Solvation thermodynamics and the physical-chemical meaning of the constant in Abraham solvation equations

Modeling the Partitioning of Anionic Carboxylic and Perfluoroalkyl Carboxylic and Sulfonic Acids to Octanol and Membrane Lipid

Perfluoroalkyl carboxylic and sulfonic acids (PFCAs and PFSAs, respectively) have low acid dissociation constant values and are, therefore, deprotonated under most experimental and environmental conditions. Hence, the anionic species dominate their partitioning between water and organic phases, including octanol and phospholipid bilayers which are often used as model systems for environmental and biological matrices. However, data for solvent-water (SW) and membrane-water partition coefficients of the anion species are only available for a few per- and polyfluoroalkyl substances (PFAS). In the present study, an equation is derived using a Born-Haber cycle that relates the partition coefficients of the anions to those of the corresponding neutral species. It is shown via a thermodynamic analysis that for carboxylic acids (CAs), PFCAs, and PFSAs, the log of the solvent-water partition coefficient of the anion, log KSW (A- ), is linearly related to the log of the solvent-water partition coefficient of the neutral acid, log KSW (HA), with a unity slope and a solvent-dependent but solute-independent intercept within a PFAS (or CA) family. This finding provides a method for estimating the partition coefficients of PFCAs and PFSAs anions using the partition coefficients of the neutral species, which can be reliably predicted using quantum chemical methods. In addition, we have found that the neutral octanol-water partition coefficient, log KOW , is linearly correlated to the neutral membrane-water partition coefficient, log KMW ; therefore, log KOW , being a much easier property to estimate and/or measure, can be used to predict the neutral log KMW . Application of this approach to KOW and KMW for PFCAs and PFSAs demonstrates the utility of this methodology for evaluating reported experimental data and extending anion property data for chain lengths that are unavailable. Environ Toxicol Chem 2023;42:2317-2328. © 2023 SETAC.

Recent advances for estimating environmental properties for small molecules from chromatographic measurements and the solvation parameter model

The transfer of neutral compounds between immiscible phases in chromatographic or environmental systems can be described by six solute properties (solute descriptors) using the solvation parameter model. The solute descriptors are size (McGowan's characteristic volume), V, excess molar refraction, E, dipolarity/polarizability, S, hydrogen-bond acidity and basicity, A and B, and the gas-liquid partition constant on n-hexadecane at 298.15 K, L. V and E for liquids are accessible by calculation but the other descriptors and E for solids are determined experimentally by chromatographic, liquid-liquid partition, and solubility measurements. These solute descriptors are available for several thousand compounds in the Abraham solute descriptor databases and for several hundred compounds in the WSU experimental solute descriptor database. In the first part of this review, we highlight features important in defining each descriptor, their experimental determination, compare descriptor quality for the two organized descriptor databases, and methods for estimating Abraham solute descriptors. In the second part we focus on recent applications of the solvation parameter model to characterize environmental systems and its use for the identification of surrogate chromatographic models for estimating environmental properties.

QSPRs for Predicting Equilibrium Partitioning in Solvent–Air Systems from the Chemical Structures of Solutes and Solvents

Poly-parameter Linear Free Energy Relationships (PPLFERs) based on the Abraham solvation model are a useful tool for predicting and interpreting equilibrium partitioning of solutes in solvent systems. The focus of this work is neutral organic solutes partitioning in neutral organic liquid solvent-air systems. This is a follow-up to previous work (Brown, 2021) which developed predictive empirical correlations between solute descriptors and system parameters, allowing system parameters to be predicted from the solute descriptors of the solvent. A database of solute descriptors, and a database of system parameters supplemented by empirical predictions, form the basis for the development of new Quantitative Structure Property Relationships (QSPRs). A total of 11 QSPRs have been developed for the E, S, A, B and L solute descriptors, and the s, a, b, v, l, and c system parameters. The QSPRs were developed using a group-contribution method referred to as Iterative Fragment Selection. The method includes robust internal and external model validation and a well-defined Applicability Domain, including estimates of prediction uncertainty. System parameters can also be predicted by combining the solute descriptor QSPRs and the empirical correlations. The predictive power of PPLFERs applied using different combinations of experimental data, empirical correlations, and QSPRs are externally validated by predicting partition ratios between solvents and air. The uncertainty for predicting the log10KSA of diverse solutes in diverse solvents using only the new QSPRs and empirical correlations is estimated to be one log10 unit or less.

Linear Solvation Energy Relationships (LSERs) for Robust Prediction of Partition Coefficients between Low Desity Polyethylene and Water Part II: Model Evaluation and Benchmarking

By neglecting the kinetics of leaching, the accumulation of leachables in a clinically relevant medium in contact with plastics is principally driven by the equilibrium partition coefficient between the polymer and the medium phase. Based on experimental partition coefficients for a wide set of chemically diverse compounds between low density polyethylene (LDPE) and water, a linear solvation energy relationship (LSER) model was obtained in part I of this study, reading: logK_i,LDPE/W=-0.529+1.098E_i-1.557S_i-2.991A_i-4.617B_i+3.886V_i. The model was proven accurate and precise (n = 156, R2 = 0.991, RMSE = 0.264).) In this part II of the study, for further evaluation and benchmarking of the LSER model ∼ 33% (n = 52) of the total observations were ascribed to an independent validation set. Calculation of partition coefficients logK_i,LDPE/W for this validation set was based on experimental LSER solute descriptors. Linear regression against the corresponding experimental values yielded R2 = 0.985 and RMSE = 0.352. When using LSER solute descriptors predicted from the compound's chemical structure by means of a QSPR prediction tool, instead, R2 = 0.984 and RMSE = 0.511 were obtained. These statistics are considered indicative for extractables with no experimental LSER solute descriptors available. By comparison to LSER models from the literature, a strong correlation between the quality of experimental partition coefficients and the chemical diversity of the training set to the model's predictability was observed, the latter of particular relevance for the application domain of the model. Further, to tentatively match partitioning into LDPE to partitioning into a liquid phase, partition coefficients logK_i,LDPE/W were converted into logK_{i,LDPEamorph/W} by considering the amorphous fraction of the polymer as effective phase volume only. A LSER model now recalibrated based on the observations for logK_{i,LDPEamorph/W} exhibited the constant in the equation above to now read -0.079 instead of -0.529 which rendered the model more similar to a corresponding LSER-model for n-hexadencane/water. Based on LSER system parameters available, the sorption behavior of LDPE could be efficiently compared to the one of polydimethylsiloxane (PDMS), polyacrylate (PA) and polyoxymethylene (POM). The latter, by offering capabilities for polar interactions due to their heteroatomic building blocks, exhibit stronger sorption than LDPE to the more polar, non-hydrophobic domain of sorbates up to an logK_i,LDPE/W range of 3 to 4. Above that range, all four polymers exhibited a roughly similar sorption behavior. Overall, LSERs were found to represent an accurate and user-friendly approach for the estimation of equilibrium partition coefficients involving a polymeric phase. All intrinsic input parameters can be retrieved from a free, web-based and curated database along with the outright calculation of the partition coefficient for any given neutral compound with a known structure for a given two-phased system.

Synergistic Computational Modeling Approaches as Team Players in the Game of Solubility Predictions

Several approaches to predict and model drug solubility have been used in the drug discovery and development processes during the last decades. Each of these approaches have their own benefits and place, and are typically used as standalone approaches rather than in concert. The synergistic effects of these are often overlooked, partly due to the need of computational experts to perform the modeling and simulations as well as analyzing the data obtained. Here we provide our views on how these different approaches can be used to retrieve more information on drug solubility, ranging from multivariate data analysis over thermodynamic cycle modeling to molecular dynamics simulations. We are discussing aqueous solubility as well as solubility in more complex mixed solvents and media with colloidal structures present. We conclude that the field of computational pharmaceutics is in its early days but with a bright future ahead. However, education of computational formulators with broad knowledge of modeling and simulation approaches is imperative if computational pharmaceutics is to reach its full potential.

Predicting Partitioning and Diffusion Properties of Nonpolar Chemicals in Biotic Media and Passive Sampler Phases by GC × GC

The chemical parameters needed to explain and predict bioavailability, biodynamics, and baseline toxicity are not readily available for most nonpolar chemicals detected in the environment. Here, we demonstrate that comprehensive two-dimensional gas chromatography (GC × GC) retention times can be used to predict 26 relevant properties for nonpolar chemicals, specifically: partition coefficients for diverse biotic media and passive sampler phases; aquatic baseline toxicity; and relevant diffusion coefficients. The considered biotic and passive sampler phases include membrane and storage lipids, serum and muscle proteins, carbohydrates, algae, mussels, polydimethylsiloxane, polyethylene, polyoxymethylene, polyacrylate, polyurethane, and semipermeable membrane devices. GC × GC-based chemical property predictions are validated with a compilation of 1038 experimental property data collected from the literature. As an example application, we overlay a map of baseline toxicity to fathead minnows onto the separated analyte signal of a polychlorinated alkanes (chlorinated paraffins) technical mixture that contains 7820 congeners. In a second application, GC × GC-estimated properties are used to parametrize multiphase partitioning models for mammalian tissues and organs. In a third example, we estimate chemical depuration kinetics for mussels. Finally, we illustrate an approach to screen the GC × GC chromatogram for nonpolar chemicals of potentially high concern, defined based on their GC × GC-estimated biopartitioning properties, diffusion properties, and baseline toxicity.

Screening-level models to estimate partition ratios of organic chemicals between polymeric materials, air and water

Polymeric materials flowing through the technosphere are repositories of organic chemicals throughout their life cycle. Equilibrium partition ratios of organic chemicals between these materials and air (KMA) or water (KMW) are required for models of fate and transport, high-throughput exposure assessment and passive sampling. KMA and KMW have been measured for a growing number of chemical/material combinations, but significant data gaps still exist. We assembled a database of 363 KMA and 910 KMW measurements for 446 individual compounds and nearly 40 individual polymers and biopolymers, collected from 29 studies. We used the EPI Suite and ABSOLV software packages to estimate physicochemical properties of the compounds and we employed an empirical correlation based on Trouton's rule to adjust the measured KMA and KMW values to a standard reference temperature of 298 K. Then, we used a thermodynamic triangle with Henry's law constant to calculate a complete set of 1273 KMA and KMW values. Using simple linear regression, we developed a suite of single parameter linear free energy relationship (spLFER) models to estimate KMA from the EPI Suite-estimated octanol-air partition ratio (KOA) and KMW from the EPI Suite-estimated octanol-water (KOW) partition ratio. Similarly, using multiple linear regression, we developed a set of polyparameter linear free energy relationship (ppLFER) models to estimate KMA and KMW from ABSOLV-estimated Abraham solvation parameters. We explored the two LFER approaches to investigate (1) their performance in estimating partition ratios, and (2) uncertainties associated with treating all different polymers as a single "bulk" polymeric material compartment. The models we have developed are suitable for screening assessments of the tendency for organic chemicals to be emitted from materials, and for use in multimedia models of the fate of organic chemicals in the indoor environment. In screening applications we recommend that KMA and KMW be modeled as 0.06 ×KOA and 0.06 ×KOW respectively, with an uncertainty range of a factor of 15.

Response to "comment on 'structural determinants of drug partitioning in surrogates of phosphatidylcholine bilayer strata'"

We used the solvatochromic correlation to explain the influence of characteristics of studied compounds on the partition coefficients (P) measured using n-hexadecane (C16) and the novel headgroup surrogate (diacetyl phosphatidylcholine, DAcPC), and compared them with those in other systems, including the C16/water (W) system. The comment analyzes why our correlation for the C16/W system has the standard deviation (SD) higher than that published previously. The main reason is that in our, much smaller, data set the measured P values are complemented by the P values predicted by a reliable, unrelated method. We believe that this approach is acceptable for the aforementioned comparison. We did not use just experimental values, as suggested in the comment, because the solvatochromic correlation, although exhibiting 35% reduction in the SD, was accompanied by a sign change of one of the regression coefficients. The recommended use of special solvatochromic solute characteristics for a few compounds and replacement of a predicted PC16/W value by the experimental value resulted in improved correlations. The observed differences between our correlation and those published in the comment and in a previous article do not affect our main conclusions regarding the solvation of solutes in the surrogates (DAcPC and C16) of intrabilayer strata.

Predicting Abraham model solvent coefficients

Background

The Abraham general solvation model can be used in a broad set of scenarios involving partitioning and solubility, yet is limited to a set of solvents with measured Abraham coefficients. Here we extend the range of applicability of Abraham’s model by creating open models that can be used to predict the solvent coefficients for all organic solvents.

Results

We created open random forest models for the solvent coefficients e, s, a, b, and v that had out-of-bag R² values of 0.31, 0.77, 0.92, 0.47, and 0.63 respectively. The models were used to suggest sustainable solvent replacements for commonly used solvents. For example, our models predict that propylene glycol may be used as a general sustainable solvent replacement for methanol.

Conclusion

The solvent coefficient models extend the range of applicability of the Abraham general solvation equations to all organic solvents. The models were developed under Open Notebook Science conditions which makes them open, reproducible, and as useful as possible.

Graphical Abstract

Sorption of the monoterpenes α-pinene and limonene to carbonaceous geosorbents including biochar

The sorption of two monoterpenes, α pinene and limonene to the carbonaceous geosorbents graphite, bituminous coal, lignite coke, biochar and Pahokee peat was quantified. Polyethylene (PE) passive samplers were calibrated for the first time for these compounds by determining the PE-water partitioning coefficients and used as a tool to determine sorption to the carbonaceous geosorbents. Log KPE-water values were 3.49±0.58 for α pinene and 4.08±0.27 for limonene. The sorption of limonene to all materials was stronger than that for α pinene (differences of 0.2-1.3 log units between distribution coefficients for the monoterpenes). Placing Kd values in increasing order for α pinene gave biochar≈Pahokee peat≈bituminous coal≈lignite coke<graphite. For limonene the order was: Pahokee peat≈biochar≈bituminous coal<graphite≈lignite coke. Micropore (defined as pores <1.5 nm) and nanopore surface area (defined as pores 1.5 nm to 50 nm) normalised carbonaceous geosorbent-water distribution coefficients were also calculated. There was no clear correlation of these distribution coefficients with SA. Elemental composition was used to assess the degree of condensation (or alteration) of the carbonaceous geosorbents. The degree of carbonisation increased in the order; Pahokee peat<lignite coke<bituminous coal<biochar<graphite, however this was not correlated with an increase in the experimental distribution coefficients.

Applications of polyparameter linear free energy relationships in environmental chemistry

Partitioning behavior of organic chemicals has tremendous influences on their environmental distribution, reaction rates, bioaccumulation, and toxic effects. Polyparameter linear free energy relationships (PP-LFERs) have been proven to be useful to characterize the equilibrium partitioning of organic chemicals in various environmental and technical partitioning systems and predict the respective partition coefficients. Over the past decade, PP-LFER solute descriptors for numerous environmentally relevant organic chemicals and system parameters for environmentally important partitioning systems have been determined, extending substantially the applicability of the PP-LFER approaches. However, the information needed for the use of PP-LFERs including descriptors and parameters is scattered over a large number of publications. In this work, we review the state of the art of the PP-LFER approaches in environmental chemical applications. The solute descriptors and system parameters reported in the literature and the availability of their database are summarized, and their calibration and prediction methods are overviewed. We also describe tips and pitfalls associated with the use of the PP-LFER approaches and identify research needs to improve further the usefulness of PP-LFERs for environmental chemistry.

Mapping environmental partitioning properties of nonpolar complex mixtures by use of GC × GC

Comprehensive two-dimensional gas chromatography (GC × GC) is effective for separating and quantifying nonpolar organic chemicals in complex mixtures. Here we present a model to estimate 11 environmental partitioning properties for nonpolar analytes based on GC × GC chromatogram retention time information. The considered partitioning properties span several phases including pure liquid, air, water, octanol, hexadecane, particle natural organic matter, dissolved organic matter, and organism lipids. The model training set and test sets are based on a literature compilation of 648 individual experimental partitioning property data. For a test set of 50 nonpolar environmental contaminants, predicted partition coefficients exhibit root-mean-squared errors ranging from 0.19 to 0.48 log unit, outperforming Abraham-type solvation models for the same chemical set. The approach is applicable to nonpolar organic chemicals containing C, H, F, Cl, Br, and I, having boiling points ≤402 °C. The presented model is calibrated, easy to apply, and requires the user only to identify a small set of known analytes that adapt the model to the GC × GC instrument program. The analyst can thus map partitioning property estimates onto GC × GC chromatograms of complex mixtures. For example, analyzed nonpolar chemicals can be screened for long-range transport potential, aquatic bioaccumulation potential, arctic contamination potential, and other characteristic partitioning behaviors.

A possible simplification of the Goss-modified Abraham solvation equation

Abraham solvation equations find widespread use in environmental chemistry and pharmaco-chemistry. Recently Goss proposed a modified Abraham solvation equation. For various partitioning processes, the present study investigates the consequences for the fit when the Abraham solvation parameter V is left out of this modified solvation equation. For air-organic solvent partition, the Abraham solvation parameter V can be omitted from the Goss-modified Abraham solvation equation without any loss of statistical quality. For air-water partitioning, organic biphasic system partitioning, as well as water-organic solvent partitioning, omitting the V parameter from the Goss-modified Abraham solvation equation leads to only a small deterioration of statistic quality.

Estimation of Abraham solvation equation coefficients for hydrogen bond formation from Abraham solvation parameters for solute acidity and basicity

Abraham solvation equations find widespread use in environmental chemistry and pharmaco-chemistry. The coefficients in these equations, which are solvent (system) descriptors, are usually determined by fitting experimental data. To simplify the determination of these coefficients in Abraham solvation equations, this study derives equations, based on Abraham solvation parameters for hydrogen acidity and basicity of the solvents involved, to estimate the value of the coefficients for hydrogen bond formation. These equations were applied to calculate Abraham solvation parameters for hydrogen acidity and basicity for polyoxymethylene, polyacrylate, sodium dodecylsulfate, some ionic liquids, alkanoyl phosphatidyl cholines, and lipids for which fitted values for Abraham coefficients for hydrogen bond formation were available.