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標題: | 生物分子化學主方程式之理論計算和模擬 Simulation and Theoretical Computation for Chemical Master Equation of Biomolecules |
作者: | Guan-Rong Huang 黃冠榮 |
指導教授: | 陳義裕(Yih-Yuh Chen) |
關鍵字: | 生物化學主方程式,布朗運動,隨機動力學,蛋白質,核醣核酸,有限差分, Chemical Master Equation,Brownian Motion,Stochastic Dynamics,Protein,DNA,mRNA,Finite difference, |
出版年 : | 2012 |
學位: | 碩士 |
摘要: | 目前為止,在物理上最廣泛應用是古典力學與量子力學。其中,量子是非決定性的,來自於物質的波粒二像性;古典是決定性的,可以明確決定一個物體的軌跡方程式。而隨機動力學是介於古典力學與量子力學之間,在某些例子中已經被證明等價。本篇論文探討DNA-mRNA-蛋白質過程,由於分子濃度很稀,系統的反應由碰撞主導;這過程可視為隨機過程,可以被伊藤引理描述。利用不同的物理想法,應用隨機動力學的方程式,組合出不同的化學主方程式。並且經由解析計算與數值方法模擬,了解蛋白質反應的機制與過程。 Chemical reactions of biomolecules in a very dilute solution are studied in which the potential energy between molecules can be ignored. Both the number of molecules and the number of collisions between molecules are large numbers, so that chemical reactions of the system can be considered as a drift-diffusion stochastic process described by Ito's lemma and Kolmogorov forward equation which led to chemical master equation (CME) and Hamilton-Jacobi equation (HJE). The Van Kampen model with a coefficient a for reaction term is used to simulate numerically the CME of DNA-mRNA-protein of linear-drift process by deterministic finite difference method to obtain the same steady states as those derived from non-deterministic method: Gillespie's algorithm (Gillespie, 1977). Finally, a diffusion term with a coefficient ϵ is added to modify the original CME. The revised equation is solved analytically and numerically again. The solution shows the competition between two phases separated by a critical value of a_c: a diffusion phase and a chemical reaction phase. The probability density function (PDF) of the former is Gaussian and PDF of the later is Gamma distribution. Our results are useful for solving a famous paradox in chemical reactions. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/16321 |
全文授權: | 未授權 |
顯示於系所單位: | 物理學系 |
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