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.

A morphometric approach for the accurate solvation thermodynamics of proteins and ligands.

We have developed a versatile method for calculating solvation thermodynamic quantities for molecules, starting from their atomic coordinates. The contribution of each atom to the thermodynamic quantities is estimated as a linear combination of four fundamental geometric measures of the atomic species, which are defined by Hadwiger's theorem, and the coefficients reflecting their solvation properties. This treatment enables us to calculate the solvation free energy with high accuracy despite of the limited computational load. The method can readily be applied to macromolecules in an all-atom molecular model, allowing the stability of these molecules' structures in solution to be evaluated.

Evaluation of protein-ligand binding free energy focused on its entropic components.

The binding free energy for FK506-binding protein-ligand systems is evaluated as a sum of two entropic components, the water-entropy gain, and the configurational-entropy loss for the protein and ligand molecules upon the binding. The two entropic components are calculated using morphometric thermodynamics combined with a statistical-mechanical theory for molecular liquids and the normal mode analysis, respectively. We find that there is an excellent correlation between the calculated and experimental values of the binding free energy. This result is compared with those of several other binding-free energy calculation methods, including MM-PB/SA. The binding can well be elucidated by competition of the two entropic components. Upon the protein-ligand binding, the total volume available to the translational displacement of the coexisting water molecules increases, leading to an increase in the number of accessible configurations of the water. The water-entropy gain, by which the binding is driven, originates primarily from this effect. This study sheds new light on the theoretical prediction of the protein-ligand binding free energy.

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.

Morphometric approach to thermodynamic quantities of solvation of complex molecules: extension to multicomponent solvent.

The morphometric approach (MA) is a powerful tool for calculating a solvation free energy (SFE) and related quantities of solvation thermodynamics of complex molecules. Here, we extend it to a solvent consisting of m components. In the integral equation theories, the SFE is expressed as the sum of m terms each of which comprises solute-component j correlation functions (j = 1,..., m). The MA is applied to each term in a formally separate manner: The term is expressed as a linear combination of the four geometric measures, excluded volume, solvent-accessible surface area, and integrated mean and Gaussian curvatures of the accessible surface, which are calculated for component j. The total number of the geometric measures or the coefficients in the linear combinations is 4m. The coefficients are determined in simple geometries, i.e., for spherical solutes with various diameters in the same multicomponent solvent. The SFE of the spherical solutes are calculated using the radial-symmetric integral equation theory. The extended version of the MA is illustrated for a protein modeled as a set of fused hard spheres immersed in a binary mixture of hard spheres. Several mixtures of different molecular-diameter ratios and compositions and 30 structures of the protein with a variety of radii of gyration are considered for the illustration purpose. The SFE calculated by the MA is compared with that by the direct application of the three-dimensional integral equation theory (3D-IET) to the protein. The deviations of the MA values from the 3D-IET values are less than 1.5%. The computation time required is over four orders of magnitude shorter than that in the 3D-IET. The MA thus developed is expected to be best suited to analyses concerning the effects of cosolvents such as urea on the structural stability of a protein.

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.

Free-energy function based on an all-atom model for proteins.

We have developed a free-energy function based on an all-atom model for proteins. It comprises two components, the hydration entropy (HE) and the total dehydration penalty (TDP). Upon a transition to a more compact structure, the number of accessible configurations arising from the translational displacement of water molecules in the system increases, leading to a water-entropy gain. To fully account for this effect, the HE is calculated using a statistical-mechanical theory applied to a molecular model for water. The TDP corresponds to the sum of the hydration energy and the protein intramolecular energy when a fully extended structure, which possesses the maximum number of hydrogen bonds with water molecules and no intramolecular hydrogen bonds, is chosen as the standard one. When a donor and an acceptor (e.g., N and O, respectively) are buried in the interior after the break of hydrogen bonds with water molecules, if they form an intramolecular hydrogen bond, no penalty is imposed. When a donor or an acceptor is buried with no intramolecular hydrogen bond formed, an energetic penalty is imposed. We examine all the donors and acceptors for backbone-backbone, backbone-side chain, and side chain-side chain intramolecular hydrogen bonds and calculate the TDP. Our free-energy function has been tested for three different decoy sets. It is better than any other physics-based or knowledge-based potential function in terms of the accuracy in discriminating the native fold from misfolded decoys and the achievement of high Z-scores.

Analysis of hepatic genes involved in the metabolism of fatty acids and iron in nonalcoholic fatty liver disease.

AIMS: Hepatic steatosis and iron cause oxidative stress, thereby progressing steatosis to steatohepatitis. We quantified the expression of genes involved in the metabolism of fatty acids and iron in patients with nonalcoholic fatty liver disease (NAFLD). METHODS: The levels of transcripts for the following genes were quantified from biopsy specimens of 74 patients with NAFLD: thioredoxin (Trx), fatty acid transport protein 5 (FATP5), sterol regulatory element-binding protein 1c (SREBP1c), fatty acid synthase (FASN), acetyl-coenzyme A carboxylase (ACAC), peroxisome proliferative activated receptor alpha (PPARalpha), cytochrome P-450 2E1 (CYP2E1), acyl-coenzyme A dehydrogenase (ACADM), acyl-coenzyme A oxidase (ACOX), microsomal triglyceride transfer protein (MTP), transferrin receptor 1 (TfR1), transferrin receptor 2 (TfR2) and hepcidin. Twelve samples of human liver RNA were used as controls. Histological evaluation followed the methods of Brunt. RESULTS: The levels of all genes were significantly higher in the NAFLD patients than in controls. The Trx level increased as the stage progressed. The levels of FATP5, SREBP1c, ACAC, PPARalpha, CYP2E1, ACADM and MTP significantly decreased as the stage and grade progressed (P < 0.05). Hepatic iron score (HIS) increased as the stage progressed. The TfR1 level significantly increased as the stage progressed (P < 0.05), whereas TfR2 level significantly decreased (P < 0.05). The ratio of hepcidin mRNA/ferritin (P < 0.001) or hepcidin mRNA/HIS (P < 0.01) was significantly lower in NASH patients than simple steatosis patients. CONCLUSIONS: Steatosis-related metabolism is attenuated as NAFLD progresses, whereas iron-related metabolism is exacerbated. Appropriate therapies should be considered on the basis of metabolic changes.

Pressure effects on structures formed by entropically driven self-assembly: illustration for denaturation of proteins.

We propose a general framework of pressure effects on the structures formed by the self-assembly of solute molecules immersed in solvent. The integral equation theory combined with the morphometric approach is employed for a hard-body model system. Our picture is that protein folding and ordered association of proteins are driven by the solvent entropy: At low pressures, the structures almost minimizing the excluded volume (EV) generated for solvent particles are stabilized. Such structures appear to be even more stabilized at high pressures. However, it is experimentally known that the native structure of a protein is unfolded, and ordered aggregates such as amyloid fibrils and actin filaments are dissociated by applying high pressures. This initially puzzling result can also be elucidated in terms of the solvent entropy. A clue to the basic mechanism is in the phenomenon that, when a large hard-sphere solute is immersed in small hard spheres forming the solvent, the small hard spheres are enriched near the solute and this enrichment becomes greater as the pressure increases. We argue that "attraction" is entropically provided between the solute surface and solvent particles, and the attraction becomes higher with rising pressure. Due to this effect, at high pressures, the structures possessing the largest possible solvent-accessible surface area together with sufficiently small EV become more stable in terms of the solvent entropy. To illustrate this concept, we perform an analysis of pressure denaturation of three different proteins. It is shown that only the structures that have the characteristics described above exhibit interesting behavior. They first become more destabilized relative to the native structure as the pressure increases, but beyond a threshold pressure the relative instability begins to decrease and they eventually become more stable than the native structure.

In vivo interferon system assessed by 2'-5' oligoadenylate synthetase activity in chronic hepatitis C virus patients treated with pegylated interferon and ribavirin.

AIM: 2',5' oligoadenylate synthetase (2-5AS), an enzyme induced by interferon, is an accurate indicator of the antiviral effect of interferon. We measured it during pegylated interferon based therapies in patients with chronic hepatitis C virus (HCV) in order to determine the dynamics of antiviral status in vivo and the relationship between the response to exogenous interferon and the outcome of therapy. METHODS: A total of 160 patients with chronic HCV were treated with pegylated interferon alfa 2a or 2b or non-pegylated interferon, with or without ribavirin. Serum 2-5AS activity was measured by radioimmunoassay assay kits every 2 weeks. RESULTS: In 60 patients treated with pegylated interferon alfa 2a or 2b, 2-5AS levels increased to 7-40 times (average 235 pmol/dL) above the pretreatment levels (30 pmol/dL), which were significantly higher than the levels during non-pegylated interferon therapy. Ribavirin did not enhance 2-5AS levels. 2-5AS levels between sustained virological response (SVR) and non-SVR, including null responders to pegylated interferon plus ribavirin therapy were not significantly different. CONCLUSION: 2-5AS levels were significantly higher in patients treated with pegylated interferon than in those treated with non-pegylated interferon, suggesting that pegylated interferon is more potent at inducing interferon response genes resulting in an improved antiviral effect. Ribavirin did not appear to be related to interferon response gene induction.

Molecular mechanism of pressure denaturation of proteins.

We investigate the molecular mechanism of pressure denaturation of proteins using the angle-dependent integral equation theory combined with the multipole water model and the morphometric approach. We argue that the hydration entropy of a protein is the key quantity. It is verified that at an elevated pressure, a swelling structure--which has only moderately less compact than the native structure but has a much larger water-accessible surface area--turns more stable than the native structure in terms of the water entropy. The swelling structure is characterized by the penetration of water into the interior. The hydration entropy is decomposed into contributions from the translational and rotational restrictions for the molecular motions of water. Each contribution is further decomposed into the water-protein pair correlation component and the water-water-protein triplet and higher-order correlation components. The pair correlation component in the translational contribution is divided into two terms arising from the excluded volume and the water structure near the protein, respectively. It is found that pressure denaturation accompanies a loss of the translational and rotational entropies at the pair correlation level but a much larger gain of the translational entropy at the triplet and higher-order correlation levels. Although the translational and rotational motions of water molecules penetrating the protein interior and contacting the protein surface are constrained, the translational restriction for the water molecules well outside the protein is greatly reduced. The latter entropic gain dominates, leading to the denaturation.

Glycosaminoglycan Binding and Non-Endocytic Membrane Translocation of Cell-Permeable Octaarginine Monitored by Real-Time In-Cell NMR Spectroscopy.

Glycosaminoglycans (GAGs), which are covalently-linked membrane proteins at the cell surface have recently been suggested to involve in not only endocytic cellular uptake but also non-endocytic direct cell membrane translocation of arginine-rich cell-penetrating peptides (CPPs). However, in-situ comprehensive observation and the quantitative analysis of the direct membrane translocation processes are challenging, and the mechanism therefore remains still unresolved. In this work, real-time in-cell NMR spectroscopy was applied to investigate the direct membrane translocation of octaarginine (R8) into living cells. By introducing 4-trifluoromethyl-l-phenylalanine to the N terminus of R8, the non-endocytic membrane translocation of 19F-labeled R8 (19F-R8) into a human myeloid leukemia cell line was observed at 4 °C with a time resolution in the order of minutes. 19F NMR successfully detected real-time R8 translocation: the binding to anionic GAGs at the cell surface, followed by the penetration into the cell membrane, and the entry into cytosol across the membrane. The NMR concentration analysis enabled quantification of how much of R8 was staying in the respective translocation processes with time in situ. Taken together, our in-cell NMR results provide the physicochemical rationale for spontaneous penetration of CPPs in cell membranes.

Water based on a molecular model behaves like a hard-sphere solvent for a nonpolar solute when the reference interaction site model and related theories are employed.

For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy µ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko-Hirata (K-H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and µ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of µ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and µ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, µ from the DRISM theory becomes too high. It is interesting that µ, U, and S from the K-H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.

Free energy surfaces of beta-hairpin and alpha-helical peptides generated by replica exchange molecular dynamics with the AGBNP implicit solvent model.

We have studied the potential of mean force of two peptides, one known to adopt a beta-hairpin and the other an alpha-helical conformation in solution. These peptides are, respectively, residues 41-56 of the C-terminus (GEWTYDDATKTFTVTE) of the B1 domain of protein G and the 13 residue C-peptide (KETAAAKFERQHM) of ribonuclease A. Extensive canonical ensemble sampling has been performed using a parallel replica exchange method. The effective potential employed in this work consists of the OPLS all-atom force field (OPLS-AA) and an analytical generalized Born (AGB) implicit solvent model including a novel nonpolar solvation free energy estimator (NP). An additional dielectric screening parameter has been incorporated into the AGBNP model. In the case of the beta-hairpin, the nonpolar solvation free energy estimator provides the necessary effective interactions for the collapse of the hydrophobic core (W43, Y45, F52, and V54), which the more commonly used surface-area-dependent nonpolar model does not provide. For both the beta-hairpin and the alpha-helix, increased dielectric screening reduces the stability of incorrectly formed salt bridges, which tend to disrupt the formation of the hairpin and helix, respectively. The fraction of beta-hairpin and alpha-helix content we obtained using the AGBNP model agrees well with experimental results. The thermodynamic stability of the beta-hairpin from protein G and the alpha-helical C-peptide from ribonuclease A as modeled with the OPLS-AA/AGBNP effective potential reflects the balance between the nonpolar effective potential terms, which drive compaction, and the polar and hydrogen bonding terms, which promote secondary structure formation.

A scoring function based on solvation thermodynamics for protein structure prediction.

We predict protein structure using our recently developed free energy function for describing protein stability, which is focused on solvation thermodynamics. The function is combined with the current most reliable sampling methods, i.e., fragment assembly (FA) and comparative modeling (CM). The prediction is tested using 11 small proteins for which high-resolution crystal structures are available. For 8 of these proteins, sequence similarities are found in the database, and the prediction is performed with CM. Fairly accurate models with average Cα root mean square deviation (RMSD) ∼ 2.0 Å are successfully obtained for all cases. For the rest of the target proteins, we perform the prediction following FA protocols. For 2 cases, we obtain predicted models with an RMSD ∼ 3.0 Å as the best-scored structures. For the other case, the RMSD remains larger than 7 Å. For all the 11 target proteins, our scoring function identifies the experimentally determined native structure as the best structure. Starting from the predicted structure, replica exchange molecular dynamics is performed to further refine the structures. However, we are unable to improve its RMSD toward the experimental structure. The exhaustive sampling by coarse-grained normal mode analysis around the native structures reveals that our function has a linear correlation with RMSDs < 3.0 Å. These results suggest that the function is quite reliable for the protein structure prediction while the sampling method remains one of the major limiting factors in it. The aspects through which the methodology could further be improved are discussed.

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.

Steatosis and hepatic expression of genes regulating lipid metabolism in Japanese patients infected with hepatitis C virus.

PURPOSE: Steatosis is a histological finding associated with the progression of chronic hepatitis C. The aims of this study were to elucidate risk factors associated with steatosis and to evaluate the association between steatosis and hepatic expression of genes regulating lipid metabolism. METHODS: We analyzed 297 Japanese patients infected with hepatitis C virus and a subgroup of 100 patients who lack metabolic factors for steatosis. We determined intrahepatic mRNA levels of 18 genes regulating lipid metabolism in these 100 patients using real-time reverse transcription-polymerase chain reaction. Levels of peroxisome proliferator-activated receptor alpha and sterol regulatory element-binding protein 1 proteins were assessed by immunohistochemistry. RESULTS: Steatosis was present in 171 (57%) of 297 patients. The presence of steatosis was independently associated with a higher body mass index, higher levels of gamma-glutamyl transpeptidase and triglyceride, and a higher fibrosis stage. Steatosis was present in 43 (43%) of 100 patients lacking metabolic factors. Levels of mRNA and protein of peroxisome proliferator-activated receptor alpha, which regulates beta-oxidation of fatty acid, were lower in patients with steatosis than in patients without steatosis. CONCLUSIONS: These findings indicate that impaired degradation of lipid may contribute to the development of hepatitis C virus-related steatosis.

Theoretical analysis on changes in thermodynamic quantities upon protein folding: essential role of hydration.

The free energy change associated with the coil-to-native structural transition of protein G in aqueous solution is calculated by using the molecular theory of solvation, also known as the three-dimensional reference interaction site model theory, to uncover the molecular mechanism of protein folding. The free energy is decomposed into the protein intramolecular energy, the hydration energy, and the hydration entropy. The folding is accompanied with a large gain in the protein intramolecular energy. However, it is almost canceled by the correspondingly large loss in the hydration energy due to the dehydration, resulting in the total energy gain about an order of magnitude smaller than might occur in vacuum. The hydration entropy gain is found to be a substantial driving force in protein folding. It is comparable with or even larger than the total energy gain. The total energy gain coupled with the hydration entropy gain is capable of suppressing the conformational entropy loss in the folding. Based on careful analysis of the theoretical results, the authors present a challenging physical picture of protein folding where the overall folding process is driven by the water entropy effect.

The severity of ultrasonographic findings in nonalcoholic fatty liver disease reflects the metabolic syndrome and visceral fat accumulation.

BACKGROUND: Nonalcoholic fatty liver disease (NAFLD) is closely associated with the metabolic syndrome. AIM: We evaluated the association among the metabolic syndrome, visceral fat accumulation, and the severity of fatty liver with a new scoring system of ultrasonographic findings in apparently healthy Japanese adults. METHODS: Subjects consisted of 94 patients who received liver biopsy and 4,826 participants who were selected from the general population. Two hepatologists scored the ultrasonographic findings from 0 to 6 points. We calculated Cohen's kappa of within-observer reliability and between-observer reliability. We evaluated the predictive value of the score by the area under a conventional receiver operating characteristic curve (AUC). RESULTS: Within-observer reliability was 0.95 (95% CI 0.93-0.97, P<0.001) and between-observer reliability was 0.95 (95% CI 0.93-0.97, P<0.001). The AUC to diagnose NAFLD was 0.980. The sensitivity was 91.7% (95% CI 87.0-95.1, P<0.001) and the specificity was 100% (95% CI 95.4-100.0, P<0.001). The AUC to diagnose visceral obesity was 0.821. The sensitivity was 68.3% (95% CI 51.9-81.9, P=0.028) and the specificity was 95.1% (95% CI 86.3-99.0, P<0.001). Adjusted odds ratio of the score for the metabolic syndrome was 1.37 (95% CI 1.26-1.49, P<0.001). CONCLUSIONS: The scoring system with abdominal ultrasonography could provide accurate information about hepatic steatosis, visceral obesity, and the metabolic syndrome in apparently healthy people who do not consume alcohol.

Crucial importance of translational entropy of water in pressure denaturation of proteins.

We present statistical thermodynamics of pressure denaturation of proteins, in which the three-dimensional integral equation theory is employed. It is applied to a simple model system focusing on the translational entropy of the solvent. The partial molar volume governing the pressure dependence of the structural stability of a protein is expressed for each structure in terms of the excluded volume for the solvent molecules, the solvent-accessible surface area (ASA), and a parameter related to the solvent-density profile formed near the protein surface. It is argued that the entropic effect originating from the translational movement of water molecules plays critical roles in the pressure-induced denaturation. We also show that the exceptionally small size of water molecules among dense liquids in nature is crucial for pressure denaturation. An unfolded structure, which is only moderately less compact than the native structure but has much larger ASA, is shown to turn more stable than the native one at an elevated pressure. The water entropy for the native structure is higher than that for the unfolded structure in the low-pressure region, whereas the opposite is true in the high-pressure region. Such a structure is characterized by the cleft and/or swelling and the water penetration into the interior. In another solvent whose molecular size is 1.5 times larger than that of water, however, the inversion of the stability does not occur any longer. The random coil becomes relatively more destabilized with rising pressure, irrespective of the molecular size of the solvent. These theoretical predictions are in qualitatively good agreement with the experimental observations.