mechanism by which long coding sequences (CDSs) could be achieved would be by the linking together of short coding pieces (exons) occurring within short ORFs and selective ejection of the intervening random sequences (introns). If substantiated, the ROSG model may provide a long sought after mechanism for the origin of introns and the split structure of spliceosomal genes as well as a functional reason for the origin of spliceosomes. Furthermore, the acceptance or rejection of this model has implications on our understanding of the essential relationship between intron-dense and intron-sparse genomes. The Model: Possible origin of split-genes from random genetic sequence The ROSG model proposes that split genes originated from prebiotic primordial genetic sequences [27]. It is based on the assumption that long chemically-synthesized DNA molecules were available in the prebiotic environment and that the genetic code (the codons) was established prebiotically, so that the coding information can be translated into proteins. If codons were assigned prebiotically, then the stop-codons were needed in the origin of protein-coding sequences. It is possible that the general code contained three stop- codons, which then would limit the average ORF length to about 60 bases in random DNA. The origin and evolution of the genetic code may have first involved 12 amino acids representing the original proteins, instead of the 20 found in modern proteins [28]. Our study assumes the genetic code with three stop codons coding for proteins with 20 amino acids, which represents the modern genetic code in majority of current life forms. The presence of three stop-codons for every 64 codons limits the average ORF length to about 60 bases in random DNA. Then ORFs longer than a few hundred bases would be exceedingly rare. As any coding sequence has to necessarily occur within an ORF, the length of the ORF will restrict its length, and therefore proteins longer than 200–250 amino acids would not be encoded. A mechanism to circumvent this problem and produce long ORFs was necessary in order to create the longer coding-sequences that code for larger proteins integral to living systems. A workable tactic would be to consecutively link the best of the short coding pieces (analogous to modern exons) available at considerable distances in a long random DNA, and remove the intervening nonsense sequences (analogous to introns), and arrive at almost any necessary length of protein-coding sequence. Results Extremely short ORFs in random DNA due to frequent stop-codons While the expected mean length (EML) of the ORFs in a random DNA sequence is 21.3 codons (61 bases), the predicted frequencies of ORFs should decrease exponentially with an increase in length. The probability of the ORFs, and thus the EMLs of random DNA required for the chance occurrence of a given ORF length, are predictable. The probability that a sequence of n codons is an ORF is given by P(ORF; n) = (3/ 64)26(61/64)n, and for the next occurring ORF in a series of ORFs is given by P(ORF; n) = (3/64)6(61/64)n. The EML of random DNA required for the chance occurrence of an ORF of n codons is n/P(ORF; n). Figure 1 shows that the probability decreases exponentially and the EMLs increases exponentially as the ORF length increases. This analysis revealed that ORFs longer than 300 bases are extremely improbable in random DNA: for example, 600-base ORFs occur only once in a random DNA length of approximately one million bases, and 750-base ORFs occur only once in 40 million bases. Origin of Split Gene Structure Figure 1. The probability of ORFs of increasing lengths. The probability of ORFs of increasing lengths was calculated based on the formula P (ORFn) = (61/64)n, where n is the ORF length in codons. The Expected Mean Length (EML) for the random DNA for the chance occurrence of ORFn is n times the reciprocal of the probability. doi:10.1371/journal.pone.0003456.g001 To test this concept, we plotted the frequency distribution of ORF lengths in a computer generated random DNA sequence of 100,000 bases (Figure 2). The shortest ORF lengths were confirmed to be the most frequent, and the frequency of longer ORFs decreased exponentially, reaching zero at a length of just 300 bases. The majority (,70%) of the ORFs were shorter than the 60 base EML. The cumulative frequency plot showed that 99% of all ORFs were shorter than 300 bases and 100% of ORFs were shorter than 500 bases. The frequency of ORFs tends to reach zero around a length of 600–750 bases in random DNA billions of bases long, limiting the length of encoded proteins to just ,250 amino acids. Hence any ORF .750 bases found in an organism’s genome can safely be considered as non-random and thus was identified as a non-conforming ORF. Figure 2. Frequency distributions of ORF lengths in random and eukaryotic DNA. The ORF lengths in all six RFs in a computer generated random DNA sequence (100,000 bases) and in the human genomic sequence [H. sapiens chromosome 1, reference: NT_ 004350.18: base 48,000,000 to base 48,100,000] were computed and the ORF length frequencies and the cumulative frequencies were plotted. doi:10.1371/journal.pone.0003456.g002 PLoS ONE | www.plosone.org 2 October 2008 | Volume 3 | Issue 10 | e3456