管子模型在高分子纽结体系中的构建和应用

Knotting is a common phenomenon of linear objects, including macroscopic chains, e.g., earphone cables, and microscopic objects, e.g., DNA, proteins, and other polymers. In recent years, experiments have demonstrated that knotting dramatically affects mechanical, rheological, and catalytic properties as well as biological functions. However, the theoretical understanding and analytical calculation of polymer knots remain little, which prevents us from revealing the mechanisms underlying knotting phenomena. The difficulty in developing the theory for polymer knots is that the conformational space of polymer knots is too complex, and it is almost impossible to directly derive knotting properties from statistical mechanics. To overcome this difficulty, we developed the tube theory (model) for polymer knots. The tube model converts the knotting problem to a confinement problem, which makes the analytical derivation possible. We visualized, materialized, and quantified the tubes for polymer knots using Monte Carlo, molecular dynamics, PERM simulations, and tube-building algorithm. Accordingly, we obtained the tube shape and tube diameters. We found that the knot tubes usually assume a beautiful heart shape. Based on the tube model and the scaling relationships of confined polymers, we derived the free energy of knots, knotting probability and knot sizes under various conditions, which agree with simulation and experimental results. In the review, we will describe our recent results of polymer knots using the tube model. © 2023 Scientia Sinica Informationis. All rights reserved.