Comma-free and synchronizable codes

Abstract

Shepherd (1981. Proc. natn. Acad. Sci. U.S.A. 78, 1596-1600), Clarke (1982. J. theor. Biol. 99, 397-403), Crick et al. (1976. Origins of Life 7, 389) have put forward the possibility that there was a code, ancestral to the existing genetic code, which was non-degenerate and comma-free. The point of a comma-free code, as first proposed in Crick et al. (1957), is that it provides immunity from frameshift reading errors. In this paper it is argued that if frameshift error immunity is to be used as a selection factor in guiding the search for a hypothetical ancestral code, then the appropriate mathematical formulation of this characteristic is not comma-freeness but synchronizability. The calling card of the comma-free notion is that it results in a limit of 20 on the number of sense codons when applied to the genetic coding system. But so does synchronizability, which includes comma-freeness as a special case. Further, using synchronizability as a constraint instead of comma-freeness yields roughly 3000 times as many potential models for an ancestral code. In particular, the RNY model becomes more compatible with immunity from frameshift error as an evolutionary constraint.