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

Enhancing thermodynamic consistency: Clarification on the application of asymmetric activity model in multi-component chromatographic separation

The single-component Mollerup model, with over 40 direct applications and 442 citations, is the most widely used activity model for chromatographic mechanistic modeling. Many researchers have extended this formula to multi-component systems by directly adding subscripts, a modification deemed thermodynamically inconsistent (referred to as the reference model). In this work, we rederived the asymmetric activity model for multi-component systems, using the van der Waals equation of state, and termed it the multi-component Mollerup model. In contrast to the reference model, our proposed model accounts for the contributions of all components to the activity. Three numerical experiments were performed to investigate the impact of the three different activity models on the chromatographic modeling. The results indicate that our proposed model represents a thermodynamically consistent generalization of the single-component Mollerup model to multi-component systems. This communication advocates adopting of the multi-component Mollerup model for activity modeling in multi-component chromatographic separation to enhance thermodynamic consistency.

Modeling multi-component separation in hydrophobic interaction chromatography with improved parameter-by-parameter estimation method

Mechanistic models are powerful tools for chromatographic process development and optimization. However, hydrophobic interaction chromatography (HIC) mechanistic models lack an effective and logical parameter estimation method, especially for multi-component system. In this study, a parameter-by-parameter method for multi-component system (called as mPbP-HIC) was derived based on the retention mechanism to estimate the six parameters of the Mollerup isotherm for HIC. The linear parameters (ks,i and keq,i) and nonlinear parameters (ni and qmax,i) of the isotherm can be estimated by the linear regression (LR) and the linear approximation (LA) steps, respectively. The remaining two parameters (kp,i and kkin,i) are obtained by the inverse method (IM). The proposed method was verified with a two-component model system. The results showed that the model could accurately predict the protein elution at a loading of 10 g/L. However, the elution curve fitting was unsatisfactory for high loadings (12 g/L and 14 g/L), which is mainly attributed to the demanding experimental conditions of the LA step and the potential large estimation error of the parameter qmax. Therefore, the inverse method was introduced to further calibrate the parameter qmax, thereby reducing the estimation error and improving the curve fitting. Moreover, the simplified linear approximation (SLA) was proposed by reasonable assumption, which provides the initial guess of qmax without solving any complex matrix and avoids the problem of matrix unsolvable. In the improved mPbP-HIC method, qmax would be initialized by the SLA and finally determined by the inverse method, and this strategy was named as SLA+IM. The experimental validation showed that the improved mPbP-HIC method has a better curve fitting, and the use of SLA+IM reduces the error accumulation effect. In process optimization, the parameters estimated by the improved mPbP-HIC method provided the model with excellent predictive ability and reasonable extrapolation. In conclusion, the SLA+IM strategy makes the improved mPbP-HIC method more rational and can be easily applied to the practical separation of protein mixture, which would accelerate the process development for HIC in downstream of biopharmaceuticals.

A parameter estimation method for chromatographic separation process based on physics-informed neural network

Chromatographic separation processes are most often modeled in the form of partial differential equations (PDEs) to describe the complex adsorption equilibria and kinetics. However, identifying parameters in such a model requires substantial computational effort. In this work, a novel parameter estimation approach using a Physics-informed Neural Network (PINN) model is developed and tested for a binary component system. Numerical accuracy of our PINN model is confirmed by validating its simulations against those of the finite element method (FEM). Furthermore, model parameters in the kinetic model are estimated by the PINN model with sufficient accuracy from the observed data at the column outlet, where parameter fitting error can be reduced by up to 35.0 % from the conventional method. In a comparison with the conventional numerical method, our approach can reduce the computational time by up to 95 %. The robustness of the PINN model has also been demonstrated by estimating model parameters from noisy artificial experimental data.

Residence time distribution in continuous virus filtration

Regulatory authorities recommend using residence time distribution (RTD) to address material traceability in continuous manufacturing. Continuous virus filtration is an essential but poorly understood step in biologics manufacturing in respect to fluid dynamics and scale-up. Here we describe a model that considers nonideal mixing and film resistance for RTD prediction in continuous virus filtration, and its experimental validation using the inert tracer NaNO3. The model was successfully calibrated through pulse injection experiments, yielding good agreement between model prediction and experiment (R 2 > ${R}^{2}\gt $  0.90). The model enabled the prediction of RTD with variations-for example, in injection volumes, flow rates, tracer concentrations, and filter surface areas-and was validated using stepwise experiments and combined stepwise and pulse injection experiments. All validation experiments achievedR 2 > ${R}^{2}\gt $  0.97. Notably, if the process includes a porous material-such as a porous chromatography material, ultrafilter, or virus filter-it must be considered whether the molecule size affects the RTD, as tracers with different sizes may penetrate the pore space differently. Calibration of the model with NaNO3 enabled extrapolation to RTD of recombinant antibodies, which will promote significant savings in antibody consumption. This RTD model is ready for further application in end-to-end integrated continuous downstream processes, such as addressing material traceability during continuous virus filtration processes.

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.

Model-assisted process development, characterization and design of continuous chromatography for antibody separation

Continuous manufacturing in monoclonal antibody production has generated increased interest due to its consistent quality, high productivity, high equipment utilization, and low cost. One of the major challenges in realizing continuous biological manufacturing lies in implementing continuous chromatography. Given the complex operation mode and various operation parameters, it is challenging to develop a continuous process. Due to the process parameters being mainly determined by the breakthrough curves and elution behaviors, chromatographic modeling has gradually been used to assist in process development and characterization. Model-assisted approaches could realize multi-parameter interaction investigation and multi-objective optimization by integrating continuous process models. These approaches could reduce time and resource consumption while achieving a comprehensive and systematic understanding of the process. This paper reviews the application of modeling tools in continuous chromatography process development, characterization and design. Model-assisted process development approaches for continuous capture and polishing steps are introduced and summarized. The challenges and potential of model-assisted process characterization are discussed, emphasizing the need for further research on the design space determination strategy and parameter robustness analysis method. Additionally, some model applications for process design were highlighted to promote the establishment of the process optimization and process simulation platform.

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.

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 mg_bsAb/mL_resin. 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 mg_bsAb/mL_resin.