Exponential Growth Models?

[petep1980]

Does anyone ever use them to predict when you'll be at certain gravities?

 

[HoppyDaze]

I usually just use reverse anti-derivitives....

 

[pompeiisneaks]

nope... but from what I understand... I don't think that would work. What you're talking about is that over time, the yeast keep reproducing and growing and eating that much more sugar w/ a model like that. From what I understand, the yeast only reproduce in the first "lag" phase of fermentation, then they basically stop reproducing, and then go into madman eating mode... the basic number of yeast stays the same from that point on... and then the number of yeast eating food is slowly decreasing as the sugars decrease, because some don't find enough food in their 'area' and go dormant, thus settling. Therefore this kind of modeling, in my understanding wouldn't work because the model is a bit wrong. Also this could depend heavily on how floculant a strain is, if its heavily floculant then you'll have a different rate than a lower floculant strain would be. (Spell check is telling me I'm spelling it wrong but gives me no spelling options... who can help me here, flocculant? floculent? )

 

[petep1980]

If that's how they yeast work, then you are correct it wouldn't work.

As for the use of reverse anti-derivatives

I like to use factor-reciprocal deed-kind likeness models. Given the time of course.

 

[ksbrain]

I have this book called Froth by Mark Denny where he comes up with simple mathematical models for yeast growth and other brewing things. I can't recall off the top of my head and don't have the book handy, but IIRC the yeast does grow exponentially but is limited by availability of O2 and sugar. And I also seem to recall that it's not until they're done growing that they get to producing alcohol.

The book advocates a very sloppy and questionable home brewing procedure, but has some interesting math if you're into that sort of thing, which it sounds like you are. Mark Denny is an English Physics professor or something like that.

 

[onemanlan]

I just got out of a Microbial Physiology class that discussed growth rates. Parts of it are algebraic while other parts are calculus based. I can posted it up if you guys want to hear about it. The thing is you need starting cell count and growth constants for each strain(they will be different). Using your timing you can estimate the potential final cell count under perfect conditions, however it really only helps you as far as the starter goes. When you transfer to the wart you introduce many different metabolites for the yeast to respond to and consume. You'll have a change in growth rate under those conditions.

 

[oldschool]

True, kinda. When yeast undergo "fermentation" they are only producing alcohol and CO2 from sugar, which is what fermentation IS. They only reproduce during the respiration phase (when 02 is present) and not afterward. It would likely be difficult to be exact to do the calculations you speak of without lab equipement every single time since it will always be different [temperature of medium, cell concentration, Oxygen present, nutrients present, (amino acids vitimins, sugars, etc.)]. Don't get me wrong, I geek out just the way you do. I just get more obsessed with making beer in the end.

 

[onemanlan]

The yeast undergo mixed-acid fermentation converting sugars to ethanol, as well as other small organic acids like fumerate and succinate as well as C02. That's partially why different strains give different flavors. Different strains produce different ratios of organic acids which is what leads to the different tastes produced .

Yeast do reproduce during the exponential of log phase which is where growth rates are concerned. Oxygen is not a requirement for growth though. Lack of oxygen forces the yeast to undergo fermentation rather than the much more chemically profitable aerobic respiration. Fermentation occurs at a much slower rate because the chemical payoff of fermentation is extremely low compared to that of respiration. I know what you're talking about is airation, but that may be introduction of oxygen to the water so the yeast can use it during early growth period. Oxygen is most definitely required for some of their metabolic processes.

Cell count is do is do'able, but it will be a tough to be accurate. It does help to be in a lab setting or have some experience though. I've been trying to think this issue through myself because I want to make my own starters and keep track of viable cells. The tough part is doing it without the equipment though. I really don't wanna break the bank for even an erlinmyer flask. Im thinking as cheap as possible while being sanitary and effective. Ill let you know if I find anything worthy.

Edit: so I was wrong. I only have growth models for organisms that reproduce via binary fision. Yeast divide by budding daughter cells of off of larger mother cells. I'm going to keep looking though

 

[peoplesbrewingcoop]

Does anyone ever use them to predict when you'll be at certain gravities?

Is this for starter yeast or yeast in the beer?

If you were to try to predict the cell density in the media after a certain amount of time you will still need to use some type of method to measure the rate of growth of that yeast strain in that media. To do that use a hemocytometer or a flow cytometer and see what is the generation time (the amount of time for one cell to divide). You also need to see how many generations it takes before the population uses up the nutrients and enters stationary phase.

Substituting the rate of growth in the lag and log phase use the exponential equation:

P(t) = P(o) e^rt

where P(t) is the final population size you are estimating, P(o) is the original population size, e is the mathematical constant, r is the rate of growth, and t is the amount of time between P(o) and P(t).

Theoretically stationary phase is the point when the number of cells that die equals the number of cells that are produced so the theoretical growth rate here is 0.

I would expect pitching would be best when cells are at their peak cell density during log phase because the cells here would have the highest viability and vitality than those in stationary phase.

 

[petep1980]

I plug in gravities in place of P(t)

So if I check a beer in 3 days it's at 1.032 from 1.052 OG, then I'll just do

32 = 52e^(k3)

I know it's incredibly crude math, but I've had pretty accurate results with it. If you take two gravities then you can have some incredibly fun math and even predict (again with incredibly crude math) your final gravity.

I am actually going to do an extra credit assignment for Calculus based on yeast growth and starters.

I'm ordering that book, and any help you guys can offer would be AWESOME!!