|Abstract: ||在自由空間中的半柔性生物高分子已經有相當多的研究，但是實際上生物高分子大多是受約 束的，而相關的理論研究並不多。例如在所有的柱狀細胞中都有MreB 及其同源體。這些分子本質 上是直的，但在細胞內卻能以螺旋形狀出現。這種分子如何形成一個穩定的螺旋是一個有趣的未解 決問題。最近我發現要使這種螺旋穩定必須考慮排斥體積效應，並它固定在圓柱面上。我還發現排 斥體積效應將導致螺旋在一定壓力下崩塌。 然而還有許多相關的問題並未解決。首先，以前的研究都在外力不變的條件下進行的。但在 細胞裡，更合理的不變量是伸長量。其次，形狀與外部條件關係之相圖尚為未知。第三，螺旋崩塌 之動力學過程也還是個問題。第四，我們尚未考慮熱效應。在考慮溫度影響後我們的主要結論是否 仍然不變亦為令人感興趣之問題。還有，除去MreB 之細胞形狀將轉為球形，這種轉變之過程亦令 人很感興趣。 另外一個受約束的系統是二維系統。最近我已發表了兩篇相關論文。然而，一個具常數或序 列相關之固有曲率的生物高分子在有限溫度及中等大小外力下的力學性質尚屬未知。還有，對短 DNA 分子而言，理論所得到的成圈機率仍然遠低於實驗值。 在新計劃裡我將研究這些問題。 同時，我對其他相關問題亦有興趣。例如蛋白質折疊，DNA 之變性，高分子之斷裂、穿透， 等等。|
Title: Physics of confined semiflexible biopolymer In theoretical studies, a semiflexible biopolymer is often modeled by a filament. Filaments in free space have been extensively studied theoretically. In contrast, there are fewer theoretical works on the confined system. However, the semiflexible biopolymers in vivo are in general subjected to various constraints. Especially, MreB and MreB homologs, which are intrinsically straight filament, are found in all rod-shaped bacteria, and can be a helix within the cell. How can such an intrinsically straight filament form a stable helix insider bacteria is therefore a significant issue, but there is not yet a proper theoretical explanation. Recently, I have showed exactly to have a stable helix it is necessary to consider the excluded-volume effect (EVE) and to confine the filament on the cylinder. Furthermore, I found that EVE can result in the collapse in extension of the filament. However, there are still many open questions in this topic. First, previous works focus on the system under constant forces. But in cell, the end-to-end distance of a filament is more likely to be fixed. Second, a phase diagram indicating the conditions of different configurations is a necessity for the fully understanding of the problem. Third, the dynamical process of the collapse in extension is also very interesting. Fourth, the thermal effect was not yet considered, and would the main characteristics of our results still be observed at finite temperature is also a significant topic. Fifth, when the MreB filaments are removed from a cell, the shape of the cell will change from a cylinder into a sphere. The process of such a transition is also intriguing. Another simple confined system is the two-dimensional system. Recently I have published two relevant papers [Phys. Rev. E 76, 061913(2007); Phys. Rev. E 80, 061911(2009)]. However, there are still many unsolved problems. At first, the mechanical response of a filament, either with constant intrinsic curvature or with sequence-dependent intrinsic curvatures, to the moderate force at finite temperature remains unknown. Moreover, while the classical theory was proposed more than two decades ago, the discrepancy for the looping probability of a short dsDNA between theory and the experiment still reaches several orders of magnitude. I found that the existing theories considered only the equilibrium distribution, but the loop forming may be more likely a dynamical process. On the other hand, the local large intrinsic curvatures may have strong effects on the looping probability, but up to now nobody considered such an effect. In the new plan, I am going to explore the above problems. Moreover, I am also interested in some other relevant problems, such as protein folding, denaturation of the dsDNA, rupture of a biopolymer, translocation of a biopolymer. If it is possible, I will also do some researches on these topics.