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Maze Exploration with Molecular-Scale Walkers

  • Darko Stefanovic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7505)

Abstract

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.

Keywords

molecular walkers maze search DNA computing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Darko Stefanovic
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of New MexicoUSA
  2. 2.Center for Biomedical EngineeringUniversity of New MexicoAlbuquerqueUSA

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