Solvation Entropy Research Articles

Structure–solubility and solvation energy relationships for propanol in different solvents using structural and empirical scales

AbstractResearch on the solubility ofn‐propanol in different solvents is important because of the wide applications ofn‐propanol in cosmetics, cleaning, printing, coatings, and chemical industries. The goal of this research was to investigate the structural or empirical properties of different solvents on the Ostwald solubility coefficient ofn‐propanol. In this research, two different approaches, that is, linear solvation energy relationship (LSER) and quantitative structure–property relationship (QSPR), have been used to predict and descript the gas‐solvent partition coefficient ofn‐propanol, as its solubility index, in 36 different solvents. In the suggested LSER model, the role of solvent–solute interactions on the solubility ofn‐propanol as a physicochemical property can be investigated. In addition to structural features, which were used in the QSPR model, the interpretation of the LSER model showed that the donor number of solvents, modified polarity scale of solvents, and entropy of solvation are three important parameters in the Ostwald solubility coefficient ofn‐propanol.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. II. Large Solvophovic Solutes.

We use molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy as a function of temperature and pressure for hard-sphere solutes with diameters ranging from 4 to 36 Å in TIP4P/2005 and Jagla water-like solvents exhibiting unusual thermodynamics. An important piece of our discussion focuses on the nanometer-sized solutes, for which simulation results are found to be accounted for by the most basic classical thermodynamic treatment contemplating bulk and interfacial contributions to the solvation free energy. Thus, since water's liquid-vapor surface tension is only special inasmuch as it takes unusually large values, solvent's water-like unusual thermodynamics manifests through a term proportional to the pressure in the solvation free energy. As a result, such solvent's unusual thermodynamics is found to be relevant to the temperature and pressure dependence of the isochoric solvation energy and entropy as well as to the isothermal density derivative of the solvation free energy. This sharply contrasts with the findings of the first part of this series indicating that the solvation free energy of small hard spheres responds to temperature and pressure changes as solvent's density does, with such a contrasting picture embodying a "pressure-density dichotomy." As for the length-scale dependence, we find the zero nominal pressure and the solvent's temperature of the maximum density as singular conditions for cavity surface-area size scaling of large solutes to occur for all solvation quantities. We finally argue that the overall study undertaken in this series suggests that water's unusual thermodynamics may be relevant to the thermodynamic stability of clusters of solvophobic units in the temperature-pressure plane. Some comments on the role of solute-solvent attractive interactions are also depicted.

Optimal Relabeling of Water Molecules and Single-Molecule Entropy Estimation

Estimation of solvent entropy from equilibrium molecular dynamics simulations is a long-standing problem in statistical mechanics. In recent years, methods that estimate entropy using k-th nearest neighbours (kNN) have been applied to internal degrees of freedom in biomolecular simulations, and for the rigorous computation of positional-orientational entropy of one and two molecules. The mutual information expansion (MIE) and the maximum information spanning tree (MIST) methods were proposed and used to deal with a large number of non-independent degrees of freedom, providing estimates or bounds on the global entropy, thus complementing the kNN method. The application of the combination of such methods to solvent molecules appears problematic because of the indistinguishability of molecules and of their symmetric parts. All indistiguishable molecules span the same global conformational volume, making application of MIE and MIST methods difficult. Here, we address the problem of indistinguishability by relabeling water molecules in such a way that each water molecule spans only a local region throughout the simulation. Then, we work out approximations and show how to compute the single-molecule entropy for the system of relabeled molecules. The results suggest that relabeling water molecules is promising for computation of solvation entropy.

Thermodynamic Analysis for Binding of 4-O-β-tri-N-acetylchitotriosyl Moranoline, a Transition State Analogue Inhibitor for Hen Egg White Lysozyme.

4-O-β-tri-N-acetylchitotriosyl moranoline (GN3M) is a transition-state analogue for hen egg white lysozyme (HEWL) and identified as the most potent inhibitor till date. Isothermal titration calorimetry experiments provided the thermodynamic parameters for binding of GN3M to HEWL and revealed that the binding is driven by a favorable enthalpy change (ΔH° = −11.0 kcal/mol) with an entropic penalty (−TΔS° = 2.6 kcal/mol), resulting in a free energy change (ΔG°) of −8.4 kcal/mol [Ogata et al. (2013) 288, 6,072–6,082]. Dissection of the entropic term showed that a favorable solvation entropy change (−TΔS solv° = −9.2 kcal/mol) is its sole contributor. The change in heat capacity (ΔC p°) for the binding of GN3M was determined to be −120.2 cal/K·mol. These results indicate that the bound water molecules play a crucial role in the tight interaction between GN3M and HEWL.

Spatially resolved free-energy contributions of native fold and molten-globule-like Crambin

The folding stability of a protein is governed by the free-energy difference between its folded and unfolded states, which results from a delicate balance of much larger but almost compensating enthalpic and entropic contributions. The balance can therefore easily be shifted by an external disturbance, such as a mutation of a single amino acid or a change of temperature, in which case the protein unfolds. Effects such as cold denaturation, in which a protein unfolds because of cooling, provide evidence that proteins are strongly stabilized by the solvent entropy contribution to the free-energy balance. However, the molecular mechanisms behind this solvent-driven stability, their quantitative contribution in relation to other free-energy contributions, and how the involved solvent thermodynamics is affected by individual amino acids are largely unclear. Therefore, we addressed these questions using atomistic molecular dynamics simulations of the small protein Crambin in its native fold and a molten-globule-like conformation, which here served as a model for the unfolded state. The free-energy difference between these conformations was decomposed into enthalpic and entropic contributions from the protein and spatially resolved solvent contributions using the nonparametric method Per|Mut. From the spatial resolution, we quantified the local effects on the solvent free-energy difference at each amino acid and identified dependencies of the local enthalpy and entropy on the protein curvature. We identified a strong stabilization of the native fold by almost 500 kJ mol−1 due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 ± 84) kJ mol−1. Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.

Mapping Water Thermodynamics on Drug Candidates via Molecular Building Blocks: a Strategy to Improve Ligand Design and Rationalize SAR.

The consideration of interactions involving water molecules in protein-ligand binding is widely appreciated in drug discovery nowadays. However, it is not ultimately clear how insights about these interactions translate into molecular design concepts. In this work, we introduce a computational strategy that, trained with high-precision experimental data, allows for the decomposition of water-related thermodynamic properties into chemically relevant building blocks (BBs) of a given ligand scaffold. For each of these BBs, a score based on solvation energy and entropy is computed, thus enabling the analysis of solvent-related affinity contributions for individual BBs. We find the nonvariable BB in a congeneric ligand pair to have a larger impact on the binding affinity than the variable part thus suggesting strong cooperative effects. Furthermore, we find enhanced solute-solvent interactions for a BB due to the presence of a C-F bond. Our investigation may be used to design drug molecules with tailored solvent thermodynamic properties.

Entropy-Entropy Compensation between the Protein, Ligand, and Solvent Degrees of Freedom Fine-Tunes Affinity in Ligand Binding to Galectin-3C.

Molecular recognition is fundamental to biological signaling. A central question is how individual interactions between molecular moieties affect the thermodynamics of ligand binding to proteins and how these effects might propagate beyond the immediate neighborhood of the binding site. Here, we investigate this question by introducing minor changes in ligand structure and characterizing the effects of these on ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and computational approaches including molecular dynamics (MD) simulations and grid inhomogeneous solvation theory (GIST). We studied a congeneric series of ligands with a fluorophenyl-triazole moiety, where the fluorine substituent varies between the ortho, meta, and para positions (denoted O, M, and P). The M and P ligands have similar affinities, whereas the O ligand has 3-fold lower affinity, reflecting differences in binding enthalpy and entropy. The results reveal surprising differences in conformational and solvation entropy among the three complexes. NMR backbone order parameters show that the O-bound protein has reduced conformational entropy compared to the M and P complexes. By contrast, the bound ligand is more flexible in the O complex, as determined by 19F NMR relaxation, ensemble-refined X-ray diffraction data, and MD simulations. Furthermore, GIST calculations indicate that the O-bound complex has less unfavorable solvation entropy compared to the other two complexes. Thus, the results indicate compensatory effects from ligand conformational entropy and water entropy, on the one hand, and protein conformational entropy, on the other hand. Taken together, these different contributions amount to entropy–entropy compensation among the system components involved in ligand binding to a target protein.

Per|Mut: Spatially Resolved Hydration Entropies from Atomistic Simulations.

The hydrophobic effect is essential for many biophysical phenomena and processes. It is governed by a fine-tuned balance between enthalpy and entropy contributions from the hydration shell. Whereas enthalpies can in principle be calculated from an atomistic simulation trajectory, calculating solvation entropies by sampling the extremely large configuration space is challenging and often impossible. Furthermore, to qualitatively understand how the balance is affected by individual side chains, chemical groups, or the protein topology, a local description of the hydration entropy is required. In this study, we present and assess the new method “Per|Mut”, which uses a permutation reduction to alleviate the sampling problem by a factor of N! and employs a mutual information expansion to the third order to obtain spatially resolved hydration entropies. We tested the method on an argon system, a series of solvated n-alkanes, and solvated octanol.

Analytical 2-Dimensional Model of Nonpolar and Ionic Solvation in Water.

A goal in computational chemistry is computing hydration free energies of nonpolar and charged solutes accurately, but with much greater computational speeds than in today's explicit-water simulations. Here, we take one step in that direction: a simple model of solvating waters that is analytical and thus essentially instantaneous to compute. Each water molecule is a 2-dimensional dipolar hydrogen-bonding disk that interacts around small circular solutes with different nonpolar and charge interactions. The model gives good qualitative agreement with experiments. As a function of the solute radius, it gives the solvation free energy, enthalpy and entropy as a function of temperature for the inert gas series Ne, Ar, Kr, and Xe. For anions and cations, it captures relatively well the trends versus ion radius. This approach should be readily generalizable to three dimensions.

Permut - Spatially Resolved Hydration Entropies from Atomistic Simulations

The thermodynamics of the first few surface water layers profoundly affects the overall free energy change in protein folding and unfolding, bilayer self-assembly, and ligand binding, and many other biomolecular processes. Whereas the enthalpy contribution can, in principle, be directly calculated from atomistic molecular dynamics simulations, the solvation shell entropy calculation suffers particularly from the poor sampling of the high dimensional configuration space. To furthermore understand, e.g., the effects of water molecules inside a binding pocket or the contribution of individual side chains to the hydration entropy, spatial resolution is required. To address these problems, we developed Per|Mut, a new method to calculate spatially resolved hydration entropies. In Per|Mut, we first employ a permutation reduction, which exploits the permutation symmetry of the identical water molecules to alleviate the sampling problem by the Gibbs factor N! without changing the physics. Next, we use a third-order mutual information expansion to obtain the hydration shell entropy. The spatial resolution and the decomposition into one- two- and three-body correlations of the translational and rotational entropies, as well as of the translation-rotation correlation, allows for an easy physical interpretation and characterization of the resolved entropy changes. In test-simulations, Per|Mut yielded accurate entropies for an argon gas test system and solvated alkanes. Applied to the solvation statistical mechanics of hydrated octanol and the protein Crambin, Per|Mut revealed the local effects of individual chemical groups or side chains on the solvation entropy.

In silico Design of Novel N-hydrosulfonylbenzamides inhibitors of dengue RNA-dependent RNA polymerase showing favorable predicted pharmacokinetic profiles

Background: In recent years, there has been a growing interest in Denv NS5 inhibition, with several reported RdRp inhibitors such as sulfonylbenzamides, non-nucleo-side inhibitors without any 3D-QSAR pharmacophore (PH4) available. In this context, we report here, in silico design and virtual evaluation of novel sulfonylbenzamides Denv RdRp inhibitors with favorable predicted pharmacokinetic profile. Methods: By using in situ modifications of the crystal structure of 5-(5-(3-hydroxyprop-1-yn-1-yl)thiophen-2-yl)-4- methoxy-2-methyl-N-(methylsulfonyl) benzamide (EHB)-RdRp complex (PDB entry 5HMZ), 3D models of RdRp-EHBx complexes were prepared for a training set of 18 EHBs with experimentally determined inhibitory potencies (half-maximal inhibitory concentrations IC50exp). In the search for active conformation of the EHB1-18, linear QSAR model was prepared, which correlated computed gas phase enthalpies of formation ∆∆HMM of RdRp-EHBx complexes with the IC50exp. Further, considering the solvent effect and entropy changes upon ligand binding resulted in a superior QSAR model correlating computed complexation Gibbs free energies (∆∆Gcom). The successive pharmacophore model (PH4) generated from the active conformations of EHBs served as a virtual screening tool of novel analogs included in a virtual combinatorial library (VCL) of compounds with scaffolds restricted to phenyl. The VCL filtered by the Lipinski’s rule-of-five was screened by the PH4 model to identify new EHB analogs. Results: Gas phase QSAR model: -log10(IC50exp) = p IC50exp =-0.1403 x ∆∆HMM _ 7.0879, R2 = 0.73; superior aqueous phase QSAR model: p IC50exp = -0.2036 x ∆∆Gcom + 7.4974, R2 = 0.81 and PH4 pharmacophore model: p IC50exp = 1.0001 x p IC50pre -0.0017, R2 = 0.97. The VCL of more than 30 million EHBs was filtered down to 125,915 analogs Lipinski’s rule. The five-point PH4 screening retained 329 new and potent EHBs with predicted inhibitory potencies p IC50pre up to 30 times lower than that of EHB1 (IC50exp = 23nM). Predicted pharmacokinetic profile of the new analogs showed enhanced cell membrane permeability and high human oral absorption compared to the alone drug to treat dengue virus. Conclusions: Combined use of QSAR models, which considered binding of the EHBs to RdRp, pharmacophore model and ADME properties helped to recognize bound active conformation of the sulfonylbenzamide inhibitors, permitted in silico screening of VCL of compounds sharing sulfonylbenzamide scaffold and identify new analogs with predicted high inhibitory potencies and favorable pharmacokinetic profiles. Keywords: ADME properties prediction, Dengue, 3-(5-ethynylthiophen-2-yl)-N-hydrosulfonylbenzamides, in silico screening, RNA-dependent RNA polymerase.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. I. Small Solvophobic Solutes.

We analyze the role of temperature, pressure, and solute's molecular size on the pattern of isochoric and isobaric solvation of small hard-sphere solutes in TIP4P/2005 water and in a water-like "Jagla" solvent exhibiting unusual thermodynamics. To this end, we employ molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy along isobaric and isothermal paths covering solvent's stable liquid and supercritical states as well as supercooled and "stretched" liquid states. Results are found to be consistent with the most primitive scaled-particle theory and the Gaussian model of small-length-scale solvation. The temperature and pressure dependence of solvation quantities embraces solvent's water-like unusual thermodynamic behavior: its density is reflected in the solvation free energy; the isochoric solvation energy and entropy; and the isothermal density derivative of the solvation free energy, its isobaric thermal expansivity in the isobaric solvation enthalpy and entropy, and its isothermal compressibility in the partial molecular volume. The solute's size or length-scale dependence is found to combine with solvent's water-like behavior to produce the "convergence thermodynamics" picture characteristic of aqueous solutions of nonpolar solutes, which is unequivocally found here to be the mapping of the water-like density maximum into the isobaric solvation enthalpy and entropy versus temperature curves for a set of solutes of varying sizes.

Advancing GIST-Based Solvent Functionals through Multiobjective Optimization of Solvent Enthalpy and Entropy Scoring Terms.

Water molecules and their impact on the enthalpy and entropy of protein-ligand binding are of considerable interest in drug discovery. In this contribution, we use multiobjective optimization to fit the solvent enthalpy and entropy scoring terms of grid inhomogeneous solvation theory (GIST)-based solvent functionals to measured isothermal titration calorimetry (ITC) data of protein-ligand-binding reactions for ligand pairs of the protein thrombin. For the investigated ligand pairs, the overwhelming contribution to the relative binding affinity difference is assumed to be attributed to the contribution of water molecules. We present different implementations of the solvent functionals and then proceed by analyzing the most successful one in more detail through error assessment and presentation of the scoring regions in the binding pocket and the unbound ligands of selected examples. We find overall good agreement between calculated and experimental data and, although physically not fully justified, the ligand-desolvation score increases binding affinity, thus suggesting that the solvent molecules on the surface of the unbound ligand constitute a proxy for interactions gained through the protein. Furthermore, we find limited transferability of the parameters even between similar protein targets, thus suggesting refitting for each new protein target. Possible reasons for the limited transferability may arise through the initial assumption of dominating water contributions to binding affinity. Nonetheless, overall our study demonstrates a consistent approach to assign thermodynamic quantities to water molecules that is sensible to measured thermodynamic signatures and enables bridging the gap between experimentally determined water positions in protein-ligand complexes and measured thermodynamic data.

(Invited) Electrolyte and Interphase Revealed By Cryogenic Electron Microscopy and Solvation Measurement

Obtaining atomic and molecular level understanding of electrolyte and electrode-electrolyte interphase is critical to the battery developments. In this talk, I will present a multimodal approach combining the powerful cryogenic electron microscopy technique, electrochemical technique and solvation entropy and free energy measurements. I will discover including: 1) atom-resolved images of solid electrolyte interphase for Li metal and Si anodes; 2) Insight on the debate on the existence of cathode electrolyte interphase; 3) the solvation structure and related thermodynamic parameters and their correlation with electrochemical performance.

Kinetic and thermodynamic insights into the inhibitory mechanism of TMG-chitotriomycin on Vibrio campbellii GH20 exo-β-N-acetylglucosaminidase

We investigated the inhibition kinetics of VhGlcNAcase, a GH20 exo-β-N-acetylglucosaminidase (GlcNAcase) from the marine bacterium Vibrio campbellii (formerly V. harveyi) ATCC BAA-1116, using TMG-chitotriomycin, a natural enzyme inhibitor specific for GH20 GlcNAcases from chitin-processing organisms, with p-nitrophenyl N-acetyl-β-d-glucosaminide (pNP-GlcNAc) as the substrate. TMG-chitotriomycin inhibited VhGlcNAcase with an IC50 of 3.0 ± 0.7 μM. Using Dixon plots, the inhibition kinetics indicated that TMG-chitotriomycin is a competitive inhibitor, with an inhibition constant Ki of 2.2 ± 0.3 μM. Isothermal titration calorimetry experiments provided the thermodynamic parameters for the binding of TMG-chitotriomycin to VhGlcNAcase and revealed that binding was driven by both favorable enthalpy and entropy changes (ΔH° = −2.5 ± 0.1 kcal/mol and −TΔS° = −5.8 ± 0.3 kcal/mol), resulting in a free energy change, ΔG°, of −8.2 ± 0.2 kcal/mol. Dissection of the entropic term showed that a favorable solvation entropy change (−TΔSsolv° = −16 ± 2 kcal/mol) is the main contributor to the entropic term.

Separating Enthalpic, Configurational, and Solvation Entropic Components in Host-Guest Binding: Application to Cucurbit[7]uril Complexes through a Full In Silico Approach via Water Nanodroplets.

Cucurbiturils are a family of supramolecular hosts obtained by condensation of glycoluril and formaldehyde. Cucurbit[7]uril, CB[7], is the most prominent member of the family for its biomolecular interest, arising from its mild solubility in water and for its strong binding with a large variety of guests containing nonpolar fragments such as adamantanes and ferrocene. For instance, CB[7] encapsulates diamantane diammonium iodide with an attomolar dissociation constant, a value unmatched even in natural encapsulation processes. Computational chemistry has been extensively employed to describe the enthalpic-entropic compensation principle of the molecular recognition process of cucurbituril hosts, but the synergistic contribution of experimental data is required for accurate results to be obtained. This paper proposes the first fully theoretical model able to reconcile the calculated thermodynamics of the complexation process with the experimental data obtained by calorimetry (ITC) for cucurbit[7]uril. The model allows the isolation and estimation of all of the enthalpic and entropic contributions coming from solute and solvent alike to the whole host-guest binding event and enables the straightforward calculation of the contribution of the solvation entropy to the binding.

SAMPL7: Host-guest binding prediction by molecular dynamics and quantum mechanics.

Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) challenges provide routes to compare chemical quantities determined using computational chemistry approaches to experimental measurements that are shared after the competition. For this effort, several computational methods have been used to calculate the binding energies of Octa Acid (OA) and exo-Octa Acid (exoOA) host-guest systems for SAMPL7. The initial poses for molecular dynamics (MD) were generated by molecular docking. Binding free energy calculations were performed using molecular mechanics combined with Poisson-Boltzmann or generalized Born surface area solvation (MMPBSA/MMGBSA) approaches. The factors that affect the utility of the MMPBSA/MMGBSA approaches including solvation, partial charge, and solute entropy models were also analyzed. In addition to MD calculations, quantum mechanics (QM) calculations were performed using several different density functional theory (DFT) approaches. From SAMPL6 results, B3PW91-D3 was found to overestimate binding energies though it was effective for geometry optimizations, so it was considered for the DFT geometry optimizations in the current study, with single-point energy calculations carried out with B2PLYP-D3 with double-, triple-, and quadruple-ζ level basis sets. Accounting for dispersion effects, and solvation models was deemed essential for the predictions. MMGBSA and MMPBSA correlated better to experiment when used in conjunction with an empirical/linear correction.

Assessment of scaled particle theory predictions of the convergence of solvation entropies

Entropy convergence is the experimental observation that the hydration entropies of families of non-polar solutes cross one another and converge at a distinct temperature above the boiling point of water. Entropy convergence has subsequently received significant theoretical and molecular simulation interest to interpret its molecular origin. Classic scaled particle theory has enjoyed success in describing entropy convergence for cavity-like, hard sphere solutes in water despite the fact it only considers water's equation-of-state and effective hard sphere diameter while neglecting liquid state inter-molecular correlations. This stands in difference to traditional interpretations of the hydrophobic effect that invoke water's three-dimensional structure when describing aqueous solutions of non-polar moieties. Here we investigate the origins of entropy convergence in classic scaled particle theory. We demonstrate convergence results from the theory's unphysical prediction that the surface tension of the solvent against a hard, flat interface exhibits a maximum as a function of temperature, indicative of a surface entropy that changes sign from negative to positive values with increasing temperature. In addition, we find that classic scaled particle theory can predict convergence like behavior in an organic liquid for which the phenomenon is unexpected.

Dominant entropic binding of perfluoroalkyl substances (PFASs) to albumin protein revealed by 19F NMR

Mechanistic insight into protein binding by poly- and perfluoroalkyl substances (PFASs) is critical to understanding how PFASs distribute and accumulate within the body and to developing predictive models within and across classes of PFASs. Fluorine nuclear magnetic resonance spectroscopy (19F NMR) has proven to be a powerful, yet underutilized tool to study PFAS binding; chemical shifts of each fluorine group reflect the local environment along the length of the PFAS molecule. Using bovine serum albumin (BSA), we report dissociation constants, Kd, for four common PFASs well below reported critical micelle concentrations (CMCs) − perfluorooctanoic acid (PFOA), perfluorononanoic acid (PFNA), perfluorohexanesulfonic acid (PFHxS), and perfluorooctanesulfonic acid (PFOS) − as a function of temperature in phosphate buffered saline. Kd values were determined based on the difluoroethyl group adjacent to the anionic headgroups and the terminal trifluoromethyl groups. Our results indicate that the hydrophobic tails exhibit greater binding affinity relative to the headgroup, and that the binding affinities are generally consistent with previous results showing that greater PFAS hydrophobicity leads to greater protein binding. However, the binding mechanism was dominated by entropic hydrophobic interactions attributed to desolvation of the PFAS tails within the hydrophobic cavities of the protein and on the surface of the protein. In addition, PFNA appears to form hemimicelles on the protein surfaces below reported CMC values. This work provides a renewed approach to utilizing 19F NMR for PFAS-protein binding studies and a new perspective on the role of solvent entropy.

F1-ATPase rotation and its inhibition from the viewpoint of solvent entropy

We compare the asymmetric packing of F1-ATPase and that of F1-ATPase containing the inhibitor protein IF1 (F1-ATPase(IF1)), which inhibits ATP hydrolysis. To analyze this asymmetric packing, we calculate the solvation entropy, S, of three subcomplexes. Subcomplexes I, II, and III contain βE, βTP, and βDP subunits, respectively. The order of |S| is subcomplex III < subcomplex II < subcomplex I for F1-ATPase, and subcomplex II < subcomplex III < subcomplex I for F1-ATPase(IF1). Thus, the packing of F1-ATPase and F1-ATPase(IF1) is different. We suggest a unified understanding of rotation and its inhibition from the viewpoint of the solvent entropy.