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研究生:王聖成
研究生(外文):Sheng-Cheng Wang
論文名稱:DNA序列的長程相干與可能的電子傳導
論文名稱(外文):Long Range Correlation and Possible Electron Conduction through DNA Sequences
指導教授:李秉政
指導教授(外文):Ping-Cheng Li
學位類別:博士
校院名稱:國立中興大學
系所名稱:物理學系所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:130
中文關鍵詞:長程相干緊束模型電子波函數
外文關鍵詞:long range correlationtight binding modelElectronic wavefunctions
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主旨在於利用長程相干與電荷傳導性來研究細菌基因組和病毒序列,首先藉由赫斯特指數(Hurst exponent)分析以及去趨勢漲落分析(DFA)來解析DNA序列數據的長程相干。酵母菌16對染色體的赫斯特指數測量值在0.6左右,故明顯地有超擴散現象;去趨勢漲落分析也得到相同的結果。第二部分則使用緊束模型(Tight binding model)來研究DNA序列中的電荷傳輸,觀察到16對染色體之總平均傳輸係數 與隨機序列和週期序列有明顯的區別,其中發現具有較佳長程相干性的序列,其電荷傳導性也較優。研究同時也利用這模型計算局域化電子波函數,並將16對染色體與隨機序列之相同本徵能量的電子波函數作比較。最後,由粗粒化組態分布來看DNA序列的本質性。
Long range correlation analysis and charge conductivity investigation are applied to sequences in some bacteria genome and virus. DNA sequence data are analyzed via Hurst’s analysis and Detrended Fluctuation Analysis (DFA) analysis. Super diffusive nature of mapping sequences are evident with measured Hurst exponent H to be around the value of 0.60 for all sequences in the Saccharomyces cerevisiae 16 chromosomes. The DFA result is consistent with the result from the Hurst analysis. Tight binding model are applied for the investigation of charge conduction through DNA sequences. The overall averaged transmission coefficients, , calculated from sixteen chromosomes are shown significantly different from values calculated from random as well as periodic sequences. Sequences had better long range correlation promise better charge conduction ability than random sequences. Delocalized electronic wave function patterns are also shown through calculations using tight binging model. Electronic wavefunctions are seen on sequences in sixteen chromosomes as compared with those obtained from random sequences on the same eigenenergies. Finally Coarse-grained configuration distribution showed the intrinsic property of DNA sequences.
論文中文摘要……………………………………………………………i
論文英文摘要……………………………………………………………ii
目錄……………………………………………………………………iii
表目錄……………………………………………………………………iv
圖目錄……………………………………………………………………v

第一章 緒論………………………………………………………………1
1.1 DNA的簡介……………………………………………………………1
1.1.1中心法則(Central Dogma) ………………………………………1
1.1.2 DNA和RNA…………………………………………………………2
1.2 GenBank資料庫………………………………………………………4
1.3 研究動機與緣起……………………………………………………4

第二章DNA的長程相干(Long Range Correlation)…………………6
2.1 DNA行走的標準差(DNA Walk Standard Deviation)……………8
2.2 R(n)(Rescaled range function)………………………………19
2.3 DFA(Detrended Fluctuation Analysis) ………………………27

第三章 DNA導電性.……………………………………………………35
3.1 DNA是否導體………………………………………………………35
3.2 緊束模型(Tight Binding Model) ……………………………36
3.2.1 緊束模型的電導………………………………………………36
3.2.2 傳輸係數(Transmission Coefficient) TN(E) ……………38
3.2.3安德森局域化(Anderson Localization)……………………44
3.2.4 波函數的平均半徑二階矩……………………………………46
3.2.5 反傅利葉轉換(Inverse Fourier Transform) ………………48
3.2.6 能階統計(Level Statistics) ………………………………51

第四章 DNA其他的統計…………………………………………………55
4.1 粗粒化組態分佈(Coarse-grained configuration distribution)…………………………………………………………55
4.2 夏倫熵(Shannon entropy)─Hn…………………………………61
4.3 廣義熵(Generalized entropy)…………………………………64
4.4 相互信息函數(Mutual information Function) ………………73

第五章 結論……………………………………………………………82

參考文獻…………………………………………………………………83
附錄一 電腦產生的亂數………………………………………………88
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