Necklace-cloverleaf transition in associating RNA-like diblock copolymers

We consider a A{m}B{n} diblock copolymer, whose links are capable of forming local reversible bonds with each other. We assume that the resulting structure of the bonds is RNA like--i.e., topologically isomorphic to a tree. We show that, depending on the relative strengths of A-A , A-B , and B-B contacts, such a polymer can be in one of two different states. Namely, if a self-association is preferable (i.e., A-A and B-B bonds are comparatively stronger than A-B contacts), then the polymer forms a typical randomly branched cloverleaf structure with the so-called roughness exponent gamma = 1/2 . On the contrary, if alternating association is preferable (i.e., A-B bonds are stronger than A-A and B-B contacts), then the polymer tends to form a generally linear necklace structure with gamma = 1 . The transition between cloverleaf and necklace states is studied in detail, and it is shown that it is a second-order phase transition.