Circuit Topology for Bottom-Up Engineering of Molecular Knots

The art of tying knots is exploited in nature and occurs multiple applications ranging from being an essential part scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular functions, their entanglement believed provide them with thermal kinetic stability. Yet, little known about the design principles naturally evolved Intra-chain contacts chain contribute folding proteins. Circuit topology, a theory that describes intra-chain contacts, was recently generalized account for entanglement. This generalization unique circuit topology not motivated by other theories. In this conceptual paper, we systematically analyze approach description linear We utilize bottom-up approach, i.e., express set four fundamental structural units subjected three (or five) binary topological operations. All found proteins form well-defined, distinct group which appears if expressed terms these basic units. believe detailed, understanding structure should be beneficial engineering.