Enthalpy−Entropy Contributions to Salt and Osmolyte Effects on Molecular-Scale Hydrophobic Hydration and Interactions

1H-NMR studies on the volume phase transition of DNA-modified pNipmam microgels

DNA functionalized pNipmam microgels, which have recently been introduced, are examined at different concentrations of sodium chloride and in PBS solutions via temperature dependent 1H-NMR measurements and are compared to pure pNipmam microgels. We show that the DNA modification shifts the volume phase transition temperature towards lower temperatures and the addition of salt and PBS further supports this effect in both materials. Thermodynamic values, i.e. enthalpy, entropy and Gibbs free energy, are determined via a non-linear fit which can be applied directly to the measurement data without further linearization.

Relationships between Molecular Structural Order Parameters and Equilibrium Water Dynamics in Aqueous Mixtures

Water's unique thermophysical properties and how it mediates aqueous interactions between solutes have long been interpreted in terms of its collective molecular structure. The seminal work of Errington and Debenedetti [Nature 2001, 409, 318-321] revealed a striking hierarchy of relationships among the thermodynamic, dynamic, and structural properties of water, motivating many efforts to understand (1) what measures of water structure are connected to different experimentally accessible macroscopic responses and (2) how many such structural metrics are adequate to describe the collective structural behavior of water. Diffusivity constitutes a particularly interesting experimentally accessible equilibrium property to investigate such relationships because advanced NMR techniques allow the measurement of bulk and local water dynamics in nanometer proximity to molecules and interfaces, suggesting the enticing possibility of measuring local diffusivities that report on water structure. Here, we apply statistical learning methods to discover persistent structure-dynamic correlations across a variety of simulated aqueous mixtures, from alcohol-water to polypeptoid-water systems. We investigate a variety of molecular water structure metrics and find that an unsupervised statistical learning algorithm (namely, sequential feature selection) identifies only two or three independent structural metrics that are sufficient to predict water self-diffusivity accurately. Surprisingly, the translational diffusivity of water across all mixed systems studied here is strongly correlated with a measure of tetrahedral order given by water's triplet angle distribution. We also identify a separate small number of structural metrics that well predict an important thermodynamic property, the excess chemical potential of an idealized methane-sized hydrophobe in water. Ultimately, we offer a Bayesian method of inferring water structure by using only structure-dynamics linear regression models with experimental Overhauser dynamic nuclear polarization (ODNP) measurements of water self-diffusivity. This study thus quantifies the relationships among several distinct structural order parameters in water and, through statistical learning, reveals the potential to leverage molecular structure to predict fundamental thermophysical properties. In turn, these findings suggest a framework for solving the inverse problem of inferring water's molecular structure using experimental measurements such as ODNP studies that probe local water properties.

Osmolytes: Wonder molecules to combat protein misfolding against stress conditions

The proper functioning of any protein depends on its three dimensional conformation which is achieved by the accurate folding mechanism. Keeping away from the exposed stress conditions leads to cooperative unfolding and sometimes partial folding, forming the structures like protofibrils, fibrils, aggregates, oligomers, etc. leading to several neurodegenerative diseases like Parkinson's disease, Alzheimer's, Cystic fibrosis, Huntington, Marfan syndrome, and also cancers in some cases, too. Hydration of proteins is necessary, which may be achieved by the presence of organic solutes called osmolytes within the cell. Osmolytes belong to different classes in different organisms and play their role by preferential exclusion of osmolytes and preferential hydration of water molecules and achieves the osmotic balance in the cell otherwise it may cause problems like cellular infection, cell shrinkage leading to apoptosis and cell swelling which is also the major injury to the cell. Osmolyte interacts with protein, nucleic acids, intrinsically disordered proteins by non-covalent forces. Stabilizing osmolytes increases the Gibbs free energy of the unfolded protein and decreases that of folded protein and vice versa with denaturants (urea and guanidinium hydrochloride). The efficacy of each osmolyte with the protein is determined by the calculation of m value which reflects its efficiency with protein. Hence osmolytes can be therapeutically considered and used in drugs.

Connecting Non-Gaussian Water Density Fluctuations to the Lengthscale Dependent Crossover in Hydrophobic Hydration

We connect density fluctuations in liquid water to lengthscale dependent crossover in hydrophobic hydration. Specifically, we employ indirect umbrella sampling (INDUS) simulations to characterize density fluctuations in observation volumes of various sizes and shapes in water and as a function of temperature and salt concentration. Consistent with previous observations, density fluctuations are Gaussian in small molecular scale volumes, but they display non-Gaussian "low-density fat tails" in larger volumes. These non-Gaussian tails are indicative of the proximity of water to its liquid to vapor phase transition and have implications on biomolecular interactions and function. We show that the onset of non-Gaussian fluctuations in large volumes is accompanied by the formation of a cavity in the observation volume. We develop a model that uses the physics of cavity-water interface formation as a key ingredient and show that it captures the nature of non-Gaussian density fluctuations over a broad region in water and in salt solutions. We discuss the limitations of this model in the very low density region of the distribution. Our calculations provide new insights into the origins of non-Gaussian density fluctuations in water and their connections to lengthscale dependent crossover in hydrophobic hydration.

Osmolyte enhanced aqueous two-phase system for virus purification

Due to the high variation in viral surface properties, a platform method for virus purification is still lacking. A potential alternative to the high-cost conventional methods is aqueous two-phase systems (ATPSs). However, optimizing virus purification in ATPS requires a large experimental design space, and the optimized systems are generally found to operate at high ATPS component concentrations. The high concentrations capitalize on hydrophobic and electrostatic interactions to obtain high viral particle yields. This study investigated using osmolytes as driving force enhancers to reduce the high concentration of ATPS components while maintaining high yields. The partitioning behavior of porcine parvovirus (PPV), a nonenveloped mammalian virus, and human immunodeficiency virus-like particle (HIV-VLP), a yeast-expressed enveloped VLP, were studied in a polyethylene glycol (PEG) 12 kDa-citrate system. The partitioning of the virus modalities was enhanced by osmoprotectants glycine and betaine, while trimethylamine N-oxide was ineffective for PPV. The increased partitioning to the PEG-rich phase pertained only to viruses, resulting in high virus purification. Recoveries were 100% for infectious PPV and 92% for the HIV-VLP, with high removal of the contaminant proteins and more than 60% DNA removal when glycine was added. The osmolyte-induced ATPS demonstrated a versatile method for virus purification, irrespective of the expression system.

Characterizing the Interplay between Polymer Solvation and Conformation

Conformational transitions of flexible molecules, especially those driven by hydrophobic effects, tend to be hindered by desolvation barriers. For such transitions, it is thus important to characterize and understand the interplay between solvation and conformation. Using specialized molecular simulations, here we perform such a characterization for a hydrophobic polymer solvated in water. We find that an external potential, which unfavorably perturbs the polymer hydration waters, can trigger a coil-to-globule or collapse transition, and that the relative stabilities of the collapsed and extended states can be quantified by the strength of the requisite potential. Our results also provide mechanistic insights into the collapse transition, highlighting that the bottleneck to polymer collapse is the formation of a sufficiently large cluster, and the collective dewetting of such a cluster. We also study the collapse of the hydrophobic polymer in octane, a nonpolar solvent, and interestingly, we find that the mechanistic details of the transition are qualitatively similar to that in water.

Enthalpy and Entropy of Scission in Wormlike Micelles

The free scission energy is the thermodynamic parameter that governs the contour length of wormlike micelles (WLMs). It is the contour length and the propensity to coil and entangle that determine the viscoelastic properties of this commercially important substance class. The free scission energy Δ F_sc and the associated change in enthalpy Δ H_sc and entropy Δ S_sc on scission have been determined for a mixed anionic/zwitterionic surfactant system (sodium laureth sulfate and cocamidopropyl betaine) at various salt concentrations (3-5 wt % NaCl). Both enthalpy Δ H_sc and entropy Δ S_sc changes decrease linearly with increasing NaCl concentration. At NaCl concentrations above 4 wt %, Δ S_sc even adopts negative values. The term TΔ S_sc decreases more rapidly than Δ H_sc around room temperature and causes the observed elongation of WLMs upon addition of NaCl. It is suggested that Δ S_sc is initially positive due to fewer bound counterions per surfactant molecule at end caps compared to the intact, cylindrical parts before scission, leading to a net release of ions upon scission. Negative values of Δ S_sc are attributed to hydrophobic hydration occurring at the end caps at high salt concentrations. ²³Na NMR measurements indicate the presence of immobilized ions, supporting a previously proposed ion-cloud model based on neutron scattering results.

Hydrophobic Hydration and the Effect of NaCl Salt in the Adsorption of Hydrocarbons and Surfactants on Clathrate Hydrates

Adsorption of functional molecules on the surface of hydrates is key in the understanding of hydrate inhibitors. We investigate the adsorption of a hydrocarbon chain, nonionic and ionic surfactants, and ions at the hydrate-aqueous interface. Our results suggest a strong connection between the water ordering around solutes in bulk and the affinity for the hydrates surface. We distinguish two types of water ordering around solutes: (i) hydrophobic hydration where water molecules form a hydrogen bond network similar to clathrate hydrates, and (ii) ionic hydration where water molecules align according to the polarity of an ionic group. The nonionic surfactant and the hydrocarbon chain induce hydrophobic hydration and are favorably adsorbed on the hydrate surface. Adsorption of ions and the ionic headgroups on the hydrate surface is not favorable because ionic hydration and the hydrogen bond structure of hydrates are incompatible. The nonionic surfactant is adsorbed by the headgroup and tail while adsorption of the ionic surfactants is not favorable through the head. Water ordering is analyzed using the hydrogen bond and tetrahedral density profiles as a function of the distance to the chemical groups. The adsorption of solutes is studied through the free energy profiles as a function of the distance to the hydrate surface. Salt lowers the melting temperature of hydrates, disrupts hydrophobic hydration, reduces the solubility of solutes in the aqueous solution, and increases the propensity of solutes to be adsorbed on hydrate surfaces. Our studies are performed by the unbiased and steered molecular dynamics simulations. The results are in line with experiments on the effect of salt and alkanes in hydrate antiagglomeration.

Hofmeister Effect on PNIPAM in Bulk and at an Interface: Surface Partitioning of Weakly Hydrated Anions

The effect of sodium fluoride, sodium trichloroacetate, and sodium thiocyanate on the stability and conformation of poly(N-isopropylacrylamide), in bulk solution and at the gold-aqueous interface, is investigated by differential scanning calorimetry, dynamic light scattering, quartz crystal microbalance, and atomic force microscopy. The results indicate a surface partitioning of the weakly hydrated anions, i.e., thiocyanate and trichloroacetate, and the findings are discussed in terms of anion-induced electrostatic stabilization. Although attractive polymer-ion interactions are suggested for thiocyanate and trichloroacetate, a salting-out effect is found for sodium trichloroacetate. This apparent contradiction is explained by a combination of previously suggested mechanisms for the salting-out effect by weakly hydrated anions.

Effect of salt valency and concentration on structure and thermodynamic behavior of anionic polyelectrolyte Na+-polyethacrylate aqueous solution

The intermolecular structure and solvation enthalpy of anionic polyelectrolyte atactic Na⁺-polyethacrylate (PEA) in aqueous solution, as a function of added salt concentration C _s (dilute to concentrated) and valency (NaCl versus CaCl₂), were investigated via molecular dynamics simulations with explicit-ion-solvent and atomistic polymer description. An increase in C _s leads to a decrease in α, which stabilizes to a constant value beyond critical C _s. A significant reduction in R _g in the presence of CaCl₂ salt was observed, due to ion bridging of PEA by Ca²⁺ ions, in agreement with results available in literature on other similar polycarboxylates. An increase in salt valency reduces the value of critical C _s for the onset of stabilization of the overall size and shape of the polymer chain. The critical C _s ratio for the divalent to monovalent salt case is in excellent agreement with results of Langevin dynamics studies on model systems available in the literature. PEA-water H-bond half-life increases with C _s for CaCl₂, but no appreciable effect is seen for NaCl. The hydration of PEA becomes stronger in the presence of divalent salt. The strength of H-bond interaction energy is greater for cations as compared to anions of the salt. The salt cation effect in displacing water molecules from the vicinity of PEA, with increase in C _s, is greater for NaCl solution. The decrease in water coordination to PEA carboxylate groups, due to increased C _s, is more pronounced in NaCl solution. The nature of the behavior of the solvation enthalpy of PEA and the type of intermolecular interactions contributing to it, is in agreement with experimental observations from the literature. The hydration enthalpy of PEA in divalent CaCl₂ aqueous salt solution is more exothermic compared to monovalent NaCl salt solution, in agreement with experimental data. The solvation of PEA is thermodynamically more favorable in the case of CaCl₂ solution. The exothermic solvation enthalpy, H-bond lifetime, number of H-bonds and H-bond interaction energy are greater in magnitude in CaCl₂ aqueous solution.

Molecular basis of the osmolyte effect on protein stability: a lesson from the mechanical unfolding of lysozyme

Osmolytes are a class of small organic molecules that shift the protein folding equilibrium. For this reason, they are accumulated by organisms under environmental stress and find applications in biotechnology where proteins need to be stabilized or dissolved. However, despite years of research, debate continues over the exact mechanisms underpinning the stabilizing and denaturing effect of osmolytes. Here, we simulated the mechanical denaturation of lysozyme in different solvent conditions to study the molecular mechanism by which two biologically relevant osmolytes, denaturing (urea) and stabilizing (betaine), affect the folding equilibrium. We found that urea interacts favorably with all types of residues via both hydrogen bonds and dispersion forces, and therefore accumulates in a diffuse solvation shell around the protein. This not only provides an enthalpic stabilization of the unfolded state, but also weakens the hydrophobic effect, as hydrophobic forces promote the association of urea with nonpolar residues, facilitating the unfolding. In contrast, we observed that betaine is excluded from the protein backbone and nonpolar side chains, but is accumulated near the basic residues, yielding a nonuniform distribution of betaine molecules at the protein surface. Spatially resolved solvent–protein interaction energies further suggested that betaine behaves in a ligand- rather than solvent-like manner and its exclusion from the protein surface arises mostly from the scarcity of favorable binding sites. Finally, we found that, in the presence of betaine, the reduced ability of water molecules to solvate the protein results in an additional enthalpic contribution to the betaine-induced stabilization.

Salting-Out of Methane in the Aqueous Solutions of Urea and Glycine-Betaine

We have studied the hydrophobic association and solvation of methane molecules in aqueous solutions of urea and glycine betaine (GB). We have calculated the potentials of mean force (PMFs) between methane molecules in water, aqueous GB, aqueous urea and aqueous urea-GB mixtures. The PMFs and equilibrium constants indicate that both urea and GB increase the hydrophobic association of methane. Calculation of thermodynamic parameters shows that the association of methane is stabilized by entropy whereas solvation is favored by enthalpy. In the case of the water-urea-GB mixture, both hydrophobic association and solvation are stabilized by entropy. From the investigation of radial distribution functions, running coordination numbers and excess coordination numbers, we infer that both urea and GB are preferentially excluded from methane surface in the mixtures of osmolytes and methane is preferentially solvated by water molecules in all the mixtures. The favorable exclusion of both urea and GB from the methane surface suggests that both urea and GB increase the interaction between methane molecules, i.e., salting-out of methane. We observe that addition of both urea and GB to water enhances local water structure. The calculated values of diffusion constants of water also suggest enhanced water-water interactions in the presence of urea and GB. The calculated free energies of methane in these mixtures show that methane is less soluble in the mixtures of urea and GB than in water. The data on solvation free energies support the observations obtained from the PMFs of methane molecules.

Ion-specific induced fluctuations and free energetics of aqueous protein hydrophobic interfaces: toward connecting to specific-ion behaviors at aqueous liquid-vapor interfaces

We explore anion-induced interface fluctuations near protein-water interfaces using coarse-grained representations of interfaces as proposed by Willard and Chandler ( J. Phys. Chem. B 2010 , 114 , 1954 - 1958 ). We use umbrella sampling molecular dynamics to compute potentials of mean force along a reaction coordinate bridging the state where the anion is fully solvated and one where it is biased via harmonic restraints to remain at the protein-water interface. Specifically, we focus on fluctuations of an interface between water and a hydrophobic region of hydrophobin-II (HFBII), a 71 amino acid residue protein expressed by filamentous fungi and known for its ability to form hydrophobically mediated self-assemblies at interfaces such as a water/air interface. We consider the anions chloride and iodide that have been shown previously by simulations as displaying specific-ion behaviors at aqueous liquid-vapor interfaces. We find that as in the case of a pure liquid-vapor interface, at the hydrophobic protein-water interface, the larger, less charge-dense iodide anion displays a marginal interfacial stability compared with that of the smaller, more charge-dense chloride anion. Furthermore, consistent with the results at aqueous liquid-vapor interfaces, we find that iodide induces larger fluctuations of the protein-water interface than chloride.

Solute's perspective on how trimethylamine oxide, urea, and guanidine hydrochloride affect water's hydrogen bonding ability

While the thermodynamic effects of trimethylamine oxide (TMAO), urea, and guanidine hydrochloride (GdnHCl) on protein stability are well understood, the underlying mechanisms of action are less well characterized and, in some cases, even under debate. Herein, we employ the stretching vibration of two infrared (IR) reporters, i.e., nitrile (C≡N) and carbonyl (C═O), to directly probe how these cosolvents mediate the ability of water to form hydrogen bonds with the solute of interest, e.g., a peptide. Our results show that these three agents, despite having different effects on protein stability, all act to decrease the strength of the hydrogen bonds formed between water and the infrared probe. While the behavior of TMAO appears to be consistent with its protein-protecting ability, those of urea and GdnHCl are inconsistent with their role as protein denaturants. The latter is of particular interest as it provides strong evidence indicating that although urea and GdnHCl can perturb the hydrogen-bonding property of water their protein-denaturing ability does not arise from a simple indirect mechanism.

Free energetics of carbon nanotube association in pure and aqueous ionic solutions

Carbon nanotubes are a promising platform across a broad spectrum of applications ranging from separations technology, drug delivery, to bio(electronic) sensors. Proper dispersion of carbon nanotube materials is important to retaining the electronic properties of nanotubes. Experimentally it has been shown that salts can regulate the dispersing properties of CNTs in aqueous system with surfactants (Niyogi, S.; Densmore, C. G.; Doorn, S. K. J. Am. Chem. Soc.2009, 131, 1144-1153); details of the physicochemical mechanisms underlying such effects continue to be explored. We address the effects of inorganic monovalent salts (NaCl and NaI) on dispersion stability of carbon nanotubes.We perform all-atom molecular dynamics simulations using nonpolarizable interaction models to compute the potential of mean force between two (10,10) single-walled carbon nanotubes (SWNTs) in the presence of NaCl/NaI and compare to the potential of mean force between SWNTs in pure water. Addition of salts enhances stability of the contact state between two SWNT's on the order of 4 kcal/mol. The ion-specific spatial distribution of different halide anions gives rise to starkly different contributions to the free energy stability of nanotubes in the contact state. Iodide anion directly stabilizes the contact state to a much greater extent than chloride anion. The enhanced stability arises from the locally repulsive forces imposed on nanotubes by the surface-segregated iodide anion. Within the time scale of our simulations, both NaI and NaCl solutions stabilize the contact state by equivalent amounts. The marginally higher stability for contact state in salt solutions recapitulates results for small hydrophobic solutes in NaCl solutions (Athawale, M. V.; Sarupria, S.; Garde, S. J. Phys. Chem. B2008, 112, 5661-5670) as well as single-walled carbon nanotubes in NaCl and CaCl2 aqueous solutions.

Structural adaptation of extreme halophilic proteins through decrease of conserved hydrophobic contact surface

Background

Halophiles are extremophilic microorganisms growing optimally at high salt concentrations. There are two strategies used by halophiles to maintain proper osmotic pressure in their cytoplasm: accumulation of molar concentrations of potassium and chloride with extensive adaptation of the intracellular macromolecules ("salt-in" strategy) or biosynthesis and/or accumulation of organic osmotic solutes ("osmolyte" strategy). Our work was aimed at contributing to the understanding of the shared molecular mechanisms of protein haloadaptation through a detailed and systematic comparison of a sample of several three-dimensional structures of halophilic and non-halophilic proteins. Structural differences observed between the "salt-in" and the mesophilic homologous proteins were contrasted to those observed between the "osmolyte" and mesophilic pairs.

Results

The results suggest that haloadaptation strategy in the presence of molar salt concentration, but not of osmolytes, necessitates a weakening of the hydrophobic interactions, in particular at the level of conserved hydrophobic contacts. Weakening of these interactions counterbalances their strengthening by the presence of salts in solution and may help the structure preventing aggregation and/or loss of function in hypersaline environments.

Conclusions

Considering the significant increase of biotechnology applications of halophiles, the understanding of halophilicity can provide the theoretical basis for the engineering of proteins of great interest because stable at concentrations of salts that cause the denaturation or aggregation of the majority of macromolecules.

Extended surfaces modulate hydrophobic interactions of neighboring solutes

Interfaces are a most common motif in complex systems. To understand how the presence of interfaces affects hydrophobic phenomena, we use molecular simulations and theory to study hydration of solutes at interfaces. The solutes range in size from subnanometer to a few nanometers. The interfaces are self-assembled monolayers with a range of chemistries, from hydrophilic to hydrophobic. We show that the driving force for assembly in the vicinity of a hydrophobic surface is weaker than that in bulk water and decreases with increasing temperature, in contrast to that in the bulk. We explain these distinct features in terms of an interplay between interfacial fluctuations and excluded volume effects--the physics encoded in Lum-Chandler-Weeks theory [Lum K, Chandler D, Weeks JD (1999) J Phys Chem B 103:4570-4577]. Our results suggest a catalytic role for hydrophobic interfaces in the unfolding of proteins, for example, in the interior of chaperonins and in amyloid formation.

Raman spectroscopic signatures of noncovalent interactions between trimethylamine N-oxide (TMAO) and water

The effects of hydration on vibrational normal modes of trimethylamine N-oxide (TMAO) are investigated by Raman spectroscopy and electronic structure computations. Microsolvated networks of water are observed to induce either red or blue shifts in the normal modes of TMAO with increasing water concentration and to also exhibit distinct spectral signatures. By taking advantage of the selective and gradual nature of the water-induced shifts and using comparisons to theoretical predictions, the assignments of TMAO's normal modes are re-examined and the structure of the hydrogen-bonded network in the vicinity of TMAO is elucidated. Agreement between experiment and theory suggests that the oxygen atom in TMAO accepts on average at least three hydrogen bonds from neighboring water molecules and that water molecules are likely not directly interacting with TMAO's methyl groups.

Effects of ionic strength on SAXS data for proteins revealed by molecular dynamics simulations

The combination of small-angle X-ray solution scattering (SAXS) experiments and molecular dynamics (MD) simulations is now becoming a powerful tool to study protein conformations in solution at an atomic resolution. In this study, we investigated effects of ionic strength on SAXS data theoretically by using MD simulations of hen egg white lysozyme at various NaCl concentrations from 0 to 1 M. The calculated SAXS excess intensities showed a significant dependence on ion concentration, which originates from the different solvent density distributions in the presence and absence of ions. The addition of ions induced a slow convergence of the SAXS data, and a ∼20 ns simulation is required to obtain convergence of the SAXS data with the presence of ions whereas only a 0.2 ns simulation is sufficient in the absence of ions. To circumvent the problem of the slow convergence in the presence of ions, we developed a novel method that reproduces the SAXS excess intensities with the presence of ions from short MD trajectories in pure water. By applying this method to SAXS data for the open and closed forms of transferrin at 1 M ion concentration, the correct form could be identified by simply using short MD simulations of the protein in pure water for 0.2 ns.

Salt effects on surface-tethered peptides in solution

The capability to manipulate proteins/peptide fragments at liquid-solid interfaces has led to tremendous applications in detectors and biotechnology. Therefore, understanding the detailed molecular behavior of proteins and peptides tethered on a hard material surface is an interesting and important topic. The inhomogeneity presented by surfaces as well as ions in the solution plays an important role in the thermodynamics and kinetics of the tethered proteins. In this study, we perform a series of molecular dynamics simulations of a pentapeptide RHSVV, a p53 epitope, tethered on a prepared microarray surface in various salt concentrations (0, 0.14, 0.5, and 1 M NaCl), as well as free in ionic solution (0, 0.5, and 1 M). The conformational space the tethered peptide visits largely overlaps with the free peptide in solution. However, surface tethering as well as the salt concentration changes both the thermodynamics and kinetics of the peptide. Frequent conformational changes are observed during the simulations and tend to be slowed down by both increasing the salt concentration and surface tethering. The local composition of ions at different salt concentrations is also compared between the tethered and free peptide.

Thermodynamics of a conformational change using a random walk in energy-reaction coordinate space: Application to methane dimer hydrophobic interactions

A random walk sampling algorithm allows the extraction of the density of states distribution in energy-reaction coordinate space. As a result, the temperature dependences of thermodynamic quantities such as relative energy, entropy, and heat capacity can be calculated using first-principles statistical mechanics. The strategies for optimal convergence of the algorithm and control of its accuracy are proposed. We show that the saturation of the error [Q. Yan and J. J. de Pablo, Phys. Rev. Lett. 90, 035701 (2003); E. Belardinelli and V. D. Pereyra, J. Chem. Phys. 127, 184105 (2007)] is due to the use of histogram flatness as a criterion of convergence. An application of the algorithm to methane dimer hydrophobic interactions is presented. We obtained a quantitatively accurate energy-entropy decomposition of the methane dimer cavity potential. The presented results confirm the previous results, and they provide new information regarding the thermodynamics of hydrophobic interactions. We show that the finite-difference approximation, which is widely used in molecular dynamic simulations for the energy-entropy decomposition of a free energy potential, can lead to a significant error.