The APS-bracket - A topological tool to classify lasso proteins, RNAs and other tadpole-like structures

The topology of biopolymers plays a crucial role in their function and properties. The standard knot-theory techniques allow one to distinguish the topology of linear polymers, however, they do not take into account the intrinsic and external interactions in the biopolymer chain, such as hydrogen or disulfide bonds. Here we introduce the APS-bracket - a topological tool developed to analyze the topology of biopolymers with intrachain interactions. We list the basic properties of the bracket and calculate its value for structures inspired by complex lasso proteins. We also introduce a set of basis structures and define the input of each separate basis structure. Finally, we discuss possible applications and generalizations of the bracket.