Azotobacter vinelandii, for example, is an obligate aerobe, so it needs some level of oxygen, but too much can be harmful when the cells are fixing nitrogen (or, at least, reduces the efficiency of the cells' product formation). So optimizing A. vinelandii culture requires determining the optimal oxygen level and how to reach that level.
What They Did
Phillips and Johnson had a reactor with pH and dissolved oxygen electrodes, aerated by agitation and sparging, and sensors of oxygen and CO2 in the exhaust gas. So a pretty nice setup.
They grew various organisms, including A. vinelandii strain O, in media with 5% glucose and measured their oxygen demands. Sometimes they added ammonia as fixed nitrogen, sometimes they didn't.
It seemed like A. vinelandii's oxygen utilization rate was the lowest, compared to E. coli, Aspergillus, and Penicillium; all of these remained constant as oxygen tension increased. It seems odd though.
In the reactor, when fixing nitrogen, A. vinelandii seemed to use excess sugar just to get rid of oxygen; its oxygen demand was much higher than expected for the growth, yield, and number of cells observed. When they added ammonia so the cells didn't fix nitrogen, they claim the same effect was observed, but I don't really understand how they reached that conclusion. Their graphs seem kind of messed up, not fitting their descriptions very well.
What This Means
Overall, the conclusion was that cells don't need more oxygen than just enough to keep the level above a critical threshold. Measuring dissolved oxygen is good for keeping above this threshold, but it doesn't help determine how much extra oxygen is needed if levels drop below measurable amounts. But when oxygen demand and uptake rates are measured, the oxygen deficit can be measured, except maybe with A. vinelandii which is more complicated.