Hello Kai!
Let me answer your questions:
Let's assume two things:
(1) - 1 gram of extract gows X Billion new cells
(2) - yeast only bud once they consumed enough resources to grow a new cell
The first proposition assumes that 1 g of yeast should have more or less some billions of new cells. However, remember that you will have a mixture of new and old cells compounding this 1 g of yeast biomass. In fact, the proportion of new/old cell depends on the viability of culture and the initial cell concentration inoculated in the wort.
This means that if there are more yeast cells per extract than can be grown from that extract not every cell will be able to grow a daughter cell. In an idealized culture (all cells consume nutrients at the same rate) no new cells should be able to grow since none of the cells will be able to consume enough nutrients to grow a daughter cell. But the culture is not ideal which means some cells will be able to consume enough nutrients to grow a daughter cell while others won't. The ones who don't grow buds will consume extract but don't actually contribute to cell growth (though it makes them healthier and better prepared for fermentation). This mechanism also means: the more initial cells are trying to consume the existing extract the fewer will be reach nutrient levels sufficient for budding. That's why I expect cell growth to drop with increased initial cell density.
This is a bit more complicated...in a batch culture, you will have non-reproducing old mother cells (which not bud anymore, but are live and nutrient-consuming cells), budding old mother cells, budding new cells, and naive new cells. All these cells consumes nutrients. Thus, if your initial cell concentration is high, the nutrients of the wort will be fast depleted and, again, the culture will reach the stationary phase of growth. In other words, the number of new cells generated will equalize the number of cells that die by aging or random mutation. After nutrient depletion, all yeast cells enter in quiescence and begins to consume its internal supply of nutrients. The concentration of intracellular nutrients depends on the age of yeast cells (new cells = more intracellular nutrients).
What is causing this limit? is it simply the available amount of nutrients or are there other mechanisms at work? I dont have my data here at work but tonight I want to check the max culture densities that I observed.
Nutrient levels, the age of the yeast cells, genetic mechanisms, among other physiological and environmental factors regulate the upper limit of cell concentration observed in stationary phase. In the lab., we can achieve high cells numbers (>10^9 cells/mL) by using a technique called "fed-batch", which increase amount of culture media is added in a bioreactor, with O2 levels, temperature, and pH being constantly monitored and kept at specific numbers. For homebrewing batch culture, this is more complicated, seems that many environmental points are not finely regulated, influencing the final number of cells in the wort.
Im wondering about that. One limiter might be the amount of alcohol that is produced when the initial sugar concentration is high.
Yes, and ethanol concentration above 15% is toxic for the majority of yeast strains. High sugar concentration leads to elevated ethanol levels in wort, restricting the cell cycle of viable cells
Its exactly those factors that affect yeast growth and the final yeast cell count that Id like to get a handle on. I think one major factor is amount of nutrients available in the wort. But I dont think that viability plays a large role here. Especially if the amount of growth is significantly more than the initial population. My thinking is that non-viable yeast cells will not consume any of the available nutrients and leave more for the others. That means that while non viable cells may not be able to grow other cells should be able to grow a bit more since they have more nutrients available.
Viability is an important factor. If you consider that non-reproducing cells are live and consuming nutrients at levels that are more or less similar to reproducing cells, your culture will reach the stationary phase. Only dead cells will not consume nutrients. It is important to note again: the batch culture used by homebrewers will be composed by a heterogeneous population of yeast cells: senescent old cells, reproducing old cells, reproducing new cells, and naive cells. All these cells consume nutrients, depleting the wort fasting if the initial cell number inoculated is high. Is possible to get a culture only composed by new cells in a batch culture? No, because the cells will age with time, originating a heterogeneous population. Is there a method used to obtain only reproducing cells? Yes, but only with special techniques and equipments (chemostats or bioreactors) not easily available for homebrewers.