Abstract
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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Nakamasu, A., Takahashi, G., Kanbe, A., Kondo, S.: Interactions between zebrafish pigment cells. Proc. Natl. Acad. Sci 106(21), 8429 (2009)
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)
Kondo, S., Miura, T.: Reaction–diffusion model as a framework for understanding biological pattern formation. Science 329(5999), 1616 (2010)
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)
Yang, L., Epstein, I.: Oscillatory Turing patterns in reaction–diffusion systems with two coupled layers. Phys. Rev. Lett. 90(17), 178303 (2003)
Pearson, J.E.: Complex patterns in a simple system. Science 261(5118), 189 (1993)
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)
Takabatake, F., Kawamata, I., Sugawara, K., Murata, S.: Discretization of chemical reactions in a periodic cellular space. New Gener. Comput. 35, 213–223 (2017)
Turing, A.M.: The chemical basis of morphogenesis. Philos. Trans. R. Soc. B Biol. Sci. 237(641), 37 (1952)
Bánsági Jr., T., Vanag, V.K., Epstein, I.R.: Tomography of reaction–diffusion microemulsions reveals three-dimensional Turing patterns. Science 331(1309), 1309 (2011)
Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proc. Natl. Acad. Sci. 107(12), 5393 (2010)
Scalise, D., Schulman, R.: Designing modular reaction–diffusion programs for complex pattern formation. Technology 02(01), 55 (2014)
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)
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)
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)
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)
Padirac, A., Fujii, T., Estévez-Torres, A., Rondelez, Y.: Spatial waves in synthetic biochemical networks. J. Am. Chem. Soc. 135(39), 14586 (2013)
Torii, K.U.: Two-dimensional spatial patterning in developmental systems. Trends Cell Biol. 22(8), 438 (2012)
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)
Villar, G., Graham, A.D., Bayley, H.: A tissue-like printed material. Science 340(6128), 48 (2013)
Elani, Y., Law, R.V., Ces, O.: Vesicle-based artificial cells as chemical microreactors with spatially segregated reaction pathways. Nat. Commun. 5, 5305 (2014)
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)
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)
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)
Wolfram, S.: Cellular automata as models of complexity. Nature 311(5985), 419 (1984)
Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign (2002)
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)
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)
Sutner, K.: On the computational complexity of finite cellular automata. J. Comput. Syst. Sci. 50(1), 87 (1995)
Scalise, D., Schulman, R.: Emulating cellular automata in chemical reaction–diffusion networks. Lect. Notes Comput. Sci. 8727, 67 (2014)
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)
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)
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)
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)
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)
Horiguchi, S., Miyamoto, K., Tokita, M., Komai, T.: Preparation of poly(N-normalpropylacrylamide) gel beads. Colloid Polym. Sci. 276(4), 362 (1998)
Qian, L., Winfree, E.: A simple DNA gate motif for synthesizing large-scale circuits. J. R. Soc. Interface 8(62), 1281 (2011)
Seelig, G., Soloveichik, D., Zhang, D.Y., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 314(5805), 1585 (2006)
Zhang, D.Y., Turberfield, A.J., Yurke, B., Winfree, E.: Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318(5853), 1121 (2007)
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)
Thachuk, C., Winfree, E., Soloveichik, D.: Leakless DNA strand displacement systems. Lect. Notes Comput. Sci. 9211, 133 (2015)
Acknowledgements
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).
Author information
Authors and Affiliations
Corresponding authors
About this article
Cite this article
Hosoya, T., Kawamata, I., Nomura, Si.M. et al. Pattern Formation on Discrete Gel Matrix Based on DNA Computing. New Gener. Comput. 37, 97–111 (2019). https://doi.org/10.1007/s00354-018-0047-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00354-018-0047-1