尾嶋 拓

<jats:title>Abstract</jats:title><jats:p>Multistate Bennett acceptance ratio (MBAR) works as a method to analyze molecular dynamics (MD) simulation data after the simulations have been finished. It is widely used to estimate free-energy changes between different states and averaged properties at the states of interest. MBAR allows us to treat a wide range of states from those at different temperature/pressure to those with different model parameters. Due to the broad applicability, the MBAR equations are rather difficult to apply for free-energy calculations using different types of MD simulations including enhanced conformational sampling methods and free-energy perturbation. In this review, we first summarize the basic theory of the MBAR equations and categorize the representative usages into the following four: (i) perturbation, (ii) scaling, (iii) accumulation, and (iv) full potential energy. For each, we explain how to prepare input data using MD simulation trajectories for solving the MBAR equations. MBAR is also useful to estimate reliable free-energy differences using MD trajectories based on a semi-empirical quantum mechanics/molecular mechanics (QM/MM) model and ab initio QM/MM energy calculations on the MD snapshots. We also explain how to use the MBAR software in the GENESIS package, which we call <jats:italic>mbar_analysis</jats:italic>, for the four representative cases. The proposed estimations of free-energy changes and thermodynamic averages are effective and useful for various biomolecular systems.</jats:p>

Proper balance between protein-protein and protein-water interactions is vital for atomistic molecular dynamics (MD) simulations of globular proteins as well as intrinsically disordered proteins (IDPs). The overestimation of protein-protein interactions tends to make IDPs more compact than those in experiments. Likewise, multiple proteins in crowded solutions are aggregated with each other too strongly. To optimize the balance, Lennard-Jones (LJ) interactions between protein and water are often increased about 10% (with a scaling parameter, lambda = 1.1) from the existing force fields. Here, we explore the optimal scaling parameter of protein-water LJ interactions for CHARMM36m in conjunction with the modified TIP3P water model, by performing enhanced sampling MD simulations of several peptides in dilute solutions and conventional MD simulations of globular proteins in dilute and crowded solutions. In our simulations, 10% increase of protein-water LJ interaction for the CHARMM36m cannot maintain stability of a small helical peptide, (AAQAA)(3) in a dilute solution and only a small modification of protein-water LJ interaction up to the 3% increase (lambda = 1.03) is allowed. The modified protein-water interactions are applicable to other peptides and globular proteins in dilute solutions without changing thermodynamic properties from the original CHARMM36m. However, it has a great impact on the diffusive properties of proteins in crowded solutions, avoiding the formation of too sticky protein-protein interactions.

The inside of a cell is highly crowded with proteins and other biomolecules. How proteins express their specific functions together with many off-target proteins in crowded cellular environments is largely unknown. Here, we investigate an inhibitor binding with c-Src kinase using atomistic molecular dynamics (MD) simulations in dilute as well as crowded protein solution. The populations of the inhibitor, 4-amino-5-(4-methylphenyl)-7-(t-butyl)pyrazolo[3,4-d]pyrimidine (PP1), in bulk solution and on the surface of c-Src kinase are reduced as the concentration of crowder bovine serum albumins (BSAs) increases. This observation is consistent with the reduced PP1 inhibitor efficacy in experimental c-Src kinase assays in addition with BSAs. The crowded environment changes the major binding pathway of PP1 toward c-Src kinase compared to that in dilute solution. This change is explained based on the population shift mechanism of local conformations near the inhibitor binding site in c-Src kinase. The intracellular compartment is a crowded environment. Here, the authors use molecular dynamics (MD) simulations to assess inhibitor binding to c-Src kinase and show how ligand binding pathways differ in crowded and dilute protein solutions, highlighting the role of c-Src Tyr82 sidechain.

Conformational changes of proteins upon ligand binding are usually explained in terms of several mechanisms including the induced fit, conformational selection, or their mixtures. Due to the slow time scales, conventional molecular dynamics (cMD) simulations based on the atomistic models cannot easily simulate the open-to-closed conformational transition in proteins. In our previous study, we have developed an enhanced sampling scheme (generalized replica exchange with solute tempering selected surface charged residues: gREST_SSCR) for multidomain proteins and applied it to ligand-mediated conformational changes in the G134R mutant of ribose-binding protein (RBPG134R) in solution. The free-energy landscape (FEL) of RBPG134R in the presence of a ribose at the binding site included the open and closed states and two intermediates, open-like and closed-like forms. Only the open and open-like forms existed in the FEL without a ribose. In the current study, the coupling between the conformational changes and ligand binding is further investigated using coarse-grained MD, multiple atomistic cMD, and free-energy calculations. The ribose is easily dissociated from the binding site of wild-type RBP and RBPG134R in the cMD simulations starting from the open and open-like forms. In contrast, it is stable at the binding site in the simulations from the closed and closed-like forms. The free-energy calculations provide the binding affinities of different structures, supporting the results of cMD simulations. Importantly, cMD simulations from the closed-like structures reveal transitions toward the closed one in the presence of a bound ribose. On the basis of the computational results, we propose a molecular mechanism in which conformational selection and induced fit happen in the first and second halves of the open-to-closed transition in RBP, respectively.

The accurate prediction of protein-ligand binding affinity is a central challenge in computational chemistry and in-silico drug discovery. The free energy perturbation (FEP) method based on molecular dynamics (MD) simulation provides reasonably accurate results only if a reliable structure is available via high-resolution X-ray crystallography. To overcome the limitation, we propose a sequential prediction protocol using generalized replica exchange with solute tempering (gREST) and FEP. At first, ligand binding poses are predicted using gREST, which weakens protein-ligand interactions at high temperatures to sample multiple binding poses. To avoid ligand dissociation at high temperatures, a flat-bottom restraint potential centered on the binding site is applied in the simulation. The binding affinity of the most reliable pose is then calculated using FEP. The protocol is applied to the bindings of ten ligands to FK506 binding proteins (FKBP), showing the excellent agreement between the calculated and experimental binding affinities. The present protocol, which is referred to as the gREST+FEP method, would help to predict the binding affinities without high-resolution structural information on the ligand-bound state.

Alchemical free energy simulations have long been utilized to predict free energy changes for binding affinity and solubility of small molecules. However, while the theoretical foundation of these methods is well established, seamlessly handling many of the practical aspects regarding the preparation of the different thermodynamic end states of complex molecular systems and the numerous processing scripts often remains a burden for successful applications. In this work, we present CHARMM-GUI Free Energy Calculator ( http://www.charmm-gui. org/input/fec) that provides various alchemical free energy perturbation molecular dynamics (FEP/MD) systems with input and post-processing scripts for NAMD and GENESIS. Four submodules are available: Absolute Ligand Binder (for absolute ligand binding FEP/MD), Relative Ligand Binder (for relative ligand binding FEP/MD), Absolute Ligand Solvator (for absolute ligand solvation FEP/MD), and Relative Ligand Solvator (for relative ligand solvation FEP/MD). Each module is designed to build multiple systems of a set of selected ligands at once for high-throughput FEP/MD simulations. The capability of Free Energy Calculator is illustrated by absolute and relative solvation FEP/MD of a set of ligands and absolute and relative binding FEP/MD of a set of ligands for T4-lysozyme in solution and the adenosine A(2A) receptor in a membrane. The calculated free energy values are overall consistent with the experimental and published free energy results (within similar to 1 kcal/mol). We hope that Free Energy Calculator is useful to carry out high-throughput FEP/MD simulations in the field of biomolecular sciences and drug discovery.

Slow polypeptide conformational changes on time scales of >1 s are generally assumed to be highly cooperative two-state transitions, reflecting the high energy barrier. However, few experimental characterizations have tested the validity of this assumption. We performed residue-specific NMR thermodynamic analysis of the 27-residue lantibiotic peptide, nukacin ISK-1, to characterize the isomerization between two topological states on the second time scale. Unexpectedly, the thermal transition behaviors were distinct among peptide regions, indicating that the topological isomerization process is a mosaic of different degrees of cooperativity. The conformational change path between the two NMR structures was deduced by a targeted molecular dynamics simulation. The unique side-chain threading motions through the monosulfide rings are the structural basis of the high energy barrier, and the nonlocal interactions in the hydrophobic core are the structural basis of the cooperativity. Taken together, we provide an energetic description of the topological isomerization of nukacin ISK-1.

Molecular recognition underpins all specific protein-ligand interactions and is essential for biomolecular functions. The prediction of canonical binding poses and distinguishing binders from nonbinders are much sought after goals. Here, we apply the generalized replica exchange with solute tempering method, gREST, combined with a flat-bottom potential to evaluate binder and nonbinder interactions with a T4 lysozyme Leu99Ala mutant. The buried hydrophobic cavity and possibility of coupled conformational changes in this protein make binding predictions difficult. The present gREST simulations, enabling enhanced flexibilities of the ligand and protein residues near the binding site, sample bindings in multiple poses, and correct portrayal of X-ray structures. The free-energy profiles of binders (benzene, ethylbenzene, and n-hexylbenzene) are distinct from those of nonbinders (phenol and benzaldehyde). Bindings of the two larger molecules seem to be associated with a structural change toward an excited conformation of the protein, which agrees with experimental findings. The protocol is generally applicable to various proteins having buried cavities with limited access for ligands with different shapes, sizes, and chemical properties.

For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy mu, 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 mu 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 mu, 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 mu. 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 vertical bar S vertical bar, mu from the DRISM theory becomes too high. It is interesting that mu, 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.

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).

We develop a new method for calculating the hydration free energy (HFE) of a protein with any net charge. The polar part of the energetic component in the HFE is expressed as a linear combination of four geometric measures (GMs) of the protein structure and the generalized Born (GB) energy plus a constant. The other constituents in the HFE are expressed as linear combinations of the four GMs. The coefficients (including the constant) in the linear combinations are determined using the three-dimensional reference interaction site model (3D-RISM) theory applied to sufficiently many protein structures. Once the coefficients are determined, the HFE and its constituents of any other protein structure are obtained simply by calculating the four GMs and GB energy. Our method and the 3D-RISM theory give perfectly correlated results. Nevertheless, the computation time required in our method is over four orders of magnitude shorter.

The new type of molecular recognition, in which an intrinsically disordered region (IDR) of a protein binds to many different target proteins with target-dependent structure formation, is indispensable to the expression of life phenomena and also implicated in a number of diseases. According to the prevailing view, the physicochemical factors responsible for the binding are also target dependent. Here we consider an IDR of the tumor suppressor p53 protein, p53CTD, as an important example related to carcinogenesis and analyze its binding to four targets accompanying the formation of target-dependent structures (i.e., helix, sheet, and two different coils) using our statistical-mechanical method combined with molecular models for water. We find that all of the seemingly different binding processes are driven by a large gain of the translational, configurational entropy of water in the system. The gain originates from sufficiently high shape complementarity on the atomic level within the p53CTD target interface. It is also required that the electrostatic complementarity be ensured as much as possible to compensate for the dehydration. Such complementarities are achieved in harmony with the portion of the target to which p53CTD binds, leading to a large diversity of structures of p53CTD formed upon binding: If they are not achievable, the binding does not occur. This finding is made possible only by calculating the changes in thermodynamic quantities upon binding and decomposing them into physically insightful components.

It is of great interest from both scientific and practical viewpoints to theoretically predict the thermal-stability changes upon mutations of a protein. However, such a prediction is an intricate task. Up to now, significantly many approaches for the prediction have been reported in the literature. They always include parameters which are adjusted so that the prediction results can be best fitted to the experimental data for a sufficiently large set of proteins and mutations. The inclusion is necessitated to achieve satisfactorily high prediction performance. A problem is that the resulting values of the parameters are often physically meaningless, and the physicochemical factors governing the thermal-stability changes upon mutations are rather ambiguous. Here, we develop a new measure of the thermal stability. Protein folding is accompanied by a large gain of water entropy (the entropic excluded-volume (EV) effect), loss of protein conformational entropy, and increase in enthalpy. The enthalpy increase originates primarily from the following: The energy increase due to the break of protein-water hydrogen bonds (HBs) upon folding cannot completely be cancelled out by the energy decrease brought by the formation of protein intramolecular HBs. We develop the measure on the basis of only these three factors and apply it to the prediction of the thermal-stability changes upon mutations. As a consequence, an approach toward the prediction is obtained. It is distinguished from the previously reported approaches in the following respects: The parameters adjusted in the manner mentioned above are not employed at all, and the entropic EV effect, which is ascribed to the translational displacement of water molecules coexisting with the protein in the system, is fully taken into account using a molecular model for water. Our approach is compared with one of the most popular approaches, FOLD-X, in terms of the prediction performance not only for single mutations but also for double, triple, and higher-fold (up to sevenfold) mutations. It is shown that on the whole our approach and FOLD-X exhibit almost the same performance despite that the latter uses the adjusting parameters. For multiple mutations, however, our approach is far superior to FOLD-X. Five multiple mutations for staphylococcal nuclease lead to highly enhanced stabilities, but we find that this high enhancement arises from the entropic EV effect. The neglect of this effect in FOLD-X is a principal reason for its ill success. A conclusion is that the three factors mentioned above play essential roles in elucidating the thermal-stability changes upon mutations. (C) 2015 AIP Publishing LLC.

In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient values, however, the many-body correlation plays significant roles in the beta-sheet formation and argument of relative stabilities of very similar structures of a protein. These results are argued in detail with respect to the four physically insightful constituents and the two factors mentioned above. The relevance to the absence or presence of hydrogen-bonding properties in the solvent is also discussed in detail. (C) 2015 AIP Publishing LLC.

AcrB, a homotrimer, is the pivotal part of a multidrug efflux pump. A functionally rotating picture has been proposed for the drug transport by AcrB, but its mechanism remains unresolved. Here, we investigate the energetics of the whole functional rotation cycle using our theoretical methods. We find that the packing efficiency of AcrB is ununiform, and this ununiformity plays imperative roles primarily through the solvent-entropy effect. When a proton binds to or dissociates from a protomer, the packing properties of this protomer and its two interfaces are perturbed overall in the direction that the solvent translational entropy is lowered. The packing properties of the other two protomers are then reorganized with the recovery or maintenance of closely packed interfaces, so that the solvent-entropy loss can be compensated. The functional structural change by an isolated protomer would cause a seriously large free-energy increase. By forming a trimer, any free-energy increase caused by a protomer is always canceled out by the free-energy decrease brought by the other two protomers via the mechanism mentioned above. The functional structural rotation is thus accomplished using the free-energy decrease arising from the transfer of only a single proton per cycle. The similarities to F-1-ATPase are also discussed.

We analyze entropic and energetic components of the hydration free energy (HFE) for hydrophobic and hydrophilic solutes under isochoric condition using the angle-dependent integral equation theory combined with a multipolar water model. The entropic component, which always makes a positive contribution to the HFE, becomes larger at high pressures and smaller at low temperatures for both solutes: it governs the pressure and temperature dependence of the HFE. For hydrophilic solutes at low temperatures, however, the energetic component becomes more important and makes them less hydrophilic. We discuss the validity of our previous studies on pressure and cold denaturating of proteins. (C) 2014 Elsevier B.V. All rights reserved.

It is a central issue to elucidate the new type of molecular recognition accompanied by a global structural change of a molecule upon binding to its targets. Here we investigate the driving force for the binding of R12 (a ribonucleic acid aptamer) and P16 (a partial peptide of a prion protein) during which P16 exhibits the global structural change. We calculate changes in thermodynamic quantities upon the R12-P16 binding using a statistical-mechanical approach combined with molecular models for water which is currently best suited to studies on hydration of biomolecules. The binding is driven by a water-entropy gain originating primarily from an increase in the total volume available to the translational displacement of water molecules in the system. The energy decrease due to the gain of R12-P16 attractive (van der Waals and electrostatic) interactions is almost canceled out by the energy increase related to the loss of R12-water and P16-water attractive interactions. We can explain the general experimental result that stacking of flat moieties, hydrogen bonding and molecular-shape and electrostatic complementarities are frequently observed in the complexes. It is argued that the water-entropy gain is largely influenced by the geometric characteristics (overall shapes, sizes and detailed polyatomic structures) of the biomolecules.

Insertion and release of a solute into and from a vessel comprising biopolymers is a fundamental function in a biological system. A typical example is found in a multidrug efflux transporter. "Multidrug efflux" signifies that solutes such as drug molecules with diverse properties can be handled. In our view, the mechanism of the multidrug efflux is not chemically specific but rather has to be based on a physical factor. In earlier works, we showed that the spatial distribution of the solute-vessel potential of mean force (PMF) induced by the solvent plays imperative roles in the insertion/release process. The PMF can be decomposed into the energetic and entropic components. The entropic component, which originates from the translational displacement of solvent molecules, is rather insensitive to the solute-solvent and vessel inner surface-solvent affinities. This feature is not shared with the energetic component. When the vessel inner surface is neither solvophobic nor solvophilic, the solvents within the vessel cavity and in the bulk offer almost the same environment to any solute with solvophobicity or solvophilicity, and the energetic component becomes much smaller than the entropic component (i.e., the latter predominates over the former). Our idea is that the multidrug efflux can be realized if the insertion/release process is accomplished by the entropic component exhibiting the insensitivity to the solute properties. However, we have recently argued that the entropic release of the solute is not feasible as long as the vessel geometry is fixed. Here we consider a model of TolC, a cylindrical vessel possessing an entrance at one end and an exit at the other end for the solute. The spatial distribution of the PMF is calculated by employing the three-dimensional integral equation theory with rigid-body models in which the constituents interact only through hard-body potentials. Since the behavior of these models is purely entropic in origin, our analysis is focused on the entropic component. We show that the entropically inserted solute can be released by a continuous variation of the vessel geometry which forms a time-dependent entropic force continuing to accelerate the solute motion to the exit. Solutes with a wide range of sizes are entropically released using the same vessel-geometry variation. The results obtained are fairly general and also applicable to the efflux pump protein AcrB and ATP-binding cassette transporter. (C) 2013 AIP Publishing LLC.

It is experimentally known that the heat-denaturation temperature of a protein is raised (i.e., its thermal stability is enhanced) by sugar addition. In earlier works, we proposed a physical picture of thermal denaturation of proteins in which the measure of the thermal stability is defined as the solvent-entropy gain upon protein folding at 298 K normalized by the number of residues. A multipolar-model water was adopted as the solvent. The polyatomic structures of the folded and unfolded states of a protein were taken into account in the atomic detail. A larger value of the measure implies higher thermal stability. First, we show that the measure remains effective even when the model water is replaced by the hard-sphere solvent whose number density and molecular diameter are set at those of real water. The physical picture is then adapted to the elucidation of the effects of sugar addition on the thermal stability of a protein. The water-sugar solution is modeled as a binary mixture of hard spheres. The thermal stability is determined by a complex interplay of the diameter of sugar molecules d(C) and the total packing fraction of the solution eta: d(C) is estimated from the volume per molecule in the sugar crystal and eta is calculated using the experimental data of the solution density. We find that the protein is more stabilized as the sucrose or glucose concentration becomes higher and the stabilization effect is stronger for sucrose than for glucose. These results are in accord with the experimental observations. Using a radial-symmetric integral equation theory and the morphometric approach, we decompose the change in the measure upon sugar addition into two components originating from the protein-solvent pair and protein-solvent many-body correlations, respectively. Each component is further decomposed into the excluded-volume and solvent-accessible-surface terms. These decompositions give physical insights into the microscopic origin of the thermal-stability enhancement by sugar addition. As an example, the higher stability of the native state relative to that of the unfolded state is found to be attributable primarily to an increase in the solvent crowding caused by sugar addition. Due to the hydrophilicity of sugar molecules, the addition of sugar by a larger amount or that with a larger molecular size leads to an increase in eta which is large enough to make the solvent crowding more serious. (C) 2013 AIP Publishing LLC.

Insertion and release of a solute into and from a cylindrical vessel comprising biopolymers is a fundamental function in biological systems. In earlier works, we reported that the solvent-entropy (SE) effect plays imperative roles for insertion. Here we show that release is also achievable by the SE effect: the solute can be moved from an entrance at one end of the vessel to an exit at the other end using a continuous variation of the vessel geometry. Since the SE effect is rather insensitive to the solute-solvent affinity, our result may provide a clue to the 'multidrug efflux' of TolC. (C) 2013 Elsevier B.V. All rights reserved.

In order to clarify the relation between network structure and dynamical phenomena in networks, we investigate the first passage and first return times of a random walker and the response to a boundary perturbation in complex networks. We introduce an efficient calculation method for the first passage time distribution (FPTD) and first return time distribution (FRTD) by introducing a perfectly absorbing node. Using this method, we calculate the FPTD and FRTD in small-world networks and study the relation between these distributions and the characteristics of network structures. We find that the characteristics of the FPTD and FRTD depend on the number of shortcuts in the network, and that the mean first passage time is not determined by the shortest path length alone. We also derive the relation between the FPTD and the complex admittance in boundary perturbation experiments, and show that the Cole-Cole diagram represents characteristic behavior depending on complex networks. The characteristics of the network structure can be understood by performing boundary perturbation experiments.

A protein folds into its native structure with the alpha-helix and/or beta-sheet in aqueous solution under the physiological condition. The relative content of these secondary structures largely varies from protein to protein. However, such structural variability is not exhibited in nonaqueous environment. For example, there is a strong trend that alcohol induces a protein to form alpha-helices, and many of the membrane proteins within the lipid bilayer consists of alpha-helices. Here we investigate the structural stability of proteins in aqueous and nonpolar environments using our recently developed free-energy function F = (Lambda - TS)/(k(B)T(0)) = Lambda/(k(B)T(0)) - S/k(B) (T-0 = 298 K and the absolute temperature T is set at T-0) which is based on statistical thermodynamics. Lambda/(k(B)T(0)) and S/k(B) are the energetic and entropic components, respectively, and k(B) is Boltzmann's constant. A smaller value of the positive quantity, -S, represents higher efficiency of the backbone and side-chain packing promoted by the entropic effect arising from the translational displacement of solvent molecules or the CH2, CH3, and CH groups which constitute nonpolar chains of lipid molecules. As for Lambda, in aqueous solution, a transition to a more compact structure of a protein accompanies the break of protein-solvent hydrogen bonds: As the number of donors and acceptors buried without protein intramolecular hydrogen bonding increases, Lambda becomes higher. In nonpolar solvent, lower Lambda simply implies more intramolecular hydrogen bonds formed. We find the following. The alpha-helix and beta-sheet are advantageous with respect to -S as well as Lambda and to be formed as much as possible. In aqueous solution, the solvent-entropy effect on the structural stability is so strong that the close packing of side chains is dominantly important, and the alpha-helix and beta-sheet contents are judiciously adjusted to accomplish it. In nonpolar solvent, the solvent-entropy effect is substantially weaker than in aqueous solution. Lambda is crucial and the alpha-helix is more stable than the beta-sheet in terms of Lambda, which develops a tendency that alpha-helices are exclusively chosen. For a membrane protein, alpha-helices are stabilized as fundamental structural units for the same reason, but their arrangement is performed through the entropic effect mentioned above. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4755755]

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.

In order to investigate the effects of cycles on the dynamical process on both regular lattices and complex networks, we introduce a finite memory walk (FMW) as an extension of the simple random walk (SRW), in which a walker is prohibited from moving to sites visited during m steps just before the current position. This walk interpolates the simple random walk (SRW), which has no memory (m = 0), and the self-avoiding walk (SAW), which has an infinite memory (m = infinity). We investigate the FMW on regular lattices and clarify the fundamental characteristics of the walk. We find that (1) the mean-square displacement (MSD) of the FMW shows a crossover from the SAW at a short time step to the SRW at a long time step, and the crossover time is approximately equivalent to the number of steps remembered, and that the MSD can be rescaled in terms of the time step and the size of memory; (2) the mean first-return time (MFRT) of the FMW changes significantly at the number of remembered steps that corresponds to the size of the smallest cycle in the regular lattice, where "smallest" indicates that the size of the cycle is the smallest in the network; (3) the relaxation time of the first-return time distribution (FRTD) decreases as the number of cycles increases. We also investigate the FMW on the Watts-Strogatz networks that can generate small-world networks, and show that the clustering coefficient of the Watts-Strogatz network is strongly related to the MFRT of the FMW that can remember two steps.

Insertion of a large solute into an even larger vessel comprising biopolymers followed by release of the same solute from it is one of the important functions sustaining life. As a typical example, an unfolded protein is inserted into a chaperonin from bulk aqueous solution, a cochaperonin acting as a lid is attached to the chaperonin rim and the protein folds into its native structure within the closed cavity, the cochaperonin is detached after the folding is finished, and the folded protein is released back to the bulk solution. On the basis of the experimental observations manifesting that the basic aspects of the protein flux through the chaperonin system is independent of the chaperonin, cochaperonin, and protein species, we adopt a simple model system with which we can cover the whole cycle of the protein flux. We calculate the spatial distribution of the solvent-mediated potential of mean force (PMF) between a spherical solute and a cylindrical vessel or vessel/lid complex. The calculation is performed using the three-dimensional integral equation theory, and the PMF is decomposed into energetic and entropic components. We argue that an unfolded protein with a larger excluded volume (EV) and weak hydrophobicity is entropically inserted into the chaperonin cavity and constrained within a small space almost in its center. The switch from insertion to release is achieved by decreasing the EV and turning the protein surface hydrophilic in the folding process. For this release, in which the energetic component is a requisite, the feature that the chaperonin inner surface in the absence of the cochaperonin is not hydrophilic plays essential roles. On the other hand, the inner surface of the chaperonin/cochaperonin complex is hydrophilic, and the protein is energetically repelled from it: The protein remains constrained within the small space mentioned above without contacting the inner surface for correct folding. The structural and inner-surface properties of the chaperonin or complex are controlled by the adenosine triphosphate (ATP) binding to the chaperonin, hydrolysis of ATP into adenosine diphosphate (ADP) and Pi, and dissociation of ADP and Pi. The function of the chaperonin system is exhibited by synchronizing the chemical cycle of ATP hydrolysis with hydration properties of a protein in the water confined on the scale of a nanometer which are substantially different from those in the bulk water. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3657856]

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.

We propose an efficient method for investigating conformational properties of a polymer in solvent. The method is a combination of a Monte Carlo (MC) simulation applied to the polymer alone and a statistical-thermodynamic approach for incorporating solvent effects. To illustrate it, we analyze conformations of a simple polymer chain stabilized in a hard-sphere solvent. The generation of polymer conformations is performed using the self-avoiding random walk on a cubic lattice. We argue that by introducing the generalized-ensemble techniques to the MC simulation part, the method can be applied to studies on protein conformations in aqueous solution under any thermodynamic condition. (C) 2011 Elsevier B. V. All rights reserved.

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

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.

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

To understand the influence of structure on the function of neural networks, we study the storage capacity and the retrieval time of Hopfield-type neural networks for four network structures: regular, small world, random networks generated by the Watts-Strogatz (WS) model, and the same network as the neural network of the nematode Caenorhabditis elegans. Using computer simulations, we find that (1) as the randomness of network is increased, its storage capacity is enhanced; (2) the retrieval time of WS networks does not depend on the network structure, but the retrieval time of C. elegans's neural network is longer than that of WS networks; (3) the storage capacity of the C. elegans network is smaller than that of networks generated by the WS model, though the neural network of C. elegans is considered to be a small-world network.

We study the subway network system for four cities, i.e., Seoul, Tokyo, Boston and Beijing, by using the global and local efficiencies. It is found that the Seoul subway network has a smaller global and local efficiencies than that of Tokyo. We suggest that the Tokyo subway system is better for an overall distance trip but is not weaker regarding incidents of disconnection. It is also validated for the four subway networks that the global efficiency is inversely proportional to the characteristic length. The Boston and Beijing local efficiencies, that depend on the number of triangular-formed topographic units, are very low and zero, respectively, and this means that these are somewhat deficiently round about routes. Especially, on comparing the characteristic length and the clustering coefficient, the global and local efficiencies seem to be more useful when both the concept of connectivity and length are needed.