A new theoretical approach to biological self-assembly

Statistical-Mechanics Analyses on Thermodynamics of Protein Folding Constructed by Privalov and Co-Workers

Privalov and co-workers estimated the changes in hydration enthalpy and entropy upon ubiquitin unfolding and their temperature dependences denoted by ΔHhyd(T) and ΔShyd(T), respectively, from experimentally measured enthalpies and entropies of transfer of various model compounds from gaseous phase to water. We calculate ΔHhyd(T) and ΔShyd(T) for ubiquitin by our statistical-mechanics theory where molecular and atomistic models are employed for water and protein structure, respectively. ΔHhyd(T) and ΔShyd(T) calculated are in remarkably good agreement with those estimated by Privalov and co-workers. By examining relative magnitudes and signs of the changes in a variety of constituents of ΔHhyd(T) and ΔShyd(T), we confirm that the hydrophobic effect is an essential force driving a protein to fold. Detailed and comprehensive explanations are given for our claim that the prevailing views of the hydrophobic effect are not capable of elucidating its weakening at low temperatures, whereas our updated view is. We find out problematic points of the changes in enthalpy and entropy upon protein unfolding denoted by ΔH°(T) and ΔS°(T), respectively, which are measured using the differential scanning calorimetry at low pH, suggesting a theoretical method of calculating ΔH°(T) and ΔS°(T) at pH ∼ 7.

The contrasting roles of co-solvents in protein formulations and food products

Protein aggregation is a major hurdle in developing biopharmaceuticals, in particular protein formulation area, but plays a pivotal role in food products. Co-solvents are used to suppress protein aggregation in pharmaceutical proteins. On the contrary, aggregation is encouraged in the process of food product making. Thus, it is expected that co-solvents play a contrasting role in biopharmaceutical formulation and food products. Here, we show several examples that utilize co-solvents, e.g., salting-out salts, sugars, polyols and divalent cations in promoting protein-protein interactions. The mechanisms of co-solvent effects on protein aggregation and solubility have been studied on aqueous protein solution and applied to develop pharmaceutical formulation based on the acquired scientific knowledge. On the contrary, co-solvents have been used in food industries based on empirical basis. Here, we will review the mechanisms of co-solvent effects on protein-protein interactions that can be applied to both pharmaceutical and food industries and hope to convey knowledge acquired through research on co-solvent interactions in aqueous protein solution and formulation to those involved in food science and provide those involved in protein solution research with the observations on aggregation behavior of food proteins.

Free-energy decomposition of salt effects on the solubilities of small molecules and the role of excluded-volume effects

The roles of cations and anions are different in the perturbation on solvation, and thus, the analyses of the separated contributions from cations and anions are useful to establish molecular pictures of ion-specific effects. In this work, we investigate the effects of cations, anions, and water separately in the solvation of n-alcohols and n-alkanes by free-energy decomposition. By utilising energy-representation theory of solvation, we address the contributions arising from the direct solute-solvent interactions and the excluded-volume effects. It is found that the change in solvation of n-alcohols and n-alkanes upon addition of salt depends primarily on the anion species. The direct interaction between the anion and solute is in agreement with the Setschenow coefficient in terms of the ranking of salting-in and salting-out for n-alkanes, which corresponds to the extent of accumulation of the anion on the solute surface. For each of the n-alcohols and n-alkanes examined, the excluded-volume component in the Setschenow coefficient is well correlated to the (total) Setschenow coefficient when the salt effects are concerned. The ranking of the excluded-volume component in the variation of the salt species is parallel to the water contribution, which is correlated further to the change in the water density upon the addition of the salt.

Physical pictures of rotation mechanisms of F1- and V1-ATPases: Leading roles of translational, configurational entropy of water

We aim to develop a theory based on a concept other than the chemo-mechanical coupling (transduction of chemical free energy of ATP to mechanical work) for an ATP-driven protein complex. Experimental results conflicting with the chemo-mechanical coupling have recently emerged. We claim that the system comprises not only the protein complex but also the aqueous solution in which the protein complex is immersed and the system performs essentially no mechanical work. We perform statistical-mechanical analyses on V₁-ATPase (the A₃B₃DF complex) for which crystal structures in more different states are experimentally known than for F₁-ATPase (the α₃β₃γ complex). Molecular and atomistic models are employed for water and the structure of V₁-ATPase, respectively. The entropy originating from the translational displacement of water molecules in the system is treated as a pivotal factor. We find that the packing structure of the catalytic dwell state of V₁-ATPase is constructed by the interplay of ATP bindings to two of the A subunits and incorporation of the DF subunit. The packing structure represents the nonuniformity with respect to the closeness of packing of the atoms in constituent proteins and protein interfaces. The physical picture of rotation mechanism of F₁-ATPase recently constructed by Kinoshita is examined, and common points and differences between F₁- and V₁-ATPases are revealed. An ATP hydrolysis cycle comprises binding of ATP to the protein complex, hydrolysis of ATP into ADP and Pi in it, and dissociation of ADP and Pi from it. During each cycle, the chemical compounds bound to the three A or β subunits and the packing structure of the A₃B₃ or α₃β₃ complex are sequentially changed, which induces the unidirectional rotation of the central shaft for retaining the packing structure of the A₃B₃DF or α₃β₃γ complex stabilized for almost maximizing the water entropy. The torque driving the rotation is generated by water with no input of chemical free energy. The presence of ATP is indispensable as a trigger of the torque generation. The ATP hydrolysis or synthesis reaction is tightly coupled to the rotation of the central shaft in the normal or inverse direction through the water-entropy effect.

Correlation between protein conformations and water structure and thermodynamics at high pressure: A molecular dynamics study of the Bovine Pancreatic Trypsin Inhibitor (BPTI) protein

Pressure-induced perturbation of a protein structure leading to its folding-unfolding mechanism is an important yet not fully understood phenomenon. The key point here is the role of water and its coupling with protein conformations as a function of pressure. In the current work, using extensive molecular dynamics simulation at 298 K, we systematically examine the coupling between protein conformations and water structures of pressures of 0.001, 5, 10, 15, 20 kbar, starting from (partially) unfolded structures of the protein Bovine Pancreatic Trypsin Inhibitor (BPTI). We also calculate localized thermodynamics at those pressures as a function of protein-water distance. Our findings show that both protein-specific and generic effects of pressure are operating. In particular, we found that (1) the amount of increase in water density near the protein depends on the protein structural heterogeneity; (2) the intra-protein hydrogen bond decreases with pressure, while the water-water hydrogen bond per water in the first solvation shell (FSS) increases; protein-water hydrogen bonds also found to increase with pressure, (3) with pressure hydrogen bonds of waters in the FSS getting twisted; and (4) water's tetrahedrality in the FSS decreases with pressure, but it is dependent on the local environment. Thermodynamically, at higher pressure, the structural perturbation of BPTI is due to the pressure-volume work, while the entropy decreases with the increase of pressure due to the higher translational and rotational rigidity of waters in the FSS. The local and subtle effects of pressure, found in this work, are likely to be typical of pressure-induced protein structure perturbation.

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.

Adsorption Energetics of Amino Acid Analogs on Polymer/Water Interfaces Studied by All-Atom Molecular Dynamics Simulation and a Theory of Solutions

Energetics of adsorption was addressed with all-atom molecular dynamics simulation on the interfaces of poly(2-methoxyethyl acrylate) (PMEA), poly(methyl methacrylate) (PMMA), and poly(butyl acrylate) (PBA) with water. A wide variety of adsorbate solutes were examined, and the free energy of adsorption was computed with the method of energy representation. It was found that the adsorption free energy was favorable (negative) for all the combinations of solute and polymer, and among PMEA, PMMA, and PBA, the strongest adsorption was observed on PMMA for the hydrophobic solutes and on PMEA for the hydrophilic ones. According to the decomposition of the adsorption free energy into the contributions from polymer and water, it was seen that the polymer contribution is larger in magnitude with the solute size. The total free energy of adsorption was correlated well with the solvation free energy in bulk water only for hydrophobic solutes. The roles of the intermolecular interaction components such as electrostatic, van der Waals, and excluded-volume were further studied, and the electrostatic component was influential only in determining the polymer dependences of the adsorption propensities of hydrophilic solutes. The extent of adsorption was shown to be ranked by the van der Waals component in the solute-polymer interaction separately over the hydrophilic and hydrophobic solutes, with the excluded-volume effect from water pointed out to also drive the adsorption.

Solvation energetics of proteins and their aggregates analyzed by all-atom molecular dynamics simulations and the energy-representation theory of solvation

Solvation is a controlling factor for the structure and function of proteins. This article addresses the effects of solvation from an energetic perspective for the fluctuations and cosolvent-induced changes in protein structures and the equilibrium of aggregate formation for a peptide. A theoretical framework to analyze the solvation effects with an explicit solvent is introduced by adopting the energy-representation theory of solvation, and the connection of the solvation free energy to the protein structure and the aggregation tendency is quantitatively described in combination with all-atom molecular dynamics simulations. The interaction components that govern the solvation effects on the structural variations of proteins are further identified through correlation analysis, and a computational scheme to assess the shift of an aggregation equilibrium due to the addition of a cosolvent is provided.

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, g_O(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, g_O(r) reveals that several CWs are stabilized by interaction networks formed between the ligand, CW, and protein. Based on the g_O(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 g_O(r) of polar heteroatoms may be used to distinguish the correct binding poses.

Reactivity of Zinc Cations under Spontaneous Accumulation of Hydrophobic Coexisting Cations in Hydrophobic Nanoporous Silicon

The ion enrichment behavior due to surface-induced phase separation and the concomitant phase transition of electrolyte solutions between a liquid and a solid confined within nanopores of porous silicon is examined using concentrated aqueous solutions. We performed open-circuit potential measurements and differential scanning calorimetry (DSC) while varying the concentration of aqueous tetraethylammonium chloride (TEACl) solution. Open-circuit potential measurements revealed that the local OH^- concentration within the nanopores increases as the bulk TEACl concentration increases. DSC measurements indicated that TEA⁺ cations are enriched within the nanopores and an extremely high concentration of TEA⁺ remarkably increases the local OH^- concentration. This increase in the local pH should realize the selective precipitation of metal hydroxides within the nanopores. However, such precipitation was not observed in our investigations using aqueous solutions containing zinc cations. The experimental results suggest that ionic species within the nanopores of porous silicon are more stable than those in a bulk solution due to the formation of ion pairs with enhanced stability as well as kinetic factors that increase the activation energy for precipitation.

Enhanced enzymatic activity exerted by a packed assembly of a single type of enzyme

In contrast to the dilute conditions employed for in vitro biochemical studies, enzymes are spatially organized at high density in cellular micro-compartments. In spite of being crucial for cellular functions, enzymatic reactions in such highly packed states have not been fully addressed. Here, we applied a protein adaptor to assemble a single type of monomeric enzyme on a DNA scaffold in the packed or dispersed states for carbonic anhydrase. The enzymatic reactions proceeded faster in the packed than in the dispersed state. Acceleration of the reaction in the packed assembly was more prominent for substrates with higher hydrophobicity. In addition, carbonic anhydrase is more tolerant of inhibitors in the packed assembly. Such an acceleration of the reaction in the packed state over the dispersed state was also observed for xylose reductase. We propose that the entropic force of water increases local substrate or cofactor concentration within the domain confined between enzyme surfaces, thus accelerating the reaction. Our system provides a reasonable model of enzymes in a packed state; this would help in engineering artificial metabolic systems.

Theoretical identification of thermostabilizing amino acid mutations for G-protein-coupled receptors

Thermostabilization of a membrane proteins, especially G-protein-coupled receptors (GPCRs), is often necessary for biochemical applications and pharmaceutical studies involving structure-based drug design. Here we review our theoretical, physics-based method for identifying thermostabilizing amino acid mutations. Its novel aspects are the following: The entropic effect originating from the translational displacement of hydrocarbon groups within the lipid bilayer is treated as a pivotal factor; a reliable measure of thermostability is introduced and a mutation which enlarges the measure to a significant extent is chosen; and all the possible mutations can be examined with moderate computational effort. It was shown that mutating the residue at a position of N_BW = 3.39 (N_BW is the Ballesteros-Weinstein number) to Arg or Lys leads to the stabilization of significantly many different GPCRs of class A in the inactive state. Up to now, we have been successful in stabilizing several GPCRs and newly solving three-dimensional structures for the muscarinic acetylcholine receptor 2 (M2R), prostaglandin E receptor 4 (EP4), and serotonin 2A receptor (5-HT_2AR) using X-ray crystallography. The subjects to be pursued in future studies are also discussed.

Methodology for Further Thermostabilization of an Intrinsically Thermostable Membrane Protein Using Amino Acid Mutations with Its Original Function Being Retained

We develop a new methodology best suited to the identification of thermostabilizing mutations for an intrinsically stable membrane protein. The recently discovered thermophilic rhodopsin, whose apparent midpoint temperature of thermal denaturation T_m is measured to be ∼91.8 °C, is chosen as a paradigmatic target. In the methodology, we first regard the residues whose side chains are missing in the crystal structure of the wild type (WT) as the "residues with disordered side chains," which make no significant contributions to the stability, unlike the other essential residues. We then undertake mutating each of the residues with disordered side chains to another residue except Ala and Pro, and the resultant mutant structure is constructed by modifying only the local structure around the mutated residue. This construction is based on the postulation that the structure formed by the other essential residues, which is nearly optimized in such a highly stable protein, should not be modified. The stability changes arising from the mutations are then evaluated using our physics-based free-energy function (FEF). We choose the mutations for which the FEF is much lower than for the WT and test them by experiments. We successfully find three mutants that are significantly more stable than the WT. A double mutant whose T_m reaches ∼100 °C is also discovered.

Accurate and rapid calculation of hydration free energy and its physical implication for biomolecular functions

Here we review a new method for calculating a hydration free energy (HFE) of a solute and discuss its physical implication for biomolecular functions in aqueous environments. The solute hydration is decomposed into processes 1 and 2. A cavity matching the geometric characteristics of the solute at the atomic level is created in process 1. Solute-water van der Waals and electrostatic interaction potentials are incorporated in process 2. The angle-dependent integral equation theory combined with our morphometric approach is applied to process 1, and the three-dimensional reference interaction site model theory is employed for process 2. Molecular models are adopted for water. The new method is characterized by the following. Solutes with various sizes including proteins can be treated in the same manner. It is almost as accurate as the molecular dynamics simulation despite its far smaller computational burden. It enables us to handle a solute possessing a significantly large total charge without difficulty. The HFE can be decomposed into a variety of physically insightful, energetic, and entropic components. It is best suited to the elucidation of mechanisms of protein folding, pressure and cold denaturation of a protein, and different types of molecular recognition.

Hydration properties of a protein at low and high pressures: Physics of pressure denaturation

Using experimentally determined structures of ubiquitin at 1 and 3000 bar, we generate sufficiently large ensembles of model structures in the native and pressure-induced (denatured) states by means of molecular dynamics simulations with explicit water. We calculate the values of a free-energy function (FEF), which comprises the hydration free energy (HFE) and the intramolecular (conformational) energy and entropy, for the two states at 1 and 3000 bar. The HFE and the conformational entropy, respectively, are calculated using our statistical-mechanical method, which has recently been shown to be accurate, and the Boltzmann-quasi-harmonic method. The HFE is decomposed into a variety of physically insightful components. We show that the FEF of the native state is lower than that of the denatured state at 1 bar, whereas the opposite is true at 3000 bar, thus being successful in reproducing the pressure denaturation. We argue that the following two quantities of hydration play essential roles in the denaturation: the WASA-dependent term in the water-entropy loss upon cavity creation for accommodating the protein (WASA is the water-accessible surface area of the cavity) and the protein-water Lennard-Jones interaction energy. At a high pressure, the mitigation of the serious water crowding in the system is the most important, and the WASA needs to be sufficiently enlarged with the increase in the excluded-volume being kept as small as possible. The denatured structure thus induced is characterized by the water penetration into the protein interior. The pressure denaturation is accompanied by a significantly large gain of water entropy.

Reduced density profile of small particles near a large particle: Results of an integral equation theory with an accurate bridge function and a Monte Carlo simulation

Solute-solvent reduced density profiles of hard-sphere fluids were calculated by using several integral equation theories for liquids. The traditional closures, Percus-Yevick (PY) and the hypernetted-chain (HNC) closures, as well as the theories with bridge functions, Verlet, Duh-Henderson, and Kinoshita (named MHNC), were used for the calculation. In this paper, a one-solute hard-sphere was immersed in a one-component hard-sphere solvent and various size ratios were examined. The profiles between the solute and solvent particles were compared with those calculated by Monte Carlo simulations. The profiles given by the integral equations with the bridge functions were much more accurate than those calculated by conventional integral equation theories, such as the Ornstein-Zernike (OZ) equation with the PY closure. The accuracy of the MHNC-OZ theory was maintained even when the particle size ratio of solute to solvent was 50. For example, the contact values were 5.7 (Monte Carlo), 5.6 (MHNC), 7.8 (HNC), and 4.5 (PY), and the first minimum values were 0.48 (Monte Carlo), 0.46 (MHNC), 0.54 (HNC), and 0.40 (PY) when the packing fraction of the hard-sphere solvent was 0.38 and the size ratio was 50. The asymptotic decay and the oscillation period for MHNC-OZ were also very accurate, although those given by the HNC-OZ theory were somewhat faster than those obtained by Monte Carlo simulations.

How Does the Recently Discovered Peptide MIP Exhibit Much Higher Binding Affinity than an Anticancer Protein p53 for an Oncoprotein MDM2?

An oncoprotein MDM2 binds to the extreme N-terminal peptide region of a tumor suppressor protein p53 (p53NTD) and inhibits its anticancer activity. We recently discovered a peptide named MIP which exhibits much higher binding affinity for MDM2 than p53NTD. Experiments showed that the binding free energy (BFE) of MDM2-MIP is lower than that of MDM2-p53NTD by approximately -4 kcal/mol. Here, we develop a theoretical method which is successful in reproducing this quantitative difference and elucidating its physical origins. It enables us to decompose the BFE into a variety of energetic and entropic components, evaluate their relative magnitudes, and identify the physical factors driving or opposing the binding. It should be applicable also to the assessment of differences among ligands in the binding affinity for a particular receptor, which is a central issue in modern chemistry. In the MDM2 case, the higher affinity of MIP is ascribed to a larger gain of translational, configurational entropy of water upon binding. This result is useful to the design of a peptide possessing even higher affinity for MDM2 as a reliable drug against a cancer.

Molecular Interactions of Cephalosporins with the Deep Binding Pocket of the RND Transporter AcrB

The drug/proton antiporter AcrB, part of the major efflux pump AcrABZ-TolC in Escherichia coli, is characterized by its impressive ability to transport chemically diverse compounds, conferring a multidrug resistance phenotype. However, the molecular features differentiating between good and poor substrates of the pump have yet to be identified. In this work, we combined molecular docking with molecular dynamics simulations to study the interactions between AcrB and two representative cephalosporins, cefepime and ceftazidime (a good and poor substrate of AcrB, respectively). Our analysis revealed different binding preferences of the two compounds toward the subsites of the large deep binding pocket of AcrB. Cefepime, although less hydrophobic than ceftazidime, showed a higher affinity than ceftazidime for the so-called hydrophobic trap, a region known for binding inhibitors and substrates. This supports the hypothesis that surface complementarity between the molecule and AcrB, more than the intrinsic hydrophobicity of the antibiotic, is a feature required for the interaction within this region. Oppositely, the preference of ceftazidime for binding outside the hydrophobic trap might not be optimal for triggering allosteric conformational changes needed to the transporter to accomplish its function. Altogether, our findings could provide valuable information for the design of new antibiotics less susceptible to the efflux mechanism.

Mechanism of protein-RNA recognition: analysis based on the statistical mechanics of hydration

We investigate the RBD1-r(GUAGU) binding as a case study using all-atom models for the biomolecules, molecular models for water, and the currently most reliable statistical-mechanical method. RBD1 is one of the RNA-binding domains of mammalian Musashi1 (Msi1), and r(GUAGU) contains the minimum recognition sequence for Msi1, r(GUAG). We show that the binding is driven by a large gain of configurational entropy of water in the entire system. It is larger than the sum of conformational-entropy losses for RBD1 and r(GUAGU). The decrease in RBD1-r(GUAGU) interaction energy upon binding is largely cancelled out by the increase in the sum of RBD1-water, r(GUAGU)-water, and water-water interaction energies. We refer to this increase as "energetic dehydration". The decrease is larger than the increase for the van der Waals component, whereas the opposite is true for the electrostatic component. We give a novel reason for the empirically known fact that protein residues possessing side chains with positive charges and with flat moieties frequently appear within protein-RNA binding interfaces. A physical picture of the general protein-RNA binding mechanism is then presented. To achieve a sufficiently large water-entropy gain, shape complementarity at the atomic level needs to be constructed by utilizing the stacking and sandwiching of flat moieties (aromatic rings of the protein and nucleobases of RNA) as fundamental motifs. To compensate for electrostatic energetic dehydration, charge complementarity becomes crucial within the binding interface. We argue the reason why the RNA recognition motif (RRM) is the most ubiquitous RNA binding domain.

Energetics of cosolvent effect on peptide aggregation

The cosolvent effect on the equilibrium of peptide aggregation is reviewed from the energetic perspective. It is shown that the excess chemical potential is stationary against the variation of the distribution function for the configuration of a flexible solute species and that the derivative of the excess chemical potential with respect to the cosolvent concentration is determined by the corresponding derivative of the solvation free energy averaged over the solute configurations. The effect of a cosolvent at low concentrations on a chemical equilibrium can then be addressed in terms of the difference in the solvation free energy between pure-water solvent and the mixed solvent with the cosolvent, and illustrative analyses with all-atom model are presented for the aggregation of an 11-residue peptide by employing the energy-representation method to compute the solvation free energy. The solvation becomes more favorable with addition of the urea or DMSO cosolvent, and the extent of stabilization is smaller for larger aggregate. This implies that these cosolvents inhibit the formation of an aggregate, and the roles of such interaction components as the electrostatic, van der Waals, and excluded-volume are discussed.

Molecular dynamics study of coil-to-globule transition in a thermo-responsive oligomer bound to various surfaces: hydrophilic surfaces stabilize the coil form

The structural and dynamical properties of 40-mer of thermo-responsive polymer PNIPAM covalently bound to different surfaces have been studied, at different temperatures, by means of molecular dynamics simulations. Evolution of the radius of gyration, Rg, of the polymer chain and radial distribution functions (RDFs) calculated for the carbon atoms of the PNIPAM backbone with water oxygens and for the hydrogen atom of the amide groups with water oxygens indicate that functionalized surfaces affect the coil-to-globule transition of PNIPAM, by means of electrostatic interactions, increasing the lower critical solution temperature (LCST) of the polymer. Such interactions, mainly represented by a H-bond, hinder the transition in the globular form while hydrophobic groups on the surface, such as -OCH3, contribute to the globular collapse. A significant alteration in the arrangement of water molecules around the polymer is testified by: (i) the absence of the second peak in the RDF between the C atoms of the PNIPAM backbone and the O atoms of water at the same temperature at which the radius of gyration decreases; (ii) the height of both the first and the second peak of the RDF between the H atom of the amide groups and water O atoms decreases when the temperature increases above the LCST. Finally, the H-bond autocorrelation function indicates that: (i) hydrogen bonds between the bound-to-surface PNIPAM acceptor groups (O[double bond, length as m-dash]C[double bond splayed right]) and the H atoms of water molecules are less persistent than H-bonds formed between the free PNIPAM acceptor groups and water; (ii) H-bonds between the PNIPAM acceptor groups and hydroxyl groups on the quartz surface are longer lived than those formed on graphene oxide.

Universal effects of solvent species on the stabilized structure of a protein

We investigate the effects of solvent specificities on the stability of the native structure (NS) of a protein on the basis of our free-energy function (FEF). We use CPB-bromodomain (CBP-BD) and apoplastocyanin (apoPC) as representatives of the protein universe and water, methanol, ethanol, and cyclohexane as solvents. The NSs of CBP-BD and apoPC consist of 66% α-helices and of 35% β-sheets and 4% α-helices, respectively. In order to assess the structural stability of a given protein immersed in each solvent, we contrast the FEF of its NS against that of a number of artificially created, misfolded decoys possessing the same amino-acid sequence but significantly different topology and α-helix and β-sheet contents. In the FEF, we compute the solvation entropy using the morphometric approach combined with the integral equation theories, and the change in electrostatic (ES) energy upon the folding is obtained by an explicit atomistic but simplified calculation. The ES energy change is represented by the break of protein-solvent hydrogen bonds (HBs), formation of protein intramolecular HBs, and recovery of solvent-solvent HBs. Protein-solvent and solvent-solvent HBs are absent in cyclohexane. We are thus able to separately evaluate the contributions to the structural stability from the entropic and energetic components. We find that for both CBP-BD and apoPC, the energetic component dominates in methanol, ethanol, and cyclohexane, with the most stable structures in these solvents sharing the same characteristics described as an association of α-helices. In particular, those in the two alcohols are identical. In water, the entropic component is as strong as or even stronger than the energetic one, with a large gain of translational, configurational entropy of water becoming crucially important so that the relative contents of α-helix and β-sheet and the content of total secondary structures are carefully selected to achieve sufficiently close packing of side chains. If the energetic component is excluded for a protein in water, the priority is given to closest side-chain packing, giving rise to the formation of a structure with very low α-helix and β-sheet contents. Our analysis, which requires minimal computational effort, can be applied to any protein immersed in any solvent and provides robust predictions that are quite consistent with the experimental observations for proteins in different solvent environments, thus paving the way toward a more detailed understanding of the folding process.

Localization switching of a large object in a crowded cavity: A rigid/soft object prefers surface/inner positioning

For living cells in the real world, a large organelle is commonly positioned in the inner region away from membranes, such as the nucleus of eukaryotic cells, the nucleolus of nuclei, mitochondria, chloroplast, Golgi body, etc. It contradicts the expectation by the current depletion-force theory in that the larger particle should be excluded from the inner cell space onto cell boundaries in a crowding media. Here we simply model a sizable organelle as a soft-boundary large particle allowing crowders, which are smaller hard spheres in the model, to intrude across its boundary. The results of Monte Carlo simulation indicate that the preferential location of the larger particle switches from the periphery into the inner region of the cavity by increasing its softness. An integral equation theory is further developed to account for the structural features of the model, and the theoretical predictions are found consistent with our simulation results.

Probabilistic analysis for identifying the driving force of protein folding

Toward identifying the driving force of protein folding, energetics was analyzed in water for Trp-cage (20 residues), protein G (56 residues), and ubiquitin (76 residues) at their native (folded) and heat-denatured (unfolded) states. All-atom molecular dynamics simulation was conducted, and the hydration effect was quantified by the solvation free energy. The free-energy calculation was done by employing the solution theory in the energy representation, and it was seen that the sum of the protein intramolecular (structural) energy and the solvation free energy is more favorable for a folded structure than for an unfolded one generated by heat. Probabilistic arguments were then developed to determine which of the electrostatic, van der Waals, and excluded-volume components of the interactions in the protein-water system governs the relative stabilities between the folded and unfolded structures. It was found that the electrostatic interaction does not correspond to the preference order of the two structures. The van der Waals and excluded-volume components were shown, on the other hand, to provide the right order of preference at probabilities of almost unity, and it is argued that a useful modeling of protein folding is possible on the basis of the excluded-volume effect.

Statistical Thermodynamics for Actin-Myosin Binding: The Crucial Importance of Hydration Effects

Actomyosin is an important molecular motor, and the binding of actin and myosin is an essential research target in biophysics. Nevertheless, the physical factors driving or opposing the binding are still unclear. Here, we investigate the role of water in actin-myosin binding using the most reliable statistical-mechanical method currently available for assessing biomolecules immersed in water. This method is characterized as follows: water is treated not as a dielectric continuum but as an ensemble of molecules; the polyatomic structures of proteins are taken into consideration; and the binding free energy is decomposed into physically insightful entropic and energetic components by accounting for the hydration effect to its full extent. We find that the actin-myosin binding brings large gains of electrostatic and Lennard-Jones attractive interactions. However, these gains are accompanied by even larger losses of actin-water and myosin-water electrostatic and LJ attractive interactions. Although roughly half of the energy increase due to the losses is cancelled out by the energy decrease arising from structural reorganization of the water released upon binding, the remaining energy increase is still larger than the energy decrease brought by the gains mentioned above. Hence, the net change in system energy is positive, which opposes binding. Importantly, the binding is driven by a large gain of configurational entropy of water, which surpasses the positive change in system energy and the conformational entropy loss occurring for actin and myosin. The principal physical origin of the large water-entropy gain is as follows: the actin-myosin interface is closely packed with the achievement of high shape complementarity on the atomic level, leading to a large increase in the total volume available to the translational displacement of water molecules in the system and a resultant reduction of water crowding (i.e., entropic correlations among water molecules).

Dynamic manipulation of the local pH within a nanopore triggered by surface-induced phase transition

Manipulating the local pH within nanopores is essential in nanofluidics technology and its applications.

Unified elucidation of the entropy-driven and -opposed hydrophobic effects

The association of nonpolar solutes is generally believed to be entropy driven, which has been shown to be true for the contact of small molecules, ellipsoids, and plates.

Free-energy analysis of protein solvation with all-atom molecular dynamics simulation combined with a theory of solutions

The structure of a protein is strongly influenced by solvation. In the present review, the solvation effect is treated within the framework of statistical thermodynamics. The key quantity is the solvation free energy of protein and a fast method for its computation with explicit solvent is introduced. The applications of the method to the structural fluctuation of protein in water, structure determination of protein-protein complex, and urea effect on protein structure are then described, and the roles of solvent water and cosolvent are discussed from the standpoint of energetics.

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.

Oligomer Formation of Amyloid-β(29-42) from Its Monomers Using the Hamiltonian Replica-Permutation Molecular Dynamics Simulation

Oligomers of amyloid-β peptides (Aβ) are formed during the early stage of the amyloidogenesis process and exhibit neurotoxicity. The oligomer formation process of Aβ and even that of Aβ fragments are still poorly understood, though understanding of these processes is essential for remedying Alzheimer's disease. In order to better understand the oligomerization process of the C-terminal Aβ fragment Aβ(29-42) at the atomic level, we performed the Hamiltonian replica-permutation molecular dynamics simulation with Aβ(29-42) molecules using the explicit water solvent model. We observed that oligomers increased in size through the sequential addition of monomers to the oligomer, rather than through the assembly of small oligomers. Moreover, solvent effects played an important role in this oligomerization process.

Effects of monohydric alcohols and polyols on the thermal stability of a protein

The thermal stability of a protein is lowered by the addition of a monohydric alcohol, and this effect becomes larger as the size of hydrophobic group in an alcohol molecule increases. By contrast, it is enhanced by the addition of a polyol possessing two or more hydroxyl groups per molecule, and this effect becomes larger as the number of hydroxyl groups increases. Here, we show that all of these experimental observations can be reproduced even in a quantitative sense by rigid-body models focused on the entropic effect originating from the translational displacement of solvent molecules. The solvent is either pure water or water-cosolvent solution. Three monohydric alcohols and five polyols are considered as cosolvents. In the rigid-body models, a protein is a fused hard spheres accounting for the polyatomic structure in the atomic detail, and the solvent is formed by hard spheres or a binary mixture of hard spheres with different diameters. The effective diameter of cosolvent molecules and the packing fractions of water and cosolvent, which are crucially important parameters, are carefully estimated using the experimental data of properties such as the density of solid crystal of cosolvent, parameters in the pertinent cosolvent-cosolvent interaction potential, and density of water-cosolvent solution. We employ the morphometric approach combined with the integral equation theory, which is best suited to the physical interpretation of the calculation result. It is argued that the degree of solvent crowding in the bulk is the key factor. When it is made more serious by the cosolvent addition, the solvent-entropy gain upon protein folding is magnified, leading to the enhanced thermal stability. When it is made less serious, the opposite is true. The mechanism of the effects of monohydric alcohols and polyols is physically the same as that of sugars. However, when the rigid-body models are employed for the effect of urea, its addition is predicted to enhance the thermal stability, which conflicts with the experimental fact. We then propose, as two essential factors, not only the solvent-entropy gain but also the loss of protein-solvent interaction energy upon protein folding. The competition of changes in these two factors induced by the cosolvent addition determines the thermal-stability change.

Asymmetrical Polyhedral Configuration of Giant Vesicles Induced by Orderly Array of Encapsulated Colloidal Particles

Giant vesicles (GVs) encapsulating colloidal particles by a specific volume fraction show a characteristic configuration under a hypertonic condition. Several flat faces were formed in GV membrane with orderly array of inner particles. GV shape changed from the spherical to the asymmetrical polyhedral configuration. This shape deformation was derived by entropic interaction between inner particles and GV membrane. Because a part of inner particles became to form an ordered phase in the region neighboring the GV membrane, free volume for the other part of particles increased. Giant vesicles encapsulating colloidal particles were useful for the model of "crowding effect" which is the entropic interaction in the cell.

Statistical thermodynamics of aromatic–aromatic interactions in aqueous solution

To elucidate the interactions between aromatic rings, which are believed to play essential roles in a variety of biological processes, we analyze the water-mediated interactions between toluene molecules along face-to-face stacked (FF) and point-to-face T-shaped (TS) paths using a statistical-mechanical theory of liquids combined with a molecular model for water.