Park Suyoun, Tandon Anshula, Cho Hyun Jae, Raza Muhammad Tayyab, Lee Sung Jin, Chopade Prathamesh, Ha Tai Hwan, Park Sung Ha
Department of Physics and Sungkyunkwan Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University, Suwon 16419, Republic of Korea.
Nanotechnology. 2019 Nov 5;31(8):085604. doi: 10.1088/1361-6528/ab5472.
Deoxyribonucleic acid (DNA) is effective for molecular computation because of its high energy efficiency, high information density, and parallel-computing capability. Although logic implementation using DNA molecules is well established in binary systems (base value of 2) via decoration of hairpin structures on DNA duplexes, systems with base values of >2 (e.g. 3, corresponding to a ternary system) are rarely discussed owing to the complexity of the design and the experimental difficulties with DNA. In this study, DNA rule tiles that participate to form algorithmic DNA crystals exhibiting the ternary representation of an N (N = 1 or 2)-input and 1-output algorithmic assembly are conceived. The number of possible algorithmic patterns is [Formula: see text] in the ternary N-input and 1-output logic gate. Thus, the number of possible rules is 27 (=3) for a 1-input and 1-output algorithmic logic gate and 19 638 (=3) for a 2-input and 1-output algorithmic logic gate. Ternary bit information (i.e. 0-, 1-, and 2-bit) is encoded on rule tiles without hairpins and with short and long hairpins. We construct converged, line-like, alternating, and commutative patterns by implementing specific rules (TR00, TR05, TR07, and TR15, respectively) for the 1-input and 1-output gate and an ascending line-like pattern (with the rule of TR3785) for the 2-input and 1-output gate. Specific patterns generated on ternary-representing rule-embedded algorithmic DNA crystals are visualized via atomic force microscopy, and the errors during the growth of the crystals are analyzed (average error rates obtained for all experimental data are <4%). Our method can easily be extended to a system having base values of >3.
脱氧核糖核酸（DNA）因其高能效、高信息密度和并行计算能力而对分子计算有效。尽管通过在DNA双链体上修饰发夹结构，在二元系统（基数为2）中使用DNA分子进行逻辑实现已经很成熟，但由于设计的复杂性和DNA实验的困难，基数大于2（例如3，对应于三元系统）的系统很少被讨论。在本研究中，构思了参与形成算法DNA晶体的DNA规则瓦片，该晶体展现了N（N = 1或2）输入和1输出算法组装的三元表示。在三元N输入和1输出逻辑门中，可能的算法模式数量为[公式：见原文]。因此，对于1输入和1输出算法逻辑门，可能的规则数量为27（=3），对于2输入和1输出算法逻辑门，可能的规则数量为19638（=3）。三元位信息（即0位、1位和2位）被编码在没有发夹以及有短发夹和长发夹的规则瓦片上。我们通过对1输入和1输出门实施特定规则（分别为TR00、TR05、TR07和TR15）以及对2输入和1输出门实施上升线状模式（规则为TR3785）来构建收敛、线状、交替和交换模式。通过原子力显微镜观察在三元表示的规则嵌入算法DNA晶体上产生的特定模式，并分析晶体生长过程中的误差（所有实验数据获得的平均误差率<4%）。我们的方法可以很容易地扩展到基数大于3的系统。
