Chemistry Obeying Arithmetic

It is well known that amino acids, triplet series, and series degeneracy are optimally distributed so that the effect of mutations of single bases is minimized. As a rule, possible consequences of the mutations such as an abrupt change of hydrophobicity are, to some extent, weakened (e.g. Sjostrom and Wold, 1985; Figureau, 1987; Knight et al., 1999). It looks like some imperfect protection against mutations. However, Shulz and Schirmer (1979) raised the question: why is it that another property of amino acids - the geometrical size of side chain - has no comparable protection though size is no less important than hydrophobicity?

One can show that the cooperative symmetry does not allow the code to enhance protection against an abrupt change of size. Histograms of hydrophobic-ity (Lacey and Mullins, 1983) and molecular size (Jungck, 1978) are combined with a calligramme fragment in Fig. 13. Trans versions are a kind of point mutations that alternate pyrimidine bases with purine bases and vice versa. All possible 3' base transversions of the largest and the most protected code set of degeneracy II are shown by arrows. Due to the cooperative symmetry of the fragment, the transversions are also centrosymmetrical in their arrangement. Recall that the triplet series are aligned as a row of monotonically increasing amino acid nucleon numbers.

The molecular size of an amino acid is generally proportional to its nucleon number. Therefore, the monotony excludes a centrosymmetrical shape of the size histogram. On the other hand, the hydrophobicity of an amino acid does not depend explicitly on its size and nucleon number. This allows the genetic code to form the centrosymmetrical shape of its hydrophobicity histogram. As a result, when amino acids are replaced through mutation the change of hydrophobicity is generally weak, while that of size is strong.

Fig. 13 Physicochemical effect of the cooperative symmetry. If a point mutation occurs, the code amino acids are to a certain extent protected against an abrupt change of their hydrophobicity but not of their geometric size. Such limited protection results from the internal cooperative symmetry and its systematization principle. Arrows denote the transversion mutations of the triplet 3' base positions and the corresponding alterations of the hydrophobicity and geometric size

Fig. 13 Physicochemical effect of the cooperative symmetry. If a point mutation occurs, the code amino acids are to a certain extent protected against an abrupt change of their hydrophobicity but not of their geometric size. Such limited protection results from the internal cooperative symmetry and its systematization principle. Arrows denote the transversion mutations of the triplet 3' base positions and the corresponding alterations of the hydrophobicity and geometric size

Freeland and Hurst (1998) showed that, compared to defense capabilities of the universal genetic code against mutations, only one code version in every million randomly generated alternative codes is more efficient against abrupt changes in the hydrophobicity. Those alternative codes generated in computer simulation can hardly ever get some exact order at random. What is more, such codes lose the original arithmetic of the actual genetic code. However, necessity to have and save arithmetic rejects this and other statistical approaches including the "RNA world." Therefore, the genetic code is a unique one rather than one in a million in this respect.

The universal genetic code is arranged optimally (Di Giulio and Medugno, 2001). Only now after its concealed order had been disclosed, one can perceive a true scale of that optimality.

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