This conjecture was investigated experimentally by Langerkvist’s group Langerkvist, 1978; Sa-
muelsson et al., 1980, that postulated a ‘‘two out of three reading’’. Under the conditions of in vitro
protein synthesis, a codon can be read by recogni- tion of only its first two nucleotides, the third
position of the codon being disregarded. These authors proved their hypothesis only for codons
of the SSN class. Jime´nez-Montan˜o et al. 1996 suggested a generalization of the hypothesis,
based on the group-theoretical analysis of codon doublets made by Danckwerts and Neubert
1975. The main result was a classification of the codons of ‘mixed type’ class WSN and SWN,
with respect to the sets M
1
and M
2
of four-fold and less than four-fold degenerate doublets, re-
spectively. It was shown in that paper that the third base degeneracy of a codon does not depend
on the exact base at the first position, but only of its H-bond character. Also Hasegawa and Miyata
1980 underlined the importance of the codon – anticodon interaction energy to understand the
pattern of degeneracy. These authors noticed a strong correlation between codon composition
and molecular weight of the coded amino acid. The further correlation, between molecular weight
and the sizecomplexity score employed here Table 1, has been fully discussed by Dufton
1997. Thus, our results extend their previous finding.
As already mentioned, the structure of the code suggests that it evolved following a course of
minimal differentiation to diversify objects. In the context of the formalism we are employing, this
means by changing a single distinctive feature of the codon at each time. From this assumption a
dynamical evolutionary pattern of the code emerges naturally, envisioned as a refinement
process.
3. The group-theoretical foundation
Nieselt-Struwe and Wills 1997 have discussed the intrinsic physical constraints that must be
satisfied before a molecular genetic coding can evolve at all. As in their work, in the present
model the selection process, which led to the evolution of a coding system, has an underlying
group-theoretical structure. However, our more specific model differs from their framework,
which is too general. It also differs from the one proposed by Hornos and Hornos 1993, that
employed a Lie group decomposition of the ‘uni- versal’ code to elucidate its structure. In this last
paper, not only was no account given for the code’s observed deviations, but ‘‘the decomposi-
tion was based on the properties of amino acids and did not reflect any obvious process of tempo-
ral refinement in the differentiated recognition of amino acids and codons’’ Nieselt-Struwe and
Wills, 1997.
Instead, the mathematical background behind the present model consists of cartesian products
of the Klein 4-group, which is the relevant group to describe the symmetries of nucleic acids
Zhang, 1997 and that underlies the hypercube structure
Jime´nez-Montan˜o and
Klump, in
preparation
2
. As shown by Danckwerts and Neu- bert 1975, the transformations among the four
bases obey a Klein 4-group. This result was ex- tended to B
1
B
2
base doublets, by Bertman and Jungck 1979, and to B
2
B
3
base doublets by Jime´nez-Montan˜o et al. 1995. However, the ex-
tension to whole codons apparently fails because, in the universal code there are three amino acids
with six codons each S, L, R, a single amino acid with three codons I, and two amino acids
with one codon each. This is an insurmountable difficulty under the assumption of an immutable
code. However, the situation changes if one as- sumes that the code evolves. As will be discussed
below, in relation to the code’s deviations, the local symmetry of the codons may change. Under
these circumstances, the above exceptions can be explained. The amino acids with six codons each
are doubly assigned: the ‘normal’ assignment of four codons and a second assignment of two
‘extra’ codons Taylor and Coates, 1989. The cases with one and three codons are the result of
a single process in which the reassignment of a
2
In a forthcoming paper, a detailed model of the structure and evolution of the genetic code based on the DNA group
will be established. This group is exhausted by a Klein 4-group and its two cosets Zhang, 1997.
codon, belonging to an amino acid with two codons B
1
B
2
R or B
1
B
2
Y, produces the 1-3 de- generacy Fig. 1.
4. The informational problem
