Mechanistic modeling of ion exchange chromatography (IEC) has become an essential tool for accelerating process development and deepening mechanistic insight in biopharmaceutical manufacturing. Although the steric mass action (SMA) model is widely used, it frequently fails to accurately describe elution behavior under high protein loading conditions, whereas the colloidal particle adsorption (CPA) model remains robust. To clarify the mechanistic advantages of the CPA framework, this study systematically compared the SMA and CPA models for describing the separation of a monoclonal antibody monomer-dimer mixture in IEC. At low loading densities (4-20 g/L), both models showed comparable performance. However, at 40 g/L, the CPA model significantly outperformed the SMA model (normalized root mean square error, NRMSE = 0.139 vs. 0.376). Simulated adsorption isotherms confirmed that this divergence originated from the fundamentally distinct representations of the nonlinear regime. Decomposition of the CPA model's nonlinear term indicated that steric hindrance accounts for over 76.9% of the overall nonlinearity, far exceeding the contribution from lateral protein-protein electrostatic interactions. These findings motivated the development of a simplified non-lateral CPA (nlCPA) model that neglects the minor lateral interaction term. For the same elution dataset, the nlCPA model achieved an overall simulation accuracy comparable to the CPA model, while outperforming the SMA model. In addition, more datasets were investigated and further confirmed the generalizability of above findings. This work established the intrinsic advantages of the CPA framework and proposed a simplified nlCPA model as a practical tool for industrial IEC process development.

The biopharmaceutical industry is increasingly shifting from batch processing to continuous manufacturing. The ICH Q13 guideline outlines regulatory considerations for the implementation of continuous manufacturing with emphasis on material traceability. Although continuous capture with Protein A affinity chromatography is widely used, the aspect of material traceability remains underexplored. In this study, a retention time distribution (ReTD) model for a twin-column continuous capture process was developed, building on the single column model and the connection condition of the process to enable material traceability. The ReTD behaviors during the startup, interconnected load and disconnected load steps were simulated, focusing on how the material are distributed in the elution peaks across subsequent switches. These simulations were validated through tracer experiments using fluorescently labeled proteins as inert tracer, showing good agreement between the model predictions and experimental results. This observed ReTD behavior is attributed to the combination effects of breakthrough dynamics, exchange effects, and operational step changes. Based on the developed ReTD model, a method for materials traceability and diversion was proposed. The ReTD behavior for materials with extended durations can be extrapolated from materials with duration shorter than one switch, owing to the periodic nature of the continuous capture process. This ReTD-based approach allows for the tracking and evaluation of disturbance entering the system at any time, as well as their persistence for varying durations. These materials can then be diverted according to the acceptable limits, facilitating real-time product release. The proposed ReTD-based method offers a practical solution for ensuring material traceability and diversion, helping meet regulatory requirements and improving real-time product release in continuous capture processes.

The capability of smart manufacturing to enable predictive and autonomous decision-making under uncertainty is highly valuable to ion-exchange chromatography (IEC), a critical purification step that is sensitive to variations in sample composition and loading density. However, conventional IEC operation relies on predefined elution conditions, including fixed elution gradient and collection window, which limits its adaptability to process variations. To address this limitation, a model-based control system was developed for the dynamic and autonomous optimization of IEC under process variations. The system incorporated the mechanistic models that combined equilibrium dispersive model and steric mass action model to quantitatively predict protein elution behavior. By integrating communication technologies, the model predictions were used to automatically determine and implement the optimal elution gradient and collection window, enabling model-based decision-making. The experimental validation demonstrated that the model-based control system consistently achieved purity above 96.0% and yield exceeding 88.0%. These results indicate that both product quality and process performance could be maintained despite process variability. Overall, the proposed model-based control system enabled the dynamic and simultaneous adjustment of elution gradient and collection window, transforming IEC operation from predefined conditions to a predictive and adaptive control approach, thereby enhancing process robustness and operational flexibility.

Biopharmaceutical manufacturing requires continuous improvement to ensure robust, efficient, and high-quality processes, yet traditional experimental designs remain resource-demanding and insufficient to capture interactions of multiple parameters. Here, we introduce a hybrid framework integrating artificial intelligence (AI)/machine learning (ML) with mechanistic modeling to optimize anion-exchange chromatography and resolve the long-standing yield-purity trade-off in PEGylated protein purification. Three critical process parameters were first identified through correlation analysis between 30 input factors and critical quality attributes/process yield from 400+ commercial manufacturing lots, which were further refined using equilibrium dispersive and steric mass action models. Over 40,000 in silico optimization via the mechanistic model resolved the yield-purity trade-off, achieving a 12% increase in yield and 33% reduction in high-molecular-weight impurities. The optimized process conditions were verified across laboratory (n = 3), pilot (n = 3), and commercial (n = 18) runs, consistently demonstrating scalability and process robustness. This study highlights the power of combining data-driven machine learning with mechanistic modeling for process optimization, leading to an improved commercial process with substantial cost savings and paving the way for upcoming intelligent biomanufacturing.

Chromatography offers a powerful platform for the purification of cell and gene therapy (CGT) products. However, commercial chromatographic resins suffer from limited capacities due to poor mass transfer, and the ideal resin structure for improving capacity remains unclear. Here, a concept of digital resin design is proposed to accelerate the structure design of high-capacity resins for CGT products. The digital design procedure was performed by generating virtual resin structures, analyzing the key structure characteristics, and simulating the dynamic diffusion of biomolecules in turn. The results revealed that nanofiber-based structures have a superior mass transfer ability for 100 nm-size model molecules compared to nanoparticle-based structures, as evidenced by 7.7 and two times improvement in the molecule breakthrough amount from structures and molecule diffusion displacement, respectively. The superiority of nanofiber-based resin was further demonstrated by mRNA adsorption experiments. These results indicate that digital resin design is a useful tool for resin development.

Regulatory authorities strongly recommend using residence time distribution (RTD) to achieve material traceability in continuous bioprocesses for non-adsorption units. For adsorption-based units, such as chromatography, retention time distribution (ReTD) is more suitable than RTD for characterizing material flow. Continuous capture chromatography is widely applied for biopharmaceutical continuous manufacturing. However, the ReTD behavior in these systems is still not fully understood. In this study, an ReTD model combining general rate model and two-component mobile phase modulator Langmuir model was developed for Protein A affinity chromatography under high breakthrough conditions. The model was calibrated using adsorption equilibrium experiments, protein breakthrough curves and elution curves. It was then validated through pulse injection experiments at varying protein loading phase. The results showed good agreement between model predictions and experimental results (R2 > 0.945). The exchange mechanism between the solid and liquid phases was further analyzed using confocal laser scanning microscopy images and model simulations, revealing that proteins with stronger binding affinity surpass the bound fraction to bind at the adsorption front while those with weaker affinity would exchange with the surface-bound fractions. Finally, simulations of protein distribution in the column during the interconnected loading step indicate that the exchange effect could broaden the ReTD in continuous chromatography. The model developed lays the groundwork for achieving material traceability and enables non-conforming material diversion strategies to facilitate real-time product release in continuous chromatography processes.

Mechanistic modeling of ion exchange chromatography (IEC) is a promising technique to improve process development. However, when considering the pH influence, model prediction becomes challenging due to the multiple pH-dependent parameters and complex interactions. In order to more effectively predict the pH gradient elution behavior, a two-step model calibration strategy was proposed for the pH-dependent steric mass action (SMA) model with the empirical correlations of characteristic charge ν and equilibrium coefficient keq. The strategy was verified through a case study of monoclonal antibody charge variants purification with IEC. All nine calibration experiments were conducted using linear salt gradient elution at three fixed pH values. The average root mean square error (RMSE) was 14.28% between the model calculation and experiments. Both ν and ln(keq) exhibited good linear correlations with pH (R2 > 0.99). Then, the well-calibrated pH-dependent SMA model showed a satisfactory capability for predicting the pH gradient elution behaviors with an RMSE of 16.18%. Moreover, the model was used for process optimization under different elution modes, including salt gradient, pH gradient, and salt-pH dual gradient, improving the yield from 70.07% to 74.91%. The optimized linear pH gradient elution was verified by experiment (RMSE = 8.30%). Finally, a methodological framework for utilizing the simplified pH-dependent SMA model developed in this work was summarized to explore its practical applications. The two-step calibration strategy proposed significantly alleviates the workload for the pH-dependent IEC modeling. The model-based process optimization effectively enables faster pH-dependent process development with minimal experiments.

A hybrid (gray-box) modeling framework, physics-informed neural networks (PINNs), has garnered significant attention. However, a huge challenge in applying PINNs to bioprocesses is developing a loss function that synergizes different bioprocess dynamics. To mitigate this challenge, a novel physics-based deep learning method was developed by integrating order-of-magnitude analysis to the loss function of PINNs (oPINNs) using biological first principles. Compared to standard PINNs and numerical methods for solving the forward problem of linear chromatographic models, oPINNs demonstrated notable improvements: an order-of-magnitude enhancement in accuracy with an equivalent sample size, or a 32-fold reduction in sample size for equivalent accuracy, along with a 1000-fold acceleration in computational speed for millisecond-scale simulation. Moreover, oPINNs showed exceptional robustness in weight determination and hyperparameter selection amidst variations in chromatographic model parameters. In summary, oPINNs represent a significant advancement in integrating physics-based deep learning into hybrid modeling of bioprocesses, particularly for developing real-time digital twins.

Quantifying the relationship between structure characteristics and mass transfer is essential for understanding the chromatographic behavior and improving the performance of resins. Here, a digital method was proposed to accurately establish this relationship by combining digital material techniques and machine learning algorithms. Digital material techniques were used to generate a large amount of structures and offer abundant data of resin structures and mass transfer. Then, machine learning algorithms were applied to develop the quantitative relationship between structure characteristics and mass transfer. The results showed that the machine learning models achieved better predictive accuracy with a reduction of 84-93% in mean absolute error (MAE) and an improvement of 1.54-2.23 times in determination coefficients (R2) compared to common empirical formulas. Moreover, feature importance analysis revealed that pore throat plays a pivotal role on the mass transfer in resins, which usually is neglected in common empirical formulas. Inspired by the finding, a empirical formula was modified by replacing porosity with throat size. The modified formula showed an improved prediction ability with a MAE value of 0.09 and an R2 value of 0.89. The quantitative relationship established in this work would serves as a prerequisite screening tool to accelerate the resin design and development.

The exosomes hold significant potential in disease diagnosis and therapeutic interventions. The objective of this study was to investigate the potential of aqueous two-phase systems (ATPSs) for the separation of bovine milk exosomes. The milk exosome partition behaviors and bovine milk separation were investigated, and the ATPSs and bovine milk whey addition was optimized. The optimal separation conditions were identified as 16% (mass) polyethylene glycol 4000, 10% (mass) dipotassium phosphate, and 1% (mass) enzymatic hydrolysis bovine milk whey. During the separation process, bovine milk exosomes were predominantly enriched in the interphase, while protein impurities were primarily found in the bottom phase. The process yielded bovine milk exosomes of 2.0 × 1011 particles per ml whey with high purity (staining rate>90%, 7.01 × 1010 particles per mg protein) and high uniformity (polydispersity index <0.03). The isolated exosomes were characterized and identified by transmission electron microscopy, zeta potential and size distribution. The results demonstrated aqueous two-phase extraction possesses a robust capability for the enrichment and separation of exosomes directly from bovine milk whey, presenting a novel approach for the large-scale isolation of exosomes.

The applications of continuous manufacturing technology in biopharmaceuticals require advanced design, monitoring, and control due to its complexity. Traditional mechanistic models, which rely on numerical solutions, suffer from long computational times, making them unsuitable for the timely demands of continuous processes and digital twin applications in biomanufacturing. This issue significantly limits the capability for real-time optimization and control. To overcome this challenge, this study proposes a Physics-Informed Neural Network (PINN) based General Rate Model (GRM) approach that greatly reduces computation time while maintaining high accuracy and reliability in simulations. The developed PINN is applicable for different parameters across wide ranges and is capable of parameter estimation. It presents excellent performance in both offline simulation of single-column breakthrough curves and online optimization of load conditions for four-column periodic counter-current chromatography (4C-PCC), achieving significant reductions in fitting time from 2608.6 to 110.7 s for offline simulations, and completing online simulations within 12 to 14 s. The results demonstrate the potential of PINN for real-time model predictive control and digital twin applications, offering a promising solution to the limitations of traditional numerical methods.

Mechanistic models offer powerful tools for process development and optimization of hydrophobic interaction chromatography (HIC). Suitable parameter estimation approaches can efficiently calibrate the models, but some unavoidable biases between model prediction and actual experiment would reduce the credibility of the model's applications. In this study, a well-calibrated HIC model was found some significant discrepancies between the predicted yield (97.3 %) and experimental yield (86.0 %) during the process optimization. Therefore, Bayesian inference with Markov Chain Monte Carlo method was employed to calculate the uncertainty of model parameters, which was then transformed into the uncertainty of model predictions. The results indicated that the model-predicted yield uncertainty interval was as large as 76.9∼96.5 %, which was consistent with the experiment. Moreover, the model prediction uncertainty analysis was integrated into process optimization to obtain a more reliable and low-risk separation condition. The re-optimized process significantly narrowed the uncertainty of the predicted yield (94.2∼98.9 %), and high experimental yield (95.8 %) was obtained. The results demonstrated that process optimization based on the uncertainty quantification could reasonably reflect model prediction deviations, assist process development and contribute to product quality improvement. Finally, a framework was proposed for process optimization based on the uncertainty analysis to improve the accuracy of model predictions and reducing the risk of model-based process development.

Development of a next-generation chromatographic model, capable of simultaneously meeting academic demands for thermodynamic consistency and industrial requirements in everyday project work, has become a focal point of research. In this study, anti-Langmuirian to Langmuirian (AL-L) elution behavior was observed in cation-exchange chromatographic separation of charge variants of industrial Fc-fusion proteins. To characterize this behavior, the multi-protein Mollerup activity model was integrated into the steric mass action (SMA) model, resulting in a new model named the generalized ion-exchange (nGIEX) isotherm for multi-protein systems. An R2 exceeding 0.95 calibrated by three elution experiments indicates an effective description of the AL-L behavior (dynamic adsorption). Using isotherm sampling, the nGIEX model exhibited sigmoidal AL-L isotherms (static adsorption). Finally, the model's extrapolation capability was externally validated through process optimization, resulting in an optimal two-step elution condition and a yield improvement of the main variant from 25.9% to 89.1% within purity specifications (>70%).

Hybrid modeling based on physics-based deep learning (PBDL) represents a transformative approach that unifies mechanistic understanding and data-driven learning, offering a pathway beyond the limitations of traditional chromatographic models. This review systematically summarizes the evolution of PBDL methods for chromatography across three generations. The first generation, surrogate-model-based solvers, accelerates simulations through mechanistic up-sampling and fast inference but remains constrained by indirect physical coupling, reflecting “data-assisted physics”. The second generation, physics-informed neural networks, embeds governing equations into the loss function, enabling simultaneous learning from physics and data, while facing challenges in loss balancing and numerical integration, representing “physics-constrained data”. The third generation, differentiable numerical simulations of physical systems, integrates neural networks within numerical solvers, achieving high-fidelity modeling and gradient-based optimization, achieving “mutual feedback between physics and data”. Collectively, these advances empower chromatographic models with the ability to self-learn complex adsorption behaviors under physical constraints, paving the way toward real-time digital twins and intelligent bioprocess modeling for the next generation of chromatographic engineering.

Adeno-associated viruses (AAVs) are widely used as gene therapy vectors due to their safety, stability, and long-term expression characteristics. The objective of this work is to develop an aqueous two-phase system (ATPS) as a universal platform for the separation and purification of AAVs. This study utilized polyethylene glycol (PEG)/salt ATPSs to separate and purify various AAV serotypes, including AAV5, AAV8, and AAV9, which focusing on serotype-specific performance and partial empty capsid removal. The results showed that all the AAV serotypes were mainly enriched in the interphase of ATPS, with achieving high recovery (> 95

Continuous bioprocessing with Protein A affinity chromatography has demonstrated great potential to increase productivity and reduce the cost of goods in monoclonal antibody (mAb) production. However, maintaining process stability and responding to dynamic changes remains significant challenges, particularly in the real-time optimization and control of multi-column periodic counter-current chromatography (PCC) for Protein A affinity chromatography, due to the computational complexity of rapidly solving mechanistic models. To address this challenge, this study developed distilled physics-informed neural networks (PINNs) based on the general rate model (GRM) to accelerate and enhance the breakthrough curve fitting and four-column PCC (4C-PCC) process optimization. The distilled PINNs achieved a balance between prediction accuracy and computational speed. The 157k-parameter distilled PINN enabled the breakthrough curve fitting and 4C-PCC process optimization approximately 10 times faster than numerical methods while improving accuracy by about 40%. A smaller 2k-parameter model achieved a 22-fold acceleration with an acceptable trade-off in accuracy, and the optimization time was reduced to 1.44 s. Explainability analyses confirmed the PINN's capability to capture nonlinear and interactive effects among key process parameters. The PINN-accelerated GRM was then integrated with real-time model predictive control (MPC) and applied to a lab-scale continuous manufacturing process. PINN-based MPC maintained robust control of binding capacity and yield, achieving a productivity of 35 g/L resin/h and resin capacity utilization of 90%, despite resin capacity decay and upstream variability. This work demonstrates that the PINNs can provide a computationally efficient and physically consistent framework for real-time optimization and control of continuous processes. Integrating a mechanistic model with neural networks can enhance process understanding and robustness, supporting the implementation of continuous biomanufacturing for therapeutic proteins.

Dynamic control is essential to guarantee the stable performance of continuous chromatography. AutoMAb dynamic control strategy has been developed to ensure a consistent protein load in twin-column CaptureSMB continuous capture by integrating the UV signal of breakthrough. In this study, the process risk of CaptureSMB continuous capture under AutoMAb control towards the feedstock variations was assessed by a mechanistic model developed by us. The effects of target protein and impurities under the variation range of ±10 mAU·min–1 on load amount, protein loss, process productivity and resin capacity utilization were investigated. The results showed that the CaptureSMB process could be successfully controlled by AutoMAb towards increased or slightly decreased concentration of feedstock. However, the load process would be out of control with drastically decreased target protein or impurities, and the decreased impurities would lead to protein loss. It was found that AutoMAb control would cause 44.7% non-operational areas and 18.3% protein loss areas in the variation range of ±10 mAU·min–1. To improve the stability of the CaptureSMB process, a modified AutoMAb control that would stop the load procedure when the absolute value of the integral area reached the preset value, was proposed to reduce the risk of protein loss and the non-operational area.

The enormous potential of mRNA-based therapeutics in vaccines and medicine has led to the consideration of various mRNA sizes, ranging from similar to 1000 to 10,000 nucleotides (nt). However, the commonly used Oligodeoxythymidine (Oligo dT) affinity resins are not initially designed for such a wide range of sizes, and present challenges in achieving optimal performance for the separation of a given mRNA. In this paper, two factors of the resin beads, pore size and grafting were focused. The effects of varying pore sizes, ranging from 150 to 850 nm, on both static and dynamic adsorption for varying-length mRNA (1000-8500 nt) were investigated. It was found that static adsorption capacity and uptake kinetics were correlated with the mRNA length. Interestingly, dynamic binding capacities (DBCs) showed an increase-then-decrease trend with increasing pore size. An optimal pore size of about 350 nm could lead to the highest DBCs for all tested mRNA. Additionally, the effects of polymer grafting on the adsorption performance were studied. The results revealed that polymer-grafted resin exhibited 24-55% higher DBCs than non-grafted resin. The enhanced DBCs could be attributed to the improved uptake rate facilitated by the polymer grafted. These investigations emphasize the importance of optimizing pore size and grafting for Oligo dT affinity resins, providing valuable guidance for selecting and designing new resins for different mRNA products.

Mixed-mode chromatography is promising for protein separation, but the structural diversities of proteins result in distinct adsorption behaviors. This study used machine learning methods to establish the quantitative structure-activity relationships (QSAR) between the protein adsorption capacity on mixed-mode resins and the molecule properties of target proteins and mixed-mode ligands. Four mixed-mode resins and twenty proteins were tested at different pHs and salt concentrations. Two machine learning models, random forest and gradient boosting, were developed successfully to predict protein adsorption capacities. The determination coefficients (R2) of the training dataset, validation dataset, and test dataset ranged around 0.94-0.97, 0.79-0.82, and 0.90-0.93, respectively. Several key descriptors that have significant impacts on adsorption capacities were identified by a two-step descriptor elimination method. Moreover, the SHapley Additive exPlanations (SHAP) method was used to reveal the mechanism of target protein adsorption on mixed-mode resins. The results provided a valuable guidance for the design and selection mixed-mode resins for the separation and purification of target proteins.

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.