  The thermodynamic binding networks (TBN) model is a tool for studying
engineered molecular systems. The TBN model allows one to reason about their
behavior through a simplified abstraction that ignores details about molecular
composition, focusing on two key determinants of a system's energetics common
to any chemical substrate: how many molecular bonds are formed, and how many
separate complexes exist in the system. We formulate as an integer program the
NP-hard problem of computing stable (a.k.a., minimum energy) configurations of
a TBN: those configurations that maximize the number of bonds and complexes. We
provide open-source software solving this integer program. We give empirical
evidence that this approach enables dramatically faster computation of TBN
stable configurations than previous approaches based on SAT solvers.
Furthermore, unlike SAT-based approaches, our integer programming formulation
can reason about TBNs in which some molecules have unbounded counts. These
improvements in turn allow us to efficiently automate verification of desired
properties of practical TBNs. Finally, we show that the TBN has a natural
representation with a unique Hilbert basis describing the "fundamental
components" out of which locally minimal energy configurations are composed.
This characterization helps verify correctness of not only stable
configurations, but entire "kinetic pathways" in a TBN.
