Adjoint-based estimation and optimization for column liquid chromatography models

Predicting multimodal chromatography of therapeutic antibodies using multiscale modeling

Multimodal chromatography has emerged as a powerful method for the purification of therapeutic antibodies. However, process development of this separation technique remains challenging because of an intricate and molecule-specific interaction towards multimodal ligands, leading to time-consuming and costly experimental optimization. This study presents a multiscale modeling approach to predict the multimodal chromatographic behavior of therapeutic antibodies based on their sequence information. Linear gradient elution (LGE) experiments were performed on an anionic multimodal resin for 59 full-length antibodies, including five different antibody formats at pH 5.0, 6.0, and 7.0 that were used for parameter determination of a linear adsorption model at low loading density conditions. Quantitative structure-property relationship (QSPR) modeling was utilized to correlate the adsorption parameters with up to 1374 global and local physicochemical descriptors calculated from antibody homology models. The final QSPR models employed less than eight descriptors per model and demonstrated high training accuracy (R² > 0.93) and reasonable test set prediction accuracy (Q² > 0.83) for the adsorption parameters. Model evaluation revealed the significance of electrostatic interaction and hydrophobicity in determining the chromatographic behavior of antibodies, as well as the importance of the HFR3 region in antibody binding to the multimodal resin. Chromatographic simulations using the predicted adsorption parameters showed good agreement with the experimental data for the vast majority of antibodies not employed during the model training. The results of this study demonstrate the potential of sequence-based prediction for determining chromatographic behavior in therapeutic antibody purification. This approach leads to more efficient and cost-effective process development, providing a valuable tool for the biopharmaceutical industry.

Parameter-by-parameter estimation method for adsorption isotherm in hydrophobic interaction chromatography

Hydrophobic interaction chromatography (HIC) is used as a critical polishing step in the downstream processing of biopharmaceuticals. Normally the process development of HIC is a cumbersome and time-consuming task, and the mechanical models can provide a powerful tool to characterize the process, assist process design and accelerate process development. However, the current estimation of model parameters relies on the inverse method, which lacks an efficient and logical parameter estimation strategy. In this study, a parameter-by-parameter (PbP) method based on the theoretical derivation and simplifying assumptions was proposed to estimate the Mollerup isotherm parameters for HIC. The method involves three key steps: (1) linear regression (LR) to estimate the salt-protein interaction parameter and the equilibrium constant; (2) linear approximation (LA) to estimate the stoichiometric parameter and the maximum binding capacity; and (3) inverse method to estimate the protein-protein interaction parameter and the kinetic coefficient. The results indicated that the LR step should be used for dilution condition (loading factor below 5%), while the LA step should be conducted when the isotherm is in the transition or nonlinear regions. Six numerical experiments were conducted to implement the PbP method. The results demonstrated that the PbP method developed allows for the systematic estimation of HIC parameters one-by-one, effectively reducing the number of parameters required for inverse method estimation from six to two. This helps prevent non-identifiability of structural parameters. The feasibility of the PbP-HIC method was further validated by real-world experiments. Moreover, the PbP method enhances the mechanistic understanding of adsorption behavior of HIC and shows a promising application to other stoichiometric displacement model-derived isotherms.

Standardized method for mechanistic modeling of multimodal anion exchange chromatography in flow through operation

Multimodal chromatography offers an increased selectivity compared to unimodal chromatographic methods and is often employed for challenging separation tasks in industrial downstream processing (DSP). Unfortunately, the implementation of multimodal polishing into a generic downstream platform can be hampered by non-robust platform conditions leading to a time and cost intensive process development. Mechanistic modeling can assist experimental process development but readily applicable and easy to calibrate multimodal chromatography models are lacking. In this work, we present a mechanistic modeling aided approach that paves the way for an accelerated development of anionic mixed-mode chromatography (MMC) for biopharmaceutical purification. A modified multimodal isotherm model was calibrated using only three chromatographic experiments and was employed in the retention prediction of four antibody formats including a Fab, a bispecific, as well as an IgG1 and IgG4 antibody subtype at pH 5.0 and 6.0. The chromatographic experiments were conducted using the anionic mixed-mode resin Capto adhere at industrial relevant process conditions to enable flow through purification. An existing multimodal isotherm model was reduced to hydrophobic interactions in the linear range of the adsorption isotherm and successfully employed in the simulation of six chromatographic experiments per molecule in concert with the transport dispersive model (TDM). The model reduction to only three parameters did prevent structural parameter non-identifiability and enabled an analytical isotherm parameter determination that was further refined by incorporation of size exclusion effects of the selected multimodal resin. During the model calibration, three linear salt gradient elution experiments were performed for each molecule followed by an isotherm parameter uncertainty assessment. Lastly, each model was validated with a set of step and isocratic elution experiments. This standardized modeling approach facilitates the implementation of multimodal chromatography as a key unit operation for the biopharmaceutical downstream platform, while increasing the mechanistic insight to the multimodal adsorption behavior of complex biologics.

Industrial ion-exchange chromatography development using discontinuous Galerkin methods coupled with forward sensitivity analysis

In this work, a discontinuous Galerkin method coupled with forward sensitivity analysis (DG-FSA) is presented. The DG-FSA method is used to reduce computational cost required for model-based ion-exchange chromatography development using industrial load samples. As an example, the design of an anion-exchange chromatography step is considered. This step is used to purify an experimental peptide product called Protein G from Novo Nordisk A/S (Bagsværd, Denmark). The results demonstrate, that a fourth order DG-FSA method can reduce computational cost of inverse problems by a factor ×16 compared to a second (low) order DG-FSA method. Furthermore, the fourth-order DG-FSA method enable the computation of probability distributions of optimized processing conditions given uncertainty in model parameters or inputs. This analysis is not possible within a reasonable timeframe when applying the second (low) order DG-FSA method. The design procedure facilitates the optimization of the Protein G purification step. In an experimental validation run, the productivity is increased by 70% while sacrificing 4% yield at a similar purity constraint compared to an experiment with baseline performance.

Estimation and statistical analysis of model parameters using sequential Monte Carlo for phenol and p-cresol separation

Model-based design and optimization methods facilitate industrial applications of chromatographic separations. The uncertainty of the model parameters must be quantified to ensure robust design and control. In this study, we propose an approach using the sequential Monte Carlo (SMC) method based on the Bayesian principle to estimate the uncertainty of the parameters. The linear driving force model for separation of phenol and p-cresol was considered as an example. By comparing different injection tests, we confirmed the necessity of pulse injection and breakthrough experiments to estimate parameters with sufficient accuracy and precision. We also found that modeling observation errors carefully is critical to obtain reasonable estimation.

Metal-Chelating Peptides Separation Using Immobilized Metal Ion Affinity Chromatography: Experimental Methodology and Simulation

Metal-Chelating Peptides (MCPs), obtained from protein hydrolysates, present various applications in the field of nutrition, pharmacy, cosmetic etc. The separation of MCPs from hydrolysates mixture is challenging, yet, techniques based on peptide-metal ion interactions such as Immobilized Metal Ion Affinity Chromatography (IMAC) seem to be efficient. However, separation processes are time consuming and expensive, therefore separation prediction using chromatography modelling and simulation should be necessary. Meanwhile, the obtention of sorption isotherm for chromatography modelling is a crucial step. Thus, Surface Plasmon Resonance (SPR), a biosensor method efficient to screen MCPs in hydrolysates and with similarities to IMAC might be a good option to acquire sorption isotherm. This review highlights IMAC experimental methodology to separate MCPs and how, IMAC chromatography can be modelled using transport dispersive model and input data obtained from SPR for peptides separation simulation.

Analysis of complex protein elution behavior in preparative ion exchange processes using a colloidal particle adsorption model

A fundamental understanding of the protein retention mechanism in preparative ion exchange (IEX) chromatography columns is essential for a model-based process development approach. For the past three decades, the mechanistic description of protein retention has been based predominantly on the steric mass action (SMA) model. In recent years, however, retention profiles of proteins have been reported more frequently for preparative processes that are not consistent with the mechanistic understanding relying on the SMA model. In this work, complex elution behavior of proteins in preparative IEX processes is analyzed using a colloidal particle adsorption (CPA) model. The CPA model is found to be capable of reproducing elution profiles that cannot be described by the traditional SMA model. According to the CPA model, the reported complex behavior can be ascribed to a strong compression and concentration of the elution front in the lower unsaturated part of the chromatography column. As the unsaturated part of the column decreases with increasing protein load density, exceeding a critical load density can lead to the formation of a shoulder in the peak front. The general applicability of the model in describing preparative IEX processes is demonstrated using several industrial case studies including multiple monoclonal antibodies on different IEX adsorber systems. In this context, the work covers both salt controlled and pH-controlled protein elution.

Protein adsorption on ion exchange adsorbers: A comparison of a stoichiometric and non-stoichiometric modeling approach

For mechanistic modeling of ion exchange (IEX) processes, a profound understanding of the adsorption mechanism is important. While the description of protein adsorption in IEX processes has been dominated by stoichiometric models like the steric mass action (SMA) model, discrepancies between experimental data and model results suggest that the conceptually simple stoichiometric description of protein adsorption provides not always an accurate representation of nonlinear adsorption behavior. In this work an alternative colloidal particle adsorption (CPA) model is introduced. Based on the colloidal nature of proteins, the CPA model provides a non-stoichiometric description of electrostatic interactions within IEX columns. Steric hindrance at the adsorber surface is considered by hard-body interactions between proteins using the scaled-particle theory. The model's capability of describing nonlinear protein adsorption is demonstrated by simulating adsorption isotherms of a monoclonal antibody (mAb) over a wide range of ionic strength and pH. A comparison of the CPA model with the SMA model shows comparable model results in the linear adsorption range, but significant differences in the nonlinear adsorption range due to the different mechanistic interpretation of steric hindrance in both models. The results suggest that nonlinear adsorption effects can be overestimated by the stoichiometric formalism of the SMA model and are generally better reproduced by the CPA model.

Modeling the impact of amino acid substitution in a monoclonal antibody on cation exchange chromatography

A vital part of biopharmaceutical research is decision making around which lead candidate should be progressed in early-phase development. When multiple antibody candidates show similar biological activity, developability aspects are taken into account to ease the challenges of manufacturing the potential drug candidate. While current strategies for developability assessment mainly focus on drug product stability, only limited information is available on how antibody candidates with minimal differences in their primary structure behave during downstream processing. With increasing time-to-market pressure and an abundance of monoclonal antibodies (mAbs) in development pipelines, developability assessments should also consider the ability of mAbs to integrate into the downstream platform. This study investigates the influence of amino acid substitutions in the complementarity-determining region (CDR) of a full-length IgG1 mAb on the elution behavior in preparative cation exchange chromatography. Single amino acid substitutions within the investigated mAb resulted in an additional positive charge in the light chain (L) and heavy chain (H) CDR, respectively. The mAb variants showed an increased retention volume in linear gradient elution compared with the wild-type antibody. Furthermore, the substitution of tryptophan with lysine in the H-CDR3 increased charge heterogeneity of the product. A multiscale in silico analysis, consisting of homology modeling, protein surface analysis, and mechanistic chromatography modeling increased understanding of the adsorption mechanism. The results reveal the potential effects of lead optimization during antibody drug discovery on downstream processing.

Prediction uncertainty assessment of chromatography models using Bayesian inference

Mechanistic modeling of chromatography has been around in academia for decades and has gained increased support in pharmaceutical companies in recent years. Despite the large number of published successful applications, process development in the pharmaceutical industry today still does not fully benefit from a systematic mechanistic model-based approach. The hesitation on the part of industry to systematically apply mechanistic models can often be attributed to the absence of a general approach for determining if a model is qualified to support decision making in process development. In this work a Bayesian framework for the calibration and quality assessment of mechanistic chromatography models is introduced. Bayesian Markov Chain Monte Carlo is used to assess parameter uncertainty by generating samples from the parameter posterior distribution. Once the parameter posterior distribution has been estimated, it can be used to propagate the parameter uncertainty to model predictions, allowing a prediction-based uncertainty assessment of the model. The benefit of this uncertainty assessment is demonstrated using the example of a mechanistic model describing the separation of an antibody from its impurities on a strong cation exchanger. The mechanistic model was calibrated at moderate column load density and used to make extrapolations at high load conditions. Using the Bayesian framework, it could be shown that despite significant parameter uncertainty, the model can extrapolate beyond observed process conditions with high accuracy and is qualified to support process development.

Water on hydrophobic surfaces: Mechanistic modeling of hydrophobic interaction chromatography

Mechanistic models are successfully used for protein purification process development as shown for ion-exchange column chromatography (IEX). Modeling and simulation of hydrophobic interaction chromatography (HIC) in the column mode has been seldom reported. As a combination of these two techniques is often encountered in biopharmaceutical purification steps, accurate modeling of protein adsorption in HIC is a core issue for applying holistic model-based process development, especially in the light of the Quality by Design (QbD) approach. In this work, a new mechanistic isotherm model for HIC is derived by consideration of an equilibrium between well-ordered water molecules and bulk-like ordered water molecules on the hydrophobic surfaces of protein and ligand. The model's capability of describing column chromatography experiments is demonstrated with glucose oxidase, bovine serum albumin (BSA), and lysozyme on Capto™ Phenyl (high sub) as model system. After model calibration from chromatograms of bind-and-elute experiments, results were validated with batch isotherms and prediction of further gradient elution chromatograms.

Application of spectral deconvolution and inverse mechanistic modelling as a tool for root cause investigation in protein chromatography

In chromatographic protein purification, process variations, aging of columns, or processing errors can lead to deviations of the expected elution behavior of product and contaminants and can result in a decreased pool purity or yield. A different elution behavior of all or several involved species leads to a deviating chromatogram. The causes for deviations are however hard to identify by visual inspection and complicate the correction of a problem in the next cycle or batch. To overcome this issue, a tool for root cause investigation in protein chromatography was developed. The tool combines a spectral deconvolution with inverse mechanistic modelling. Mid-UV spectral data and Partial Least Squares Regression were first applied to deconvolute peaks to obtain the individual elution profiles of co-eluting proteins. The individual elution profiles were subsequently used to identify errors in process parameters by curve fitting to a mechanistic chromatography model. The functionality of the tool for root cause investigation was successfully demonstrated in a model protein study with lysozyme, cytochrome c, and ribonuclease A. Deviating chromatograms were generated by deliberately caused errors in the process parameters flow rate and sodium-ion concentration in loading and elution buffer according to a design of experiments. The actual values of the three process parameters and, thus, the causes of the deviations were estimated with errors of less than 4.4%. Consequently, the established tool for root cause investigation is a valuable approach to rapidly identify process variations, aging of columns, or processing errors. This might help to minimize batch rejections or contribute to an increased productivity.

Modeling and simulation of anion-exchange membrane chromatography for purification of Sf9 insect cell-derived virus-like particles

Recombinant protein-based virus-like particles (VLPs) are steadily gaining in importance as innovative vaccines against cancer and infectious diseases. Multiple VLPs are currently evaluated in clinical phases requiring a straightforward and rational process design. To date, there is no generic platform process available for the purification of VLPs. In order to accelerate and simplify VLP downstream processing, there is a demand for novel development approaches, technologies, and purification tools. Membrane adsorbers have been identified as promising stationary phases for the processing of bionanoparticles due to their large pore sizes. In this work, we present the potential of two strategies for designing VLP processes following the basic tenet of 'quality by design': High-throughput experimentation and process modeling of an anion-exchange membrane capture step. Automated membrane screenings allowed the identification of optimal VLP binding conditions yielding a dynamic binding capacity of 5.7 mg/mL for human B19 parvovirus-like particles derived from Spodoptera frugiperda Sf9 insect cells. A mechanistic approach was implemented for radial ion-exchange membrane chromatography using the lumped-rate model and stoichiometric displacement model for the in silico optimization of a VLP capture step. For the first time, process modeling enabled the in silico design of a selective, robust and scalable process with minimal experimental effort for a complex VLP feedstock. The optimized anion-exchange membrane chromatography process resulted in a protein purity of 81.5%, a DNA clearance of 99.2%, and a VLP recovery of 59%.

Next generation vaccines and vectors: Designing downstream processes for recombinant protein-based virus-like particles

In recent years, the development of novel recombinant virus-like particles (VLPs) has been generating new perspectives for the prevention of untreated and arising infectious diseases. However, cost-reduction and acceleration of manufacturing processes for VLP-based vaccines or vectors are key challenges for the global health system. In particular, the design of rapid and cost-efficient purification processes is a critical bottleneck. In this review, we describe and evaluate new concepts, development strategies and unit operations for the downstream processing of VLPs. A special focus is placed on purity requirements and current trends, as well as chances and limitations of novel technologies. The discussed methods and case studies demonstrate the advances and remaining challenges in both rational process development and purification tools for large biomolecules. The potential of a new era of VLP-based products is highlighted by the progress of various VLPs in clinical phases.