Abstract
We employ a model for self-assembling graph-theoretical complexes using tiles representing branched-junction DNA molecules with free cohesive ends. We determine the minimum number of tile and bond-edge types necessary to create a given graph as a self-assembled complex under three different scenarios: (1) where the incidental creation of complexes of smaller size than the target graph is acceptable; (2) where the incidental creation of complexes the same size as the target graph is acceptable, but not smaller complexes; and (3) where no complexes the same size as or smaller than the target graph are acceptable. In each of these cases, we find bounds for the minimum number of tile and bond-edge types that must be designed, and give specific minimum values for common graph classes (including cycles and trees, as well as complete, bipartite, and regular graphs). For these classes of graphs, we provide either explicit descriptions of optimal tile sets or efficient algorithms for generating the desired set.
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Acknowledgements
We thank Dan Archdeacon, Natasha Jonoska, Bruce Sagan, Ned Seeman, and Anna Staninska for a number of informative conversations. We also thank Saint Michael’s College students Brian Hopper and Paul Jarvis, who considered some closely related problems.
Support was provided by the National Science Foundation through award 1001408, by the National Security Agency, and by the Vermont Genetics Network through Grant Number P20 RR16462 from the INBRE Program of the National Center for Research Resources (NCRR), a component of the National Institutes of Health (NIH). The contents of this chapter are solely the responsibility of the authors and do not necessarily represent the official views of the NSF, NCRR, or NIH.
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Ellis-Monaghan, J., Pangborn, G., Beaudin, L., Miller, D., Bruno, N., Hashimoto, A. (2014). Minimal Tile and Bond-Edge Types for Self-Assembling DNA Graphs. In: Jonoska, N., Saito, M. (eds) Discrete and Topological Models in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40193-0_11
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