Multirule-Combined Algorithmic Assembly Demonstrated by DNA Tiles

Abstract

DNA molecules have been used to demonstrate logic gates through algorithmic rule implementation to DNA base sequences. A multirulecombined algorithmic assembly formed by a combination of individual rules is introduced in this study. Fifteen possible algorithmic lattices can be constructed using multirule-combined algorithmic rules with one-input one-output logic gates. The algorithmic lattices are categorized into three classes (such as full deterministic, half random, and full random in lattices) depending upon the output probabilities and four patterns (no pattern, infinite line pattern, finite line pattern, and random pattern) based on the observation of patterns on lattices. Single-rule (i.e., R0, R1, R2, and R3), two-rule-combined (e.g., R02, R12, and R13), three-rule-combined (e.g., R012 and R123), and four-rule-combined (i.e., R0123) algorithmic assemblies are demonstrated experimentally, along with a comprehensive discussion with simulation. The experimentally obtained algorithmic lattices (visualized using an atomic force microscope) were very similar to the simulation results. Although singlerule algorithmic lattices show that fully deterministic, multirule-combined lattices reveal partially or fully nondeterministic outputs in lattices owing to the outputs' probabilistic characteristics. In addition, the occurrence probabilities, P N (I,O), are discussed in detail. P N (I,O) is the probability of obtaining the output of O with an initial input of I after the N-step. Owing to the growth of DNA algorithmic lattices that follow the given rules, P N (I,O) obtained experimentally is very similar to P N (I,O) obtained analytically. Consequently, the multirule-combined algorithmic assembly will help generate more interesting patterns or circuits governed by a combination of individual logic gates.

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