Takashi Yoshidome

Thermodynamics of apoplastocyanin folding: Comparison between experimental and theoretical results

It has been experimentally shown that the folding of apoplastocyanin (apoPC) accompanies a very large enthalpic loss [N. Baden et al., J. Chem. Phys. 127, 175103 (2007)]. This implies that an even larger entropic gain occurs in stabilizing the folded structure to overcome the enthalpic loss. Here, we calculate the water-entropy gain upon the folding of apoPC using the angle-dependent integral equation theory combined with the multipolar water model and the recently developed morphometric approach. It is demonstrated that the calculated value is in quantitatively good accord with the value estimated from the experimental data by accounting for the conformational-entropy loss. According to a prevailing view, the water adjacent to a hydrophobic group is unstable especially in terms of the rotational entropy and the folding is driven primarily by the release of such unfavorable water to the bulk through the burial of nonpolar side chains. We show, however, that the resultant entropic gain is too small to elucidate the experimental result. The great entropic gain observed is ascribed to the reduction in the restriction for the translational motion of water molecules in the whole system.

Molecular mechanism of pressure denaturation of proteins.

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

Rotation Mechanism of F1-ATPase: Crucial Importance of the Water Entropy Effect

We propose a novel picture of the rotation mechanism of F(1)-ATPase, a rotary-motor protein complex. Entropy, which originates from the translational displacement of water molecules, is treated as the key factor in the proposal. We calculate the water entropy gains upon formation of the α-β, α-γ, and β-γ subunit pairs. The gain is given as the difference between the hydration entropy of a subunit pair and the sum of the hydration entropies of the separate subunits forming the pair. The calculation is made using a hybrid of a statistical-mechanical theory for molecular liquids and morphometric approach. The water entropy gain is considered as a measure of tightness of the packing at each subunit interface. The results are highly correlated with the numbers of stable contacts at the subunit interfaces estimated by a molecular dynamics simulation. We also calculate the hydration entropies of three different subcomplexes comprising the γ subunit, one of the β subunits, and two α subunits adjacent to them. The major finding is that the packing in F(1)-ATPase is highly asymmetrical, and this asymmetry is ascribed to the water entropy effect. We discuss how the rotation of the γ subunit is induced by such chemical processes as ATP binding, ATP hydrolysis, and release of the products. In our picture, the asymmetrical packing plays crucially important roles, and the rotation is driven by the water entropy effect.

Effects of side-chain packing on the formation of secondary structures in protein folding.

We have recently shown that protein folding is driven by the water-entropy gain. When the alpha-helix or beta-sheet is formed, the excluded volumes generated by the backbone and side chains overlap, leading to an increase in the total volume available to the translational displacement of water molecules. Primarily by this effect, the water entropy becomes higher. At the same time, the dehydration penalty (i.e., the break of hydrogen bonds with water molecules) is compensated by the formation of intramolecular hydrogen bonds. Hence, these secondary structures are very advantageous units, which are to be formed as much as possible in protein folding. The packing of side chains, which leads to a large increase in the water entropy, is also crucially important. Here we investigate the roles of the side-chain packing in the second structural preference in protein folding. For some proteins we calculate the hydration entropies of a number of structures including the native structure with or without side chains. A hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach is employed in the calculation. Our major findings are as follows. For the structures without side chains, there is an apparent tendency that the water entropy becomes higher as the alpha-helix or beta-sheet content increases. For the structures with side chains, however, a higher content of alpha-helices or beta-sheets does not necessarily lead to larger entropy of water due to the effect of the side-chain packing. The thorough, overall packing of side chains, which gives little space in the interior, is unique to the native structure. To accomplish such specific packing, the alpha-helix and beta-sheet contents are prudently adjusted in protein folding.

A theoretical analysis on characteristics of protein structures induced by cold denaturation

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 et al., 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.

Free‐energy function based on an all‐atom model for proteins

We have developed a free‐energy function based on an all‐atom model for proteins. It comprises two components, the hydration entropy (HE) and the total dehydration penalty (TDP). Upon a transition to a more compact structure, the number of accessible configurations arising from the translational displacement of water molecules in the system increases, leading to a water‐entropy gain. To fully account for this effect, the HE is calculated using a statistical‐mechanical theory applied to a molecular model for water. The TDP corresponds to the sum of the hydration energy and the protein intramolecular energy when a fully extended structure, which possesses the maximum number of hydrogen bonds with water molecules and no intramolecular hydrogen bonds, is chosen as the standard one. When a donor and an acceptor (e.g., N and O, respectively) are buried in the interior after the break of hydrogen bonds with water molecules, if they form an intramolecular hydrogen bond, no penalty is imposed. When a donor or an acceptor is buried with no intramolecular hydrogen bond formed, an energetic penalty is imposed. We examine all the donors and acceptors for backbone‐backbone, backbone‐side chain, and side chain‐side chain intramolecular hydrogen bonds and calculate the TDP. Our free‐energy function has been tested for three different decoy sets. It is better than any other physics‐based or knowledge‐based potential function in terms of the accuracy in discriminating the native fold from misfolded decoys and the achievement of high Z‐scores. Proteins 2009.

Molecular origin of the negative heat capacity of hydrophilic hydration.

The hydrophobic and hydrophilic hydrations are analyzed with the emphasis on the sign of the heat capacity of hydration (HCH). The angle-dependent integral equation theory combined with a multipolar water model is employed in the analysis. The hydration entropy (HE) is decomposed into the translational and orientational parts. It is found that the orientational part governs the temperature dependence of the HE. The orientational part is further decomposed into the solute-water pair correlation component (component 1) and the water reorganization component (component 2). For hydrophilic solutes, components 1 and 2 are negative and positive, respectively. As the temperature becomes higher, component 1 increases while component 2 decreases: They make positive and negative contributions to the HCH, respectively. The strong solute-water electrostatic attractive interactions induce the distortion of water structure near the solute and the break of hydrogen bonds. As the temperature increases, the effect of the attractive interactions becomes smaller and the distortion of water structure is reduced (i.e., more hydrogen bonds are recovered with increasing temperature). The latter effect dominates, leading to negative HCH. During the heat addition the formation of hydrogen bonds, which accompanies heat generation, occurs near the solute. Consequently, the addition of the same amount of heat leads to a larger increase in the thermal energy (or equivalently, in the temperature) than in the case of pure water. The hydrophobic hydration, which is opposite to the hydrophilic hydration in many respects, is also discussed in detail.

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. Proteins 2011;

Effects of heme on the thermal stability of mesophilic and thermophilic cytochromes c: comparison between experimental and theoretical results.

We have recently proposed a measure of the thermal stability of a protein: the water-entropy gain at 25 °C upon folding normalized by the number of residues, which is calculated using a hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach. A protein with a larger value of the measure is thermally more stable. Here we extend the study to analyses on the effects of heme on the thermal stability of four cytochromes c (PA c(551), PH c(552), HT c(552), and AA c(555)) whose denaturation temperatures are considerably different from one another despite that they share significantly high sequence homology and similar three-dimensional folds. The major conclusions are as follows. For all the four cytochromes c, the thermal stability is largely enhanced by the heme binding in terms of the water entropy. For the holo states, the measure is the largest for AA c(555). However, AA c(555) has the lowest packing efficiency of heme and the apo polypeptide with hololike structure, which is unfavorable for the water entropy. The highest stability of AA c(555) is ascribed primarily to the highest efficiency of side-chain packing of the apo polypeptide itself. We argue for all the four cytochromes c that due to covalent heme linkages, the number of accessible conformations of the denatured state is decreased by the steric hindrance of heme, and the conformational-entropy loss upon folding becomes smaller, leading to an enhancement of the thermal stability. As for the apo state modeled as the native structure whose heme is removed, AA c(555) has a much larger value of the measure than the other three. Overall, the theoretical results are quite consistent with the experimental observations (e.g., at 25 °C the α-helix content of the apo state of AA c(555) is almost equal to that of the holo state while almost all helices are collapsed in the apo states of PA c(551), PH c(552), and HT c(552)).

Entropic potential field formed for a linear-motor protein near a filament: Statistical-mechanical analyses using simple models.

We report a new progress in elucidating the mechanism of the unidirectional movement of a linear-motor protein (e.g., myosin) along a filament (e.g., F-actin). The basic concept emphasized here is that a potential field is entropically formed for the protein on the filament immersed in solvent due to the effect of the translational displacement of solvent molecules. The entropic potential field is strongly dependent on geometric features of the protein and the filament, their overall shapes as well as details of the polyatomic structures. The features and the corresponding field are judiciously adjusted by the binding of adenosine triphosphate (ATP) to the protein, hydrolysis of ATP into adenosine diphosphate (ADP)+Pi, and release of Pi and ADP. As the first step, we propose the following physical picture: The potential field formed along the filament for the protein without the binding of ATP or ADP+Pi to it is largely different from that for the protein with the binding, and the directed movement is realized by repeated switches from one of the fields to the other. To illustrate the picture, we analyze the spatial distribution of the entropic potential between a large solute and a large body using the three-dimensional integral equation theory. The solute is modeled as a large hard sphere. Two model filaments are considered as the body: model 1 is a set of one-dimensionally connected large hard spheres and model 2 is a double helical structure formed by two sets of connected large hard spheres. The solute and the filament are immersed in small hard spheres forming the solvent. The major findings are as follows. The solute is strongly confined within a narrow space in contact with the filament. Within the space there are locations with sharply deep local potential minima along the filament, and the distance between two adjacent locations is equal to the diameter of the large spheres constituting the filament. The potential minima form a ringlike domain in model 1 while they form a pointlike one in model 2. We then examine the effects of geometric features of the solute on the amplitudes and asymmetry of the entropic potential field acting on the solute along the filament. A large aspherical solute with a cleft near the solute-filament interface, which mimics the myosin motor domain, is considered in the examination. Thus, the two fields in our physical picture described above are qualitatively reproduced. The factors to be taken into account in further studies are also discussed.