Nonlinear Analysis of tRNAs Nucleotide Sequences by Random Walks: Randomness and Order in the Primitive Informational Polymers

In order to test the hypothesis that the nucleotide sequences of the primitive informational polymers might not be chosen randomly and in the attempt to compare among taxa, we propose a comparison of computer-generated random sequences with tRNAs nucleotide sequences present in the bacterial and archaeal genomes, being tRNAs molecules possible “fossils” of the time (billions years ago) in which life arose. Our approach is based on the analysis of sequences of tRNAs described as random walks and the distances from the origin evaluated by the use of nonlinear indexes (largest Lyapunov exponent, entropy, BDS statistic). Six different tRNAs of Bacteria and Archaea (ten Archaea and ten Bacteria, thermophilic and mesophilic ones; n = 120), and computer-generated random sequences (n = 50) were studied. Our data show that tRNAs present indices statistical lower than the ones of computer-generated random data (tRNAs own a more ordered sequence than random ones: Lyapunov, p < 0.01; entropy, p < 0.05; BDS, p < 0.01). The observed deviation from pure randomness should be arisen from some constraints like the secondary structure of this biologic macromolecule and/or from a “frozen” stochastic transition, or even from the possible peculiar origin of tRNA by replication of older proto-RNA. Comparing between taxa, in the species studied, Bacteria present BDS and Base ratio (G+C)/(A+T) indexes statistically lower than in Archaea, together which a 20 % of entropy increase. The analysis of a greater number of tRNAs and species will permit to explain if this finding, showing a higher randomness in the bacterial tRNAs sequences, is linked to the different base ratio, to the different environments in which the microorganisms live or to an evolutionary effect.