Tips for a good mechanistic modeling workflow

The scope of the study was to optimize an ion-exchange chromatography polishing. The feed is composed of ~ 72% monoclonal antibody as main species, ~ 18% acidic charge variants, and ~ 10% basic charge variant. The acceptance criteria for the process are a final pooled product with a purity of > 95%, while maintaining a yield of at least 80%. Here, the acidic variants are considered a critical impurity, while the basic variant was not classified as a critical impurity and therefore acceptable in the pooled fraction. To meet the purification requirements, a two-step method is to be optimized for process pH and for salt concentration during elution. A small elution volume and high load density are the secondary requirements for high process productivity, which are to be targeted by optimizing the load density and elution volume.

The chromatography setup and non-variable process parameters were selected based on prior knowledge with a comparable molecule and experimental experience.

Chromatography setup:

• System: ÄKTA pure™ 25
• Column format: Tricorn™ 10/100 f(x) column, a prepacked and precharacterized column that replaces column characterization experiments.

Non- variable process parameters:

• Process mode: bind and elute
• Resin: Capto™ SP ImpRes, a strong cation exchanger that was chosen due to its high resolution for separation of closely related charge variants that have only small differences between the target variant and the acidic species
• Resin properties: one resin lot was used
• Load composition: analyzed feed material from one batch was used
• Analytics: an existing HPLC (high performance liquid chromatography) ion exchange method was applied for analysis of target molecule and charge variants
• Buffer system: 25 mM sodium phosphate with NaCl for elution
• Flowrate: flowrate was set to 150 cm/h, corresponding to 2 mL/min.

Variable process parameters:

• Process pH: pH during binding, wash, and elution; not varied between steps
• Method: elution volume of first and second elution step
• Method: salt concentration during elution, %B for first step
• Load density: applied amount of biomolecule feed material per volume of resin

Generally, all parameters that are defined here as non-variable process parameters or are part of the chromatography setup could be defined as variable process parameters to fulfill a desired project goal. For example, varying load composition could be modeled to assess the robustness of the process. Or flowrate, system, and column dimension could be adapted to predict a process at larger scale.

The following variable parameters were considered for optimization of the process:

Process pH and salt concentration during elution:

No prior knowledge on a suitable process pH range was available. The pI of the protein was known to be around pH 9. To derive a suitable pH center point and boundaries for optimization, three salt gradient elution experiments were performed in which the salt concentration was increased from 0 to 1000 mM NaCl at pH 6, pH 7 and pH 8.

Fig 1. Process pH screening with linear gradient elution.

Observations:

• Comparable peak resolution for pH 6 and pH 7.
• Load material analysis showed increased formation of critical acidic variants at pH 8.
• Complete elution achieved below 600 mM NaCl for all tested pH values.

Conclusion:

• pH 7 was selected as center point for optimization, with boundaries of ± 0.5 pH units
• Salt concentration of buffer B (elution buffer) was set to 600 mM NaCl

Load density:

No prior knowledge on the dynamic binding capacity (DBC) of the molecule on the selected resin and pH range was available. A DBC run at the defined center point pH 7 was performed.

Observations:

• DBC at 10% breakthrough at ~ 123 g/L

Conclusion:

• Target for chromatography process optimization of at least 50% of DBC at 10% breakthrough, which equals a loading of at least 60 g/L

Based on the conclusions drawn from these prescreening experiments, the boundaries of the variable process parameters were defined, narrowing down the parameter space for optimization and providing the required input for experimental planning in the next step.

Fig 2. Parameter space before and after definition of boundaries for variable process parameters.

Characterization of fluid dynamics:

Fluid-dynamic effects in the system and column are captured by performing a system and column characterization. A procedure with detailed experimental outline and interpretation of results can be accessed here.

First, the system is characterized by performing a simple tracer experiment:

Table 1. System characterization

To reduce experimental efforts for column characterization, a precharacterized Capto SP ImpRes f(x) column in Tricorn 10/100 format was selected. The f(x) columns are characterized using standardized, reliable, and consistent methods. They provide all parameters relevant for model building on the results of analysis (RofA) sheet and reduce the introduction of unwanted parameter variation for model calibration.

Table 2. Overview of required system and column parameters and experimental derivation. All parameters are provided on the RofA sheet delivered with every f(x) column.

Biomolecule experiments:

The following experimental plan was executed. The load density, pH, and salt concentration for step and gradient elution were set based on the previously defined boundaries. We recommend performing all calibration experiments on the same system and column to keep variations (e.g., column porosity or system flow path between calibration experiments) to a minimum.

Find general experimental guidance here.

Typically, three linear gradient elution (LGE) runs at low load density (#1 to #3), one LGE at moderate load density (#4), and one or two step elution experiments (#6 and #7) are the minimum required mandatory experiments. Additional LGE runs are required if a high load density is a process target (#5) or to accommodate a pH dependency (#8 to #11), see Table 3. To ensure correct modeling of the pH trace, we recommend to always calibrate the respective sensor prior to running any experiments.

Apart from performing the biomolecule experiments, the load composition and concentration needs to be analyzed. It is crucial for modeling to ensure closing mass balances. In other words, the defined injected amount of load material (concentration and composition) should equal the measured peak area in the chromatogram to simulate the biomolecule behavior accurately.

Table 3. Project-specific experimental plan with biomolecule load

* The number of linear gradient experiments to describe a pH dependency is project dependent. One experiment can be sufficient, but two to three experiments at different gradient length per pH value are recommended.
† No fraction collection required as peak resolution was sufficient to identify individual species.
‡ Step height was selected based on the salt concentration at peak retention time seen in gradient experiments (run #1 to #3).
§ Number of analyzed fractions depends on the peak shape of the chromatogram.

Analytics are necessary for experiments where the target biomolecule and relevant impurities are not distinguishable by the UV trace such as in the case of a step elution with only one sum peak. Being able to distinguish individual biomolecule traces is required to simulate the behavior of each biomolecule.

Extracting biomolecule traces:

There are two ways to extract individual biomolecule traces: collecting and analyzing fractions for impurity and target content offline or using the peak finding tool in GoSilico™ chromatography modeling software. Dependent on the resulting chromatogram, one or both methods combined provide the relevant information for model calibration.

Method 1: collecting and analyzing fractions

Fractions with a recommended fraction size of 0.5 CV are collected throughout the elution phase of the experiments. Based on the resulting peak shape, specific fractions are selected for analysis. The analytical effort can be reduced by analyzing only every second fraction. It is not recommended to pool fractions for analysis. The analysis of fewer but narrower fractions provides data points with higher precision for model calibration than broader fractions do.

Method 2: peak finding tool

The peak finding tool supports or replaces offline analytics and uses the load composition and chromatogram shape or fraction data as an input. It mathematically deconvolutes the peak by placing modified and/or skewed Gaussian curves for each molecule under the sum peak. These calculated peaks are then used as input data for the calibration, providing an information source on peak shape and retention time of the biomolecule.

The peak profile needs a certain degree of resolution to allow for identifying different species. Figure 3 exemplifies how the two methods can be applied to generate relevant information in addition to the UV measurement. The bottom row depicts the extracted information from peak finding tool and/or fraction analysis that is used as input for model calibration.

Fig 3. Peak finding tool

The first step in representing the process digitally is to set up the properties of the biomolecules, system, and column in the software. Next, methods and experimental results are exported from UNICORN™ software and imported into GoSilico chromatography modeling software. Suitable data formats are .zip, .res, and .xlsx or .csv. Typically, UV sensor data, conductivity, and pH traces are imported.

A conductivity check is performed by comparing the imported conductivity traces to the simulated conductivity traces to ensure that system dead volumes and mixing effects are captured correctly. Especially for step elutions, the point of conductivity increase needs to be captured correctly. The simulated and measured pH values are compared in a similar manner — this is especially relevant for pH-sensitive processes or pH-induced elution.

Find more information on the conductivity check here.

First, a model to describe the fluid-dynamic effects is selected. The combination of a transport dispersive column model and a lumped rate pore model accounts for the effects of convection, axial dispersion, and mass transfer. The mass transfer of the component from interstitial to pore volume is accounted for by a lumped film diffusion coefficient.

To describe the thermodynamic interactions of ion-exchange chromatography, we recommend using the colloidal particle adsorption (CPA) model . The following requirements need to be met for the separation problem at hand:

High load density should be modeled accurately:

The CPA model describes the elution behavior in both the linear and nonlinear range of protein loading and has shown superior performance and good accuracy for high load densities. High load densities can result in unusual, shoulder-like, trapezoidal peak shapes, which the CPA model can describe accurately as seen in Briskot et al. (1).

Dependency of pH on the process needs to be described:

The CPA model describes the pH influence on binding by means of a second order polynomial, which accounts for the influence on surface charge. Briskot et al. (1) has shown the CPA model to be an accurate choice for a pH dependent process over wide and small pH ranges.

Step 1: overview of biomolecule binding parameters to be calibrated

The CPA model distinguishes between resin parameters and biomolecule parameters. In total, 35 yet unknown parameters need to be identified:

3 resin parameters
8 biomolecule parameters × 4 biomolecule species* = 32 parameters
*target mAb, basic variant, two acidic variants

While this sounds like a large number, the optimization problem of mathematically estimating these parameters can be significantly reduced by conducting the following steps.

Step 2: deriving parameters from correlations, literature, or the RofA of the f(x) column

Due to the physical meaning of the CPA model parameters, measured values, correlations, literature values, or the results of analysis (RofA) sheet provided with all f(x) columns can be used to derive values for the parameters.

Table 4. Isotherm parameters

* for antibodies see Lavoisier and Schlaeppi (2)

This step reduced the optimization problem to:

1 resin parameter
7 biomolecule parameters × 4 biomolecule species = 28 parameters

Step 3: Yamamoto’s method

Yamamoto’s method uses linear gradient elution experiments at three different gradient slopes (run #1 to #3 and #8 to #11) as input to correlate gradient slope and salt concentration at peak retention. Based on this correlation, charge and equilibrium parameters can be derived.

Table 5. Isotherm parameters

While Yamamoto's method provided reliable parameter values in this case study, it is possible that these parameters need further refinement in form of mathematical estimation with optimization algorithms for other cases.

This step reduced the optimization problem further to:

1 resin parameter
3 biomolecule parameters × 4 biomolecule species = 12 parameters

Step 4: mathematical estimation

To derive the remaining parameters, the experiments using step elutions and higher load conditions (run #4 to #5) are used as additional input for mathematical estimation. Moreover, the initial guess for the specific adsorber surface is refined.

Table 6. Isotherm parameters

Typically, the mathematical estimation starts with an algorithm screening a large parameter space, for example, with a heuristic algorithm such as adaptive simulated annealing. It is advisable to refine all model parameters using a deterministic algorithm (e.g., Levenberg-Marquardt). The number of parameters defines the dimensionality of the search space. Thus, to further break down the complexity for the mathematical solver, start with the estimation of model parameters for only the target species (species with highest concentration) first and then calibrate the impurities.

The model is calibrated when experimental and simulated traces match, as seen in the chromatograms in Figure 6.

Fig 6. Calibrated model, from left to right: run #2, run #4, and run #7

GoSilico chromatography modeling software supports the model quality assessment with different indicators and tools. In addition to assessing model quality, experimental model validation will follow in the subsequent step.

Visual fit

The visual match of experimental and simulated traces can be investigated qualitatively by visually comparing simulation and experiment in the software. Additionally, a quantitative evaluation of the visual fit using the R² value is possible.

Confidence levels

Typically, the confidence intervals of all relevant estimated parameters are calculated and displayed in form of violin plots, as depicted in Figure 7. The narrower the depicted violin plot, the higher the confidence. Broader confidence intervals, visualized as broader plots, indicate more uncertainty in the determined binding parameters. The interpretation of the calculated absolute values allows you to assess the risk associated with each uncertain parameter. As example, the basic variant, which is a noncritical impurity, has a higher uncertainty in the binding parameters. So the risk of having a potentially less accurate prediction for this noncritical impurity is acceptable. Contrarily, the uncertainty for the parameters describing binding of the target molecule should be relatively low to ensure good predictions for the component of interest.

The next step is to run a sampling based on the calculated covariances. This means that for each variable for which the model confidence was assessed, a normally distributed sampling around the mean value of the respective variable is performed. The width of the distribution is based on the calculated confidence intervals. By overlaying the resulting chromatograms, the impact of model uncertainty can be visualized. The plot in Figure 7 shows an overlay of 100 runs, indicating robust model parameters (depicted as it would be seen in GoSilico software).

Fig 7. Model quality check. A) violin plots visualizing the confidence intervals of selected model parameters. B) Overlay of 100 sampling runs for three calibration experiments.

The model is validated with a two-step process at center point conditions (pH 7) and a 21.5% B concentration for the first elution step. The experimental method determined during in silico process optimization was executed as wet-lab experiment. Peak shape as well as the results of the analytics performed on the collected pool were evaluated. The predicted and experimental UV trace show a good match. Purity is predicted very well (model prediction: 96%, experimental validation: 97%) and yield shows a good match (model prediction: 87%, experimental validation: 83%) with an acceptable offset between model prediction and experimental validation.

In any case, the variation of the analytical method(s) used to confirm the model predictions should be considered when assessing whether the prediction was successful. For example, if particular assays come with error bars of 15%–20%, you should decide on an acceptable offset.

Fig 8. Model validation

An in silico process optimization was performed to achieve high yield and purity of the target species while keeping the elution volume small and load density high. Therefore, variable process parameters such as the process pH value and the salt concentration of the first step, load density, and method phase length were selected as variables. The best run was validated experimentally.

For process optimization, GoSilico chromatography modeling software aims to maximize an objective function by altering selected variables within defined boundaries.

Objective function

GoSilico chromatography modeling software allows you to set up the objective function using various objectives (yield, purity, quantity of biomolecule, self-defined objectives, etc.) and connect those via mathematical operators.

This way, objectives can be weighted. For example, for the polishing step at hand, purity is the most relevant objective while maximizing yield and minimizing elution volume.

Variables and boundaries

Analytical evaluation of the best run’s fractions shows very good agreement of prediction and experimental validation. Thus, the final process met all acceptance criteria, achieving a purity of 97% while maintaining a yield of 86%. The elution volume of the first step could be further reduced to 6.5 CV, compared to the validation run with 10 CV elution volume.

Analytical results (HPLC-IEX):

* Yield is calculated as follows: Y = quantity of main and basic in pool/quantity of main and basic in load
† Purity is calculated as follows: P = quantity of main + basic in pool / quantity of total biomolecule in pool
‡ Basic variant is defined as noncritical impurity.