Comparison And Evolution Analyse Of Protein And RNA Structures

With the development of human genome project and proteomics project, it brings a great lot of biological sequences and molecule structure data. To analyze and interpret these data becomes an important task of molecule biology. Molecule structures gave more evident effect on biological activity and function than biological sequences, while the understand of molecule structures and function is less than that of biological sequences. Therefore, it is a very basic and important topic to compare and analyze molecule structures by mathematical and computational methods.The main contents of this thesis are list as follows:In Chapter 2, we consider a characterization of the folding of 3-D model proteins by the partial order relation. In this characterization, we describe the different kinds of 3-step path conformation, then construct an augmented Hasse matrix which reflects some properties of the protein folding. This method can characterize the folding degree of 3-D model proteins and evaluate the similarity/diversity of these five model proteins.Topology of protein structure (TOPS) are simplified descriptions of structural topology of proteins in 2-D. This is a coarse level description of protein structures. The comparison of protein structures is very important for the study of protein functions, and for the analysis of possible evolutionary relationships. In Chapter 3, we give LZ complexity of TOPS strings, define the distances between them, and analyze the possible evolutionary relationships of 36 protein structures.In Chapter 4, In terms of the classification of the protein secondary structures, i.e.,α-helix,β-strand and coil, we propose a 2-D "three horizontal lines" graphical representation of protein secondary structure sequences. The representation are used to display, analyze, and compare the secondary structure sequences. Based on this representation, we assign the structural class to the protein, and verify the advantage or disadvantage of the methods of predicted protein second structure.In the last chapter, we propose a 3-D representation of RNA secondary structures. Based on this representation, we outline an approach by constructing a 3-component vector whose components are the normalized leading eigenvalues of the L/L matrices associated with RNA secondary structure. The examination of similarities/dissimilarities among the secondary structure at the 3'-terminus of different viruses illustrates the utility of the approach.