Tibor Antal, P. L. Krapivsky
Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface covered by single-stranded segments of DNA called substrates when the substrate DNA is complementary to the leg DNA. If the motion of a spider does not affect the substrates, the spider behaves asymptotically as a random walk. We compute the diffusion coefficient for bipedal spiders with an upper limit on the distance between the legs. In experimental realizations legs usually convert substrates into the products (shorter segments). The binding of legs to products is weaker, so the hopping rate from the substrates is slower. This makes the problem non-Markovian and we investigate it numerically. We demonstrate the emergence of a very counter-intuitive behavior: the more spiders are slowed down on unvisited sites, the more motile they become.
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http://arxiv.org/abs/1204.6429
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