Media Analysis

When developing a cell line, there is the option to custom formulate the media or to use media from a supplier.  If the latter approach is taken, then there's the need to characterize the different media and their ratios upon the culture.  In work completed by Subramanian at the University of Nebraska, they characterized EAA, NEAA, ITS and lipids from Gibco upon the viable cell density.  I'd like to point out that the article is open source AND it included all the data.  Thanks!

Their approach was to implement a response surface.  The experiment involved 50 runs!  The whole model results were fairly good; however, my F ratio would lead me to believe that the model isn't as good as it could be.  In principle, focusing on just the statistically significant terms should improve the model.
ANOVA Results from Fit to Whole Model

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	20	250.90346	12.5452	2.5721
Error	29	141.44474	4.8774	Prob > F
C. Total	49	392.34820		0.0101*

Parameter Estimates from Fit to Whole Model

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		10.629137	0.765356	13.89	<.0001*
Glutamine		-1.009144	0.3517	-2.87	0.0076*
EAA		0.5448557	0.3517	1.55	0.1322
NEAA		1.0784807	0.3517	3.07	0.0047*
ITS		0.4322307	0.3517	1.23	0.2290
Lipids		-0.2868	0.356825	-0.80	0.4281
Glutamine*Glutamine		0.257788	0.390589	0.66	0.5145
Glutamine*EAA		-0.83606	0.394892	-2.12	0.0429*
EAA*EAA		-1.054712	0.390589	-2.70	0.0114*
Glutamine*NEAA		-0.126685	0.394892	-0.32	0.7507
EAA*NEAA		-0.051685	0.394892	-0.13	0.8968
NEAA*NEAA		-1.135962	0.390589	-2.91	0.0069*
Glutamine*ITS		0.0920648	0.394892	0.23	0.8173
EAA*ITS		0.0858148	0.394892	0.22	0.8295
NEAA*ITS		-0.29231	0.394892	-0.74	0.4651
ITS*ITS		-0.873462	0.390589	-2.24	0.0332*
Glutamine*(Lipids-0.04)		-0.319903	0.399728	-0.80	0.4300
EAA*(Lipids-0.04)		0.5300965	0.399728	1.33	0.1951
NEAA*(Lipids-0.04)		0.1207215	0.399728	0.30	0.7648
ITS*(Lipids-0.04)		0.0894715	0.399728	0.22	0.8245
(Lipids-0.04)*(Lipids-0.04)		-0.229712	0.390589	-0.59	0.5610

When only the statistically significant terms are included, the F ratio improves as the model shifts the majority of degrees of freedom to estimating the error term while maintaining that all the factors remain statistically significant.
ANOVA Results from Fit to Statistically Significant Terms

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	6	208.66396	34.7773	8.1413
Error	43	183.68424	4.2717	Prob > F
C. Total	49	392.34820		<.0001*

Parameter Estimates from Fit to Statistically Significant Terms

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		10.65275	0.584584	18.22	<.0001*
Glutamine		-0.98875	0.326792	-3.03	0.0042*
NEAA		1.08125	0.326792	3.31	0.0019*
Glutamine*EAA		-0.826563	0.365365	-2.26	0.0288*
EAA*EAA		-1.052813	0.365365	-2.88	0.0062*
ITS*ITS		-0.871563	0.365365	-2.39	0.0215*
NEAA*NEAA		-1.134063	0.365365	-3.10	0.0034*

The profiler can now be used to give us some insight into the VCD as the process is varied.  The VCD is linearly affected by the glutamine.  There are also pairwise and square terms in the model and from the figure it's apparent that the VCD is at a saddle point for some of these.

Variation in the VCD as a Function of Media Additives

As the glutamine is reduced, the NEAA and EAA components have to be adjusted to remain at the top of the saddle point.  These results provide a formulation strategy for maximizing the VCD that the authors pursue.

Maximizing VCD as a Function of Media Additives

The process involved 50 runs and raises an interesting strategy question.  Could the same results have been achieved in fewer runs?  Starting with a screening design that looks for main effects only, 8 runs would identify that Glutamine and NEAA were important.  The upper and lower limits were set to match the coded values used in the experiment.

Proposed Screening Design

JMP can then be used to create a new design that takes the results from the screening design and expands it to a full-factorial.  This leads to an additional 8 experiments for a total of 16 completed

Augmented Design to Initial Screening Design

The results would miss the square terms and the interaction between glutamine and EAA.  How would the interpretation of the current data look with only the Glutamine and NEAA?  The ANOVA results suggest the model with Glutamine and NEAA is comparable to the response surface approach.

ANOVA Results using Only Glutamine and NEAA Main Effects

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	2	94.08109	47.0405	7.0990
Error	48	318.06714	6.6264	Prob > F
C. Total	50	412.14824		0.0020*

The appealing element of this approach is the low number of experiments.  With just 16 experiments, we could have a model that captures the basic behavior of the VCD.  An additional set of runs, three as an example, at the center point would then provide confirmation of the model.  The interpretation re-enforces  the importance of balancing the number of experiments and the desired outcome.  Where possible, I always start with the lowest number of experiments and then augment as necessary.