Effects of uncertainties in experimental conditions on the estimation of adsorption model parameters in preparative chromatography

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.

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.

Coupling of multivariate curve resolution-alternating least squares and mechanistic hard models to investigate antibody purification from human plasma using ion exchange chromatography

A two steps proposal for the purification of immunoglobulin G from human blood plasma is investigated. The first step is precipitation using cold ethanol based on the Cohn method with some modification and the second step is a chromatographic separation by DEAE-Sepharose FF resin as a weak anion exchanger. The presence of interferent in the region3 of chromatographic fractions, which is co-eluted with IgG, restricts the application of the mechanistic chromatography model. Therefore, multivariate cure resolution-alternating least squares (MCR-ALS) as a soft method is employed on measured absorbance data matrix from eluted fractions to recover pure concentration and spectral profiles. Besides, possible solutions for resolved concentration and spectral profiles are investigated. The reaction-dispersive model as a mechanistic hard model for the column is utilized for the evaluation of the ion exchange chromatography. Using a genetic algorithm as a global optimization method, mobile phase modulator (MPM) adsorption model parameters such as β, k_des,0, and K_eq,0, were fitted to the concentration profiles from MCR-ALS as 1.96, 2.87×10^-4 m³ mol^-1s^-1, and 1883, respectively. Furthermore, a new resampling incorporated non-parametric statistics is conducted to assess parameters' uncertainty. Values of 2.00, 1.10×10^-3 m³ mol^-1s^-1, and 549.80 are estimated median, and values of 0.05, 2.5×10^-3, and 691.00 are calculated interquartile range (IQR) for β, k_des,0, and K_eq,0, respectively. Finally, results show three and two outliers for β and k_des,0, respectively.

Robust mechanistic modeling of protein ion-exchange chromatography

Mechanistic models for ion-exchange chromatography of proteins are well-established and a broad consensus exists on most aspects of the detailed mathematical and physical description. A variety of specializations of these models can typically capture the general locations of elution peaks, but discrepancies are often observed in peak position and shape, especially if the column load level is in the non-linear range. These discrepancies may prevent the use of models for high-fidelity predictive applications such as process characterization and development of high-purity and -productivity process steps. Our objective is to develop a sufficiently robust mechanistic framework to make both conventional and anomalous phenomena more readily predictable using model parameters that can be evaluated based on independent measurements or well-accepted correlations. This work demonstrates the implementation of this approach for industry-relevant case studies using both a model protein, lysozyme, and biopharmaceutical product monoclonal antibodies, using cation-exchange resins with a variety of architectures (SP Sepharose FF, Fractogel EMD SO₃^-, Capto S and Toyopearl SP650M). The modeling employs the general rate model with the extension of the surface diffusivity to be variable, as a function of ionic strength or binding affinity. A colloidal isotherm that accounts for protein-surface and protein-protein interactions independently was used, with each characterized by a parameter determined as a function of ionic strength and pH. Both of these isotherm parameters, along with the variable surface diffusivity, were successfully estimated using breakthrough data at different ionic strengths and pH. The model developed was used to predict overloads and elution curves with high accuracy for a wide variety of gradients and different flow rates and protein loads. The in-silico methodology used in this work for parameter estimation, along with a minimal amount of experimental data, can help the industry adopt model-based optimization and control of preparative ion-exchange chromatography with high accuracy.

Model-based monitoring of industrial reversed phase chromatography to predict insulin variants

Downstream processing in the manufacturing biopharmaceutical industry is a multistep process separating the desired product from process- and product-related impurities. However, removing product-related impurities, such as product variants, without compromising the product yield or prolonging the process time due to extensive quality control analytics, remains a major challenge. Here, we show how mechanistic model-based monitoring, based on analytical quality control data, can predict product variants by modeling their chromatographic separation during product polishing with reversed phase chromatography. The system was described by a kinetic dispersive model with a modified Langmuir isotherm. Solely quality control analytical data on product and product variant concentrations were used to calibrate the model. This model-based monitoring approach was developed for an insulin purification process. Industrial materials were used in the separation of insulin and two insulin variants, one eluting at the product peak front and one eluting at the product peak tail. The model, fitted to analytical data, used one component to simulate each protein, or two components when a peak displayed a shoulder. This monitoring approach allowed the prediction of the elution patterns of insulin and both insulin variants. The results indicate the potential of using model-based monitoring in downstream polishing at industrial scale to take pooling decisions.

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.

Chromatographic parameter determination for complex biological feedstocks

The application of mechanistic models for chromatography requires accurate model parameters. Especially for complex feedstocks such as a clarified cell harvest, this can still be an obstacle limiting the use of mechanistic models. Another commonly encountered obstacle is a limited amount of sample material and time to determine all needed parameters. Therefore, this study aimed at implementing an approach on a robotic liquid handling system that starts directly with a complex feedstock containing a monoclonal antibody. The approach was tested by comparing independent experimental data sets with predictions generated by the mechanistic model using all parameters determined in this study. An excellent agreement between prediction and experimental data was found verifying the approach. Thus, it can be concluded that RoboColumns with a bed volume of 200 μL can well be used to determine isotherm parameters for predictions of larger scale columns. Overall, this approach offers a new way to determine crucial model input parameters for mechanistic modelling of chromatography for complex biological feedstocks. © 2018 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 34:1006–1018, 2018