According to White and Zainasheff: Yeast: The Practical Guide to Beer Fermentation By Chris White and Jamil Zainasheff, wort should have 10 mg/L (10 ppm) with dissolved oxygen before pitching. This means that the initial metabolism will be aerobic. Aerobic metabolism of sugar yields no alcohol, but still reduces the gravity.
My question is: how much gravity is lost to aerobic metabolism due to 10 ppm oxygen?
"This means that the initial metabolism will be aerobic. Aerobic metabolism of sugar yields no alcohol, but still reduces the gravity."
Well, actually this isn't true in virtually all fermentation situations involving Saccharomyces yeasts. S. cerevisiae is what is known as Crabtree-positive, i.e. it experiences the Crabtree effect.
What this means is that, at glucose levels above somewhere around 0.1-0.2%, purely oxidative physiology (respiration) is overridden and the yeast produces ethanol and carbon dioxide regardless of the presence of oxygen. For comparison, you could expect to find glucose levels of roughly 1% in any wort you might try to ferment. By the time this glucose is utilized and this repression of respiration is lifted, all oxygen will long since have been taken up, ensuring anaerobic conditions for the rest of the fermentation (hopefully).
However, oxygenation can have an effect on alcohol production that is completely unrelated to this. Higher levels of initial oxygen may lead to over-production of yeast biomass (high levels of yeast growth). In this situation energy derived from sugar is diverted away from the alcohol-producing metabolic pathways towards biosynthetic metabolism. So sugar that would otherwise have been utilized for ethanol production instead goes to making new yeast. In some situations this can reduce the effciency of a fermentation (from an ethanol yield standpoint). In reality it's not likely to be any kind of issue for homebrewers, though, and so isn't much to worry about. It is the kind of thing that very big breweries may worry about though, as small changes in efficiency can lead to very large costs.
As FranklinPC rightly points out very little will go into aerobic respiration, some will as the TCA cycle is not shutdown, but it is trivial.
Mostly the 10ppm of O2 is there to ensure that the yeast has sufficient oxygen to produce sterols for incorporation into the cell membranes. These are needed to ensure the cell membrane functions correctly.
Hull et al, carried out an interesting experiment substituting Olive Oil for Oxygenation of the wort. As Olive Oil is high in the precursors for the sterol synthesis pathways that would be the main consumer of O2 in a fermentation situation.
At the most basic level of matter conversion resulting in loss of gravity in the beer it must exit as a volatile (gas co2,o2), or be converted into a larger molecule that uses more space than before and increases dissolved volume.
With 10ppm o2 is only 0.001% of the mass.
When oxygen is taken up by yeast biomass is the product. Biomass is not a factor adding to disolved solution volume, because it settles out as trub. In fact it increases a typical wort solutions specific gravity. Because yeast cell is 70% water. (Harden: note on the water content of the yeast cell pg. 608).
In practical brewing, I believe this is the culprit for many skewed readings in attenuation calculations. Not from uptake of sugar that doesn't result in ethanol.
As for how much sugar is "wasted" and not converted to ethanol. I don't think it's measurable outside of lab conditions and is not a major concern to a homebrewer.
