What They Saw
They grew A. vinelandii OP (aka CA) in chemostats, fixing nitrogen, with limited carbon (3 g/L of sucrose, acetate, or citrate). They stressed the culture with oxygen by increasing the aeration for 6-minute periods. They measured acetylene reduction, and nitrogen fixation directly (by fixed nitrogen increase). They also measured oxygen levels going in and coming out, to determine consumption.
As usual, with sucrose, they observed that respiration rates increased as oxygen levels rose. At a given oxygen level, respiration also increased as the dilution rate D increased. The amount of respiration increase wasn't the same at different dilution rates though, even with the same change in oxygen. The oxygen maintenance requirement increases as oxygen increases, but not linearly (the rate of increase goes down).
With acetate or citrate, the oxygen maintenance coefficient (and respiration at a given oxygen level) was much lower than with sucrose. Also as D increased, respiration with citrate increased linearly, but with acetate it leveled off at some point.
The rate of nitrogen fixation depended only on D, and increased linearly with D. The carbon source didn't affect it.
When they did the oxygen challenges, they found that up to D = 0.15 h-1, increasing the oxygen shut off nitrogenase completely. Above that D, the shut-off was less severe. With a less severe challenge, there was less shut-off at the same D too, as expected. Substrate didn't seems to matter.
They couldn't measure a change in respiration from oxygen stress directly, because it was too short, but they knew that cultures grown in acetate or citrate couldn't increase their respiration because they had already consumed all the substrate. There was still residual sucrose though, but the amount didn't seem to change with oxygen challenge, so they concluded that respiration didn't suddenly increase.
Finally they tried controlling nitrogenase activity by giving cells small amounts of ammonium, not enough to repress nitrogen fixation, just reduce it. So giving cells 1 mM ammonium when D = 0.16 resulted in the same nitrogenase activity as when D = 0.06 with no ammonium. And they found that an equivalent oxygen challenge led to the same amount of nitrogenase shut-off.
What This Means
So the rate of oxygen consumption doesn't affect how severe the nitrogenase shut-off is, only the rates of substrate feeding and nitrogenase activity, and more so the latter.
This is kinda weird, because if respiration is how the cells protect nitrogenase from oxygen by removing it (respiratory protection), then higher respiration should correlate with higher nitrogenase activity, but it doesn't seem to here. Also, oxygen level and oxygen consumption should correlate linearly, but they don't, especially considering different carbon substrates.
The authors propose that, instead of respiratory protection, the cells' redox state is what matters: nitrogenase requires a reduced state to function, and more oxygen leads to a more oxidized state. Reduction is made possible by the carbon substrate, which provides energy and electrons; at higher dilution rates, more reduction is possible, so the nitrogenase activity can be higher. That also explains why at higher D, the same oxygen challenge leads to less nitrogenase shut-off, because the change in the redox state is less severe. That way, the cells don't need to create an anaerobic environment in their cytoplasm, just maintain a low redox potential and good flow of electrons.
Respiratory protection as a concept is still useful, since it is still true that the cells' respiration increases as oxygen increases when fixing nitrogen, to allow nitrogenase to function; it's just the details that have been challenged here.