Abstract

Designing a programmable molecular machine is a fundamental problem in nano-technology. DNA is a good candidate for building these machines due to its small size and combinatorial nature. One experimentally promising direction towards obtaining such machines is a DNA walker, which is a DNA structure that moves along some pre-assembled substrate. A DNA walker can also be a useful tool for controllable molecular transportation. In this paper, we propose and analyze DNA walkers that can simulate arbitrary Turing machines within expected linear (in the execution length of the Turing Machine) time. We also develop a formal model and proof techniques for analyzing DNA walkers. Specifically, we define two classes of “safety properties”, and prove that a walker will operate correctly and efficiently, even in the presence of adversarial operations which disrupt the system, as long as it satisfies these properties, which our walkers do. Our walker consumes much less energy than previous proposed designs (linear as opposed to quadratic in the running time of the Turing machine being simulated), and is the first that can directly simulate arbitrary Turing Machines and the first that satisfies the safety properties.

Citations