  Backbone-assisted assembly processes -- such as protein folding -- allow the
assembly of a large number of structures with high accuracy from only a small
handful of fundamental building blocks. We aim to explore general principles
underlying this phenomenon by studying variants of the temperature-1 abstract
tile assembly model (aTAM). We consider the existence of finite sets of tile
types that can deterministically assemble any shape producible by a given
assembly model; we call such tile type sets universal assembly kits. Our first
model, which we call the ``backboned aTAM", generates backbone-assisted
assembly by forcing tiles to be be added to lattice positions neighbouring the
immediately preceding tile, using a predetermined sequence of tile types. We
demonstrate the existence of universal assembly kit for the backboned aTAM, and
show that the existence of this set is maintained even under stringent
restrictions to the rules of assembly. We hypothesise that the advantage of the
backboned aTAM relative to the conventional aTAM -- which does not possess such
a set -- is in part due to the specification of a sequence, and in part due to
the geometric restrictions imposed by the backbone. To explore this intuition,
we develop a second model call the ``sequenced aTAM". The sequenced aTAM uses a
predetermined sequence of tiles, but does not constrain a tile to neighbour the
immediately preceding tiles. We prove that this model has no universal assembly
kit. The lack of such a kit is surprising, given that the number of tile
sequences of length $N$ scales faster than the number of producible shapes of
size $N$ for a sufficiently large -- but finite -- set of tiles.
