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A calculator for stepped starters

Hopfrog

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I finally got tired of fiddling with the settings of various online starter calculators, trying to find out how much yeast my starters were producing, and decided to make my own. I've put it up on the web to share with the home brewing community. It is built around the data from Chris White's "Yeast" book. It correlates very well with Mr. Malty.

http://www.yeastcalc.com/
 
Sorry, I'm on call for work...and my dog ate my f'n homework.

Seriously, I like it! 

Thanks for doing this!

Mark
 
HopFrog
I've got a similar program in Excel, however, the new cell growth I get is about twice what you are getting.  I also start with very small amounts of yeast, about 500-1000 cells on a slant with about 1 billion cells into the first wort step.  I appears that your program rounds off the number of cells to the nearest billion.  This is fine above 10-20 billion cells, but it seems to affect the accuracy at lower cell counts.

I have attached my XLS spreadsheet.  I can't see your assumptions; I would appreciate if you would look at what I have compared to what you have.  I based my calculations on Chris White's "Yeast" book also.

David
david at ddhnet dot com
 

Attachments

  • Pitching_Rate-Starter_Calculator.xls
    30.5 KB · Views: 371
Thank you for your input dharalson. I looked at your spreadsheet, and found a few possible errors. I have annotated them in the spreadsheet itself. Please correct me on any mistakes you feel I have made. I am looking at adjusting my own calculator to accommodate smaller cell count numbers, and possibly an option to enter volumes in milliliters. Thanks.
 
HopFrog
Thanks for the input.  I admit to fudging the numbers from YEAST a little bit.  Those "tweaks" didn't really have much effect on the answer.  The original data is from testing and is not exact data and subject to experimental or testing errors.  I adjusted the numbers to get the least square fit curve to go through the points I wanted. (or as close as I could)

What I did do was go back and reread that section of Yeast; it had been awhile.  The problem with my algorithm stems for the term "Number of Doublings" used in YEAST.  Since under ideal conditions yeast growth is exponential (ie doubling) I used the explicitly.
One Doubling is 1 => 2; Two Doublings is 1=> 2 => 4; Three Doublings is 1=> 2 => 4 => 8, etc.  The number in YEAST is actually a factor NOT a Doubling.  "Three Doublings" is actually 3 times the original number of cells NOT 8 times ! !

I have reworked the algorithm, but I haven't cleaned up the XLS yet.  I will get it fixed in the next couple of days and repost it.

Thanks, David
 
So which one of you guys ended up closer? Was there any resolution? I have been looing for a good step calculator and appreciate your efforts.
 
I don't really know.  I haven't done need enough "scientific" work to give a real answer.  The version I first posted used an incorrect algorithm.  I read the words "doubling" and took it literally as a x 2n when it really 2 x n.  That will make my original growth significantly lower and probably match HopFrog closer. 

However, my growth protocol from drops of yeast to pitchable yeast is:
2 drops on slant  (3-4 days)
10 ml wort
100 ml wort
1000-1600 ml wort

this resulted in a 22 ml of yeast at about 8 Bil per ml or 176 Billion.
but more important I opened the first bottle last night and I was very happy  (American IPA)

My personal opinion is the Stir Plate factor is much higher than 2.  Yeast does tend to grow exponentially (ie double); with a doubling every 3-4 hours under ideal conditions and should be able to achieve up to 10 doublings before a given cell is exhausted.  [This is NOT based on science, rather hearsay (ie google) and limited personal experience). 

So to rap up.  The two methods are the same and are based on the same published data from YEAST by White.  My Excel spreadsheet allows the user to change, tweak (and of course screw up as I did) the calculations.  My is not set up for distribution.  HopFrog's program is readily available, can be used by anyone, however you can't change any of the parameters.  In the end, establish a protocol that works from you and stick with that.

Now having said all of that, Aeration is very important in propagating yeast.  In the aerobic environment yeast will generate CO2 and water AND reproduce prolifically.  In the anaerobic environment, yeast will generate CO2, Alcohol (yea!) and reproduce slower.  White's data is based on NO aeration; yeast do grow exponentially in ideal conditions.  A stir plate will generate the best conditions us homebrewers can get.

I attached the current version of my XLS.  I took a quick look at it and there may still be a slight problem in my alorithm (I may have forgotten to subtract by 1 in some calculations).   

David
 

Attachments

  • Pitching_Rate-Starter_Calculator.xls
    34 KB · Views: 294
For what it's worth, YeastCalc is almost identical in it's calculations to Mr. Malty; and while dharalson is correct in his assumption that the stir plate factor should be much higher, this assumption only applies to low inoculation rates; for example, pitching into 5 gallons of beer. At the inoculation rates we are dealing with when it comes to starters, there simply isn't enough food available for the yeast to achieve a 10 fold increase or even a 4 fold increase, no matter how much oxygen or nutrient you give it. Dialing down the stir plate multiplier for starters with huge inoculation rates i.e. 50 - 100 million cells/ml gives a more accurate representation of actual final cell counts.
 
@ Rottnme & HopFrog
The two calculators yield the same growth numbers.  HopFrog increased the number of significant digits since the last time I ran a comparison.  I just ran through a 3 step starter and the numbers are close enough.  I used excel to calculate an equation to the data points published by White.  I am sure that is the difference between the two algorithms.

HopFrog, thanks for increasing the number of significant digits; it allowed me to validate my calculations.

I'm going to disagree on effect of aeration and stir plates. I am basing this on the following article
"Yeast Propagation and Maintenance: Principles and Practices" by MB Raines-Casselman, Ph.D.
http://www.pivarstvo.info/forum/files/yeast_propagation_and_maintenance_128.pdf
"Continuous agitation/aeration can yield as high as a 10- to 15-fold increase in yeast cell number."
This is based on test data.  I'm not going to repeat the data here, the full article is only a click away.

All the best, David
 
Great article. I use a lower starter wort concentration (about 1.025-1.030) because in higher gravities, the yeast is trying a little harder to make beer than biomass (Crabtree Effect.) Respiration, even in the presence of oxygen will be reduced and the yeast begins to go anaerobic which is what we want when we make beer (Pasteur Effect.) Initial aerobic respiration produces better cell walls to bud daughter cells. 
 
Thanks dharalson, I'm very familiar with that article, and I have several problems with it. Looking at fig. 1 from the article "effect of aeration on yeast cell number", it says that 500 ml of BrewTek Superwort was pitched with a saturated 10 ml superstarter culture of BrewTek yeast. Okay, that doesn't tell me much; what was the inoculation rate of the starters? The other thing that bothers me is that the control starter for the "experiment" was done with an airlock as opposed to tinfoil, by a different person with a different strain of yeast made by a different manufacturer, under who knows what conditions. How does that qualify as a controlled experiment? It doesn't.
I have taken 2 liters of wort and split it into two 1 liter flasks. One flask had no aeration whatsoever, the other flask was put on a stir plate. Each flask received 1 White Labs vial of 1056 yeast (with the same expiration date), giving them an inoculation rate of about 100 million cells/ml. Both were left to ferment for 24 hours, then cold crashed for 24 hours. Since I don't have a hemacytometer, I figured the thickness of the yeast cake would be a pretty good indicator of growth, if there was indeed a 10 fold increase in yeast cell count the slurry in the aerated starter would be significantly thicker, but at the end of the experiment both flasks had approximately the same amount of slurry. My conclusion was that a given volume of wort has a saturation point for yeast cells, and this will be dependent upon the inoculation rate. Chris White has stated that this saturation point is about 200 million cells/ml, which means if you pitch 100 billion cells into 1000 ml of wort it will never grow to much more than about 200 billion cells, no matter how much oxygen you give it, the yeast will simply run out of food. This seems to correlate with my experiment, and the calculations from YeastCalc. I hope to someday obtain a hemacytometer, and microscope. I would like to do more experimenting with different inoculation rates, so as to really nail down a good formula for calculating stir plate growth. Until then this is what I'm going with.

Cheers.
 
HopFrog
I noticed the same "flaws" in the article.  And I do discount the very high growth of the stir plate, but the trend is in the right direction.  Your Stir Plate test has inspired me to try my own this weekend.

I'll keep you advised on my results.  I don't have a specific test plan yet, but I will aim for a low innoculation rate somewhere around 20-40M/ml.  That is the range of most of my growth steps.  I will use White Labs equivalent to 1056. [1056 is Wyeast]

I understand that the amount of sugar is a limiting factor, but I have not found number to use; do you know of a reference

@ghwren, thanks for the input on the effect of Gravity on the cell wall effects.  I have not seen (or at least remembered) that before but it does make since.


All the best, David
 
Just curious dharalson, why do you use 20-40M/ml as the inoculation rate for your steps?
 
I am still working through the propocol, but I am culturing up from drops of yeast not trying to double the size of a smack pack.  This is a typical growth cycle

two drop of sterile yeast water
100-200 cells  ==> slant  ==> 0.5-1.0 B cells
1.0B cells  ==>      50 ml  ==> innoc 19M/ml  ==>    3.0 B cell
3.0B cells  ==>    500 ml  ==> innoc  6M/ml  ==>  36.0 B cell  (stir plate factor = 2)
17.3B cells ==> 1500 ml  ==> innoc  22M/ml ==> 172.0B cell  (stir plate factor = 2)

I am still adjusting the steps need a few more brews to stabilize the protocol
One thing I am still struggling with is to rack off the "spent" wort or just pour the whole liquid and yeast in the next step.  If I do use up all of the sugar the liquid will just be taking up space, but there is also the delay to allow the yeast to settle out.  Sometimes life hits us with these difficult decisions  :)

The starting amount of yeast has a very small influence; if I change the orginal pitch off the slant to .5B the final result is 168B cells.  This amount of yeast is very adequate for the beers that I brew.

I currently have six strains of yeast stored in 10ml vials in sterile water at room temperature.  I have a working vial that I collect from and a master vial that will be used to generate the next set of storage vials.  The plan is to regenerate the "seed" stock once a year.  Based on the material I have read the yeast should last "forever" in this environment. (or maybe only 5 years)

David
 
HopFrog
I ran my stirplate test this past weekend and I got some very interesting results.  So interesting that I plan to rerun and make sure I measure and double check everything.

I opened the Wyeast 1056 Pack and removed the nutrient pack without opening it.  I agitated and pour the contents in to measuring cup.  I chilled this to get a measure of the amount of yeast in the pack. 
Based on that measurement, I pitched 8 B cells 1 ml of yeast) into 400 ml of 1.040 wort for a 20M/ml inoculation rate into 1 Qt Mason jars.
I shook both for about 30 secs to thoroughly agitate and aerate. 
One on the stir plate and the other right next to it.  I allowed the fermentation for 36 hours. 
I chilled both for 12 hours and then decanted off 200 ml of the liquid to concentrate the mixture to allow for a little more accurate comparison. 
After decanting, I re-suspended yeast and drew off a 24 ml sample of each into 24 ml vials.  This was chilled to allow the yeast to settle out.

Results
Baseline (non-Stir Plate):  OG 1.040  FG 1.022
The yeast and trub did not separate cleanly.  I could not get an accurate measure of the yeast volume

Test Case (w/Stir Plate):  OG 1.040  FG 1.009
First strangeness the yeast settled out first and quickly.  I measured 2.6 ml of yeast in 24 ml total for a yeast ratio of 0.11 ml yeast to liquid.  Since I doubled the concentration with the decanting the original ratio would be .05 ml yeast / ml liquid (round down).  There was originally 400 ml wort, so the final yeast count is 0.05 x 400 = 20 ml. 
The original pitch was 1 ml.  This yields a grow factor of 19 ! ! !  I am remeasuring the amount of yeast with a second draw into the 24 ml vial to double check.  That seems incredibly high which is why I need to run it again.

I'll run it again and make sure I check all of the steps; and I will allow the fermentation to run longer to allow the non-Stir Plate to ferment to a lower FG
I have some photos that I will put into a mini-results report

All the best, David
 
Interesting results; Obviously, the non-stirred starter was still fermenting, I wonder if this had something to do with the yeast not flocculation properly. I'm not sure I understand why you pulled 25 ml from each jar, seems like this would introduce a variable. Why not just let the yeast settle to the bottom of the jar and measure the thickness? You could then calculate the volume of the jar/cylinder and thereby determine the volume of yeast in the bottom. All in all it sounds like a good experiment. I hope you find time to repeat it, I'd be interested to see if you can reproduce the results.
 
The 24 ml put was to get a sample that would fit into the 24 ml vials.  The mason jar has a low enough aspect ratio (diameter to height) that it is difficult to measure the thickness of the yeast. 
I allowed the yeast to settle out of the starter, then decant off some of the liquid to concentrate the remaining solution.  This was agitated to re-suspend the yeast.  The 24ml was supposed to be a "representative" sample of the whole.  The 24 ml vial was filled up and the yeast allowed to settle out of this concentrated solution.  This will allow a more accurate measure of the "stuff" at the bottom and make a determination of how much of the "stuff" is yeast and how much trub.

I have since decanted off most of the liquid from the entire starter volume.  This is currently in the refrig settling out.  It is looking like there is about 15-20ml of stuff the looks like yeast to me.  If that is the case I got a growth factor of about 15-20.

I have been reading some more scholarly (hopefully) articles.  Yeast growth is exponential with doublings every 2-3 hours, until limited by some environmental factor, such as lack of food, or increase in alcohol, etc.  I am going to continue my "research" or "playing around" depending on your view.  I am currently postulating that yeast growth is not controlled by the inoculation rate but rather either running out of food or crossing into an anaerobic condition and polluting their environment with alcohol.  I am going to hold the amount of sugar (grams of DME) constant and vary the volume of water (ie SG) and vary the amount of yeast pitched.  If my hypothesis is correct, I should get the same amount of yeast (in the final count) in each case (as long as I can keep the sugar as the limiting factor)

All the best, David
 
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