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
One of the main features of the present model is to give a rigorous characterization of appropri-
ately differentiated codons, through the introduc- tion
of codon
classes with
different local
symmetries Fig. 1. From this characterization, we propose a mechanism for the progressive dif-
ferentiation of the coding assignments, starting from a point in which rudimentary translation
machinery had a relative small threshold of trans- lational accuracy.
The four bases occurring in RNA, adenine A, cytosine C, guanine G, and uracyl U or
thymine T in DNA defines a four-letter alpha- bet X: {A, C, G, U T}. They may be categorized
according to i chemical type C: {R, Y}, where R: A, G are purines and Y: C, U are pyrimidi-
nes, and according to ii H-bonding, H: {W, S}, where W: A, U are weak and S: C, G strong
bases. The third possible partition into amino M:{A, C}, keto {U, G} classes is not independent
from the former ones Fig.1 in Jime´nez-Montan˜o et al., 1996, and is irrelevant for the description
of the codon – anticodon mapping, but is impor- tant to distinguish between the two classes of
aminoacyl tRNA synthetases see Results.
Denoting the chemical type by C
i
and the H- bond category of the base B
i
, by H
i
at position i of a codon i = 1, 2, 3, our basic assumption is
that: The codon – anticodon Gibbs free-energy of in-
teraction obeys a hierarchical order, symbolically represented as
C
2
\ H
2
\ C
1
\ H
1
\ C
3
\ H
3
1 This means, that the most important characteris-
tic determining the codon – anticodon interaction is the chemical type of the base in the second
position. The next most important characteristic is whether there is a weak or strong base in this
position, then the chemical type of the first base and so on Jime´nez-Montan˜o et al., 1996. Em-
ploying the categorizations of the bases defined above, corresponding categorizations may be
defined for codons, e.g. NSN, RGY, UNW, etc. where N = A, C, G, U. With the help of these
syntactic categories the codons can be partitioned into
classes Jime´nez-Montan˜o,
1994. The
classes, displayed in Fig. 1, rigorously characterize ‘‘appropriately differentiated codons’’ Nieselt-
Struwe and Wills, 1997. They specify the differ- ent stages in the evolution of the code, and the
possible amino acid groups at each stage. To derive them I make the following considerations.
The expansion of the amino acid alphabet, following a minimum change coding principle
Swannson, 1984, is equivalent to fulfilling the following requirements, a at any stage in the
development of the code the codon classes will differ, at most, in a single feature and, b these
changes must obey a partial order, defined by a set of inequalities like Eq. 1 above. This means
that the possible extensions of the vocabulary, by the incorporation of new amino acids, are ar-
ranged in a subset relationship. According to the subset principle Berwick, 1986, distinctive fea-
tures are not determined independently of one another. Rather, some distinctive features can be
fixed after other features are set. The system will make the smallest differentiation distinction
consistent with its current state of development, characterized by the codon – anticodon recogni-
tion fidelity. Since the capacity to distinguish dif- ferent
codons depends
on the
stage of
development of the system i.e. fidelity increases in time, a minimum change is a relative concept.
From the structure of the ‘universal’ code, we now that, at the present time, a minimum change
corresponds to a change in H
3
, for example, be- tween AUA Isolucine and AUG Methionine.
Therefore, in order to go back in time, to the beginning of the development of a coding system,
we have to move from the right side to left side of the inequalities Eq. 1. Thus, at the beginning a
change in the chemical type of the second base C
2
of a codon was a minimal change. Since all other changes are associated with smaller interac-
tion energy, the translation machinery can not
distinguish them. However, at the following stage, the threshold energy for minimal differentiation
decreases because of better enzymes. Therefore, the previous change is not the smallest any more.
The H-bonding of the second base H
2
becomes the new differentiation threshold, and so on. The
key idea is that the inequalities Eq. 1 determine a definite order in which new features are used, to
form new codon classes, which codify for the recently introduced amino acids. The new classes
are formed by splitting of existing classes, with the split based on the order given by the basic as-
sumption. In this way, a huge number of develop- mental pathways are eliminated because of the
order in which a small number of parameters are set.
A split must be triggered by a detectable physico – chemical difference between at least one
of the members of an existing codon class and the rest of the members. This event could be, e.g. the
change of the middle base from a purine to a pyrimidine. In order to guarantee incremental
evolution, the next available unused distinctive feature must be used as a point of refinement, i.e.
the splitting occurs at the leading edge of the directed graph Fig. 1 by successive refinement of
existing classes. This is a powerful constraint for the possible evolution of a coding system. Sup-
pose that this constraint did not exist, then a non-gradual evolution of the code would imply
that codons differing in two or more features would be assigned to different amino acids. It
would then be possible to form a new class parti- tion based on distinguishing both features without
first using one of them to form a codon class. Therefore, there would be no class that would
correctly accommodate a codon that has one value of the first feature and the contrary value of
the second one. One way to remedy this problem would be to allow the system to go back and
rebuild the classes that have already been formed, but this would violate the developmental order,
with the corresponding perturbations at the protein level. Therefore, as a result of following a
minimum change-coding path, at each stage the narrowest code is formed, consistent with the
capability of the system to distinguish among different codon classes. If two codons cannot be
distinguished they must codify for the same amino acid, remaining synonymous
3
.
5. Results
