Modified Hamiltonian in FEP Calculations for Reducing the Computational Cost of Electrostatic Interactions.

The free-energy perturbation (FEP) method predicts relative and absolute free-energy changes of biomolecules in solvation and binding with other molecules. FEP is, therefore, one of the most essential tools in in silico drug design. In conventional FEP, to smoothly connect two thermodynamic states, the potential energy is modified as a linear combination of the end-state potential energies by introducing scaling factors. When the particle mesh Ewald is used for electrostatic calculations, conventional FEP requires two reciprocal-space calculations per time step, which largely decreases the computational performance. To overcome this problem, we propose a new FEP scheme by introducing a modified Hamiltonian instead of interpolation of the end-state potential energies. The scheme introduces nonuniform scaling into the electrostatic potential as used in Replica Exchange with Solute Tempering 2 (REST2) and does not require additional reciprocal-space calculations. We tested this modified Hamiltonian in FEP calculations in several biomolecular systems. In all cases, the calculated free-energy changes with the current scheme are in good agreement with those from conventional FEP. The modified Hamiltonian in FEP greatly improves the computational performance, which is particularly marked for large biomolecular systems whose reciprocal-space calculations are the major bottleneck of total computational time.

Encounter complexes and hidden poses of kinase-inhibitor binding on the free-energy landscape.

Modern drug discovery increasingly focuses on the drug-target binding kinetics which depend on drug (un)binding pathways. The conventional molecular dynamics simulation can observe only a few binding events even using the fastest supercomputer. Here, we develop 2D gREST/REUS simulation with enhanced flexibility of the ligand and the protein binding site. Simulation (43 µs in total) applied to an inhibitor binding to c-Src kinase covers 100 binding and unbinding events. On the statistically converged free-energy landscapes, we succeed in predicting the X-ray binding structure, including water positions. Furthermore, we characterize hidden semibound poses and transient encounter complexes on the free-energy landscapes. Regulatory residues distant from the catalytic core are responsible for the initial inhibitor uptake and regulation of subsequent bindings, which was unresolved by experiments. Stabilizing/blocking of either the semibound poses or the encounter complexes can be an effective strategy to optimize drug-target residence time.

Modified Protein-Water Interactions in CHARMM36m for Thermodynamics and Kinetics of Proteins in Dilute and Crowded Solutions.

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, λ = 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 (λ = 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.

Prediction of Protein-Ligand Binding Pose and Affinity Using the gREST+FEP Method.

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.

Population Shift Mechanism for Partial Agonism of AMPA Receptor.

α-amino-3-hydroxy-5-methyl-4-isoaxazolepropionic acid (AMPA) ionotropic glutamate receptors mediate fast excitatory neurotransmission in the central nervous system, and their dysfunction is associated with neurological diseases. Glutamate binding to ligand-binding domains (LBDs) of AMPA receptors induces channel opening in the transmembrane domains of the receptors. The T686A mutation reduces glutamate efficacy so that the glutamate behaves as a partial agonist. The crystal structures of wild-type and mutant LBDs are very similar and cannot account for the observed behavior. To elucidate the molecular mechanism inducing partial agonism of the T686A mutant, we computed the free-energy landscapes governing GluA2 LBD closure using replica-exchange umbrella sampling simulations. A semiclosed state, not observed in crystal structures, appears in the mutant during simulation. In this state, the LBD cleft opens slightly because of breaking of interlobe hydrogen bonds, reducing the efficiency of channel opening. The energy difference between the LBD closed and semiclosed states is small, and transitions between the two states would occur by thermal fluctuations. Evidently, glutamate binding to the T686A mutant induces a population shift from a closed to a semiclosed state, explaining the partial agonism in the AMPA receptor.

De Novo Prediction of Binders and Nonbinders for T4 Lysozyme by gREST Simulations.

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.

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).

A highly efficient hybrid method for calculating the hydration free energy of a protein.

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.

Binding of an RNA aptamer and a partial peptide of a prion protein: crucial importance of water entropy in molecular recognition.

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.

Essential roles of protein-solvent many-body correlation in solvent-entropy effect on protein folding and denaturation: comparison between hard-sphere solvent and water.

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 ß-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.

On the physics of thermal-stability changes upon mutations of a protein.

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.

GENESIS 2.1: High-Performance Molecular Dynamics Software for Enhanced Sampling and Free-Energy Calculations for Atomistic, Coarse-Grained, and Quantum Mechanics/Molecular Mechanics Models.

GENeralized-Ensemble SImulation System (GENESIS) is a molecular dynamics (MD) software developed to simulate the conformational dynamics of a single biomolecule, as well as molecular interactions in large biomolecular assemblies and between multiple biomolecules in cellular environments. To achieve the latter purpose, the earlier versions of GENESIS emphasized high performance in atomistic MD simulations on massively parallel supercomputers, with or without graphics processing units (GPUs). Here, we implemented multiscale MD simulations that include atomistic, coarse-grained, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. They demonstrate high performance and are integrated with enhanced conformational sampling algorithms and free-energy calculations without using external programs except for the QM programs. In this article, we review new functions, molecular models, and other essential features in GENESIS version 2.1 and discuss ongoing developments for future releases.

Effects of sugars on the thermal stability of a protein.

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 dC and the total packing fraction of the solution η: dC is estimated from the volume per molecule in the sugar crystal and η 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 η which is large enough to make the solvent crowding more serious.

On the physics of multidrug efflux through a biomolecular complex.

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.

Structural stability of proteins in aqueous and nonpolar environments.

A protein folds into its native structure with the α-helix and∕or ß-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 α-helices, and many of the membrane proteins within the lipid bilayer consists of α-helices. Here we investigate the structural stability of proteins in aqueous and nonpolar environments using our recently developed free-energy function F = (Λ - TS)∕(k(B)T(0)) = Λ∕(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. Λ∕(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 CH(2), CH(3), and CH groups which constitute nonpolar chains of lipid molecules. As for Λ, 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, Λ becomes higher. In nonpolar solvent, lower Λ simply implies more intramolecular hydrogen bonds formed. We find the following. The α-helix and ß-sheet are advantageous with respect to -S as well as Λ 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 α-helix and ß-sheet contents are judiciously adjusted to accomplish it. In nonpolar solvent, the solvent-entropy effect is substantially weaker than in aqueous solution. Λ is crucial and the α-helix is more stable than the ß-sheet in terms of Λ, which develops a tendency that α-helices are exclusively chosen. For a membrane protein, α-helices are stabilized as fundamental structural units for the same reason, but their arrangement is performed through the entropic effect mentioned above.

Use of multistate Bennett acceptance ratio method for free-energy calculations from enhanced sampling and free-energy perturbation.

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 mbar_analysis, for the four representative cases. The proposed estimations of free-energy changes and thermodynamic averages are effective and useful for various biomolecular systems.

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

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

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

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

Potential of mean force between a large solute and a biomolecular complex: a model analysis on protein flux through chaperonin system.

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.

Unraveling the Coupling between Conformational Changes and Ligand Binding in Ribose Binding Protein Using Multiscale Molecular Dynamics and Free-Energy Calculations.

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.