Joint optimization of replicative rate and information storage set the letter size of primordial genetic alphabet

The simplest possible informational heteropolymer requires only a two-letter alphabet to be able to store information. The evolutionary choice of four monomers in the informational biomolecules RNA/DNA or their progenitors is intriguing, given the inherent difficulties in the simultaneous and localized prebiotic synthesis of all four monomers of progenitors of RNA/DNA from common precursors on early Earth. Excluding the scenario where a two-letter alphabet genome eventually expanded to include two more letters to code for more amino acids on teleological grounds, we show here that a replicatively superior heteropolymer sequence in an RNA-world-like scenario would have to be composed of at least four letters in order to predictably fold into a specific secondary structure, and hence must have out-competed the two-letter alphabet genomes. As a consequence of our earlier demonstration of the replicative rate advantage of maximal-nucleotide-skew sequences, in this follow-up article, we show that the competing constraints of maximum replicative rate and predictable secondary structure formation can be simultaneously satisfied only by maximally-skewed palindromic heteropolymer sequences composed of a minimum of four letters.