Theoretical analysis on thermal stability of a protein focused on the water entropy

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).

Signatures of protein thermal denaturation and local hydrophobicity in domain specific hydration behavior: a comparative molecular dynamics study

We investigate, using atomistic molecular dynamics simulations, the association of surface hydration accompanying local unfolding in the mesophilic protein Yfh1 under a series of thermal conditions spanning its cold and heat denaturation temperatures. The results are benchmarked against the thermally stable protein, Ubq, and behavior at the maximum stability temperature. Local unfolding in Yfh1, predominantly in the beta sheet regions, is in qualitative agreement with recent solution NMR studies; the corresponding Ubq unfolding is not observed. Interestingly, all domains, except for the beta sheet domains of Yfh1, show increased effective surface hydrophobicity with increase in temperature, as reflected by the density fluctuations of the hydration layer. Velocity autocorrelation functions (VACF) of oxygen atoms of water within the hydration layers and the corresponding vibrational density of states (VDOS) are used to characterize alteration in dynamical behavior accompanying the temperature dependent local unfolding. Enhanced caging effects accompanying transverse oscillations of the water molecules are found to occur with the increase in temperature preferentially for the beta sheet domains of Yfh1. Helical domains of both proteins exhibit similar trends in VDOS with changes in temperature. This work demonstrates the existence of key signatures of the local onset of protein thermal denaturation in solvent dynamical behavior.

Mechanism of One-to-Many Molecular Recognition Accompanying Target-Dependent Structure Formation: For the Tumor Suppressor p53 Protein as an Example

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.

Physicochemical origin of high correlation between thermal stability of a protein and its packing efficiency: a theoretical study for staphylococcal nuclease mutants

There is an empirical rule that the thermal stability of a protein is related to the packing efficiency or core volume of the folded state and the protein tends to exhibit higher stability as the backbone and side chains are more closely packed. Previously, the wild type and its nine mutants of staphylococcal nuclease were compared by examining their folded structures. The results obtained were as follows: The stability was not correlated with the number of intramolecular hydrogen bonds, intramolecular electrostatic interaction energy, or degree of burial of the hydrophobic surface; though the empirical rule mentioned above held, it was not the proximate cause of higher stability; and the number of van der Waals contacts N vdW, or equivalently, the intramolecular van der Waals interaction energy was an important factor governing the stability. Here we revisit the wild type and its nine mutants of staphylococcal nuclease using our statistical-mechanical theory for hydration of a protein. A molecular model is employed for water. We show that the pivotal factor is the magnitude of the water-entropy gain upon folding. The gain originates from an increase in the total volume available to the translational displacement of water molecules coexisting with the protein in the system. The magnitude is highly correlated with the denaturation temperature T m. Moreover, the apparent correlation between N vdW and T m as well as the empirical rule is interpretable (i.e., their physicochemical meanings can be clarified) on the basis of the water-entropy effect.

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.

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.

Competitive adsorption on graphite investigated using frequency-modulation atomic force microscopy: interfacial liquid structure controlled by the competition of adsorbed species

The competitive adsorption of long-chain (C18 and C24) carboxylic acids versus n-decanol on graphite was investigated using frequency-modulation atomic force microscopy. A long-range-ordered monolayer of the solute (stearic acid or lignoceric acid) developed in saturated decanol solution, whereas an ordered decanol monolayer was deposited from dilute solutions. The piconewton-order tip-surface force was observed in solutions as a function of the vertical and lateral coordinates, together with the topography of the monolayers. The tip-surface force was periodically modulated, which was interpreted with a solution structure commensurate with the ordered assembly of adsorbed monolayers. These results show that the solution structure at the interface was controlled by the competitively adsorbed species and thus was sensitive to the composition of the bulk solution.

Structural stability of proteins in aqueous and nonpolar environments

A protein folds into its native structure with the α-helix and∕or β-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 β-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 β-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 β-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.

Structural characteristics of yeast F1-ATPase before and after 16-degree rotation of the γ subunit: theoretical analysis focused on the water-entropy effect

We have recently proposed a novel picture of the rotation mechanism for F(1)-ATPase [T. Yoshidome, Y. Ito, M. Ikeguchi, and M. Kinoshita, J. Am. Chem. Soc. 133, 4030 (2011)]. In the picture, the asymmetric packing in F(1)-ATPase, originating from the water-entropy effect, plays the key role in the rotation. Here, we analyze the differences between the experimentally determined structures of yeast F(1)-ATPase before and after 16° rotation of the γ subunit with the emphasis on the water-entropy effect. For each of these structures, we calculate the hydration entropies of three sub-complexes comprising the γ subunit, one of the β subunits, and two α subunits adjacent to them. The β(E), β(TP), and β(DP) subunits are involved in sub-complexes I, II, and III, respectively. The calculation is performed using a hybrid of the angle-dependent integral equation theory combined with the molecular model for water and the morphometric approach. The absolute value of the hydration entropy is in the following order: sub-complex I > sub-complex II > sub-complex III. The packing efficiency of the sub-complex follows the opposite order. The rotation gives rise to less efficient packing in sub-complex III and a corresponding water-entropy loss. However, the other two sub-complexes, accompanying water-entropy gains, become more efficiently packed. These results are consistent with our picture of the rotation mechanism, supporting its validity. The water-entropy analysis shows that the interfaces of α(DP)-β(DP) and α(E)-β(E) become more open after the rotation, which is in accord with the experimental observation.

Physical origin of hydrophobicity studied in terms of cold denaturation of proteins: comparison between water and simple fluids

A clue to the physical origin of the hydrophobicity is in the experimental observations, which show that it is weakened at low temperatures. By considering a solvophobic model protein immersed in water and three species of simple solvents, we analyze the temperature dependence of the changes in free energy, energy, and entropy of the solvent upon protein unfolding. The angle-dependent and radial-symmetric integral equation theories and the morphometric approach are employed in the analysis. Each of the changes is decomposed into two terms, which depend on the excluded volume and on the area and curvature of the solvent-accessible surface, respectively. The excluded-volume term of the entropy change is further decomposed into two components representing the protein-solvent pair correlation and the protein-solvent-solvent triplet and higher-order correlation, respectively. We show that water crowding in the system becomes more serious upon protein unfolding but this effect becomes weaker as the temperature is lowered. If the hydrophobicity originated from the water structuring near a nonpolar solute, it would be strengthened upon lowering of the temperature. Among the three species of simple solvents, considerable weakening of the solvophobicity at low temperatures is observed only for the solvent where the particles interact through a strong attractive potential and the particle size is as small as that of water. Even in the case of this solvent, however, cold denaturation of a protein cannot be reproduced. It would be reproducible if the attractive potential was substantially enhanced, but such enhancement causes the appearance of the metastability limit for a single liquid phase.

Characterization of experimentally determined native-structure models of a protein using energetic and entropic components of free-energy function

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.

Importance of water entropy in rotation mechanism of F1-ATPase

We briefly review our theoretical study on the rotation scheme of F1-ATPase. In the scheme, the key factor is the water entropy which has been shown to drive a variety of self-assembly processes in biological systems. We decompose the crystal structure of F1-ATPase into three sub-complexes each of which is composed of the γ subunit, one of the β subunits, and two α subunits adjacent to them. The βE, βTP, and βDP subunits are involved in the sub-complexes I, II, and III, respectively. We calculate the hydration entropy of each sub-complex using a hybrid of the integral equation theory for molecular liquids and the morphometric approach. It is found that the absolute value of the hydration entropy follows the order, sub-complex I > sub-complex II > sub-complex III. Moreover, the differences are quite large, which manifests highly asymmetrical packing of F1-ATPase. In our picture, this asymmetrical packing plays crucially important roles in the rotation of the γ subunit. We discuss how the rotation is induced by the water-entropy effect coupled with such chemical processes as ATP binding, ATP hydrolysis, and release of the products.

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.

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.