Molecular robots guided by prescriptive landscapes.

Traditional robots rely for their function on computing, to store internal representations of their goals and environment and to coordinate sensing and any actuation of components required in response. Moving robotics to the single-molecule level is possible in principle, but requires facing the limited ability of individual molecules to store complex information and programs. One strategy to overcome this problem is to use systems that can obtain complex behaviour from the interaction of simple robots with their environment. A first step in this direction was the development of DNA walkers, which have developed from being non-autonomous to being capable of directed but brief motion on one-dimensional tracks. Here we demonstrate that previously developed random walkers-so-called molecular spiders that comprise a streptavidin molecule as an inert 'body' and three deoxyribozymes as catalytic 'legs'-show elementary robotic behaviour when interacting with a precisely defined environment. Single-molecule microscopy observations confirm that such walkers achieve directional movement by sensing and modifying tracks of substrate molecules laid out on a two-dimensional DNA origami landscape. When using appropriately designed DNA origami, the molecular spiders autonomously carry out sequences of actions such as 'start', 'follow', 'turn' and 'stop'. We anticipate that this strategy will result in more complex robotic behaviour at the molecular level if additional control mechanisms are incorporated. One example might be interactions between multiple molecular robots leading to collective behaviour; another might be the ability to read and transform secondary cues on the DNA origami landscape as a means of implementing Turing-universal algorithmic behaviour.

Molecular system for an exponentially fast growing programmable synthetic polymer.

In this paper, we demonstrate a molecular system for the first active self-assembly linear DNA polymer that exhibits programmable molecular exponential growth in real time, also the first to implement "internal" parallel insertion that does not rely on adding successive layers to "external" edges for growth. Approaches like this can produce enhanced exponential growth behavior that is less limited by volume and external surface interference, for an early step toward efficiently building two and three dimensional shapes in logarithmic time. We experimentally demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism and results in the exponential growth of a population of polymers per unit time. In the supplementary material, we note that an "extension" beyond conventional Turing machine theory is needed to theoretically analyze exponential growth itself in programmable physical systems. Sequential physical Turing Machines that run a roughly constant number of Turing steps per unit time cannot achieve an exponential growth of structure per time. In contrast, the "active" self-assembly model in this paper, computationally equivalent to a Push-Down Automaton, is exponentially fast when implemented in molecules, but is taxonomically less powerful than a Turing machine. In this sense, a physical Push-Down Automaton can be more powerful than a sequential physical Turing Machine, even though the Turing Machine can compute any computable function. A need for an "extended" computational/physical theory arises, described in the supplementary material section S1.