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.

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.

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 achieved R 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.

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.

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.

Realization of digital twin for dynamic control toward sample variation of ion exchange chromatography in antibody separation.

Digital twin (DT) is a virtual and digital representation of physical objects or processes. In this paper, this concept is applied to dynamic control of the collection window in the ion exchange chromatography (IEC) toward sample variations. A possible structure of a feedforward model-based control DT system was proposed. Initially, a precise IEC mechanistic model was established through experiments, model fitting, and validation. The average root mean square error (RMSE) of fitting and validation was 8.1% and 7.4%, respectively. Then a model-based gradient optimization was performed, resulting in a 70.0% yield with a remarkable 11.2% increase. Subsequently, the DT was established by systematically integrating the model, chromatography system, online high-performance liquid chromatography, and a server computer. The DT was validated under varying load conditions. The results demonstrated that the DT could offer an accurate control with acidic variants proportion and yield difference of less than 2% compared to the offline analysis. The embedding mechanistic model also showed a positive predictive performance with an average RMSE of 11.7% during the DT test under >10% sample variation. Practical scenario tests indicated that tightening the control target could further enhance the DT robustness, achieving over 98% success rate with an average yield of 72.7%. The results demonstrated that the constructed DT could accurately mimic real-world situations and perform an automated and flexible pooling in IEC. Additionally, a detailed methodology for applying DT was summarized.

Evaluation of dynamic control of continuous capture with periodic counter-current chromatography under feedstock variations.

Multi-column periodic counter-current chromatography is a promising technology for continuous antibody capture. However, dynamic changes due to disturbances and drifts pose some potential risks for continuous processes during long-term operation. In this study, a model-based approach was used to describe the changes in breakthrough curves with feedstock variations in target proteins and impurities. The performances of continuous capture of three-column periodic counter-current chromatography under ΔUV dynamic control were systematically evaluated with modeling to assess the risks under different feedstock variations. As the concentration of target protein decreased rapidly, the protein might not breakthrough from the first column, resulting in the failure of ΔUV control. Small reductions in the concentrations of target proteins or impurities would cause protein losses, which could be predicted by the modeling. The combination of target protein and impurity variations showed complicated effects on the process performance of continuous capture. A contour map was proposed to describe the comprehensive impacts under different situations, and nonoperation areas could be identified due to control failure or protein loss. With the model-based approach, after the model parameters are estimated from the breakthrough curves, it can rapidly predict the process stability under dynamic control and assess the risks under feedstock variations or UV signal drifts. In conclusion, the model-based approach is a powerful tool for continuous process evaluation under dynamic changes and would be useful for establishing a new real-time dynamic control strategy.

Physics-informed neural networks to solve lumped kinetic model for chromatography process.

Numerical method is widely used for solving the mechanistic models of chromatography process, but it is time-consuming and hard to response in real-time. Physics-informed neural network (PINN) as an emerging technology combines the structure of neural network with physics laws, and is getting noticed for solving physics problems with a balanced accuracy and calculation speed. In this research, a proof-of-concept study was carried out to apply PINN to chromatography process simulation. The PINN model structure was designed for the lumped kinetic model (LKM) with all LKM parameters. The PINN structure, training data and model complexity were optimized, and an optimal mode was obtained by adopting an in-series structure with a nonuniform training data set focusing on the breakthrough transition region. A PINN for LKM (LKM-PINN) consisting of four neural networks, 12 layers and 606 neurons was then used for the simulation of breakthrough curves of chromatography processes. The LKM parameters were estimated with two breakthrough curves and used to infer the breakthrough curves at different residence times, loading concentrations and column sizes. The results were comparable to that obtained with numerical methods. With the same raw data and constraints, the average fitting error for LKM-PINN model was 0.075, which was 0.081 for numerical method. With the same initial guess, the LKM-PINN model took 160 s to complete the fitting, while the numerical method took 7 to 72 min, depending on the fitting settings. The fitting speed of LKM-PINN model was further improved to 30 s with random initial guess. Thus, the LKM-PINN model developed in this study is capable to be applied to real-time simulation for digital twin.

Improved process design for monoclonal antibody charge variants separation with multicolumn counter-current solvent gradient purification.

The multicolumn counter-current solvent gradient purification (MCSGP) method has proven effective in addressing the issue of elution profile overlap for difficult-to-separate proteins, leading to improved purity and recovery. However, during the MCSGP process, the flow rate and proportion of loaded proteins undergo changes, causing a significant discrepancy between the elution profiles of batch process design and the actual MCSGP process. This mismatch negatively impacts the purity and recovery of the target protein. To address this challenge, an improved process design (reDesign) was proposed with the first-run MCSGP to mimic the actual continuous process and obtain elution profiles that closely resemble the real ones. The reDesign was demonstrated with both a model protein mixture and a sample of monoclonal antibody (mAb) with charge variants. For model protein mixture, the reDesign-based MCSGP process (reMCSGP) showed a remarkable improvement in recovery, increasing from 83.6% to 97.8% while maintaining a purity of more than 95%. For mAb sample, the recovery of reMCSGP improved significantly to 93.9%, surpassing the performance of normal MCSGP processes at a given purity level of more than 84%. In general, the new process design strategy developed in this work could generate a more representative elution profile that closely mirrors actual conditions in continuous processes, which enhances the separation performance of MCSGP.

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.