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Title page for etd-0914110-162400


URN etd-0914110-162400 Statistics This thesis had been viewed 1431 times. Download 9 times.
Author Siang-Ning Zeng
Author's Email Address No Public.
Department Math
Year 2009 Semester 2
Degree Master Type of Document Master's Thesis
Language English Page Count 58
Title The study on combinatorial properties of RNA secondary structures
Keyword
  • RNA secondary structure
  • saturated structure
  • pseudoknot
  • generating function
  • schröder number.
  • schröder number.
  • generating function
  • pseudoknot
  • saturated structure
  • RNA secondary structure
  • Abstract RNA (Ribonucleic acid) is an important molecule in the cell, which participates in a lot of basic biological functions including regulation of DNA replication, synthesis of protein, and construction of RNA virus. The study of RNA has become a popular research topic. Unlike the helix structure of DNA, various structures can be formed by an RNA primary structure. Since most functions of RNA depend on their secondary structures, the enumeration of RNA secondary structures is very important.
    In this thesis, we study combinatorial properties of RNA secondary structures. In the first part, we simplify the element definitions of RNA secondary structures so that they can be well-classified. We also propose skeleton trees to concisely represent the classes. By generating functions, we enumerate various classes of RNA secondary structures and point out incorrect results in literatures. In addition, some classes of RNA secondary structures with pseudoknots are enumerated.
    In the second part, we concentrate on saturated RNA secondary structures. A saturated secondary structure is an RNA structure in which no additional basepair can be added. In the Nussinov-Jacobson free energy model, a secondary structure with maximum number of basepairs will have minimum free energy, and thus is most stable so that it is called an optimal structure. A t-saturated secondary structure contains  fewer basepairs than an optimal one. In this thesis, we study properties of saturated secondary structures, enumerate near-optimal t-saturated secondary structures, and extended study some related topics.
    Advisor Committee
  • Hsun-Wen Chang - advisor
  • Files indicate in-campus access only
    Date of Defense 2010-06-21 Date of Submission 2010-09-14


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