Multiple Molecular Spiders With a Single Localized Source - the One-Dimensional Case

Molecular spiders are nanoscale walkers made with DNA enzyme legs attached to a common body. They move over a surface of DNA substrates, cleaving them and leaving behind product DNA strands, which they are able to revisit. Simple one-dimensional models of spider motion show significant superdiffusive motion when the leg-substrate bindings are longer-lived than the leg-product bindings. This gives the spiders potential as a faster-than-diffusion transport mechanism. However, analysis shows that single-spider motion eventually decays into an ordinary diffusive motion, owing to the ever increasing size of the region of cleaved products. Inspired by cooperative behavior of natural molecular walkers, we propose a model for multiple walkers moving collectively over a one-dimensional lattice. We show that when walkers are sequentially released from the origin, the collective effect is to prevent the leading walkers from moving too far backwards. Hence there is an effective outward pressure on the leading walkers that keeps them moving superdiffusively for longer times, despite the growth of the product region.

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