Defining ILPZ as the CFD modeling output to predict HMW level
The integrated low-pH zone (ILPZ) is the critical value to predict HMW level in the VI operation. The variables and constants of the equation for ILPZ calculation were studied. It was reported that although product aggregates were detected in VIN pools, their precursors in deed were generated during VIA due to the exposure of the PAE pool to the localized low-pH zones (pH ≤ 3.3) (Jin et al., 2019). Therefore, ApH3.3 was defined as the boundary of low-pH zone as the critical variable of the equation for ILPZ calculation.
The growth of low-pH zones (≤ pH 3.3) in the acidified PAE pool during VIA are shown in Figures 3A-3B using lots S100_1 and A2_1 as examples. The conditions of these two lots are presented in Table III. Both of two lots had high HMW levels (≥ 7%) in VIN pools. TheApH3.3 profiles of all training runs are shown in Figure 3C, indicating that the two examples are representatives of two types of the training runs. In the case of S100_1,ApH3.3 increased 17-fold from 0.00233 m2 at 1 s to 0.0390 m2 at 192 s. Exposure to a large low-pH zone even with only a short duration caused excessive product aggregation. Conversely, in the case of A2_1,ApH3.3 increased 5-fold from 4.34 × 10-5 m2 at 1 s to 2.20 × 10-4 m2 at 2,580 s. The long exposure duration to the low-pH zone also caused excessive product aggregation. Taking into consideration both the size of and the exposure duration to the low-pH zone, a time integral of low-pH zone over the VIA duration was chosen as the backbone of the equation for ILPZ calculation.
The time span between the instant MF0.1N HCl(MF0.1N HCl,t ) and MFpH3.3also affected the growth of low-pH zone. As shown in Figure 3D, linearMF0.1N HCl growth profiles were observed during VIA in all training runs. Diffusion of 0.1 N HCl into PAE is driven by background HCl concentration, presented as MF0.1N HCl,t . The closer MF0.1N HCl,t approaches toMFpH3.3 , the slower 0.1 N HCl diffuses to PAE, which was the main factor that caused the expansion of the low-pH zone with the progress of VIA processing. Taking into consideration the exponential growth of ApH3.3 shown in Figure 3C, the variable MF0.1N HCl,t and constantMFpH3.3 were combined into the termMFpH3.3 /(MFpH3.3MF0.1N HCl,t ) in the equation for ILPZ calculation.
As previously reported, HMW formation also impacted by the PAE protein concentration (Jin et al. 2019). Titration experiments were performed to determine HMW level (%) after a 10 min hold at pH 3.3 (MpH3.3 ). This value was used as the measure of initial HMW formation rate. It appears that there was the secondary order correlation between MpH3.3 and protein concentration as shown in Figure 4A. For a given VIA run, theMpH3.3 value would be determined from the correlation curve and used as a constant in the equation for ILPZ calculation to reflect the impact of PAE concentration.
Based on the above data analysis, Eq. 3 was defined to calculate ILPZ, which captures the CFD modeling output and PAE property. The ILPZ profiles are shown in Figure 3E. Exponential growth of ILPZ profiles were observed during VIA. The total HMW amount of the VIN pool (HMWtotal,VIN , g) of the training runs are shown in Figure 3F. It appears that the higher ILPZ value corresponds to the higher HMWtotal,VIN .
\(\text{ILPZ}=\sum_{t=0}^{n}{M_{\text{pH}3.3}\bullet A_{pH3.3}^{1.5}\bullet t\bullet F_{pH3.3}/(F_{pH3.3}}-\text{MF}_{0.1N\ HCl,\ t})\)(3)