Algebraic Systems Motivated by DNA Origami

We initiate an algebraic approach to study DNA origami structures. We identify two types of basic building blocks and describe a DNA origami structure by their composition. These building blocks are taken as generators of a monoid, called the origami monoid, and motivated by the well studied Temperley-Lieb algebras, we identify a set of relations that characterize the origami monoid. We present several observations about Green’s relations for the origami monoid and study the relations to a direct product of Jones monoids, which is a morphic image of an origami monoid.