| 摘要: | 由於其在許多生物過程中扮演的重要角色，半柔軟的生物高分子的形狀和力學性質近年來吸引了相當多的關注。單分子技術上的進展，也提供了人們直接操控和觀察單個生物分子的彈性性質的強大工具。理論上，經常使用細長桿作為研究生物分子的模型。在我最近的一篇論文中(Phys. Rev. E, in press)，我研究了一根有均勻自發曲率的二維細長桿的形狀及其力學性質。我推導出了細長桿的穩定形狀所滿足的方程式，並求出了其解析解。在有限溫度下，我推導出其配分函數所滿足的微分方程，並且求出了不受外力時配分函數的解析解。在受到很小的外力和很大的外力的情況下，我也求出了細長桿力與伸長的關係。在新的計畫中，我將拓展之前的工作以考慮成圈效應、排斥體積效應、鹼基對的長程關聯的效應，以及在有限溫度下，受到中等外力拉伸時細長桿的彈性性質。 另一方面，螺旋是自然界中最簡單常見的形狀，因此形成螺旋所需的條件，以及螺旋的穩定性和彈性性質，都是相當有趣的問題。在我最近的兩篇論文中[Phys. Rev. E 71, 052801(2005); Modern Physics Letters B21, 1895-1913 (2007)]，我推導出一根具有自發曲率和自發扭曲的細長桿的形狀方程，並且為零溫下螺旋的力學性質提供了一個完整的圖像。在新的計畫裡，我將從靜態和動態兩方面來研究，形成不同於螺旋的其他形狀的條件及其相關的穩定性。我也將研究溫度對螺旋力學性質的影響。 再者，構成生物分子的單體間的交互作用如何導致一個螺旋形狀的機制，是相當重要的基本問題。在絕大多數的模型中，一個最基本的假設就是：「一個等向性的單體交互作用，不足以產生穩定的螺旋。」然而，最近一篇論文的模擬結果顯示，一個等向性的單體交互作用也能導致穩定的螺旋。這兩種模型所產生的螺旋的力學性質的是否有差異，是一個很值得研究的課題。 同時，在基因表達的調控，以及折疊 DNA 進入細胞核等生物過程中，雙股 DNA 分子必須彎折成圈。瞭解 DNA 成圈的基本物理機制，對於這類生物過程的定量描述是必要的。但是到目前為止，各種理論所得到的成圈機率仍然遠低於實驗的觀測值。我將著手研究dsDNA成圈的動力學過程，以及局域性的自發曲率對於成圈機率的影響。
The conformational and mechanical properties of semiflexible biopolymers have attracted considerable attentions due to its importance in understanding many biological processes. Recent progresses in single molecule techniques have provided powerful tools to manipulate and observe directly the elastic behavior of a single biomolecule. In theoretical studies, a biopolymer is often modeled by a filament. In a recent paper (Phys. Rev. E, in press), I have studied the conformal and mechanical properties of a two-dimensional filament with constant spontaneous curvature. I derived the equation that governs the stable shape of the filament and obtain analytical solutions for the equation. At finite temperature, I derived the differential equation that governs the partition function and find exact solution of the partition function for a filament free of force. I also obtained closed-form expressions on the force-extension relation for a filament under low force and for a long filament under strong stretching force. In the new plan, I will extend my previous work and consider the effects of looping, excluded volume and long-range correlation in basepairs of dsDNA, as well as the elastic response to the moderate force at finite temperature. On the other hand, the conditions to form a helix from a rod and its relevant stability and elasticity are in particular interesting topics since the helix is one of most simple filamentary structures found in nature. In my two recent papers [Phys. Rev. E 71, 052801(2005); Modern Physics Letters B21, 1895-1913 (2007)], I have derived the general shape equations in terms of the Euler angles for a uniform rod with spontaneous torsion and curvatures, and provided a full picture for the conformal and mechanical properties of a helix at zero temperature. In the new plan, I am going to investigate the conditions of the transition and the relevant stability, both static and dynamical, of the shapes other than helix. I will also study thermal effects on a helix. Moreover, the essential mechanism of how a helical polymer arises from the basic interactions between its constituent monomers is of great fundamental interest. An underlying assumption in the vast majority of these models is: ‘‘an isotropic potential interaction is not sufficient to produce helical ground states.’’ However, a recent work presents simulation results for a polymer model using only pairwise isotropic monomer interactions, and demonstrates that this model can form stable helices. Whether there is any difference on conformal and mechanical properties between these two models is a significant topic and I am going to explore it. Meanwhile, bending of double-stranded dsDNA molecules into loops is important for such biological processes as regulation of gene expression and DNA packaging into nucleosomes. Understanding the underlying physics of DNA looping is necessary for any quantitative description of these biological processes. However, the theoretical expectations for the looping probability are still far smaller than experimental observations. I am going to approach the dynamical process of loop formation, and the effects of the local spontaneous curvature on the looping probability. |
