Nothing is perfect in this world, not even the translation of mRNA into protein. The error rate is one amino acid misincorporated into a protein for every 10,000 or so done correctly — but these results are for one celled organisms (E. Coli, yeast). I can’t find a number for mammals, primates etc. etc.
This means that occasionally one of the 3 codons which tell the ribosome to quit (stop codons), will be misread as an amino acid. This is called readthrough, and means that the ribosome will merrily march on producing a much larger protein than coded for by the mRNA until one of two things happens. l. the ribosome reaches the end of the mRNA and stops. 2. the mRNA contains another stop codon (there are 3). The probability of this is 3/64 per codon. If stop codons are randomly distributed (which they are most certainly not in the protein coding segment of an mRNA) the chances of 100 codons in a row not containing a stop codon is under 1% (.822 % to be exact). So any protein containing more than 100 amino acids is a statistical freak in this sense. Since the 3′ untranslated region (3’UTR) of mRNA doesn’t code for protein, they should have stop codons randomly distributed (there being no selective pressure to keep them away).
Enter Nature vol. 534 pp. 719 – 723 ’16 — if you attach a 3′ UTR section of an mRNA to a normal protein sequence (mimicking readthrough) you get much less protein. The authors think the 3’UTRs code for peptide sequences destabilizing the attached protein. They don’t know what this might be, so it’s terra incognita for researchers, and a worthwhile PhD project to figure it out. Another example of ‘coding’ by a presumably nonCoding sequence in the genome. It may also tell us something about protein structure.