And by divisible by 3, this is to mean the product of the division is a whole number, and not a decimal.
And by divisible by 3, this is to mean the product of the division is a whole number, and not a decimal.
No. For at least two reasons:
The 5' UTR is part of the first exon and the 3' UTR is part of the last exon. Since these exons contain both coding and non-coding sequence, there is no reason why their length would be a multiple of three.
Splice sites do not have to be in frame. It is very common that nucleotide 1 of a codon is on one exon and nucleotides 2 and 3 of the codon are in the next exon (or 1 and 2 in the first exon and 3 in the next).
+1 @Lars Juhl Jensen: Thanks, that's what I though, which means I'm still misunderstanding something. Posted a followup question.
Lars' answer is good +1. I would edit his point #2 to say: Splice sites do not themselves constrain exon length to be perfectly divisible by 3. The splice site must maintain the proper reading frame for the entire message.
In a broader context, I have never heard of anyone that I can recall talking about constraints on exon length - and certainly not, as pertaining to this question - to the detail of perfect division by 3. There are some thoughts that exons represent protein domains or functional units but this is disputed by others.
There have been publications that examine constraints on exon length, intron length, divisibility by 3, etc. In the context of biologically functional alternative isoforms that arise by simple exon skipping there may be some enrichment for divisibility by 3 as this allows an alternative isoform with a modified but frame maintained protein product.
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What you are really trying to ask is whether exon splice sites always line up with codon boundaries.