NPK are commonly called the macronutrients, as plants neeed and use more of them than the other mineral nutrients, the micronutrients and/or trace elements. Submerse plants generally require less P than emerse plants, something like ~7+ parts N to 1 part P. Planted tank folk tend to work at about 10:1::N

, largely because it is not critical and the math is simpler. They also work at N=K approximately.
Phosphate is the great energy element - ATP* and its ilk are the energy mediators in both plants and animals. I have forgotten the relative percentages in dry plant mass for aquatics, but if you are in phosphate lack, everything from photosynthesis to growth stops. Producing energy storage compounds? Phosphate compunds are absolutely required. Burning those componds? Phosphate is the mediator again.
This led to the great fallacy of phosphate-limitation to control algae, a theory which dominated planted tanks for a long time. Over-zealous P control arrested plant growth, which of course allowed algae to take up the slack. Many grower spent more time testing than maintaining their tanks. Many were saved more by the inadequacy of the tests than by the validity of the theory. But I am sure it helped Hach and LaMotte's business but ever their tests are good to very good field grade, which is well short of lab grade.
Phosphate levels are not tightly critical in planted tanks so long as there is enough to be non-limiting, and not far above 3ppm in other than the highest light/CO2 fastest growth tanks.
*
http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/A/ATP.html
None of the nutrient lists commonly include C (carbon, specifically bioavailable carbon), which is just over 40% of plant's dry mass, because it comes free in the air - for terrestrials. Unfortunately it is not free for tanks other than low-light slow-growth setups.