Segmental Lennard-Jones interactions for semi-flexible polymer networks

Simulating soft matter systems such as the cytoskeleton can enable deep understanding of experimentally observed phenomena. One challenge of modelling such systems is realistic description of the steric repulsion between nearby polymers. Previous models of the polymeric excluded volume interaction have the deficit of being non-analytic, being computationally expensive, or allowing polymers to erroneously cross each other. A recent solution to these issues, implemented in the MEDYAN simulation platform, uses analytical expressions obtained from integrating an interaction kernel along the lengths of two polymer segments to describe their repulsion. Here, we extend this model by re-deriving it for lower-dimensional geometrical configurations, deriving similar expressions using a steeper interaction kernel, comparing it to other commonly used potentials, and showing how to parameterise these models. We also generalise this new integrated style of potential by introducing a segmental Lennard-Jones potential, which enables modelling both attractive and repulsive interactions in semi-flexible polymer networks. These results can be further generalised to facilitate the development of effective interaction potentials for other finite elements in simulations of softmatter systems.

对诸如细胞骨架（cytoskeleton）这类软物质系统进行模拟，能够帮助我们深入理解实验中观测到的各类现象。对这类系统进行建模的一大挑战，在于如何精准描述邻近聚合物间的空间位阻排斥作用。此前针对聚合物排除体积相互作用的各类模型，均存在一定缺陷：要么是非解析形式，要么计算成本高昂，甚至会出现聚合物相互穿透的错误结果。近期，在MEDYAN模拟平台中实现的一种解决方案，通过沿两条聚合物链段的长度积分相互作用核，得到解析表达式来描述二者间的排斥作用，从而解决了上述问题。本研究对该模型进行了拓展：针对低维几何构型重新推导该模型，使用更陡的相互作用核推导出同类表达式，将其与其他常用势能进行对比，并阐明了这些模型的参数化方法。此外，我们通过引入链段伦纳德-琼斯势（Lennard-Jones potential），对这种新型积分式势能进行了推广，使其能够对半柔性聚合物网络中的吸引与排斥相互作用进行建模。本研究结果还可进一步推广，助力软物质系统模拟中其他有限元的高效相互作用势能开发工作。