The primary goal of fermentation is the production of alcohol, while the goal of propagation is increasing the yeast biomass. On one hand, anaerobic yeast respiration converts sugar into alcohol, carbon dioxide, and some energy. Aerobic reparation, on the other hand, converts sugar and oxygen into water, carbon dioxide and about twenty times as much energy. The real difference between these two is that with oxygen more energy is produced. Without oxygen more alcohol is produced.
The two things that yeast need from the wort to make new cells is material (sugar) and energy. While both of these are available during both aerobic and anaerobic respiration there is much more energy during aerobic respiration. This is why a stir plate, that provides constant oxygenation, is commonly used for starters.
Oxygen is good for propagation, but how much is required, and how can it be used to maximize cell growth?
Aerobic yeast respiration is as follows:
C6H12O6 + 6 O2 → 6 CO2 + 6 H2O + 31 ATP (see footnote 1)
180g C6H12O6 + 192g O2 → 264g CO2 + 108g H2O + 31 ATP
Converting from moles to grams we can see that for every gram of fermentable extract 1.07 grams of oxygen are required for aerobic respiration. For a 10°P (1.040) wort that would be a whopping 107,000ppm! With pure oxygen gas the saturation point of water is only 50ppm. So in terms of aerobic respiration, there is no practical limit to the amount of oxygen that can be utilized. Oxygen, however, is toxic to yeast in high concentrations.
Because oxygen is always in short supply anaerobic respiration dominates the metabolic activities. For this reason, the anaerobic reaction very closely resembles Balling observation. When the reaction is converted to moles it can be seen that the "losses" that balling describes are the sugar converting to other materials.
C6H12O6 → 2 CH3CH2OH + 2 CO2 + 2 ATP(see footnote 2)
1.9553g C6H12O6→ 1g CH3CH2OH + 0.9553g CO2 + 2 units ATP
2.0665g C6H12O6 → 1g CH3CH2OH + 0.9565g CO2 + 0.11g biomass (see footnote 3)
The Carbon Dioxide is virtually identical and the difference in glucose mass is almost exactly the yeast biomass.
If the two things that yeast need are sugar and energy to reproduce then how much more yeast would be generated from aerobic respiration. For every 2 units of ATP 0.11g of yeast are generated. If there were 31 units of yeast then 1.705g of yeast could be generated. This would require 3.6603g of sugar and adequate oxygen. Anaerobic respiration produces 0.053g of yeast per gram of fermentable extract. At 20 billion cells (dry mass) per gram that's 1 billion cells generated per gram of extract. Aerobic respiration could produce 0.4658g of yeast per gram of fermentable extract. This makes 9.316 billion cells per gram.
With adequate oxygen the yeast propagation could be almost 10 fold above what is typical of fermenting beer!
So how can we get anywhere near the 107 thousand parts per million, and what is the maximum the yeast can tolerate? Don't worry, I've got a plan and a set of experiments to prove it.
(3) Balling C. J. N. 1865. “Die Bierbrauerei” Verlag von
Friedrich Temski, Prague, CHZ. As cited in:
MODELING OF ALCOHOL FERMENTATION IN BREWING – SOME
PRACTICAL APPROACHES, Ivan Parcunev, Vessela Naydenova, Georgi Kostov, Yanislav Yanakiev, Zhivka Popova, Maria Kaneva, Ivan Ignatov http://www.scs-europe.net/conf/ecms2012/ecms2012%20accepted%20papers/mct_ECMS_0032.pdf