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Optimizing Tile Concentrations to Minimize Errors and Time for DNA Tile Self-assembly Systems

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DNA Computing and Molecular Programming (DNA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6518))

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Abstract

DNA tile self-assembly has emerged as a rich and promising primitive for nano-technology. This paper studies the problems of minimizing assembly time and error rate by changing the tile concentrations because changing the tile concentrations is easy to implement in actual lab experiments. We prove that setting the concentration of tile T i proportional to the square root of N i where N i is the number of times T i appears outside the seed structure in the final assembled shape minimizes the rate of growth errors for rectilinear tile systems. We also show that the same concentrations minimize the expected assembly time for a feasible class of tile systems. Moreover, for general tile systems, given tile concentrations, we can approximate the expected assembly time with high accuracy and probability by running only a polynomial number of simulations in the size of the target shape.

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References

  1. 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)

    Google Scholar 

  2. Adleman, L., Cheng, Q., Goel, A., Huang, M.-D., Kempe, D., Moisset de Espans, P., Rothemund, P.: Combinatorial optimization problems in self-assembly. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pp. 23–32 (2002)

    Google Scholar 

  3. Barish, R.D., Rothemund, P.W.K., Winfree, E.: Two computational primitives for algorithmic self-assembly: Copying and counting. Nano Letters 5(12), 2586–2592 (2005)

    Article  Google Scholar 

  4. Barish, R.D., Schulman, R., Rothemund, P.W.K., Winfree, E.: An information-bearing seed for nucleating algorithmic self-assembly. Proceedings of the National Academy of Sciences 106, 6054–6059 (2009)

    Article  Google Scholar 

  5. Bishop, J., Klavins, E.: An improved autonomous DNA nanomotor. Nano Letters 7(9), 2574–2577 (2007)

    Article  Google Scholar 

  6. Chen, H.-L., Goel, A.: Error free self-assembly using error prone tiles. In: Proceedings of the 10th International Meeting on DNA Based Computers, pp. 62–75 (2004)

    Google Scholar 

  7. Chen, H.-L., Luhrs, C., Goel, A.: Dimension augmentation and combinatorial criteria for efficient error-resistant DNA self-assembly. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 409–418 (2008)

    Google Scholar 

  8. 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)

    Google Scholar 

  9. Dietz, H., Douglas, S., Shih, W.: Folding DNA into twisted and curved nanoscale shapes. Science 325, 725–730 (2009)

    Article  Google Scholar 

  10. Ding, B., Seeman, N.: Operation of a DNA robot arm inserted into a 2D DNA crystalline substrate. Science 384, 1583–1585 (2006)

    Article  Google Scholar 

  11. 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)

    Google Scholar 

  12. 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)

    Google Scholar 

  13. Green, S., Bath, J., Turberfield, A.: Coordinated chemomechanical cycles: a mechanism for autonomous molecular motion. Physical Review Letters (101), 238101 (2008)

    Google Scholar 

  14. Sahu, S., Reif, J., Yin, P.: Compact error-resilient computational DNA tiling assemblies. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 293–307. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. 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)

    Google Scholar 

  16. Lagoudakis, M., LaBean, T.: 2D DNA self-assembly for satisfiability. In: Proceedings of the 5th DIMACS Workshop on DNA Based Computers. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 54, pp. 141–154 (1999)

    Google Scholar 

  17. 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)

    Google Scholar 

  18. Rothemund, P.W.K.: Folding DNA to create nanoscale shapes and patterns. Nature (440), 297–302 (March 2006)

    Google Scholar 

  19. Rothemund, P.W.K., Papadakis, N., Winfree, E.: Algorithmic self-assembly of DNA Sierpinski triangles. PLOS Biology 2, 424–436 (2004)

    Article  Google Scholar 

  20. Schulman, R., Winfree, E.: Programmable control of nucleation for algorithmic self-assembly. In: Proceedings of the 10th International Meeting on DNA Based Computers, pp. 319–328 (2004)

    Google Scholar 

  21. Schulman, R., Winfree, E.: Self-replication and evolution of DNA crystals. In: Proceedings of the 5th European Conference on Artificial Life, pp. 734–743 (2005)

    Google Scholar 

  22. Seelig, G., Soloveichik, D., Zhang, D., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 314, 1585–1588 (2006)

    Article  Google Scholar 

  23. Sherman, W.B., Seeman, N.C.: A precisely controlled DNA bipedal walking device. Nano Letters 4, 1203–1207 (2004)

    Article  Google Scholar 

  24. 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)

    Google Scholar 

  25. Shin, J.-S., Pierce, N.A.: A synthetic DNA walker for molecular transport. Journal of American Chemistry Society 126, 10834–10835 (2004)

    Article  Google Scholar 

  26. Soloveichik, D., Cook, M., Winfree, E.: Combining self-healing and proofreading in self-assembly. Natural Computing (7), 203–218 (2008)

    Google Scholar 

  27. Soloveichik, D., Winfree, E.: Complexity of self-assembled shapes. SIAM Journal on Computing 36, 1544–1569 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wang, H.: Proving theorems by pattern recognition ii. Bell Systems Technical Journal 40, 1–42 (1961)

    Article  Google Scholar 

  29. Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology, Pasadena (1998)

    Google Scholar 

  30. Winfree, E., Bekbolatov, R.: Proofreading tile sets: Error correction for algorithmic self-assembly. In: Proceedings of the 9th International Meeting on DNA Based Computers, pp. 126–144 (2003)

    Google Scholar 

  31. Winfree, E., Liu, F., Wenzler, L., Seeman, N.: Design and self-assembly of two-dimensional DNA crystals, 6 pages. Nature (394), 539–544 (August 1998)

    Google Scholar 

  32. Yurke, B., Turberfield, A., Mills Jr., A., Simmel, F., Neumann, J.: A DNA-fuelled molecular machine made of DNA. Nature (406), 605–608 (August 2000)

    Google Scholar 

  33. Zhang, Y., Seeman, N.: Construction of a DNA-truncated octahedron. Journal of American Chemical Society 116(5), 1661 (1994)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Center for Mathematics of Information, California Institute of Technology, Pasadena, CA, 91101, USA

    Ho-Lin Chen & Ming-Yang Kao

  2. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, 60208, USA

    Ho-Lin Chen & Ming-Yang Kao

Authors
  1. Ho-Lin Chen
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  2. Ming-Yang Kao
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Editor information

Editors and Affiliations

  1. Department of Biosciences and Informatics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, 223-8522, Yokohama, Japan

    Yasubumi Sakakibara

  2. Department of Chemical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Yongli Mi

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© 2011 Springer-Verlag Berlin Heidelberg

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Chen, HL., Kao, MY. (2011). Optimizing Tile Concentrations to Minimize Errors and Time for DNA Tile Self-assembly Systems. In: Sakakibara, Y., Mi, Y. (eds) DNA Computing and Molecular Programming. DNA 2010. Lecture Notes in Computer Science, vol 6518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18305-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-18305-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18304-1

  • Online ISBN: 978-3-642-18305-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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