一個二維半柔性生物高分子模型的基本物理性質

Basic physical properties of a model for two-dimensional semiflexible biopolymer

10.6846/TKU.2011.00276

戴偉帆

半柔性生物高分子 ； 計算機模擬 ； 分子結構 ； semiflexible biopolymers ； computer simulation ； configurations

淡江大學物理學系碩士班學位論文

2011年

碩士

周子聰

繁體中文

我們用布朗動力學的方法研究一個二維半柔性生物高分子的新模型在有限溫度下的基本物理性質。新模型採用了一個尚未見報導過的最近鄰交互作用位能，該位能對最近鄰粒子的距離有比較強的限制，因此有可能更好地近似高分子中最近鄰分子的共價鍵。 本工作主要是測試及修改新程式，因此尚未考慮外力的作用及固有曲率的影響。通過監控模擬過程中物理量的穩定性，我們確定了在溫度範圍(0.01，0.2)內使系統(即分子鍊)處於穩定的狀態所需要的模擬參數，即步距，總步數及總樣品數。我們確認了端點粒子的x座標平均值，平均端點距離以及平均迴轉半徑皆隨溫度上升而減小，符合由於在常溫下熵主導高分子之行為，因此高分子傾向於捲曲成團之行為，由此亦可證實程式應該是正確的。我們發現分子鍊的迴轉半徑有反常行為，其原因尚有待於進一步考察。我們的模擬結果表明平均端點距離與平均迴轉半徑呈現一定的比例。該比例常數隨溫度增加而緩慢改變。

Using Brownian dynamics, we study the basic physical properties of a new model for two-dimensional semiflexible biopolymers at finite temperature. The new model adopts a new nearest neighbor interaction. The new potential has stronger constraint on the distances between nearest monomers, therefore may provide a better approximation to the biopolymers with covalent-bond between the nearest-neighbor monomers. This work focuses on the testing and modifying the new program, and has not yet considered the influences of the external force and the intrinsic curvatures. By monitoring some quantities in simulation, we find the proper simulation parameters (the time step, total simulation time and number of samples) in the temperature range (0.01, 0.2) for our system (a chain of monomers). We find that the mean x-coordinate of the end particle, the mean end-to-end distance and the mean radius of gyration decrease with increasing temperature. These results agree with the well known fact that the entropy dominates the behavior of the biopolymers at normal temperature, and provide evidences for the correctness of the program. We also find that the radius of gyration of the chain has abnormal behavior, but the origin of the abnormal behavior is still unclear so requires a further investigation. Moreover, our results indicate that there is linear relation between the mean end-to-end distance and the mean radius of gyration, and the proportional constant increases slowly with increasing temperature.

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1. 陳柏翰(2015)。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。淡江大學物理學系碩士班學位論文。2015。1-52。 
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