Suppose I made a 0.5 liter starter, put it on a stir plate for a few days, cold crashed and decanted, and then stepped up with another liter of starter wort. How/why does the yeast cell count response to this differ from using a 1.5 liter starter?
(depending on growth model): 0.5L & 1.0L (2-step) = 2.9x - 4x growth 1.5L (1-step) = 3.16x - 2.8x growth See bottom of this page: http://www.brewersfriend.com/yeast-pitch-rate-and-starter-calculator/ The how/why is mostly due to amount of available sugars. In a 0.5L solution even though it has the sugar density as a starter at 1.5L it has 33% of the sugar. Thus the yeast hits a wall earlier, once the sugar supply is depleted. I would say 2-step when time allows is preferred as you are allowing the healthy yeast to duplicate more and entering in another step of filtering out the old/dead yeast, hence in part probably why the 2-step has more potential.
Growth rates are all about inoculation rates. There is a sweet spot range for inoculation from an efficiency perspective. In general, a reasonable two-step starter with same total wort volume as a one step starter will be more efficient. Some calculators, like YeastCalc, support multi-step starters. BrewCipher advances it a step further (or dumbs it down, depending on your perspective), by automatically deciding how many steps are needed (and their sizes of course).
1) I was just explaining why the yeast cannot keep multiplying in a smaller 0.5L starter 2) When you decant the liquid off the top, you will be left with 2 layers of sediment, the top layer (lighter color) is live/healthy yeast. The bottom layer of darker sediment is old/dead yeast (more common in yeast cultivating multiple generations at home, you probably won't see this if you're just creating a starter from yeast you got at the store) I use this a lot as well to help judge slurry density, helps as a visual confirmation that the yeast growth is living up to its "calculation" http://www.wyeastlab.com/com-yeast-harvest.cfm The top # is # of cells per mL (250M ranging up to 1.4B) The bottom # represents % yeast solids in slurry. Take a look at your settled slurry (0.5L or 500ml) and judge % of yeast solids. That should tell you # cells per mL you have. For 500ml and 40% solids in your container you would have roughly 500B cells total.
I am just making a starter from yeast I got a store. That is the circumstance for which my question should be framed. Does it change the answer? I'm not trying to rinse yeast from a re-harvest.
This is the easiest use of a calculator/computing-steps. If you go to yeastcalculator or Brewers Friends or Brewcipher you can first determine how many cells you need. Then enter the date of your yeast and determine viability (how many cells you have). Either of these calculators can then determine how many steps are needed to reach your goal and the most efficient way to do it. If you are doing a routine packet that's say a month old, you can expect a viability of around 80% (call it 80B cells). If making a routine 5 gallon brew you can almost always accomplish this with a single starter below 2L if using a stir plate. Where I find the steps handy is when you have a lower starting count, making a lager, or limited by size of starter. Example: My biggest flask is 2L which I never fill above 1.5L. So I enter a single step of 1.5L in the menu and see if it hits the target. If short of what's needed then I need to add a step . . . there's a little trail/error involved (except for Brewcipher) but usually less than a minute to get your steps computed. You know you want your steps to increase with size, just start with something reasonable and look for the end result. Because yeast do not always grow at a linear rate. As stated by Vikeman, the inoculation rate (yeast pitching rate) determines the most efficient way to grow yeast. This inoc rate is in the fine print on yeastcalculator and Brewers Friend (not sure about Brewcipher). If you operate in the range of 40 - 125 million cells/ml of wort you will produce the most growth for the least amount of wort and the yield factor is linear (mostly). In this zone you're getting the most bang for the buck. Outside this zone the yeast will still grow, it's just not as efficient. If you have Yeast, this is all detailed on pages 139 - 145. When you approach extreme inoculation rates you get some extreme results. One poster here pitched 300B cells in a 0.5L and got nothing (as predicted by the calculator). Other examples: If you started 50B cells at 0.5L and stepped to 1.5L you would end up with 290+B cells. If you started the same 50B at 1.5L and made the second step at 0.5L you will end up with 230B. Both used 2.0 liters of wort, but in the second case the inoc rate is initially too low, then too high in the second step. The yeast will grow, they're just not happy about how you are feeding them. When you pitch 100B in a 20L primary, the maximum number of cells that can be grown is ~600B. Adding more wort will not increase your yeast growth. When I harvest dregs it takes 4 to 5 steps to reach a goal of ~200B, with each step progressively higher. If I dumped the dregs into a 2.0L starter (extreme low inoc rate) they would never start. The yeast probably don't care if you're using the best inoc rate (except for the extreme limits), but it's easy enough to compute . . . the calculator does all the work. Also, there are some variables unaccounted for that probably effect the results, but I find using the calculator to be a good starting point. Ironically, the calculator at Mr Malty is not programmed to compute steps. . . not unusual to see it compute starters in the 4 - 5 L range . . . it lets the end result compute a single starter without regard to inoc rate.
Yeast does a good job of explaining it. It's a parabola of food to yeast ratio to a certain point and then they tank out. I explain it to myself as they are lazy when there's too much food or too little food to eat. If you do a one liter starter and another liter starter, it's not the same as a two liter starter. You're generally best off keeping the yeast count low and the food level high, to a point. When you get into 1+1+1 liter starers, there's a point where you are just sustaining a colony of yeast. You stop growing unless you split the colony.
BrewCipher doesn't display the actual achieved inoculation rate. Not a bad idea though. But in the parameters, you can set the minimum inoculation rate, as well as the rate that is forced if the minimum rate would not have naturally been achieved. AFAIK, it's the only calculator that has these user adjustable parameters. With a calculator like YeastCalc, you play with starter size as a user input, watching the change in the output cell count as you dial it in. With BrewCipher, you set the parameters "once and done" (or go with the default parameters), and let the rules automatically determine the starter size(s) for each recipe. There's something to be said for both approaches. I loved to use YeastCalc before I built BrewCipher.
A better (simpler) example of how steps are more effective: 20B cells in a 1.5L starter with stir plate (inoc rate of 13m/ml, which is on the low side) yields 113B. 20B cells in a 0.5L starter (inoc of 40m/ml), stepped to a 1.0L (inoc of 68m/ml) yields 184B. This is a 63% increase in cells because your yeast pitching rate (inoculation rate) was in the optimum range (40 - 125 million cells per ml of wort).
The explanations of models based on inoculation rate are helpful, but I'm trying to understand this at a physiological or ecological level. What makes this 40-125 million cells per mL of wort the magic range? Looking for the physical explanation that underlies the statistical models. Why does crowding the yeast initially result in a higher cell count, when the same amount of resource is consumed. One thought that I have is that crashing, decanting, and adding new wort provides yeast with a new environment not polluted by their own waste. Alcohol inhibition? Seems a little off-target, though, because we know yeast have alcohol tolerance. Other thoughts, either speculative or confirmed, are welcome.
Part of what's going on is this... When you pitch at a very high inoculation rate, the yeast check out the environment and make a group decision that there's not enough food for much growth (i.e. most of the cells wouldn't be able to divide even once), so rather than doing much cell division, they will eat what's there just to sustain themselves. When you pitch at a very low inoculation rate, there's plenty of food, but there's a limit to the number of divisions each cell can do. Not limited by food, but by other things, like how much sterols they can produce and store before propagation starts. So they divide as much as they can, and then go into sustainment mode with the rest of the (lots of) food.
I believe VikeMan has hit the high points. Remember, these yeasts are wild animals and they got to where they are by learning how to survive. A bunch of geeks in lab coats have broken this down into useful parameters for brewing. As brewers we put emphasis on cell-count, while the primary purpose of the starter is yeast health. Yes, you want to boost the count but health is overriding. There is nothing mystical about the 40 - 125 inoculation range. IIRC, Brewcipher uses 25 - 140 because VikeMan reads the graph a little differently. But the yeast will grow outside this range. In the example above, if I only needed 113B cells I would probably make a single 1.5L starter which is outside the optimum range. If DME was terribly expensive you could get the same 113B by stepping from a 0.25L to a 0.5L . . . half the wort in the preferred range will produce the same 113B. But of course you double the time and risk of contamination. With a starter the express intent is yeast health/growth, the resulting beer is a by-product. When pitching yeast into a primary the game changes. Here you want an inoculation rate that favors the production of beer. While the yeast certainly grows, this is not the goal. For making beer we use inoc rates around 0.75 million cells/ml of wort/degree P (ales) which is a fraction of optimum rate for starters. We want the emphasis to be ethanol and flavor compounds and accept whatever yeast growth occurs. If 100B cells were pitched in a 20L batch (inoc rate of 5m/ml) the growth tops out around 600B. This is an inefficient way to grow yeast but a great way to make beer. If those same 100B were pitched in a 1L starter (inoc rate 100m/ml), the results exceed 200B cells because the pitch rate is optimum for yeast growth (but you only produced 1L of beer). While the numbers can be intimidating, I can find several free calculators that make all of this easy. Just like computing carb-level/sugar, or ABV, or mash/strike-water it's pretty intuitive. Now if I could just understand the Advanced Water Calculator!
Sorry for invoking mysticism. Definitely was being facetious. I accept the growth models, but am trying to understand the underlying biology. The models themselves are empirical and not physical-based. In ecology, we talk about density dependent population growth and mostly we witness negative density dependence, where increasing population density decreases growth rate. The yeast models suggest that there is a zone of positive density dependence, where increase density increases growth rate. We see this in some ecological interactions where the presence of an individual can foster the success of another. I wish to understand why this occurs in yeast.
Interesting premise. The idea of "group decisions" reminds me of some bacteria interactions where the bacteria appear detect the presence of others, which influences their metabolism. Multiple resource limitation (not just sugar for energy, but something else that influences cell structure) adds some complexity to consider. A lot of my question boils down to "if I were still teaching ecology, how would I explain the biology that underlies these pitching models?" It's probably out there in some yeast or microbial ecology textbook.