The surface exposed amino acid residues of monomeric proteins determine the partitioning in aqueous two-phase systems

An overview of descriptors to capture protein properties - Tools and perspectives in the context of QSAR modeling

Proteins are important ingredients in food and feed, they are the active components of many pharmaceutical products, and they are necessary, in the form of enzymes, for the success of many technical processes. However, production can be challenging, especially when using heterologous host cells such as bacteria to express and assemble recombinant mammalian proteins. The manufacturability of proteins can be hindered by low solubility, a tendency to aggregate, or inefficient purification. Tools such as in silico protein engineering and models that predict separation criteria can overcome these issues but usually require the complex shape and surface properties of proteins to be represented by a small number of quantitative numeric values known as descriptors, as similarly used to capture the features of small molecules. Here, we review the current status of protein descriptors, especially for application in quantitative structure activity relationship (QSAR) models. First, we describe the complexity of proteins and the properties that descriptors must accommodate. Then we introduce descriptors of shape and surface properties that quantify the global and local features of proteins. Finally, we highlight the current limitations of protein descriptors and propose strategies for the derivation of novel protein descriptors that are more informative.

Aqueous Two-Phase Systems and Microfluidics for Microscale Assays and Analytical Measurements

Phase separation is a common occurrence in nature. Synthetic and natural polymers, salts, ionic liquids, surfactants, and biomacromolecules phase separate in water, resulting in an aqueous two-phase system (ATPS). This review discusses the properties, handling, and uses of ATPSs. These systems have been used for protein, nucleic acid, virus, and cell purification and have in recent years found new uses for small organics, polysaccharides, extracellular vesicles, and biopharmaceuticals. Analytical biochemistry applications such as quantifying protein-protein binding, probing for conformational changes, or monitoring enzyme activity have been performed with ATPSs. Not only are ATPSs biocompatible, they also retain their properties at the microscale, enabling miniaturization experiments such as droplet microfluidics, bacterial quorum sensing, multiplexed and point-of-care immunoassays, and cell patterning. ATPSs include coacervates and may find wider interest in the context of intracellular phase separation and origin of life. Recent advances in fundamental understanding and in commercial application are also considered.

Salt-containing aqueous two-phase system shows predictable partition of proteins with surface amino acids residues

Aqueous two-phase system (ATPS) containing salts has been used for protein purification and enrichment. However, it is unclear how proteins are partitioned in the top or bottom phases of the system. In this study, we demonstrate that the partition of proteins in salt-containing ATPS (SATPS) depends only on the relation between the protein-surface amino acids and the type of salt using SATPS. The partition coefficients of four proteins changed depending on the kind of salt, according to the Hofmeister series. Interestingly, the partition coefficients of the proteins correlated to those of the combination of the amino acids in the surface of the protein with the correlation coefficients of >0.9. The results suggest that the interaction between the protein surface and aqueous ions plays an indispensable role for the partition of proteins in SATPS that can help in the design of protein partition in ATPS for purification and enrichment.

Selective separation method of aggregates from IgG solution by aqueous two-phase system

Aggregation of immunoglobulin G (IgG) is a serious concern that results in immunogenicity in pharmaceutical applications. Removal of the small and soluble aggregates in protein solutions through a simple method remains challenging. Here we show that an aqueous two-phase system (ATPS) can be used for the elimination of soluble aggregates from IgG solution. Polyethylene glycol (PEG) and dextran (DEX) were selected as components of the ATPS. As expected, IgG monomers were partitioned into the top or bottom phases of ATPS. Interestingly, almost all the small and soluble aggregates of IgG were extracted to the interface between top and bottom phases, rather than in the liquid phases. The partitioning of monomers and aggregates of IgG can be attributed to the solubility of these protein states in PEG and DEX. Thus, ATPS using PEG and DEX can be employed for the simple removal method of soluble aggregates from IgG solution.

Emerging Biotechnology Applications of Aqueous Two-Phase Systems

Liquid-liquid phase separation between aqueous solutions containing two incompatible polymers, a polymer and a salt, or a polymer and a surfactant, has been exploited for a wide variety of biotechnology applications throughout the years. While many applications for aqueous two-phase systems fall within the realm of separation science, the ability to partition many different materials within these systems, coupled with recent advances in materials science and liquid handling, has allowed bioengineers to imagine new applications. This progress report provides an overview of the history and key properties of aqueous two-phase systems to lend context to how these materials have progressed to modern applications such as cellular micropatterning and bioprinting, high-throughput 3D tissue assembly, microscale biomolecular assay development, facilitation of cell separation and microcapsule production using microfluidic devices, and synthetic biology. Future directions and present limitations and design considerations of this adaptable and promising toolkit for biomolecule and cellular manipulation are further evaluated.

Solvent interaction analysis as a proteomic approach to structure-based biomarker discovery and clinical diagnostics

Proteins have several measurable features in biological fluids that may change under pathological conditions. The current disease biomarker discovery is mostly based on protein concentration in the sample as the measurable feature. Changes in protein structures, such as post-translational modifications and in protein-partner interactions are known to accompany pathological processes. Changes in glycosylation profiles are well-established for many plasma proteins in various types of cancer and other diseases. The solvent interaction analysis method is based on protein partitioning in aqueous two-phase systems and is highly sensitive to changes in protein structure and protein-protein- and protein-partner interactions while independent of the protein concentration in the biological sample. It provides quantitative index: partition coefficient representing changes in protein structure and interactions with partners. The fundamentals of the method are presented with multiple examples of applications of the method to discover and monitor structural protein biomarkers as disease-specific diagnostic indicators.

Partitioning in aqueous two-phase systems: Analysis of strengths, weaknesses, opportunities and threats

For half a century aqueous two-phase systems (ATPSs) have been applied for the extraction and purification of biomolecules. In spite of their simplicity, selectivity, and relatively low cost they have not been significantly employed for industrial scale bioprocessing. Recently their ability to be readily scaled and interface easily in single-use, flexible biomanufacturing has led to industrial re-evaluation of ATPSs. The purpose of this review is to perform a SWOT analysis that includes a discussion of: (i) strengths of ATPS partitioning as an effective and simple platform for biomolecule purification; (ii) weaknesses of ATPS partitioning in regard to intrinsic problems and possible solutions; (iii) opportunities related to biotechnological challenges that ATPS partitioning may solve; and (iv) threats related to alternative techniques that may compete with ATPS in performance, economic benefits, scale up and reliability. This approach provides insight into the current status of ATPS as a bioprocessing technique and it can be concluded that most of the perceived weakness towards industrial implementation have now been largely overcome, thus paving the way for opportunities in fermentation feed clarification, integration in multi-stage operations and in single-step purification processes.

Effects of osmolytes on protein–solvent interactions in crowded environments: study of sucrose and trehalose effects on different proteins by solvent interaction analysis

The logarithms of the partition coefficients of proteins in the presence of 0.5 M sucrose and trehalose are linearly interrelated.

Structural features important for differences in protein partitioning in aqueous dextran-polyethylene glycol two-phase systems of different ionic compositions

Partitioning of 15 proteins in dextran-70-polyethylene glycol (PEG)-8000 aqueous two-phase systems (ATPSs) in the presence of 0.01M sodium phosphate buffer, pH7.4 was studied. The effect of salt additives (NaCl, CsCl, Na2SO4, NaClO4 and NaSCN) at different concentrations on the protein partition behavior was examined. The salt effects on protein partitioning were analyzed by using the Collander solvent regression relationship between the protein partition coefficients in ATPSs with and without salt additives. The results obtained show that the presence and concentration of salt additives affect the protein partition behavior. Analysis of ATPSs in terms of the differences between the relative hydrophobicity and electrostatic properties of the phases does not explain the protein partition behavior. The differences between protein partitioning could not be explained by the protein size. The structural signatures for the proteins were constructed from partition coefficient values in four ATPSs with different salt additives, and the structural distances were calculated using cytochrome c as the reference structure. The structural distances for all the examined proteins (except lysozyme) were found to be interrelated. Analysis of about 50 different descriptors of the protein structures revealed that the partition behavior of proteins is determined by the peculiarities of their surfaces (e.g., the number of water-filled cavities and the averaged hydrophobicity of the surface residues) and by the intrinsic flexibility of the protein structure measured in terms of the B-factor (or temperature factor).

Kinetics of protein unfolding at interfaces

The conformation of protein molecules is determined by a balance of various forces, including van der Waals attraction, electrostatic interaction, hydrogen bonding, and conformational entropy. When protein molecules encounter an interface, they are often adsorbed on the interface. The conformation of an adsorbed protein molecule strongly depends on the interaction between the protein and the interface. Recent time-resolved investigations have revealed that protein conformation changes during the adsorption process due to the protein-protein interaction increasing with increasing interface coverage. External conditions also affect the protein conformation. This review considers recent dynamic observations of protein adsorption at various interfaces and their implications for the kinetics of protein unfolding at interfaces.

Aqueous two-phase systems for protein separation: a perspective

Aqueous two-phase systems (ATPS) that are formed by mixing a polymer (usually polyethylene glycol, PEG) and a salt (e.g. phosphate, sulphate or citrate) or two polymers and water can be effectively used for the separation and purification of proteins. The partitioning between both phases is dependent on the surface properties of the proteins and on the properties of the two phase system. The mechanism of partitioning is complex and not very easy to predict but, as this review paper shows, some very clear trends can be established. Hydrophobicity is the main determinant in the partitioning of proteins and can be measured in many different ways. The two methods that are more attractive, depending on the ATPS used (PEG/salt, PEG/polymer), are those that consider the 3-D structure and the hydrophobicity of AA on the surface and the one based on precipitation with ammonium sulphate (parameter 1/m*). The effect of charge has a relatively small effect on the partitioning of proteins in PEG/salt systems but is more important in PEG/dextran systems. Protein concentration has an important effect on the partitioning of proteins in ATPS. This depends on the higher levels of solubility of the protein in each of the phases and hence the partitioning observed at low protein concentrations can be very different to that observed at high concentrations. In virtually all cases the partition coefficient is constant at low protein concentration (true partitioning) and changes to a different constant value at a high overall protein concentration. Furthermore, true partitioning behavior, which is independent of the protein concentration, only occurs at relatively low protein concentration. As the concentration of a protein exceeds relatively low values, precipitation at the interface and in suspension can be observed. This protein precipitate is in equilibrium with the protein solubilized in each of the phases. Regarding the effect of protein molecular weight, no clear trend of the effect on partitioning has been found, apart from PEG/dextran systems where proteins with higher molecular weights partitioned more readily to the bottom phase. Bioaffinity has been shown in many cases to have an important effect on the partitioning of proteins. The practical application of ATPS has been demonstrated in many cases including a number of industrial applications with excellent levels of purity and yield. This separation and purification has also been successfully used for the separation of virus and virus-like particles.

Solvent properties governing protein partitioning in polymer/polymer aqueous two-phase systems

Distribution coefficients of various proteins were measured in aqueous Dextran-Ficoll, Dextran-PES, and Ficoll-PES two-phase systems, containing 0.15M NaCl in 0.01 M phosphate buffer, pH 7.4. The acquired data were combined with data for the same proteins in different systems reported previously and known solvatochromic solvent properties of the systems to characterize the protein-solvent interactions. The relative susceptibilities of proteins to solvent dipolarity/polarizability, solvent hydrogen bond acidity, solvent hydrogen bond basicity, and solvent ability to participate in ion-ion and ion-dipole interactions were characterized. These parameters, which are representative of solute-solvent interactions, adequately described the partitioning of the proteins in each system. It was found that the relative susceptibilities of proteins to solvent dipolarity/polarizability are interrelated with their relative susceptibilities to solvent hydrogen bond acidity and solvent hydrogen bond basicity similarly to those established previously for small nonionic organic compounds.

Identification of the roles of conserved charged residues in the extracellular domain of an epithelial sodium channel (ENaC) subunit by alanine mutagenesis

Epithelial sodium channels (ENaC) are composed of three homologous subunits whose extracellular domains (ECD) form a funnel that directs ions from the lumen into the pore of ENaC. To examine the roles of conserved charged residues (Asp, Glu, Arg, and Lys) on ECD, we mutated 16 residues in human α-ENaC to alanine. The modified cRNAs were expressed in Xenopus laevis oocytes together with wild-type β- and γ-ENaC. The effect of each mutation was examined on three parameters: amiloride-sensitive Na(+) conductance (assayed by the two-electrode voltage-clamp method), Na(+)-dependent self-inhibition of ENaC, and oocyte cell surface expression of ENaC (quantitated by confocal microscopy of yellow fluorescent protein linked to γ-ENaC). Mutation of 13 of 16 residues reduced the ENaC Na(+) conductance (to 40-80% of WT). Mutation of only six residues showed a significant effect on the Na(+) self-inhibition time constant (τ). All 16 mutants showed a strong correlation between ENaC activity and oocyte surface expression (r = 0.62). Exclusion of four mutants showing the greatest effect on self-inhibition kinetics (Glu250 and Arg350 with τ = ~30% of WT, and Asp393 and Glu530 with τ = ~170% of WT) increased the correlation to r = 0.87. In the ASIC1 homotrimeric model, the homologs of α-ENaC Asp400 and Asp446 are exposed on the protein surface far from the other two chains. The mutations of these two residues showed the strongest effect on cell surface expression but had no effect on self-inhibition. Control mutations to a homologous charged residue (e.g., Asp to Glu) did not significantly affect ENaC activity. Changes in the two parameters, Na(+) self-inhibition and oocyte surface expression level, accounted for the magnitude of reduction in ENaC activity as a result of the mutation to Ala. These results establish that while some conserved charged residues are part of the structure responsible for Na(+) self-inhibition, most are essential for transport to the oocyte cell surface.

Methods of calculating protein hydrophobicity and their application in developing correlations to predict hydrophobic interaction chromatography retention

Hydrophobic interaction chromatography (HIC) is a key technique for protein separation and purification. Different methodologies to estimate the hydrophobicity of a protein are reviewed, which have been related to the chromatographic behavior of proteins in HIC. These methodologies consider either knowledge of the three-dimensional structure or the amino acid composition of proteins. Despite some restrictions; they have proven to be useful in predicting protein retention time in HIC.

Formulation Development for Hydrophobic Therapeutic Proteins

The major challenges in formulation development for hydrophobic proteins are low solubility often combined with a strong tendency for adsorption. Human serum albumin (HSA) is frequently used as excipient to overcome these problems. Due to several drawbacks with HSA, new ways need to be found to circumvent the use of this excipient in protein formulations. One possible approach is to select an appropriate formulation pH and ionic strength in combination with excipients that provide sufficient stability and solubility for the hydrophobic protein. A reduction in adsorption can be achieved by adding surfactants or using special containers.

"On the Collander equation": protein partitioning in polymer/polymer aqueous two-phase systems

Distribution coefficients of randomly selected proteins were measured in aqueous two-phase systems (ATPSs) formed by different combinations of Dextran-75 (Dex), Ficoll-70, polyethylene glycol-8000 (PEG), hydroxypropyl starch-100 (PES), and Ucon50HB5100 (Ucon, a random copolymer of ethylene glycol and propylene glycol) at particular polymer concentrations, all containing 0.15M NaCl in 0.01 M phosphate buffer, pH 7.4. Most of the proteins in the PEG-Ucon system precipitated at the interface. In the other ATPSs, namely, PES-PEG, PES-Ucon, Ficoll-PEG, Ficoll-Ucon, and in Dex-PEG and Dex-Ucon described earlier the distribution coefficients for the proteins were correlated according to the solvent regression equation: lnKi=aiolnKo+bio, where Ki and Ko are the distribution coefficients for any protein in the ith and oth two-phase systems. Coefficients aio and bio are constants, the values of which depend upon the particular compositions of the two-phase systems under comparison.

DeltaG(CH2) as solvent descriptor in polymer/polymer aqueous two-phase systems

Phase diagrams were determined for aqueous two-phase systems (ATPSs) formed by different paired combinations of Dextran (Dex-75), Ficoll-70, polyethylene glycol (PEG-8000), hydroxypropyl starch (PES-100), and Ucon50HB5100 (a random copolymer of ethylene glycol and propylene glycol) all containing 0.15M NaCl in 0.01M phosphate buffer, pH 7.4, at 23 degrees C. Partition coefficients of a series of dinitrophenylated (DNP) amino acids with aliphatic side-chains were studied in all the ATPSs at particular polymer concentrations. Free energies of transfer of a methylene group between the coexisting phases, DeltaG(CH(2)), were determined as measures of the difference between the hydrophobic character of the phases. Furthermore, partition coefficients of tryptophan (Trp) and its di- and tri-peptides and a set of p-nitrophenyl (NP)-monosaccharides were measured in all the two-phase systems, and the data obtained compared with the DeltaG(CH(2)) values obtained in the systems. It was established that for eight out of 10 of two-phase systems of different polymer compositions the partition coefficients for Trp peptides correlate well with the DeltaG(CH(2)) values. Similar correlations for NP-monosaccharides were valid for seven out of 10 two-phase systems. These observations indicate that the difference between the hydrophobic characters of the coexisting phases represented by the DeltaG(CH(2)) value cannot be used as a single universal measure for comparison of the ATPSs of different polymer compositions.

Effect of excipients on the encapsulation efficiency and release of human growth hormone from dextran microspheres

The possibility was investigated to modulate the encapsulation efficiency and release of human growth hormone (hGH) from hydroxyl ethyl methacrylated dextran (dex-HEMA) hydrogel microspheres by using excipients. Microspheres were prepared by polymerization of dex-HEMA in an aqueous two-phase system of this polymer and PEG with or without excipients (Tween 80, pluronic F68, sucrose, NaCl, urea or methionine). High hGH encapsulation efficiencies (50-70%) were obtained for microspheres prepared without excipients and with Tween 80, NaCl or methionine. Substantially lower encapsulation efficiencies (27% and 19%, respectively) were obtained for microspheres prepared in the presence of sucrose and urea, which was attributed to the more favoured partitioning of hGH over the PEG-phase due to higher hydrophobicity of the (partly) denatured hGH. Likely, differences in precipitate size of the encapsulated hGH resulted in different release profiles between microspheres prepared without excipients (biphasic release: 2 days delay time followed by 6 days release) and the release profile for microspheres prepared with Tween 80, pluronic F68, sucrose, NaCl and urea (release over a period of 6-8 days (without a delay time)). Microspheres prepared with methionine showed a concentration-dependent delay time varying from 0 to 2 days followed by almost zero-order release over 6 days, attributed to the effect of methionine on the polymerization of dex-HEMA. Especially, Tween 80 and methionine are attractive excipients since hGH was encapsulated in high yield (60-70%) and the protein was released from the microspheres mainly in its monomeric form without a delay time and with an almost zero-order release over 6-8 days.

Current insights on protein behaviour in hydrophobic interaction chromatography

This paper gives a summary of different aspects for predicting protein behaviour in hydrophobic interaction chromatography (HIC). First, a brief description of HIC, hydrophobic interactions, amino acid and protein hydrophobicity is presented. After that, several factors affecting protein chromatographic behaviour in HIC are described. Finally, different approaches for predicting protein retention time in HIC are shown. Using all this information, it could be possible to carry out computational experiments by varying the different operating conditions for the purification of a target protein; and then selecting the best conditions in silico and designing a rational protein purification process involving an HIC step.

Prediction of retention time of cutinases tagged with hydrophobic peptides in hydrophobic interaction chromatography

Hydrophobic interaction chromatography (HIC) is an important technique for protein purification, which exploits the separation of proteins based on hydrophobic interactions between the stationary phase ligands and hydrophobic regions on the protein surface. One way of enhancing the purification efficiency by HIC is the addition of short sequences of peptide tags to the target protein by genetic engineering, which could reduce the need for extra and expensive chromatographic steps. In the present work, a methodology for predicting retention times of cutinases tagged with hydrophobic peptides in HIC is presented. Cutinase from Fusarium solani pisi fused to tryptophan-proline (WP) tags, namely (WP)2 and (WP)4, and produced in Saccharomyces cerevisiae strains, were used as model proteins. From the simulations, the methodology based on tagged hydrophobic definition proposed by Simeonidis et al. (Phitagged), associated to a quadratic model for predicting dimensionless retention times, showed small differences (RMSE<0.022) between observed and estimated retention times. The difference between observed and calculated retention times being lower than 2.0% (RMSE<0.022) for the two tagged cutinases at three different stationary phases, except for the case of cut_(wp)2 in octyl sepharose-2 M ammonium sulphate. Therefore, we consider that the proposed strategy, based on tagged surface hydrophobicity, allows prediction of acceptable retention times of cutinases tagged with hydrophobic peptides in HIC.

Hydrodynamically coupled water in surface adsorbed amino acids as a tool to study hydrated peptides

The influence of different amino acid residues on properties of a protein surface is of great interest and importance. Hydrodynamically coupled water in the amino acids has the potential to be used as a tool to study surface properties of proteins. The contribution of this coupled water fraction in design of a hydropathy scale in surface adsorbed amino acid films on solid using quartz crystal microbalance is presented in this work. This scale compares well with the hydropathy scale of Guy reported in the literature and can be correlated with the solid/liquid interfacial tension and work of adhesion of the adsorbed amino acid films. Using Graphical Representation and Analysis of Surface Properties (GRASP) the free energy of transfer from Octanol to water for the amino acids has been estimated and shows approximately an inverse relationship with the coupled water fraction. This scale has been applied in a benchmark test for a native Laminin peptide YIGSR and its mutated sequences (with mutations carried out at 'Y and 'R' positions). The experimentally measured coupled water fractions seem to compare well with that obtained from the present scale assuming the total solvent fraction to be a linear function of the amino acids in the sequence. A survey of the protein data bank showed that sets of sequences based on this scale occur in membrane insertion domain or in trans-membrane proteins suggesting that the scale is suitable to study structure-function correlation in proteins.

Classification of protein adsorption and recovery at low salt conditions in hydrophobic interaction chromatographic systems

There is significant interest in establishing appropriate bioprocessing conditions for protein adsorption in hydrophobic interaction chromatographic (HIC) systems without the need for high salt concentrations. In this paper, the adsorption and recovery of proteins under low salt conditions in HIC systems was investigated using a variety of experimental and computational techniques. Parallel batch screening was employed to determine protein adsorption and recovery. Experiments were carried out with twenty six proteins using five resins with different ligand chemistry, ligand density and backbone chemistry. Proteins were classified based on various combinations of adsorption and recovery behavior. In order to gain insight into the effect of protein properties on this behavior, molecular descriptors were computed based on protein crystal structure and primary sequence information as well as a set of hydrophobicity descriptors based on the solvent accessible surface area of the proteins. Finally, classification software CART was employed to determine the key molecular descriptors associated with various types of adsorption behavior.

Aqueous two-phase extraction for protein recovery from corn extracts

Corn has been used as an expression host for several recombinant proteins with potential for large-scale production. Cost-effective downstream initial recovery, separation and concentration remain a challenge. Aqueous two-phase (ATP) partitioning has been used to recover and concentrate proteins from fermentation broths and offers advantages for integration of those steps with biomass removal. To examine the applicability of ATP partitioning to recombinant protein purification from corn endosperm and germ, ATP system parameters including poly(ethylene glycol) (PEG) molecular weight (MW), phase-forming salt, tie line length (TLL), and pH were manipulated to control partitioning of extracted native proteins from each fraction. Moderate PEG MW, reduction of phase ratio, and added NaCl effected complete recovery of the hydrophobic model protein lysozyme in the top phase with ca. 5x enrichment and illustrates a favorable match of recombinant protein characteristics, expression host, and separation method. Furthermore, integration of protein extraction with the partitioning reduced the load of contaminating host proteins relative to the more traditional separate steps of extraction followed by partitioning. Performance of the integrated partitioning was hindered by endosperm solids loading, whereas for germ, which has ca. 35x higher aqueous soluble protein, the limit was protein solubility. For more hydrophilic model proteins (the model being cytochrome c), effective separation required further reduction of PEG MW to effect more partitioning of host proteins to the top phase and enrichment of the model protein in the lower phase. The combination of PEG MW of 1450 with 8.5 wt.% NaCl addition (Na(2)SO(4) as the phase-forming salt) provided for complete recovery of cytochrome c in the lower phase with enrichment of 9x (germ) and 5x (endosperm). As a result of lower-phase recovery, the advantage of simultaneous removal of solids is lost. The lower solubility of native endosperm proteins results in higher purity for the same enrichment.

Electrostatic calculations and quantitative protein retention models for ion exchange chromatography

A novel set of protein descriptors has been developed to increase the understanding of protein behavior on chromatographic media. The protein descriptors are pH-dependent and based on electrostatic and hydrophobic properties of mainly the surface of the proteins as revealed by their three-dimensional structure. Interpretable and predictive quantitative structure property relationship (QSPR) models were then obtained for protein retention in ion exchange chromatography at different pH values. In most cases the calculated average surface potential could be directly related to retention times. Moreover, the high retention of human lactoferrin observed in cation exchange even at high pH values could be modeled by adding descriptors of the charge asymmetry.