臺灣博碩士論文加值系統

基因調控是生物一項重要且十分複雜的過程，因為它取決很多的因素，而本篇內容著重於基因調控網路其基因表現過程內雜訊的討論。基因調控網路中轉錄因子的生成、解離可以用反應速率方程式來描述，在此我們藉著一個雙穩態的模型，建構出其所對應的兩種隨機微分方程式Langevin equation 及Fokker-Plank equation。搭配這兩個隨機微分方程並用數值模擬的方式，我們計算系統內在雜訊對穩態間跳躍所需的平均時間與接通率，並進行進一步的討論、分析。

Gene regulation is a very complicated and important biological process for which, there are many factors involved. In this thesis, we investigate the effect of intrinsic noise in the process of genetic regulation. The synthesis and dissociation of Transcription Factors can be mathematically described by rate equation. To include the effect, we combine the two stochastic equation, Langevin equation and Fokker-Plank equation, in a bi-stable regulation model with two stochastic differential equations, we can calculate the mean first-passage time and switch rate between bi-stable states numerically. Further analysis of the results are also given.

目錄
中文摘要..................................................I
Abstract.................................................II
目錄....................................................III
圖目錄...................................................IV
表目錄....................................................V
第一章 簡介 .............................................1
第二章 模型系統及其定性分析 .............................5
2-1一維模型及其雙穩態 .........................5
2-2 Langevin方程式 ...........................11
2-3 Fokker-Plank方程式 .......................15
第三章 平均首通時間及接通率 ............................20
第四章 討論與結論 ......................................31
參考文獻.................................................32

圖目錄
圖1 正向調控與負向調控示意圖.............................2
圖2 正向的基因調控網路模型...............................6
圖3 轉錄因子濃度x與其等效位能U(x)關係圖.................9
圖4 分子數的流入與流出..................................16
圖5 穩態間的差..........................................19
圖6 擴散係數倒數1/D與接通率，x_s1→x_s2..................22
圖7 擴散係數倒數1/D與接通率，x_s2→x_s1..................23
圖8 系統體積倒數1/Ω與平均接通時間，x_s1→x_s2............26
圖9 系統體積倒數1/Ω與平均接通時間，x_s2→x_s1............26
圖10 系統體積Ω與接通率，x_s1→x_s2.........................27
圖11 系統體積Ω與接通率，x_s2→x_s1.........................27
圖12 不同體積Ω下，Fokker-Plank equation的位能圖.........30

表目錄
表1 Fokker-Plank equation在不同Ω下，其對應的穩定與不穩定的平衡態...........................................18

[1]駒野徹、酒井裕，分子生物學入門,科技圖書,2002
[2]M.Ptashne,“A Genetic Switch: Phage λ and Higher
Organisms”, 2nd ed.(Cell Press and Blackwell Science,
Cambrdge, MA, 1992)
[3]Paul Smolen, D.A. Baxter and J.H. Byrne, Am. J. Physiol.
274, C531 (1998)
[4] G.W. Gardiner, Handbook of Stochastic Methods, 2nd ed. 1990
(Spriger)
[5]W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P.
Flannery, Numerical Recipes in Fortran, Cambridge
University Press, 1992.
[6]H. Risken, The Fokker-Plank Equation,3nd ed.1996(Springer)
[7]D.T. Gillespie. J. Phys. Chem.81, 2340 (1977)
[8]Quan Liu, Ya Jia, Phys. Rev. E70,041907 (2004)
[9]D. Chandler, Chapter 3 in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B.J. Berne, G. Ciccotti, and D.F. Coker (World Scientific, Singapore,1998), pgs. 51-66
[10]Gavin E. Crooks and David Chandler, Phys. Rev. E64 , 026109
(2001)
[11]Christoph Dellago, Peter G. Bolhuis, and David Chandler.
J. Chem. Phys., Vol. 110, No. 14, 8 April 1999