Rauscher Phillip M, Rowan Stuart J, de Pablo Juan J
Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA.
Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA.
Phys Rev E. 2020 Sep;102(3-1):032502. doi: 10.1103/PhysRevE.102.032502.
Despite decades of interdisciplinary research on topologically linked ring polymers, their dynamics remain largely unstudied. These systems represent a major scientific challenge as they are often subject to both topological and hydrodynamic interactions (HI), which render dynamical solutions either mathematically intractable or computationally prohibitive. Here we circumvent these limitations by preaveraging the HI of linked rings. We show that the symmetry of ring polymers leads to a hydrodynamic decoupling of ring dynamics. This decoupling is valid even for nonideal polymers and nonequilibrium conditions. Physically, our findings suggest that the effects of topology and HI are nearly independent and do not act cooperatively to influence polymer dynamics. We use this result to develop highly efficient Brownian dynamics algorithms that offer enormous performance improvements over conventional methods and apply these algorithms to simulate catenated ring polymers at equilibrium, confirming the independence of topological effects and HI. The methods developed here can be used to study and simulate large systems of linked rings with HI, including kinetoplast DNA, Olympic gels, and poly[n]catenanes.
尽管对拓扑连接的环形聚合物进行了数十年的跨学科研究，但其动力学在很大程度上仍未得到研究。这些系统是一项重大的科学挑战，因为它们常常受到拓扑相互作用和流体动力学相互作用（HI）的影响，这使得动力学解决方案在数学上难以处理或在计算上令人望而却步。在这里，我们通过对连接环的HI进行预平均来规避这些限制。我们表明，环形聚合物的对称性导致环动力学的流体动力学解耦。这种解耦即使对于非理想聚合物和非平衡条件也是有效的。从物理角度来看，我们的发现表明拓扑和HI的影响几乎是独立的，并且不会协同作用来影响聚合物动力学。我们利用这一结果开发了高效的布朗动力学算法，该算法比传统方法具有巨大的性能提升，并应用这些算法来模拟处于平衡状态的连环环形聚合物，证实了拓扑效应和HI的独立性。这里开发的方法可用于研究和模拟具有HI的连接环的大型系统，包括动质体DNA、奥林匹克凝胶和聚[n]索烃。
