Statistical evaluation of linear solvation energy relationship models used to characterize chemical selectivity in micellar electrokinetic chromatography

Characterization of retention and selectivity differences between surfactants in micellar electrokinetic chromatography (MEKC) using linear solvation energy relationships (LSERs) has been given a significant amount of attention in the last four years. This report evaluates the validity of using the two LSER models that have been used to fit retention in MEKC in the literature. The results and the fit of the revised model and parameters developed by Abraham and coworkers are compared to the original model developed by Kamlet, Taft, and coworkers. LSERs can generally only be used as a comparative tool to describe the selectivity differences between surfactant systems used in MEKC. With this in mind, it was determined that the results of both models essentially provide the same information about these differences. However, the revised model and parameters have been found to yield a statistically better fit of the MEKC retention data as well as providing more chemically sound LSER coefficients.     

The chemical interpretation and practice of linear solvation energy relationships in chromatography

This review focuses on the use of linear solvation energy relationships (LSERs) to understand the types and relative strength of the chemical interactions that control retention and selectivity in the various modes of chromatography ranging from gas chromatography to reversed phase and micellar electrokinetic capillary chromatography. The most recent, widely accepted symbolic representation of the LSER model, as proposed by Abraham, is given by the equation: SP=c + eE + sS + aA + bB + vV, in which, SP can be any free energy related property. In chromatography, SP is most often taken as logk' where k' is the retention factor. The letters E, S, A, B, and V denote solute dependent input parameters that come from scales related to a solute's polarizability, dipolarity (with some contribution from polarizability), hydrogen bond donating ability, hydrogen bond accepting ability, and molecular size, respectively. The e-, s-, a-, b-, and v-coefficients and the constant, c, are determined via multiparameter linear least squares regression analysis of a data set comprised of solutes with known E, S, A, B, and V values and which span a reasonably wide range in interaction abilities. Thus, LSERs are designed to probe the type and relative importance of the interactions that govern solute retention. In this review, we include a synopsis of the various solvent and solute scales in common use in chromatography. More importantly, we emphasize the development and physico-chemical basis of - and thus meaning of - the solute parameters. After establishing the meaning of the parameters, we discuss their use in LSERs as applied to understanding the intermolecular interactions governing various gas-liquid and liquid-liquid phase equilibria. The gas-liquid partition process is modeled as the sum of an endoergic cavity formation/solvent reorganization process and exoergic solute-solvent attractive forces, whereas the partitioning of a solute between two solvents is thermodynamically equivalent to the difference in two gas/liquid solution processes. We end with a set of recommendations and advisories for conducting LSER studies, stressing the proper chemical and statistical application of the methodology. We intend that these recommendations serve as a guide for future studies involving the execution, statistical evaluation, and chemical interpretation of LSERs.     

Efficient and accurate solvation energy calculation from polarizable continuum models

A new approach is proposed to enhance the efficiency and accuracy for calculation of the long-range electrostatic interaction from implicit solvation models, i.e., the polarizable continuum model (PCM) and its variants, conductorlike PCM/conductorlike screening model and integral equation formalism PCM. In these methods the solvent electrostatics effects are represented by a set of discrete apparent charges distributed on tesserae of the molecular cavity surface embedding the solute. In principle, the accuracy of these methods is improved if the cavity surface is tessellated to finer tesserae; however, the computational time is increased rapidly. We show that such undesired dependency between accuracy and efficiency is a result of the inaccurate treatment of the apparent charge self-contribution to the potential and/or electric field. By taking into account the full effects due to the size and curvature of the segment occupied by each apparent charge, the error in calculated electrostatic solvation free energy is essentially zero for ions (point charge at the center of a sphere) regardless of the degree of tessellation used. For molecules where gradient of apparent charge density is nonzero at the cavity surface, we propose a multiple-sampling technique which significantly lowers the calculated error compared to the original PCM methods, especially when very few numbers of tesserae are used.     

A method for calculating the Gibbs energy of nonspecific solvation

A method for calculating the Gibbs energy of nonspecific solvation of nonelectrolytes was suggested. The new equation for the Gibbs energy of nonspecific solvation contains one solvent parameter that characterize nonspecific solvent-solute interactions and two experimental Gibbs energies of solvation in two standard solvents. The method is applicable to a wide range of solutes and solvents. It was successfully used to describe some 800 Gibbs energies of solvation for systems without specific solvent-solute interactions.     

Computational prediction of monosaccharide binding free energies to lectins with linear interaction energy models

The linear interaction energy (LIE) method to compute binding free energies is applied to lectin‐monosaccharide complexes. Here, we calculate the binding free energies of monosaccharides to the Ralstonia solanacearum lectin (RSL) and the Pseudomonas aeruginosa lectin‐II (PA‐IIL). The standard LIE model performs very well for RSL, whereas the PA‐IIL system, where ligand binding involves two calcium ions, presents a major challenge. To overcome this, we explore a new variant of the LIE model, where ligand–metal ion interactions are scaled separately. This model also predicts the saccharide binding preference of PA‐IIL on mutation of the receptor, which may be useful for protein engineering of lectins. © 2012 Wiley Periodicals, Inc.     

Characterization of temperature dependent modifier effects in SFC using linear solvation energy relationships

Summary Linear solvation energy relationships (LSERs) are used to probe the changes in mobile and stationary phase properties of a carbon dioxide-based mobile phase and a polymeric stationary phase under near-critical conditions. Four mobile phase modifiers are compared with respect to dipolarity/polarizability, hydrogen bond donating and accepting ability, and other intermolecular interactions as a function of temperature. As temperature nears the mixture critical point, the differences in these properties between the mobile and stationary phases change to reflect the growing heterogeneity in mobile phase component distribution at the chromatographic interface. The stationary phase loses many of its original characteristics and takes on characteristics typical of the mobile phase modifier due to preferential adsorption of the modifier at the surface of the stationary phase.     

Binding affinity prediction with different force fields: examination of the linear interaction energy method

A systematic study of the linear interaction energy (LIE) method and the possible dependence of its parameterization on the force field and system (receptor binding site) is reported. We have calculated the binding free energy for nine different ligands in complex with P450cam using three different force fields (Amber95, Gromos87, and OPLS-AA). The results from these LIE calculations using our earlier parameterization give relative free energies of binding that agree remarkably well with the experimental data. However, the absolute energies are too positive for all three force fields, and it is clear that an additional constant term (gamma) is required in this case. Out of five examined LIE models, the same one emerges as the best for all three force fields, and this, in fact, corresponds to our earlier one apart from the addition of the constant gamma, which is almost identical for the three force fields. Thus, the present free energy calculations clearly indicate that the coefficients of the LIE method are independent of the force field used. Their relation to solvation free energies is also demonstrated. The only free parameter of the best model is gamma, which is found to depend on the hydrophobicity of the binding site. We also attempt to quantify the binding site hydrophobicity of four different proteins which shows that the ordering of gamma's for these sites reflects the fraction of hydrophobic surface area.     

Characterization of some functionalized RP-HPLC phases by the use of linear solvation energy relationships

The linear solvation energy relationship equation developed by Abraham and coworkers was applied to the retention factors k of a series of 20 polar solutes on four chemically different RP-HPLC phases. Three of them were specially synthesized and are functionalized with ether, phenylsulfide or phenylsulfoxide groups. Their retention properties are compared with those of a nonpolar octadecylsiloxane (ODS) phase. The phase properties r, the excess molar refraction; s, the dipolarity; a and b, the hydrogen-bond basicity and acidity; and v, the cavity factor show significant differences on the four phases and are used here to suggest a classification of stationary phases based on the type of interactions that are important for the retention. The hydrophilic system properties r, s, a and b are the reason for different elution orders of a set of solutes on the four phases. The intrinsic hydrophobicity of the system, the v/A ratio (A is the surface coverage in μmol/m²), shows a dependence on the mobile phase composition as do the normalized phase properties r/v, s/v, a/v and b/v. Averaging the constants over a large span of mobile phase composition should be done very carefully. The LSER model is used to predict the elution order on the stationary phases for five phenols which show coelution on ODS. On the phenylsulfide phase they are resolved. Received: 3 December 1998 / Revised: 1 February 1999 / Accepted: 8 February 1999     

Application of linear solvation energy relationships to polymeric pseudostationary phases in micellar electrokinetic chromatography

Polymerized sodium 11-acrylamidoundecanoate (poly(Na 11-AAU)) was used as a pseudostationary phase (PSP) for micellar electrokinetic chromatography to separate uncharged compounds. The polymer PSP showed signifcantly different solute migration behaviors from conventional micelles including sodium dodecyl sulfate and poly (sodium 10-undecylenate), giving high separation efficiencies (>200000 theoretical plates/m). Linear solvation energy relationships were used to evaluate and characterize the chemical interactions that influence the retention behavior in the poly (Na 11-AAU) micellar system. It was found that the solute volume and solute hydrogen bond basicity mainly influenced the retention. The characteristic feature of the poly (Na 11-AAU) micellar system is that the micelle has a significantly higher capacity for dipole-dipole and dipole-induced dipole interactions as well as a slightly higher capacity for electron pair interactions than the aqueous phase. Due to its unique selectivity, the poly(Na 11-AAU) micellar system would become an attractive new option for selectivity optimization on methods development.     

Improving the performance of the coupled reference interaction site model-hyper-netted chain (RISM-HNC)/simulation method for free energy of solvation

The coupled reference interaction site model-hyper-netted chain (RISM-HNC)/ simulation methodology determines solvation free energies as a function of the set of all radial distribution functions of solvent atoms about atomic solute sites. These functions are determined from molecular dynamics (MD) or Monte Carlo (MC) simulations rather than from solving the RISM and HNC equations iteratively. Previous applications of the method showed that it can predict relative free energies of solvation for small solutes accurately. However, the errors scale with the system size. In this study, we propose the use of the hard-sphere free energy as the reference and a linear response approximation to improve the performance, i.e., accuracy and robustness, of the method, particularly removing the size dependency of the error. The details of the new formalism are presented. To validate the proposed formalism, solvation free energies of N-methylacetamide and methylamine are computed using the new RISM-HNC-based expressions in addition to a linear response expression, which are compared to previous thermodynamic integration and thermodynamic perturbation results performed with the same force field. Additionally, free energies of solvation for cyclohexane, pyridine, benzene and derivatives, and other small organic molecules are calculated and compared to experimental values.     

A new quantum method for electrostatic solvation energy of protein

A new method that incorporates the conductorlike polarizable continuum model (CPCM) with the recently developed molecular fractionation with conjugate caps (MFCC) approach is developed for ab initio calculation of electrostatic solvation energy of protein. The application of the MFCC method makes it practical to apply CPCM to calculate electrostatic solvation energy of protein or other macromolecules in solution. In this MFCC-CPCM method, calculation of protein solvation is divided into calculations of individual solvation energies of fragments (residues) embedded in a common cavity defined with respect to the entire protein. Besides computational efficiency, the current approach also provides additional information about contribution to protein solvation from specific fragments. Numerical studies are carried out to calculate solvation energies for a variety of peptides including alpha helices and beta sheets. Excellent agreement between the MFCC-CPCM result and those from the standard full system CPCM calculation is obtained. Finally, the MFCC-CPCM calculation is applied to several real proteins and the results are compared to classical molecular mechanics Poisson-Boltzmann (MM/PB) and quantum Divid-and-Conque Poisson-Boltzmann (D&C-PB) calculations. Large wave function distortion energy (solute polarization energy) is obtained from the quantum calculation which is missing in the classical calculation. The present study demonstrates that the MFCC-CPCM method is readily applicable to studying solvation of proteins.     

Characterization of Ascentis RP-Amide column: Lipophilicity measurement and linear solvation energy relationships

This study investigates lipophilicity determination by chromatographic measurements using the polar embedded Ascentis RP-Amide stationary phase. As a new generation of amide-functionalized silica stationary phase, the Ascentis RP-Amide column is evaluated as a possible substitution to the n  -octanol/water partitioning system for lipophilicity measurements. For this evaluation, extrapolated retention factors, log k^′_w$\text{log}{k^{\prime }}_w$, of a set of diverse compounds were determined using different methanol contents in the mobile phase. The use of n-octanol enriched mobile phase enhances the relationship between the slope (S  ) of the extrapolation lines and the extrapolated log k^′_w$\text{log}{k^{\prime }}_w$ (the intercept of the extrapolation), as well as the correlation between log P   values and the extrapolated log k^′_w$\text{log}{k^{\prime }}_w$ (1:1 correlation, r² = 0.966). In addition, the use of isocratic retention factors, at 40% methanol in the mobile phase, provides a rapid tool for lipophilicity determination. The intermolecular interactions that contribute to the retention process in the Ascentis RP-Amide phase are characterized using the solvation parameter model of Abraham. The LSER system constants for the column are very similar to the LSER constants of the n-octanol/water extraction system. Tanaka radar plots are used for quick visual comparison of the system constants of the Ascentis RP-Amide column and the n-octanol/water extraction system. The results all indicate that the Ascentis RP-Amide stationary phase can provide reliable lipophilic data.     

Monte Carlo-based linear Poisson-Boltzmann approach makes accurate salt-dependent solvation free energy predictions possible

The prediction of salt-mediated electrostatic effects with high accuracy is highly desirable since many biological processes where biomolecules such as peptides and proteins are key players can be modulated by adjusting the salt concentration of the cellular milieu. With this goal in mind, we present a novel implicit-solvent based linear Poisson-Boltzmann (PB) solver that provides very accurate nonspecific salt-dependent electrostatic properties of biomolecular systems. To solve the linear PB equation by the Monte Carlo method, we use information from the simulation of random walks in the physical space. Due to inherent properties of the statistical simulation method, we are able to account for subtle geometric features in the biomolecular model, treat continuity and outer boundary conditions and interior point charges exactly, and compute electrostatic properties at different salt concentrations in a single PB calculation. These features of the Monte Carlo-based linear PB formulation make it possible to predict the salt-dependent electrostatic properties of biomolecules with very high accuracy. To illustrate the efficiency of our approach, we compute the salt-dependent electrostatic solvation free energies of arginine-rich RNA-binding peptides and compare these Monte Carlo-based PB predictions with computational results obtained using the more mature deterministic numerical methods.     

Quantitative calculations of antibody--antigen binding: steroid--DB3 binding energies by the linear interaction energy method

Linear interaction energy/molecular dynamics calculations have been used to compute steroid/antibody binding energies. The absolute binding affinities of 10 steroids to antibody DB3 and of a hapten to catalytic antibody 1E9 are computed and compared to experiment. A detailed analysis of the molecular origins of the observed binding patterns is provided. The binding energy of an untested steroid is predicted.     

Linear solvation energy relations

Solvents have been parameterized by scales of dipolarity/polarizability ^*, hydrogen-bond donor (HBD) strength , and hydrogen-bond acceptor strength . Linear dependence (LSER's) on these solvent parameters are used to correlate and predict a wide variety of solvent effects, as well as to provide an analysis in terms of knowledge and theoretical concepts of molecular structural effects. Some recent applications utilizing this approach are presented. Included are analyses of solvent effects on (a) the free energies of transfer of tetraalkylammonium halide ion pairs and dissociated ions, (b) rates of nucleophilic substitution reactions, (c) the contrast in solvent effects of water (HBD) and dimethyl sulfoxide (non-HBD) on the acidities of m- and p-substituted phenols, (d) partition coefficients of non-HBD solutes between solvent bilayers, and (e) family relationships between proton transfer (and non-protonic Lewis acid) basicities and corresponding values for monomer HBA. A comprehensive summary of LSER with references is given.Session lecture, Ninth International Conference on Non-Aqueous Solutions, Pittsburgh, PA, August 1984.     

Use of linear solvation energy relationships for characterization of hypercrosslinked polystyrene stationary phases

Linear solvation energy relationships (LSER model) was tested for the characterization of hypercrosslinked polystyrene (HCPS) stationary phases for high-performance liquid chromatography (HPLC). Analysis of LSER coefficients showed that hydrophobic and electrostatic interactions are the major contributors to retention on HCPS. Fluorine atoms in HCPS increase the fractions of both hydrophobic and electrostatic interactions in the retention. The utility of fluorinated HCPS in the separation of di-n-phthalate mixtures by reversed-phase liquid chromatography was demonstrated.     

A solvolysis model for 2-chloro-2-methyladamantane based on the linear solvation energy approach

Solvolysis/dehydrohalogenation rates of 2-chloro-2-methyladamantane (CMA) in 15 hydrogen-bond acidic and/or basic solvents are studied. The rates of reaction in these solvents have been correlated with the solvation equation developed by Kamlet, Abraham, and Taft. The linear solvation energy relationship (LSER) derived from this study is given by the following equation: log k = -5.409 + 2.219 + 2.505alpha(1) - 1.823beta(1) where , alpha(1), and beta(1) are the solvation parameters that measure the solvent dipolarity/polarizability, hydrogen-bond acidity (electrophilicity), and hydrogen-bond basicity (nucleophilicity). A high correlation coefficient (r = 0.996, SD = 0.191) was achieved. The cavity term, which includes the Hildebrand parameter for solvent cohesive energy density, delta(H), was not found to be statistically significant for this reaction substrate. The resulting equation allows calculated rates of reaction in other solvents and provides insight into the reaction pathway. In a previously reported correlation for another tertiary chloride, tert-butyl chloride (TBC), the coefficients for alpha(1) and are significantly larger and the coefficient for is statistically significant. In addition, the coefficient for beta(1) in the TBC correlation is positive, rather than negative, indicating that the transition states for TBC and CMA are significantly different. These results demonstrate why the uses of simple solvolytic correlation methods may be invalid even for comparisons of similar type substrates, e.g., tertiary chlorides. Also, these results provide confidence in the use of multiple linear regression analysis for predicting solvolytic rates in additional solvents.