Maze Exploration With Molecular-Scale Walkers

Molecular spiders are nanoscale walkers made with catalytic DNA legs attached to a rigid body. They move in a matrix of DNA substrates, cleaving them and leaving behind product DNA strands. Unlike a self-avoiding walker, a spider is able to revisit the products. However, the legs cleave and detach from substrates more slowly than they detach from products. This difference in residence time and the presence of multiple legs make a spider move differently from an ordinary random walker. The number of legs, and their lengths, can be varied, and this defines the spider’s local gait, which affects its behavior in global tasks. In this work we define an abstract model of molecular spiders, and within it we study the efficiency of maze exploration as a function of the spider structure. For a fixed geometry, there is an optimal setting of chemical kinetics parameters that minimizes the mean time to traverse a maze.

1

Theory and Practice of Natural Computing