Question for Kaiser Regarding Yeast Growth Model

I'm having trouble understanding the second part of your yeast growth model.

I understand the first part:

If (initial cells < 1.4 Billion/gram extract)
yeast growth is 1.4 Billion / gram extract

Assuming 1L of 1.040 wort using 114g DME:
1.4*114=159.6


I don't understand the second part:

If (initial cells between 1.4 and 3.5 Billion / gram extract)
yeast growth is 2.33 - 0.67 * Billion initial cells per gram extract

Assuming the same inputs as above:
2.33-.67=1.66
1.66*114=189.24

The BF calculator says that there would be 155B cells of new growth; not 189B.

I suspect that I'm screwing up the last part. Instead of multiplying 1.66 by 114, I would multiply 1.66 by 93.37 to get 155B cells. What does 93.37 represent?

The lower yeast growth per sugar is something I observed in my experiments while I don't have an exact justification for the actual numbers yet I have a theory of what's going on.

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

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.

I'm still working on solidifying or disproving this theory with additional experiments. If the theory is correct, the drop in yeast growth should be earlier and more pronounced with old cultures compared to fresh cultures since old cultures have depleted their reserves further. I have experimental data on this, but the results are not as clear as I hoped them to be. I think I have to control a few more parameters.

Kai

d_striker said:

I don't understand the second part:

If (initial cells between 1.4 and 3.5 Billion / gram extract)
yeast growth is 2.33 - 0.67 * Billion initial cells per gram extract

Assuming the same inputs as above:
2.33-.67=1.66
1.66*114=189.24

The BF calculator says that there would be 155B cells of new growth; not 189B.

Click to expand...

Please correct me if I am wrong here, but it seems the OP is having trouble with the math more than the theory.

Two things look like they are going on here. First, I think you're missing the order of operations. Second the billion initial cells per gram extract is not the same as grams extract.

Say you were pitching 100 billion cells into that litter of 1.040 wort. That would be 100/114 = 0.877 billion cells per gram extract putting you in the first range. If you pitched 200 billion cells it would be 1.75 billion cells per gram extract putting you in the second range.

0.67 * 1.75 = 1.17, 2.33-1.17= 1.16 billion cells grown per gram extract.
1.16*114 = 132 billion cells grown.

WoodlandBrew said:

Please correct me if I am wrong here, but it seems the OP is having trouble with the math more than the theory.

Two things look like they are going on here. First, I think you're missing the order of operations. Second the billion initial cells per gram extract is not the same as grams extract.

Say you were pitching 100 billion cells into that litter of 1.040 wort. That would be 100/114 = 0.877 billion cells per gram extract putting you in the first range. If you pitched 200 billion cells it would be 1.75 billion cells per gram extract putting you in the second range.

0.67 * 1.75 = 1.17, 2.33-1.17= 1.16 billion cells grown per gram extract.
1.16*114 = 132 billion cells grown.

Click to expand...

Thanks for explaining that. That's exactly what I was looking for.