How much non-coding DNA do eukaryotes require?
  Despite tremendous advances in the field of genomics, the amount and function of the large non-coding part of the genome in higher organisms remains poorly understood. Here we report an observation, made for 37 fully sequenced eukaryotic genomes, which indicates that eukaryotes require a certain minimum amount of non-coding DNA (ncDNA). This minimum increases quadratically with the amount of DNA located in exons. Based on a simple model of the growth of regulatory networks, we derive a theoretical prediction of the required quantity of ncDNA and find it to be in excellent agreement with the data. The amount of additional ncDNA (in basepairs) which eukaryotes require obeys Ndef = 1/2 (Nc / Np) (Nc - Np), where Nc is the amount of exonic DNA, and Np is a constant of about 10Mb. This value Ndef corresponds to a few percent of the genome in Homo sapiens and other mammals, and up to half the genome in simpler eukaryotes. Thus our findings confirm that eukaryotic life depends on a substantial fraction of ncDNA and also make a prediction of the size of this fraction, which matches the data closely. 
Sebastian Ahnert, Thomas Fink, Andrei Zinovyev