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Re: yeast

In a fermentation setting they will not reproduce unless they have 
sufficient stored energy as  fermentation is only a subsistence 
lifestyle.  That is to say that production of alcohol from carbohydrates 
does not provide enough energy for budding.  When Oxygen is present they 
can furthur oxidize the alcohol and derive far more energy.  Most of 
which the cells don't need so they store it for use during times when 
oxygen is not present.  

Brewers yeast is produced in aerobic conditions that promote energy 
storage.  So that the little yeast that is introduced into the wort will 
reproduce rapidly to produce the number of cells needed to make alchol 
in a timely fashion.  The yeast from the first batch of alchol can be 
reused several more times if they use all of it.  But in subsequent 
fermentations the yeast has no more stored energy and will not 
reproduce.  Eventually the yeast is completly depleted and won't be 
useful for fermentation.  This is where we get bread yeast from.

Also in terms of the yeast in the bottom being less active:  This may 
not be strictly true.  If your talking top flocculating yeast then that 
probably is the case.  But bottom flocculating yeast like to be on the 
bottom thus there may be less active yeast toward the top as well.

Also, If your gonna reuse the yeast its best to keep all of it because 
of the reduced ability to reproduce.  Keeping Only a small portions 
should theoretically not work.  But having said that:  1% glucose causes 
metabolite repression.  I.e. even if oxygen is present the yeast won't 
engage in aerobic metabolism.  So in a glucose solution spent yeast 
cannot reproduce.  I suspect that in the sucrose solutions that we tend 
to use that metabolite repression does not occur, and the oxygen that is 
introduced with fresh solution is enough to at least partially allow 
some reproduction.