The Enumeration Of RNA Secondary Structure

RNA molecular is composed of the four nucleotids A, C, G, U. RNA secondary structure is a single-stranded chain of the nucleotide in which part of the molecule can base-pair with a complementary nucleotide in another part by folding oneself.Based on the relationship between the structure and function, a lot of research have been performed on predicting base-pair which is indispensable to the RNA three-dimensional strcutrue. The tools and methods in Combinatorics and Statistics will play important roles in studying linear sequences of biomolocular units . Similarly, we can present the geometric representation of biological sequences and structures. So the genometric topology and group theory are important also.Predicting all the RNA secondary structures is to calculate the best structures of the sequences of given length. At present it is very difficult to predict all the RNA secondary structures. So it is the mathematical mission to predict all the RNA secondary structures of given length. This thesis mainly make a further discussion about the enumeration of RNA secondary structure. The main contents of the thesis can be summarized as follows:In Chapter 2, we introduce some basic knowledge of molecular biology. Most of the terms and concepts used in this paper are explained briefly here.In Chapter 3, some information of the RNA secondary structure is introduced in detail, such as denotation of RNA,the cardinal principle, some basic definitions and so on. Then a common enumeration problem of RNA secondary structure and substructure is studied with the method of combinatorial enumeration.In Chapter 4, there are two important structures, loops and stacks for an abstract single-strand RNA. Based on the method of combinatorial enumeration, we make a new discussion about the enumeration problem and get its approximation with the limited length of end loop.