## Friday, February 15, 2013

### Cell growth as a function of sugar

In the early 1800s, Karl Balling made an observation about fermentation.  What he saw then was just as true then as it is now.  It's an equation that is often quoted by brewing chemists, and can be used to give you a better cell count estimate than any online calculator I have seen.

Hearing that there is a better way to estimate cells than the online calculators is likely not a surprise if you have ever counted cells produced by a starter.  I've done a number of tests on starters, and most of them have concluded that the cell growth in my starters don't match that on the calculators.  From other people that I have talked to that count the cells produced by their starters they see this as well.

Most online calculators use the initial cell count and the volume of wort to estimate the final cell count.   What I have found is that cell growth is rarely a function of volume or initial cell population, but a function of consumed sugar.  My observations roughly follows the old brewers rule of 10 billion cells produced per liter per °P.  I've struggled to fine where this rule comes from.  Today I read a post by a well respected brewing chemist who quoted Balling observation of normal fermentation:

2.0665g sucrose -> 1g Ethanol + 0.9565g CO2 + 0.11g of other constitutes.

But instead of "other constitutes" he said "yeast."  Of course this makes sense!  The sucrose is used to store energy as ATP and NAHD in the yeast, create sterols in the yeast, build cell walls... all in the yeast!

Converting the equation for 1 litter of 1°P wort we have:

10g sucrose -> 4.84g Ethanol + 4.63g CO2 + 0.532g yeast

The dry weight of yeast is 20 billion cells per gram.  0.532 * 20 = 10.6 billion cells!

Or put another way, for every gram of sugar consumed we get 1 billion cells.

It really is this easy:

1g fermentable extract = 1billion cells.

For your starter you'll want to add about 20-30% extra malt to compensate for the sugars that cannot be fermented.  A refractometer is a wonderful tool for measuring the composition of small worts such as starters.  Using an initial gravity and final gravity reading you will be able to estimate the number of cells grown in the wort at any given time.  When measuring with a refractometer the sugar content needs to be compensated for alcohol.  (1)(2) This can be worked into the equation:

Number of cells per litter = 16.25*OG-15.7*FG-3.25
(this equation is tabulated at the end of this post)

If you want, use the popular online calculators to get your starter setup, and then take gravity reading to get a much better idea of how many cells you actually have.  Crash it in the refrigerator when you get to the number you need for your beer.  As an alternative, let it ferment to completion and estimate the cell count based on change in gravity.  Then pitch just what you need of the slurry.

Try it and let me know. I bet you will be within 15% of your anticipated cell count given normal fermentation conditions.  There are other factors.  This is in terms of sugar consumed.  Un-metabolised sugar will not be converted to yeast.  Oxygen can be a limiting factor, but if your pitch rate is under about 100 million cells per ml and give the container a good shake when pitching things should work.  Alcohol generated can kill yeast so you'll want to keep the gravity at or below 10°P (1.040) or about 100g per liter of water. (1/4c DME in 1 quart)
 FG 0 1 2 3 4 5 6 7 3 46 30 14 4 62 46 30 15 5 78 62 47 31 15 6 94 79 63 47 31 16 OG 7 111 95 79 63 48 32 16 8 127 111 95 80 64 48 33 17 9 143 127 112 96 80 65 49 33 10 159 144 128 112 96 81 65 49 11 176 160 144 128 113 97 81 66 12 192 176 160 145 129 113 98 82 13 208 192 177 161 145 130 114 98 14 224 209 193 177 161 146 130 114
Billion cells per litter
columns listed across the top are the final gravity as read by a refractometer.  These number are compensated for alcohol.
rows listed down the left side are the original gravity as read by a refractometer.

(1) http://woodlandbrew.blogspot.com/2013/02/abv-without-og.html

#### 1 comment:

1. Thanks for posting this.
I was always suspicious to calculators that predict yeast growth since they mostly follow C. White's experiment with non-agitated starter, and then simply extrapolate results to stirred starter.
One other thing that also bothered me was amount of available sugars since all wort's aren't same gravity and fermentability.. Kai did a nice experiment about this.

Since I am starting to culture yeast in slants (used to freeze it in 15% glycerol solution) I wanted to study yeast growth and its dependencies on other factors more detailed (inoculation rate, no. of folds, amount of sugar in starter..).

I remember that HBT member Saccharomyes while ago stated that starter with unlimited oxygen (eg. on a stir plate) and plenty of available nutrients presents ideal conditions for yeast growth, and should yield between 10M and 15M cells per mL/*P of wort.. this quote keeps tackling my mind from then, these days I found that it has scientific stronghold. It is one more reason why not to trust blindly to calculators.. and was a positive shock to me.

Keep up the good work and thanks!