"Is it possible to culture probiotics to increase their numbers sort of like proofing yeast? For example, could one take a probiotic capsule, put the contents in some warm water with some amino acids (say from protein powder) and a little sugar and reasonably expect their numbers to increase?"
Actually, what you are suggesting pretty much already exists and has for a few thousand years. It is called Kefir (pronounced kafir).
Kefir is available both milk and water based. The good bacteria within it feeds off the sugars in the liquid and the end product/drink has virtually no sugar in it.
The milk based kefir has very little sugar to start with. I use milk ONLY from grass fed cows. No additional sugar is needed for milk kefir.
To make water kefir, you do add about 8 ounces per to about 60 ounces of water BUT the sugar magically disappears as the bacteria feeds off of it and the end result is a probiotic drink that tastes pretty good, is loaded with beneficial bacteria and is very low in sugar.
Timing with both varieties. I make about 32oz of milk kefir at a time and it is ready in about 24 hours. I make 64oz of water kefir at a time and from start to finish takes 4 days to complete (it is technically ready in two days but I flavor the water kefir with fruit and do a 2nd fermentation which adds two days to the process). In any case, if you time it right, the finished product can be sugar free or pretty close to sugar free. If you ferment the mix too long, alcohol starts to form.
If you want, you can naturally 'carbonate' the drink so it is as bubbly as any store bought soda. This is very, very easy to do. Also, there are many, many options when it comes to flavors. The drink is quite good!
I have been making and consuming kefir for about 2 -3 years. It takes me about 15 minutes every 2 days to prepare and is very easy to do. I drink well over 60 ounces of it a day, every day.
If you are interested in more information, you may find this link of interest:
http://www.thewalkingencyclopedia.com/k ... Milk_Kefir
There is a lot of useful information in the above article, one of the most interesting points to me is:
"A major characteristic of kefir is that the probiotics contained in kefir attach themselves to the colon,
sweeps away all the harmful substances and colonizes the intestines."