  The recently introduced Thermodynamic Binding Networks (TBN) model was
developed with the purpose of studying self-assembling systems by focusing on
their thermodynamically favorable final states, and ignoring the kinetic
pathways through which they evolve. The model was intentionally developed to
abstract away not only the notion of time, but also the constraints of
geometry. Collections of monomers with binding domains which allow them to form
polymers via complementary bonds are analyzed to determine their final, stable
configurations, which are those which maximize the number of bonds formed (i.e.
enthalpy) and the number of independent components (i.e. entropy). In this
paper, we first develop a definition of what it means for a TBN to perform a
computation, and then present a set of constructions which are capable of
performing computations by simulating the behaviors of space-bounded Turing
machines and boolean circuits. In contrast to previous TBN results, these
constructions are robust to great variability in the counts of monomers
existing in the systems and the numbers of polymers that form in parallel.
Although the Turing machine simulating TBNs are inefficient in terms of the
numbers of unique monomer types required, as compared to algorithmic
self-assembling systems in the abstract Tile Assembly Model (aTAM), we then
show that a general strategy of porting those aTAM system designs to TBNs
produces TBNs which incorrectly simulate computations. Finally, we present a
refinement of the TBN model which we call the Geometric Thermodynamic Binding
Networks (GTBN) model in which monomers are defined with rigid geometries and
form rigid bonds. Utilizing the constraints imposed by geometry, we then
provide a GTBN construction capable of simulating Turing machines as
efficiently as in the aTAM.
