Limits...
A unified model of the standard genetic code

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.


Representation of the action of the generators of the group over the set of nucleotides, where a represents transversions and b transitions. Purines are coloured in yellow and pyrimidines in green.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5383835&req=5

RSOS160908F1: Representation of the action of the generators of the group over the set of nucleotides, where a represents transversions and b transitions. Purines are coloured in yellow and pyrimidines in green.

Mentions: The genetic code is then represented as a 6D hypercube. This geometric figure can also be interpreted as a graph G = (V, E) of vertices, representing the codons, and edges, joining the codons at distance one, making it possible to analyse its symmetries through the group of automorphisms of the graph. This group consists of all the bijective functions of the graph G, that preserve its adjacencies. With the metric defined above, these automorphisms comprise all the isometric transformations of the cube. It is worth mentioning that there are, in essence, only three different Cayley graphs that determine the action of the group over the nucleotides. The pairs of opposite edges of the graph chosen here (figure 1) represent the generators of the group (transversions and transitions), which is in agreement with a common evolutionary interpretation [51]. In our previous approach [16,21,24], the distance of a codon and its anticodon in the 6D hypercube is at the maximum distance of 6. It is worth remarking that, if the Cayley graph associated with our previous works is used, the interchange of the action a for ab, and ab for a, applied as described above, will result in the same conclusions. Hence, the two approaches do not contradict each other, neither in biological aspects nor in mathematical ones, owing to the fact that with the present approach the ordering of nucleotides and arbitrary binary assignments are not required. In fact, the four nucleotides A,C,G,U can be situated at the vertices of a given rectangle in 4! = 24 ways. Interestingly, the assumption that a and b represent transversion and transition, respectively, being a the transversion that converts each nucleotide into its complementary, reduces all the possible graphs to only three.Figure 1.


A unified model of the standard genetic code
Representation of the action of the generators of the group over the set of nucleotides, where a represents transversions and b transitions. Purines are coloured in yellow and pyrimidines in green.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSOS160908F1: Representation of the action of the generators of the group over the set of nucleotides, where a represents transversions and b transitions. Purines are coloured in yellow and pyrimidines in green.
Mentions: The genetic code is then represented as a 6D hypercube. This geometric figure can also be interpreted as a graph G = (V, E) of vertices, representing the codons, and edges, joining the codons at distance one, making it possible to analyse its symmetries through the group of automorphisms of the graph. This group consists of all the bijective functions of the graph G, that preserve its adjacencies. With the metric defined above, these automorphisms comprise all the isometric transformations of the cube. It is worth mentioning that there are, in essence, only three different Cayley graphs that determine the action of the group over the nucleotides. The pairs of opposite edges of the graph chosen here (figure 1) represent the generators of the group (transversions and transitions), which is in agreement with a common evolutionary interpretation [51]. In our previous approach [16,21,24], the distance of a codon and its anticodon in the 6D hypercube is at the maximum distance of 6. It is worth remarking that, if the Cayley graph associated with our previous works is used, the interchange of the action a for ab, and ab for a, applied as described above, will result in the same conclusions. Hence, the two approaches do not contradict each other, neither in biological aspects nor in mathematical ones, owing to the fact that with the present approach the ordering of nucleotides and arbitrary binary assignments are not required. In fact, the four nucleotides A,C,G,U can be situated at the vertices of a given rectangle in 4! = 24 ways. Interestingly, the assumption that a and b represent transversion and transition, respectively, being a the transversion that converts each nucleotide into its complementary, reduces all the possible graphs to only three.Figure 1.

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.