| 摘要: | 由於過去在實驗上能夠對於一條具有螺旋結構的去氧核醣核酸(DNA)長鏈的彈 性有所了解，因此希望從理論及電腦模擬的方面來進一步探討。在這篇論文中， 利用蒙地卡羅法(Monte-Carlo Simulations)及一個粗粒化的高分子晶格模型—鍵 振盪模型(Bond Fluctuation Model)，來研究一條具有螺旋狀的高分子長鏈在外部 拉力下，伸長量與拉力的關係。除了在拉力較小時滿足Hook’s law 線性關係的 範圍外，我們主要針對拉力較大時滿足Pincus law 非線性關係的範圍，也就是伸 長量與拉力成指數關係。這個非線性關係遵守尺度定律(Scaling law)，可由尺度 函數(Scaling function)來描述，並且此非線性關係與所使用的模型無關。比較之 前研究一條柔軟高分子長鏈的結果，我們模擬結果顯示一條較硬的高分子長鏈其 從線性到Pincus 之間的範圍較小。此外，我們利用扭曲度(Writhe)，鍵向量相關 連函數(Correlation Function of Bond vectors)及改變鍵角(Bending angle)與扭角 (dihedral angle)方向的硬度來描述對螺旋結構的變化，特別是描述一條從無序結 構到有螺旋結構的高分子長鏈。因此，從模擬結果也可以了解在外部拉力下具有 螺旋狀的高分子長鏈的幾何結構變化。 In the past decade, advances in experimental techniques using magnetic beads, optical tweezers, or shear flow made it feasible for detailed experimental studies of the conformations of single long molecules, especially in helical double-stranded DNA molecules, so we hope to realize it more theoretically and by simulations. In the thesis, the static properties of a single stiff helical polymer chain under stretching is investigated by Monte Carlo simulations with the bond-fluctuation model. The primary purpose is to describe the change of conformations and the persistence length of a helical chain due to the rigidity of the chain and measure the extension of the chain under an external stretching force. We attempt to employ the measures such as the correlation function of bond vectors, average of the Writhe, radius gyrations, dihedral angles and bending angles to describe the helical structures. At the high scaled temperatures, the chain behaves like a disordered coil chain, however, at low scaled temperatures, the local he lical structures emerge. This properties can be verified by the above the measured quantities. As for stretching the helical polymer chain, we focus deformation of the chain on the linear force regime and non-linear Pincus regime mainly because both of the regimes have the universal scaling behaviors. We observed that the width of the regime from the linear to Pincus behaviors for the chain with the rigidity parameter becomes more narrow than one of the flexible chain involving only excluded volume interactions. Finally, our simulation data also show the changes of geometry such as sinθ, sinψ, writhe, and the pitch due to the stretching force. |
