Regression analysis revealed that linear (Xi
) and quadratic effects (Xi
i) were more significant than cross product interactions (Xi
), as based on the p-
values obtained (Table ). Among all independent variables, Glutamine (negative effect, X1
: −2.79) and NEAA (positive effect, X3
: 3.07) had the greatest effects on the cell density, while EAA showed an effect when combined with Glutamine (X2
). Among the pairwise interactions, EAA and Glutamine exhibited the greatest effect. Although NEAA squared (X3
) and NEAA (X3
) by itself were significant, they did not have a great effect when compared with the other variables, as judged by the p
-value. The response surface plots were then plotted to see the effect of EAA and NEAA (Fig. ), EAA and Glutamine (Fig. ), NEAA and Glutamine (Fig. ) on the response which is the viable cell density (Y
). ITS and Lipids were found to have no effect. The R2
value for the total model is 0.6339. To simplify the model, the variables of ITS and Lipids were removed from the model and the data were re-analyzed using the reduced model. The polynomial regression model used for three variables was
When the variables ITS and Lipids were kept constant, the lack of fit is found to be insignificant, suggesting that the model was adequate to explain the effect of these three variables on the response. The R2
value of the reduced model decreases to 0.502, as denoted in Table . As Table shows, the Glutamine (X
1) had significant linear effects and interacted with EAA (X
2). EAA and NEAA had significant quadratic effects (X
2 × X
2 and X
3 × X
3) while NEAA (X
3) also had a linear effect on the cell density.
The t- and p- values of full model with X1, X2, X3, X4, X5 as independent variables
Response surface plot showing the effect of EAA, NEAA, and their mutual effect on the response (viable cell density). Other variables were held at zero level
Response surface plot showing the effect of EAA, glutamine and their mutual effect on the response (viable cell density). Other variables were held at zero level
Response surface plot showing the effect of NEAA, glutamine and their mutual effect on the response (viable cell density). Other variables were held at zero level
The t- and p- values of the reduced model with X1, X2, X3 as independent variables
Canonical analysis is a mathematical approach used to examine the overall shape of the response surface and to determine if the estimated response point is a maximum, minimum or a saddle point. If the stationary point is maximum or minimum, a corresponding increase or decrease will result in the response. In the case of a saddle point, the response may increase or decrease when we move away from the stationary point, depending on which direction is taken. Maximizing the viable cell density is of interest; however the stationary point was a saddle point, so we move on the ridge in the direction to get the maximum response.
The points on the ridge that increased the response were found using the RIDGEMAX option of the SAS/RSREG procedure, and are shown in Table . From Tables and , glutamine showed a negative effect on cell density while EAA, NEAA showed a positive effect. Therefore the glutamine values for the ridge moved in the negative direction and the values for EAA and NEAA moved in the positive direction. Following the ridge in Table , the highest cell density was 1.37E + 06 cells/mL, but this prediction was not very reliable due to a large standard error obtained (144554). Based on the ridge analysis, the glutamine concentrations at high cell densities were found to decreasing, to a level of 1 mM or lower. Glutamine values smaller than 1 mM were thought to be unreasonable and therefore additional experiments were conducted on the ridge below glutamine values of 1 mM.
Ridge of steepest ascent for X1, X2, X3 independent variables, and estimated response and standard error
To further explore the surface, we used the reduced model from Table , and obtained predicted cell densities at constant glutamine concentrations at different coded levels from ‘0’ to ‘−3’, NEAA at ‘0.5’ and various values of EAA. The results are shown in Table . The results suggest that cell density increases as EAA (X2) increases when glutamine values are low. Figure shows the effect of EAA and NEAA on VCD when glutamine is controlled at coded level ‘−1’.
Effect on EAA, NEAA and VCD when glutamine is controlled at different coded levels
Response surface plot showing the effect of EAA (X2), NEAA (X3) and their mutual effect on the Y (viable cell density), when glutamine (X1) is controlled at −1 coded level
EAA values up to a coded level of 14.5 (uncoded value = 12.625 X) are unfeasible because of osmotic effects or inhibition of metabolic pathways due to overfeeding the nutrients. According to the above results, however, it appears that with reduced Glutamine levels and concentrations of EAA and NEAA at a 0.5 coded level, large cell densities could possibly be obtained.
To further evaluate the surface we ran some alternate experiments at different levels of glutamine (from coded level ‘0’ to’ −3’), keeping EAA constant at coded levels 2 and 4. We expected low cell growth at a glutamine value less than ‘−1.5 coded level’ and no cell growth at zero (‘−2’ coded level) glutamine concentration. We also expected the EAA coded level of ‘2’ to result in higher cell densities compared to EAA coded level ‘4,’ due to osmotic effects and the inhibition of metabolic pathways from overfeeding. Therefore 14 additional experiments were conducted, four on the ridge, four at different levels of Glutamine keeping EAA at coded level ‘2,’ four at EAA coded level ‘4,’ and two controls (basal medium) as shown in Table .
Alternate experiments carried out on ridge and glutamine controlled at different coded levels, keeping EAA constant at coded levels 2 and 4
These experiments were conducted under the same conditions as the initial experiments. The starting density of the cultures was 2 × 105 cells/mL, and the cells were allowed to adapt to the medium in four passages. The final viable cell densities were derived as an average of the third and the fourth passage, as shown in Table .
Medium-6 had a higher cell density compared to the controls (13 and 14), but the last passage of medium 3, 9, and 5 were nearly equal to the control medium, as shown in Fig. . Media which had results equivalent to, or better than medium-0, were carried out for one more passage (up to 8 days), to validate the data. The results are shown in Fig. . From passage 5, the viable cell density attained in medium 6 after 5 days of culture was about 1.6 times higher than the control.
Viable cell density versus medium number tested. The plot shows the viable density obtained in the last passage (passage 4) of alternate experiments undertaken. Details on media are listed in Table 9
Results of the alternate experiments conducted to further explore the surface
To validate the above results, the cells in the control medium were taken out of a frozen state, and the experiment was repeated three times with control medium and medium-6. Cells were allowed to go for four passages and the final viable cell densities were taken as an average of passage 3 and passage 4. The results are presented in Fig. .
Results of the triplicate experiments of Medium-6 and the Control Medium
In medium-6, a viable cell density of 1.45 × 106 cells/mL was attained, which was found to be 1.4 times higher than for the control medium and within two standard errors of 1.23E + 06 from the original run of medium 6 (standard error = 215,928 cells/mL for medium 6). After four passages, if the cells were allowed to grow to passages of 5–7 the viable cell density obtained in medium-6 increased to 1.6 × 106 cells/ml. The viable cell density in the control experiment in these passages (passages 5–7) was between 9.2 × 105 cells/mL and 1.1 × 106 cells/mL, with in the standard deviation of 128,103 cells/mL (data not shown).
Assuming the specific antibody production (mg protein per cell per day) depends on the cell density, we expect to see an increase in the specific antibody production with an increase in the cell density. As detailed in the methods section, transformed cells were cultured in control and the optimized medium, medium-6, and the antibody titer was estimated in the supernatant, the specific antibody production was determined. Standard deviation was calculated in these media from triplicate experiments. The results are shown in Fig. . The antibody titer was determined for all the initial medium (~50) experiments, and the results were analyzed using SAS/STAT procedures. We observed the same trend for antibody production as well, where the stationary point is a saddle point, and the ridge values for the glutamine were moving in the negative direction and in positive direction for EAA and NEAA, shown in Table . The R2 value for the model was 0.75 which shows adequacy of the model in explaining the effect of the variables on the response which is antibody production. Thus the antibody titer in medium-6 was estimated to be 1.6 times higher than the control medium and the composition of the variables in medium-6, that was found to be optimal in our present study, is listed is Table .
Antibody production in Medium-6 and the Control Medium
Ridge of steepest ascent of the reduced model for getting maximum antibody production with independent variables X1, X2, X3. X4 and X5 are kept constant at their zero−level
Concentrations of the five variables of the optimal medium