New Generation Computing

, Volume 37, Issue 1, pp 97–111 | Cite as

Pattern Formation on Discrete Gel Matrix Based on DNA Computing

  • Takuto Hosoya
  • Ibuki KawamataEmail author
  • Shin-ichiro M. Nomura
  • Satoshi MurataEmail author
Research Paper


In this paper, we consider the implementation of a cellular automaton by DNA computing. The proposed system is a reaction–diffusion system built on a structured hydrogel matrix that mimics cellular compartments of biological tissues. Since the cellular automaton is materialized by a hydrogel matrix, the system is called gellular automaton which is theoretically capable of pattern formation and computation by chemical reactions. We focus on technical aspects of the implementation of the gellular automata, such as fabrication of the array of cells, the realization of inter-cellular molecular communication, and how to realize state transitions of cells. Along with the evaluation of each technical element, some simple experimental demonstrations of pattern formation are described.


Chemical implementation of cellular automata Gellular automata Molecular computing DNA computing Reaction–diffusion system 



This research was supported by Grant-in-Aid for Scientific Research on Innovative Areas “Molecular Robotics” Japan Society for the Promotion of Science (JP) (no. 24104005), Grant-in-Aid for Scientific Research(A) 15H01715, and Grant-in-Aid for Young Scientists (Start-up, 26880002).


  1. 1.
    Nakamasu, A., Takahashi, G., Kanbe, A., Kondo, S.: Interactions between zebrafish pigment cells. Proc. Natl. Acad. Sci 106(21), 8429 (2009)CrossRefGoogle Scholar
  2. 2.
    Sheth, R., Marcon, L., Bastida, M.F., Junco, M., Quintana, L., Dahn, R., Kmita, M., Sharpe, J., Ros, M.A.: Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism. Science 338(6113), 1476 (2012)CrossRefGoogle Scholar
  3. 3.
    Kondo, S., Miura, T.: Reaction–diffusion model as a framework for understanding biological pattern formation. Science 329(5999), 1616 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Castets, V., Dulos, E., Boissonade, J., de Kepper, P.: Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. Phys. Rev. Lett. 64(24), 2953 (1990)CrossRefGoogle Scholar
  5. 5.
    Yang, L., Epstein, I.: Oscillatory Turing patterns in reaction–diffusion systems with two coupled layers. Phys. Rev. Lett. 90(17), 178303 (2003)CrossRefGoogle Scholar
  6. 6.
    Pearson, J.E.: Complex patterns in a simple system. Science 261(5118), 189 (1993)CrossRefGoogle Scholar
  7. 7.
    Míguez, D., Alonso, S., Muñuzuri, A., Sagués, F.: Experimental evidence of localized oscillations in the photosensitive chlorine dioxide-iodine-malonic acid reaction. Phys. Rev. Lett. 97(17), 178301 (2006)CrossRefGoogle Scholar
  8. 8.
    Takabatake, F., Kawamata, I., Sugawara, K., Murata, S.: Discretization of chemical reactions in a periodic cellular space. New Gener. Comput. 35, 213–223 (2017)CrossRefGoogle Scholar
  9. 9.
    Turing, A.M.: The chemical basis of morphogenesis. Philos. Trans. R. Soc. B Biol. Sci. 237(641), 37 (1952)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Bánsági Jr., T., Vanag, V.K., Epstein, I.R.: Tomography of reaction–diffusion microemulsions reveals three-dimensional Turing patterns. Science 331(1309), 1309 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proc. Natl. Acad. Sci. 107(12), 5393 (2010)CrossRefGoogle Scholar
  12. 12.
    Scalise, D., Schulman, R.: Designing modular reaction–diffusion programs for complex pattern formation. Technology 02(01), 55 (2014)CrossRefGoogle Scholar
  13. 13.
    van Roekel, H.W.H., Rosier, B.J.H.M., Meijer, L.H.H., Hilbers, P.A.J., Markvoort, A.J., Huck, W.T.S., de Greef, T.F.A.: Programmable chemical reaction networks: emulating regulatory functions in living cells using a bottom-up approach. Chem. Soc. Rev. 44, 7465–7483 (2015)CrossRefGoogle Scholar
  14. 14.
    Chirieleison, S.M., Allen, P.B., Simpson, Z.B., Ellington, A.D., Chen, X.: Pattern transformation with DNA circuits. Nat. Chem. 5(12), 1000 (2013)CrossRefGoogle Scholar
  15. 15.
    Zambrano, A., Zadorin, A.S., Rondelez, Y., Estévez-Torres, A., Galas, J.C.: Pursuit-and-evasion reaction–diffusion waves in microreactors with tailored geometry. J. Phys. Chem. B 119(17), 5349 (2015)CrossRefGoogle Scholar
  16. 16.
    Zadorin, A.S., Rondelez, Y., Galas, J.C., Estevez-Torres, A.: Synthesis of programmable reaction–diffusion fronts using DNA catalyzers. Phys. Rev. Lett. 114(6), 069301 (2015)CrossRefGoogle Scholar
  17. 17.
    Padirac, A., Fujii, T., Estévez-Torres, A., Rondelez, Y.: Spatial waves in synthetic biochemical networks. J. Am. Chem. Soc. 135(39), 14586 (2013)CrossRefGoogle Scholar
  18. 18.
    Torii, K.U.: Two-dimensional spatial patterning in developmental systems. Trends Cell Biol. 22(8), 438 (2012)CrossRefGoogle Scholar
  19. 19.
    Tompkins, N., Li, N., Girabawe, C., Heymann, M., Ermentrout, G.B., Epstein, I.R., Fraden, S.: Testing Turing’s theory of morphogenesis in chemical cells. Proc. Natl. Acad. Sci. 111(12), 4397 (2014)CrossRefGoogle Scholar
  20. 20.
    Villar, G., Graham, A.D., Bayley, H.: A tissue-like printed material. Science 340(6128), 48 (2013)CrossRefGoogle Scholar
  21. 21.
    Elani, Y., Law, R.V., Ces, O.: Vesicle-based artificial cells as chemical microreactors with spatially segregated reaction pathways. Nat. Commun. 5, 5305 (2014)CrossRefGoogle Scholar
  22. 22.
    Booth, M.J., Schild, V.R., Graham, A.D., Olof, S.N., Bayley, H.: Light-activated communication in synthetic tissues. Sci. Adv. 2(4), e1600056 (2016)CrossRefGoogle Scholar
  23. 23.
    Kawamata, I., Yoshizawa, S., Takabatake, F., Sugawara, K., Murata, S.: Discrete DNA reaction–diffusion model for implementing simple cellular automaton. Lect. Notes Comput. Sci. 9276, 168 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Zenk, J., Scalise, D., Wang, K., Dorsey, P., Fern, J., Cruz, A., Schulman, R.: Stable DNA-based reaction–diffusion pattern. RSC Adv. 7(29), 18032 (2017)CrossRefGoogle Scholar
  25. 25.
    Wolfram, S.: Cellular automata as models of complexity. Nature 311(5985), 419 (1984)CrossRefGoogle Scholar
  26. 26.
    Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign (2002)zbMATHGoogle Scholar
  27. 27.
    Hagiya, M., Wang, S., Kawamata, I., Murata, S., Isokawa, T., Peper, F., Imai, K.: On DNA-based gellular automata. Lect. Notes Comput. Sci. 8553, 177 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Kawamata, I., Hosoya, T., Takabatake, F., Sugawara, K., Nomura, S.I., Isokawa, T., Peper, F., Hagiya, M., Murata, S.: Pattern formation and computation by autonomous chemical reaction diffusion model inspired by cellular automata. In: The Fourth International Symposium on Computing and Networking, pp. 215–221 (2016)Google Scholar
  29. 29.
    Sutner, K.: On the computational complexity of finite cellular automata. J. Comput. Syst. Sci. 50(1), 87 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Scalise, D., Schulman, R.: Emulating cellular automata in chemical reaction–diffusion networks. Lect. Notes Comput. Sci. 8727, 67 (2014)CrossRefzbMATHGoogle Scholar
  31. 31.
    Jonoska, N., Seeman, N.C.: Molecular ping-pong Game of Life on a two-dimensional DNA origami array. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 373(2046), 20140215 (2015)CrossRefGoogle Scholar
  32. 32.
    Isokawa, T., Peper, F., Kawamata, I., Matsui, N., Murata, S., Hagiya, M.: Universal totalistic asynchronous cellular automaton and its possible implementation by DNA. Lect. Notes Comput. Sci. 6714, 182 (2016)CrossRefzbMATHGoogle Scholar
  33. 33.
    Yamashita, T., Isokawa, T., Peper, F., Kawamata, I., Hagiya, M.: Turing-completeness of asynchronous non-camouflage cellular automata. Lect. Notes Comput. Sci. 8155, 187 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Machado, A.H.E., Lundberg, D., Ribeiro, A.J., Veiga, F.J., Miguel, M.G., Lindman, B., Olsson, U.: Encapsulation of DNA in macroscopic and nanosized calcium alginate gel particles. Langmuir 29(51), 15926 (2013)CrossRefGoogle Scholar
  35. 35.
    Grassi, M., Sandolo, C., Perin, D., Coviello, T., Lapasin, R., Grassi, G.: Structural characterization of calcium alginate matrices by means of mechanical and release tests. Molecules 14(8), 3003 (2009)CrossRefGoogle Scholar
  36. 36.
    Horiguchi, S., Miyamoto, K., Tokita, M., Komai, T.: Preparation of poly(N-normalpropylacrylamide) gel beads. Colloid Polym. Sci. 276(4), 362 (1998)CrossRefGoogle Scholar
  37. 37.
    Qian, L., Winfree, E.: A simple DNA gate motif for synthesizing large-scale circuits. J. R. Soc. Interface 8(62), 1281 (2011)CrossRefGoogle Scholar
  38. 38.
    Seelig, G., Soloveichik, D., Zhang, D.Y., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 314(5805), 1585 (2006)CrossRefGoogle Scholar
  39. 39.
    Zhang, D.Y., Turberfield, A.J., Yurke, B., Winfree, E.: Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318(5853), 1121 (2007)CrossRefGoogle Scholar
  40. 40.
    Yurke, B., Turberfield, A.J., Mills Jr., A.P., Simmel, F.C., Neumann, J.L.: A DNA-fuelled molecular machine made of DNA. Nature 406(6796), 605 (2000)CrossRefGoogle Scholar
  41. 41.
    Thachuk, C., Winfree, E., Soloveichik, D.: Leakless DNA strand displacement systems. Lect. Notes Comput. Sci. 9211, 133 (2015)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Ohmsha, Ltd. and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tohoku UniversitySendaiJapan

Personalised recommendations