Backbone-assisted assembly is the primary method through which biological systems produce their complex structures. Backbone-assisted assembly begins with templated polymer copying as a first step, where a template heteropolymer has information stored in its sequence of monomers copied onto a product heteropolymer. Monomers in the product polymer, chained by a molecular backbone, then undergo auxiliary interactions, folding the product polymer into specific structures. Compared to backbone-free self-assembly, backbone-assisted assembly is striking in its ability to produce a vast multitude of structures specifically with only a handful of fundamental subunits.

This thesis will attempt to make progress on several open questions pertaining to backbone-assisted assembly processes. First, while it is intuitively clear that backbones facilitate the assembly of structures using a small number of subunits, a formalization of this intuition has not been attempted. Second, biological templated copying processes are heterogeneous – for instance, in RNA, an A-U base pair has a different binding energy than a C-G base pair, and some biological templated copying processes, such as RNA copying, involve the simultaneous separation of the copy from the template during the copy process. Whereas the consequences of simultaneous separation and heterogeneity have been analyzed separately, the interplay of both is not well understood. Finally, while work has been done on the nonequilibrium thermodynamics of copying and the typically equilibrium thermodynamics of folding, the overall thermodynamics of the complete backbone-assisted assembly process encompassing both copying and folding remains elusive. In particular, it is unclear how information is channeled from genotypes to phenotypes via a copy sequence. Over the course of investigating this final question, I developed a method for the calculation of marginalized spin probabilities in a class of 1D quenched Ising systems, which may be useful for the further study of backbone-assisted assembly processes.