Large-Scale Monte-Carlo Simulations of Biopolymer Systems using Event-Chain Algorithms

本项目的总体目标是将事件链MC算法推广到聚合物系统中的各种应用，例如细胞骨架纤维系统，以便为这类重要的系统开发一种新的有效方法。除了模拟半柔性聚合物外，由无限细针或具有显式交联剂或分支剂（如ARP 2/3）的聚合物系统组成的聚合物，甚至三角化的弹性表面/胶囊也可以在一般的通用事件链框架中进行模拟。我们预期效率会显著提高。提高采样效率是一个持续的努力，在这个课题上我们将与Prof. Krauth和Dr. Michel合作。作为模拟聚合物网络的先驱，我们将研究（接近）平衡，均匀和等热带（半柔性）聚合物熔体作为初始构型的产生。可选的交换运动和ECa在致密体系中的优势应该使研究这种熔体的凝固成为可能。我们建议研究的主要系统是处于平衡状态的聚合物网络，其中吸引相互作用由一般均匀的方阱势或（瞬态）交联剂或分支剂的显式模拟介导。本文将重点研究束状网络的自组装，并提出在二维上对新兴的泡沫状结构进行广泛的研究。计划与Schnauß博士的合作将允许我们的数字与（最小）体外系统进行彻底的比较。与二维聚合物网络相反，新兴结构具有泡沫状性质（由自由能最小化驱动），三维情况变得更加复杂。网络将最小化总束长，但泡沫会减少总面积，这在聚合物网络系统中没有很好的定义。至于第二部分，我们想把重点放在二维或三维胶体系统包含密集的硬针或球柱作为液晶的模型。从各向同性到二维（拟）向列相的转变可能是Kosterlitz-Thouless型，其中（拟）向列相仅表现出准长程阶。在D=3时，液晶主体体系中的附加胶体通过引入附加的边界条件产生拓扑缺陷，从而诱导胶体之间的有效相互作用。这可能导致胶体的四价化学，这意味着（受控）自组装的可能性。

The general aim of this project is to generalize the event-chain MC algorithm for various applications in polymer systems, e.g. cytoskeletal filament systems, in order to develop a new and efficient method for this important class of systems. Besides the simulation of semiflexible polymers, polymers consisting of infinitely thin needles or polymer systems with explicit crosslinkers or branching agents (like ARP 2/3) and even triangulated, elastic surfaces / capsules can be simulated in a general, universal event chain framework. We expect a significant increase in efficiency. It is an ongoing effort to improve the sampling efficiency, on this topic we will cooperate with Prof. Krauth and Dr. Michel.As a precursor to the simulation of polymer networks, we will investigate the generation of (nearly) equilibrated, homogeneous and isotropical (semiflexible) polymer melts as initial configurations. The optional swap move and the advantage of ECa in dense systems should make it possible to study the solidification of such melts.The main system we propose to investigate are polymer networks in equilibrium, where the attractive interaction is mediated by a generic homogeneous square well potential or by the explicit simulation of (transient) crosslinkers or branching agents. Here, we focus on the self-assembly of bundle networks and propose to extensively study the emerging foam-like structures in two dimensions. The planned collaboration with Dr. Schnauß will allow a thorough comparison of our numerics to (minimal) in-vitro systems. Contrary to two-dimensional polymer networks, where the emerging structure has foam-like properties (driven by free energy minimization), the situation becomes more complex in three dimensions. The network will minimize the total bundle length, but a foam will reduce the total area, which is not well defined in the polymer network system.As to the second part, we want to focus on two- or three-dimensional colloidal systems containing dense hard needles or sphero-cylinders as an model for a liquid crystal. The transition from an isotropic to a (quasi-)nematic phase in two dimensions is presumably of Kosterlitz-Thouless type, where the (quasi-)nematic phase exhibits only quasi-long-range order. In D=3, additional colloids in a liquid crystal host system produce topological defects by introducing additional boundary conditions, which induce an effective interaction between colloids. This may lead to a tetravalent chemistry of colloids, which implies the possibility of (controlled) self-assembly.