Molecular computation at equilibrium via programmable entropy
Synthetic molecular information processing is typically designed through programming kinetic pathways, so that molecules bind, unbind, or incur conformational changes in some desired order. In DNA nanotechnology, this paradigm is exemplified by strand displacement cascades that control signal transmission through toehold sequestering, and algorithmic tile assembly where correct computation emerges from enforcing ordered growth. In contrast, thermodynamic programming focuses solely on the desired end-state rather than the path, often allowing simpler reasoning and requiring fewer parameters, as well as avoiding energetically-favored, yet undesired, error states that often frustrate kinetic approaches. Here we demonstrate a thermodynamics-first paradigm based on the Thermodynamic Binding Networks (TBN) model, where the systems equilibrium is determined by two simple factors: maximizing the number of complementary domain-level bonds while favoring configurations with more separate molecular complexes. We first validate the model by quantitatively measuring the free energy benefit of configurations with more separate complexes but identical binding, confirming the entropic driving force central to the TBN abstraction. We then construct signal propagation circuits including fan-in and fan-out, seeded-assembly systems that perform Boolean logic computation, and systems for synthesis of concatemers of size quadratic in that of the substrates (by computing their least common multiple). Realizing these TBN constructions required addressing experimental challenges including ensuring geometric feasibility of desired complexes through systematic domain ordering and compensating for multi-arm junction penalties. Our work may enable new ways to engineer complex molecular behaviors and help inform the understanding of the computational power of kinetics versus thermodynamics for molecular systems.