This study describes the optimization of loading conditions for a MAb polishing step to obtain the window of operation for Capto adhere. In order to find the optimal conditions, a full factorial DoE was used with three variables: pH, conductivity, and load. A brief discussion of the basic principles of DoE precedes the experimental details and results. The results demonstrate that it is possible to find a wide window of operation in terms of pH and conductivity.

As previously discussed, DoE is a systematic approach to investigate how variations in factors (X’s) affect the responses (Y’s) in a system (i.e., determining the mathematical relationship between X and Y). DoE is used to plan experiments so that the maximum amount of information can be extracted from the performed experiments. The factors in a DoE study are simultaneously varied so that they are independent of each other in a statistical sense. This makes it possible to evaluate the effect on the response of each factor separately (main effects). In addition, interaction effects between factors can be evaluated. For optimizing purposes, the use of DoE greatly increases the likelihood that the real optimum for a response is found.

A commonly used type of DoE is full factorial design, which is used both for screening and optimization purposes. A great advantage with the full factorial design is that all main effects and interaction effects are independent of each other, and therefore their effect on the response can be resolved in the evaluation. A disadvantage with the full factorial design is that the number of experiments increases as the number of factors studied increases—the number of experiments is 2n, where n is the number of factors. A full factorial design with seven factors would need 27 = 128 experiments. When many factors are included in the design, there are other types of DoE that can be used that will significantly reduce the number of experiments, with the trade-off being that some information is lost.

Center points are important for DoE. The center points are usually replicated and will give information on experimental noise. The center points will also provide information on possible curvature in the data.

## Method design and optimization

Balancing product yield against product purity is the major consideration when optimizing a method. When running in flowthrough mode, loading conditions will usually be a compromise between conditions favoring yield and those favoring contaminant clearance. By adjusting pH and conductivity of the sample as well as the sample load, conditions can be obtained where most contaminants are adsorbed while the monomeric antibodies pass through the column. Optimization of loading conditions is preferably performed by using DoE. A common approach in DoE is to define a reference experiment (center point) and perform representative experiments around that point. To be able to define the center point and the variable ranges, some initial experiments are required.

## Establish nonbinding conditions

To find conditions suitable for the DoE, initial experiments can be performed in binding mode, using a pH gradient for elution (Figure 4.1). The elution position (i.e., pH at peak maximum) defines the lower pH in the design. The upper pH in the design should normally be about two pH units higher. Experiments can also be performed in flowthrough mode, keeping the conductivity constant at a moderate level. A comparison of chromatograms (Figure 4.2). At high pH (i.e., close to pI for the antibodies) the breakthrough during sample load is delayed, the breakthrough and wash curves are shallow, and significant amounts of MAb binds to the adsorbent. A decrease in pH (i.e., further from the pI) results in weaker electrostatic interaction between the antibodies and the adsorbent, steeper breakthrough and wash curves, and increased yield.

An alternative approach to determine experimental conditions for the DoE is to screen conditions using high-throughput formats (Figures 2a to 2c). As large experimental spaces can be explored with high-throughput formats, the use of these formats will greatly enhance process understanding.

Figure 4.1.Establishing suitable conditions for DoE on Capto adhere in binding mode.

Figure 4.2.Establishing suitable conditions for DoE on Capto adhere in flowthrough mode. Comparison of chromatograms obtained at different pH: pH 8.0 (blue curve) and pH 6.0 (green curve).

In the DoE, pH, conductivity, and load must be included. It is important to include conditions at the higher pH range resulting in lower yield and higher purity, as well as conditions at lower pH range resulting in higher yield and lower purity.

#### Setup of a full factorial DoE with three parameters

Below is a stepwise description of how to set up a full factorial design.

#### 1. Work prior to actual setup of the design

Perform initial loading experiments at varying pH, as described above. Choose parameters to include and define parameter ranges and responses.

#### 2. Choose design for screening or optimization

Full factorial design is commonly used in both screening and optimization. A full factorial DoE in three parameters will give 23 = 8 experiments + center points. A graphical view of how the experiments are organized (Figure 4.3).

#### 3. Choose center points for the design

Center points are important in DoE because they give an indication if there is curvature in the data. Replicated center points are recommended. For example, a full factorial design in three parameters with three center points gives a total of 11 experiments.

#### 4. Systematic variation of the parameters

Limiting values, high and low, should be used for each parameter. The high and low values should be combined in a way that makes the parameters independent (to be able to separate effects).

Figure 4.3.Graphical representation of a full factorial design in three variables with center points.

### DoE used for purification of an IgG1 MAb

DoE was applied for the optimization of loading conditions for an antibody, previously purified on non-agarose based recombinant protein A chromatographic medium. The experiments were designed and evaluated using Umetrics Modde™ 7.0 software (www.umetrics.com).

The feed contains a monoclonal IgG1 expressed in Chinese hamster ovary (CHO) cell supernatant with pI of approximately 9. The impurity levels after protein A were determined: leached protein A, 36 ppm; dimers and aggregates (D/A), 3.3%; and HCP, 210 ppm. The experimental setup was a full factorial design with three variables: load, pH (Figures 4.1 and 4.2), and conductivity, with additional points to resolve curvature effects (Table 4.1). In total, 14 experiments were included in the model, and the measured responses were yield and concentration of impurities ( protein A [ppm], D/A [%], and HCP [ppm]) in the flowthrough pool. For each response a separate model was calculated. The models were fitted to multiple linear regression (MLR) and are well explained and show good stability to cross validation. Response surfaces were obtained for yield as well as for clearance of key contaminants.

Table 4.1.Design setup includes two center points (bold) and four additional points at pH 7 to resolve curvature effects

## Results

### Parameters Affecting the Yield

The parameters that affect the yield are shown in the coefficient plot1 (Figure 4.4). The plot shows that high sample load, low pH, and high conductivity result in high yield. The interaction effects (load × pH, load × conductivity) are also significant for the yield response. The response surfaces (Figure 4.5) show that higher loads will give a larger pH window with yield > 90%.

1 The coefficient plot describes the impact of investigated parameters on the yield. In this experiment, load is positively correlated to the yield, implying that a higher load will give a higher yield; pH is negatively correlated to the yield, meaning that a lower pH will give a higher yield; and conductivity is positively correlated to yield, but to a smaller extent, meaning that a higher conductivity will give higher yield. The interaction effects that are present in the coefficient plot (load × pH, load × conductivity) mean that if pH is changed, the yield will not only change with the effect of pH but also with the effect of load at that specific pH. The same discussion can be applied to the load × conductivity interaction effect.

Figure 4.4.Coefficient plot for the yield model.

Figure 4.5.Response surfaces for the yield model. Load versus pH at different conductivities, with yield expressed in percent (labels).

### Parameters Affecting the Protein A Clearance

The coefficient plot shows that a high pH will give good protein A clearance (Figure 4.6). The conductivity alone does not affect the response, but there is a significant interaction effect for pH × conductivity. If this term is high, the protein A clearance will be low. Load was not a significant factor for this response.

The response surfaces (Figure 4.7) show that high pH and low conductivity will give high protein A clearance.

Figure 4.6.Coefficient plot for the Protein A clearance model.

Figure 4.7.Response surfaces for the Protein A clearance model, conductivity versus pH. Protein A concentration expressed in ppm.

### Parameters Affecting D/A Clearance

The coefficient plot shows that pH is the most important parameter and that high pH will give a high D/A clearance in the flowthrough pool (Figure 4.8). The load parameter is also significant, but very small. The load should be low to give high D/A clearance. There is a significant curvature effect assigned to pH. If pH is too high or too low, the clearance will be less efficient. The conductivity did not significantly affect D/A clearance.

The response curve (Figure 4.9) shows that the load has only a small effect on D/A clearance, so only pH needs to be considered.

Figure 4.10.Coefficient plot for the HCP clearance model.

Figure 4.11.Response surfaces for the HCP clearance model, conductivity versus pH at different loads. HCP concentration is expressed in ppm.

Each MAb is unique, and the level of contaminants varies between different cell lines and differences in previous purification steps. This implies that it may be difficult to predict optimal loading conditions. However, based on DoE performed with several different antibodies, some general trends have been identified (Figure 4.12):

• For best yield, load should be high, the pH low, and conductivity high.
• For the best D/A clearance, the pH should be high, while load and conductivity should be low. D/A clearance is typically less affected by conductivity than protein A and HCP clearance.
• For the best protein A and HCP clearance, the pH should be high and conductivity low.

Loading conditions will therefore be a compromise between conditions favoring yield and conditions favoring contaminant clearance. Optimal loading conditions will be a balance between load, pH, and conductivity. Consequently, for optimization of the loading step, all three parameters should be varied in the same experimental series.

Figure 4.12.General trends with respect to loading conditions for yield, D/A, and Protein A and HCP clearance.

Optimal loading conditions for five MAbs together with yield and contaminant clearance results from a two-step process, including protein A medium and Capto adhere (Table 4.2.) pH should normally be well below the pI, while optimal conductivity is more difficult to predict. The response surfaces above show the influence of sample load, pH, and conductivity on four different responses (yield of monomeric MAb and clearance of protein A, D/A, and HCP, respectively), and how to reach desired values for each of them. Even though the optimal conditions for each response are not the same, there is a large area where acceptable values can be obtained for all four responses. Suggested loading conditions for this MAb when purified with Capto adhere are a sample load of 200 mg/mL, pH 7, and conductivity 8.5 mS/cm. The expected outcome would be a yield of over 90%, leached protein A below the detection limit, D/A < 0.5%, and HCP concentration < 15 ppm.

Table 4.2.Optimal loading conditions for different MAbs with regard to yield and clearance of HCP, Protein A, and D/A
Materials