A DNA ring acting as a thermal ratchet

Abstract
Several DNA nanomotors have been recently constructed in laboratories worldwide. These machines are, however, relatively slow and do not perform continuous rotations. We have recently proposed a rotary DNA nanomachine that shows a continuous rotation with a frequency of 10(2)-10(4) Hz. This motor is a closed DNA ring whose elastic features are tuned such that it can be externally driven via e.g. periodic temperature changes. As a result, the twirling ring propels itself through the fluid with a speed of tens of nanometres up to a few microns per second. The current paper gives a more detailed presentation of this motor and provides a derivation of the low- and high-frequency asymptotic behaviour of thermal ratchets in general.