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A unified model of the standard genetic code

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ABSTRACT

The Rodin–Ohno (RO) and the Delarue models divide the table of the genetic code into two classes of aminoacyl-tRNA synthetases (aaRSs I and II) with recognition from the minor or major groove sides of the tRNA acceptor stem, respectively. These models are asymmetric but they are biologically meaningful. On the other hand, the standard genetic code (SGC) can be derived from the primeval RNY code (R stands for purines, Y for pyrimidines and N any of them). In this work, the RO-model is derived by means of group actions, namely, symmetries represented by automorphisms, assuming that the SGC originated from a primeval RNY code. It turns out that the RO-model is symmetric in a six-dimensional (6D) hypercube. Conversely, using the same automorphisms, we show that the RO-model can lead to the SGC. In addition, the asymmetric Delarue model becomes symmetric by means of quotient group operations. We formulate isometric functions that convert the class aaRS I into the class aaRS II and vice versa. We show that the four polar requirement categories display a symmetrical arrangement in our 6D hypercube. Altogether these results cannot be attained, neither in two nor in three dimensions. We discuss the present unified 6D algebraic model, which is compatible with both the SGC (based upon the primeval RNY code) and the RO-model.

No MeSH data available.


Six-dimensional hypercube of the SGC coloured by amino acid polar requirement values [41]. The four-dimensional hypercubes are yellow (upper); blue (left); red (lower); green (right); Stop codon are in black (UUA, UAG and UGA).
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RSOS160908F3: Six-dimensional hypercube of the SGC coloured by amino acid polar requirement values [41]. The four-dimensional hypercubes are yellow (upper); blue (left); red (lower); green (right); Stop codon are in black (UUA, UAG and UGA).

Mentions: PR was scaled into four categories [41]. We assign a particular colour (red, yellow, blue and green) to each scale. When such categories are set on the 6D genetic code, new symmetries emerge (figure 3). Now the SGC in six dimensions can be symmetrically divided into four colours according to the PR. Each category, or colour, comprises 16 codons that are arranged in 4D hypercubes, whose symmetry is given by the wreath product S2WrS4, where Sn is a permutation group of n elements [54]. Such group can be represented by the group of orthogonal matrices of 4 × 4 whose entries are all integers [54]. To interchange whole categories, it is sufficient to use the symmetries of a square (figure 3). Hence, the 6D representation of the SGC can reflect this property using its automorphisms as a biological classifier.Figure 3.


A unified model of the standard genetic code
Six-dimensional hypercube of the SGC coloured by amino acid polar requirement values [41]. The four-dimensional hypercubes are yellow (upper); blue (left); red (lower); green (right); Stop codon are in black (UUA, UAG and UGA).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5383835&req=5

RSOS160908F3: Six-dimensional hypercube of the SGC coloured by amino acid polar requirement values [41]. The four-dimensional hypercubes are yellow (upper); blue (left); red (lower); green (right); Stop codon are in black (UUA, UAG and UGA).
Mentions: PR was scaled into four categories [41]. We assign a particular colour (red, yellow, blue and green) to each scale. When such categories are set on the 6D genetic code, new symmetries emerge (figure 3). Now the SGC in six dimensions can be symmetrically divided into four colours according to the PR. Each category, or colour, comprises 16 codons that are arranged in 4D hypercubes, whose symmetry is given by the wreath product S2WrS4, where Sn is a permutation group of n elements [54]. Such group can be represented by the group of orthogonal matrices of 4 × 4 whose entries are all integers [54]. To interchange whole categories, it is sufficient to use the symmetries of a square (figure 3). Hence, the 6D representation of the SGC can reflect this property using its automorphisms as a biological classifier.Figure 3.

View Article: PubMed Central - PubMed

ABSTRACT

The Rodin–Ohno (RO) and the Delarue models divide the table of the genetic code into two classes of aminoacyl-tRNA synthetases (aaRSs I and II) with recognition from the minor or major groove sides of the tRNA acceptor stem, respectively. These models are asymmetric but they are biologically meaningful. On the other hand, the standard genetic code (SGC) can be derived from the primeval RNY code (R stands for purines, Y for pyrimidines and N any of them). In this work, the RO-model is derived by means of group actions, namely, symmetries represented by automorphisms, assuming that the SGC originated from a primeval RNY code. It turns out that the RO-model is symmetric in a six-dimensional (6D) hypercube. Conversely, using the same automorphisms, we show that the RO-model can lead to the SGC. In addition, the asymmetric Delarue model becomes symmetric by means of quotient group operations. We formulate isometric functions that convert the class aaRS I into the class aaRS II and vice versa. We show that the four polar requirement categories display a symmetrical arrangement in our 6D hypercube. Altogether these results cannot be attained, neither in two nor in three dimensions. We discuss the present unified 6D algebraic model, which is compatible with both the SGC (based upon the primeval RNY code) and the RO-model.

No MeSH data available.