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Cooperative linear cargo transport with molecular spiders

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Abstract

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 symmetric exclusion process model for multiple walkers interacting as they move 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. Multi-spider systems move faster and farther than single spiders or systems with multiple simple random walkers.

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Notes

  1. A preliminary report on this research was presented at the 17th International Conference on DNA Computing and Molecular Programming (Semenov et al. 2011).

  2. The value of k −P is a free parameter in the model. We choose time units so that rate k −P is normalized to 1, hence all time units are measured relative to 1/k −P  = 1.

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Acknowledgments

We thank Paul L. Krapivsky for insights into the behavior of multiple random walkers with an infinitely strong source (Krapivsky 2012). This material is based upon work supported by the National Science Foundation under grants 0829896 and 1028238.

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Authors and Affiliations

  1. Department of Computer Science, University of New Mexico, Albuquerque, USA

    Oleg Semenov, Mark J. Olah & Darko Stefanovic

  2. Center for Biomedical Engineering, University of New Mexico,  Albuquerque,  USA

    Darko Stefanovic

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  1. Oleg Semenov
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  2. Mark J. Olah
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  3. Darko Stefanovic
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Correspondence to Darko Stefanovic.

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Semenov, O., Olah, M.J. & Stefanovic, D. Cooperative linear cargo transport with molecular spiders. Nat Comput 12, 259–276 (2013). https://doi.org/10.1007/s11047-012-9357-2

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