Journal of Molecular Evolution

, Volume 80, Issue 2, pp 81–85 | Cite as

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

  • G. Bianciardi
  • L. Borruso
Letter to the Editor


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.


Nonlinear analysis Genomic sequences Random walks tRNA Molecular evolution Early evolution of life 


The “Genomic tRNA Database” (Chan and Lowe 2009),; SPLITSdb (Sugahara et al 2008),

  1. Adami C, Ofria C, Collier TC (2000) Evolution of biological complexity. PNAS 97(9):4463–4468PubMedCentralPubMedCrossRefGoogle Scholar
  2. Anastassiou D (2001) Genomic signal processing. IEEE Signal Proc 18(4):8–20CrossRefGoogle Scholar
  3. Arneodo A, Bacry E, Graves PV et al (1995) Characterizing long-range correlations in DNA sequences from wavelet analysis. Phys Rev Lett 74:3293–3296PubMedCrossRefGoogle Scholar
  4. Berger JA, Mitra SK, Carli M et al (2002) New approaches to genome sequence analysis based on digital signal processing. IEEE Workshop on GENSIPS:1–4Google Scholar
  5. Berger JA, Mitra SK, Carli M et al (2004) Visualization and analysis of DNA sequences using DNA walks. J Frankl Inst 341:37–53CrossRefGoogle Scholar
  6. Brock WA (1986) Distinguishing random and deterministic systems: abridged version. J Econ Theory 40:168–195CrossRefGoogle Scholar
  7. Ciccarelli FD, Doerks T, von Mering C et al (2006) Toward automatic reconstruction of a highly resolved tree of life. Science 311:1283–1287PubMedCrossRefGoogle Scholar
  8. Claverie J-M (1997) Computational methods for the identification of genes in vertebrate genomic sequences. Hum Mol Genet 6:1735–1744PubMedCrossRefGoogle Scholar
  9. Eigen M, Lindemann BF, Tietze M et al (1989) How old is the genetic code? Statistical geometry of tRNA provides an answer. Science 244:673–679PubMedCrossRefGoogle Scholar
  10. Fasold M, Langenberger D, Binder H et al (2011) DARIO: a ncRNA detection and analysis tool for next-generation sequencing experiments. Nucleic Acids Res 39:W112–W117PubMedCentralPubMedCrossRefGoogle Scholar
  11. Feller W (1968) An introduction to probability theory and its applications, 3rd edn., Wiley series in probability and mathematical statisticsWiley, Wiley Google Scholar
  12. Fujishima K, Kanai A (2014) tRNA gene diversity in the three domains of life. Frontiers Genet 5(142):1–11. doi: 10.3389/fgene.2014.00142 Google Scholar
  13. Gayle KP, Freeland SJ (2011) Did evolution select a nonrandom “alphabet” of amino acids? Astrobiology 11:235–240CrossRefGoogle Scholar
  14. Grassberger P, Procaccia I (1983) Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A 28:2591–2593CrossRefGoogle Scholar
  15. Haimovich AD, Byrne B, Ramaswamy R, Welsh WJ (2006) Wavelet analysis of DNA walks. J Comp Biol 13(7):1289–1298CrossRefGoogle Scholar
  16. Hamori E, Ruskin J (1983) H-curves, a novel method of representation of nucleotide series especially suited for long DNA sequences. J Biol Chem 258:1318–1327PubMedGoogle Scholar
  17. Higgs PG, Wu M (2012) The importance of stochastic transitions for the origin of life. Orig Life Evol Biosph 42:453–457. doi: 10.1007/s11084-012-9307-0 PubMedCrossRefGoogle Scholar
  18. Howland JL (2000) The surprising archaea. Oxford University Press, LondonGoogle Scholar
  19. Koonin EV, Yutin N (2014) The dispersed archaeal eukaryome and the complex archaeal ancestor of eukaryotes. Cold Spring Harb Perspect Biol 1–16. doi:  10.1101/cshperspect.a016188
  20. Mizrahi E, Ninio J (1985) Graphical coding of nucleic acid sequences. Biochimie 67:445–448CrossRefGoogle Scholar
  21. Press WH, Teukolsky SA (1992) Portable random number generators. Comput Phys 6:522–524CrossRefGoogle Scholar
  22. Rodin AS, Szathmáry E, Rodin SN (2011) On origin of genetic code and tRNA before translation. Biol Direct 6:14PubMedCentralPubMedCrossRefGoogle Scholar
  23. Sprott JC, Rowlands G (1995) Chaos data analyzer. Physics Academic Software, New YorkGoogle Scholar
  24. Videm P, Rose D, Costa F, Backofen R (2014) BlockClust: efficient clustering and classification of non-coding RNAs from short read RNA-seq profiles. Bioinformatics 30(21):274–282CrossRefGoogle Scholar
  25. Weiss O, Jiménez-Montaño MA, Herzelm H (2000) Information content of protein sequences. J Theor Biol 206:379–386PubMedCrossRefGoogle Scholar
  26. Wolf A, Swift JB, Swinney HL et al (1985) Determining Lyapunov exponents from a time series. Phys D 16:285–317CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Medical BiotechnologiesUniversity of SienaSienaItaly
  2. 2.Faculty of Science and TechnologyFree University of Bolzano/BozenBolzanoItaly

Personalised recommendations