組合學在計算分子生物學的應用

Abstract

這個研究的主旨是在於應用圖論演算法與組合設計來研究並解決計 算分子生物學中的一些問題。 計算分子生物學(Computational Molecular Biology)是近十年來發展最 為快速，影響最深遠的一門科學。由於人們對人體基因排列有著更深入了 解的期待，希望能夠經由對它的了解而能利用這些知識來做更有益於人類 福祉的工作，例如，疾病的預防與治療，有機體的複製。因此，近十多年 來，投入生物相關研究的人力與物力均大幅增加；而數學家也有大的比例 參與相關研究。由於，在比對DNA 數列時，電腦扮演非常重要的角色， 實驗設計也不惶多讓，所以，離散數學自然扮演著非常重要的角色。於是， 組合數學中的幾個重要分枝(Disciplines)，圖論、組合設計、演算法等紛紛 派上用場，來協助完成預期的工作。我們期望未來的三年能有具體的貢獻。

This study focuses on the applications of graph theory, algorithms and combinatorial designs in solving the problems occurring in computational molecular biology. Because of the effort on accomplishing Human Genome Project, computational molecular biology becomes one of the most important topics in sciences (mathematical science). Moreover, the outcome of this research has a tremendous impact on the real world, namely, improvement of diagnosis of disease, design of drugs based on individual genetic profiles, development of new energy befuels and organic cloning etc. Since the object is to chart human DNA, to position genes, the job can not be accomplished without using those tools developed from discrete mathematics. Starting from the first step, genetic mapping, the notion from graph theory－interval graph and algorithms play a key role. In a word, there are quite a few problems in molecular biology which can be modeled and solved by using combinatorial disciplines. Therefore, in this three years’ project, we shall work on both of“finding better techniques＂and“applying combinatorics＂in order that some known problems in molecular biology can be solved or achieved a better solution comparing to an earlier one.