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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/16321完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳義裕(Yih-Yuh Chen) | |
| dc.contributor.author | Guan-Rong Huang | en |
| dc.contributor.author | 黃冠榮 | zh_TW |
| dc.date.accessioned | 2021-06-07T18:09:41Z | - |
| dc.date.copyright | 2013-03-06 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-10 | |
| dc.identifier.citation | [1] K. Ito, Proc. Imperial Acad. (Tokyo) 20, 519-524 (1944).
[2] L. Onsager and S. Machlup, Phys. Rev. 91, 1505-1512 (1953). [3] H. Haken, Zeit. Physik B 24, 321-326 (1976). [4] H. Dekker, Phys. Rev. A 19, 2102-2111 (1979). [5] G. Hu, Chinese Phys. Lett. 2, 217 (1988). [6] M. I. Dykman, Eugenia Mori, John Ross, and P. M. Hunt, J. Chem. Phys. 100 (8), 5735-5750 (1994). [7] C. Escudero and A. Kamenev, Phys. Rev. E 79, 041149 (2009). [8] M. Assaf and B. Meerson, Phys. Rev. E 81, 021116 (2010). [9] A. Martirosyan and D. B. Saakian, Phys. Rev. E 84, 021122 (2011). [10] S. Karlin and H.M. Taylor, A First Course in Stochastic Processes, 2nd ed. (Acad- emic Press, New York, 1975). [11] S. Karlin and H.M. Taylor, A Second Course in Stochastic Processes, 2nd ed. (Ac- ademic Press, New York, 1980). [12] H. Goldstein, Classical Mechanics, 3rd ed., P. 368-374, P. 430-434 (Addison –We- sley Pub, 2000). [13] H. Ge and H. Qian, Analytical Mechanics in Stochastic Dynamics: Most Probable Path, Large-Deviation Rate Function and Hamilton-Jacobi Equation (2011). [14] N. G. Van Kampen, Stochastic Process in Physics and Chemistry (North-Holland, Elsevier Science, 2007). [15] S. R. S. Varadhan, Comm. Pure Appl. Math. 19, 261-286 (1966). [16] N. Friedman, L. Cai, and X. S. Xie, Phys. Rev. Lett. 97, 168302 (2006). [17] L. Cai, N. Friedman, and X. S. Xie, Nature (London) 440, 358 (2006). [18] F. Hayot and C. Jayaprakash, A tutorial on cellular stochasticity and Gillespie’s al- gorithm (2006). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/16321 | - |
| dc.description.abstract | 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。 | zh_TW |
| dc.description.abstract | 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. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-07T18:09:41Z (GMT). No. of bitstreams: 1 ntu-101-R99222064-1.pdf: 786409 bytes, checksum: d7598b4fd7e2649fc2efdc42da409e0a (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 口試委員會審定書 #
誌謝 i 中文摘要 ii ABSTRACT iii CONTENTS iv LIST OF FIGURES vi LIST OF TABLES vii Chapter 1 Introduction 1 Chapter 2 Diffusion Process 6 2.1 Brownian Motion 7 2.2 Ito’s Lemma 10 2.3 Kolmogorov Forward Equation 14 Chapter 3 Hamilton-Jacobi Equation 18 3.1 Canonical Transformation 19 3.2 Hamilton-Jacobi Equation 20 3.3 Large Deviation Rate Function 22 Chapter 4 Formulism of Chemical Master Equation 26 4.1 CME in Physical Opinion 26 4.2 Linear-Drift Gaussian Process 28 4.3 Path Integral For Probability of Chemical Reaction 31 4.4 Van Kampen Model with Poisson Noise 33 Chapter 5 Solution to CME 37 5.1 Finite Difference Method 37 5.2 No Diffusion Term 42 5.3 With Diffusion Term 48 Chapter 6 Conclusion 60 Chapter 7 References 61 Chapter 8 Appendix 62 8.1 The Coefficients of Forward Differences 62 8.2 Series Expansion of Kummer’s Function 63 | |
| dc.language.iso | en | |
| dc.subject | 隨機動力學 | zh_TW |
| dc.subject | 生物化學主方程式 | zh_TW |
| dc.subject | 布朗運動 | zh_TW |
| dc.subject | 蛋白質 | zh_TW |
| dc.subject | 核醣核酸 | zh_TW |
| dc.subject | 有限差分 | zh_TW |
| dc.subject | Stochastic Dynamics | en |
| dc.subject | Finite difference | en |
| dc.subject | mRNA | en |
| dc.subject | DNA | en |
| dc.subject | Protein | en |
| dc.subject | Brownian Motion | en |
| dc.subject | Chemical Master Equation | en |
| dc.title | 生物分子化學主方程式之理論計算和模擬 | zh_TW |
| dc.title | Simulation and Theoretical Computation
for Chemical Master Equation of Biomolecules | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 胡進錕(Chin-Kun Hu),余瑞琳(Jui-Ling Yu) | |
| dc.subject.keyword | 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, | zh_TW |
| dc.subject.keyword | Chemical Master Equation,Brownian Motion,Stochastic Dynamics,Protein,DNA,mRNA,Finite difference, | en |
| dc.relation.page | 63 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2012-07-10 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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| ntu-101-1.pdf 未授權公開取用 | 767.98 kB | Adobe PDF |
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