Multivariate Analysis: Pick Actionable Factors Redux

When performing multivariate analysis, say multiple linear regression, there's typically an objective (like "higher yields" or "troubleshoot campaign titers"). And there's typically a finite set of parameters that are within control of the production group (a.k.a. operators/supervisors/front-line managers).

This finite parameter set is what I call, "actionable factors," or "process knobs." For biologics manufacturing, parameters like

• Inoculation density
• pH/temperature setpoint
• Timing of shifts
• Timing of feeds
• Everything your process flow diagram says is important

are actionable factors.

Examples of non-actionable parameters include:

• Peak cell density
• Peak lactate concentration
• Final ammonium
• etc.

In essence, non-actionable parameters are generally measured and cannot be changed during the course of the process.

Why does this matter to multivariate analysis? I pick on this one study I saw where someone built a model against a commercial CHO process and proved that final NH4+ levels inversely correlates with final titer.



What are we to do now?  Reach into the bioreactor with our ammonium-sponge and sop up the extra NH4+ ion?

With the output of this model, I can do absolutely nothing to fix the lagging production campaign. Since NH4+ is evolved as a byproduct of glutamine metabolism, this curious finding may lead you down the path of further examining CHO metabolism and perhaps some media experiments, but there's no immediate action nor medium-term action I can take.

On the other hand, had I discovered that initial cell density of the culture correlates with capacity-based volumetric productivity, I could radio into either the seed train group or scheduling and make higher inoc densities happen.

by Oliver Yu

Contamination Time Window Redux

by Oliver Yu

There's a little LinkedIn brouhaha going on regarding the calculation of contamination time windows.

In the perfect world, there are no bioreactor or fermentor contaminations.

But if you were to have contaminations, the next best thing would to omnisciently know exactly what the true root cause is.

Since omniscience is not an option here, the next best thing is to narrow down the list of sterile-envelope manipulating actions on the contaminated bioreactor and perform root cause analysis to come up with MPC (most probable cause).

There are a lot of parallels between a crime scene investigation and bioreactor decontamination response. Just as crime-scene investigators attempt to determine the time of death to rule out potential causes outside the time frame, it is a good idea to compute a contamination time-window to rule in/out potential causes.

There are several assumptions in the contamination time-window calculation and which assumptions you use depends on your organization's risk profile. As in, which is worse?

• Coming up with too narrow a time window and risk eliminating the true root cause
• Coming up with too wide a time window and having too many potential causes to investigate?

To summarize, you run the exponential growth equation twice: the first use is to try to figure out the growth rate of the organism.

Step 1: Collect sterility samples and send samples to QC Micro.

Step 2: Get 2 pieces of information from QC Micro:

1. Concentration of contaminants in last sample (X)
2. Timestamp of last clean sample. (t₀)

Note, you already know the timestamp of the last sample (t).

Step 3: Pick an X₀ and try to compute μ.

X = X₀ e^{μ(t - t₀)}

bold is known.
blue is estimated.
red is what you're trying to determine.

The rational number to input here is the limit of detection of your sampling method.   If you're going for a narrower window, pick a higher number.

Now you have an estimated growth rate (μ) of the contaminant.

Step 4: Now try to determine the earliest insult (t₀)

X = X₀ e^{μ(t - t₀)}

Again, bold is known; blue is estimated; and red is what you're trying to determine.  Here, the key is to guess the concentration of the initial insult.  If you're afraid of ruling out the true root cause, pick 1 CFU.  If you're going after a realistic time frame to reduce scope, pick what you think a small bolus of contaminants would contain.

When you've solved for t₀, the second time, you now have computed the earliest time of contamination.

As you can see from this process, there are some serious assumptions.  But if applied correctly, you have a scientific and defensible basis for narrowing down potential bioreactor contamination causes and focusing your limited resources on rooting out the most probable cause.

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