Abstract
We introduce a theoretical model of DNA chemical reaction-diffusion network capable of performing a simple cellular automaton. The model is based on well-characterized enzymatic bistable switch that was reported to work in vitro. Our main purpose is to propose an autonomous, feasible, and macro DNA system for experimental implementation.
As a demonstration, we choose a maze-solving cellular automaton. The key idea to emulate the automaton by chemical reactions is assuming a space discretized by hydrogel capsules which can be regarded as cells. The capsule is used both to keep the state uniform and control the communication between neighboring capsules.
Simulations under continuous and discrete space are successfully performed. The simulation results indicate that our model evolves as expected both in space and time from initial conditions. Further investigation also suggests that the ability of the model can be extended by changing parameters. Possible applications of this research include pattern formation and a simple computation. By overcoming some experimental difficulties, we expect that our framework can be a good candidate to program and implement a spatio-temporal chemical reaction system.
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Acknowledgement
We appreciate Masami Hagiya to motivate this research. Helpful advice from the experimental viewpoints were given by Hiroyuki Asanuma, Takashi Arimura, Yusuke Hara, and Nobuyoshi Miyamoto. We thank Teijiro Isokawa and Ferdinand Peper for discussion including the suggestion to simulate a normal automaton by a cellular automaton. This research was supported by Grant-in-Aid for Scientific Research on Innovative Areas “Molecular Robotics” (No. 24104005) and Grant-in-Aid for Young Scientists (Start-up, 26880002).
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A Reaction diffusion model
A Reaction diffusion model
The equations of our model are shown below. Terms for diffusion, which we added to the original equations, are highlighted by red color.
where
As kinetic parameters, we used the fitted values of the original article [25]. Diffusion coefficient of DNA in solution was roughly estimated from experimental values [34, 35].
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Kawamata, I., Yoshizawa, S., Takabatake, F., Sugawara, K., Murata, S. (2016). Discrete DNA Reaction-Diffusion Model for Implementing Simple Cellular Automaton. In: Amos, M., CONDON, A. (eds) Unconventional Computation and Natural Computation. UCNC 2016. Lecture Notes in Computer Science(), vol 9726. Springer, Cham. https://doi.org/10.1007/978-3-319-41312-9_14
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DOI: https://doi.org/10.1007/978-3-319-41312-9_14
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