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.

Mechanistic modelling of a recombinase‐based two‐input temporal logic gate

“…6 also supports the notion that the efficiency of recombination induction via integrase B must be superior to that of integrase A since identical efficiencies would be expected to result in a 50:50 split for dT = 0. This inequality in integrase-mediated inversion was previously observed in [25], but no mechanistic comparisons had been performed at that time. Consequently, it remains to experimentally examine functional differences between distinct integrases as these properties may allow for specific logic operations dependent on the pair of integrases selected, the arrangement of the associated attachment sites and the specific roles each integrase input is assigned in the circuit.…”

“…The biological logic gate has the capacity for even further functional advantages when considering the temporal induction of integrase inputs [25]. As previously described, sequential positioning of two distinct attachment site pairs will provide a maximum of four outputs due to staggered induction events giving rise to the same end state, but alternative initial arrangements are capable of providing additional information.…”

“…The model of [25] describes the transitioning of the temporal logic gate from the original DNA state (S 0 ) to each of the three end states (S a , S b and S ab ) via three corresponding rate constants describing inversion mediated by TP901-1 (integrase A), and both deletion and inversion mediated by Bxb1 (integrase B). We replace these all-encompassing parameters with a mechanistic integration reaction structure, in which inversion and deletion events are initiated by the binding of one integrase dimer at each of the associated attachment sites (four integrase monomers in total) and are strictly unidirectional [26,27] (Fig.…”

“…Our data was generated as part of the research presented in [25], but was not presented in that publication. It is comprised of both red fluorescent protein (RFP) and green fluorescent protein (GFP) levels (state 2 and state 4, respectively) under eight distinct experimental conditions.…”

“…These simulations demonstrate the increased Model simulations generated using our optimal parameter set. Data generated as part of the research presented in [25] (Fig. 7b).…”