Elsevier

Biosystems

Volume 111, Issue 3, March 2013, Pages 175-180
Biosystems

Research article
Codon–anticodon interaction and the genetic code evolution

https://doi.org/10.1016/j.biosystems.2013.02.004Get rights and content

Abstract

The evolution of the genetic code, with 20 amino acids encoded from the beginning, is analyzed from the viewpoint of codon–anticodon interaction. Imposing a minimum principle for the interaction, in the framework of the so called crystal basis model of the genetic code, we determine the structure of the anticodons in the ancient, archetypal and early genetic codes, that are all reconciled in a unique frame. Most of our results agree with the generally accepted scheme.

Introduction

For long time the genetic code was thought to be immutable. Now it is commonly believed that the genetic code has undergone (and is undergoing) an evolutionary process, see Knight et al. (2001) for a review, even if there is not a unique theory of the evolution.

It has been proposed that the evolution of the genetic code is based on the “codon capture theory”, see Ohama et al. (2008) for a recent review. In this scheme, the number of the encoded amino acids (a.a.) is kept constant and equal to 20 and the coding codons change in the evolution, a key role in this process being played by the anticodon. Inside the scheme of the fixed, from the very beginning, total number of a.a., it has been proposed a mechanism for the reassignment of the codons, alternative to the codon capture theory, called “ambiguous intermediate scenario” (Schultz and Yarus, 1996). The main difference between the two schemes is that in the former “codon disappearance” by mutation pressure is assumed while in the latter an anticodon can read more than one codon. A comparison between that two schemes based on a physical model is presented in Yamashita and Narikiyo (2011).

One can distinguish two important steps in the genetic code evolution, characterized by the Ancient Genetic Code later followed by the Early one. An alternative primordial code has been proposed by Jukes (1983) and called “archetypal genetic code”, in which only sixteen anticodons are involved.

Recently, we have proposed a minimum principle for the codon–anticodon interaction (Sciarrino and Sorba, 2012), in the framework of the so called “crystal basis model” of the genetic code (Frappat et al., 1998). The aim of the present paper is to analyze and to mathematically model the evolution of the genetic code on the light of the scheme proposed in Sciarrino and Sorba (2012).

Examining each of the mentioned genetic codes from the codon–anticodon interaction, itself evolving in time, we propose a mathematical scenario exhibiting the successive passages from the ancient to the archetypal code and then to the Early one, thus conciliating these three codes.

For completeness, we shortly recall the main ideas of the model introduced in Frappat et al. (1998). In that paper we have proposed a mathematical framework in which the codons appear as composite states of nucleotides. The four nucleotides being assigned to the fundamental irreducible representation (irrep.) of the quantum group Uq(su(2)su(2)) in the limit q  0, the codons are obtained as tensor product of nucleotides. Indeed, the properties of quantum group representations in the limit q  0, or crystal basis, are crucial to take into account the fact that a codon is an ordered triple of nucleotides. The nucleotide content of the (JH = 1/2, JV = 1/2) (fundamental) representation of Uq0(su(2)su(2)), i.e. the eigenvalues of JH,3, JV,3, is chosen as follows:

C+12,+12U12,+12G+12,12A12,12where the first su(2) – denoted su(2)H – corresponds to the distinction between the purine bases A, G and the pyrimidine ones C, U and the second one – denoted su(2)V – corresponds to the hydrogen bond complementarity rule C/G and U/A. Thus to represent a codon, we have to perform the tensor product of three (1/2, 1/2) or fundamental representations of Uq0(su(2)su(2)) and we get the results, reported in Table 1.

In the following, whenever ambiguity may arise, we denote the quantities which refer to anticodons (codons) with an upper label a (respectively c). The minimum principle introduced in Sciarrino and Sorba (2012) assumes that an anticodon WZaXa pairs to the codon XZN, where ZaXa = ZcXc (Nc denotes the nucleotide complementary to the nucleotide N according to the Watson–Crick pairing rule), if it minimizes the operator T, explicitly written in Eq. (2) and computed between the “states”, which can be read from Table 1, describing the codon and anticodon in the “crystal basis model”.

T=8cHJHc·JHa+8cVJVc·JVawhere cH, cV are constants a priori depending on the “biological species” and on the encoded a.a., JHc,JVc (resp. JHa,JVa) are the labels of Uq→0(su(2)H  su(2)V) specifying the state (Frappat et al., 1998) describing the codon XZN (resp. the anticodon WZcXc pairing the codon XYZ) and which can be read from Table 1, Jαc·Jαa (α = H, V) should be read as

JαcJαa=12JαcJαa2Jαc2Jαa2and JαcJαaJαT stands for the irrep. which the codon and anticodon states under consideration belongs to, the tensor product of Jαc and Jαa being performed according to the rule of Kashiwara (1990), choosing the codon as first vector and the anticodon as second vector. Note that Jα2 should be read as the Casimir operator whose eigenvalues are given by Jα(Jα + 1).

We write both codons and anticodons in the 5″→3″ direction. As an anticodon is antiparallel to its corresponding codon, the 1st nucleotide (respectively the 3rd nucleotide) of the anticodon is paired to the 3rd (respectively the 1st) nucleotide of the codon. We assume that the second and third nucleotide of an anticodon are always the complementary of, respectively, the second and first nucleotide of the corresponding codon, in agreement with most of the experimental observations.

Let us remark that in our approach we have mainly followed some simple assumptions, which we still keep in the present work:

  • we have assumed a simple YES or NO model, i.e. the only anticodon chosen is the one which minimizes the interaction. Indeed one should consider that a codon is chosen with a probability related to the value of the interaction,

  • in the choice of the solutions we have independently minimized each term depending on cH and cV to prevent solutions depending on a fine tuning between the two constants. The values of the constants, even if not explicitly indicated in order not to make heavier the notation, depend from the multiplet encoding a determined a.a.,1

  • we have assumed the codon usage frequency as a fixed external data. This is not correct as the usage of a particular codon depends on the total G+C content and on the presence and abundance of the anticodon(s) which can match with. Indeed the frequency of the codon and the frequency of the anticodon are related by a kind of “bootstrap” relation, i.e. by a self-consistent process ruled by the reciprocal effects codon–anticodon.

Finally, let us emphasize that we are not addressing the very crucial issue of the optimality of the genetic code. We recall that in Sciarrino (2003) a mathematical model, always in the framework of the “crystal basis model”, has been presented in which the main features (numbers of encoded a.a., dimensions and structure of synonymous codon multiplet) are obtained, requiring stability of the genetic code against mutations, modeled by suitable operators, and we will make a few comments in the conclusions.

Section snippets

The evolution of the genetic code

In this Section we discuss in our scheme the evolution from the ancient code to the early one, very similar to the mitochondrial one.

Discussion and conclusions

Let us discuss and comment our results. The pattern of the ancient code, as reported in Table 2 of Ohama et al. (2008), can be summarized by saying that in this primordial code the a.a., which would be encoded by a doublet of the type XZY are encoded by a codon ending with a C. Similarly the a.a. which would be encoded by a doublet of the type XZR are encoded by a codon ending with a G.

As already remarked by merely considering the hydrogen bond between the nucleotides, there is no reason for

Acknowledgments

We are indebted to the referees for their remarks and suggestions, in particular, we warmly thank a referee for suggesting the figure illustrating in Table 5.

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