标题： 双折叠随机分支环状聚合物的涌现动力学 显示英文标题

标题： The emergent dynamics of double-folded randomly branching ring polymers

摘要： 随机分支双折叠环状聚合物的统计特性与RNA的二级结构、螺旋DNA的大规模分支（因此包括细菌染色体）、单环状聚合物通过障碍物阵列时的构象，以及真核染色体和皱缩的非连接环状聚合物熔体的构象统计有关。 双折叠环状聚合物根据双折叠所依赖的随机树状图是淬火的还是退火的，以及这些树状图是否可以在其空间嵌入中自由进行布朗运动，而属于不同的动力学普适类。 在局部上，可以区分（i）围绕固定树的类似repton的质量传输，（ii）侧枝的自发生成和删除，以及（iii）树节点的位移，在这种情况下互补的环段在空间中一起扩散。 在这里，我们采用适合的弹性晶格聚合物模型的动态蒙特卡洛模拟，研究了不同组合的上述局部模式在三种不同系统中的介观动力学：理想不相互作用的环、自避环以及熔融状态下的环。 我们观察到了环状物的蛇形运动的预期标度区域，双折叠环在障碍物阵列中的动力学，以及Rouse-like树状动力学作为极限情况。 特别值得注意的是，对于具有$\nu=1/3$的皱缩环，$g_1\sim t^{0.4}$的单体均方位移类似于细菌染色体中观察到的亚扩散区域。 在我们的分析中，我们关注不同局部动力学模式对涌现动力学的贡献在多大程度上是简单的叠加。 值得注意的是，当所有三种类型的局部运动都存在时，我们揭示了相互作用环的动力学出现了非平凡的加速。 显示英文摘要

摘要： The statistics of randomly branching double-folded ring polymers are relevant to the secondary structure of RNA, the large-scale branching of plectonemic DNA (and thus bacterial chromosomes), the conformations of single-ring polymers migrating through an array of obstacles, as well as to the conformational statistics of eukaryotic chromosomes and melts of crumpled, non-concatenated ring polymers. Double-folded rings fall into different dynamical universality classes depending on whether the random tree-like graphs underlying the double-folding are quenched or annealed, and whether the trees can undergo unhindered Brownian motion in their spatial embedding. Locally, one can distinguish (i) repton-like mass transport around a fixed tree, (ii) the spontaneous creation and deletion of side branches, and (iii) displacements of tree node, where complementary ring segments diffuse together in space. Here we employ dynamic Monte Carlo simulations of a suitable elastic lattice polymer model of double-folded, randomly branching ring polymers to explore the mesoscopic dynamics that emerge from different combinations of the above local modes in three different systems: ideal non-interacting rings, self-avoiding rings, and rings in the melt state. We observe the expected scaling regimes for ring reptation, the dynamics of double-folded rings in an array of obstacles, and Rouse-like tree dynamics as limiting cases. Of particular interest, the monomer mean-square displacements of $g_1\sim t^{0.4}$ observed for crumpled rings with $\nu=1/3$ are similar to the subdiffusive regime observed in bacterial chromosomes. In our analysis, we focus on the question to which extent contributions of different local dynamical modes to the emergent dynamics are simply additive. Notably, we reveal a non-trivial acceleration of the dynamics of interacting rings, when all three types of local motion are present.