Kinetics of metal detection by luminescence-based whole-cell biosensors: connecting biosensor response to metal bioavailability, speciation and cell metabolism

Luminescent whole-cell metal biosensors are genetically engineered cells used for the detection of metals in e.g. aqueous solutions. Herein, we detail the quantitative connections between time-response of luminescent bacterial metal sensors and the bioavailability of free and complexed metal species. To that end, we formulate the biophysicochemical dynamics of metal partitioning at a biosensor/solution interface and integrate the required metabolism contribution to cell response. The formalism explains the ways in which cell signal depends on: coupled Eigen kinetics of metal complexation and diffusion of metal species to/from the interface; kinetics of metal excretion, Michaelis–Menten bioaccumulation and ensuing metal depletion from bulk solution; and kinetics of bioluminescence production following intracellular metal sequestration by regulatory metalloproteins. In turn, an expression is derived for the time-dependent cell signal as a function of interrelated (bioavai)lability of metal species and (thermo)dynamic descriptors of extra/intracellular metal complexation. Quantitative criteria are elaborated to identify scenarios where equilibrium modeling of metal speciation is incorrect, bulk metal depletion is operative, metal biouptake kinetics is governed by metal diffusion, or labile metal complexes fully contribute to cell response. Remarkably, in agreement with experiments, the theory predicts time-shifts of bioluminescence peaks with increasing concentration of biosensor and/or metal ligand in solution. We show that these shifts originate from the crosstalk between activation kinetics of cell photoactivity and speciation-dependent kinetics of bulk metal depletion. Overall, the work paves the way for the elaboration of new strategies to exploit the bioluminescence response of metal lux-biosensors at a dynamic level and evaluate metal bioavailability properties in environmental or biological aqueous samples.