Ion exchange chromatography of proteins-prediction of elution curves and operating conditions. I. Theoretical considerations

A mathematical model is proposed for the elution of proteins on ion exchange columns by a linear gradient increase and stepwise increase of ionic strength in order to predict relationships between the elution characteristics (the peak position, the peak width, etc.) and the operating conditions (the flow rate, the slope of gradient, etc). This model is in principle based on the continuous-flow plate theory, in which the protein concentration and ionic strength dependent distibution coefficient between proteins and ion exchangers and zone sperading effects are taken into consideration. The advantage of this model is its simplicity since it requires only two parameters: The distribution coefficient and the number of plates. Since the distribution coefficient of proteins depends on both the protein concentration and ionic strength of the elution buffer, the number of plates should vary with time. However, it is extremely difficult to take into consideration the time-dependent number of plates. Therefore, we assume that the number of plates is constant and related to that number derived from a mass balance model which includes longitudinal dispersion and gel phase diffusion. On the basis of these assumptions, a method for determining the number of plates by the moment method is presented. Although the dependencies of the peak position and peak width on the slope of linear gradient are predictable by numerical calculations of the present model, simpler methods for prediction of these dependencies are desirable. A graphical method is proposed for prediction of the peak position. For prediction of the peak width, an asymptotic solution is derived from a quasi-steady-state model.     

A Stereoselective Synthesis of (±)-endo-Brevicomin,a Pheromone Inhibitor Produced by Dendroctonus Bark Beetles

Prediction of elution curves in gel chromatography was attempted on the basis of a mass balance model which gave consideration to gel phase diffusion and longitudinal dispersion in a column. The basic differential equations for the model were solved by means of Laplace transformation, and then the solution in Laplace domain was inverted into time domain numerically. The calculated elution curves were in good agreement with the experimental ones of NaCl and myoglobin with various Sephadex gel columns. This indicated the validity of the calculation method and the model employed in this study.

Furthermore, the elution curves were calculated tentatively for various combinations of the parameters appearing in the mass balance model. Then, the magnitude of peak asymmetry, the shift of peak position and the maximum peak height of the elution curves were correlated with various parameters and operational variables. These correlations might permit prediction of suitable operational conditions for gel chromatography, especially for molecular weight determination.     

Predicting the elution behavior of proteins in affinity chromatography on non-porous particles.

Affinity chromatography on non-porous particles of microsize is particularly useful for the rapid analysis and micropreparative separation of proteins. The elution behavior of proteins in an affinity column packed with non-porous copolymerized particles of styrene, methyl methacrylate and glycidyl methacrylate was investigated both theoretically and experimentally, using the lysozyme-Cibacron Blue 3G-A affinity system. Equations used to predict the elution profiles, resulting from the elution by increasing the ionic strength (NaCl concentration) in the mobile phase, were obtained. The maximum adsorbate concentration, desorption rate constant and equilibrium constant under elution conditions were determined by matching experimental data with predicted elution profiles. Based on the parameters determined at a flow-rate of 0.5 ml/min and with 1 M NaCl in the elution buffer, the model equations could predict the elution profiles for other experimental runs, where different flow-rates and sodium chloride concentrations were used. Both the experimental and predicted results revealed that the affinity interaction kinetics are not significantly influenced by the flow-rate and, hence, the film mass transfer. To elute bound lysozyme from immobilized dye ligand, a higher value of the ionic strength leads to a faster elution and a sharper elution peak. The influence of elution conditions on the kinetic and thermodynamic parameters and, consequently, on the elution peak profiles was evaluated. The model equations can also predict the behavior of protein elution from an affinity column by changing the pH of the mobile phase, according to a previous study.     

Performance of hydrophobic chromatography in purification of alpha-amylase

Hydrophobic ligands were introduced onto agarose beads, and the adsorption capacity of the beads was measured. The adsorption capacity increased with increase in the carbon number of the ligand, ionic strength of the buffer solution, and temperature. Crude alpha-amylase was purified with these hydrophobic adsorbents and the breakthrough and elution curves were estimated based on the mass transfer theory. Under strongly hydrophobic conditions, impurities contained in crude feeds and the lack of uniformity of packing caused by aggregation of beads affected adsorption and elution behaviors.     

Mathematical modeling of elution curves for a protein mixture in ion exchange chromatography applied to high protein concentration

Protein elution curves in ion exchange chromatography (IEC) were simulated with a rate model. Three pure proteins and their mixture were used (α‐lactalbumin, BSA, and conalbumin) under different operational conditions. The anionic matrix Q‐Sepharose FF was used packed in a 1 mL column. A high protein concentration (37.5 mg/mL of total protein injected into the column) was used in order to extend the utility of the model. Mass transfer parameters were calculated using empiric correlations, where the axial dispersion was negligible (Pe > 300) and the mass transfer was controlled by the intraparticle diffusion (Bi > 10). The model assumes a modulator–eluite relationship were the equilibrium constant of the Langmuir isotherm was a function of salt concentration. Adsorption kinetic parameters were estimated from experimental data. The parameters for pure proteins were determined, and elution curves for changes in flow rate, ionic strength gradient, concentration, and sample size were predicted by the model. Then the kinetic parameters of the mixture were determined under the same operational conditions and some of the parameters had to be modified to take into account effects such as protein–protein interactions, competition, and displacement. Experimental elution curves obtained for changes in operational conditions such as flow rate and ionic strength gradient were simulated by the rate model for the protein mixture with a relative error in retention time of visible peaks <5%. IEC operational conditions and the peak fraction collection can be selected using a cost function of the production process which considers yield, purity, concentration, and process time that are obtained from simulations. Operational conditions that gave the minimum cost were selected. Simulations allows to diminish experimental time and cost. Biotechnol. Bioeng. 2009; 104: 572–581 © 2009 Wiley Periodicals, Inc.     

Prediction of formic acid chromatogram in gradient elution chromatography

Optimal operation in chromatography is needed to save operation time and the solvent used in multiple chromatographic runs. To this end, many simulation studies of chromatography process have been performed. The relationship between the distribution coefficient and the ionic strength is important in gradient elution ion chromatography. Experimental runs and computer simulation were carried out under linear gradient elution conditions in order to compare the experiments and the simulation. Experiments were performed with formic acid under isocratic conditions to determine the simulation equation parameters. Computer simulation was based on three equations which related distribution with ionic strength as follows;K=αI ^−β, K=A+BI+Cl² and. The effects of gradient slope on the chromatograms are discussed, and good agreement between the experimental and the simulated results is shown.     

Mathematical modeling of elution curves for a protein mixture in ion exchange chromatography and for the optimal selection of operational conditions

Elution curves in ionic exchange chromatography (IEC) for a three-protein mixture (alpha-lactoalbumin, ovalbumin, and beta-lactoglobulin), carried out under different flow rates and ionic strength conditions, were simulated using two different mathematical models. These models were the Plate Model and the more fundamentally based Rate Model. Relatively low protein concentrations were used to avoid protein-protein interactions. Simulated elution curves were compared with experimental data not used for parameter identification. Deviation between experimental data and the simulated curves using the Plate Model was less than 0.0189 (absorbance units); a slightly higher deviation [0.0252 (absorbance units)] was obtained when the Rate Model was used. A cost function was built that included the effect of the different production stages, namely fermentation, purification, and concentration. These considered the effect on the performance of IEC; yield, purity, concentration and the time needed to accomplish the separation. Operational conditions in the IEC such as flow rate, ionic strength gradient and the operational time can be selected using this model in order to find the minimum cost for the protein production process depending on the characteristics of the final product desired such as purity and yield. This cost function was successfully used for the selection of the operational conditions as well as the fraction of the product to be collected (peak cutting) in IEC. It can be used for protein products with different characteristics and qualities, such as purity and yield, by choosing the appropriate parameters.     

Studies on specific elution of rabbit muscle phosphofructokinase with allosteric ligands]

The specific elution of rabbit skeletal muscle phosphofructokinase (PFK) from DEAE-cellulose is studied in the linear gradient of different allosteric ligands. Citrate and fructose-6-phosphate elute PFK at concentrations of 1.0 and 2.5 mM respectively, i.e. without increasing the ionic strength of the starting buffer (similar to 0.12). The specificity of elution is confirmed by comparison of the ionic strength of these solutions with that of buffer eluting PFK in buffer gradient (mu=0.17) as well as by comparison with the eluting ability of other ligands. Fructose-1,6-diphosphate elutes PFK only at the concentration of 5.5 mM which corresponds to the ionic strength 0.17. MgATP and AMP are inefficient as specific eluents whereas ATP and ADP elute only a small part of PFK with concomitant substantial increase of the ionic strength (up to 0.17--0.18). These results are discussed in terms of a charge compensation mechanism as a result of the displacement of PFK conformers equilibrium under the influence of the allosteric ligands.     

Evaluation of different parameters for the purification of inulinase using an ion exchange fixed bed

The main conditions affecting the downstream process for purification of inulinase from Kluyveromyces marxianus var. bulgaricus ATCC 16045 were investigated. Parameters including the elution mode, linear rate, ionic strength, and elution pH were evaluated in order to achieve the best purification factor and recovery. The best purification factor and recovery were achieved in run 6 using a gradient elution mode with concentrations of NaCl ranging from 0 to 1 M, a linear flow rate of 100 cm/h and a pH value of 4.1. Under these conditions, the recovery was ∼ 67.5% and the purification factor ∼ 6.6-fold.     

Evaluation of differences between dual salt‐pH gradient elution and mono gradient elution using a thermodynamic model: Simultaneous separation of six monoclonal antibody charge and size variants on preparative‐scale ion exchange chromatographic resin

The efficiencies of mono gradient elution and dual salt‐pH gradient elution for separation of six mAb charge and size variants on a preparative‐scale ion exchange chromatographic resin are compared in this study. Results showed that opposite dual salt‐pH gradient elution with increasing pH gradient and simultaneously decreasing salt gradient is best suited for the separation of these mAb charge and size variants on Eshmuno^® CPX. Besides giving high binding capacity, this type of opposite dual salt‐pH gradient also provides better resolved mAb variant peaks and lower conductivity in the elution pools compared to single pH or salt gradients. To have a mechanistic understanding of the differences in mAb variants retention behaviors of mono pH gradient, parallel dual salt‐pH gradient, and opposite dual salt‐pH gradient, a linear gradient elution model was used. After determining the model parameters using the linear gradient elution model, 2D plots were used to show the pH and salt dependencies of the reciprocals of distribution coefficient, equilibrium constant, and effective ionic capacity of the mAb variants in these gradient elution systems. Comparison of the 2D plots indicated that the advantage of opposite dual salt‐pH gradient system with increasing pH gradient and simultaneously decreasing salt gradient is the noncontinuous increased acceleration of protein migration. Furthermore, the fitted model parameters can be used for the prediction and optimization of mAb variants separation in dual salt‐pH gradient and step elution. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:973–986, 2018     

Self-association of alpha-chymotrypsin at low ionic strength in the vicinity of its pH optimum.

The self-association of alpha-chymotrypsin and its di-isopropyl phosphoryl derivative in in I0.03 sodium phophate buffer, pH7,9, was investigated by velocity sedimentation, equilibrium sedimentation and difference gel chromatography. No differences between the native and chemically modified enzyme were observed in the ultracentrifuge studies, and only a marginal (0.6%) difference in weight-average elution volume was detected by difference gel chromatography of 5g/litre solutions on Sephadex G-75. From quantitative analyses of sedimentation velocity and sedimentation-equilibrium distributions obtained with iPr2P (di-isopropylphosphoryl)-chymotrypsin, the polymerizing system is postulated to involve an indefinite association of dimer (with an isodesmic association constant of 0.68 litre/g) that is formed by a discrete dimerization step with equilibrium constant 0.25 litre/g. In addition to providing the best fit of the experimental results, this model of chymotrypsin polymerization at low ionic strength is also consistent with an earlier observation that dimer formation is a symmetrical head-to-head phenomenon under conditions of higher ionic strength (I0.29, pH7.9) where association is restricted to a monomer-dimer equilibrium. It is proposed that the dimerization process is essentially unchanged by variation in ionic strength at pH7.9, and that higher polymers are formed by an entirely different mechanism involving largely electrostatic interactions between dimeric species.     

One-step chromatography method for efficient separation and purification of R-phycoerythrin from Polysiphonia urceolata

Phycoerythrins have been widely used in food, cosmetics, immunodiagnostics and analytical reagents. An efficient one-step chromatography method for purification of R-phycoerythrins from Polysiphonia urceolata was described in this paper. Pure R-phycoerythrin was obtained with an absorbance ratio A(565)/A(280) of 5.6 and a high recovery yield of 67.33% using a DEAE-Sepharose Fast Flow chromatography with a gradient elution of pH, alternative to common gradient elution of ionic strength. The absorption spectrum of R-phycoerythrin was characterized with three absorbance maxima at 565, 539 and 498 nm, respectively and the fluorescence emission spectrum at room temperature was measured to be 580 nm. The results of native-PAGE, and SDS-PAGE showed no contamination by other proteins in the phycoerythrin solution, which suggests an efficient method for the separation and purification of R-phycoerythrins from Polysiphonia urceolata.     

Characterization of solubilized insulin receptors from rat liver microsomes. Existence of two receptor species with different binding properties

Insulin receptors were solubilized from rat liver microsomes by the nonionic detergent Triton X-100. After gel filtration of the extract on Sepharose CL-6B, two insulin-binding species (peak I and peak II) were obtained. The structure and binding properties of both peaks were characterized. Gel filtration yielded Stokes radii of 9.2 nm (peak I) and 8.0 nm (peak II). Both peaks were glycoproteins. At 4 degrees C peak I showed optimal insulin binding at pH 8.0 and high ionic strength. In contrast, peak II had its binding optimum at pH 7.0 and low ionic strength, where peak I binding was minimal. For peak I the change in insulin binding under different conditions of pH and ionic strength was due to a change in receptor affinity only. For peak II an additional change in receptor number was found. Both peaks yielded non-linear Scatchard plots under most of the buffer conditions examined. At their binding optima at 4 degrees C the high affinity dissociation constants were 0.50 nM (peak I) and 0.55 nM (peak II). Sodium dodecyl sulfate/polyacrylamide gel electrophoresis of peak I revealed five receptor bands with Mr 400 000, 365 000, 320 000, 290 000, and 245 000 under non-reducing conditions. For peak II two major receptor bands with Mr 210 000 and 115 000 were found. The peak II receptor bands were also obtained after mild reduction of peak I. After complete reduction both peaks showed one major receptor band with Mr 130 000. The reductive generation of the peak II receptor together with molecular mass estimations suggest that the peak I receptor is the disulfide-linked dimer of the peak II receptor. Thus, Triton extracts from rat liver microsomes contain two receptor species, which are related, but differ considerably in their size and insulin-binding properties.     

The nonequilibrium character of DNA melting: effects of the heating rate on the fine structure of melting curves.

To investigate the effects of heating rate on the DNA melting profile and to test the predictions of the theory of slow relaxation processes in DNA melting (1) concerning these effects, we obtained differential melting curves for the Bsp I C1 fragment of T7 DNA (1461 bp) and the Sma I-Eco RI fragment of Col E1 DNA (1291 bp) at heating rates of 0.05 and 0.5 deg/min. At low ionic strength (0.02 M Na+) the heating rate has been shown to affect the position of the third peak in melting curve for C1 fragment. According to the melting maps (2), this peak corresponds to the unwinding of the section between the end of the molecule and the region already melted. At high ionic strength (0.2 M Na+), when the melting of this DNA is reversible (3), the position of the peaks does not depend on the heating rate. In the case of the Col E1 DNA fragment the heating rate affects, as might be expected from the melting maps (4), only the last peak, as the melting of the last section is always nonequilibrium. The results of the study are in good qualitative agreement and in satisfactory quantitative agreement with the theoretical predictions (1).     

A ‘simple clock’ approach of circadian rhythms: An easy way to predict the clock's singularity

A graphical method is presented which allows the prediction of phase resetting curves of circadian rhythms for both type 1 and type 0 resetting, starting from one experimentally determined phase resetting curve. Calculations were based on literature data for the pupal eclosion rhythm of Drosophila pseudoobscura. The method is based on the assumption that for all practical purposes the rhythm may be approached as a “simple clock”, i.e. an oscillator with only one state variable, namely its phase or circadian time, CT. Besides predicting both “types” of phase resetting the method is capable to locate the “position” of the phase singularity and thus the transition from type 1 to type 0 resetting. This graphical method is an elaboration of the “transformation method”, developed in 1972 by A. Johnsson and H. G. Karlsson, which was effective in predicting phase resetting by “strong” stimuli, but failed in the case of “weak” stimuli. Predictions made using the extended transformation method are in good agreement with experimental results obtained with Drosophila. Also for the flesh fly, Sarcophaga argyrostoma, a prediction is made of the position of the phase singularity of the eclosion rhythm and compared with experimental results.     

Displacement effects in large-scale chromatography?

Displacement effects in large-scale (total column volume v(t) = 150 L) and preparative ion-exchange chromatography purifying human erythrocyte superoxide dismutase are described in the present article. The biomolecules are eluted in a very small peak elution volume (<0.2 v(o)) behind the salt wave using a step gradient. The theoretical peak width and retention behavior are calculated according to the model of Yamamoto. The theoretical values are then compared with the experimental data. There was a difference observed between the elution type I (also called fronting) and the experimentally obtained elution. Some instructions are given on how to achieve these phenomenona because a beneficial effect in respect to resolution and recovery of a biomolecule is observed.     

Multiple enzyme purifications from muscle extracts by using affinity-elution-chromatographic procedures.

1. Starting with (NH4)2SO4 fractions of muscle extracts, procedures for purifying four to six separate enzymes from each fraction by using affinity-elution-chromatographic techniques are described. 2. Schemes for purifying 12 separate enzymes from rabbit muscle, and eight from chicken muscle extracts, are included. In nearly all cases the overall procedure involves three steps: the initial (NH4)2SO4 fractionation, the ion-exchange chromatography with affinity elution of the enzyme, and gel filtration. The specific activities of the enzymes so purified are comparable with the highest values in the literature. 3. The five schemes described include illustrations of affinity elution of the separate enzymes at different pH values, at different ionic strengths and in combination with conventional gradient elution. They also include stepwise adsorption on columns at different pH values. 4. Separation of two electrophoretically differing forms of phosphoglycerate kinase was achieved by gradient affinity elution from CM-cellulose. The lower-pI form was eluted by a lower concentration of substrate than the higher-pI form.     

Selectivity of IMAC columns in trypsin inhibitor purification

The properties of an adsorbent and the parameters in an adsorption process affect the resolution of chromatographic purifications. This is reflected in the elution profile, which shows the relative affinity of different proteins for a specific adsorbent. In the work presented here, elution profiles for trypsin inhibitor were used to study the effects of the concentration of trypsin inhibitor, ionic strength of the protein solution, slope of the elution gradient, and the regeneration treatment of the chromatography column on the selectivity of the adsorbent Cellufine Chelate-Cu(II)(ida). Cytochrome c was used as a reference protein. Variations in the concentrations of trypsin inhibitor and in the ionic strength of the buffered solution did not have any effects on the elution profile. On the other hand, changes in the slope of the pH gradient used for elution caused shifting of the elution peaks toward lower values of the elution volume, resulting in the best strategy to modify the elution profile of the system. Finally, using a constant slope pH gradient of elution, the variation of the selectivity of the adsorbent for trypsin inhibitor when subjected to cleaning treatments with 0.5 N NaOH was studied. Appropriate cleaning practices used in industry were followed. The adsorbent showed only a slight tendency for resolution loss in the order of 2 x 10(-4) days(-1). The results presented here show a good stability of the adsorbent when compared to other biospecific adsorbents commonly used.     

Separation of porphyrin isomers by high-performance liquid chromatography.

A reversed-phase gradient elution system is described for the simultaneous separation of the type I and type III isomers of 8-, 7-, 6-, 5- and 4-carboxylated porphyrins and isocoproporphyrins. The method, adaptable for isocratic and stepwise separation of individual groups of isomers, is also suitable for preparative isolation of pure porphyrins. The analyses of porphyrin isomers in the urine and faeces of porphyric patients are examples of applications.     

Expanded bed chromatography of proteins in small-diameter columns. II. Methods development and scale up

The scaled down system developed in Part I of this series was further validated by using a 1-cm diameter column for method development studies for the separation of two model proteins, alcohol dehydrogenase and -glucosidase, from unclarified yeast homogenate by hydrophobic interaction expanded bed chromatography based on the STREAMLINE matrix. The efficacy of solids removal and establishment of optimal binding and separation condition by stepwise elution were investigated. Equilibration of the EBA column and loading at high salt strengths affected the subsequent recovery of the two target proteins. Although good resolution between the target proteins could be achieved, peak tailing was found to be a consistent problem. The optimised separation protocol was scaled up 25-fold to a column diameter of 5.0 cm. The results were in good agreement with the run conducted in the 1-cm column, indicating the potential of using the small columns as an viable approach for method scouting and development studies.