Paper:

# Discrete Biochemistry of DNA: Arithmetic DNA Molecules for Binary Additions, Naturally Found Genetic Logic Circuits for Plant Sensing, and DNA-Based Animation

## Asuka Kikuchi and Tomonori Kawano

The University of Kitakyushu

1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan

To date, a number of researchers are seeking for and/or designing novel molecules which function as arithmetic molecular engines. Biomolecules such as deoxyribonucleic acid (DNA) and proteins are examples of promising candidate molecules. In the present article, we showed our view that DNA-based molecules could be used as a novel class of platforms for discrete mathematical operations or tools for natural computation. Here, we report on a novel molecular logic circuit combining exclusive disjunction (XOR) gate and conjunction (AND) gate implemented on a single DNA molecule performing arithmetic operations with simple binary numbers through polymerase chain reactions (PCR); which was inspired by previously developed protein-based computing model allowing simple polynomial algebra over fields through algebraic representation of cyclic inter-conversions in the catalytic modes of a plant enzyme as a cyclic additive group. In addition, we showed that DNA can be used as the platform for image coding and processing leading to DNA-coded animation by using novel PCR-based protocols. Lastly, we discussed the significance of recent attempts in the stream of natural computing and synthetic biological research, by handling DNA and related biomolecules as the media for discrete mathematical operations.

- [1] K. D. Joshi, “Fundamentals of discrete mathematics,” Wiley-Interscience, 1989.
- [2] K. McComb, C. Packer, and A. Pusey, “Roaring and numerical assessment in contests between groups of female lions, Panthera leo,” Animal Behaviour, Vol.47, pp. 379-387, 1994.
- [3] C. Agrillo, M. Dadda, G. Serena, and A. Bisazza, “Do fish count? Spontaneous discrimination of quantity in female mosquitofish,” Animal Cognition, Vol.11, pp. 495-503, 2008.
- [4] S. Ruschioni, J. J. A. van Loon, H. M. Smid, and J. C. van Lenteren, “Insects can count: Sensory basis of host discrimination in parasitoid wasps revealed,” PLoS One, Vol.10, e0138045, 2015.
- [5] T. Kawano, F. Bouteau, and S. Mancuso, “Finding and defining the natural automata acting in living plants: Towards the synthetic biology for robotics and informatics
*in vivo*,” Commun. Integ. Biol., Vol.5, pp. 519-526, 2012. - [6] K. Otsuka, S. Maruta, A. Noriyasu, K. Nakazawa, F. Bouteau, S. Mancuso, and T. Kawano, “On-chip platform for biological cellular automata models using swimming paramecium cells,” ICIC Exp. Lett. B., Vol.6, pp. 299-304, 2015.
- [7] A. Tero, S. Takagi, T. Saigusa, K. Ito, D. P. Bebber, M. D. Fricker, K. Yumiki, R. Kobayashi, and T. Nakagaki, “Rules for biologically inspired adaptive network design,” Science, Vol.327, pp. 439-442, 2010.
- [8] S. Tsuda, M. Aono, and Y-P. Gunji, “Robust and emergent Physarum logical-computing,” Biosystems, Vol.73, pp. 45-55, 2004.
- [9] T. Kawano, “Biomolecule-assisted natural computing approaches for simple polynomial algebra over fields,” ICIC Exp. Lett., Vol.7, pp. 2023-2028, 2013.
- [10] T. Head, X. Chen, M. Yamamura, and S. Gal, “Aqueous computing: A survey with an invitation to participate,” J. Comput. Sci. Technol., Vol.17, No.6, pp. 672-681, 2002.
- [11] D. R. Simon, “On the power of quantum computation,” SIAM J. Computing, Vol.26, pp. 1474-1483, 1997.
- [12] T. Kawano, “Printable optical logic gates with CIELAB color coding system for Boolean operation-mediated handling of colors,” Proc. of 6th Int. Conf. on Genetic and Evolutionary Computing (Kitakyushu, Japan), pp. 270-275, 2012 (DOI 10.1109/ICGEC.2012.121).
- [13] A. Kameda, M. Yamamoto, H. Uejima, M. Hagiya, K. Sakamoto, and A. Obuchi, “Hairpin-based state machine and conformational addressing: Design and experiment,” Natural Computing, Vol.4, pp. 103-126, 2005.
- [14] T. Kawano, “Primitive optical computing model with films: Boolean conjunction of the square matrix-arrayed color codes,” J. Adv. Comput. Intell. Intell. Inform., Vol.17, No.6, pp. 791-798, 2013.
- [15] K. Moritaka and T. Kawano, “Use of colored reflectors for negation or highlighting of scanned color information on film-based CIELAB-coded optical logic gate models,” J. Adv. Comput. Intell. Intell. Inform., Vol.17, No.6, pp. 799-804, 2013.
- [16] K. Moritaka and T. Kawano, “Spectroscopic analysis of the model color filters used for computation of CIELAB-based optical logic gates,” ICIC Exp. Lett. Part B: Applications, Vol.5, No.6, pp. 1715-1720, 2014.
- [17] J. W. Goodman, “Introduction to Fourier optics,” Green Wood Village, CO: Roberts & Co., 2004.
- [18] Y. Benenson, “Biocomputers: from test tubes to live cells,” Molecular Biosystems, Vol.5, No.7, pp. 675-685, 2009.
- [19] Y. Benenson, “Biocomputing: DNA computes a square root,” Nat. Nanotechnol., Vol.6, pp. 465-467, 2011.
- [20] T. Kawano, “Roles of the reactive oxygen species-generating peroxidase reactions in plant defense and growth induction,” Plant Cell Rep., Vol.21, pp. 829-837, 2003.
- [21] M. Kimura, Y. Umemoto, and T. Kawano, “Hydrogen peroxide-independent generation of superoxide by plant peroxidase: Hypotheses and supportive data employing ferrous ion as a model stimulus,” Frontiers in Plant Science, Vol.5, article 285, 2014.
- [22] A. Takayama, T. Kadono, and T. Kawano, “Heme redox cycling in soybean peroxidase: Hypothetical model and supportive data,” Sens. Mater., Vol.24, No. 2, pp. 87-97, 2012.
- [23] L. M. Adleman, “Molecular computation of solutions to combinatorial problems,” Science, Vol.266, pp. 1021-1024, 1994.
- [24] S. Y. Shin, L. H. Lee, D. Kim, and B. T. Zhang, “Multiobjective evolutionary optimization of DNA sequences for reliable DNA computing,” IEEE Trans. Evolut. Comput., Vol.9, pp. 143-158, 2005.
- [25] K. Yokawa, T. Kadono, Y. Suzuki, T. Suzuki, K. Uezu, and T. Kawano, “DNA-mediated sensitive detection and quantification of rare earth ions using polymerase chain reaction,” Sens. Mater., Vol.23, pp. 219-228, 2011.
- [26] T. Kawano, “Run-length encoding graphic rules, molecular biologically editable designs, and steganographical on-image numeric data embedment for DNA-based cryptographical coding system,” Commun. Integ. Biol., Vol.6, article e23478, 2013.
- [27] R. Daniel, J. R. Rubens, R. Sarpeshkar, and T. K. Lu, “Synthetic analog computing in living cells,” Nature, Vol.497, pp. 619-623, 2013.
- [28] T. Nojima, T. Yamamoto, H. Kimura, and T. Fujii, “Polymerase chain reaction-based biochemical logic gate coupled with cell-free transcription-translation of green fluorescent protein as a report gate,” Chem. Commun., Vol.2008, pp. 3771-3773, 2008.
- [29] T. Nojima, S. Kaneda, H. Kimura, T. Yamamoto, and T. Fujii, “Application of cell-free expression of GFP for evaluation of microsystems,” Front. Biosci., Vol.17, pp. 1931-1939, 2012.
- [30] K. Yokawa, T. Kagenishi, and T. Kawano, “Prevention of oxidative DNA degradation by copper-binding pepti,” Biosci. Biotechnol. Biochem., Vol.75, pp. 1377-1379, 2011.
- [31] M. Amos, “Theoretical and Experimental DNA computation,” Springer-Verlag, Berlin-Heiderburg, Germany, 2005.
- [32] N. MacRae, “John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (2nd ed.),” American Mathematical Soc. (ISBN-13: 978-0821826768), 1999.
- [33] R. L. Redondo, J. Kim, A. L. Arons, S. Ramirez, X. Liu, and S. Tonegawa, “Bidirectional switch of the valence associated with a hippocampal contextual memory engram,” Nature, Vol.513, pp. 426-430, 2014.
- [34] S. Tonegawa, “The great time in Basel,” Cell, Vol.S116, pp. S99-S101, 2004.
- [35] N. Iqbal, A. Trivellini, A. Masood, A. Ferrante, and N. A. Khan, “Current understanding on ethylene signaling in plants: the influence of nutrient availability,” Plant Physiol. Biochem., Vol.73, pp. 128-138, 2013.
- [36] T. Kawano, “Run-length encoding graphic rules, molecular biologically editable designs, and steganographical on-image numeric data embedment for DNA-based cryptographical coding system,” Commun. Integr. Biol., Vol.6, No. 2, e23478, 2013.
- [37] Y. Hara and T. Kawano, “Run-length encoding graphic rules applied to DNA-coded images and animation editable by polymerase chain reactions,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.1, pp. 5-10, 2015.
- [38] O. Avery, C. MacLeod, and M. McCarty, “Studies on the chemical nature of the substance inducing transformation of pneumococcal types. Inductions of transformation by a desoxyribonucleic acid fraction isolated from pneumococcus type III,” J. Exper. Medicine, Vol.79, No.2, pp. 137-158, 1944.
- [39] J. D. Watson and F. H. Crick, “A structure for deoxyribose nucleic acid,” Nature, Vol.171, pp. 737-738, 1953.
- [40] E. A. Carlson, “Defining the gene: an evolving concept,” Amer. J. Human Genetics, Vol.49, No.2, pp. 475-487, 1991.
- [41] J. C. Venter and other 173 authors, “The sequence of the human genome,” Science, Vol.291, pp. 1304-1351, 2001.
- [42] H. Rauhe, G. Vopper, U. Feldkamp, W. Banzhaf, and J. C. Howard, “Digital DNA molecules,” Proc. 6th DIMACS Workshop on DNA Based Computers, Leiden, Netherlands, pp. 13-17, 2000.
- [43] D. Heider and A. Barnekow, “DNA-based watermarks using the DNA-Crypt algorithm,” BMC Bioinformatics, Vol.8, article 176, 2007.
- [44] C. T. Clelland, V. Risca, and C. Bancroft, “Hiding messages in DNA microdots,” Nature, Vol.399, pp. 533-534, 1999.
- [45] A. Gehan, T. H. LaBean, and J. H. Reif, “DNA-based cryptography,” Discr. Math. Theor. Comput. Sci., Vol.54, pp. 233-249, 2000.
- [46] S. Blackmore, “The meme machine,” Oxford University Press, Oxford, UK, 1999.