arXiv 1503.010232015-03cond-mat.softmath-phmath.MP

半柔性聚合物的圆柱约束

Cylindrical confinement of semiflexible polymers

Pablo Vázquez-Montejo, Zachary McDargh, Markus Deserno, Jemal Guven

备注：: 33 pages, 16 figures
发表信息：: Phys. Rev. E 91, 063203 (2015)
DOI：: 10.1103/PhysRevE.91.063203

摘要：

本文描述了封闭半柔性高分子与圆柱体结合的平衡态。这可能是通过限制或通过收缩。封闭的完全束缚态由两个整数标记：振荡的次数，$n$，和它缠绕圆柱的次数，$p$，后者是拓扑不变量。我们研究这些状态的行为，作为循环的长度增加，通过评估的能量，保守的轴向扭矩和接触力。给定$p$的基态是具有$n=1$的状态;具有$p=1$的短环是平行线的椭圆变形;随着其长度的增加，它沿着圆柱轴伸长，具有两个发夹末端。具有$n\geq2$和$p=1$的激发态具有$n$折叠轴对称性。短（长）环具有能量$\approx p E_0$（$nE_0$），其中$E_0$是具有与圆柱体相同半径的圆形环的能量;在长环中，轴向扭矩为零。受限的束缚激发态最初是不稳定的;然而，在临界长度以上，每个$n$折叠状态变得稳定：折叠的发夹不能被展开。每个$p$的基态最初也是不稳定的，相对于变形旋转环离开表面进入内部。一个封闭的平面弹性曲线沿圆柱轴对齐，使其两侧的圆柱接触被确定为一个封闭的回路的基态。外部束缚态的行为非常不同，如果自由解除束缚，如接触力符号的反转所示。如果是$p=1$，则所有这些状态都是不稳定的。然而，如果是$p \geq 2$，则存在完全解除绑定的拓扑障碍。如果环很短，则与$p=2$和$n=1$的结合状态提供了圆柱体的稳定收缩，随着长度的增加部分解除结合。这一主题可能与理解发动蛋白环介导的膜分裂过程有关。

英文摘要：

Equilibrium states of a closed semiflexible polymer binding to a cylinder are described. This may be either by confinement or by constriction. Closed completely bound states are labeled by two integers: the number of oscillations, $n$, and the number of times it winds the cylinder, $p$, the latter a topological invariant. We examine the behavior of these states as the length of the loop is increased by evaluating the energy, the conserved axial torque and the contact force. The ground state for a given $p$ is the state with $n=1$; a short loop with $p=1$ is an elliptic deformation of a parallel; as its length increases it elongates along the cylinder axis, with two hairpin ends. Excited states with $n\geq2$ and $p=1$ possess $n$-fold axial symmetry. Short (long) loops possess energies $\approx p E_0$ ($nE_0$), with $E_0$ the energy of a circular loop with same radius as the cylinder; in long loops the axial torque vanishes. Confined bound excited states are initially unstable; however, above a critical length each $n$-fold state becomes stable: the folded hairpin cannot be unfolded. The ground state for each $p$ is also initially unstable with respect to deformations rotating the loop off the surface into the interior. A closed planar elastic curve aligned along the cylinder axis making contact with the cylinder on its two sides is identified as the ground state of a confined loop. Exterior bound states behave very differently, if free to unbind, as signaled by the reversal in the sign of the contact force. If $p=1$, all such states are unstable. If $p \geq 2$, however, a topological obstruction to complete unbinding exists. If the loop is short, the bound state with $p=2$ and $n=1$ provides a stable constriction of the cylinder, partially unbinding as the length is increased. This motif could be relevant to an understanding of the process of membrane fission mediated by dynamin rings.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文