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.

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