Primarily by this effect, the water entropy becomes higher. At the same time, the dehydration penalty (i.e., the break of hydrogen bonds with water molecules) is compensated by the formation of intramolecular hydrogen bonds. Hence, these secondary structures are very advantageous units, which are to be formed as much as possible in protein folding. The packing of side chains, which leads to a large increase in the water entropy, is also crucially important. Here we investigate the roles of the side-chain packing in the second structural preference in protein folding. For some proteins we calculate the hydration entropies of a number of structures including the native structure with or without side chains. A hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach is employed in the calculation. Our major findings are as follows. For the structures without side chains, there is an apparent tendency that the water entropy becomes higher as the alpha-helix or beta-sheet content increases. For the structures with side chains, however, a higher content of alpha-helices or beta-sheets does not necessarily lead to larger entropy of water due to the effect of the side-chain packing. The thorough, overall packing of side chains, which gives little space in the interior, is unique to the native structure. To accomplish such specific packing, the alpha-helix and beta-sheet contents are prudently adjusted in protein folding.