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.     

Nonlinear gradient isotherm parameter estimation for proteins with consideration of salt competition and multiple forms.

Salt gradients in ion-exchange chromatography are routinely used to speed separation of proteins and to concentrate products, but systematic optimization of these gradients requires protein equilibrium data as a function of salt concentration. An understanding of conformational changes, aggregation, and salt effects, which include both competition and affinity modulation, is important for equilibrium isotherm parameter estimation. In this study, gradient elution of bovine serum albumin (BSA) in anion exchange was well predicted by a salt-modulated nonlinear isotherm which considers salt competition. The isotherm was able to predict BSA gradient elution from batch equilibrium data. The same isotherm was also able to predict elution for various gradient slopes when fitted to an intermediate slope gradient experiment. If multiple forms due to aggregation or denaturation exist, isotherm parameters are readily averaged in batch experiments because of the long equilibration times. Similarly, gradient experiments yield averaged parameters because the salt gradient tends to merge the closely eluting forms. However, in isocractic elution, if the reaction rate is not rapid enough to give a merged peak, the estimated isotherm parameters are only fair predictors of gradient behavior and vice versa. Slower flow rates in isocratic elution can help reduce the discrepancy by allowing forms to merge through interconversion. As an alternative to determining averaged parameters, consideration of two binding forms, using VERSE-LC, an advanced rate model, gave good agreement with experimental data over the entire range of salt gradient durations.     

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.     

Fractionation of complex protein mixture by virtual three-dimensional liquid chromatography based on combined pH and salt steps

The complexity and diversity of biological samples in proteomics require intensive fractionation ahead of mass spectrometry identification. This work developed a chromatographic method called virtual three-dimensional chromatography to fractionate complex protein mixtures. By alternate elution with different pHs and salt concentrations, we implemented pH and salt steps by turns on a single strong cation exchange column to fully exploit its chromatographic ability. Given standard proteins that were not resolved solely by pH or salt gradient elution could be successfully separated using this combined mode. With a reversed phase column tandem connected behind, we further fractionated as well as desalted proteins as the third dimension. This present strategy could readily be adapted with respect to special complexity of biological samples. Crude plasma without depleting high abundance proteins were fractionated by this three-dimensional mode and then analyzed by reversed phase liquid chromatography coupled with LTQ mass spectrometry. In total, 1933 protein groups with wide dynamic ranges were identified from a single experiment. Some characteristics that correlated to the behavior of proteins on strong cation exchange columns are also discussed.     

Prediction of the Quantity and Purity of an Antibody Capture Process in Real Time

Regulatory recommendations for quality by design instead of quality by testing raise increasing interest in new sensor technologies. An online monitoring system for downstream processes is developed, which is based on an array of online detectors. Besides standard detectors (UV, pH, and conductivity), our chromatographic workstation is equipped with a fluorescence and a mid‐infrared spectrometer, a light scattering, and a refractive index detector. The combination of these sensors enables the prediction of specific protein concentration and various purity attributes, such as high molecular weight impurities, DNA and host cell protein content during the elution phase of a chromatographic antibody capture process. Prediction models solely based on online signals are set up providing real‐time predictions. No mechanistic models or information about the chromatographic runs is used. These predictions allow online pooling decisions replacing time‐ and labor‐intensive laboratory measurements. Different process variations, such as changes in the column load or elution buffer, are introduced to test the predictive power of the models. Extrapolation of the models worked well when the column load is changed, whereas model adjustment is necessary when the elution conditions are changed considerably.     

Comparison of maximum production rates and optimum operating/design parameters in overloaded elution and displacement chromatography

The results of a study of the optimization of the experimental conditions for maximum production rate in overloaded elution and displacement chromatography are discussed. This study is based on the use of the equilibrium-dispersive model of chromatography and the competitive Langmuir isotherms to calculate individual band profiles in the elution and displacement modes, and of a simplex algorithm to optimize the production rate. The operating parameters (sample size, mobile phase velocity, and the displacer concentration in the displacement model) and the column design parameters (column length and average particle diameter) are optimized simultaneously. Binary mixtures having relative concentrations 3:1 and 1:3, and separation factors of 1.2 to 1.8 are investigated. One of our major results is that, in both modes of chromatography, the maximum production rate is achieved at very low values of the retention factors, k', much lower than those used in current practice. In all cases, unless k' exceeds greatly that optimum value, the production rate is higher in overloaded elution than in displacement chromatography. This is particularly true for the extraction of a minor component, which is eluted second. (c) 1993 John Wiley & Sons, Inc.     

Effects of ionic strength on lysozyme uptake rates in cation exchangers. I: Uptake in SP Sepharose FF

Fluorescence scanning confocal microscopy was used in parallel with batch uptake and breakthrough measurements of transport rates to study the effect of ionic strength on the uptake of lysozyme into SP Sepharose FF. In all cases the adsorption isotherms were near-rectangular. As described previously, the intraparticle profiles changed from slow-moving self-sharpening fronts at low salt concentration, to fast-moving diffuse profiles at high salt concentration, and batch uptake rates correspondingly increased with increasing salt concentration. Shrinking core and homogeneous diffusion frameworks were used successfully to obtain effective diffusivities for the low salt and high salt conditions, respectively. The prediction of column breakthrough was generally good using these frameworks, except for low-salt uptake results. In those cases, the compressibility of the stationary phase coupled with the shrinking core behavior appears to reduce the mass transfer rates at particle-particle contacts, leading to shallower breakthrough curves. In contrast, the fast uptake rates at high ionic strength appear to reduce the importance of mass transfer limitations at the particle contacts, but the confocal results do show a flow rate dependence on the uptake profiles, suggesting that external mass transfer becomes more limiting at high ionic strength. These results show that the complexity of behavior observable at the microscopic scale is directly manifested at the column scale and provides a phenomenological basis to interpret and predict column breakthrough. In addition, the results provide heuristics for the optimization of chromatographic conditions.     

Kinetic modeling of microbial growth,enzyme activity,and gene deletions: An integrated model of β-glucosidase function in Cellvibrio japonicus

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene-deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacterium Cellvibrio japonicus grown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics of C. japonicus using either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild-type strain as well as in β-glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non-diauxic growth and metabolite consumptions of the wild-type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially-useful strains. Importantly, the model is able to explain the role of the different β-glucosidases and their behavior under genetic perturbations. This integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.     

Mass Balance Model with Donnan Equilibrium Accurately Describes Unusual pH and Excipient Profiles during Diafiltration of Monoclonal Antibodies

There is extensive experimental data showing that the final pH and buffer composition after protein diafiltration (DF), particularly with monoclonal antibodies, can be considerably different than that in the DF buffer due to electrostatic interactions between the charged protein and the charged ions. Previous models for this behavior have focused on the final (equilibrium) partitioning and are unable to explain the complex pH and concentration profiles during the DF process. The objective of this study is to develop a new model for antibody DF based on solution of the transient mass balance equations, with the permeate concentrations of the charged species evaluated assuming Donnan equilibrium across the semipermeable membrane in combination with electroneutrality constraints. Model predictions are in excellent agreement with experimental data obtained during DF of both acidic and basic monoclonal antibodies, with the protein charge determined from independent electrophoretic mobility measurements. The model is able to predict the entire pH/histidine concentration profiles during DF, providing a framework for the development of DF processes that yield the desired antibody formulation.     

Zonal rate model for stacked membrane chromatography part II: characterizing ion-exchange membrane chromatography under protein retention conditions

The Zonal Rate Model (ZRM) has previously been shown to accurately account for contributions to elution band broadening, including external flow nonidealities and radial concentration gradients, in ion-exchange membrane (IEXM) chromatography systems operated under nonbinding conditions. Here, we extend the ZRM to analyze and model the behavior of retained proteins by introducing terms for intra-column mass transfer resistances and intrinsic binding kinetics. Breakthrough curve (BTC) data from a scaled-down anion-exchange membrane chromatography module using ovalbumin as a model protein were collected at flow rates ranging from 1.5 to 20 mL min(-1). Through its careful accounting of transport nonidealities within and external to the membrane stack, the ZRM is shown to provide a useful framework for characterizing putative protein binding mechanisms and models, for predicting BTCs and complex elution behavior, including the common observation that the dynamic binding capacity can increase with linear velocity in IEXM systems, and for simulating and scaling separations using IEXM chromatography. Global fitting of model parameters is used to evaluate the performance of the Langmuir, bi-Langmuir, steric mass action (SMA), and spreading-type protein binding models in either correlating or fundamentally describing BTC data. When combined with the ZRM, the bi-Langmuir, and SMA models match the chromatography data, but require physically unrealistic regressed model parameters to do so. In contrast, for this system a spreading-type model is shown to accurately predict column performance while also providing a realistic fundamental explanation for observed trends, including an observed increase in dynamic binding capacity with flow rate.     

Apolipoprotein A-I(Milano) anion exchange chromatography: Self association and adsorption equilibrium

The self-associative properties of apolipoprotein A-I(Milano) (apoA-I(M)) were investigated in relationship to its anion exchange behavior on Q-Sepharose-HP with and without the addition of urea as a denaturant. Self-association was dependent on protein and urea concentration and both influenced interactions of the protein with the chromatographic surface. In the absence of urea, apoA-I(M) was highly associated and existed primarily as a mixture of homodimer, tetramer and hexamer forms. Under these conditions, since the binding strength was greater for the oligomer forms, broad, asymmetrical peaks were obtained in both isocratic and gradient elution. Adding urea depressed self-association and caused unfolding. This resulted in sharper peaks but also decreased the binding strength. Thus, under these conditions chromatographic elution occurred at lower salt concentrations. The adsorption isotherms obtained at high protein loadings were also influenced by self-association and by the varying binding strength of the differently associated and unfolded forms. The isotherms were thus dependent on protein, urea, and salt concentration. Maximum binding capacity was obtained in the absence of urea, where adsorption of oligomers was shown to be dominant. Adding urea reduced the apparent binding capacity and weakened the apparent binding strength. A steric mass action model accounting for competitive binding of the multiple associated forms was used to successfully describe the equilibrium binding behavior using parameters determined from isocratic elution and isotherm experiments.     

The effect of pore-size distribution on the binding of proteins to porous resin beads

The effect of the distribution of pore radii in the resin beads on protein binding was taken into account to analyze the elution profiles of proteins from the polymer-packed column obtained by repetitive injection method. By assuming that the distribution of pore radii in the resin beads is logarithmic Gaussian, the theoretical curves obtained agreed well with the experimental data.     

Ultra scale‐down approach to correct dispersive and retentive effects in small‐scale columns when predicting larger scale elution profiles

Ultra scale‐down approaches represent valuable methods for chromatography development work in the biopharmaceutical sector, but for them to be of value, scale‐down mimics must predict large‐scale process performance accurately. For example, one application of a scale‐down model involves using it to predict large‐scale elution profiles correctly with respect to the size of a product peak and its position in a chromatogram relative to contaminants. Predicting large‐scale profiles from data generated by small laboratory columns is complicated, however, by differences in dispersion and retention volumes between the two scales of operation. Correcting for these effects would improve the accuracy of the scale‐down models when predicting outputs such as eluate volumes at larger scale and thus enable the efficient design and operation of subsequent steps. This paper describes a novel ultra scale‐down approach which uses empirical correlations derived from conductivity changes during operation of laboratory and pilot columns to correct chromatographic profiles for the differences in dispersion and retention. The methodology was tested by using 1 mL column data to predict elution profiles of a chimeric monoclonal antibody obtained from Protein A chromatography columns at 3 mL laboratory‐ and 18.3 L pilot‐scale. The predictions were then verified experimentally. Results showed that the empirical corrections enabled accurate estimations of the characteristics of larger‐scale elution profiles. These data then provide the justification to adjust small‐scale conditions to achieve an eluate volume and product concentration which is consistent with that obtained at large‐scale and which can then be used for subsequent ultra scale‐down operations. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

The range implications of lizard traits in changing environments

Aim Most predictions of species ranges are based on correlating current species localities to environmental conditions. These correlative models do not explicitly include a species' biology. In contrast, some mechanistic models link traits to energetics and population dynamics to predict species distributions. These models enable one to ask whether considering a species' biology is important for predicting its range. I implement mechanistic models to investigate how a species' morphology, physiology and life history influence its range. Location North America. Methods I compare the mechanistic model predictions with those of correlative models for eight species of North American lizards in both current environments and following a uniform 3 °C temperature warming. I then examine the implications of superimposing habitat and elevation requirements on constraints associated with environmental tolerances. Results In the mechanistic model, species with a narrower thermal range for activity are both predicted and observed to have more restricted distributions. Incorporating constraints on habitat and elevation further restricts species distributions beyond areas that are thermally suitable. While correlative models generally outperform mechanistic models at predicting current distributions, the performance of mechanistic models improves when incorporating additional factors. In response to a 3 °C temperature warming, the northward range shifts predicted by the mechanistic model vary between species according to trait differences and are of a greater extent than those predicted by correlative models. Main conclusions These findings highlight the importance of species traits for understanding the dynamics of species ranges in changing environments. The analysis demonstrates that mechanistic models may provide an important complement to correlative models for predicting range dynamics, which may underpredict climate‐induced range shifts.     

Modeling of preparative reversed-phase HPLC of insulin

The adsorption isotherms of three recombinant proteins, human insulin, porcine insulin, and Lispro, were measured by frontal analysis on a YMC-ODS C18 column with an aqueous solution at 31% acetonitrile (0.1% TFA) as the mobile phase. The retention behavior of insulin, its related molecular structure, its conformation, and its aggregation in this phase system are discussed. The experimental isotherm data were fitted to the Langmuir, the Langmuir-Freundlich, and the Toth models. The results allow for a quantitative comparison of the saturation capacities, the equilibrium constants, and the exponents that represent the heterogeneity of the stationary phase obtained for the different insulin variants studied. The Toth model provided the best fit of the experimental data. The overloaded band profiles were calculated using the lumped pore diffusion and the equilibrium-dispersive model of chromatography. An excellent agreement between calculated and experimental profiles was demonstrated.     

A new kinetic model of protein adsorption on suspended anion-exchange resin particles.

The kinetics of adsorption of bovine serum albumin on an anion-exchange resin were measured in a batch system using a flow cell and ultraviolet absorbance, as a function of initial liquid-phase protein concentration and solid-to-liquid phase ratio. A new mathematical model for adsorption kinetics is presented that fits the experimental data to give a highly linear relationship with time, following a short transient period. Numerical integration of the differential form of the new composite nonlinear (CNL) kinetic model, containing three independent parameters, is shown to describe the dynamics of batch adsorption much better than alternative lumped parameter models. Although the new model is phenomenological rather than mechanistic, its principal parameter is shown to be a direct linear function of a physically measurable quantity. This study demonstrates that the model can accurately simulate protein concentration-time profiles using parameter estimates derived from correlations over a wide range of initial protein concentrations and phase ratios. The new CNL model is shown to be considerably superior to the Langmuir and solid-film linear kinetic models in this regard, having the additional advantage that an equilibrium isotherm for the system is not required.