I have some mycelium growing on cardboard but I am wondering what is in the cardboard other than carbon, oxygen and hydrogen that the fungus can use. How is it meeting it's need for nitrogen and other elements ?
Oyster mushrooms (and others) can grow and fruit on cardboard alone, or dried wood chips or straw alone - as long as their requirements for water, light, temperature, and ventilation are met.
The effect of nitrogen on mushroom production is best considered with the metric called Biological Efficiency (BE), which is the ratio of the weight of mushrooms produced to the dry weight of the substrate used.
So where you may get 7 lbs. of mushrooms from a 10 lb. (dry) bag of un-supplemented straw or cardboard (a 70% BE), you could get 11 lbs. from a 10 lb. bag of nitrogen supplemented straw (110% BE).
The ability of oyster mushrooms to grow and produce quite well on un-supplemented substrates makes them great for beginners because very few other organisms can compete with them. Most bacteria and molds need more nitrogen to grow quickly.
However when you start looking to increase BE, supplementing with nitrogen (from alfalfa, bran, fertilizer, even urine) is the most effective way to do so. The problem is that this higher nitrogen substrate is now also a great environment for the common mushroom contaminants. Extra steps and care area needed to grow mushrooms in supplemented media.
Other common "additives" are gypsum, limestone, and sometimes hydrated lime. These provide micronutrients and can stabilize pH. The lime can be used to pasteurize the bulk substrate prior to inoculation.
Pleurotus genus is essentially cellulolytic (Silva et al., 2012a), however, there are fungi that grow on substrates with low nitrogen content in the range from 0.03% to 1.0% (Machado et al., 2015). Ortega et al. (1992), in their studies with Pleurotus spp. cultured on bagasse supplemented, described a nitrogen increase in mushrooms related to the amount present in the initial substrate plus the nitrogen amount present in the inoculum, indicating a possible fixation of this element by mushrooms. Sturion and Oetterer (1995) also observed a nitrogen increase in the residual substrate, which ranged from 4% to 37% in the cultivation of Pleurotus spp. on different substrates, suggesting the possibility that this genus fixes nitrogen, or the presence of fixing bacteria associated with the mushroom.