UC Davis

Designing engineered molecular systems typically requires specialized knowledge of theparticular substrate; however, one can also reason about such systems in a substrate- independent fashion, by examining the underlying energetics that govern any chemical substrate: the formation of molecular bonds and the number of complexes formed. The thermodynamic binding networks (TBN) model was developed to study such systems, and in particular, to determine fault-tolerance in molecular systems such as DNA strand displacement cascades. This dissertation details an extended form of the model in which complexes can merge together or split apart at an energetic benefit/cost. This extension allows one to also reason about reachability of configurations with respect to energy barriers. Several theoretical constructions are presented here which demonstrate that such energy barriers can be programmably large, implement catalytic and autocatalytic behavior, and be part of larger, modular systems in which complex behavior can be realized. Indeed, reasoning about the energy barrier between configurations in such systems is proved here to be PSPACE-hard, even to a c-factor approximation. This dissertation also contains details of integer and constraint programming formulations that can solve certain questions related to a system's energetics. Also made formal here is the connection between TBNs and the well-studied combinatorial concept of Hilbert bases, and examples are given which illustrate how one can use a Hilbert basis to verify particular aspects of TBN designs. Finally, the details of an experiment attempting to implement one of the programmable TBN constructions are given, along with empirical results and interpretations.