Klotz Alexander R, Anderson Caleb J, Dimitriyev Michael S
Department of Physics and Astronomy, California State University, Long Beach, USA.
Department of Materials Science and Engineering, Texas A&M University, USA.
Soft Matter. 2024 Sep 11;20(35):7044-7058. doi: 10.1039/d4sm00729h.
Motivated by the observation of positive Gaussian curvature in kinetoplast DNA networks, we consider the effect of linking chirality in square lattice molecular chainmail networks using Langevin dynamics simulations and constrained gradient optimization. Linking chirality here refers to ordering of over-under versus under-over linkages between a loop and its neighbors. We consider fully alternating linking, maximally non-alternating, and partially non-alternating linking chiralities. We find that in simulations of polymer chainmail networks, the linking chirality dictates the sign of the Gaussian curvature of the final state of the chainmail membranes. Alternating networks have positive Gaussian curvature, similar to what is observed in kinetoplast DNA networks. Maximally non-alternating networks form isotropic membranes with negative Gaussian curvature. Partially non-alternating networks form flat diamond-shaped sheets which undergo a thermal folding transition when sufficiently large, similar to the crumpling transition in tethered membranes. We further investigate this topology-curvature relationship on geometric grounds by considering the tightest possible configurations and the constraints that must be satisfied to achieve them.
受动质体DNA网络中正向高斯曲率观测结果的启发，我们使用朗之万动力学模拟和约束梯度优化方法，研究了方形晶格分子链甲网络中连接手性的影响。这里的连接手性是指一个环与其相邻环之间上下连接与下上连接的排序。我们考虑了完全交替连接、最大非交替连接和部分非交替连接的手性。我们发现，在聚合物链甲网络的模拟中，连接手性决定了链甲膜最终状态的高斯曲率的符号。交替网络具有正向高斯曲率，类似于动质体DNA网络中观察到的情况。最大非交替网络形成具有负向高斯曲率的各向同性膜。部分非交替网络形成扁平的菱形片，当足够大时会发生热折叠转变，类似于束缚膜中的褶皱转变。我们通过考虑可能的最紧密构型以及实现这些构型必须满足的约束条件，从几何角度进一步研究这种拓扑 - 曲率关系。
