Molecular Spiders with Memory

Abstract

Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg detaches from a segment of the surface for the first time it alters that segment, and legs subsequently bound to these altered segments more weakly. Inspired by these experiments we investigate spiders moving along a one-dimensional substrate, whose legs leave newly visited sites at a slower rate than revisited sites. For a random walk (one-leg spider) the slowdown does not effect the long time behavior. For a bipedal spider, however, the slowdown generates an effective bias towards unvisited sites, and the spider behaves similarly to the excited walk. Surprisingly, the slowing down of the spider at new sites increases the diffusion coefficient and accelerates the growth of the number of visited sites.

10 pages, 3 figures

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Cited by in corpus (9)

• Superdiffusive transport by multivalent molecular walkers moving under load
• Designing, Synthesizing and Modeling Active Fluids
• First Passage Properties of Molecular Spiders
• Symmetric Exclusion Process with a Localized Source
• Cooperative effects enhance the transport properties of molecular spider teams
• Molecular Spiders on the Plane
• Tethered single-legged molecular spiders on independent 1D tracks
• Lattice gases with a point source
• Spiders in random environment