Optimal Research On Protein Structure Prediction And Comparison

In 1980's, bioinformatics was regard as a new interdisciplinary field and widely studiedby scientists. The development of structure biology has attracted a great deal of attention inbioinformatical research. It offers challenge to Operations Research in finding biological rules bysimple mathematical model and extracting knowledge from vast biomedical data. Consideringthe complexity of biology system in essence and the lack of complete theory in life science,it is a matter of primary importance to establish the effective mathematical optimal modeland employ the resultful optimistic algorithm. In this disseration, these improtant problemsrelated with the protein structure are investigated from mathematical optimal viewpoint. Themain works include that the mathematical models of protein structure prediction problem andprotein structure comparison problem are established respectively, and numerical simulation oftwo problems are implemented by the corresponding algorithms constructed.The disseration includes five chapters, which is summarized as follows:In Chapterâ… , the actuality and main research objects of bioinformatics are instroduced,which shows theoretical significance and pratical value of research. The relationship of pro-tein structure with protein sequence and protein function is summarized. The five subjectsresearched heatedly of protein structure are generalized in bioinformatical field, which are pro-tein structure confirmation, protein structure comparision, protein structure prediction, proteinstructure classification and interaction of proteins.Chapterâ…¡, as preliminaries, introduces several algorithms which will be used to solveprotein structure prediction problem and protein structure comparison problem and notationsof these methods. These methods are Elastic Net Algorithm, Dynamical Programming andComplete Information Set Method, respectively.The chapterâ…¢focuses on a simple model of protein structure prediction, which is to foldthe amino acid sequenc on the lattice. In the past, researchers mainly pay attention to algorithmsand numerical results. In this disseration, based on the thought of mathematical optimizationtheory, 2D HP model and 3D HP model are established, respectively. Some properties of modelsare proved about the feasible region, the objective function and optimal solution.The elastic net algorithm is modified in Chapterâ…£. Then it is applied to obtain theminimal free energy conformation of amino acid sequence on the lattice for the first time. Thelattice partition strategy and local search methodes are proposed to improved the performance of the modified elastic net algorithm. On the 2D compact HP lattice model, 2D noncompactHP lattice model and 3D cubic lattice model, the computation and analysis of several HPBenchmark instances are involved. The results show that our algorithm can find states of aminoacid sequencs with lower free energy. The hybrid of these methods is suitable for the generaldiscrete matching problem. At last, the designability of the protein strucure is analysed betweenthe compact model and incompact model.In the final Chapter, the protein structure comparison is studied. By Completed Infor-mation Set of protein chain, the sequences are abstracted as completed characteristic set. Themathematical optimal model is established by taking the discrepancy value of two sequences asobjective function and the quatities and position of gaps inserted in sequences as variables. Theexistence of optimistic solution for model is proved. The hybrid of improved complete informa-tion set method and double dynamic programming is employed to solve the protein structurecomparison problem. The protein sequence information is combined with the protein structureinformation ideally.