Abstract. Bennett’s proposed chemical Turing machine is one of the most important thought experiments in the study of the thermodynamics of computation. Yet the sophistication of molecular engineering required to physically construct Bennett’s hypothetical polymer substrate and enzyme has deterred experimental implementations. Here we propose a chemical implementation of stack machines — a Turing-universal model of computation similar to Turing machines — using strand displacement cascades as the underlying chemical primitive. More specifically, the mechanism described herein is the addition and removal of monomers from the end of a polymer, controlled by strand displacement logic. We capture the motivating feature of Bennett’s scheme — that physical reversibility corresponds to logically reversible computation, and arbitrarily little energy per computation step is required. Further, as a method of embedding logic control into chemical and biological systems, polymer-based chemical computation is significantly more efficient than geometry-free chemical reaction networks. 1

Abstract. Recently we have shown how molecular logic circuits with many components arranged in multiple layers can be built using DNA strand displacement reactions. The potential applications of this and similar technologies inspire the study of the computation time of multilayered molecular circuits. Using mass action kinetics to model DNA strand displacement-based circuits, we discuss how computation time scales with the number of layers. We show that depending on circuit architecture, the time-complexity does not necessarily scale linearly with the depth as is assumed in the usual study of circuit complexity. We compare circuits with catalytic and non-catalytic components, showing that catalysis fundamentally alters asymptotic time-complexity. Our results rely on simple asymptotic arguments that should be applicable to a wide class of chemical circuits. These results may help to improve circuit performance and may be useful for the construction of faster, larger and more reliable molecular circuitry.

We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures. 1

Abstract. DNA strand displacement has been used to construct a variety of components, devices, and circuits. The sequences of involved nucleic acid molecules can greatly influence the kinetics and function of strand displacement reactions. To facilitate consideration of spurious reactions during the design process, one common strategy is to subdivide DNA strands into domains, continuous nucleic acid bases that can be abstracted to act as a unit in hybridization and dissociation. Here, considerations for domain-based sequence design are discussed, and heuristics are presented for the sequence design of domains. Based on these heuristics, a randomized algorithm is implemented for sequence design. 1

This paper presents a collection of computational modules implemented with chemical reactions: an inverter, an incrementer, a decrementer, a copier, a comparator, and a multiplier. Unlike previous schemes for chemical computation, ours produces designs that are dependent only on coarse rate categories for the reactions (“fast ” vs. “slow”). Given such categories, the computation is exact and independent of the specific reaction rates. We validate our designs through stochastic simulations of the chemical kinetics. Although conceptual for the time being, our methodology has potential applications in domains of synthetic biology such as biochemical sensing and drug delivery. We are exploring DNA-based computation via strand displacement as a possible experimental chassis.

This paper describes a scheme for implementing a binary counter with chemical reactions. The value of the counter is encoded by logical values of “0 ” and “1 ” that correspond to the absence and presence of specific molecular types, respectively. It is incremented when molecules of a trigger type are injected. Synchronization is achieved with reactions that produce a sustained three-phase oscillation. This oscillation plays a role analogous to a clock signal in digital electronics. Quantities are transferred between molecular types in different phases of the oscillation. Unlike all previous schemes for chemical computation, this scheme is dependent only on coarse rate categories for the reactions (“fast ” and “slow”). Given such categories, the computation is exact and independent of the specific reaction rates. Although conceptual for the time being, the methodology has potential applications in domains of synthetic biology such as biochemical sensing and drug delivery. We are exploring DNA-based computation via strand displacement as a possible experimental chassis. 1.

Abstract. DNA catalysts have been developed as methods of amplifying single-stranded nucleic acid signals. The maximum turnover (gain) of these systems, however, often varies based on strand and complex purities, and has so far not been well-controlled. Here we introduce methods for controlling the asymptotic turnover of strand displacement-based DNA catalysts and show how these could be used to construct linear classifier systems. 1

Visual DSD is an implementation of the programming language for composable DNA circuits described in (Phillips & Cardelli, 2009). The language includes basic elements of sequence domains, toeholds and branch migration, and assumes that strands do not possess any secondary structure. The Visual DSD tool compiles a collection of DNA molecules into a set of chemical reactions. It also

Visual DSD is an implementation of the programming language for composable DNA circuits described in (Phillips & Cardelli, 2009). The language includes basic elements of sequence domains, toeholds and branch migration, and assumes that strands do not possess any secondary structure. The Visual DSD tool compiles a collection of DNA molecules into a set of chemical reactions. It also

doi:10.1093/nar/gkq088 Robustness and modularity properties of a non-covalent DNA catalytic reaction