摘要：SummaryA wide range of physical systems can be formally mapped to a linear chain of sorted objects. Upon introduction of intrachain interactions, such a chain can “fold” to elaborate topological structures, analogous to folded linear polymer systems. Two distinct chain-topology theories, knot theory and circuit topology, have separately provided insight into the structure, dynamics, and evolution of folded linear polymers such as proteins and genomic DNA. Knot theory, however, ignores intrachain interactions (contacts), whereas chain crossings are ignored in circuit topology. Thus, there is a need for a universal approach that can provide topological description of any folded linear chain. Here, we generalize circuit topology in order to grasp particularities typically addressed by knot theory. We develop a generic approach that is simple, mathematically rigorous, and practically useful for structural classification, analysis of structural dynamics, and engineering applications.Graphical AbstractDisplay OmittedHighlights•We develop a topology framework for folded linear chains•Our theory accounts for both intra-chain contacts and chain entanglement•The topology framework provides a 3D description of a chain spatial conformation•A quantitative measure of topological similarity of different chains is developedPolymer Chemistry; Theoretical Chemistry; Molecular Network; Biophysics
