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.     

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.     

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.     

Protein purification using chromatography: selection of type, modelling and optimization of operating conditions

To achieve a high level of purity in the purification of recombinant proteins for therapeutic or analytical application, it is necessary to use several chromatographic steps. There is a range of techniques available including anion and cation exchange, which can be carried out at different pHs, hydrophobic interaction chromatography, gel filtration and affinity chromatography. In the case of a complex mixture of partially unknown proteins or a clarified cell extract, there are many different routes one can take in order to choose the minimum and most efficient number of purification steps to achieve a desired level of purity (e.g. 98%, 99.5% or 99.9%). This review shows how an initial 'proteomic' characterization of the complex mixture of target protein and protein contaminants can be used to select the most efficient chromatographic separation steps in order to achieve a specific level of purity with a minimum number of steps. The chosen methodology was implemented in a computer- based Expert System. Two algorithms were developed, the first algorithm was used to select the most efficient purification method to separate a protein from its contaminants based on the physicochemical properties of the protein product and the protein contaminants and the second algorithm was used to predict the number and concentration of contaminants after each separation as well as protein product purity. The application of the Expert System approach was experimentally tested and validated with a mixture of four proteins and the experimental validation was also carried out with a supernatant of Bacillus subtilis producing a recombinant beta-1,3-glucanase. Once the type of chromatography is chosen, optimization of the operating conditions is essential. Chromatographic elution curves 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. 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. In order to optimize operating conditions, a cost function was built that included the effect of the different production stages, namely fermentation, purification and concentration. This cost function was also successfully used for the determination of the fraction of product to be collected (peak cutting) in chromatography. It can be used for protein products with different characteristics and qualities, such as purity and yield, by choosing the appropriate parameters.     

“Ordered” structure in solutions and gels of a globular protein as studied by small angle neutron scattering

Small-angle neutron scattering measurements were used for structural investigation of β-lactoglobulin solutions and heat-set gels in conditions of strong double layer repulsions. At pH 9 and low ionic strength, a correlation peak was observed on the scattering curves of the solutions whatever the protein concentration C used (in the range C = 0.02–0.10 g/mL). The wave vector value q_max corresponding to these maxima scaled as C^0.25. This exponent value is in agreement with those reported in the literature for other globular proteins in the same concentration range. Increasing the ionic strength decreased the peak which vanished without changing position at 0.1M NaCl. This polyelectrolyte-like behaviour suggests a local structure in the protein solution due to double layer repulsions. In the case of heat-set aggregates and gels (0.02–0.13 g/mL) formed at pH 9 and low ionic strength, a peak in the scattering curves was also observed indicating that even after gelation a correlation is still present; q_max varied as C^0.5. As in the case of the solutions, the correlation peak decreased with increasing ionic strength, and it vanished at 0.06M NaCl. The dilution of the aggregates in order to determine their intraparticle structure factor showed that the correlations were lost and that the aggregates displayed the same internal structure as the elementary subunit in the gels. At high ionic strength, fractal structures of the aggregates down to a length scale of about 40 Å were observed with d_f = 1.3–1.75 ± 0.05, increasing with protein concentration. Subsequent dilution didn't change the fractal dimension of these structures. © 1996 John Wiley & Sons, Inc.     

Refolding of denatured/reduced lysozyme at high concentrations by artificial molecular chaperone‐ion exchange chromatography

Development of high efficiency and low cost protein refolding methods is a highlighted research focus in biotechnology. Artificial molecular chaperone (AMC) and protein folding liquid chromatography (PFLC) are two attractive refolding methods developed in recent years. In the present work, AMC and one branch of PFLC, ion exchange chromatography (IEC), are integrated to form a new refolding method, artificial molecular chaperone‐ion exchange chromatography (AMC‐IEC). This new method is applied to the refolding of a widely used model protein, urea‐denatured/dithiothreitol‐reduced lysozyme. Many factors influencing the refolding of lysozyme, such as urea concentration, β‐cyclodextrin concentration, molar ratio of detergent to protein, mobile phase flow rate, and type of detergent, were investigated, respectively, to optimize the conditions for lysozyme refolding by AMC‐IEC. Compared with normal IEC refolding method, the activity recoveries of lysozyme obtained by AMC‐IEC were much higher in the investigated range of initial protein concentrations. Moreover, the activity recoveries obtained by using this newly developed refolding method were still quite high for denatured/reduced lysozyme at high initial concentrations. When the initial protein concentration was 200 mg mL^?1, the activity recovery was over 60%. In addition, the lifetime of the chromatographic column during AMC‐IEC was much longer than that during protein refolding by normal IEC. Therefore, AMC‐IEC is a high efficient and low cost protein refolding method. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Systematic interpolation method predicts protein chromatographic elution from batch isotherm data without a detailed mechanistic isotherm model

Predicting protein elution for overloaded ion exchange columns requires models capable of describing protein binding over broad ranges of protein and salt concentrations. Although approximate mechanistic models are available, they do not always have the accuracy needed for precise predictions. The aim of this work is to develop a method to predict protein chromatographic behavior from batch isotherm data without relying on a mechanistic model. The method uses a systematic empirical interpolation (EI) scheme coupled with a lumped kinetic model with rate parameters determined from HETP measurements for non‐binding conditions, to numerically predict the column behavior. For two experimental systems considered in this work, predictions based on the EI scheme are in excellent agreement with experimental elution profiles under highly overloaded conditions without using any adjustable parameters. A qualitative study of the sensitivity of predicting protein elution profiles to the precision, granularity, and extent of the batch adsorption data shows that the EI scheme is relatively insensitive to the properties of the dataset used, requiring only that the experimental ranges of protein and salt concentrations overlap those under which the protein actually elutes from the column and possess a ±10% measurement precision.     

Single-step ion exchange purification of the coagulant protein from Moringa oleifera seed

The coagulant protein from Moringa oleifera (MO) seed was purified using a single-step batch ion exchange (IEX) method. Adsorption and elution parameters were optimized. Impact of the purification on the reduction of organic and nutrient release to the water was studied. The matrix was equilibrated using ammonium acetate buffer, and the optimum ionic strength of NaCl for elution was 0.6 M. The time for adsorption equilibrium was between 90 and 120 min. Maximum adsorption capacity of the matrix, estimated with the Langmuir model, was 68 mg protein/g adsorbent. The purified protein does not release organic and nutrient loads to the water, which are the main concerns of the crude extract. This work suggests that a readily scalable single-step IEX purification method can be used to produce the coagulant protein and it can be carried out with locally available facilities. This will promote the use of MO in large water treatment plants and other industries.     

A proposed solution for the determination of the ionization constants of sets of ionizinggroups in proteins

A mixture of acids with known pK′ and in a known concentration was dissolved to simulate the ionic character of hemoglobin. The titration curves of the mixture were obtained in water and 3.6 M KCl at 20°C. These curves were subjected to analysis by a reiterative curve-fitting procedure to determine if one could evaluate both the group ionization constants and the numbers of groups. This approach was successful in that the calculated parameters were within the experimental error encountered in obtaining these constants on each of the model compounds. However, analysis for the electrostatic interaction parameter w indicated that there was a possible effect on the ionization of formic acid, pyridine, imidazole, and the α-amino group of glycylglycine in water and on imidazole and the α-amino group of glycylglycine in 3.6 M KCl.     

Ion exchange chromatography of proteins-predictions of elution curves and operating conditions. II. Experimental verification

The applicability and validity of the model developed in Part I were confirmed experimentally. In this article, various proteins were eluted both by stepwise and linear gradient elution on DEAE ion exchangers under a variety of experimental conditions. Adsorption isotherms were measured as a function of ionic strength in batch experiments. The moment method was empolyed for the determination of various parameteres such as the gel-phase diffusion coefficient and the longitudinal dispersion coefficient. By use of these parameters and the experimentally measured ionic strength of the peak position, the number opf plates was determined according to the method described in Part I. Theoretical elution curves were calculated with the experimentally measured adsorption eqluilibria and the number of plates. Good agreement was observed between theory an experiments. Various factors affecting the separation were investigated. It was found that the effect of the number of plates for salts, N'(p), was negligible except the case of stepwise elution of high ionic strength buffer. When elution curves were symmetrical, the widths of the elution curves were inversely proportional to the square root of the number of plates of proteins, N(p), as in other chromatographic techniques. A simple graphical method for prediction of the peak position in linear gradient elution described in Part I was found applicable when the elution curves were symmetrical. A useful correlation of prediction of the peak width in a linear gradient elution was proposed on the basis of the approximate solution derived in Part I of this study. This graphical method and correlation permit easy prediction of the peak position and peak width in linear gradient elution in the case of symmetrical elution curves.     

The effects of arginine on protein binding and elution in hydrophobic interaction and ion-exchange chromatography

Arginine is effective in suppressing aggregation of proteins and may be beneficial to be included during purification processes. We have shown that arginine reduces non-specific protein binding in gel permeation chromatography and facilitates elution of antibodies from Protein-A columns. Here we have examined the effects of arginine on binding and elution of the proteins during hydrophobic interaction (HIC) and ion- exchange chromatographies (IEC) using recombinant monoclonal antibodies (mAbs) and human interleukin-6. In the case of HIC, the proteins were bound to a phenyl-Sepharose column in the presence of ammonium sulfate (AS) with or without arginine and eluted with a descending concentration of AS. While use of 1 M AS in the loading buffer resulted in complete binding of the mAb, inclusion of 1 M arginine in loading and equilibration buffer, only when using low-substituted phenyl-Sepharose, resulted in weaker binding of the proteins. While decreasing AS concentration to 0.75 M resulted in partial elution of the mAB, elution was facilitated with inclusion of 0.5-1 M arginine. In the case of IEC, arginine was included in the loading samples. Inclusion of arginine during binding to the IEC columns resulted in a greater recovery and less aggregation even when elution was done in the absence of arginine. These results indicate that arginine enhances elution of proteins bound to the resin, suggesting its effectiveness as a solvent for elution in HIC and IEC.     

Modelling regeneration effects on protein A affinity chromatography

The effect of in-place regeneration of protein A adsorbents on protein adsorption characteristics is investigated. Regeneration with sodium hydroxide and time of exposure determined the protein capacity of the adsorbent, but no effect was observed on the adsorbent protein affinity. Fixed-bed adsorption of human immunoglobulin G was studied. Breakthrough curves were measured for protein adsorption on fixed-bed columns. These data were analyzed by a simple kinetic model to determine the rate constants for the adsorption process. It was found that forward adsorption rate constant remained constant along the chemical treatment exposure time. Protein A adsorbent selectivity was determined using mouse serum immunoglobulins G ₁ and G ₃ . Column linear gradient elution showed that adsorbent selectivity decreased with the exposure time chemical treatment. The implications of these results on the design and optimization of protein A chromatographic process are discussed.     

Kinetic studies of recA protein binding to a fluorescent single-stranded polynucleotide

Fluorescence spectroscopy was used to investigate the binding of Escherichia coli recA protein to a single-stranded polynucleotide. Poly(deoxy-1,N6-ethenoadenylic acid) was prepared by reaction of chloroacetaldehyde with poly(deoxyadenylic acid). The fluorescence of poly(deoxy-1,N6-ethenoadenylic acid) was enhanced upon recA protein binding. The kinetics of the binding process were studied as a function of several parameters: ionic concentration (KCl and MgCl2), pH, nature of the nucleoside triphosphate [adenosine 5'-triphosphate or adenosine 5'-O-(gamma-thiotriphosphate)], protein and polynucleotide concentrations, polynucleotide chain length, and order of sequential additions. The observed kinetic curves exhibited a lag phase followed by a slow binding process characteristic of a nucleation-elongation mechanism with an additional slow step governing the rate of the association process. The lag phase reflecting the nucleation step was not observed when the protein was first bound to the polynucleotide before addition of adenosine 5'-triphosphate. Adenosine 5'-triphosphate induced a dissociation of the recA protein, which was immediately followed by binding of the recA-adenosine 5'-triphosphate-Mg2+ ternary complex. The origin of this "mnemonic effect" and of the different kinetic steps is discussed with respect to protein conformational changes and aggregation phenomena.     

Systematic interpolation method predicts protein chromatographic elution with salt gradients,pH gradients and combined salt/pH gradients

A methodology is presented to predict protein elution behavior from an ion exchange column using both individual or combined pH and salt gradients based on high‐throughput batch isotherm data. The buffer compositions are first optimized to generate linear pH gradients from pH 5.5 to 7 with defined concentrations of sodium chloride. Next, high‐throughput batch isotherm data are collected for a monoclonal antibody on the cation exchange resin POROS XS over a range of protein concentrations, salt concentrations, and solution pH. Finally, a previously developed empirical interpolation (EI) method is extended to describe protein binding as a function of the protein and salt concentration and solution pH without using an explicit isotherm model. The interpolated isotherm data are then used with a lumped kinetic model to predict the protein elution behavior. Experimental results obtained for laboratory scale columns show excellent agreement with the predicted elution curves for both individual or combined pH and salt gradients at protein loads up to 45 mg/mL of column. Numerical studies show that the model predictions are robust as long as the isotherm data cover the range of mobile phase compositions where the protein actually elutes from the column.     

A simple method for calculating the productivity of polyphenol separations by polymer-based chromatography

A simple method for calculating the productivity of chromatography processes was proposed based on the iso-resolution curve concept. The model separation system was polyphenol separations by polystyrene divinylbenzene resins with the ethanol–water mixture mobile phase. The distribution coefficient K was determined as a function of ethanol concentration I by linear gradient elution experiments. The HETP-mobile phase velocity u curves were determined as a function of I. Using K and HETP, the iso-resolution curve was calculated, from which the productivity was determined as a function of I. It was found that there is an optimum I, where the highest productivity with the minimum amount of mobile phase consumption is obtained.     

On the mechanism of SDS‐induced protein denaturation

To understand the mechanism of ionic detergent‐induced protein denaturation, this study examines the action of sodium dodecyl sulfate on ferrocytochrome c conformation under neutral and strongly alkaline conditions. Equilibrium and stopped‐flow kinetic results consistently suggest that tertiary structure unfolding in the submicellar and chain expansion in the micellar range of SDS concentrations are the two major and discrete events in the perturbation of protein structure. The nature of interaction between the detergent and the protein is predominantly hydrophobic in the submicellar and exclusively hydrophobic at micellar levels of SDS concentration. The observation that SDS also interacts with a highly denatured and negatively charged form of ferrocytochrome c suggests that the interaction is independent of structure, conformation, and ionization state of the protein. The expansion of the protein chain at micellar concentration of SDS is driven by coulombic repulsion between the protein‐bound micelles, and the micelles and anionic amino acid side chains. © 2009 Wiley Periodicals, Inc. Biopolymers 93: 186–199, 2010. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Recovery of potassium clavulanate from fermentation broth by ion exchange chromatography and desalting electrodialysis

Ion exchange chromatography (IEC) and desalting electrodialysis (DSED) processes were developed for the recovery and purification of potassium clavulanate (KCA) from fermentation broth. A strong anion exchanger, Amberlite IRA 400 resin, a potassium acetate solution as equilibrium buffer, and a potassium chloride (KCl) solution as elution buffer were used for the recovery of KCA in IEC. In order to determine optimal operating conditions, the effects of various operating parameters such as equilibrium buffer pH and concentration, elution buffer concentration, gradient length, and volumetric flow rate on KCA recovery and by-product removal were investigated using a simulated fermentation broth. In the subsequent step of DSED, employing cation (Neocepta CMS, Tokuyama, Japan) and anion (Neocepta ACS, Tokuyama, Japan) exchange membranes were carried out to remove KCl that existed in a large amount in the ion exchanged solution. The effects of operation voltage and feed composition on the performance of DSED were investigated. Based on the operating conditions determined above, IEC and DSED were applied in sequence to an ultrafiltered fermentation broth. Almost complete removal of KCl was possible with no significant loss of KCA, although the KCA recovery was slightly lower than that with the simulated fermentation broth. Based on this observation, it was concluded that IEC and DESD could be an effective process combination for the recovery of KCA from fermentation broth.     

Concentration of protein in fibrin fibers and fibrinogen polymers determined by refractive index matching

We have used refractive index matching to determine the concentration of protein in the fibers in fibrin clots and of needlelike crystals of native fibrinogen. Our results are in agreement with those of Carr and Hermans [(1978) Macromolecules 11 , 46–50], as determined by light scattering—namely, that protein makes up about 20% of the volume of the fiber. However, we have found that the protein concentration is strongly dependent on ionic strength. An increase in ionic strength caused a substantial drop in the protein concentration. In a buffer containing 100 mM NaCl, the protein concentration was 26.6–29.8 g of protein per 100 cm³ of polymer, and at 200 mM NaCl it was reduced to 22.1–23.1 g/100 cm³.     

Kinetics of protein aggregation. Quantitative estimation of the chaperone-like activity in test-systems based on suppression of protein aggregation

The experimental data on the kinetics of irreversible aggregation of proteins caused by exposure to elevated temperatures or the action of denaturing agents (guanidine hydrochloride, urea) have been analyzed. It was shown that the terminal phase of aggregation followed, as a rule, first order kinetics. For the kinetic curves registered by an increase in the apparent absorbance (A) in time (t) the methods of estimation of the corresponding kinetic parameters A _lim and k _I (A _lim is the limiting value of A at t and k _I is the rate constant of the first order) have been proposed. Cases are revealed when the reaction rate constant k _I calculated from the kinetic curve of aggregation of the enzymes coincides with the rate constant for enzyme inactivation. Such a situation is interpreted as a case when the rate of aggregation is limited by the stage of denaturation of the enzyme. A conclusion has been made that, in order to establish the mechanism of protein aggregation, the kinetic investigations of aggregation should be carried out over a wide range of protein concentrations. The refolding experiments after denaturation of proteins by guanidine hydrochloride or urea have been also analyzed. It was shown that aggregation accompanying refolding follows first order kinetics at the final phase of the process. The model of protein refolding explaining such a kinetic regularity has been proposed. When aggregation of protein substrate follows first order kinetics, parameters A _lim and k _I may be used for the quantitative characterization of the chaperone-like activity in the test-systems based on suppression of protein aggregation.