Maybe I can be of assistance. S. cerevisiae is my old AHA user name and YeastWhisper is a user name I use on a British site. I have a lot of older posts on this site under S. cerevisiae. Searching on my old user name may be a good place to start. You can also start with a few blog entries on my blog @ https://www.experimentalbrew.com/blogs/saccharomyces
While it may be a little bit on the trivial side for you, "Yeast Cultures are Like Nuclear Weapons" will answer some your questions with respect to biomass growth rate. The blog entry "Have You Seen Ester" details the biochemistry behind higher alcohol and ester production, which is the result of brewing yeast cells using their significantly less efficient fermentative metabolic pathway to transform carbon into ATP.
With that said, my ex-wife started her career in biology in cancer cell culture. Culturing yeast cells is trivial compared to culturing cancer cells. All yeast cells need is a medium composed of dry malt extract and water in a boiled and cooled solution between 5 and 10% w/v. The solution needs to be aerated before the yeast is pitched. Brewer's yeast does not respire when the medium is above 0.2% w/v due to being Crabtree positive. Carbon is transformed to ATP via the fermentative metabolic pathway. What brewer's yeast cells do is shunt a small amount of carbon and O2
to the resparitive metabolic pathway during the lag phase for the synthesis of ergosterol and unsaturated fatty acids, which are needed to keep cell plasma membranes pliable. The basic fermentative cycle is lag phase -> log phase (a.k.a exponential growth) -> stationary phase -> quiescence. The biomass stops increasing in cell count after the culture hits maximum cell density, which is roughly 200 million cells per milliliter (or 200 billion cells per liter). Maximum cell density causes a shift from exponential growth (log phase) to the stationary phase where all cell production is for replacement only. It is easy to see when this shift occurs because a starter or batch of beer will reach high krausen. That is when a foamy head appears on the medium or wort. High krausen is when you want to step the culture up in volume because doing preserves ergosterol and UFA reserves. The mother cells that were alive during the lag phase share their ergosterol and UFA reserves with all of their daughters, their daughters share their reserves with their daughters, and so forth. If allowed to ferment beyond high krausen, mother cells will needlessly waste their ergosterol and UFA reserves on the production of replacement cells, which results in longer lag phases and higher O2
requirements when cultures are stepped. Most brewers only step a starter one time. Unlike things were when I started brewing back in the early nineties, liquid cultures are so large that a starters basically serves to bring the culture out of quiescence and allow it to replicate a couple of times at most. For most of my brewing career, I have maintained a yeast bank on malt agar slants, which means I performed steps while making a starter. The first one or two steps were made with pressure cooked (autoclaved) wort with the inoculation on the first step being perfomed aseptically with a loop.