Preferential Solvation: Dividing Surface vs Excess Numbers

Unifying sorption isotherms in reversed-phase liquid chromatography

The use of adsorption isotherm models has contributed to understanding retention in chromatography. However, the common isotherm models (such as Langmuir, BET, and GAB) assume site-specific, layer-by-layer adsorption on a uniform surface, which is at odds with the reality of chromatographic interfaces (heterogeneous surfaces with sorbate mobility and adsorption-partitioning duality). Our goal is to clarify the interactions underlying chromatographic retention while overcoming the above contradiction caused by the overly idealized or unrealistic assumptions of the traditional isotherm models. This can be achieved by the statistical thermodynamic fluctuation theory and the ABC isotherm derived from it, which is capable not only of capturing the mono-, di-, and tri-sorbate interactions as its parameters but also of encompassing the Langmuir, BET, GAB, and even anti-Langmuir isotherm models as its special cases. We demonstrate how the parameters from the traditional models can be reinterpreted via sorbate interactions. The sorbate-sorbate interaction plays a key role in elucidating the origin of different IUPAC isotherm types: Type I (convex upward) and Type III (convex downward) represent the opposite end of sorbate-sorbate repulsion and attraction that are independent of sorbate concentration, whereas Type II lies in-between, in which sorbate-sorbate interaction, which is repulsive at low concentration, turns attractive once sufficient quantity of sorbate is present at the interface (convex upward to convex downward).

Lysozyme in Mixtures of Hydrogen Bond Acceptor Solvents with Water: Enthalpies and Entropies of Preferential Solvation

The main focus of this work is to clarify how enzyme macromolecules become solvated in water-organic mixtures and to estimate the enthalpies and entropies of this solvation process. Isothermal calorimetry and water/organic solvent adsorption measurements were used to investigate the preferential solvation of hen egg white lysozyme in hydrogen bond acceptor solvents at 298.15 K. Dimethyl sulfoxide, N,N-dimethylformamide, acetonitrile, 1,4-dioxane, and acetone were used as model organic cosolvents. Preferential solvation was described by analyzing the excess thermodynamic functions of the mixing. The novelty of this approach is that the enthalpies and entropies of protein, water, and organic solvents can be simultaneously investigated across the entire range of water content. There are three composition regimes in water-organic mixtures. Stabilization of the protein as a result of the preferential hydration of lysozyme was detected in the water-rich region. Protein stabilization is driven by the positive change in entropy. The residual enzyme activity values are close to 100%, compared with those for pure water. In the intermediate region, lysozyme has a higher affinity for organic solvent molecules than for water. The cosolvent-induced inactivation of lysozyme was detected at intermediate water content, and residual enzyme activity is close to zero. At the lowest water content, the cosolvent molecules are preferentially excluded from the protein surface, resulting in preferential hydration and nonzero residual enzyme activity. In the water-poor region, protein stabilization is driven by the exothermic enthalpy change. The present study clearly demonstrates that the preferential solvation thermodynamic quantities strongly depend on the acceptance strength of the cosolvent hydrogen bond.

Gas and Liquid Isotherms: The Need for a Common Foundation

Sorption isotherms for gases and liquids have long been formulated separately. There is a fundamental problem with this approach: the popular isotherm models (such as Langmuir, BET, and GAB) for gases cannot be applied straightforwardly to sorption from solution. This contrasts with the theory of liquid solutions, where solute-solute interaction, mediated by the solvent, is captured as the potential of mean force, providing powerful interpretive tools (e.g., virial expansion) founded on the gas-liquid analogy. This analogy will be extended to sorption by adopting sorbate numbers and their fluctuations as the common foundation. This enables the gas and liquid isotherm equations to have an analogous mathematical form with a universal language for interfaces and liquid solutions.

Molecular dynamics and solvation structures of the β-glucosidase from Humicola insolens (BGHI) in aqueous solutions containing glucose

The β-glucosidase enzyme is a glycosyl hydrolase that breaks down the β-1,4 linkage of cellobiose. It is inhibited by glucose at high concentrations due to competitive inhibition. However, at lower glucose concentrations, the glucose-tolerant β-glucosidase from Humicola insolens (BGHI) undergoes stimulation. Proteins, in aqueous sugar solutions, tend to be preferentially hydrated, which generally promotes their stabilization. Thus, solvation phenomena may contribute to both glucose tolerance and stimulation processes. We have performed atomistic classical Molecular Dynamics (MD) simulations of BGHI at different glucose concentrations to mimic the conditions found in the catalytic experiments. A detailed examination of the solvent environment through the calculation of minimum distance distribution functions (MDDFs) and Kirkwood-Buff (KB) integrals was performed. The enzyme is preferentially hydrated in the presence of glucose at all concentrations. Nevertheless, the hydration does not prevent the glucose from directly interacting with the BGHI surface or from entering the active site. Based on the obtained results, we hypothesize that preferential hydration is beneficial for enzyme activity. At the same time, product inhibition has little effect at lower concentrations of glucose, and at higher glucose concentrations, competition for the active site becomes predominant and the enzyme is primarily inhibited.

Understanding the relationship between preferential interactions of peptides in water-acetonitrile mixtures with protein-solvent contact surface area

The influence of polar, water-miscible organic solvents (POS) on protein structure, stability, and functional activity is a subject of significant interest and complexity. This study examines the effects of acetonitrile (ACN), a semipolar, aprotic solvent, on the solvation properties of blocked Ace-Gly-X-Gly-Nme tripeptides (where Ace and Nme stands for acetyl and N-methyl amide groups respectively and X is any amino acid) through extensive molecular dynamics simulations. Individual simulations were conducted for each peptide, encompassing five different ACN concentrations within the range of χACN = 0.1-0.9. The preferential solvation parameter (Γ) calculated using the Kirkwood-Buff integral method was used for the assessment of peptide interactions with water/ACN. Additionally, weighted Voronoi tessellation was applied to obtain a three-way data set containing four time-averaged contact surface area types between peptide atoms and water/ACN atoms. A mathematical technique known as N-way Partial Least Squares (NPLS) was utilized to anticipate the preferential interactions between peptides and water/ACN from the contact surface areas. Furthermore, the temperature dependency of peptide-solvent interactions was investigated using a subset of 10 amino acids representing a range of hydrophobicities. MD simulations were conducted at five temperatures, spanning from 283 to 343 K, with subsequent analysis of data focusing on both preferential solvation and peptide-solvent contact surface areas. The results demonstrate the efficacy of utilizing contact surface areas between the peptide and solvent constituents for successfully predicting preferential interactions in water/ACN mixtures across various ACN concentrations and temperatures.

Modulating Weak Protein-Protein Cross-Interactions by the Addition of Free Amino Acids at Millimolar Concentrations

In this paper, we quantify weak protein-protein interactions in solution using cross-interaction chromatography (CIC) and surface plasmon resonance (SPR) and demonstrate that they can be modulated by the addition of millimolar concentrations of free amino acids. With CIC, we determined the second osmotic virial cross-interaction coefficient (B23) as a proxy for the interaction strength between two different proteins. We perform SPR experiments to establish the binding affinity between the same proteins. With CIC, we show that the amino acids proline, glutamine, and arginine render the protein cross-interactions more repulsive or equivalently less attractive. Specifically, we measured B23 between lysozyme (Lys) and bovine serum albumin (BSA) and between Lys and protein isolates (whey and canola). We find that B23 increases when amino acids are added to the solution even at millimolar concentrations, corresponding to protein/ligand stoichiometric ratios as low as 1:1. With SPR, we show that the binding affinity between proteins can change by 1 order of magnitude when 10 mM glutamine is added. In the case of Lys and one whey protein isolate (WPI), it changes from the mM to the M range, thus by 3 orders of magnitude. Interestingly, this efficient modulation of the protein cross-interactions does not alter the protein's secondary structure. The capacity of amino acids to modulate protein cross-interactions at mM concentrations is remarkable and may have an impact across fields in particular for specific applications in the food or pharmaceutical industries.

Synergistic Solvation as the Enhancement of Local Mixing

Mixing two solvents can sometimes make a much better solvent than expected from their weighted mean. This phenomenon, called synergistic solvation, has commonly been explained via the Hildebrand and Hansen solubility parameters, yet their inability in other solubilization phenomena, most notably hydrotropy, necessitates an alternative route to elucidating solubilization. While, recently, the universal theory of solubilization was founded on the statistical thermodynamic fluctuation theory (as a generalization of the Kirkwood-Buff theory), its demand for experimental data processing has been a hindrance for its wider application. This can be overcome by the solubility isotherm theory, which is founded on the fluctuation theory yet reduces experimental data processing significantly to the level of isotherm analysis in sorption. The isotherm analysis identifies the driving force of synergistic solvation as the enhancement of solvent mixing around the solute, opposite in behavior to hydrotropy (characterized by the enhancement of demixing or self-association around the solute). Thus, the fluctuation theory, including its solubility isotherms, provides a universal language for solubilization across the historic subcategorization of solubilizers, for which different (and often contradictory) mechanistic models have been proposed.

Sorption Hysteresis: A Statistical Thermodynamic Fluctuation Theory

Hysteresis is observed commonly in sorption isotherms of porous materials. Still, there has so far been no unified approach that can both model hysteresis and assess its underlying energetics. Standard approaches, such as capillary condensation and isotherms based on interfacial equations of state, have not proved to be up to the task. Here, we show that a statistical thermodynamic approach can achieve the following needs simultaneously: (i) showing why adsorption and desorption transitions may be sharp yet continuous; (ii) providing a simple (analytic) isotherm equation for hysteresis branches; (iii) clarifying the energetics underlying sorption hysteresis; and (iv) providing macroscopic and nanoscopic perspectives to understanding hysteresis. This approach identifies the two pairs of parameters (determinable by fitting experimental data) that are required to describe the hysteresis: the free energy per molecule within the pore clusters and the cluster size in the pores. The present paper focuses on providing mechanistic insights to IUPAC hysteresis types H1, H2(a), and H2(b) and can also be applied to the isotherm types IV and V.

Protecting Proteins from Desiccation Stress Using Molecular Glasses and Gels

Faced with desiccation stress, many organisms deploy strategies to maintain the integrity of their cellular components. Amorphous glassy media composed of small molecular solutes or protein gels present general strategies for protecting against drying. We review these strategies and the proposed molecular mechanisms to explain protein protection in a vitreous matrix under conditions of low hydration. We also describe efforts to exploit similar strategies in technological applications for protecting proteins in dry or highly desiccated states. Finally, we outline open questions and possibilities for future explorations.

Replacing the Langmuir Isotherm with the Statistical Thermodynamic Fluctuation Theory

In the age of all-atom simulations, primitive isotherm models, such as Langmuir, BET, and GAB, are still used widely for analyzing experimental data. However, their routine applications to complex materials are not in line with their underlying assumptions (i.e., statistically independent adsorption sites with no interfacial structural changes), which manifests as the temperature dependence of the monolayer capacity. Our proposal is to replace these models with the statistical thermodynamic fluctuation theory because the ABC isotherm derived from it (i) contains these primitive models as its special cases, (ii) is applicable to any interfacial geometry, and (iii) is linked to molecular distribution functions, sharing the same language as simulations. Rectifying the inability of the primitive isotherm models to handle attractive and repulsive interactions consistently leads to a reconsideration of how physical interpretations should be attributed to the isotherms of empirical origin (e.g., Freundlich).

Actual Amount Adsorbed as Estimated from the Surface Excess Isotherm

The amount of adsorption at equilibrium is commonly used for reporting solid/solution isotherms, despite the admonishment by the International Union of Pure and Applied Chemistry (IUPAC) against equating the surface excess (i.e., the measurable quantity for sorption, signifying the competitive sorption of adsorbate and solvent) with the actual amount adsorbed. The consensus, more generally stated, is that the surface excess cannot be divided into individual isotherms for sorbate and solvent unless simplifying model assumptions are introduced. Here we show, contrary to the IUPAC report, that there exists a simple method for assigning the total isotherm to the sorbate's actual amount adsorbed and to the individual solute isotherm. This requires a combination of isotherm and volumetric measurements. For dilute sorbates, we establish criteria to show if the total isotherm is dominated by the amount of sorption at the interface, in agreement with the common assumption in the practical literature. In the absence of the volume data, we propose an approximate yet more versatile method based on the specific surface area to carry out order-of-magnitude analysis to examine whether the actual amount adsorbed dominates surface excess. Application of our methods to the adsorption of sodium decyl sulfate on polystyrene latex, malachite green on activated carbons, and thiophenes on a metal-organic framework all demonstrated the dominance of the actual amount adsorbed, significantly simplifying isotherm analysis in terms of the underlying interactions (i.e., surface-sorbate and net self-interactions at the interface), eliminating the need for excess surface quantities. Analysis of fully miscible solvent-sorbate isotherms (e.g., the mixtures of organic solvents adsorbed on mesoporous silica and carbonaceous adsorbents) indicates the contributions from both sorbate and solvent isotherms.

Not Always Sticky: Specificity of Protein Stabilization by Sugars Is Conferred by Protein-Water Hydrogen Bonds

Solutes added to buffered solutions directly impact protein folding. Protein stabilization by cosolutes or crowders has been shown to be largely driven by protein-cosolute volume exclusion complemented by chemical and soft interactions. By contrast to previous studies that indicate the invariably destabilizing role of soft protein-sugar attractions, we show here that soft interactions with sugar cosolutes are protein-specific and can be stabilizing or destabilizing. We experimentally follow the folding of two model miniproteins that are only marginally stable but in the presence of sugars and polyols fold into representative and distinct secondary structures: β-hairpin or α-helix. Our mean-field model reveals that while protein-sugar excluded volume interactions have a similar stabilizing effect on both proteins, the soft interactions add a destabilizing contribution to one miniprotein but further stabilize the other. Using molecular dynamics simulations, we link the soft protein-cosolute interactions to the weakening of direct protein-water hydrogen bonding due to the presence of sugars. Although these weakened hydrogen bonds destabilize both the native and denatured states of the two proteins, the resulting contribution to the folding free energy can be positive or negative depending on the amino acid sequence. This study indicates that the significant variation between proteins in their soft interactions with sugar determines the specific response of different proteins, even to the same sugar.

Cooperativity in Sorption Isotherms

We present a general theory of cooperativity in sorption isotherms that can be applied to sorbent/gas and sorbent/solution isotherms and is valid even when sorbates dissolve into or penetrate the sorbent. Our universal foundation, based on the principles of statistical thermodynamics, is the excess number of sorbates (around a probe sorbate), which can capture the cooperativities of sigmoidal and divergent isotherms alike via the ln-ln gradient of an isotherm (the excess number relationship). The excess number relationship plays a central role in deriving isotherm equations. Its combination with the characteristic relationship (i.e., a succinct summary of the sorption mechanism via the dependence of excess number on interfacial coverage or sorbate activity) yields a differential equation whose solution is an isotherm equation. The cooperative isotherm equations for convergent and divergent cooperativities derived from this novel method can be applied to fit experimental data traditionally fitted via various isotherm models, with a clear statistical thermodynamic interpretation of their parameters..

Sorption from Solution: A Statistical Thermodynamic Fluctuation Theory

Given an experimental solid/solution sorption isotherm, how can we gain insight into the underlying sorption mechanism on a molecular basis? Classifying sorption isotherms, for both completely and partially miscible solvent/sorbate systems, has been useful, yet the molecular foundation of these classifications remains speculative. Isotherm models, developed predominantly for solid/gas sorption, have been adapted to solid/solution isotherms, yet how their parameters should be interpreted physically has long remained ambiguous. To overcome the inconclusiveness, we establish in this paper a universal theory that can be used for interpreting and modeling solid/solution sorption. This novel theory shares the same theoretical foundation (i.e., the statistical thermodynamic fluctuation theory) not only with solid/gas sorption but also with solvation in liquid solutions and solution nonidealities. The key is the Kirkwood-Buff χ parameter, which quantifies the net self-interaction (i.e., solvent-solvent and sorbate-sorbate interactions minus solvent-sorbate interaction) via the Kirkwood-Buff integral in the same manner as the solvation theory and, unlike the Flory χ, is not limited to the lattice model. We will demonstrate that the Kirkwood-Buff χ is the key not only to isotherm classification but also to generalizing our recent statistical thermodynamic gas (vapor) isotherm, which is capable of fitting most of the solid/solution isotherm types.

Understanding Sorption Mechanisms Directly from Isotherms

Currently, more than 100 isotherm models coexist for the six IUPAC isotherm types. However, no mechanistic insights can be reached when several models, each claiming a different mechanism, fit an experimental isotherm equally well. More frequently, popular isotherm models [such as the site-specific models like Langmuir, Brunauer-Emmett-Teller (BET), and Guggenheim-Anderson-de Boer (GAB)] have been applied to real and complex systems that break their basic assumptions. To overcome such conundrums, we establish a universal approach to model all isotherm types, attributing the difference to the sorbate-sorbate and sorbate-surface interactions in a systematic manner. We have generalized the language of the traditional sorption models (such as the monolayer capacity and the BET constant) to the model-free concepts of partitioning and association coefficients that can be applied across the isotherm types. Through such a generalization, the apparent contradictions, caused by applying the site-specific models alongside with cross-sectional area of sorbates for the purpose of surface area determination, can be eliminated straightforwardly.

Dichloromethane replacement: towards greener chromatography via Kirkwood-Buff integrals

Dichloromethane (DCM) is a useful and advantageous solvent used in pharmaceutical development due to its low cost, miscibility with other organic solvents, high volatility, and ability to solubilize drug molecules of variable polarities and functionalities. Despite this favourable behaviour, efforts to identify safer and more sustainable alternatives to hazardous, halogenated solvents is imperative to the expansion of green chemistry. In this work, bio-derived esters tert-butyl acetate, sec-butyl acetate, ethyl isobutyrate, and methyl pivalate are experimentally identified as safe and sustainable alternatives to directly replace DCM within thin-layer chromatography (TLC) in the analysis of small, common drug molecules. To elucidate the intermolecular interactions influencing retardation factors (R_f) a statistical thermodynamic framework, which quantifies the driving molecular interactions that yield empirical TLC measurements, is presented. Within this framework, we are able to deduce R_f dependence on polar eluent concentration, in the presence of a low-polar mediating solvent, between the stationary and mobile phases. The strength of competitive analyte-eluent (and analyte-solvent interactions) are quantified through Kirkwood-Buff integrals (KBIs); resulting KBI terms at the dilute eluent limit provide a theoretical foundation for the observed suitability of alternative green solvents for the replacement of dichloromethane in TLC.

Does Urea Preferentially Interact with Amide Moieties or Nonpolar Sidechains? A Question Answered Through a Judicious Selection of Model Systems

The transfer model suggests that urea unfolds proteins mainly by increasing the solubility of the amide backbone, probably through urea-induced increase in hydrogen bonding. Other studies suggest that urea addition increases the magnitude of solvent-solute van der Waals interactions, which increases the solubility of nonpolar sidechains. More recent analyses hypothesize that urea has a similar effect in increasing the solubility of backbone and sidechain groups. In this work, we compare the effects of urea addition on the solvation of amides and alkyl groups. At first, we study the effects of urea addition upon solvent hydrogen bonding acidity and basicity through the perturbation in the fluorescence spectrum of probes 1-AN and 1-DMAN. Our results demonstrate that the solvent's hydrogen bonding properties are minimally affected by urea addition. Subsequently, we show that urea addition does not perturb the intra-molecular hydrogen bonding in salicylic acid significantly. Finally, we investigate how urea preferentially interacts with amide and alkyl groups moieties in water by comparing the effects of urea addition upon the solubility of acetaminophen and 4-tertbutylphenol. We show that urea affects amide and t-butyl solubility (lowers the transfer free energy of both amide (backbone) and alkyl (sidechain) groups) in a similar fashion. In other words, preferential interaction of urea with both moieties contributes to protein denaturation.

Cooperative Sorption on Heterogeneous Surfaces

Heterogeneous adsorbents, those composed of multiple surface and pore types, can result in stepwise isotherms that have been difficult to model. The complexity of these systems has often led to appealing to empirical equations without physical insights, unrealistic assumptions with many parameters, or applicability limited to a particular class of isotherms. Here, we present a statistical thermodynamic approach to model stepwise isotherms, those consisting of either an initial rise followed by a sigmoid or multiple sigmoidal steps, founded on the rigorous statistical thermodynamic theory of sorption. Our only postulates are (i) the finite ranged nature of the interface and (ii) the existence of several different types of microscopic interfacial subsystems that act independently in sorption. These two postulates have led to the superposition scheme of simple surface (i.e., Langmuir type) and cooperative isotherms. Our approach has successfully modeled the adsorption on micro-mesoporous carbons, gate-opening adsorbents, and hydrogen-bonded organic frameworks. In contrast to the previous models that start with a priori assumptions on sorption mechanisms, the advantages of our approach are that it can be applied universally under the above two postulates and that all of the fitting parameters can be interpreted with statistical thermodynamics, leading to clear insights on sorption mechanisms.

Surface Area Estimation: Replacing the Brunauer-Emmett-Teller Model with the Statistical Thermodynamic Fluctuation Theory

Surface area estimation using the Brunauer-Emmett-Teller (BET) analysis has been beset by difficulties. The BET model has been applied routinely to systems that break its basic assumptions. Even though unphysical results arising from force-fitting can be eliminated by the consistency criteria, such a practice, in turn, complicates the simplicity of the linearized BET plot. We have derived a general isotherm from the statistical thermodynamic fluctuation theory, leading to facile isotherm fitting because our isotherm is free of the BET assumptions. The reinterpretation of the monolayer capacity and the BET constant has led to a statistical thermodynamic generalization of the BET analysis. The key is Point M, which is defined as the activity at which the sorbate-sorbate excess number at the interface is at its minimum (i.e., the point of strongest sorbate-sorbate exclusion). The straightforwardness of identifying Point M and the ease of fitting by the statistical thermodynamic isotherm have been demonstrated using zeolite 13X and a Portland cement paste. The adsorption at Point M is an alternative for the BET monolayer capacity, making the BET model and its consistency criteria unnecessary. The excess number (i) replaces the BET constant as the measure of knee sharpness and monolayer coverage, (ii) links macroscopic (isotherms) to microscopic (simulation), and (iii) serves as a measure of sorbate-sorbate interaction as a signature of sorption cooperativity in porous materials. Thus, interpretive clarity and ease of analysis have been achieved by a statistical thermodynamic generalization of the BET analysis.

Macromolecular Crowding Is More than Hard-Core Repulsions

Cells are crowded, but proteins are almost always studied in dilute aqueous buffer. We review the experimental evidence that crowding affects the equilibrium thermodynamics of protein stability and protein association and discuss the theories employed to explain these observations. In doing so, we highlight differences between synthetic polymers and biologically relevant crowders. Theories based on hard-core interactions predict only crowding-induced entropic stabilization. However, experiment-based efforts conducted under physiologically relevant conditions show that crowding can destabilize proteins and their complexes. Furthermore, quantification of the temperature dependence of crowding effects produced by both large and small cosolutes, including osmolytes, sugars, synthetic polymers, and proteins, reveals enthalpic effects that stabilize or destabilize proteins. Crowding-induced destabilization and the enthalpic component point to the role of chemical interactions between and among the macromolecules, cosolutes, and water. We conclude with suggestions for future studies. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Temperature Dependence of Sorption

Understanding how sorption depends on temperature on a molecular basis has been made difficult by the coexistence of isotherm models, each assuming a different sorption mechanism and the routine application of planar, multilayer sorption models (such as Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-de Boer (GAB)) beyond their premises. Furthermore, a common observation that adsorption isotherms measured at different temperatures fall onto a single "characteristic curve" when plotted against the adsorption potential has not been given a clear explanation, due to its ambiguous foundation. Extending our recent statistical thermodynamic fluctuation theory of sorption, we have generalized the classical isosteric theory of sorption into a statistical thermodynamic fluctuation theory and clarified how sorption depends on temperature. We have shown that a characteristic curve exists when sorbate number increment contributes purely energetically to the interface, whereas the correlation between sorbate number and entropy drives the temperature dependence of an isotherm. This theory rationalizes the opposite temperature dependence of water vapor sorption on activated carbons with uniform versus broad pore size distributions and can be applied to moisture sorption on starch gels. The adsorption potential is a convenient variable for sorption in its ability to unify sorbate-sorbate fluctuation and the isosteric thermodynamics of sorption.

Cooperative Sorption on Porous Materials

The functional shape of a sorption isotherm is determined by underlying molecular interactions. However, doubts have been raised on whether the sorption mechanism can be understood in principle from analyzing sorption curves via a range of competing models. We have shown recently that it is possible to translate a sorption isotherm to the underlying molecular interactions via rigorous statistical thermodynamics. The aim of this paper is to fill the gap between the statistical thermodynamic theory and analyzing experimental sorption isotherms, especially of microporous and mesoporous materials. Based on a statistical thermodynamic approach to interfaces, we have derived a cooperative isotherm, as a generalization of the Hill isotherm and our cooperative solubilization model, without the need for assumptions on adsorption sites, layers, and pore geometry. Instead, the statistical characterization of sorbates, such as the sorbate-interface distribution function and the sorbate number distribution, as well as the existence of statistically independent units of the interface, underlies the cooperative sorption isotherm. Our isotherm can be applied directly to literature data to reveal a few key system attributes that control the isotherm: the cooperative number of sorbates and the free energy of transferring sorbates from the saturated vapor to the interface. The sorbate-sorbate interaction is quantified also via the Kirkwood-Buff integral and the excess numbers.

Sorption: A Statistical Thermodynamic Fluctuation Theory

Can the sorption mechanism be proven by fitting an isotherm model to an experiment? Such a question arises because (i) multiple isotherm models, with different assumptions on sorption mechanisms, often fit an experimental isotherm equally well, (ii) some isotherm models [such as Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-de Boer (GAB)] fit experimental isotherms that do not satisfy the underlying assumptions of the model, and (iii) some isotherms (such as Oswin and Peleg) are empirical equations that do not have a well-defined basis on sorption mechanisms. To overcome these difficulties, we propose a universal route of elucidating the sorption mechanism directly from an experimental isotherm, without an isotherm model, based on the statistical thermodynamic fluctuation theory. We have shown that how sorbate-sorbate interaction depends on activity is the key to understanding the sorption mechanism. Without assuming adsorption sites and planar layers, an isotherm can be derived, which contains the Langmuir, BET, and GAB models as its special cases. We have constructed a universal approach applicable to adsorption and absorption, solid and liquid sorbents, and vapor and liquid sorbates and demonstrated its efficacy using the humidity sorption isotherm of sucrose from both the solid and liquid sides.

Role of Hydrotropes in Sparingly Soluble Drug Solubilization: Insight from a Molecular Dynamics Simulation and Experimental Perspectives

Drug molecules' therapeutic efficacy depends on their bioavailability and solubility. But more than 70% of the formulated drug molecules show limited effectiveness due to low water solubility. Thus, the water solubility enhancement technique of drug molecules becomes the need of time. One such way is hydrotropy. The solubilizing agent of a hydrophobic molecule is generally referred to as a hydrotrope, and this phenomenon is termed hydrotropy. This method has high industrial demand, as hydrotropes are noninflammable, readily available, environmentally friendly, quickly recovered, cost-effective, and not involved in solid emulsification. The endless importance of hydrotropes in industry (especially in the pharmaceutical industry) motivated us to prepare a feature article with a clear introduction, detailed mechanistic insights into the hydrotropic solubilization of drug molecules, applications in pharma industries, and some future directions of this technique. Thus, we believe that this feature article will become an adequate manual for the pharmaceutical researchers who want to explore all of the past perspectives of the hydrotropic action of hydrotropes in pharmaceutics.

Cooperativity in micellar solubilization

Sudden onset of solubilization is observed widely around or below the critical micelle concentration (CMC) of surfactants. It has also been reported that micellization is induced by the solutes even below CMC and the solubilized solute increases the aggregation number of the surfactant. These observations suggest enhanced cooperativity in micellization upon solubilization. Recently, we have developed a rigorous statistical thermodynamic theory of cooperative solubilization. Its application to hydrotropy revealed the mechanism of cooperative hydrotropy: hydrotrope self-association enhanced by solutes. Here we generalize our previous cooperative solubilization theory to surfactants. We have shown that the well-known experimental observations, such as the reduction of CMC in the presence of the solutes and the increase of aggregation number, are the manifestations of cooperative solubilization. Thus, the surfactant self-association enhanced by a solute is the driving force of cooperativity and a part of a universal cooperative solubilization mechanism common to hydrotropes and surfactants at low concentrations.

Fluctuation adsorption theory: quantifying adsorbate-adsorbate interaction and interfacial phase transition from an isotherm

How adsorbate-adsorbate interaction determines the functional shape of an adsorption isotherm is an important and challenging question. Many models for the adsorption isotherm have been proposed to answer this question. However, a successful fitting of an isotherm on its own is insufficient to prove the correctness of the model assumptions. Instead, starting from the principles of statistical thermodynamics, we propose how adsorbate-adsorbate interactions can be quantified from an isotherm. This was made possible by extending the key tools of solution statistical thermodynamics to adsorbates at the interface, namely, the Kirkwood-Buff and McMillan-Mayer theories, as well as their relationship to the thermodynamic phase stability condition. When capillary condensation and interfacial phase transition are absent, adsorbate-adsorbate interactions can be quantified from an isotherm using the Kirkwood-Buff integrals, and virial coefficients can yield multiple-body interaction between adsorbates. Such quantities can be obtained directly from the fitting parameters for the well-known isotherm models (e.g., Langmuir, BET). The size of the adsorbate cluster involved in capillary condensation and interfacial phase transition can also be evaluated from the isotherm, which was demonstrated for the adsorption isotherm of water on activated carbons of varying pore sizes from the literature. Signatures of isotherm classifications by IUPAC have been characterized in terms of multiple-body interactions between adsorbates.

Dissecting Dynamic and Hydration Contributions to Sequence-Dependent DNA Minor Groove Recognition

Sequence selectivity is a critical attribute of DNA-binding ligands and underlines the need for detailed molecular descriptions of binding in representative sequence contexts. We investigated the binding and volumetric properties of DB1976, a model bis(benzimidazole)-selenophene diamidine compound with emerging therapeutic potential in acute myeloid leukemia, debilitating fibroses, and obesity-related liver dysfunction. To sample the scope of cognate DB1976 target sites, we evaluated three dodecameric duplexes spanning >10³-fold in binding affinity. The attendant changes in partial molar volumes varied substantially, but not in step with binding affinity, suggesting distinct modes of interactions in these complexes. Specifically, whereas optimal binding was associated with loss of hydration water, low-affinity binding released more hydration water. Explicit-atom molecular dynamics simulations showed that minor groove binding perturbed the conformational dynamics and hydration at the termini and interior of the DNA in a sequence-dependent manner. The impact of these distinct local dynamics on hydration was experimentally validated by domain-specific interrogation of hydration with salt, which probed the charged axial surfaces of oligomeric DNA preferentially over the uncharged termini. Minor groove recognition by DB1976, therefore, generates dynamically distinct domains that can make favorable contributions to hydration release in both high- and low-affinity binding. Because ligand binding at internal sites of DNA oligomers modulates dynamics at the termini, the results suggest both short- and long-range dynamic effects along the DNA target that can influence their effectiveness as low-MW competitors of protein binding.

Salt-induced LCST-type thermal gelation of methylcellulose: quantifying non-specific interactions via fluctuation theory

What drives the phase separation of water-soluble polymers in the presence of electrolytes was quantified on a molecular scale via statistical thermodynamic fluctuation theory. Quantifying polymer-water and polymer-salt interactions enabled us to identify the dominant interaction for phase separation. As a model system, the lower critical solution temperature (LCST) type thermal gelation of methylcellulose (MC) in aqueous salt solutions was chosen. The Kirkwood-Buff integrals for intermolecular interactions, calculated from the published calorimetric and volumetric data, showed that (1) the accumulation of salts around MC molecules (favourable interaction between salts and MC) inhibits thermal gelation and the depletion of salts from MC (unfavourable interaction between salts and MC) promotes the gelation, and (2) this salt-MC interaction is the dominant factor (50-100 times stronger than the water-MC interaction). This insight from the fluctuation theory is at odds with the age-old consensus regarding the driving force of thermal gelation: water structure change in the presence of salts induces the promotion or inhibition of thermal gelation. However, our conclusion is founded upon the ability of the fluctuation theory to quantify water-MC and salt-MC interaction independently via the Kirkwood-Buff integrals. Flory-Huggins (FH) theory, on the contrary, could not separate these two interactions owing to the lack of a thermodynamic degree of freedom because the lattice solution is assumed to be fully packed. In addition, the dominant contribution from salt depletion poses difficulty for the χ parameter, which is essentially the difference of contact energies. Our approach, requiring calorimetric and volumetric data alone as input, provides a simple and versatile method towards elucidating the effect of cosolvents on biopolymer phase separation of physiological importance.

Kramers’ Theory and the Dependence of Enzyme Dynamics on Trehalose-Mediated Viscosity

The disaccharide trehalose is accumulated in the cytoplasm of some organisms in response to harsh environmental conditions. Trehalose biosynthesis and accumulation are important for the survival of such organisms by protecting the structure and function of proteins and membranes. Trehalose affects the dynamics of proteins and water molecules in the bulk and the protein hydration shell. Enzyme catalysis and other processes dependent on protein dynamics are affected by the viscosity generated by trehalose, as described by the Kramers’ theory of rate reactions. Enzyme/protein stabilization by trehalose against thermal inactivation/unfolding is also explained by the viscosity mediated hindering of the thermally generated structural dynamics, as described by Kramers’ theory. The analysis of the relationship of viscosity–protein dynamics, and its effects on enzyme/protein function and other processes (thermal inactivation and unfolding/folding), is the focus of the present work regarding the disaccharide trehalose as the viscosity generating solute. Finally, trehalose is widely used (alone or in combination with other compounds) in the stabilization of enzymes in the laboratory and in biotechnological applications; hence, considering the effect of viscosity on catalysis and stability of enzymes may help to improve the results of trehalose in its diverse uses/applications.

Thermodynamic stability condition can judge whether a nanoparticle dispersion can be considered a solution in a single phase

Establishing that a nanoparticle dispersion can, in fact, be treated as a solution has an important practical ramification, namely the application of solubility theories for solvent selection. However, what distinguishes a solution and dispersion has remained ambiguously understood. Based on the recent progress in statistical thermodynamics on multiple-component solutions, here we establish the condition upon which a nanoparticle dispersion can be considered a single-phased solution. We shall provide experimental evidence already found in the literature showing the solution nature of nanoparticle dispersions.

Preferential solvation of p-nitroaniline in a binary mixture of chloroform and hydrogen bond acceptor solvents: the role of specific solute-solvent hydrogen bonding

Preferential solvation of solvatochromic probe p-nitroaniline (PNA) has been studied in binary mixtures of chloroform with different hydrogen bond acceptor (HBA) solvents using the spectroscopic transition energy (E_T). Analyses of the solvatochromic shifts of the absorption spectra of PNA in different neat solvents as a function of the solvent polarity parameters reveal the major contribution from the solvent dipolarity/polarizability and HBA basicity in the solvation of PNA. The event of preferential solvation in the chloroform-HBA binary mixtures and the preference of one solvent above the other in the solvation shell have been attributed to the hydrogen bond donor and acceptor ability of the solvent mixtures. HBA solvents form a strong hydrogen bond with the amino group while chloroform forms a hydrogen bond with the nitro group of PNA. This specific functional group recognition increases the local concentration at specific sites resulting in location specific preferential solvation and synergistic preferential solvation. Solvents with comparable polarity have been found to show significant synergistic behavior as a result of the formation of stronger solvent-solvent hydrogen bonded S₁-S₂ species. These propositions were found to be supported by theoretical solvation models, calculated HOMO-LUMO energy gaps, the effect of deuterated solvent on the extent of PS, and ¹H NMR spectral analyses.

The shift in urea orientation at protein surfaces at low pH is compatible with a direct mechanism of protein denaturation

The protonation of acidic side-chains promotes a orientational shift of urea molecules, but only locally, with the interactions with other protein moieties being preserved.

Quantifying non-specific interactions via liquid chromatography

Determinations of solute-cosolute interactions from chromatography have often resulted in problems, such as the "antibinding" (or a negative binding constant) between the solute and micelle in micellar liquid chromatography (MLC) or indeterminacy of salt-ligand binding strength in high-performance affinity chromatography (HPAC). This shows that the stoichiometric binding models adopted in many chromatographic analyses cannot capture the non-specific nature of solvation interactions. In contrast, an approach using statistical thermodynamics handles these complexities without such problems and directly links chromatographic data to, for example, solubility data via a universal framework based on Kirkwood-Buff integrals (KBI) of the radial distribution functions. The chromatographic measurements can now be interpreted within this universal theoretical framework that has been used to rationalize small solute solubility, biomolecular stability, binding, aggregation and gelation. In particular, KBI analysis identifies key solute-cosolute interactions, including excluded volume effects. We present (i) how KBI can be obtained directly from the cosolute concentration dependence of the distribution coefficient, (ii) how the classical binding model, when used solely as a fitting model, can yield the KBIs directly from the literature data, and (iii) how chromatography and solubility measurements can be compared in the unified theoretical framework provided via KBIs without any arbitrary assumptions about the stationary phase. To perform our own analyses on multiple datasets we have used an "app". To aid readers' understanding and to allow analyses of their own datasets, the app is provided with many datasets and is freely available on-line as an open-source resource.

On empirical decomposition of volumetric data

Volumetric characterization of proteins and their recognition events has been instrumental in providing information on the role of intra- and intermolecular interactions, including hydration, in stabilizing biomolecules. The credibility of molecular models and interpretation schemes used to rationalize experimental data are essential for the validity of microscopic insights derived from volumetric results. Current empirical schemes used to interpret volumetric data suffer from a lack of theoretical and computational substantiation. In this contribution, we take advantage age of recent MD simulations of proteins in solution coupled with Voronoi-Delaunay tessellation of simulated structures that have provided an exceptional level of structural detail on the nature of protein-water interfaces. We use these structural insights to re-evaluate empirical frameworks used for interpretation of volumetric data. An important issue in this respect is the actual dividing surface between water and protein atoms that is used in volumetric studies when the solute and solvent are treated as hard spheres enclosed within their respective van der Waals surfaces. In one development, using Voronoi tessellation of MD simulated protein-water systems the dividing surface has been defined as the points equidistant from the water and protein atoms. The interstitial void volume between the solute and the dividing surface corresponds to thermal volume envisaged by Scaled Particle Theory. In this communication, we explicitly account for the contributions of thermal volume to the partial molar volume, compressibility, and expansibility of proteins and re-examine and redefine the intrinsic and hydration volumetric contributions. We discuss the implications of our results for protein transitions and association events.

A shell-resolved analysis of preferential solvation of coffee ingredients in aqueous mixtures of the ionic liquid 1-ethyl-3-methylimidazolium acetate

Ionic liquids increase the solubility of various coffee ingredients in aqueous solution but little is known about the underlying mechanism. Kirkwood-Buff integrals as well as the potential of mean force indicate that the imidazolium cations are accumulated at the surface of the solutes, removing water molecules from the solute surface. Although hydrogen bonding of the anions to hydroxy groups of the solutes can be detected, their concentration at the surface is less enhanced compared to the cations. The decomposition into solvation shells by Voronoi tessellation reveals that structural features are only observed in the first solvation shell. Nevertheless, the depletion of water and the excess concentration of the ions and, in particular, of the cations are visible in the next solvation shells as well. Therefore, classical arguments of hydrotropic theory fail to explain this behavior.

ATP as a biological hydrotrope

Hydrotropes are small molecules that solubilize hydrophobic molecules in aqueous solutions. Typically, hydrotropes are amphiphilic molecules and differ from classical surfactants in that they have low cooperativity of aggregation and work at molar concentrations. Here, we show that adenosine triphosphate (ATP) has properties of a biological hydrotrope. It can both prevent the formation of and dissolve previously formed protein aggregates. This chemical property is manifested at physiological concentrations between 5 and 10 millimolar. Therefore, in addition to being an energy source for biological reactions, for which micromolar concentrations are sufficient, we propose that millimolar concentrations of ATP may act to keep proteins soluble. This may in part explain why ATP is maintained in such high concentrations in cells.