The role of the concentration scale in the definition of transfer free energies

Concentration Scales and Solvation Thermodynamics: Some Theoretical and Experimental Observations Regarding Spontaneity and the Partition Ratio

The solvation thermodynamics (ST) formalism proposed by A. Ben-Naim is a mathematically rigorous and physically grounded theory for describing properties related to solvation. It considers the solvation process as the transfer of a molecule ("solute") from a fixed position in the ideal gas phase to a fixed position within the solution. Thus, it removes any contribution to the solvation process that is not related to the interactions between this molecule and its environment in the solution. Because ST is based on statistical thermodynamics, the natural variable is number density, which leads to the amount (or "molar") concentration scale. However, this choice of concentration scale is not unique in classical thermodynamics and the solvation properties can be different for commonly used concentration scales. We proposed and performed experiments with diethylamine in a water/hexadecane heterogeneous mixture to confront the predictions of the ST, based on the amount (or "molar") concentration scale, and the Fowler-Guggenheim formalism, based on the mole fraction scale. By means of simple acid-base titration and 1H NMR measurements, it was established that the predictions of differences in the solvation Gibbs energy and the partition ratio (or "partition coefficient") of diethylamine between water and hexadecane are consistent with the ST formalism. Additionally, with current literature data, we have shown additional experimental support for the ST. However, due to the arbitrariness of the relative amount of solvents in the partition ratio, the choice of a single concentration scale within the classical thermodynamics is still not possible.

Reframing the Protein Folding Problem: Entropy as Organizer

It has been a long-standing conviction that a protein's native fold is selected from a vast number of conformers by the optimal constellation of enthalpically favorable interactions. In marked contrast, this Perspective introduces a different mechanism, one that emphasizes conformational entropy as the principal organizer in protein folding while proposing that the conventional view is incomplete. This mechanism stems from the realization that hydrogen bond satisfaction is a thermodynamic necessity. In particular, a backbone hydrogen bond may add little to the stability of the native state, but a completely unsatisfied backbone hydrogen bond would be dramatically destabilizing, shifting the U(nfolded) ⇌ N(ative) equilibrium far to the left. If even a single backbone polar group is satisfied by solvent when unfolded but buried and unsatisfied when folded, that energy penalty alone, approximately +5 kcal/mol, would rival almost the entire free energy of protein stabilization, typically between -5 and -15 kcal/mol under physiological conditions. Consequently, upon folding, buried backbone polar groups must form hydrogen bonds, and they do so by assembling scaffolds of α-helices and/or strands of β-sheet, the only conformers in which, with rare exception, hydrogen bond donors and acceptors are exactly balanced. In addition, only a few thousand viable scaffold topologies are possible for a typical protein domain. This thermodynamic imperative winnows the folding population by culling conformers with unsatisfied hydrogen bonds, thereby reducing the entropy cost of folding. Importantly, conformational restrictions imposed by backbone···backbone hydrogen bonding in the scaffold are sequence-independent, enabling mutation─and thus evolution─without sacrificing the structure.

Molecular Forces in Liquid-Liquid Extraction

The phase transfer of ions is driven by gradients of chemical potentials rather than concentrations alone (i.e., by both the molecular forces and entropy). Extraction is a combination of high-energy interactions that correspond to short-range forces in the first solvation shell such as ion pairing or complexation forces, with supramolecular and nanoscale organization. While the latter are similar to the long-range solvent-averaged interactions in the colloidal world, in solvent extraction they are associated with lower characteristic lengths of the nanometric domain. Modeling of such complex systems is especially complicated because the two domains are coupled, whereas the resulting free energy of extraction is around k_BT to guarantee the reversibility of the practical process. Nevertheless, quantification is possible by considering a partitioning of space among the polar cores, interfacial film, and solvent. The resulting free energy of transfer can be rationalized by utilizing a combination of terms which represent strong complexation energies, counterbalanced by various entropic effects and the confinement of polar solutes in nanodomains dispersed in the diluent, together with interfacial extractant terms. We describe here this ienaics approach in the context of solvent extraction systems; it can also be applied to further complex ionic systems, such as membranes and biological interfaces.

Phase separation of binary mixtures induced by soft centrifugal fields

We use the model system ethanol-dodecane to demonstrate that giant critical fluctuations induced by easily accessible weak centrifugal fields as low as 2000g can be observed above the miscibility gap of a binary liquid mixture. Moreover, several degrees above the phase transition, i.e. in the one-phase region, strong gradients of ethanol concentration occur upon centrifugation. In this case, the standard interpretation of sedimentation equilibrium in the analytical ultracentrifuge (AUC) yields an apparent molar mass of ethanol three orders of magnitude higher than the real value. Notably, these composition gradients have no influence on the distribution gradient of solutes such as dyes like Nile red. The thick opaque interphase formed upon centrifugation does not appear as the commonly observed sharp meniscus, but as a turbidity zone, similar to critical opalescence. This layer is a few millimeters thick and separates two fluids with low compositional gradients. All these effects can be qualitatively understood and explained using the Flory-Huggins solution model coupled to classical density functional theory (DFT). In this domain hetero-phase fluctuations can be triggered by gravity even far from the critical point. Taking into account Jean Perrin's approach to external fields in colloids, a self-consistent definition of the Flory effective volume and an explicit calculation of the total free energy per unit volume is possible.

A minimal predictive model for better formulations of solvent phases with low viscosity

The viscosity increase of the organic phase when liquid–liquid extraction processes are intensified causes difficulties for hydrometallurgical processes on industrial scale. In this work, we have analyzed this problem for the example of N,N-dialkylamides in the presence of uranyl nitrate experimentally. Furthermore, we present a minimal model at nanoscale that allows rationalizing the experimental phenomena by connecting the molecular, mesoscopic and macroscopic scale and that allows predicting qualitative trends in viscosity. This model opens broad possibilities in optimizing constraints and is a further step towards knowledge-based formulation of extracting microemulsions formed by microstructures with low connectivity, even at high load with heavy metals.

A microfluidic study of synergic liquid–liquid extraction of rare earth elements

A membrane based liquid–liquid extraction microfluidic device coupled with X-ray fluorescence enables the first quantification of free energies of transfer dependence for a complex mixture of rare earth elements and iron using synergic extractants.

Multicomponent Model for the Prediction of Nuclear Waste/Rare-Earth Extraction Processes

We develop a minimal model for the prediction of solvent extraction. We consider a rare earth extraction system for which the solvent phase is similar to water-poor microemulsions. All physical molecular quantities used in the calculation can be measured separately. The model takes into account competition complexation, mixing entropy of complexed species, differences of salt concentrations between the two phases, and the surfactant nature of extractant molecules. We consider the practical case where rare earths are extracted from iron nitrates in the presence of acids with a common neutral complexing extractant. The solvent wetting of the reverse aggregates is taken into account via the spontaneous packing. All the water-in-oil reverse aggregates are supposed to be spherical on average. The minimal model captures several features observed in practice: reverse aggregates with different water and extractant content coexist dynamically with monomeric extractant molecules at and above a critical aggregate concentration (CAC). The CAC decreases upon the addition of electrolytes in the aqueous phase. The free energy of transfer of an ion to the organic phase is lower than the driving complexation. The commonly observed log-log relation used to determine the apparent stoichiometry of complexation is valid as a guideline but should be used with care. The results point to the fact that stoichiometry, as well as the probabilities of a particular aggregate, is dependent on the composition of the entire system, namely the extractant and the target solutes' concentrations. Moreover, the experimentally observed dependence of the extraction efficiency on branching of the extractant chains in a given solvent can be quantified. The evolution of the distribution coefficient of particular rare earth, acid, or other different metallic cations can be studied as a function of initial extractant concentration through the whole region that is typically used by chemical engineers. For every chemical species involved in the calculation, the model is able to predict the exact equilibrium concentration in both the aqueous and the solvent phases at a given thermodynamic temperature.

How Osmolytes Counteract Pressure Denaturation on a Molecular Scale

Life in the deep sea exposes enzymes to high hydrostatic pressure, which decreases their stability. For survival, deep sea organisms tend to accumulate various osmolytes, most notably trimethylamine N-oxide used by fish, to counteract pressure denaturation. However, exactly how these osmolytes work remains unclear. Here, a rigorous statistical thermodynamics approach is used to clarify the mechanism of osmoprotection. It is shown that the weak, nonspecific, and dynamic interactions of water and osmolytes with proteins can be characterized only statistically, and that the competition between protein-osmolyte and protein-water interactions is crucial in determining conformational stability. Osmoprotection is driven by a stronger exclusion of osmolytes from the denatured protein than from the native conformation, and water distribution has no significant effect on these changes at low osmolyte concentrations.

TMAO-Protein Preferential Interaction Profile Determines TMAO's Conditional In Vivo Compatibility

Trimethylamine N-oxide (TMAO) exemplifies how Nature uses the solute effect as a simple chemical strategy to cope with hydrodynamic pressure or urea stress to maintain proteostasis. It is a gut-microbe-generated metabolite that strongly promotes the development of atherosclerosis. It remains unclear how TMAO exerts its effects. In this study, we experimentally characterized the profile of the preferential interaction potential of TMAO with proteins, a thermodynamic key to understanding the effects of TMAO on protein processes and the distinction of TMAO among osmolytes. TMAO is thus found to be highly preferentially excluded from most types of protein surface, which explains why TMAO is a strong globular protein stabilizer and identifies the dominant stabilizing factor as the unfavorable interaction of TMAO with the hydrophobic surface exposed upon unfolding. We dissected the mechanism of the counteracting effects of TMAO and urea: the contrary feature of the interaction profiles of the two solutes maximizes the possibility for them to offset each other's perturbing effect on protein processes. The interaction profile also predicts that TMAO promotes aggregation of amyloidogenic intrinsically disordered peptide, as demonstrated here in Aβ42, and that TMAO has a strong potential to impact protein processes in the absence of stressors. Our data suggest that although TMAO is an evolutionally selected chemical chaperone for some organisms or organs, its compatibility in vivo is conditional and determined by its interaction profile with biopolymers and the nature of the essential biopolymer processes. Our thermodynamic framework plus the TMAO-protein interaction profile provides a basis for exploring the broad biological significance of TMAO, including its pathological impact in the absence of stressors. We argue for the general importance of controlling in vivo background solutes and the pathological significance of a control failure.

On Atomistic Models for Molecular Oxygen

Molecular oxygen (O₂) is key to all life on earth, as it is constantly cycled via photosynthesis and cellular respiration. Substantial scientific effort has been devoted to understanding every part of this cycle. Classical molecular dynamics (MD) simulations have been used to study some of the key processes involved in cellular respiration: O₂ permeation through alveolar monolayers and cellular membranes, its binding to hemoglobin during transport in the bloodstream, as well as its transport along optimal pathways toward its reduction sites in proteins. Moreover, MD simulations can help interpret the results of several imaging techniques in which O₂ is used because of its paramagnetic nature. However, despite the widespread use of computational models for the O₂ molecule, their performances have never been systematically evaluated. In this paper, we assess the performances of 14 different models of O₂ available in the literature by calculating four thermodynamic properties: density, heat of vaporization, free energy of hydration, and free energy of solvation in hexadecane. For each property, reliable experimental data are available. Most models perform reasonably well in predicting the correct trends, but they fail to reproduce the experimental data quantitatively. We then develop new models for O₂, with and without a quadrupole moment, and compare their behavior with the behavior of previously published models. The new models show significant improvement in terms of density, heat of vaporization, and free energy of hydration. However, quantitative agreement with water-oil partitioning is not reached due to discrepancies between the calculated and measured free energies of solvation in hexadecane. We suggest that classical pairwise-additive models may be inadequate to properly describe the thermodynamics of solvation of apolar species, such as O₂, in apolar solvents.

Thermodynamic and Structural Evidence for Reduced Hydrogen Bonding among Water Molecules near Small Hydrophobic Solutes

The structure of water molecules near a hydrophobic solute remains elusive despite a long history of scrutiny. Here, we re-examine the subtle issue by a combination of thermodynamic analysis for Henry's constants of several nonpolar gases over a broad range of temperatures and molecular dynamic simulations for the water structure in the hydration shell using several popular semiempirical models of liquid water. Both the structural and thermodynamic data indicate that hydrophobic hydration reduces the degree of the hydrogen bonding among water molecules, and the effect becomes more prominent at high temperatures. Hydrogen-bond formation is slightly hindered near a hydrophobic solute due to the restriction of the degree of freedom for water molecules in the solvation shell, and the confinement effect becomes more significant as temperature increases. Reduction in the extent of hydrogen bonding is fully consistent with a positive contribution of a small hydrophobic solute to the solution heat capacity. As predicted by the scaled-particle theory, both Henry's constants and simulation results suggest that the hydration entropy is determined primarily by cavity formation in liquid water, with its magnitude rising with the solute size but declining with temperature.

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.