# How to Compute Production Culture KPI

Production culture/fermentation is the process step where the active pharmaceutical ingredient (API) is produced. The KPI for production cultures relates to how much product gets produced.

The product concentration (called "titer") is what is typically measured. Operators submit a sterile sample to QC who have validated tests that produce a result in dimensions of mass/length3, for biologics processes, this is typically grams/liter.

Suppose you measured the titer periodically from the point of inoculation; it would look something like this:

The curve for the majority of cell cultures is an "S"-shaped, also called "sigmoidal," curve. The reason for this "S"-shaped curve was described by Malthus in 1798 where he described population growth as geometric (i.e. exponential growth) while increases in agricultural production was arithmetic (i.e. linear); at some point, the food supply is incapable of carrying the population and thus the population crashes.

In the early stages of the production culture, there is a surplus of nutrients and cells - unlimited by nutrient supply - grow exponentially. Unlike humans and agriculture, however, a production fermentation does necessarily have an increasing supply of nutrient, so the nutrient levels are fixed. Some production culture processes are fed-batch, meaning at some point during the culture, you send in more nutrients. Regardless, at some point, the nutrients run low and the cell population is unable to continue growing. Hence the growth curve flattens and basically heads east.

In many cases, the titer curve looks similar to the biomass curve. In fact, the integral (area under that biomass curve) is what the titer curve typically mimicks.

The reason this titer curve is so important is because the slope of the line drawn from the origin (0,0) to the last point on the curve is the volumetric productivity.

Volumetric Productivity
Titer/culture duration (g/L culture/day)

The steeper this slope, the greater the volumetric productivity. Assuming your bioreactors are filled to capacity and that supplying the market with as much product as fast as possible, then maximizing volumetric productivity ought to be your goal.

Counter-intuitively, maximizing your rate of production means shortening your culture duration. Due to the Malthusian principles described above, your titer curve flattens out as your cell population stagnates from lack of nutrients. Maximizing your volumetric productivity means stopping your culture when the cells are just beginning to stagnate. End the culture early and you lose the opportunity cost of producing more product; end the culture late and you've wasted valuable bioreactor time on dying cells.

The good news is that maximizing your plant's productivity is a scheduling function:

1. Get non-routine samples going to measure the in-process titer to get the curve.
2. Study this curve and and draw a line from the origin tangent to this curve.
3. Draw a straight line down to find the culture duration that maximizes volumetric productivity.
4. Call the Scheduling Department and tell them the new culture duration.
5. Tell your Manufacturing Sciences department to control chart this KPI to reduce variability

There's actually more to this story for Production Culture KPI, which we'll cover next.