Current state of implementation of in silico tools in the biopharmaceutical industry-Proceedings of the 5th modeling workshop.

The fifth modeling workshop (5MW) was held in June 2023 at Favrholm, Denmark and sponsored by Recovery of Biological Products Conference Series. The goal of the workshop was to assemble modeling practitioners to review and discuss the current state, progress since the last fourth mini modeling workshop (4MMW), gaps and opportunities for development, deployment and maintenance of models in bioprocess applications. Areas of focus were four categories: biophysics and molecular modeling, mechanistic modeling, computational fluid dynamics (CFD) and plant modeling. Highlights of the workshop included significant advancements in biophysical/molecular modeling to novel protein constructs, mechanistic models for filtration and initial forays into modeling of multiphase systems using CFD for a bioreactor and mapped strategically to cell line selection/facility fit. A significant impediment to more fully quantitative and calibrated models for biophysics is the lack of large, anonymized datasets. A potential solution would be the use of specific descriptors in a database that would allow for detailed analyzes without sharing proprietary information. Another gap identified was the lack of a consistent framework for use of models that are included or support a regulatory filing beyond the high-level guidance in ICH Q8-Q11. One perspective is that modeling can be viewed as a component or precursor of machine learning (ML) and artificial intelligence (AI). Another outcome was alignment on a key definition for "mechanistic modeling." Feedback from participants was that there was progression in all of the fields of modeling within scope of the conference. Some areas (e.g., biophysics and molecular modeling) have opportunities for significant research investment to realize full impact. However, the need for ongoing research and development for all model types does not preclude the application to support process development, manufacturing and use in regulatory filings. Analogous to ML and AI, given the current state of the four modeling types, a prospective investment in educating inter-disciplinary subject matter experts (e.g., data science, chromatography) is essential to advancing the modeling community.

Application of linear pH gradients for the modeling of ion exchange chromatography: Separation of monoclonal antibody monomer from aggregates.

The mobile phase pH is a key parameter of every ion exchange chromatography process. However, mechanistic insights into the pH influence on the ion exchange chromatography equilibrium are rare. This work describes a mechanistic model capturing salt and pH influence in ion exchange chromatography. The pH dependence of the characteristic protein charge and the equilibrium constant is introduced to the steric mass action model based on a protein net charge model considering the number of amino acids interacting with the stationary phase. This allows the description of the adsorption equilibrium of the chromatographed proteins as a function of pH. The model parameters were determined for a monoclonal antibody monomer, dimer, and a higher aggregated species based on a manageable set of pH gradient experiments. Without further modification of the model parameters the transfer to salt gradient elution at fixed pH is demonstrated. A lumped rate model was used to predict the separation of the monoclonal antibody monomer/aggregate mixture in pH gradient elution and for a pH step elution procedure-also at increased protein loadings up to 48 g/L packed resin. The presented model combines both salt and pH influence and may be useful for the development and deeper understanding of an ion exchange chromatography separation.

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.

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.

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.

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.

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.

Modeling and simulation of protein elution in linear pH and salt gradients on weak, strong and mixed cation exchange resins applying an extended Donnan ion exchange model.

Process development and characterization based on mathematic modeling provides several advantages and has been applied more frequently over the last few years. In this work, a Donnan equilibrium ion exchange (DIX) model is applied for modelling and simulation of ion exchange chromatography of a monoclonal antibody in linear chromatography. Four different cation exchange resin prototypes consisting of weak, strong and mixed ligands are characterized using pH and salt gradient elution experiments applying the extended DIX model. The modelling results are compared with the results using a classic stoichiometric displacement model. The Donnan equilibrium model is able to describe all four prototype resins while the stoichiometric displacement model fails for the weak and mixed weak/strong ligands. Finally, in silico chromatogram simulations of pH and pH/salt dual gradients are performed to verify the results and to show the consistency of the developed model.