負值的固有曲率對二維半柔性生物高分子力學性質的影響

Effect of a negative intrinsic curvature on the mechanical property of a two dimensional semiflexible biopolymer.

陳柏翰(Bo-Hen Chen)

指導教授 ： 周子聰

淡江大學/理學院/物理學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00228

摘要

在二維的非格點系統(non-lattice system)中，我們用蒙地卡羅法(Monte Carlo method)研究負值的固有曲率(negative intrinsic curvature)對一個二維半柔性生物高分子(semiflexible biopolymers)彈性模型之力學性質的影響，並將其結果與蠕蟲鏈模型(Worm-Like Chain -WLC)做比較。
　　當固有曲率為負值時，我們可以證明兩個模型的基態是相同的，且兩個模型有很強的相似性，其中「有很強的相似性」的意思是指：在有限溫度下，對Model 2任意給定負值的固有曲率c、彎曲剛度 k2 後，總可以在Model 1中找到一個對應的彎曲剛度 k1，使得兩個模型的力學性質(如：相對伸長量與力的關係、端點座標y分量的平方平均值與力的關係)在實際情形下難以區分，兩模型以力為函數的平均能量僅差一個常數。
　　我們的結果說明負值的固有曲率在Model 2中扮演了提高有效彎曲剛度的角色。在很強相似性的條件下，格點系統(lattice system)與非格點系統(off-lattice system)的固有曲率c與有效彎曲剛度k1皆呈線性關係，但格點系統與非格點系統的線性關係斜率不同，在相同的k2時，在格點系統中斜率變化比較大。

關鍵字

非格點系統 ； 蠕蟲鏈模型(WLC) ； 負值的固有曲率 ； 半柔性生物高分子 ； 蒙地卡羅法 ； 力學性質

並列摘要

We studied the effect of a negative intrinsic curvature on the mechanical property of a two dimensional semiflexible biopolymer in two-dimensional off-lattice system by Monte Carlo method, and compare the results with that of the worm-like chain model.
　　We can prove that the ground state of the two models are the same, and at finite temperature the two models are almost indistinguishable, when the intrinsic curvature is negative. Where the "indistinguishable" mean that for any given negative intrinsic curvature c and bending rigidity k2 in the Model 2, we can always find a corresponding bending rigidity k1 in the Model 1, so that in experiment the mechanical properties, such as the relationship between extensions and force, the vs force, etc., of two models are difficult to distinguish, where yN is the component of position vector of the endpoint, and the mean energy of two models are differed by a constant only.
　　Our results indicate that the negative intrinsic curvature in the model 2 plays a role in increasing the effective bending rigidity. We also find that when the mechanical properties are almost indistinguishable, the bending rigidity k1 and the intrinsic curvature c have linear relation, in both the lattice system and off-lattice system. However, the slope of the linear relationship between lattice system and off-lattice system is not the same. With the same k2, the change in slope of the lattice system is relatively large.

並列關鍵字

off-lattice system ； worm-like chain(WLC) ； negative intrinsic curvature ； semiflexible biopolymers ； Monte Carlo method ； mechanical property

參考文獻

[35] 戴偉帆, 一個二維半柔性生物高分子模型的基本物理性質, 淡江大學 (2011).

[36] 吳浩雲, 一維和二維半柔性生物高分子之力學性質, 淡江大學 (2013).

[11] A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu Opt. Lett. 11 (1986), 288.

[23] P. P. Boyle, Journal of Financial 4 (1977), 323.

[1] Philip Nelson, Biological Physics: Energy, Information, Life, (W. H. Freeman and Co, New York and Basingstoke, 2004).