Plasticity of the truth table of low-leakage genetic logic gates

The design and implementation of genetic logic gates is a fundamental component of biological computation. In this article we show that the function of a common class of synthetic genetic AND and NAND gates is not completely dictated by the circuit connectivity, even if promoter leakage is very small. Rather the logic function is strongly determined by a simple power law relationship between the promoter leakage rate and the binding affinity of the protein complex carrying the information from the input to the output of the gate. Depending on the value of the power law exponent, a circuit designed to be an AND gate can actually operate as a TRUE, OR, AND or FALSE gate, even if the leakage rate is practically negligible. Surprisingly all these functionalities are compatible with the physiological range of parameter values showing that the design of genetic logic gates which preserve functionality across cell types and conditions requires careful consideration of both circuit connectivity and parameter values.