Abstract
Self-assembly is the process in which small and simple components assemble into large and complex structures without explicit external control. The nubot model generalizes previous self-assembly models (e.g. aTAM) to include active components which can actively move and undergo state changes. One main difference between the nubot model and previous self-assembly models is its ability to perform exponential growth.
In the paper, we study the problem of finding a minimal set of features in the nubot model which allows exponential growth to happen. We only focus on nubot systems which assemble a long line of nubots with a small number of supplementary layers. We prove that exponential growth is not possible with the limit of one supplementary layer and one state-change per nubot. On the other hand, if two supplementary layers are allowed, or the disappearance rule can be performed without a state change, then we can construct nubot systems which grow exponentially.
The first two authors make equal contribution to the paper and are listed in alphabetical order.
H.-Y. Chen—Research supported in part by MOST grant number 104-2221-E-002-045-MY3.
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Nubot-simulator (2014). https://github.com/domardfern/Nubot-Simulator
Adleman, L., Cheng, Q., Goel, A., Huang, M.-D.: Running time and program size for self-assembled squares. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp. 740–748 (2001)
Barish, R.D., Rothemund, P.W.K., Winfree, E.: Two computational primitives for algorithmic self-assembly: copying and counting. Nano Lett. 5(12), 2586–2592 (2005)
Bishop, J., Klavins, E.: An improved autonomous DNA nanomotor. Nano Lett. 7(9), 2574–2577 (2007)
Chen, H.-L., Doty, D., Holden, D., Thachuk, C., Woods, D., Yang, C.-T.: Fast algorithmic self-assembly of simple shapes using random agitation. In: Murata, S., Kobayashi, S. (eds.) DNA 2014. LNCS, vol. 8727, pp. 20–36. Springer, Cham (2014). doi:10.1007/978-3-319-11295-4_2
Chen, H.-L., Schulman, R., Goel, A., Winfree, E.: Error correction for DNA self-assembly: preventing facet nucleation. Nano Lett. 7, 2913–2919 (2007)
Cheng, Q., Goel, A., Moisset, P.: Optimal self-assembly of counters at temperature two. In: Proceedings of the 1st Conference on Foundations of Nanoscience: Self-Assembled Architectures and Devices, pp. 62–75 (2004)
Dietz, H., Douglas, S., Shih, W.: Folding DNA into twisted and curved nanoscale shapes. Science 325, 725–730 (2009)
Ding, B., Seeman, N.: Operation of a DNA robot arm inserted into a 2D DNA crystalline substrate. Science 384, 1583–1585 (2006)
Dirks, R.M., Pierce, N.A.: Triggered amplification by hybridization chain reaction. Proc. Natl. Acad. Sci. 101(43), 15275–15278 (2004)
Doty, D.: Randomized self-assembly for exact shapes. In: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, pp. 85–94 (2009)
Douglas, S., Dietz, H., Liedl, T., Hogberg, B., Graf, F., Shih, W.: Self-assembly of DNA into nanoscale three-dimensional shapes. Nature 459, 414–418 (2009)
Fu, T.-J., Seeman, N.C.: DNA double crossover structures. Biochemistry 32, 3211–3220 (1993)
Green, S., Bath, J., Turberfield, A.: Coordinated chemomechanical cycles: a mechanism for autonomous molecular motion. Phys. Rev. Lett. 101, 238101 (2008)
Kao, M.-Y., Schweller, R.: Reducing tile complexity for self-assembly through temperature programming. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 571–580 (2006)
Lagoudakis, M., LaBean, T.: 2D DNA self-assembly for satisfiability. In: Proceedings of the 5th DIMACS Workshop on DNA Based Computers in DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 54, pp. 141–154 (1999)
Pei, R., Taylor, S., Stojanovic, M.: Coupling computing, movement, and drug release (2007)
Reif, J.H., Sahu, S.: Autonomous programmable DNA nanorobotic devices using DNAzymes. In: Proceedings of the Thirteenth International Meeting on DNA Based Computers. Memphis, TN, June 2007
Rothemund, P., Winfree, E.: The program-size complexity of self-assembled squares (extended abstract). In: Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, pp. 459–468 (2000)
Rothemund, P.W.K.: Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006)
Rothemund, P.W.K., Papadakis, N., Winfree, E.: Algorithmic self-assembly of DNA sierpinski triangles. PLoS Biol. 2, 424–436 (2004)
Seelig, G., Soloveichik, D., Zhang, D., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 314, 1585–1588 (2006)
Sherman, W.B., Seeman, N.C.: A precisely controlled DNA bipedal walking device. Nano Lett. 4, 1203–1207 (2004)
Shih, W.M., Quispe, J.D., Joyce, G.F.A.: A 1.7-kilobase single-stranded DNA that folds into a nanoscale octahedron. Nature 427, 618–621 (2004)
Shin, J.-S., Pierce, N.A.: A synthetic DNA walker for molecular transport. J. Am. Chem. Soc. 126, 10834–10835 (2004)
Soloveichik, D., Winfree, E.: Complexity of self-assembled shapes. SIAM J. Comput. 36, 1544–1569 (2007)
Tian, Y., He, Y., Chen, Y., Yin, P., Mao, C.: A DNAzyme that walks processively and autonomously along a one-dimensional track. Angew. Chem. 44, 4355–4358 (2005)
Venkataraman, S., Dirks, R.M., Rothemund, P.W.K., Winfree, E., Pierce, N.A.: An autonomous polymerization motor powered by DNA hybridization. Nat. Nanotechnol. 2, 490–494 (2007)
Win, M.N., Smolke, C.D.: Higher-order cellular information processing with synthetic rna devices. Science 322(5900), 456 (2008)
Winfree, E.: Algorithmic Self-Assembly of DNA. Ph.D. thesis, California Institute of Technology, Pasadena (1998)
Winfree, E., Liu, F., Wenzler, L., Seeman, N.: Design and self-assembly of two-dimensional DNA crystals. Nature 394, 539–544 (1998)
Woods, D., Chen, H.-L., Goodfriend, S., Dabby, N., Winfree, E., Yin, P.: Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In: Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, ITCS 2013, pp. 353–354 (2013)
Yin, P., Choi, H.M.T., Calvert, C.R., Pierce, N.A.: Programming biomolecular self-assembly pathways. Nature 451, 318–322 (2008)
Yin, P., Turberfield, A.J., Sahu, S., Reif, J.H.: Designs for autonomous unidirectional walking DNA devices. In: Proceedings of the 10th International Meeting on DNA Based Computers. Milan, Italy, June 2004
Yurke, B., Turberfield, A., Mills Jr., A., Simmel, F., Neumann, J.: A DNA-fuelled molecular machine made of DNA. Nature 406, 605–608 (2000)
Zhang, D.Y., Turberfield, A.J., Yurke, B., Winfree, E.: Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318, 1121–1125 (2007)
Zhang, Y., Seeman, N.: Construction of a DNA-truncated octahedron. J. Am. Chem. Soc. 116(5), 1661 (1994)
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Chin, YR., Tsai, JT., Chen, HL. (2017). A Minimal Requirement for Self-assembly of Lines in Polylogarithmic Time. In: Brijder, R., Qian, L. (eds) DNA Computing and Molecular Programming. DNA 2017. Lecture Notes in Computer Science(), vol 10467. Springer, Cham. https://doi.org/10.1007/978-3-319-66799-7_10
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