What They Saw
In batch with 5 g/L glucose, bacteria started producing PHB near the end of the exponential phase. They stopped when they had consumed all the glucose, and then consumed the PHB, but this didn't help them increase in density, possibly because the PHB itself had been a proportion of the bacterial density; it seemed to permit the increase in actual biomass.
When glucose was 20 g/L, the cells continued producing PHB and the bacterial dry weight kept increasing long after exponential phase ended; the polymer got up to 74% of the dry weight.
Using an oxygen electrode, they observed that PHB production didn't start until dissolved oxygen reached 0%, at which point exponential phase was over. So they thought it might be oxygen limitation that induced the production, unlike in other organisms where nitrogen limitation is the inducer. But to be sure that it was really oxygen and not nitrogen, they turned to chemostats.
They found that nitrogen limitation didn't induce PHB formation at any dilution rate, though growth yield increased as D increased. In contrast, in oxygen-limited conditions, the PHB content (as a proportion of dry weight) and yield seemed to decreased as D increased, starting around 45% and going down to 20%, while growth yield seemed to peak at mid-range and then fall. Glucose limitation didn't induce PHB either, though some was produced at lower dilution rates.
The sudden imposition of oxygen limitation on nitrogen-limited cultures immediately induced PHB formation, and content increased over at least 10 hours. Dry weight and OD initially went up but then back down below what it had been, possibly reflecting more efficient growth until oxygen was completely depleted. They don't show it, but claim that PHB went back down from 45% to 20% after 32 hours.
What This Means
The authors speculate that the limitation of low oxygen comes in at the level of the TCA cycle; acetyl-CoA stops being oxidized as much as before, so it starts going toward PHB synthesis.
So limited oxygen might be the best condition for these microbes: they have some but not too much, their growth is more efficient, and they produce a nice storage polymer to save food for harder times.