I've not seen a detailed article on it, but the idea is that with some systems, especially ULNS systems, the corals may benefit for additional nutrition since their zoox are at near starvation levels.
I do not know if it is useful, but it may be and many folks think they are useful in their systems. I've recommended some in the past, and in that "older" context, I discuss them briefly here:
The “How To” Guide to Reef Aquarium Chemistry for Beginners, Part 2: What Chemicals Must be Supplemented
http://reefkeeping.com/issues/2007-04/rhf/index.php
from it:
http://reefkeeping.com/issues/2007-04/rhf/index.php#15
Supplementing Amino Acids
The deposition of calcium carbonate into intricately structured skeletons is one of the wonders of corals that aquarists marvel at. At the molecular level, corals often guide the precipitation of calcium carbonate with organic materials, encouraging precipitation on some parts of the skeleton or inhibiting it elsewhere. Often these organic materials are proteins that contain negatively charged amino acids, such as aspartic acid. These negatively charged amino acids may interact strongly with positively charged calcium as it is deposited, allowing the proteins to guide the precipitation.
It turns out that some corals cannot make enough aspartic acid to meet their demand, and must get it from foods or from the water. Depending on the species of coral involved and the foods provided to the aquarium, the supplied foods may not be an appropriate source of aspartic acid for corals, and supplemental aspartic acid has the potential to be useful. It might be taken up directly or be taken up by other organisms that are, in turn, consumed by the coral (e.g., bacteria).
I do not presently add any amino acids to my aquarium, but some aquarists do. Those who do sometimes report improvements in the appearance of their corals. I do not know if this is a true cause and effect, or a coincidence, but aquarists might consider dosing certain amino acids. A number of commercial amino acid supplements are available to hobbyists, and some might also be obtained in suitable form from a health food store (beware of phosphate as one of the other ingredients in human supplements).
I don’t have a recommended dose. If you choose to experiment, start with a low dose, say, 1/8 teaspoon (0.5 gram) of solid amino acid or the equivalent amount of a solution, to a 100-gallon aquarium once a week. Then, slowly ramp up the dose, looking for positive or negative effects.
Note, however, that not all amino acids are beneficial. Many may just drive bacterial growth, and all contain nitrogen, so they may contribute to the nitrogenous waste that ends up as nitrate in many aquaria.
Additional discussion of the effects of amino acids and other organics on calcification by corals appears in this article:
The Chemical & Biochemical Mechanisms of Calcification in Corals
http://www.advancedaquarist.com/issues/apr2002/chem.htm