The impeller mixes nutrients and disperses oxygen from the sparger
bubbles through the broth; growth rate depends on how close
temperature and dissolved oxygen (DO) are to the cells' optimum,
and on how much fresh feed is being supplied. Too little agitation
starves cells of oxygen in the bulk liquid; too much shears them.
μ = μmax · (1 − |T − 37|/8) · (DO / (DO + Kdo)) · feed_factor
dX/dt = μ·X − death_rate·X
dP/dt = qp·X (product accumulates with viable cells)
- Agitation (RPM) — impeller speed; drives mixing and oxygen transfer (kLa), but excess shear raises the death rate at very high RPM.
- Feed rate — nutrient/glucose bolus rate; fed-batch and perfusion modes use it to sustain growth far longer than a simple batch culture.
- Temperature — culture set-point; growth peaks near 37 °C for mammalian cell culture and falls off sharply away from it.
- DO setpoint — target dissolved-oxygen percentage maintained by sparging; growth stalls when DO is too low (bubble colour shifts toward red as sparging intensifies to compensate).
This mirrors real Process Analytical Technology (PAT): VCD, titer
and DO are exactly the online signals engineers watch to decide
feed and control-loop adjustments during a real run.