I do ferments of 6 kg of sugar in a final volume of 24 litres.(250 mg/ml)
A yeast is a eukaryote (i.e. has mitochondria) but also has a tough chitin cell wall (like a lobster). It is 90% water and the 10% dry weight is roughly half protein /half carbohydrate. About a third of the protein is stored as free amino acids (i.e. available for re-use by another yeast).
On average , nitrogen is 16% of he weight of any protein (1/6 th).
A growth medium will grow 2-3 g/litre (dry weight) of yeast so in a 25 litre bucket , I am growing a 50-75g yeast (dry weight) which is about 500-750g or an armored jellyfish about the size of a squirrel.
What do I need to grow such a pet?
1) carbohydrate, sugar, treated starch
2) protein - because of the cell wall yeasts can only absorb ammonia or amino acids not larger proteins.
Ammonia can be sourced via sulphate of ammonia (from the garden shop) or the more pure DAP (diammonium phosphate) which is 21% nitrogen. So one gram a litre of DAP supplies 200 mg/litre of nitrogen.
The yeast assimilable nitrogen (YAN) from dead yeast is 3-5%.
Below 150 mg/ litre nitrogen , one gets a stuck ferment and you can put in as much as 500 mg/l but get many more esters and ethyl acetate. The optimal amount of nitrogen (YAN) for a 6 kg sugar wash is 250 mg/l.
I put in 50- 75 g of (dead) brewers yeast (3-5% of 2-3 g/l YAN or 60-150mg/l nitrogen) -plus 12-24 g DAP (100-200 mg/l N).
If my lobster jellyfish yeast only has 5-7.5 g of nitrogen in it, why do we need 5 times as much nitrogen in the water. Well survival of the fittest. The early generation yeasts die and their proteins are unusable. This is also why you should only put half of the nutrient in at the start and wait until 1/3 sugar depletion (about 12-24 hours) before adding the second half.
3) fat is only 2% of the yeasts weight but is not unimportant. A strong cell membrane prevents rupture by concentrated alcohol especially if going for an 18% alcohol brew. Ergosterol is too expensive to buy but a dietary supplement choline which is a precursor is cheap and only a quarter of a gram is enough. However unsaturated fat decreases ethyl ester formation so perhaps I should add a gram of butter next time. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2223249/" onclick="window.open(this.href);return false;" rel="nofollow
4) minerals. The most prevalent ion is potassium so if using sugar, you should add at least 3g of KCl to achieve an intracellular concentration of 150 mol/l.
Epsom salts 1.5 g. Calcium- add some gypsum or chalk. There are enough minerals in a vitamin tablet to supply the yeast. For optimal minerals, 50-75 g dead yeast is pretty good.
Zinc needs to be between 0.4 - 1 ppm ( mg/l) (<0.05 or > 10 is toxic)
5) vitamins - again dead brewers yeast is cheap and has everything. Many vitamin tablets lack things like folate because it would make the tablet too big (which means I have to add Vegemite as well!) There's no disadvantage adding too many vitamins to a wash that you are going to distil. It's not like wine.
6) sulphur - apparently the pantothenate (vitamin b5) : YAN ratio is important to prevent off smells. Keep the pantothenate levels above 500 mcg/l or 12 mg a batch which is a twentieth of a pantothenate tablet but 50% more pantothenate than in one my vitamin tablets. Low pantothenate also means low fats and a weak cell wall. Tomato paste is rich in B5.
Selenium - all fungi accumulate this trace element possibly as a defense mechanism but it is used in sulfur metabolism. I grate in a brazil nut into my wash just to be sure.
7) pH - the science for this in mycology is woeful and is just waiting for a decent phd project. Citric acid calculators on the web suggest adding 0.2 g of citric acid and yet turbo put 45g of the stuff in their batch. Citric acid can be converted to acetic acid (vingar). In human physiology, pH is calculated using a fourth order quadratic polynomial according to the Stewart hypothesis using concentrations of strong ions ( sodium, potassium, magnesium etc) and balanced by proteins, phosphates and sulphates. Um, maybe, er follow a recipe?
http://www.anaesthetist.com/mnm/wine/Findex.htm" onclick="window.open(this.href);return false;" rel="nofollow

In laboratory conditions a yeast can convert its own body weight of sugar to alcohol every minute so my armored jellyfish could chew up the 6kg of sugar in about two hours. We don't want laboratory conditions because a high YAN makes nasty flavours but don't be too afraid of a fast ferment if you've put the right stuff in at the right time. Over a week implies you're running the wash with a vitamin or mineral deficiency or too cold.