Molecular Spiders on the Plane
arXiv:1204.6429 · doi:10.1103/PhysRevE.85.061927
Abstract
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 study the diffusion coefficient and the number of visited sites for spiders moving on the square lattice with a substrate in each lattice site. The spider's legs hop to nearest-neighbor sites with the constraint that the distance between any two legs cannot exceed a maximal span. We establish analytic results for bipedal spiders, and investigate multileg spiders numerically. In experimental realizations legs usually convert substrates into products (visited sites). The binding of legs to products is weaker, so the hopping rate from the substrates is smaller. This makes the problem non-Markovian and we investigate it numerically. We demonstrate the emergence of a counter-intuitive behavior - the more spiders are slowed down on unvisited sites, the more motile they become.
12 pages, 4 figures; added references, published version
References in corpus (7)
- Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors
- Phase Coexistence in Driven One Dimensional Transport
- Intra-cellular transport by single-headed kinesin KIF1A: effects of single-motor mechano-chemistry and steric interactions
- Molecular Spiders with Memory
- A "Burnt Bridge'' Brownian Ratchet
- Molecular Spiders in One Dimension
- Anomalous transport in disordered exclusion processes with coupled particles
Cited by in corpus (5)
- Superdiffusive transport by multivalent molecular walkers moving under load
- Interacting quantum walkers: Two-body bosonic and fermionic bound states
- First Passage Properties of Molecular Spiders
- Cooperative effects enhance the transport properties of molecular spider teams
- Self-Repelling Bi-Exploration Process