My main concern was regarding whether codons can be viewed as ‘signs’ or not, in the sense that ‘signs’ are abstract. If one says that ‘signs’ don’t have to be abstract, nor arbitrary, (e.g. footprints being ‘signs’ of an animal past presence and direction) I don’t think we disagree on that.
Regarding the arbitrariness or randomness of codon assignment was a secondary point, but I will address this here.
That’s a very good example. Although, one can point out that E (or the phonetic sounds it represents) being the most common in the English language is also arbitrary, or perhaps more accurately described as ‘historically contingent’. This may not be the case for the amino acids nor the nucleobases.
Well… there are actually are chemical aspects regarding codons that do have a correspondence in the genetic code. When a codon (of an mRNA) interacts with the anti-codon (of the tRNA) each base pair is not equal. For one, GC interactions involve 3 hydrogen bonds while AU interactions have only 2. This has a significant effect on the strength of the interaction, and thus the reliability of one particular codon compared to another. This is also true for the position; e.g. the 2nd base pair of the codon is stronger compared to the first, and both are stronger than the third position which is prone to form wobble base-pairing. Hence, why the third codon tends to be fully or partially redundant, except for a very few interesting cases. There is also an interesting correspondence between the codons and the biochemical synthesis of the amino acids, such that codon assignments may have roots in the physical “rules” of the biochemistry observed in metabolism, which in turn may have roots in geochemistry. I explain such details here as well. The exact reason for that is unclear, but a possible explanation is given by one scientists I like to follow on the topic of the origin of life (Eric Smith). Here is a quote from one of his books.
In Chapter 5 we show that the translation system from RNA to proteins – a system that has clearly been under evolutionary pressure to provide a buffer between the idiosyncratic structure of metabolism and the flatter opportunity space provided by sequence combinatorics – is organized in a way that heavily recapitulates the order of metabolism. Relations between the assignments of amino acids to nucleotide triplets in the genetic code have been recognized since the 1970s [901], but the information we assign to such associations becomes even greater when we recognize that it extends also to the selection of the biological amino acid inventory. Part of the reflection of biochemistry in the code can likely be accounted for by precisely the code’s function of buffering [276, 327, 833]: to minimize the leakage of metabolic pattern through the coding process when errors occur, the assignments must make use of redundancies in the underlying chemistry. We will show, however, that the regularity of the code is even more fundamentally a biosynthetic pathway regularity, which can only be rationalized if it arose when the precursor to the modern translation system was an embedded system coevolving with metabolism.