Topology of Folded Molecular Chains: From Single Biomolecules to Engineered Origami

Circuit topology and knot theory are mathematically rigorous ways of describing the topology of a folded molecular chain. Conversions between topological states can be understood in terms of simple rules within developed mathematical frameworks.

The circuit topology of proteins and changes to their topology can be readily extracted from Protein Data Bank structures. The circuit topology of proteins underlies their evolution, folding, functionally relevant structures, and dynamics.

Knotted proteins exhibit distinct cellular, thermodynamic, and kinetic properties and are evolutionarily conserved. Studies of knotted polymers yield information about folding and molecular structure more generally.

Protein origami design principles were defined and provided in the form of a computational platform for the design of arbitrary complex CCPO polyhedra.