Phase-based genetic logic circuits

Bio-computation is the implementation of computational operations using biological substrates, such as cells engineered with synthetic genetic circuits. These genetic circuits can be composed of DNA parts with specific functions, such as promoters that initiate transcription, ribosome binding sites that initiate translation, and coding sequences that are translated into proteins. Compositions of such parts can encode genetic circuits in which the proteins produced by genes regulate each other in different ways. The expression level of each gene may be considered as a signal which may be high or low, encoding binary logic, and the combinations of genes can then encode logic circuits. This is equivalent to the level-based logic used in modern electronic computers in which the voltage forms the logical high or low states. A different approach to binary logic is to encode the high and low states in the phase of an oscillating signal. In this approach a signal in phase with a reference represents high, and a signal antiphase with the reference represents the logical low state. We present here designs and models for phase-based genetic NOT, OR, AND, MAJORITY and complementary MAJORITY gates, which together form multiple complete logical sets. We derive analytical expressions for the optimal model parameters for circuit function. Our simulation results suggest that this approach to genetic logic is feasible and could be less sensitive to gate input-output mismatch than level-based genetic logic. To demonstrate the scaleability of phase-based genetic logic, we used our complementary MAJORITY and NOT gates to design and simulate a fully functional 4-bit ripple adder circuit, and showed that it was robust to molecular noise. ### Competing Interest Statement The authors have declared no competing interest.