Emergence of a code in the polymerization of amino acids along RNA templates

Abstract

The origin of the genetic code in the context of an RNA world is a major problem in the field of biophysical chemistry. In this paper, we describe how the polymerization of amino acids along RNA templates can be affected by the properties of both molecules. Considering a system without enzymes, in which the tRNAs (the translation adaptors) are not loaded selectively with amino acids, we show that an elementary translation governed by a Michaelis-Menten type of kinetics can follow different polymerization regimes: random polymerization, homopolymerization and coded polymerization. The regime under which the system is running is set by the relative concentrations of the amino acids and the kinetic constants involved. We point out that the coding regime can naturally occur under prebiotic conditions. It generates partially coded proteins through a mechanism which is remarkably robust against non-specific interactions (mismatches) between the adaptors and the RNA template. Features of the genetic code support the existence of this early translation system.

Figure 1. Model of the elementary translation system.

(a) Synthetase with cognate tRNA (structure 1ZJW from Protein Data Bank). (b) Kinetic scheme of the elementary translation process. Two types of tRNAs (complementary to two template codons) are unselectively loaded with two types of amino acids (the rates of loading are only concentration-dependent). The grey rugby ball is a stabilizing cofactor (see text for explanations). (c) Characteristic regimes of the polymerization process.

Figure 2. Relative abundance of primitive amino acids.

Relative abundance of the 10 most frequent amino acids of the genetic code synthesized in an experiment thought to reproduce the conditions of the prebiotic Earth. Graph established from the data of Table 3 in ref. .

Figure 3. Effect of the local environment on a reaction rate.

Relative reaction rates (k _rel) of a bimolecular reaction and some corresponding intramolecular reactions. In the intramolecular systems, the nucleophilic attack (indicated by a small arrow in compound I) leads to the cyclization of the compounds. Adapted from ref. .

Figure 4. Amino acids side-chains and kinetics of peptide bond formation.

Elementary translation and expected effect of the side-chains of alanine, glycine, aspartic acid and valine on the kinetics of peptide bond formation (k _cat) (discussed in the text).

Figure 5. Regimes of the polymerization process.

(a) Effect of the value of the ratio k _cat(1)/k _−(I) on the polymerization process: p(1|I) and p(2|II) as a function of b for three significant values of d when a = 10² and c = 10⁻². When d = 1, either homopolymerization of aa₂ (b<1), or random polymerization (b≫1) are observed. When d = 0.1, a coding regime Σ = 0.835 is observed at the transition between two types of homopolymerization, which occurs at b = 1. When d = 0.01, either random polymerization (b≪1) or homopolymerization of aa₁ (b>1) are observed. (b) Level of coding Σ as a function of c when a = 10² and d = 10⁻¹. Three significant values of Σ are indicated. The inset shows a plot similar to (a) for three particular values of c (reported from the main graph).

Figure 6. Effect of mismatches on the polymerization process.

Probabilities p(1|I)* and p(2|II)* as a function of b for five values of e≤1 (a = 10²; b = 1; c = 10⁻²; d = 0.1). This diagram shows that the intersection between p(1|I)* and p(2|II)* (which defines the coding regime Σ*) is only slightly affected by mismatches, as long as the dissociation constant of these mismatches (k _−(mm)) remains equal (e = 1) or higher (e<1) than the highest dissociation constant of the complementary matches (k _−(II)).