Theoretical analysis on changes in thermodynamic quantities upon protein folding: Essential role of hydration

Towards a universal method for calculating hydration free energies: a 3D reference interaction site model with partial molar volume correction

We report a simple universal method to systematically improve the accuracy of hydration free energies calculated using an integral equation theory of molecular liquids, the 3D reference interaction site model. A strong linear correlation is observed between the difference of the experimental and (uncorrected) calculated hydration free energies and the calculated partial molar volume for a data set of 185 neutral organic molecules from different chemical classes. By using the partial molar volume as a linear empirical correction to the calculated hydration free energy, we obtain predictions of hydration free energies in excellent agreement with experiment (R = 0.94, σ = 0.99 kcal mol (- 1) for a test set of 120 organic molecules).

Association thermodynamics and conformational stability of beta-sheet amyloid beta(17-42) oligomers: effects of E22Q (Dutch) mutation and charge neutralization

Amyloid fibrils are associated with many neurodegenerative diseases. It was found that amyloidogenic oligomers, not mature fibrils, are neurotoxic agents related to these diseases. Molecular mechanisms of infectivity, pathways of aggregation, and molecular structure of these oligomers remain elusive. Here, we use all-atom molecular dynamics, molecular mechanics combined with solvation analysis by statistical-mechanical, three-dimensional molecular theory of solvation (also known as 3D-RISM-KH) in a new MM-3D-RISM-KH method to study conformational stability, and association thermodynamics of small wild-type Abeta(17-42) oligomers with different protonation states of Glu(22), as well the E22Q (Dutch) mutants. The association free energy of small beta-sheet oligomers shows near-linear trend with the dimers being thermodynamically more stable relative to the larger constructs. The linear (within statistical uncertainty) dependence of the association free energy on complex size is a consequence of the unilateral stacking of monomers in the beta-sheet oligomers. The charge reduction of the wild-type Abeta(17-42) oligomers upon protonation of the solvent-exposed Glu(22) at acidic conditions results in lowering the association free energy compared to the wild-type oligomers at neutral pH and the E22Q mutants. The neutralization of the peptides because of the E22Q mutation only marginally affects the association free energy, with the reduction of the direct electrostatic interactions mostly compensated by the unfavorable electrostatic solvation effects. For the wild-type oligomers at acidic conditions such compensation is not complete, and the electrostatic interactions, along with the gas-phase nonpolar energetic and the overall entropic effects, contribute to the lowering of the association free energy. The differences in the association thermodynamics between the wild-type Abeta(17-42) oligomers at neutral pH and the Dutch mutants, on the one hand, and the Abeta(17-42) oligomers with protonated Glu(22), on the other, may be explained by destabilization of the inter- and intrapeptide salt bridges between Asp(23) and Lys(28). Peculiarities in the conformational stability and the association thermodynamics for the different models of the Abeta(17-42) oligomers are rationalized based on the analysis of the local physical interactions and the microscopic solvation structure.

The behavior of ions near a charged wall-dependence on ion size, concentration, and surface charge

A renormalization of the 3D-RISM-HNC integral equation is used to study the solvent and ion distributions at neutral and negatively charged planar atomistic surfaces. The charge density of the surfaces ranged from 0.0 to 0.4116 C/m(2), and the modeled electrolyte solutions consist of the salts NaCl, KCl, and CsCl at concentrations of 0.1, 0.25, and 1.0 M in SPC/E water. The results are qualitatively compared to the results from other integral equation methods and simulations for similar models. We find that the 3D-IEs predict an electric multilayer screening behavior in the solvent and ion distributions in contrast to the double layer anticipated from Poisson-Boltzmann theory. It is observed that the cation size has a significant effect on the distributions near the surface up to three solvation layers beyond which the behavior is the same among the different cations. The response of the distributions to the charged surface is described as an increase in ion and solvent density near the wall. The higher concentration solutions screen the electrostatic source more strongly at the wall as expected. The importance of ion-solvent and ion-ion correlations near the surface is shown through three-body correlation functions which are obtainable from the 3D-IEs in this study.

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.

Molecular thermodynamics of trifluoroethanol-induced helix formation: analysis of the solvation structure and free energy by the 3D-RISM theory

It has been shown that trifluoroethanol (TFE) induces helical structure in peptides and proteins. The molecular mechanism is, however, still not completely elucidated. In this study, the TFE effects on the solvation structure and on the free energy change associated with the helix-coil transition of a polypeptide are analyzed by using the three-dimensional reference interaction site model (3D-RISM) molecular theory of solvation. The theoretical result shows that TFE preferentially solvates at low concentrations around 30 vol% both for the helix and coil structures. However, the characteristic preferential solvation is not as significant in the TFE-induced helix stabilization as generally considered. It is also found that the overall energy contributes to the free energy difference more substantially than the solvation entropy.

Pressure effects on structures formed by entropically driven self-assembly: illustration for denaturation of proteins

We propose a general framework of pressure effects on the structures formed by the self-assembly of solute molecules immersed in solvent. The integral equation theory combined with the morphometric approach is employed for a hard-body model system. Our picture is that protein folding and ordered association of proteins are driven by the solvent entropy: At low pressures, the structures almost minimizing the excluded volume (EV) generated for solvent particles are stabilized. Such structures appear to be even more stabilized at high pressures. However, it is experimentally known that the native structure of a protein is unfolded, and ordered aggregates such as amyloid fibrils and actin filaments are dissociated by applying high pressures. This initially puzzling result can also be elucidated in terms of the solvent entropy. A clue to the basic mechanism is in the phenomenon that, when a large hard-sphere solute is immersed in small hard spheres forming the solvent, the small hard spheres are enriched near the solute and this enrichment becomes greater as the pressure increases. We argue that "attraction" is entropically provided between the solute surface and solvent particles, and the attraction becomes higher with rising pressure. Due to this effect, at high pressures, the structures possessing the largest possible solvent-accessible surface area together with sufficiently small EV become more stable in terms of the solvent entropy. To illustrate this concept, we perform an analysis of pressure denaturation of three different proteins. It is shown that only the structures that have the characteristics described above exhibit interesting behavior. They first become more destabilized relative to the native structure as the pressure increases, but beyond a threshold pressure the relative instability begins to decrease and they eventually become more stable than the native structure.

Incorporating dipolar solvents with variable density in Poisson-Boltzmann electrostatics

We describe a new way to calculate the electrostatic properties of macromolecules that goes beyond the classical Poisson-Boltzmann treatment with only a small extra CPU cost. The solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. The method effectively unifies both the Poisson-centric view and the Langevin Dipole model. The model results in a variable dielectric constant epsilon(r) in the solvent region and also in a variable solvent density rho(r) that depends on the nature of the closest exposed solute atoms. The model was calibrated using small molecules and ions solvation data with only two adjustable parameters, namely the size and dipolar moment of the solvent. Hydrophobicity scales derived from the solvent density profiles agree very well with independently derived hydrophobicity scales, both at the atomic or residue level. Dimerization interfaces in homodimeric proteins or lipid-binding regions in membrane proteins clearly appear as poorly solvated patches on the solute accessible surface. Comparison of the thermally averaged solvent density of this model with the one derived from molecular dynamics simulations shows qualitative agreement on a coarse-grained level. Because this calculation is much more rapid than that from molecular dynamics, applications of a density-profile-based solvation energy to the identification of the true structure among a set of decoys become computationally feasible. Various possible improvements of the model are discussed, as well as extensions of the formalism to treat mixtures of dipolar solvents of different sizes.

When cells lose water: Lessons from biophysics and molecular biology

Organisms living in deserts and anhydrobiotic species are useful models for unraveling mechanisms used to overcome water loss. In this context, late embryogenesis abundant (LEA) proteins and sugars have been extensively studied for protection against desiccation stress and desiccation tolerance. This article aims to reappraise the current understanding of these molecules by focusing on converging contributions from biochemistry, molecular biology, and the use of biophysical tools. Such tools have greatly advanced the field by uncovering intriguing aspects of protein 3-D structure, such as folding upon stress. We summarize the current research on cellular responses against water deficit at the molecular level, considering both plausible water loss-sensing mechanisms and genes governing signal transduction pathways. Finally, we propose models that could guide future experimentation, for example, by concentrating on the behavior of selected proteins in living cells.

An Integral Equation Study of the Hydrophobic Interaction between Graphene Plates

The hydrophobic association of two parallel graphene sheets is studied using the 3D-RISM HNC integral equations with several theoretical methods for the solvent distribution functions. The potential of mean force is calculated to study the effects of the aqueous solvent models and methods on the plates as a function of distance. The results of several integral equations (IE) are compared to MD simulations for the same model. The 3D-IEs are able to qualitatively reproduce the nature of the solvent effects on the potential of mean force but not quantitatively. The local minima in the potential of mean force occur at distances allowing well defined layers of solvent between the plates but are not coincident with those found in simulation of the same potential regardless of the theoretical methods tested here. The dewetting or drying transition between the plates is generally incorrectly dependent on steric effects with these methods even for very hydrophobic systems without solute-solvent attractions, in contradiction with simulation.

Hydration effects on the HET-s prion and amyloid-beta fibrillous aggregates, studied with three-dimensional molecular theory of solvation

We study the thermodynamic properties of the experimental fragments of the amyloid fibril made of the HET-s prion proteins (the infectious element of the filamentous fungus Podospora anserina) and of amyloid-beta proteins (the major component of Alzheimer's disease-associated plaques) by using the three-dimensional molecular theory of solvation. The full quantitative picture of hydration effects, including the hydration thermodynamics and hydration structure around the fragments, is presented. For both the complexes, the hydration entropic effects dominate, which results in the entropic part offsetting the unfavorable energetic part of the free energy change upon the association. This is in accord with the fact that the hydrophobic cooperativity plays an essential role in the formation of amyloid fibrils. By calculating the partial molar volume of the proteins, we found that the volume change upon the association in both the systems is large and positive, with the implication that high pressure causes destabilization of the fibril. This observation is in good agreement with the recent experimental results. We also found that both the HET-s and amyloid-beta pentamers have loose intermolecular packing with voids. The three-dimensional molecular theory of solvation predicts that water molecules can be locked in the interior cavities along the fibril axis for both the HET-s and amyloid-beta proteins. We provide a detailed molecular picture of the structural water localized in the interior of the fibrils. Our results suggest that the interior hydration plays an important role in the structural stability of fibrils.

Comparison of DNA hydration patterns obtained using two distinct computational methods, molecular dynamics simulation and three-dimensional reference interaction site model theory

Because proteins and DNA interact with each other and with various small molecules in the presence of water molecules, we cannot ignore their hydration when discussing their structural and energetic properties. Although high-resolution crystal structure analyses have given us a view of tightly bound water molecules on their surface, the structural data are still insufficient to capture the detailed configurations of water molecules around the surface of these biomolecules. Thanks to the invention of various computational algorithms, computer simulations can now provide an atomic view of hydration. Here, we describe the apparent patterns of DNA hydration calculated by using two different computational methods: Molecular dynamics (MD) simulation and three-dimensional reference interaction site model (3D-RISM) theory. Both methods are promising for obtaining hydration properties, but until now there have been no thorough comparisons of the calculated three-dimensional distributions of hydrating water. This rigorous comparison showed that MD and 3D-RISM provide essentially similar hydration patterns when there is sufficient sampling time for MD and a sufficient number of conformations to describe molecular flexibility for 3D-RISM. This suggests that these two computational methods can be used to complement one another when evaluating the reliability of the calculated hydration patterns.

Folding domain B of protein A on a dynamically partitioned free energy landscape

The B domain of staphylococcal protein A (BdpA) is a small helical protein that has been studied intensively in kinetics experiments and detailed computer simulations that include explicit water. The simulations indicate that BdpA needs to reorganize in crossing the transition barrier to facilitate folding its C-terminal helix (H3) onto the nucleus formed from helices H1 and H2. This process suggests frustration between two partially ordered forms of the protein, but recent varphi value measurements indicate that the transition structure is relatively constant over a broad range of temperatures. Here we develop a simplistic model to investigate the folding transition in which properties of the free energy landscape can be quantitatively compared with experimental data. The model is a continuation of the Muñoz-Eaton model to include the intermittency of contacts between structured parts of the protein, and the results compare variations in the landscape with denaturant and temperature to varphi value measurements and chevron plots of the kinetic rates. The topography of the model landscape (in particular, the feature of frustration) is consistent with detailed simulations even though variations in the varphi values are close to measured values. The transition barrier is smaller than indicated by the chevron data, but it agrees in order of magnitude with a similar alpha-carbon type of model. Discrepancies with the chevron plots are investigated from the point of view of solvent effects, and an approach is suggested to account for solvent participation in the model.