Abstract
Molecular spiders are nanoscale walkers made with catalytic DNA legs attached to a rigid body. They move over a surface of DNA substrates, cleaving them and leaving behind product DNA strands, which they are able to revisit. The cleavage and detachment from substrates together take more time than the detachment from products. This difference in residence time between substrates and products, in conjunction with the plurality of the legs, makes a spider move differently from an ordinary random walker. The number of legs, and their lengths, can be varied, and this defines how a spider moves on the surface, i.e., its gait. Here we define an abstract model of molecular spiders in two dimensions. Then, using Kinetic Monte Carlo simulation, we study how efficiently the spiders with various gaits are able to find specific targets on a finite two-dimensional lattice. Multi-legged spiders with certain gaits find their targets faster than regular random walkers. The search performance of spiders depends both on their gait and on the kinetic rate r, which describes the relative substrate/product “stickiness.” Spiders with gaits that allow more freedom of leg movement find their targets faster than spiders with more restrictive gaits. For each gait, there is an optimal value of r that minimizes the time to find all target sites. Spiders influence each other’s motion through stigmergy, and this also affects the search performance.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-642-37577-4_18
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Notes
- 1.
Elsewhere we study additional kinetic details using more elaborate and more computationally expensive models [8]. These models do permit useful characterization of mechanical motor properties, but they do not alter the basic walking behavior.
- 2.
In the laboratory, an uncleavable, pure-DNA substrate has been used [2] for the purpose. In envisaged applications, the targets presented on the cell surface will not necessarily be DNA strands. To bind to non-DNA targets, in addition to the legs a spider may carry an “arm,” an aptamer molecule that specifically binds to the target.
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Acknowledgments
We thank Paul L. Krapivsky and Mark J. Olah for many discussions of spider behaviors. A preliminary version of this work was presented at WIVACE 2012; we thank the conference reviewers for their incisive and detailed comments. This material is based upon work supported by the National Science Foundation under grants 0829896 and 1028238.
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Semenov, O., Stefanovic, D., Stojanovic, M.N. (2014). The Effects of Multivalency and Kinetics in Nanoscale Search by Molecular Spiders. In: Cagnoni, S., Mirolli, M., Villani, M. (eds) Evolution, Complexity and Artificial Life. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37577-4_11
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