The design of autonomous DNA nano-mechanical devices: Walking and rolling DNA

We provide designs for the first autonomousDNA nanomechanical devices that execute cycles of motion without external environmental changes. These DNA devices translate along a circular strand of ssDNA and rotate simultaneously. The designs use various energy sources to fuel the movements, include (i) ATP consumption by DNA ligase in conjunction with restriction enzyme operations, (ii) DNA hybridization energy in trapped states, and (iii) kinetic (heat) energy. We show that each of these energy sources can be used to fuel random bidirectional movements that acquire after n steps an expected translational deviation of O(√n). For the devices using the first two fuel sources, the rate of stepping is accelerated over the rate of random drift due to kinetic (heat) energy. Our first DNA device, which we call walking DNA, achieves random bidirectional motion around a circular ssDNA strand by use of DNA ligase and two restriction enzymes. Our other DNA device, which we call rolling DNA, achieves random bidirectional motion without use of DNA ligase or any restriction enzyme, and instead using hybridization energy. We also describe how to modify the design for the rolling DNA device to include a ``latching mechanism'' that fixes the wheels position at specified location along the road, so as to provide for overall unidirectional translational movement.