Using high-throughput methods

In the last week or so, I caught this note from the process development team at BI who use automation to screen cation exchange resins for conditions that led to significant improvements in their main isoform.  I love the experimental layout

One of these days, I've got to set up a 96-well plate with multiple resins.  The options are just too fun to consider.  In this example, I would have proposed a different design.  For example, a central composite design with 8 centerpoints completed in replicate would use up all 32-wells.  Recognizing that the pH is the harder variable to change, then JMP include this to generate a design that is easily programmed.  The result would be data with significant statistical power and improved predictive ability for scale-up.

Critical versus non-critical process parameters

How to use the previous data to establish if the load and load conductivity are critical process parameter?  The outcome of that decision is going to have profound affects down range as the commercial organization takes on the responsibility of commercial production.  A good place to start is with the regulatory guidances (see the links to the right).  Starting from Q8, the critical process parameters are those

"whose variability has an impact on a critical quality attribute and therefore should be monitored or controlled to ensure the process produces the desired quality." 

The previous post related the changes of the aggregate percentages and CHO HCP levels, along with the recovery.  Of these, only the former two would be considered as quality attributes (recovery being a business factor).  

Protein aggregation is hard to argue against as a critical quality attribute and that means the load and load conductivity would be critical process parameters.  The next step is to scientifically justify the greatest acceptable operating range for the process and JMP provides some exceptionally useful tools to assist in this effort.

We could begin with a graphical representation of the space we want to claim as our acceptable operating space

How much do our product quality attributes vary within this region?  The prediction profiler within JMP allows the two prediction curves to be shown simultaneously.  Translating the limits from the previous figure establishes the initial lower and upper operating limits (LOL, UOL).  These are shown as dashed, red vertical lines in the figure.  The cross-hairs are set approximately at the center point of this region.

From a quality perspective, the design space is really one sided all product quality attributes meet our design criteria below the lower operating limit.  The yield may take a hit, but that's a business problem - not quality.  Examining the lower and upper edges of the design space offer predictions as to how the product quality attributes vary with the process

Product Quality at Lower Operating Limit

Product Quality at Upper Operating Limit

Increasing the model's power, in terms of communication, simulations offer additional insight into the process.  The load is set to a the lower operating limit, under the assumption that this number can be readily set within the batch record, and then the load conductivity is allowed to vary by 2 mS/cm.  Another feature is the ability to include the standard deviation from the experiment into the responses and then allow the simulation to proceed for an N=5000.

The result is a graphical representation of the expected process variation and it's impact upon the product quality attributes.  These can then be used in supporting the overall process control strategy.  When the process is at its upper limits, there is a significant portion of the samples that would not meet the upper limit of 0.8 % aggregate.  The operating limits may have to be adjusted lower, at the expense of recovery, to ensure the maintenance of the product quality.

Thus, an iterative process of defining and modeling enables a scientific justification for the acceptable operating range of the critical process parameters.

Need some motivation?

I made some figures for those days when I need a refresher because the noise of the day has distracted me from the big picture.  I hope all y'all find them as motivating.

Here's a picture of how cancer is distributed around the globe

I was fairly amazed at that distribution until I looked into where the majority of money is spent to treat cancer:

A significant contribution to this situation is tied to the distribution of wealth on the planet.  

• Over 1 billion people live on less than $1/day
• Over 2.7 billion people live on less than $2/day

Along with those very sobering numbers is how the rest of the world is spending its money to take care of its citizens.

The impact of these numbers only begins to paint the picture of the challenges to be overcome.  For example, the distribution of public health:

The impact is a patient has to rely on themselves, or family members, when it comes to treating a problem.  

Looking at the dose cost of some anti-cancer drugs, these prices aren't accessible for the rest of the world even if there were medical personnel who were available to offer them:

To bring anti-cancer treatments to the 2.7 billion people living on less than $2/day, the cost of treatment has to be about $1/dose (my estimate, based upon UNICEF numbers for vaccines).  The implication is that the cost of making the drug has to be about $0.1/dose (again, my estimate).  As a process development engineer, that's the number I'm chasing.  As a result, I'll use scale,  cost of goods, and anything else I can find to get me as close as possible to that value because the closer I am to there, the greater the patient opportunity for the medication.

If you need a couple of outstanding references, check out this paper by Brian Kelley as well as Suzanne S. Farid.  These papers offer valuable insight into the economic forces at play in biopharmaceutical manufacturing. 

Optimizing recovery and aggregation in the stream

The previous post demonstrated the ability of Capto Adhere to recover the antibody with minimal losses when used in the weak exchange partitioning mode.  Product quality is also an important criteria for a purification step.  For antibodies, one of the essential product qualities is aggregation.  Aggregation is a major concern in the field and will probably need an entire post (with refs) detailing how these impact the development process as well as the risk to patients.  With that said, the analysis of the aggregation percentages (determined by size exclusion chromatography) using the model for the response surface results in the following ANOVA and parameter estimates, respectively:

ANOVA Results

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	5	0.00002046	4.092e-6	4.6700
Error	4	0.00000350	8.7624e-7	Prob > F
C. Total	9	0.00002397		0.0803

Parameter Estimates

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		0.0078988	0.00054	14.61	0.0001*
Load(93,312)		0.0004262	0.000453	0.94	0.4002
Load cond(10,30)	Biased	-0.000279	0.000415	-0.67	0.5386
Load pH(6,7.5)	Zeroed	0	0	.	.
Load*Load		-0.001182	0.001377	-0.86	0.4389
Load*Load cond	Biased	0.0020644	0.000462	4.47	0.0111*
Load cond*Load cond	Biased	0.000571	0.001144	0.50	0.6439
Load*Load pH	Zeroed	0	0	.	.
Load cond*Load pH	Zeroed	0	0	.	.
Load pH*Load pH	Zeroed	0	0	.	.

The parameter estimates show the only statistically significant model is the pairwise interaction of the load and the load conductivity.  Based upon the chemistry of the Capto Adhere resin, this should make a fair amount of sense.  The antibody is binding through electrostatic interactions when operating in the weak exchange partitioning mode.  As a result, the conductivity is going to play a significant role; however, I wouldn't have expected that the pairwise term would be significant only.  As a result, the final model will have all three terms: the load, the load conductivity and their pairwise term (despite working from the belief that only statistically significant terms should be included in a final model).  The resulting ANOVA shows a reasonably good fit to the data and the parameter estimates continue to show that only the pairwise interaction is statistically significant.

ANOVA Results

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	3	0.00001970	6.5664e-6	9.2358
Error	6	0.00000427	7.1097e-7	Prob > F
C. Total	9	0.00002397		0.0115*

Parameter Estimates

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		0.0075547	0.000268	28.23	<.0001*
Load(93,312)		0.0005093	0.000353	1.44	0.1989
Load cond(10,30)		-0.000359	0.000363	-0.99	0.3614
Load*Load cond		0.0019552	0.000401	4.88	0.0028*

Based upon the actual by predicted, the model's overall fit is quite good.

Fit of Aggregate Results to Model Prediction

Does the model improve using only the pairwise interaction?  Yes!  The F-ratio has increased significantly - primarily as a function of only the single degree of freedom taken by our model!

ANOVA Results using only Statistically Significant Term

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	1	0.00001758	0.000018	22.0356
Error	8	0.00000638	7.979e-7	Prob > F
C. Total	9	0.00002397		0.0016*

Notice that the Mean Square of the Pure Error is 7.979e-7?  The square root of the is value gives an estimate of the pure error in the model.  The result (0.09%) is in pretty good agreement to what I'd estimate is the precision of the SEC assay.  With the model established, the next step is to optimize the process.

Now, JMP allows us to combine the model for the recovery and the aggregate to guide us in our decisions about the process limits.  In this case, a contour plot allows for a good visualization.

The recovery lower limit is set to 95% and the upper limit to the aggregate is 0.8%.  The resulting contour plot then removes the region that wont give 95% recovery (in red) and the less than 0.8% aggregate (green).  The white space represents a first step towards establishing acceptable operating space for the process.  When the results from the CHO HCP ELISA are included, the operating space undergoes even greater definition.

The upper limit to the HCP content is set at 20 ppm with the assumption that a downstream purification step would provide additional clearance.  The process space then becomes restricted to a region centered around the cross hairs.  The contour plot may then be used to provide a scientific justification to the regulatory agencies for the manufacturing control strategy and process validation approach.  In fact, the relationship of this data to the commercial strategy will probably take up several postings in the future!

JMP also allows the exporting of these results as a flash file.  These can be particularly useful when trying to message the results to management.  I'll try to upload a flash file in the future.

The Capto Adhere Evaluation, continued

*NOTE - This may show up as a new post, but I had to do some edits to make sure the figures went in properly.  I'm still building my workflow.*

In the previous post, I was completing an analysis of a central composite design using the load amount, load conductivity, and load pH as inputs for the study.  The initial results identified that all three factors were important; however, there were no pairwise interactions present (nor higher terms, such as quadratic).  In the original paper, the authors point out that one of their runs had an abnormally low recovery percentage and so was omitted.  Let's take a look at how the model changes when this is done.

First, notice where the point (red triangle) falls in the plot of the actual vs predicted:

It's pretty clear this point is having a significant impact on the model through leveraging.  When the model of main effects only is applied to the results, the ANOVA results are

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	2	0.06547415	0.032737	8.7720
Error	7	0.02612395	0.003732	Prob > F
C. Total	9	0.09159810		0.0124*

and the parameters estimates, along with their probabilities are

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		0.8820829	0.019367	45.55	<.0001*
Load(93,312)		0.1042488	0.025469	4.09	0.0046*
Load cond(10,30)	Biased	-0.028196	0.024983	-1.13	0.2963
Load pH(6,7.5)	Zeroed	0	0	.	.

The load conductivity and load pH are no longer statistically significant; however, looking at the actual vs predicted, several points are observed to be outside the confidence intervals.

As this was a CCD, we are justified adding some higher order terms.  Re-starting the analysis with a response surface model, the ANOVA shows the following results

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	5	0.08642340	0.017285	13.3609
Error	4	0.00517470	0.001294	Prob > F
C. Total	9	0.09159810		0.0132*

with the parameter estimated as

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		0.9453904	0.020768	45.52	<.0001*
Load(93,312)		0.1032109	0.017412	5.93	0.0041*
Load cond(10,30)	Biased	-0.026721	0.01594	-1.68	0.1690
Load pH(6,7.5)	Zeroed	0	0	.	.
Load*Load		-0.135078	0.052907	-2.55	0.0631
Load*Load cond	Biased	0.0373873	0.017758	2.11	0.1030
Load cond*Load cond	Biased	0.023048	0.043967	0.52	0.6278
Load*Load pH	Zeroed	0	0	.	.
Load cond*Load pH	Zeroed	0	0	.	.
Load pH*Load pH	Zeroed	0	0	.	.

Now, what to do?  The dominant effect is the load and maybe the load*load term (p=0.0631).  There are some camps that say a model should only be the statistically significant terms while others would argue that the fit should be of the entire model.  Taking only the statistically significant terms, the ANOVA was

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	2	0.07851582	0.039258	21.0059
Error	7	0.01308228	0.001869	Prob > F
C. Total	9	0.09159810		0.0011*

What is interesting to note is how the F ratio has slowly increased as we reach our best fit.  This comes with the increasing degrees of freedom for the error term.  The final model only has two degrees of freedom (load, load^2), resulting in the error term having 7 degrees of freedom to estimate the mean square error (0.001869).  The estimated RMSD is obtained by applying the square root to the mean square error term.

Finally, the Prediction Profiler may be used to predict how the recovery changes as a function of load:

The sweet spot is around 200 g/L; after that point, a modest improvement in recovery results with the higher load.  Of note: look at how quickly the recovery drops!  At 175 g/L, it's down to 90% and then continues to plummet.