Steric Mass Action Research Articles

Using the reactive/transport dispersive models to simulate a monolithic anion exchanger: Experimental parameter determination, simultaneous model evaluation, and validation.

Selecting an adequate model to represent the mass transfer mechanisms occurring in a chromatographic process is generally complicated, which is one of the reasons why monolithic chromatography is scarcely simulated. In this study, the chromatographic separation of model proteins bovine serum albumin (BSA), β-lactoglobulin-A, and β-lactoglobulin-B on an anion exchange monolith was simulated based on experimental parameter determination, simultaneous model testing, and validation under three statistical criteria: retention time, dispersion accuracies, and Pearson correlation coefficient. Experimental characterization of morphologic, physicochemical, and kinetic parameters was performed through volume balances, pressure drop analysis, breakthrough curve analysis, and batch adsorptions. Free Gibbs energy indicated a spontaneous adsorption process for proteins and counterions. Dimensionless numbers were estimated based on height equivalent to a theoretical plate analysis, finding that pore diffusion controlled β-lactoglobulin separation, whereas adsorption/desorption kinetics was the dominant mechanism for BSA. The elution profiles were modeled using the transport dispersive model and the reactive dispersive model coupled with steric mass action (SMA) isotherms because these models allowed to consider most of the mass transport mechanisms that have been described. RDM-SMA presented the most accurate simulations at pH 6.0 and at low (250mM) and high (400mM) NaCl concentrations. This simulation will be used as reference to forecast the purification of these proteins from bovine whey waste and to extrapolate this methodology to other monolith-based separations using these three statistical criteria that have not been used previously for this purpose.

Mechanistic modeling of minute virus of mice surrogate removal by anion exchange chromatography in micro scale

Biopharmaceutical products are often produced in Chinese hamster ovary (CHO) cell cultures that are vulnerable to virus infections. Therefore, it is a regulatory requirement that downstream purification steps for biopharmaceuticals can remove viruses from feedstocks. Anion exchange chromatography (AEX) is one of the downstream unit operations that is most frequently used for this purpose and claimed for its capability to remove viruses. However, the impact of various process parameters on virus removal by AEX is still not fully understood. Mechanistic modeling could be a promising way to approach this gap, as these models require comparatively few experiments for calibration. This makes them a valuable tool to improve understanding of viral clearance, especially since virus spiking studies are costly and time consuming.In this study, we present how the virus clearance of a MVM mock virus particle by Q Sepharose FF resin can be described by mechanistic modeling. A lumped kinetic model was combined with a steric mass action model and calibrated at micro scale using three linear gradient experiments and an incremental step elution gradient. The model was subsequently verified for its capability to predict the effect of different sodium chloride concentrations, as well as residence times, on virus clearance and was in good agreement with the LRVs of the verification runs. Overall, models like this could enhance the mechanistic understanding of viral clearance mechanisms and thereby contribute to the development of more efficient and safer biopharmaceutical downstream processes.

High‐throughput in silico workflow for optimization and characterization of multimodal chromatographic processes

AbstractWhile high‐throughput (HT) experimentation and mechanistic modeling have long been employed in chromatographic process development, it remains unclear how these techniques should be used in concert within development workflows. In this work, a process development workflow based on HT experiments and mechanistic modeling was constructed. The integration of HT and modeling approaches offers improved workflow efficiency and speed. This high‐throughput in silico (HT‐IS) workflow was employed to develop a Capto MMC polishing step for mAb aggregate removal. High‐throughput batch isotherm data was first generated over a range of mobile phase conditions and a suite of analytics were employed. Parameters for the extended steric mass action (SMA) isotherm were regressed for the multicomponent system. Model validation was performed using the extended SMA isotherm in concert with the general rate model of chromatography using the CADET modeling software. Here, step elution profiles were predicted for eight RoboColumn runs across a range of ionic strength, pH, and load density. Optimized processes were generated through minimization of a complex objective function based on key process metrics. Processes were evaluated at lab‐scale using two feedstocks, differing in composition. The results confirmed that both processes obtained high monomer yield (>85%) and removed of aggregate species. Column simulations were then carried out to determine sensitivity to a wide range of process inputs. Elution buffer pH was found to be the most critical process parameter, followed by resin ionic capacity. Overall, this study demonstrated the utility of the HT‐IS workflow for rapid process development and characterization.

Pore-blocking steric mass-action model for adsorption of bioparticles

The steric mass-action (SMA) model has been widely reported to describe the adsorption of proteins in different types of chromatographic adsorbents. Here in the present work, a pore-blocking steric mass-action model (PB-SMA) was developed for the adsorption of large-size bioparticles, which usually exhibit the unique pore-blocking characteristic on the adsorbent and thus lead to a fraction of ligands in the deep channels physically inaccessible to bioparticles adsorption, instead of being shielded due to steric hindrance by adsorbed bioparticles. This unique phenomenon was taken into account by introducing an additional parameter, Lin, which is defined as the inaccessible ligand densities in the physically blocked pore area, into the PB-SMA model. This fraction of ligand densities (Lin) will be deducted from the total ligand (Lt) for model development, thus the steric factor (σ) in the proposed PB-SMA will reflect the steric shielding effect on binding sites by adsorbed bioparticles more accurately than the conventional SMA model, which assumes that all ligands on the adsorbent have the same accessibility to the bioparticles. Based on a series of model assumptions, a PB-SMA model was firstly developed for inactivated foot-and-mouth disease virus (iFMDV) adsorption on immobilized metal affinity chromatography (IMAC) adsorbents. Model parameters for static adsorption including equilibrium constant (K), characteristic number of binding sites (n), and steric factor (σ) were determined. Compared with those derived from the conventional SMA model, the σ values derived from the PB-SMA model were dozens of times smaller and much closer to the theoretical maximum number of ligands shielded by a single adsorbed iFMDV, indicating the modified model was more accurate for bioparticles adsorption. The applicability of the PB-SMA model was further validated by the adsorption of hepatitis B surface antigen virus-like particles (HBsAg VLPs) on an ion exchange adsorbent with reasonably improved accuracy. Thus, it is considered that the PB-SMA model would be more accurate in describing the adsorption of bioparticles on different types of chromatographic adsorbents.

A model-based performance analysis of integrated chromatography-ultrafilter separation systems for monoclonal antibody (mAb) manufacturing

Robust and accurate modelling of bioprocess systems offers the opportunity to visualise strategies for rapid-scale up of production platforms from benchtop to industrial scale, but few studies investigate how mechanistic and hybrid models can be used to design integrated bio-manufacturing. This is especially true for downstream purification technologies used to separate mAbs from culture by-products, e.g. host cell proteins. Polishing chromatography (cation-exchange mode) is commonly used to remove these by-products, but optimal bind and elution operation of these columns is complex. Ultrafiltration is typically applied in conjunction with diafiltration post-polishing chromatography in order to obtain suitable final product titers and excipient concentrations. This study presents a combination of dynamic models to probe batch polishing chromatography and ultrafiltration operating strategies achieving industrial specifications for recovery yield and mAb titer. A series of elution and filtration strategies are implemented, resulting in a total of 40 flowsheets explored. A steric mass action model with 7 pH-dependent parameters is employed to simulate scale-up polishing chromatography column behaviour. Moreover, a published gel layer ultrafiltration model based on Darcy’s law is implemented to purify the outlet of the polishing chromatography column. Strategies that are successful in achieving the target 90% recovery yield and 100 g L−1 concentration specifications are compared via a comprehensive analysis, to deduce the operational protocols which offer minimised salt consumption and pressure drop whilst respecting design criteria.

Standardized approach for accurate and reliable model development of ion-exchange chromatography based on parameter-by-parameter method and consideration of extra-column effects.

Developing an accurate and reliable model for chromatographic separation that meets regulatory requirements and ensures consistency in model development remains challenging. In order to address this challenge, a standardized approach was proposed in this study with ion-exchange chromatography (IEC). The approach includes the following steps: liquid flow identification, system and column-specific parameters determination and validation, multi-component system identification, protein amount validation, steric mass action parameters determination and evaluation, and validation of the calibrated model's generalization ability. The parameter-by-parameter (PbP) calibration method and the consideration of extra-column effects were integrated to enhance the accuracy of the developed models. The experiments designed for implementing the PbP method (five gradient experiments for model calibration and one stepwise experiment for model validation) not only streamline the experimental workload but also ensure the extrapolation abilities of the model. The effectiveness of the standardized approach is successfully validated through an application about the IEC separation of industrial antibody variants, and satisfactory results were observed with R2 ≈ 0.9 for the majority of calibration and validation experiments. The standardized approach proposed in this work contributes significantly to improve the accuracy and reliability of the developed IEC models. Models developed using this standardized approach are ready to be applied to a broader range of industrial separation systems, and are likely find further applications in model-assisted decision-making of process development.

Model based process optimization of an industrial chromatographic process for separation of lactoferrin from bovine milk

Model based process development using predictive mechanistic models is a powerful tool for in-silico downstream process development. It allows to obtain a thorough understanding of the process reducing experimental effort. While in pharma industry, mechanistic modeling becomes more common in the last years, it is rarely applied in food industry. This case study investigates risk ranking and possible optimization of the industrial process of purifying lactoferrin from bovine milk using SP Sepharose Big Beads with a resin particle diameter of 200 µm, based on a minimal number of lab-scale experiments combining traditional scale-down experiments with mechanistic modeling. Depending on the location and season, process water pH and the composition of raw milk can vary, posing a challenge for highly efficient process development.A predictive model based on the general rate model with steric mass action binding, extended for pH dependence, was calibrated to describe the elution behavior of lactoferrin and main impurities. The gained model was evaluated against changes in flow rate, step elution conditions, and higher loading and showed excellent agreement with the observed experimental data. The model was then used to investigate the critical process parameters, such as water pH, conductivity of elution steps, and flow rate, on process performance and purity. It was found that the elution behavior of lactoferrin is relatively consistent over the pH range of 5.5 to 7.6, while the elution behavior of the main impurities varies greatly with elution pH. As a result, a significant loss in lactoferrin is unavoidable to achieve desired purities at pH levels below pH 6.0. Optimal process parameters were identified to reduce water and salt consumption and increase purity, depending on water pH and raw milk composition. The optimal conductivity for impurity removal in a low conductivity elution step was found to be 43 mS/cm, while a conductivity of 95 mS/cm leads to the lowest overall salt usage during lactoferrin elution. Further increasing the conductivity during lactoferrin elution can only slightly lower the elution volume thus can also lead to higher total salt usage. Low flow rates during elution of 0.2 column volume per minute are beneficial compared to higher flow rates of 1 column volume per minute.The, on lab-scale, calibrated model allows predicting elution volume and impurity removal for large-scale experiments in a commercial plant processing over 106 liters of milk per day. The successful model extrapolation was possible without recalibration or detailed knowledge of the manufacturing plant. This study therefore provides a possible pathway for rapid process development of chromatographic purification in the food industries combining traditional scale-down experiments with mechanistic modeling.

Bovine serum albumin and myoglobin separation on HAp

The separation of the proteins Bovine Serum Albumin (BSA) and Myoglobin (Mb) was achieved experimentally by the simulated moving bed (SMB) technology using HAp as adsorbent and by performing a buffer step-elution in the FlexSMB-LSRE unit. Batch experiments determined the BSA and Mb adsorption equilibrium using pH 7 at different buffer concentrations. Then, fixed bed experiments were also performed for both proteins using the same buffer concentration. The validity of a phenomenological mathematical model, specifically the general rate model combined with steric mass action equilibrium, was confirmed through experimental validation using fixed bed dynamic adsorption tests at various buffer concentrations. Based on the results, a separation region was computed, and suitable operating conditions for an SMB experiment were chosen from within this region. Experimental verification was performed to validate the selected operating point, and purity, recovery, and productivity of Mb on the extract were 92%, 87% and 1.04×10-3 molprotein · kgads−1· day−1, and for BSA on the raffinate were 95%, 98%, and 1.24×10-3 molprotein · kgads−1· day−1 respectively.

Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET

Packed bed liquid chromatography is widely applied in academia and industry. Model-based methods are increasingly utilized for process development and optimization, demanding multitudes of complex simulations. We derive spatial arbitrary order discontinuous Galerkin (DG) discretizations for three commonly used chromatography models, including the general rate model (GRM). The methods are integrated in the open source CADET software, making efficient implementations publicly available for the first time. The DG CADET code is validated and benchmarked against the original finite volume CADET code. We observe great performance advantages for DG, depending on the discrete problem size. For a four-component steric mass action GRM, we achieve a speed-up of an order of magnitude for an error range typical for engineering applications. We explore the performance of a collocation Legendre–Gauß–Lobatto (LGL) quadrature DG method in comparison to an exact integration DG method. Our performance benchmarks indicate a slight advantage for collocation DG.

Benefits and Limitations of Artificial Neural Networks in Process Chromatography Design and Operation

Due to the progressive digitalization of the industry, more and more data is available not only as digitally stored data but also as online data via standardized interfaces. This not only leads to further improvements in process modeling through more data but also opens up the possibility of linking process models with online data of the process plants. As a result, digital representations of the processes emerge, which are called Digital Twins. To further improve these Digital Twins, process models in general, and the challenging process design and development task itself, the new data availability is paired with recent advancements in the field of machine learning. This paper presents a case study of an ANN for the parameter estimation of a Steric Mass Action (SMA)-based mixed-mode chromatography model. The results are used to exemplify, discuss, and point out the effort/benefit balance of ANN. To set the results in a wider context, the results and use cases of other working groups are also considered by categorizing them and providing background information to further discuss the benefits, effort, and limitations of ANNs in the field of chromatography.

Isotherm model discrimination for multimodal chromatography using mechanistic models derived from high-throughput batch isotherm data

In this work, we have examined an array of isotherm formalisms and characterized them based on their relative complexities and predictive abilities with multimodal chromatography. The set of isotherm models studied were all based on the stoichiometric displacement framework, with considerations for electrostatic interactions, hydrophobic interactions, and thermodynamic activities. Isotherm parameters for each model were first determined through twenty repeated fits to a set of mAb – Capto MMC batch isotherm data spanning a range of loading, ionic strength, and pH as well as a set of mAb – Capto Adhere batch data at constant pH. The batch isotherm data were used in two ways—spanning the full range of loading or consisting of only the high concentration data points. Predictive ability was defined through the model's capacity to capture prominent changes in salt gradient elution behavior with respect to pH for Capto MMC or unique elution patterns and yield losses with respect to gradient slope for Capto Adhere. In both cases, model performance was quantified using a scoring metric based on agreement in peak characteristics for column predictions and accuracy of fit for the batch data. These scores were evaluated for all twenty isotherm fits and their corresponding column predictions, thereby producing a statistical distribution of model performances. Model complexity (number of isotherm parameters) was then considered through use of the Akaike information criterion (AIC) calculated from the score distributions. While model performance for Capto MMC benefitted substantially from removal of low protein concentration data, this was not the case for Capto Adhere; this difference was likely due to the qualitatively different shapes of the isotherms between the two resins. Surprisingly, the top-performing (high accuracy with minimal number of parameters) isotherm model was the same for both resins. The extended steric mass action (SMA) isotherm (containing both protein-salt and protein-protein activity terms) accurately captured both the pH-dependent elution behavior for Capto MMC as well as loss in protein recovery with increasing gradient slope for Capto Adhere. In addition, this isotherm model achieved the highest median score in both resin systems, despite it lacking any explicit hydrophobic stoichiometric terms. The more complex isotherm models, which explicitly accounted for both electrostatic and hydrophobic interaction stoichiometries, were ill-suited for Capto MMC and had lower AIC model likelihoods for Capto Adhere due to their increased complexity. Interestingly, the ability of the extended SMA isotherm to predict the Capto Adhere results was largely due to the protein-salt activity coefficient, as determined via isotherm parameter sensitivity analyses. Further, parametric studies on this parameter demonstrated that it had a major impact on both binding affinity and elution behavior, therein fully capturing the impact of hydrophobic interactions. In summary, we were able to determine the isotherm formalisms most capable of consistently predicting a wide range of column behavior for both a multimodal cation-exchange and multimodal anion-exchange resin with high accuracy, while containing a minimized set of model parameters.

Understanding adsorption behavior of antiviral labyrinthopeptin peptides in anion exchange chromatography

Lantipeptides from bacterial sources are increasingly important as biopharmaceuticals because of their broad range of applications. However, the availability of most lantipeptides is low, and systematic approaches for downstream processing of this group of peptides is still lacking. Model-based development for chromatographic separations has proven to be a useful tool for developing reliable purification processes. One important compound of such a model is the adsorption behavior of the components of interest. In ion-exchange chromatography, the adsorption equilibrium between salt and proteins can be described using the steric mass action (SMA) formalism. Beyond, the model parameters may be related to the lanthipeptides physico-chemical properties.In this study, the antiviral lantipeptides labyrinthopeptin A1 and A2, purified from Actinomadura namibiensis culture broth, were characterized for their adsorption behavior in anion-exchange chromatography in the range from pH 5.0–7.4. The experiments necessary to determine the three SMA parameters were chosen in a way to limit the amount of peptides needed. Linear gradient elution was applied successfully to separate A1 and A2 and to determine the characteristic charge νi and the equilibrium constant keqi. Batch adsorption experiments using a robotic workstation for high throughput and accuracy provided non-linear adsorption isotherms and the steric factor σi.Labyrinthopeptin A1 and A2 show a very different adsorption behavior even though the fundamental structure of the two peptides is similar. keq of A1 ranging from 0.18 to 0.88 are approximately one order of magnitude smaller than that of A2 ranging from 3.44 to 9.73 indicating the higher affinity of A2 to the stationary phase. At pH 7.0 σ was 1.12 and 0.60 for A1 and A2, respectively which was expected based on the molecular weight of the peptides. The characteristic charge for both peptides was also theoretically estimated from the amino acids involved in electrostatic interactions which was in good agreement with experimental data. Thereby, this work provides an useful approach to estimate SMA parameters based on simple structural information that can be applied early in chromatographic ion-exchange process development for peptides and may help adapting the processes for future designed lanthipeptides.

A comprehensive method for modeling and simulating ion exchange chromatography of complex mixtures

In recent years, many biological-based products have been developed, representing a significant fraction of income in the pharmaceutical market. Ion exchange chromatography is an important downstream step for the purification of target recombinant proteins present in clarified cell extracts, together with many other unknown impurities. This work develops a robust approach to model and simulate the purification of untagged heterologous proteins, so that the improved conditions to carry out an ion exchange chromatography are identified in a rational basis prior to the real purification run itself. Purification of the pneumococcal surface protein A (PspA4Pro) was used as a case study. This protein is produced by recombinant Escherichia coli and is a candidate for the manufacture of improved pneumococcal vaccines. The developed method combined experimental and computational procedures. Different anion exchange operating conditions were mapped in order to gather a broad range of representative experimental data. The equilibrium dispersive and the steric mass action equations were used to model and simulate the process. A training strategy to fit the model and separately describe the elution profiles of PspA4Pro and other proteins of the cell extract was applied. Based on the simulation results, a reduced ionic strength was applied for PspA4Pro elution, leading to increases of 14.9% and 11.5% for PspA4Pro recovery and purity, respectively, compared to the original elution profile. These results showed the potential of this method, which could be further applied to improve the performance of ion exchange chromatography in the purification of other target proteins under real process conditions.

Anti-Langmuir elution behavior of a bispecific monoclonal antibody in cation exchange chromatography: Mechanistic modeling using a pH-dependent Self-Association Steric Mass Action isotherm

The objective of this scientific work was to model and simulate the complex anti-Langmuir elution behavior of a bispecific monoclonal antibody (bsAb) under high loading conditions on the strong cation exchange resin POROS™ XS. The bsAb exhibited anti-Langmuirian elution behavior as a consequence of self-association expressed both in uncommon retentions and peak shapes highly atypical for antibodies. The widely applied Steric Mass Action (SMA) model was unsuitable here because it can only describe Langmuirian elution behavior and is not able to describe protein-protein interactions in the form of self-association. For this reason, a Self-Association SMA (SAS-SMA) model was applied, which was extended by two activity coefficients for the salt and protein in solution. This model is able to describe protein-protein interactions in the form of self-dimerization and thus can describe anti-Langmuir elution behavior. Linear gradient elution (LGE) experiments were carried out to obtain a broad dataset ranging from pH 4.5 to 7.3 and from 50 to 375 mmol/L Na+ for model parameter determination. High loading LGE experiments were conducted with an increasing load from 0.5 up to 75.0 mgbsAb/mLresin. Thereby, pH-dependent empirical correlations for the activity coefficient of the solute protein, for the equilibrium constant of the self-dimerization process and for the shielding factor could be set up and ultimately incorporated into the SAS-SMA model. This pH-dependent SAS-SMA model was thus able to simulate anti-Langmuir behavior over extended ranges of pH, counterion concentration, and column loading. The model was confirmed by experimental verification of simulated linear pH gradient elutions up to a load of 75.0 mgbsAb/mLresin.

Parameter-by-parameter method for steric mass action model of ion exchange chromatography: Simplified estimation for steric shielding factor

Mechanistic models play a crucial role in the process development and optimization of ion-exchange chromatography (IEC). Recent researches in steric mass action (SMA) model have heightened the need for better estimation of nonlinear parameter, steric shielding factor σ. In this work, a straightforward approach combination of simplified linear approximation (SLA) and inverse method (IM) was proposed to initialize and further determine σ, respectively. An existed, unique, and positive σ can be derived from SLA. Compared with linear approximation (LA) developed in our previous study, σ of the multi-component system can be calculated easily without solving the complex system of linear equations, leading to a time complexity reduction from O(n3) to O(n). The proposed method was verified first in numerical experiments about the separation of three charge variants. The calculated σ was more reasonable than that of LA, and the error of elution profiles with the parameters estimated by SLA+IM was only one-sixth of that by LA in numerical experiments. Moreover, the error accumulation effect could also be reduced. The proposed method was further confirmed in real-world experiments about the separation of monomer-dimer mixtures of monoclonal antibody. The results gave a lower error and better physical understanding compared to LA. In conclusion, SLA+IM developed in the present work provides a novel and straightforward way to determine σ. This simplification would help to save the effort of calibration experiments and accelerate the process development for the multi-component IEC separation.

Parameter-by-parameter method for steric mass action model of ion exchange chromatography: Theoretical considerations and experimental verification

Ion exchange chromatography (IEC) is one of the most widely-used techniques for protein separation and has been characterized by mechanistic models. However, the time-consuming and cumbersome model calibration hinders the application of mechanistic models for process development. A new methodology called "parameter-by-parameter method (PbP)" was proposed with mechanistic derivations of the steric mass action (SMA) model of IEC. The protocol includes four steps: (1) first linear regression (LR1) for characteristic charge; (2) second linear regression (LR2) for equilibrium coefficient; (3) linear approximation (LA) for shielding factor; (4) inverse method (IM) for kinetic coefficient. Four SMA parameters could be one-by-one determined in sequence, reducing the number of unknown parameters per species from four to one, and predicting almost consistent retention. Numerical single-component experiments were investigated firstly, and the PbP method showed excellent agreement between experiments and simulations. The effects of loadings on the PbP and Yamamoto methods were compared. It was found that the PbP method had higher accuracy and robustness than the Yamamoto method. Moreover, a five-experiment strategy was suggested to implement the PbP method, which is straightforward to reduce the cost of calibration experiments. Finally, a real-world multi-component separation was challenged and further confirmed the feasibility of the PbP method. In general, the proposed method can not only reliably estimate the SMA parameters with comprehensive physical understanding but also accurately predict retention over a wide range of loading conditions.

Bayesian optimization using multiple directional objective functions allows the rapid inverse fitting of parameters for chromatography simulations

The modeling of chromatographic separations can speed up downstream process development, reducing the time to market and corresponding development costs for new products such as pharmaceuticals. However, calibrating such models by identifying suitable parameter values for mass transport and sorption is a major, time-consuming challenge that can hinder model development and improvement. We therefore designed a new approach based on Bayesian optimization (BayesOpt) and Gaussian processes that reduced the time required to compute relevant chromatography parameters by up to two orders of magnitude compared to a multistart gradient descent and a genetic algorithm. We compared the three approaches side by side to process several internal and external datasets for ion exchange chromatography (based on a steric mass action isotherm) and hydrophobic interaction chromatography (a modified version of a recently published five-parameter isotherm) as well as different input data types (gradient elution data alone vs gradient elution and breakthrough data). We found that BayesOpt computation was consistently faster than the other approaches when using either single-core or 12-cores computer processing units. The error of the BayesOpt parameter estimates was higher than that of the competing algorithms, but still two orders of magnitude less than the variability of our experimental data, indicating BayesOpts applicability for chromatography modeling. The low computational demand of BayesOpt will facilitate rapid model development and improvement even for large datasets (e.g., > 100 proteins) and increase its suitability for research laboratories or small and medium enterprises lacking access to dedicated mainframe computers.

Application of the Steric Mass Action formalism for modeling under high loading conditions: Part 1. Investigation of the influence of pH on the steric shielding factor

In ion exchange chromatography, the Steric Mass Action (SMA) formalism is frequently used to simulate sorption processes at low and high column load conditions. To apply the SMA model for describing protein elution over wide ranges of pH, it is necessary to use pH-dependent model parameters. In the past, some publications have already described the pH-dependence of the characteristic protein charge and the equilibrium constant, while the influence of pH on the steric shielding factor has been mostly neglected. In this work, the pH-dependences of all relevant model parameters, including the shielding factor, were investigated, described, and implemented into the SMA model. Therefore, the elution behavior of a bispecific monoclonal antibody on the strong cation exchange resin POROS™ XS was modeled over broad ranges of pH, salt concentrations, and protein concentrations. Linear gradient elution experiments were performed to generate an extensive data set by using increasing column loadings from 0.5 up to 75.0 mgbsAb/mLresin. By using an inverse peak fitting method, shielding factors were estimated at various pH values ranging from 4.5 to 8.9. The results showed that an increasing buffer pH resulted in strongly increasing shielding factors. A semi-empirical correlation describing the shielding factor as a function of pH was established and implemented into the SMA formalism. This approach led to precise prediction of protein elution behavior using a single-component simulation. This was demonstrated by accurate simulation of linear salt, pH and dual gradient elution experiments conducted under high loading conditions.

Application of the Steric Mass Action formalism for modeling under high loading conditions: Part 2. Investigation of high loading and column overloading effects

The application of a model-based approach for industrial chromatography development requires the capability of the model to describe protein elution under high loading and overloading conditions. In a previous work, an extensive dataset was created to model the elution behavior of a bispecific antibody (bsAb) on the strong cation exchange resin POROS™ XS. Thereby, the pH-dependence of the model parameters in the Steric Mass Action (SMA) model could be examined and described over a pH range of 4.5 to 8.9. However, discrepancies between simulated and experimental data were observed under high loading and overloading conditions, particularly in the lower pH range (pH 4.5 to 5.3) and in the higher pH range (pH 6.0 to 9.0). In this work, these discrepancies are studied by performing new experiments which show that these differences were primarily not caused by limitations of the SMA model. At lower pH values, overloading phenomena such as protein breakthrough during the loading phase, additional peaks, and peak shoulders occurred. The application of various experiments performed with different Na+ concentrations and different loading times during sample loading revealed that intraparticle diffusion effects and conformational changes of the bsAb are responsible for these overloading phenomena at low pH. The applied lumped rate mass transfer model is not adequate and should be extended to consider these effects. At higher pH, the assumption of describing the bsAb's elution behavior with only one simulated species was insufficient to predict complex peak shapes that arise because of multi-component elution of the bsAb's charge variants. The extension of the model to a simple multi-component system consisting of two variants allowed the prediction of a majority of the complex elution profiles.

Need for a Next Generation of Chromatography Models—Academic Demands for Thermodynamic Consistency and Industrial Requirements in Everyday Project Work

Process chromatography modelling for process development, design, and optimization as well as process control has been under development for decades. Still, the discussion of scientific potential and industrial applications needs is open to innovation. The discussion of next-generation modelling approaches starting from Langmuirian to steric mass action and multilayer or thermodynamic consistent real and ideal adsorption theory or colloidal particle adsorption approaches is continued.