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Distribution of Graph-Distances in Boltzmann Ensembles of RNA Secondary Structures

  • Rolf Backofen
  • Markus Fricke
  • Manja Marz
  • Jing Qin
  • Peter F. Stadler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8126)

Abstract

Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be separated by very long introns. Similar effects appear in the processing of RNA virus genomes. Albeit a crude measure, the distribution of spatial distances in thermodynamic equilibrium therefore provides useful information on the overall shape of the molecule can provide insights into the interplay of its functional domains. Spatial distance can be approximated by the graph-distance in RNA secondary structure. We show here that the equilibrium distribution of graph-distances between arbitrary nucleotides can be computed in polynomial time by means of dynamic programming. A naive implementation would yield recursions with a very high time complexity of O(n 11). Although we were able to reduce this to O(n 6) for many practical applications a further reduction seems difficult. We conclude, therefore, that sampling approaches, which are much easier to implement, are also theoretically favorable for most real-life applications, in particular since these primarily concern long-range interactions in very large RNA molecules.

Keywords

Secondary Structure Partition Function Graph Distance Inside Path Boltzmann Ensemble 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Rolf Backofen
    • 1
    • 2
  • Markus Fricke
    • 3
  • Manja Marz
    • 3
  • Jing Qin
    • 4
  • Peter F. Stadler
    • 4
    • 5
    • 6
    • 7
    • 8
  1. 1.Department of Computer Science, BioinformaticsUniversity of FreiburgFreiburgGermany
  2. 2.Center for Biological Signaling Studies (BIOSS)Albert-Ludwigs-UniversitätFreiburgGermany
  3. 3.Bioinformatics/High Throughput Analysis Faculty of Mathematics und Computer ScienceFriedrich-Schiller-University JenaJenaGermany
  4. 4.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  5. 5.Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for BioinformaticsUniversity of LeipzigLeipzigGermany
  6. 6.Fraunhofer Institut for Cell Therapy and ImmunologyLeipzigGermany
  7. 7.Institute for Theoretical ChemistryUniversity of ViennaViennaAustria
  8. 8.Santa Fe InstituteSanta FeUSA

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