A population‐based temporal logic gate for timing and recording chemical events

Abstract

Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two‐input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single‐cell responses that translated into analog population responses. Furthermore, when single‐cell genetic states were aggregated into population‐level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub‐populations could be used to deduce order, timing, and duration of transient chemical events. image A synthetic temporal logic gate is combined with stochastic single‐cell digital response to achieve population‐level encoding of the order, timing, and duration of two chemical inputs. Bacteriophage integrases can be used to create a synthetic temporal logic gate that records the timing and duration of two chemical inputs. Based on the sequence of events, single cells have four possible final genetic states. While single cells have digital states, stochastic noise translates into population distributions that are analog with response to timing and duration of input signals. A combination of mathematical model simulations and in vivo E. coli experiments was used to show that the final proportion of cells in each state provides detailed information about past events that cannot be deduced from single cell analysis alone. The stochasticity and delays inherent in biological systems can and should be utilized to provide additional avenues of information and control in synthetic systems.