Decoding the Time-Dependent Response of Bioluminescent Metal-Detecting Whole-Cell Bacterial Sensors

The signal produced by aqueous dispersions of bioluminescent, metal-responsive whole-cell bacterial sensors is indicative of the concentration of bioavailable metal ions in solution. The conventional calibration-based strategy followed for measuring this concentration is however inadequate to provide any quantitative prediction of the cell response over time as a function of, e.g., their growth features, their defining metal accumulation properties, or the physicochemical medium composition. Such an evaluation is still critically needed for assessing on a mechanistic level the performance of biosensors in terms of metal bioavailability and toxicity monitoring. Herein we report a comprehensive formalism unraveling how the dependence of bioluminescence on time is governed by the dynamics of metal biouptake, by the activation kinetics of lux-based reporter gene, and by the ensuing rate of luciferase production, the kinetics of light emission, and quenching. It is shown that the bioluminescence signal corresponds to the convolution product between two time-dependent functions, one detailing the dynamic interplay of the above micro- and nanoscale processes, and the other pertaining to the change in concentration of photoactive cell sensors over time. Numerical computations illustrate how the shape and magnitude of the bioluminescence peak(s) are intimately connected to the dependence of the photoactive cell concentration on time and to the magnitudes of Deborah numbers that compare the relevant time scales of the biointerfacial and intracellular events controlling light emission. Explicit analytical expressions are further derived for practical situations where bioluminescence is proportional to the concentration of metal ions in solution. The theory is further quantitatively supported by experiments performed on luminescent cadmium-responsive lux-based Escherichia coli biosensors.