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Phylogeny and Evolution of RNA Structure

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RNA Sequence, Structure, and Function: Computational and Bioinformatic Methods

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1097))

Abstract

Darwin’s conviction that all living beings on Earth are related and the graph of relatedness is tree-shaped has been essentially confirmed by phylogenetic reconstruction first from morphology and later from data obtained by molecular sequencing. Limitations of the phylogenetic tree concept were recognized as more and more sequence information became available. The other path-breaking idea of Darwin, natural selection of fitter variants in populations, is cast into simple mathematical form and extended to mutation-selection dynamics. In this form the theory is directly applicable to RNA evolution in vitro and to virus evolution. Phylogeny and population dynamics of RNA provide complementary insights into evolution and the interplay between the two concepts will be pursued throughout this chapter. The two strategies for understanding evolution are ultimately related through the central paradigm of structural biology: sequence ⇒ structure ⇒ function. We elaborate on the state of the art in modeling both phylogeny and evolution of RNA driven by reproduction and mutation. Thereby the focus will be laid on models for phylogenetic sequence evolution as well as evolution and design of RNA structures with selected examples and notes on simulation methods. In the perspectives an attempt is made to combine molecular structure, population dynamics, and phylogeny in modeling evolution.

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Notes

  1. 1.

    Sequences are ordered strings of elements s k (k = 1, …, l), which in case of RNA are chosen from the alphabet \(\mathcal{A} =\{ \mbox{ A,U,C,G}\}\). The notions of sequence space and structure or shape space are essential for the definition of structure and function as results of mappings.

  2. 2.

    For convenience we define \(\boldsymbol{\pi }\) as column vector but to save space we write it as a transposed row vector \(\boldsymbol{\pi }^\prime\).

  3. 3.

    Exceptions are only very special sequences, homopolynucleotides, for example.

  4. 4.

    Timescale number one is the evolutionary process itself. In order to be relevant for evolutionary dynamics the second timescale has to be substantially faster than the first one.

  5. 5.

    By definition of fitness values, f i  ≥ 0, and mutation frequencies, Q ji  ≥ 0, W is a non-negative matrix and the reachability condition boils down to the condition: Wk ≫ 0, i.e., there exists a k such that Wk has exclusively positive entries and Perron–Frobenius theorem applies [88].

  6. 6.

    An exact calculation of \(\bar{f}_{-m}\) is difficult because it requires knowledge of the stationary concentrations of all variants in the population: \(\bar{x}_{i};\, x = 1,\ldots,n\). For computational details see [23, 89, 91, 92].

  7. 7.

    It should be noted that artificially synthesized two letter (DU; D = 2,6-diamino-purine) ribozymes have perfect catalytic properties [93].

  8. 8.

    Zero or negative concentrations of sequences clearly contradict the exact results described above and are an artifact of the perturbation approach. Nevertheless, the agreement between the exact solutions and the perturbation results up to the error threshold as shown in Fig. 15 is remarkable.

  9. 9.

    The seed s indeed defines all details of the landscape that in turn is completely defined by s and the particular type of the pseudorandom number generator.

  10. 10.

    Several measures for the distance between structures can be applied. Here we have chosen the Hamming distance between the parentheses notation of structures, d S.

  11. 11.

    The smallness record is currently hold by Nanoarchaeum equitans with a genome size of 490,885 base pairs.

  12. 12.

    An early paper [168] claimed that zero fitness values are incompatible with the existence of quasispecies and error threshold. The result, however, turned out to be an artifact of a rather naıve linear sequence space , since later works demonstrated that selection and mutation on realistic sequence spaces sustain error thresholds also in the presence of lethal variants [113, 114].

  13. 13.

    Random replication expresses the fact that error accumulation destroys the relation between template and copy and inheritance is no longer possible.

  14. 14.

    The variants ara + and ara − differ in a single point mutation and in the capacity to utilize arabinose as nutrient. In growth media free of arabinose the mutation \(ar{a}^{+} \leftrightarrow ar{a}^{-}\) is neutral [173].

  15. 15.

    Most Escherichia coli strains are unable to live on citrate buffer because they have no mechanism for uptake of citrate or citric acid into the cell. The growth medium used by Lenski et al. in the long time evolutions experiment contained citrate buffer for pH control.

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Acknowledgements

The authors wish to express their gratitude to Carolin Kosiol for helpful discussions. T.G. is funded by a mobility fellowship of the Austrian genome research program GEN-AU and the GEN-AU project “Bioinformatics Integration Network III.”

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Authors and Affiliations

  1. Department of Structural and Computational Biology, University of Vienna, Vienna, Austria

    Tanja Gesell

  2. University of Vienna, Vienna, Austria

    Peter Schuster

  3. Santa Fe Institute, Santa Fe, NM, USA

    Peter Schuster

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  1. Tanja Gesell
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Editors and Affiliations

  1. Center for non-coding RNA in Technology and Health, IKVH University of Copenhagen, Frederiksberg, Denmark

    Jan Gorodkin

  2. University of Washington Dept. Computer Science & Engineering, Seattle, Washington, USA

    Walter L. Ruzzo

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Gesell, T., Schuster, P. (2014). Phylogeny and Evolution of RNA Structure. In: Gorodkin, J., Ruzzo, W. (eds) RNA Sequence, Structure, and Function: Computational and Bioinformatic Methods. Methods in Molecular Biology, vol 1097. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-709-9_16

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  • DOI: https://doi.org/10.1007/978-1-62703-709-9_16

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